Interactive Learner Guide
Transcript of Interactive Learner Guide
Interactive Learner Guide
Cambridge IGCSETM Cambridge IGCSETM(9ndash1)Mathematics 0580 0980
For examination from 2020
Interactive
2
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3
About this guide 4
Section 1 Syllabus content ndash what you need to know about 5
Section 2 How you will be assessed 6
Section 3 What skills will be assessed 11
Section 4 Example candidate response 13
Section 5 Revision 24
Contents
4
This guide introduces you to your Cambridge IGCSE Mathematics course and how you will be assessed You should use this guide alongside the support of your teacher
It will help you to
9 understand what skills you should develop by taking this course
9 understand how you will be assessed
9 understand what we are looking for in the answers you write
9 plan your revision programme
9 revise by providing revision tips and an interactive revision checklist (Section 6)
About this guide
Key benefits
The course will help you to build your skills and knowledge across a range of mathematical techniques You will be able to develop your problem solving and reasoning skills in a variety of situations
The Extended course will provide you with a strong foundation to continue to study mathematics qualifications beyond IGCSE The Core course will equip you with skills needed to support your learning in other subjects and in your general working life
5
This section gives you an outline of the syllabus content for this course Only the top-level topics of the syllabus have been included here which are the same for both the Core and Extended courses In the lsquooverviewrsquo column you are given a very basic idea of what each topic covers Highlighted cells show Extended-only content
Learners taking the Extended course need to know all of the Core content as well as some extra content This extra content requires learners to explore topics and sub-topics of the Core syllabus in more detail to cover some more complex techniques and to learn new sub-topics
Ask your teacher for more detail about each topic including the differences between the Core and Extended courses You can also find more detail in the revision checklists in Section 6 of this guide
Topic Overview
Number Number sets and Venn diagrams squares and cubes directed numbers fractions decimals and percentages ordering indices lsquofour rulesrsquo estimates bounds ratio proportion rate percentage time money and finance Growth and decay (Extended only)
Algebra and graphs Basic algebra algebraic manipulation equations formulae sequences drawing sketching and interpreting graphs of functionsAlgebraic fractions harder simultaneous equations proportion linear programming functions gradients of curves derived functions and differentiation (Extended only)
Co-ordinate geometry Straight-line graphs
Vectors and transformations Vectors (column) transformations
Magnitude of a vector represent vectors by directed line segments position vectors (Extended only)
Geometry Language construction symmetry angle properties congruence similarity
Mensuration Measures mensuration
Trigonometry Bearings trigonometry in right-angled triangles
Sine rule cosine rule trig graphs solving simple trig equations (Extended only)
Probability Probability
Conditional probability (Extended only)
Statistics Statistics
Section 1 Syllabus content ndash what you need to know about
Make sure you always check the latest syllabus which is available at wwwcambridgeinternationalorg
6
You will be assessed at the end of the course using two written examinations The papers that you will sit are different for the Core and Extended courses
bull Paper 1 ndash Short-answer questionsbull Paper 3 ndash Structured questions
bull Paper 2 ndash Short-answer questionsbull Paper 4 ndash Structured questions
Components at a glanceThe table summarises the key information about each component
Component How long and how many marks Skills assessed Percentage of the
qualificationCore Paper 1
(Short-answer questions)
1 hour
56 marks Mathematical techniques as listed in the Core syllabus and applying those techniques to solve problems
35
Paper 3 (Structured questions)
2 hours
104 marks 65
Extended Paper 2 (Short-answer questions)
1 hour 30 minutes
70 marksMathematical techniques as listed in the Core and Extended syllabus and applying those techniques to solve problems
35
Paper 4 (Structured questions)
2 hours 30 minutes
130 marks 65
Section 2 How you will be assessed
Core Extended
Make sure you find out from your teacher which course you will be following
7
About the componentsIt is important that you understand the different types of question in each paper so you know what to expect
Core Paper 1 (Short-answer questions) and Paper 3 (Structured questions)
You need to answer all questions on each paper
Paper 3Paper 1
You can use an electronic calculator in both papers Ask your teacher to recommend a suitable calculator
Paper 1 contains lots of short-answer questions These are usually worth 1ndash3 marks each Some might be broken up into two parts
Write your working and answers in the spaces provided
The number of marks for each part is shown
Paper 3 contains structured questions Each question is split into many parts with each part usually being worth 1ndash4 marks Here for example question 1 is split over two pages
Often the answers to later parts will depend on the answers to earlier parts
8
Extended Paper 2 (Shortndashanswer questions) and Paper 4 (Structured questions)
You need to answer all questions on both papers
Paper 2 questions are short-answer questions Most questions are worth 1ndash3 marks with some being worth 4 or 5 marks Some questions might be broken up into two parts
Write your working and answers in the spaces provided
The number of marks for each part is shown
Paper 4Paper 2
You can use an electronic calculator in both papers Ask your teacher to recommend a suitable calculator
Paper 4 contains structured questions Each question is split into many parts with each part usually being worth 1ndash6 marks Here for example question 2 is split over two pages
Often the answers to later parts will depend on the answers to earlier parts
9
Equipment for the examMake sure you have
bull a blue or black pen (a spare pen is always a good idea)bull a pencil (for graphs and diagrams)bull an electronic calculatorbull a protractorbull a pair of compassesbull a ruler
1 Read the questions carefully to make sure that you understand what is being asked
2 Give your answers to the accuracy indicated in the question If none is given and the answer isnrsquot exact then
bull give your answer to three significant figures 123 9 12298 x
bull if the answer is in degrees then give it to one decimal place 231deg 9 23deg x
3 Include units with your answers if they are not given on the paper For example 1 kg of apples costs hellip pound120 9 120 x
4 Show your working Show as much working as you can for all your questions
5 If you make a mistake clearly cross out any working or answers that you do not want the examiner to mark
Use the value of π from your calculator or use 3142 which is given on the front page of the question paper
Timingbull If you are stuck on a question dont waste too much time trying to answer it ndash go on to the next question and
come back to the one you are stuck on at the endbull Use any time that you have left at the end of the exam to go back and check your answers and working
Make sure that you give your answer in the form asked for in the question eg some questions ask for answers to be given in terms of π For lengths areas and volumes give answers in decimals (not in surds or in terms of π) unless you are told to given an exact answer
You can gain marks for the correct working even if you have an incorrect answer or cannot complete the whole question
If you need more space ask for extra of paper and clearly indicate where the rest of the answer is written On the additional paper make it clear which questions(s) you are answering
General advice for all Papers
10
The areas of knowledge understanding and skills that you will be assessed on are called assessment objectives (AOs) There are two AOs for this course
AO1 Demonstrate knowledge and
understanding of mathematical techniques
AO2 Reason interpret and communicate
mathematically when solving problems
AO1 Demonstrate knowledge and understanding of mathematical techniquesYou need to show that you can recall and apply mathematical knowledge terminology and definitions to carry out single or multi-step solutions in mathematical and everyday situations
Section 3 What skills will be assessed
This means that you need to show that you can
bull organise process and present information accurately in written tabular graphical and diagrammatic forms
bull use and interpret mathematical notation correctly
bull perform calculations and procedures by suitable methods including using a calculator
bull understand systems of measurement in everyday use and make use of these
bull estimate approximate and work to degrees of accuracy appropriate to the context and convert between equivalent numerical forms
bull use geometrical instruments to measure and to draw to an acceptable degree of accuracy
bull recognise and use spatial relationships in two and three dimensions
AO1 is assessed in all papers
Use tables graphs and diagrams
An example of degress of accuracy include significant figures or decimal places
An example of converting between equivalent numerical forms include between fractions decimals and percentages or between normal numbers and standard form
eg a pair of compasses a protractor and a ruler
11
AO2 Reason interpret and communicate mathematically when solving problemsYou need to demonstrate that you can analyse a problem select a suitable strategy and apply appropriate techniques to obtain a solution
This means that you need to show that you can
bull make logical deductions make inferences and draw conclusions from given mathematical data
bull recognise patterns and structures in a variety of situations and form generalisations
bull present arguments and chains of reasoning in a logical and structured way
bull interprete and communicate information accurately and change from one form of presentation to another
bull assesses the validity of an argument and critically evaluate a given way of presenting information
bull solve unstructured problems by putting them into a structured form involving a series of processes
bull apply combinations of mathematical skills and techniques using connections between different areas of mathematics in problem solving
bull interprete results in the context of a given problem and evaluate the methods used and solutions obtained
AO2 is assessed in all papers
Recognise and extent patterns
Take information and organise it to answer a problem
12
Section 4 Command wordsA command word is the part of the question that tells you what you need to do with your knowledge For example you might need to describe something explain something argue a point of view or list what you know The table below includes command words used in the assessment for this syllabus The use of the command word(s) within an question will relate to the context
Cambridge IGCSE Mathematics 0580 syllabus for 2020 2021 and 2022 Details of the assessment
37wwwcambridgeinternationalorgigcseBack to contents page
Command wordsThe table below includes command words used in the assessment for this syllabus The use of the command word will relate to the subject context
Command word What it means
Calculate work out from given facts figures or information generally using a calculator
Construct make an accurate drawing
Describe state the points of a topicgive characteristics and main features
Determine establish with certainty
Explain set out purposes or reasons make the relationships between things evident provide why andor how and support with relevant evidence
Give produce an answer from a given source or recallmemory
Plot mark point(s) on a graph
Show (that) provide structured evidence that leads to a given result
Sketch make a simple freehand drawing showing the key features
Work out calculate from given facts figures or information with or without the use of a calculator
Write give an answer in a specific form
Write down give an answer without significant working
The question below is taken from Paper 4 and illustrates the use of two command words
The command words lsquoWrite downrsquo indicates that you do not need to show your working and the answer should just be written down The mark allocation [1] also supports this
The command words lsquoShow thatrsquo indicate that you need to provide evidence in the form of a clear mathematical explanation to demonstrate that you know how to obtain the given result In other words you need to show a method that leads to the result
The answer space in this case does not contain a dotted answer line as there is no single lsquoanswerrsquo to be found Your working that leads to the given result should be written in the blank working space
13
This section takes you through an example question and learner response from one of the 2020 specimen papers for this course It will help you to identify the command words and other key instructions within questions and to understand what is required in your response
This section is structured as follows
QuestionThe command words and instructions in the question have
been highlighted and explained This should help you to understand clearly what is required by the question
Mark schemeThis tells you as clearly as possible what an examiner expects
from an answer to award marks
Example candidate responseThis an exemplar answer written in the style of
a high level candidate
How the answer could have been improvedThis summarises what could be done to gain more marks
All information and advice in this section is specific to the example question and response being demonstrated It should give you an idea of how your responses might be viewed by an examiner but it is not a list of what to do in all questions In your own examination you will need to pay careful attention to what each question is asking you to do
Common mistakesThis will help you to avoid common mistakes made by
candidates So often candidates lose marks in their exams because they misread or misinterpret the questions
Section 5 Example candidate response
14
QuestionThe question used in this example is from Specimen Paper 3 (Core) It represents the type of structured question you will see in both Paper 3 (Core) and Paper 4 (Extended) A structured question means that it is broken into several parts Often later parts will depend on your answers to earlier parts
This means that you cannot find the answer by
measuring the diagramWork out indicates that the answer should be calculated from the given information so measurement will not score marks
The allocation of 1 mark indicates that the answer can be obtained with minimum working
Give reasons for your answer indicates that your answer should be supported with reasons using the correct mathematical terminology You must justify your answer
Use trigonometry to calculate indicates that you should use this method with the given information to find the answer and that a calculator is needed to solve the problem If you did not use trigonometry you would not be awarded any marks
15
Show that indicates the answer is given and you need to write down all of the steps in a method that leads to the given answer You need to provide evidence that you understand and know how the answer is reached
Work out indicates that you should calculate the answer from the given information The mark allocation of 4 marks suggests that you will need to include several steps of working in order to get to the answer
Learner Guide
16
Answer Mark Notes(a)(i) 35 1 This is the only acceptable answer for this part of the question
(a)(ii) 74 1 This is the only acceptable answer for this part of the question
(b) 43deg and correct mathematical reasons
3 Two marks are awarded for the final answer of 43deg
The third mark is awarded for a fully correct reason for example angles on a straight line add up to 180deg and angles in a triangle add up to 180deg There are other correct reasons that could be also be used
If 43deg is not obtained one method mark can be awarded if the following calculation is seen in the working
180 ndash 128 or 128 ndash 85
(c) 322 or 3223hellip 2 This is the only acceptable answer for this part of the question
The answer has to be rounded correct to three significant figures or can be given with more figures in the answer
Those that did not get this answer can score one method mark for showing the following in their working
sin = 8 divide 15
(d)(i) 2 2300 225+2 This does not have to be shown in one step as long as the method shown is the same as this overall Those that do not
show this can have one method mark for showing the following in their working
300deg + 225deg
(d)(ii) 15 35 4 The answer 3 35pm is also acceptable for 4 marks
If the correct answer is not found one method mark is available for showing 375 divide 450 in their working and a second method mark can be awarded for sight of them multiplying their answer to this by 60 to change it to hours A third method mark can be awarded for adding their answer in hours to 14 45 ndash this shows the correct method so only one mark is lost for an incorrect final answers
Mark schemeYour examination papers will be marked and the overall number of marks for each paper will be recorded Your marks across all papers will then be converted to a grade
Final answer This value is what the examiner expects to see The answer has to be exactly as given in the mark scheme unless there are acceptable alternatives The mark scheme will always make it clear if there are acceptable alternative answers
Method marks Sometimes method marks are awarded for lines of working as well as for the final answer This means that you could get the final answer incorrect but still get some marks if you include the correct working The mark scheme does not include all possible methods so if you use a method not included in the mark scheme but it is accurate and relevant then the examiner will still award marks for the appropriate parts of the working ndash unless the questions asks you to use a specific method
example of a final answer
example of a method mark
17
Example candidate responseNow letrsquos look at the sample candidatersquos response to question 8 The examiners comments are in the orange boxes The candidate was awarded 8 marks out of 13
180 ndash 74 + 71 = 177
177
74
0 out of 1
The candidates working suggests they understand that the angle sum of a triangle is 180deg but they did not include brackets around 74 + 71 The answer 177deg is not sensible for this question
1 out of 1
The candidate recognises that there are parallel lines and that angle y is a corresponding angle to angle 74deg
180 ndash 128 = 52 180 ndash 85 ndash 52 = 43
43 angles on a straight line add up to 180deg
2 out of 3
The candidate has given a correct answer for w and shown correct working in two steps They have given a correct reason for 52deg using correct mathematical languge But they have not provided a reason to explain the angle 43deg They lose a mark for not also stating angle sum of a triangle is 180deg
sin p = 8 divide 15 = 053
p = sinndash1 (053)
p = 32005 320
1 out of 2
The candidate has correctly used trigonometry in their method They are awarded one method mark for the first line of working However they have rounded 05333333hellip (the result of 8 divide 15) to 052 and then calculated the inverse sin of 052 rather than 05333333 This has resulted in an inaccurate final answer This is called lsquopremature approximationrsquo and it is a very common error to make
18
AB2 = 3002 + 2252
= 140625
AB = 375
1 out of 2
The candidate has recognised the right-angled triangle and correctly used Pythagorasrsquo theorem in the first line of working However they have missed out an important step by not showing that you need to take the square root of 140625 to get 375 As this is a lsquoshow thatrsquo question and they missed a key step in the method they cannot be awarded full marks as the complete working is not shown One method mark is earned for the first line
T = = = 08333333hellip
08333333 hours = 08333333 times 60 minutes = 50 minutes
arrives at 14 45 + 50 mins = 3 35
DS
375450
3 35
3 out of 4
The candidate has found the time by correctly dividing the distance by the speed and recognised that this is in hours When converting the answer to a decimal they have not rounded the decimal but left its full value on the calculator to get 50 mins which is the correct approach Unfortunately after converting the time from 24 hour clock to 12 hour clock they did not include lsquopmrsquo to indicate that the time is in the afternoon and so the final answer is not quite right So 3 marks are awarded for all of a correct method but a mark is lost due to the accuracy of the final answer
19
How the answer could have been improvedThis answer could have been improved by
bull In part (a)(i) the answer of 177deg was not sensible given the diagram in the question If the candidate had checked their answer for sense they would have realised they had made a mistake It is always a good idea to check that your answer seems sensible before you move on to another question
bull In part (b) the candidate did all the correct steps but failed to provide both reasons There were two steps to the method which should have indicated to the candidate that there were two steps to justify and therefore two reasons should have been provided The mark allocation for the question [3] also indicates that more than one reason would be required one mark for the value of 43deg leaving two marks one mark for each of two reasons The candidate should have read the question carefully and again checked their response seemed reasonable
bull In part (c) the candidate rounded an intermediate answer which affected the accuracy of the final answer This caused them to lose a mark despite using a correct method You should only ever round the final answer do not round intermediate values If you can store the intermediate values in your calculator and so that you can use the full value in your calcuations If youre not able to do this and you have to round the intermediate values do not round them to less than three significant figures
bull In part (d)(i) the candidate missed out a step in the method As this was a show that question they needed to show all the steps in the method Its important to show all steps even if they seem obvious
bull In part (d)(ii) the candidate made a silly error by not stating that the time was pm When working with time answers are accepted in either 24 clock or 12 clock time but if you give your answer in the 12 hour clock then it must include am or pm as well
Common mistakesThere were a number of common mistakes made by other candidates on this question
bull Accuracy of answers
In parts (c) and (d)(ii) a common error was premature rounding ndash rounding intermediate values in the method before the final answer which resulted in their final answer not being accurate Other candidates gave the final answer to less than three significant figures ignoring the instruction on the front of the paper to round to three significant figures
bull Using incorrect terminology when giving reasons
In part (b) the most common error was to not give full reasons to support the answer Another common error was to provide a reason that did not use the correct mathematical language such as lsquoThey add up to 180degrsquo and lsquoIt is a straight linersquo which could not be awarded marks
bull Lack of knowledge
In part (c) a number of candidates had limited knowledge of trigonometry and did not choose the correct trig ratio which was the sine ratio This is why good revision is important
bull Not checking answers
In part (a)(i) even though the diagram is drawn NOT TO SCALE it is possible to see that the angle is an acute angle and should therefore not be bigger than 90deg This should alert candidate that if their answer is over 90deg it is not a sensible answer and they should go back and check their working
20
bull Inefficient method shown
In part (c) the lsquoShow thatrsquo question a number of candidates omitted an important step from the method this is often common in lsquoShow thatrsquo questions where every step must be shown no matter how obvious them seem
General adviceIn order to do your best when answering a mathematics question make sure you
bull revise all of the topics for the syllabus you are studying before the exam
bull understand what all the key terms and command words in the question mean
bull read the questions carefully and consider what you need to do before you do it
bull only round the final answer not intermediate values
bull show all steps in your working and show them clearly
bull round to the correct degree of accuracy
bull use the correct mathematical terminology
bull check your answers seem reasonable given the context or details of the question
21
It is important that you plan your revision in plenty of time for the examinations and that you develop a revision technique that works for you The advice in this section will help you revise and prepare for the examinations It is divided into general advice for all papers
Use the tick boxes to keep a record of what you have done what you plan to do or what you understand
For more advice on revision see the Cambridge Learner Revision Guide on our website
Section 6 Revision
Find out when the examinations are and plan your revision so you have time to revise Create a revision timetable and divide it into sections to cover each topic
Spend most of your time focussing on specific skills knowledge or issues that you have found more difficult when practicing them either during revision or earlier in the course
Write a summary of all the key information for a topic ndash use the checklists at the end of this section
Know the meaning of the command words used in questions and how to apply them to the information given Look at past examination papers and highlight the command words and check what they mean
Make revision notes and work on practice questions Reading alone does not work you need to be active and practice your maths
Work for shorter periods then have a break Revise small sections of the syllabus at a time but do this regularly
Test yourself by trying out some past exam questions Use the mark schemes to assess yourself and to be familiar with how marks are awarded for different questions
Be organised in advance with your notes texts exercise books revision guides and revision websites so you do not waste valuable revision time trying to find things
Make notes of key mathematical words that you should use in questions that ask you to lsquodescribersquo or give lsquogeometrical reasons forrsquo eg in describing transformations or giving reasons in circle theorem questions Look at the mark schemes for these types of questions from past papers to see how marks are awarded
Make sure you have all of the correct mathematical equipment ready for the exam particularly your calculator Make sure you are familiar with the all of the important functions on your calculator
Practice the areas you can do well not just those that you find more difficult
Take breaks and do things to relax when you take your breaks this will help you to be more productive when you are revising
Before the examination
22
During the examination
Plan your time according to the marks for each question For example a question worth one mark requires less time than a question one worth 4 marks If a question has several parts then the parts with more marks will need more time
Read each question very carefully
Identify the command words ndash you could underline or highlight them
Identify the other key words and information and perhaps underline them too particularly where
questions require reasoning or problem solving
Read the questions careully and make you have answered the question that is being asked
Show your working this is particularly important for questions where you are asked to lsquoshow that helliprsquo
Set your working out clearly so that it is easy to follow this makes it easier to keep track of what you have done and makes checking back through your work easier and it makes it easier for the examiner to mark your work try to write it in a logical order in the answer space
Write answers clearly if you want to change an answer then you should cross the answer out and write a replacement if your answer is on the answer line cross it out and write the replacement answer above it do not try to change numbers on the answer line as this can lead to unclear figures
Check your working and answers to avoid errors
Give your answer to the appropriate level of accuracy either the accuracy indicated in the question or the accuracy given on the front of the paper
Avoid rounding intermediate values part way through your calculation only round the final answer
Check that the answer that you have given is sensible and realistic for what is being asked
Use a pencil when drawing diagrams or completing graphs this means that you can change your answer more easily if you have made a mistake
Take care when reading scales
If you are asked for reasons for your answer then use the correct mathematical terms
Use the mark allocation given with the questionsparts of questions to try to judge how much work is needed to answer each part
23
Top tips for revision of Cambridge IGCSE Mathematics1 Summarise recall and applyMake sure that you can recall and apply the key information and mathematical techniques on each topic that you need for the exam
i Write a summary of the key information of a topicii Collect together some questions that test the knowledge and skills of this topic Ask your teacher for practice
questions or suitable past examination questions or use practice books or textbooksiii Test your recall by covering over the summary and trying to remember the details or use the summary as part of
the lsquoTeach the topicrsquo (Tip 3) or lsquoQuestion and answer cardsrsquo (Tip 4) activities iv After you have spent some time revising and practising the knowledge and skills answer the questions that you
collected together on the topic You might do this later on the same day as revising or a few days later Answer as many questions as you can in order to practise applying your knowledge
v Try creating your own questions by adapting existing ones and use these for practice when you return to a topic
On graph questions straight lines should be ruled and curves should be drawn freehand with a smooth curve
Donrsquot spend too long on any one part of a question If you are really stuck on a question then move on and come back to the question later if you have time As a rough guide each mark on the paper should take about one minute
2 Concept mapsConcept maps are a great way to revise the links between different factors or to explore a larger topic They can also be used to collect together your ideas
i Use a blank sheet of paper and turn it on its side (landscape)ii Put the topic title in the middle of the page and build the concept map outwards using lines called lsquobranchesrsquo
ndash The first branches are from the central topic to sub-topics draw these as thick lines
ndash Add new branches from the sub-topics to include more detail draw these as thinner lines
ndash Add even more detail to a point by adding more branches
This creates a hierarchy of information from lsquooverviewrsquo (the thick branches) to lsquofine detailrsquo (thinnest branches)
iii Write single key words or phrases along a branch and add drawings for visual impactiv Use different colours highlighter pens symbols and arrows to highlight key facts or issuesIt is a good idea to use a large piece of plain A3 (or larger) paper and lots of coloured pens
24
3 Teach the topicThis is a very simple but effective technique that focusses on knowledge recall It tests the brain and rehearses the information you need to know for a certain topic and so will help your revision
i Create some topic cards with key bullet points of information on Leave space for ticksii Give these to your parents family or friends for exampleiii Give yourself 10 minutes maximum to teach your audience the main points of the topic You could use a mini-
whiteboard or flip chart to helpiv Your audience tick off all the points you mention in your presentation and give you a final scoreThe brain loves competition so if you do not score full marks you can try again the next day or compete against friends This system of repeat and rehearsal is very effective especially with more complex topics and doesnt take much preparation
4 Question and answer (QampA) cardsThis is very similar to Teach the topic but less formal and less public for those who dislike performing in front of others It tests knowledge recall and rehearses the information you need to know for a certain topic
i Pick a topic and create two sets of cards question cards and answer cards You might find it helpful to make the question cards a different size or use different coloured card for answers
ii Make sure you have the topic or something appropriate depending on what you are focusing on as a heading on each card The questions should test your knowledge and understanding of key areas of the course
iii A friend or family member uses the cards to test you in short 5 or 10 minute periods at any time during the dayiv You could also do this alone by reading the questions to yourself giving the answer and then checking the
correct answer cardv This game can be adapted by using the cards to find matching pairs turn all cards face down across the space
in front of you Turn over two cards leaving them where they are If they match (one is a question card and the other is the corresponding answer card) pick up the pair and put them to one side If they dont match try to remember where they are and what is on each card then turn them back over Turn over two other cards Continue until you have matched all pairs
5 Question paper and mark schemesLooking at past question papers and the mark scheme helps you to familiarise yourself with what to expect and what the standard is
i Ask your teacher for past paper questions with mark schemes for the course ndash ask your teacher for help to make sure you are answering the correct questions and to simplify the mark scheme
ii Look at the revision checklist and identify which topic a given question relates to ndash you might need to ask your teacher to help you do this
iii Once you have finished revising a topic or unit time yourself answering some appropriate exam questions Check the mark schemes to see how well you would have scored or give the answers to your teacher to check
iv Add details or notes to the mark scheme where you missed out on marks in your original answers using a different coloured pen Use these notes when you revise and try the question again later
You can find plenty of past exam papers and mark schemes on the Cambridge International public website
httpwwwcambridgeinternationalorgprogrammes-and-qualificationscambridge-igcse-mathematics-0580past-papers
25
Other useful revision advice for Cambridge IGCSE Mathematics bull Before the exam make sure that you are familiar with your calculator and confident in using it
bull Look at the Example Candidate Response earlier in this guide Can you identify the strengths of the response andwhere they have made mistakes or lost marks
bull When you are attempting a past paper (or questions from a past paper) complete it without referring to yournotes so that you get a true idea of your strengths and weaknesses Then go back through the paper using yournotes and a different coloured pen to make corrections and changes After you have done as much as you can onthe paper mark it using the mark scheme Take notes of any points that you lost marks on
bull Donrsquot just revise the topics that you enjoy and are confident in If you identify an area that you are weaker inthen try to revisit the topic by reviewing your notes and doing some practice questions then use exam questionsto check whether you now understand
bull Return to topics later in your revision to check that you still remember and understand the topic and to help toensure that you recall more of the material when you get to the examination
Revision checklists for Cambridge IGCSE MathematicsThe tables on the following pages can be used as a revision checklist They do not contain all the detailed knowledge you need to know just an overview For more detail see the syllabus and talk to your teacher
You can use the tick boxes in the checklists to show when you have revised and are happy that you do not need to return to it Tick the lsquoRrsquo lsquoArsquo and lsquoGrsquo column to record your progress as follows
bull R = RED means you are really unsure and lack confidence in that area you might want to focus your revisionhere and possibly talk to your teacher for help
bull A = AMBER means you are reasonably confident in a topic but need some extra practicebull G = GREEN means you are very confident in a topic
As your revision progresses you can concentrate on the RED and AMBER topics in order to turn them into GREEN topics You might find it helpful to highlight each topic in red orange or green to help you prioritise
You can use the lsquoCommentsrsquo column to
bull add more information about the details for each pointbull include a reference to a useful resourcebull include a list of formulae or notationbull add learning aids such as rhymes poems or word playbull highlight areas of difficulty or things that you need to talk to your teacher about
There is a set of checklist for the Core syllabus and a different set for the Extended syllabus
Learner Guide
26
Core syllabus contentCore Number
Category You should be able to R A G CommentsNumber Identify and use
bull natural numbers
bull integers (positive negative and zero)
bull prime numbers
bull write a number as a product of its prime factors
bull square numbers and cube numbers
bull common factors and highest common factor of two numbers
bull common multiples and lowest common multiple of two numbers
bull rational numbers
bull irrational numbers (eg π radic2 )
bull real numbers
bull reciprocals
Learner Guide
27
Core Number
Question type You should be able to R A G CommentsSets and Venn diagrams
Understand notation of Venn diagrams
Definition of sets
eg A = xx is a natural number
B = abchellip
Notation
Number of elements in set A n(A)
Universal set
Union of A and B A cup B
Intersection of A and B A cap B
Squares square roots cubes and cube roots
Calculate
bull squares and cubes of numbers
bull square roots and cube roots of numbers
Learner Guide
28
Core Number
Question type You should be able to R A G CommentsDirected numbers
Use directed numbers in practical situations for example temperature changes
Fractions decimals and percentages
Use the language and notation of simple vulgar and decimal fractions and percentages
Recognise equivalent fractions decimals and percentages
Convert between fractions decimals and percentages
Ordering Order quantities by magnitude and demonstrate familiarity with the symbols = ne gt lt ⩾ ⩽
Indices and standard form (links to Algebraic manipulation)
Evaluate indices eg 25 5ndash2 1000 64frac12 8ndash23
Use the rules of indices for
bull multiplication of indices eg 4ndash3 times 45
bull division of indices eg 57 divide 53
bull index numbers raised to an index eg (23)2 (43)2
Use the standard form A times 10n where n is a positive or negative integer and 1 ⩽ A lt 10
bull convert numbers into and out of standard form
bull calculate with numbers in standard form
Learner Guide
29
Core Number
Question type You should be able to R A G CommentsFour rules
( + ndash times divide )
Use the four rules for calculations with
bull whole numbers
bull decimals
bull vulgar and mixed fractions
bull correct ordering of operations (BIDMAS) and use of bracketsEstimates Make estimates of numbers quantities and lengths
Give approximations to a specified number of
bull significant figures
bull decimal places
Round off answers to reasonable accuracy in the context of a given problem
Bounds Give upper and lower bounds for data given to a specified accuracy eg measured lengths
Ratio proportion rate
Understand ratio
Divide a quantity in a given ratio
Understand direct and inverse proportion
Use scales in practical situations
Use common measures of rate (formulae for other rates eg density and pressure will be given in the question)
Calculate average speed
Learner Guide
30
Core Number
Question type You should be able to R A G CommentsPercentages Calculate a percentage of a quantity
Express one quantity as a percentage of another quantity
Calculate percentage increase or decrease
Use of an electronic calculator
Use a calculator efficiently
Check accuracy of calculations
Time Calculate times in terms of the 24-hour and 12-hour clock
Read
bull clocks
bull dials
bull timetables
Money Calculate using money
Convert from one currency to another
Learner Guide
31
Core Number
Question type You should be able to R A G CommentsPersonal and small business finance
Use given data to solve problems on
bull earnings
bull simple interest
bull compound interest (you will need to know the compound interest formula)
bull discount
bull profit and loss
Extract data from tables and charts
Learner Guide
32
Core Algebra and graphs
Question type You should be able to R A G CommentsBasic algebra Use letters to express generalised numbers
Express basic arithmetic processes algebraically
Substitute numbers in formulae
Construct simple expressions and set up simple equations
Rearrange simple formulae
Algebraic manipulation
Manipulate directed numbers
Use brackets
bull expand a single bracket eg 3x(2x ndash4y)
bull expand a pair of brackets eg (x + 3) (x ndash 7)
Extract common factors eg factorise 9x2 + 15xy
Rules of indices Use and interpret positive negative and zero indices
Use the rules of indices eg to simplify algebra such as
bull 3x4 times 5x
bull 10x3 divide 2x2
bull (x6)2
Learner Guide
33
Core Algebra and graphs
Question type You should be able to R A G CommentsEquations and inequalities
Derive and solve simple linear equations in one unknown
Derive and solve simultaneous linear equations in two unknowns
Number sequences
(links to Squares square roots cubes and cube roots)
Continue a number sequence
Recognise patterns in sequences
Recognise relationships between difference sequences
Find the nth term of sequences for
bull liner sequences
bull simple quadratic sequences
bull cubic sequences
Practical graphs
(links to Mensuration)
Interpret and use graphs in practical situations including
bull travel graphs
bull conversion graphs
Draw graphs from given data
Learner Guide
34
Core Algebra and graphs
Question type You should be able to R A G CommentsGraphs of functions
(links to Co-ordinate geometry)
Construct tables of values for functions of the form
bull ax + b (linear)
bull plusmn x2 + ax + b (quadratic)
bull (x ne 0) (reciprocal)
where a and b are integer constants
Draw and interpret such graphs
Solve linear and quadratic equations approximately by graphical methods
Recognise and sketch the graphs of linear and quadratic functions
ax
Learner Guide
35
Core Co-ordinate geometry
Question type You should be able to R A G CommentsCo-ordinates Work with co-ordinates in two dimensions
Gradients Find the gradient of a straight line graph
Equation of straight line
Interpret and obtain the equation of a straight line graph in the form y = mx + c where the graph is given
Parallel lines Determine the equation of a straight line parallel to a given line eg find the equation of a line parallel to y = 4x ndash 1 that passes through (0 ndash3)
Learner Guide
36
Core Geometry
Question type You should be able to R A G CommentsGeometrical language
Use and interpret the geometrical terms
bull point
bull line
bull parallel
bull perpendicular
bull bearing
bull right angle acute obtuse and reflex angles
bull similar
bull congruent
Use and interpret the vocabulary of
bull triangles right-angled scalene isosceles equilateral
bull quadrilaterals
bull circles
bull polygons
bull simple solid figures including nets
Learner Guide
37
Core Geometry
Question type You should be able to R A G CommentsGeometrical constructions
Measure and draw lines and angles
Construct a triangle given the three sides using a ruler and a pair of compasses only
Scale drawings Read and make scale drawings
Similar figures Calculate lengths of similar figures
Congruent Recognise congruent shapes
Symmetry Recognise symmetry properties for triangles quadrilaterals and circles
Recognise line symmetry in two dimensions
Recognise and find the order of rotational symmetry in two dimensions
Learner Guide
38
Core Geometry
Question type You should be able to R A G CommentsAngle properties Calculate unknown angles explaining the properties that you
are using in geometrical language for angles
bull angles at a point
bull angles on a straight line and intersecting straight lines
bull angles within parallel lines
bull angles in triangles
bull angles in quadrilaterals
bull angles in regular polygons
bull angle in a semi-circle
bull angle between tangent and radius of a circle
Learner Guide
39
Core Mensuration
Question type You should be able to R A G CommentsMeasures bull Use current units of
bull mass
bull length
bull area
bull volume
bull capacity
Express quantities in terms of smaller or larger units including units of area and volume
Convert between units including units of area and volume
Perimiter Carry out calculations involving
bull perimeter and area of a rectangle
bull perimeter and area of a triangle
bull perimeter and area of parallelogram
bull perimeter and area of a trapezium
bull perimeter and area of shapes made by combining
bull rectangles triangles parallelograms andor trapeziums
Learner Guide
40
Core Mensuration
Question type You should be able to R A G CommentsCircles Carry out calculations involving circumference and area of a
circle
Solve simple problems involving the arc length and sector area of a circle where the sector angle is a factor of 360deg
Surface area and volume
Carry out calculations involving
bull surface area and volume of a cuboid prism and cylinder (no formulae will be given for these shapes)
bull surface area and volume of a sphere pyramid and cone (formulae will be given for these shapes)
Areas and volumes of compound shapes
Carry out calculations involving the areas and volumes of compound shapes made from combinations of the shapes in Perimeter or Surface area and volume
Learner Guide
41
Core Trigonometry
Question type You should be able to R A G CommentsBearings Use and interpret three-figure bearings measured clockwise
from the North ie 000degndash360degTrigonometry Find unknown sides andor angles in right-angled triangles by
applying
bull Pythagorasrsquo theorem
bull sine cosine and tangent ratios for acute angles in right-angled triangles
Learner Guide
42
Core Vectors and transformations
Question type You should be able to R A G CommentsVectors in two dimensions (links to Trigonometry)
Describe a translation by using a vector represented by
AB or a
Add and subtract vectors
Multiply a vector by a scalar
Transformations Reflect simple shapes in horizontal or vertical lines
Rotate simple shapes through multiples of 90deg about
bull the origin
bull their vertices
bull the midpoints of their sides
Construct translations of simple shapes
Construct enlargements of simple shapes (positive and fractional scale factors)
Recognise and describe using the correct language
bull reflections
bull rotations
bull translations
bull enlargements (positive and fractional scale factors)
( )x
y
Learner Guide
43
Core Probability
Question type You should be able to R A G CommentsSingle events Calculate the probability of a single event as a fraction decimal
or percentage (not a ratio)Probability scale Understand and use the probability scale from 0 to 1
Sum to 1 Understand that the probability of an event occurring = 1 ndash the probability of the event not occurring
Relative frequency
Understand relative frequency as an estimate of probability
Work out expected frequencies using relative frequencyCombined events Calculate the probability of simple combined events using
bull tree diagrams
bull possibility diagrams (points on a grid)
bull Venn diagrams (2 sets only)
Learner Guide
44
Core Statistics
Question type What I need to do R A G CommentsClassify Collect classify and tabulate data
Interpret and compare
Read interpret and draw simple inferences from tables and statistical diagrams
Compare sets of data using
bull tables
bull graphs
bull statistical measures
Be aware of restrictions when making conclusions from data
Charts Construct and use
bull bar charts
bull pie charts
bull pictograms
bull stem-and-leaf diagrams
bull frequency distributions
bull histograms with equal intervals
bull scatter diagrams
Learner Guide
45
Question type What I need to do R A G CommentsAverages Calculate for individual and discrete data
bull mean
bull median
bull mode
bull range
and distinguish between their useCorrelation Understand what is meant by positive negative and zero
correlation with reference to a scatter diagramLine of best fit Draw interpret and use a ruled line of best fit by eye
Learner Guide
46
Extended syllabus content (includes required Core content)Extended Number
Question type You should be able to R A G CommentsNumber Identify and use
bull natural numbers
bull integers (positive negative and zero)
bull prime numbers
bull write a number as a product of its prime factors
bull square and cube numbers
bull common factors and highest common factor of two or more numbers
bull common multiples and lowest common multiple of two or more numbers
bull rational numbers
bull irrational numbers (eg π radic2 )
bull real numbers
bull reciprocals
Learner Guide
47
Extended Number
Question type You should be able to R A G CommentsSet notation and language
Use language notation and Venn diagrams to describe sets and represent relationships between sets as follows
Definition of sets egA = x x is a natural number
B = (xy) y = mx + c
C = x a ⩽ x ⩽ b
D = a b c hellip
Notation egnumber of elements in set A n(A)
lsquois an element ofrsquo isin
lsquois not an element ofrsquo notin
complement of set A
the empty set empty
the universal set
A is a subset of B A sube B
A is a proper subset of B A sub B
A is not a subset of B A ⊈ B
A is not a proper subset of B A nsub B
union of A and B A cup B
intersection of A and B A cap B
Learner Guide
48
Extended Number
Question type You should be able to R A G CommentsSquares square roots cubes and cube roots
Calculatebull squares of numbers
bull square roots of numbers
bull cubes of numbers
bull cube roots of numbers
bull other powers and roots of numbers
Directed numbers
Use directed numbers in practical situations for example temperature changes
Fractions decimals and percentages
Use the language and notation of simple vulgar and decimal fractions and percentages in appropriate contexts
Recognise equivalent fractions decimals and percentages
Convert between fractions decimals and percentages
Convert recurring decimals to fractions
Ordering Order quantities by magnitude and demonstrate familiarity with the symbols = ne gt lt ⩾ ⩽
Learner Guide
49
Extended Number
Question type You should be able to R A G CommentsIndices and standard form (links to Algebraic manipulation)
Evaluate indices including fractional negative and zero
eg 25 5ndash2 1000 10012 8ndash23
Use the rules of indices forbull multiplication of indices eg 43 times 45
bull division of indices eg 57 divide 53
bull index numbers raised to an index eg (43)2
Use the standard form A times 10n where n is a positive or negative integer and 1 ⩽ A lt 10bull convert into and out of standard form
bull calculate with numbers in standard form
Four rules
( + ndash times divide )
Use the four rules for calculations withbull whole numbers
bull decimals
bull vulgar and mixed fractions
bull correct ordering of operations (BIDMAS) and use of brackets
Learner Guide
50
Extended Number
Question type You should be able to R A G CommentsEstimates Make estimates of numbers quantities and lengths
Give approximations to a specified number of
bull significant figures
bull decimal places
Round off answers to reasonable accuracy in the context of a given problem
Bounds Give upper and lower bounds for data given to a specified accuracy eg measured lengths
Obtain appropriate upper and lower bounds to solutions of simple problems given to a specified accuracy eg the lower and upper bounds for the area of a rectangle
Ratio proportion rate
(links to Direct and inverse proportion)
Understand ratio
Divide quantities in a given ratio
Increase and decrease a quantity by a given ratio
Understand numerical problems involving direct and inverse proportion
Use ratio and scales in practical situations
Use common measures of rate (formulae for other rates eg density and pressure will be given in the question)
Calculate average speed
Learner Guide
51
Extended Number
Question type What I need to do R A G CommentsPercentages Calculate a percentage of a quantity
Express one quantity as a percentage of another quantity
Calculate percentage increase or decrease
Calculate reverse percentages eg finding the cost price given the selling price and the percentage profit
Use of an electronic calculator
Use a calculator efficiently
Check accuracy of calculations
Time Calculate times in terms of the 24-hour and 12-hour clock
Read clocks dials and timetables
Money Calculate using money
Convert from one currency to another
Learner Guide
52
Extended Number
Question type You should be able to R A G CommentsPersonal and small business finance
Use given data to solve problems on
bull earnings
bull simple interest
bull compound interest
ndash you must know the compound interest formula
bull discount
bull profit and loss
Extract data from tables and charts
Exponential growth and decay
Use exponential growth and decay in population and finance eg depreciation bacteria growth
Learner Guide
53
Extended Algebra and graphs
Question type You should be able to R A G CommentsBasic algebra Use letters to express generalised numbers
Express basic arithmetic processes algebraically
Substitute numbers in complicated formulae
Construct and rearrange complicated formulae eg where the subject appears twice
Algebraic manipulation
Manipulate directed numbers
Use bracketsbull expand a single bracket eg expand 3x(2x ndash 4y)
bull expand a pair of brackets eg (x ndash 4)(x + 7)
bull expand products of more than two brackets eg (x + 4)(x ndash 7)(2x + 1)
Extract common factors eg factorise 9x2 + 15xy
Factorise expressions of the formbull ax + bx + kay + kby
bull asup2xsup2 ndash bsup2ysup2
bull asup2 + 2ab + bsup2
bull axsup2 + bx + c
Learner Guide
54
Extended Algebra and graphs
Question type You should be able to R A G CommentsAlgebraic fractions
Manipulate algebraic fractions eg
bull
bull
bull
bull
bull
Factorise and simplify algebraic fractions such as
Rules of indices Use and interpret positive negative and zero indices
Use and interpret fractional indices eg solve 32x = 2
Use the rules of indices to simplify algebra eg
x3 + x ndash 4
22x3 +
3(x ndash 5)2
3a4 +
5ab3
3a4 divide
9a10
1x ndash 2 +
2x ndash 3
x2 ndash 2xx2 ndash 5x + 6
3xndash4 times23
x12
32x5( )
3
2xndash2divide25
x12
Learner Guide
55
Extended Algebra and graphs
Question type You should be able to R A G CommentsEquations and inequalities
bull Derive and solve simple linear equations in one unknown
bull Derive and solve simultaneous linear equations in two unknowns
bull Derive and solve simultaneous equations involving one linear and one quadratic
Solve quadratic equations by
bull factorisation
bull completing the square
bull using the formula
Derive and solve simple linear inequalities including representing solutions on a number line
Linear programming
Represent inequalities graphically including using the conventions of
bull broken lines for strict inequalities
bull shading unwanted regions
Solve simple linear programming problems using graphical representations of inequalities
Learner Guide
56
Extended Algebra and graphs
Question type You should be able to R A G CommentsNumber sequences (links to Squares square roots cubes and cube roots)
Continue a number sequence
Recognise patterns in sequences
Recognise relationships between different sequences
Find the nth term of sequences of
bull linear sequences
bull quadratic sequences
bull cubic sequences
bull exponential sequences
and simple combinations of these
Direct and inverse proportion (links to Ratio proportion rate)
Express direct proportion algebraically
Express inverse proportion algebraically
Use algebraic expressions of direct and inverse proportion to find unknown quantities
Practical graphs
(links to Coordinate geometry)
Interpret and use graphs in practical situations including
bull travel graphs
bull conversion graphs
Draw graphs from given data
Learner Guide
57
Extended Algebra and graphs
Question type You should be able to R A G CommentsPractical graphs (links to Coordinate geometry) continued
Apply the idea of rate of change to simple kinematics involving
bull distancendashtime graphs
bull speedndashtime graphs
bull acceleration and deceleration
This may involve estimation and interpretation of the gradient of a tangent at a point
Calculate distance travelled as an area under a linear speedndash time graph
Learner Guide
58
Extended Algebra and graphs
Question type You should be able to R A G CommentsGraphs of functions (links to Coordinate geometry)
Construct tables of values and draw graphs for functions of the form
bull axn where a is a rational constant and n = minus2 minus1 0 1 2 3 and simple sums of not more than three of these
bull abx + c where a and c are rational constants and b is a positive integer
Solve associated equations approximately by graphical methods including finding and interpreting roots and finding turning points of quadratics by completing the square
Draw and interpret graphs representing exponential growth and decay problems
Recognise sketch and interpret graphs of
bull linear
bull quadratic
bull cubic
bull reciprocal
bull exponential
(knowledge of turning points and asymtotes is required)Tangents Estimate gradients of curves by drawing tangents
Learner Guide
59
Extended Algebra and graphs
Question type You should be able to R A G CommentsFunctions Use function notation eg
f(x) = 3x ndash 5 f x α 3x ndash5 to describe simple functions
Find inverse functions f ndash1 (x)
Form composite functions as defined by gf(x) = g(f(x))
Derivatives Understand the idea of a derived function
Use derivatives of the form axn and simple sums of not more than three of these (a is a rational constant and n is a positive integer or 0)
Apply differentiation to gradients and turning points (stationary points)
Use any method to explain whether the turning point is a maximum or a minimum eg second derivative or gradient of function on either side of turning point
Learner Guide
60
Extended Co-ordinate geometry
Question type You should be able to R A G CommentsStraight line graphs
Work with co-ordinates in two dimensions
Gradient Find the gradient of a straight line graph
Calculate the gradient of a straight line from the co-ordinates of two points on it
Length and midpoint
Calculate the length and the co-ordinates of the midpoint of a straight line segment from the co-ordinates of its end points
Equation of line Interpret and obtain the equation of a straight line graph
Parallel lines Determine the equation of a straight line parallel to a given line eg find the equation of a line parallel to y = 4x ndash 1 that passes through (0 ndash3)
Perpendicular lines
Find the gradient of parallel and perpendicular lines eg
bull find the gradient of a line perpendicular to y = 3x + 1
bull find the equation of a line perpendicular to one passing through the co-ordinates (1 3) and (ndash2 ndash9)
Learner Guide
61
Extended Geometry
Question type You should be able to R A G CommentsGeometrical language
Use and interpret the geometrical terms
bull point
bull line
bull parallel
bull perpendicular
bull bearing
bull right angle acute obtuse and reflex angles
bull similar
bull congruent
Use and interpret the vocabulary of
bull triangles right-angled scalene isosceles equilateral
bull quadrilaterals
bull circles
bull polygons
bull simple solid figures including nets
Learner Guide
62
Extended Geometry
Question type What I need to do R A G CommentsGeometrical constructions
Measure and draw lines and angles
Construct a triangle given the three sides using a ruler and a pair of compasses only
Scale drawings Read and make scale drawings
Similar figures Calculate lengths of similar figures
Use relationships between areas of similar triangles and in similar figures
Use relationships between volumes and surface areas of similar solids
Congruent triangles
Use the congruence criteria for triangles (SSS ASA SAS RHS)
Symmetry Recognise symmetry properties for triangles quadrilaterals and circles
Recognise line symmetry in two dimensions
Recognise and find the order of rotational symmetry in two dimensions
Learner Guide
63
Extended Geometry
Question type You should be able to R A G CommentsSymmetry (continued)
Use the following symmetry properties of circles
bull equal chords are equidistant from the centre
bull perpendicular bisector of a chord passes through the centre
bull tangents from an external point are equal in length
Recognise and use symmetry properties of
bull prism cylinder cone and pyramid
Learner Guide
64
Extended Geometry
Question type You should be able to R A G CommentsAngle properties Calculate unknown angles explaining the properties that
you are using in geometrical language for the following geometrical properties
bull angles at a point
bull angles at a point on a straight line and intersecting straight lines
bull angles formed within parallel lines
bull angle properties of triangles and quadrilaterals
bull angle properties of regular polygons
bull angle in a semi-circle
bull angle between tangent and radius of a circle
bull angles properties of irregular polygons
bull angle at the centre of a circle is twice the angle at the circumference
bull angles in the same segment are equal
bull angles in opposite segments are supplementary cyclic quadrilaterals
bull alternate segment theorem
Learner Guide
65
Extended Mensuration
Question type What I need to do R A G CommentsMeasures Use current units of
bull mass
bull length
bull area
bull volume
bull capacity
Express quantities in terms of smaller or larger units including units of area and volume
Perimeter Carry out calculations involving
bull perimeter and area of a rectangle
bull perimeter and area of a triangle
bull perimeter and area of parallelogram
bull perimeter and area of a trapezium
bull perimeter and area of compound shapes made by combining rectangles triangles parallelograms andor trapeziums
Learner Guide
66
Extended Mensuration
Question type You should be able to R A G CommentsCircles Carry out calculations involving circumference and area of a
circle
Solve problems involving arc length and sector area of a circle
Surface area and volume
Carry out calculations involving
bull surface area and volume of a cuboid prism and cylinder (no formulae will be given for these shapes)
bull surface area and volume of a sphere pyramid and cone (formulae will be given for these shapes)
Compound shapes
Carry out calculations involving
bull area of a shape made by combining cuboids prisms andor cylinders
bull volume of a shape made by combining cuboids prisms andor cylinders
Learner Guide
67
Extended Trigonometry
Question type You should be able to R A G CommentsBearings Use and interpret three-figure bearings measured clockwise
from the North ie 000degndash360degTrigonometry Find unknown sides andor angles in right-angled triangles by
applying
bull Pythagorasrsquo theorem
bull sine cosine and tangent ratios for acute angles in right-angled triangles
Solve problems in two dimensions involving angles of elevation and depression
Know that the perpendicular distance from a point to a line is the shortest distance to the line
Trig graphs and equations
Recognise sketch and interpret graphs of simple trigonometric functions
Graph and know the properties of trigonometric functions
Solve simple trigonometric equations for values between 0deg
and 360deg eg Solve sin x = radic32
for values of x between 0deg and
360degGeneral trig Solve problems using sine and cosine rules for any triangle
Find the area of any triangle using frac12absinC
Trig in 3D Solve simple trigonometrical problems in three dimensions including angle between a line and a plane
Learner Guide
68
Extended Vectors and transformations
Question type You should be able to R A G CommentsVectors in two dimensions (links to Trigonometry)
Describe a translation by using a vector represented by
AB or a
Add and subtract vectors
Multiply a vector by a scalar
Transformations Reflect simple shapes in horizontal or vertical lines
Rotate simple shapes through multiples of 90deg about any point
Construct translations of simple shapes
Construct enlargements of simple shapes (positive fractional and negative scale factors)
Recognise and describe
bull reflections
bull rotations
bull translations
bull enlargements (positive fractional and negative scalefactors)
( )x
y
Learner Guide
69
Extended Vectors and transformations
Question type You should be able to R A G CommentsHarder vectors
Calculate the magnitude of a vector as and
understand that magnitude is denoted by modulus signs |A B| or |a|
Represent vectors by directed line segments
Use the sum and difference of two vectors
Use position vectors
( )x
yradicx2 + y2
Learner Guide
70
Extended Probability
Question type You should be able to R A G CommentsProbability (links to Four rules)
Calculate the probability of a single event as a fraction decimal or percentage (not a ratio)
Probability scale Understand and use the probability scale from 0 to 1
Sum to 1 Understand that the probability of an event occurring = 1 ndash the probability of the event not occurring
Relative frequency
Understand relative frequency as an estimate of probability
Work out expected frequencies using relative frequency
Combined events Calculate the probability of combined events using
bull tree diagrams
bull possibility diagrams
bull tables
Learner Guide
71
Extended Statistics
Question type You should be able to R A G CommentsClassify Collect classify and tabulate data
Interpret and compare
Read interpret and draw simple inferences from tables and statistical diagrams
Compare sets of data using
bull tables
bull graphs
bull statistical measures
Be aware of restrictions when making conclusions from data
Charts Construct and use
bull bar charts
bull pie charts
bull pictograms
bull stem ndash and ndash leaf diagrams
bull frequency distributions
bull histograms with equal and unequal intervals
bull scatter diagrams
Learner Guide
72
Extended Statistics
Question type You should be able to R A G CommentsAverages Calculate for individual and discrete data
bull mean
bull median
bull mode
bull range
and distinguish between their use
Estimated mean Calculate an estimate of the mean for grouped and continuous data
Identify the modal class from a grouped frequency distributionCumulative frequency
Construct and use cumulative frequency diagrams to estimate and interpret
bull the median
bull percentiles
bull quartiles
bull inter-quartile range
Construct and interpret box-and-whisker plots
Correlation Understand what is meant by positive negative and zero correlation with reference to a scatter diagram
Lines of best fit Draw interpret and use a ruled line of best fit by eye
Cambridge Assessment International Education1 Hills Road Cambridge CB1 2EU United Kingdomt +44 1223 553554e infocambridgeinternationalorg wwwcambridgeinternationalorg
Copyright copy UCLES October 2017
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- Text Field 355
- Check Box 1094 Off
- Check Box 1095 Off
- Check Box 1096 Off
- Text Field 224
- Check Box 1032 Off
- Check Box 1033 Off
- Check Box 1034 Off
- Text Field 225
- Check Box 1035 Off
- Check Box 1036 Off
- Check Box 1037 Off
- Check Box 1038 Off
- Check Box 1039 Off
- Check Box 1040 Off
- Check Box 1041 Off
- Check Box 1042 Off
- Check Box 1043 Off
- Text Field 220
- Check Box 1044 Off
- Check Box 1045 Off
- Check Box 1046 Off
- Text Field 276
- Check Box 1047 Off
- Check Box 1048 Off
- Check Box 1049 Off
- Check Box 10146 Off
- Check Box 10147 Off
- Check Box 10148 Off
- Check Box 10188 Off
- Check Box 10189 Off
- Check Box 10190 Off
- Check Box 10191 Off
- Check Box 10192 Off
- Check Box 10193 Off
- Check Box 10194 Off
- Check Box 10195 Off
- Check Box 10196 Off
- Check Box 10197 Off
- Check Box 10198 Off
- Check Box 10199 Off
- Check Box 10200 Off
- Check Box 10201 Off
- Check Box 10202 Off
- Text Field 278
- Check Box 1050 Off
- Check Box 1051 Off
- Check Box 1052 Off
- Check Box 1053 Off
- Check Box 1054 Off
- Check Box 1055 Off
- Check Box 1056 Off
- Check Box 1057 Off
- Check Box 1058 Off
- Check Box 1059 Off
- Check Box 1060 Off
- Check Box 1061 Off
- Text Field 277
- Check Box 1062 Off
- Check Box 1063 Off
- Check Box 1064 Off
- Check Box 1065 Off
- Check Box 1066 Off
- Check Box 1067 Off
- Check Box 10203 Off
- Check Box 10204 Off
- Check Box 10205 Off
- Check Box 10206 Off
- Check Box 10207 Off
- Check Box 10208 Off
- Text Field 281
- Check Box 10209 Off
- Check Box 10210 Off
- Check Box 10211 Off
- Text Field 282
- Check Box 10212 Off
- Check Box 10213 Off
- Check Box 10214 Off
- Check Box 10215 Off
- Check Box 10216 Off
- Check Box 10217 Off
- Check Box 102010 Off
- Check Box 102011 Off
- Check Box 102012 Off
- Check Box 10218 Off
- Check Box 10219 Off
- Check Box 10220 Off
- Check Box 10221 Off
- Check Box 10222 Off
- Check Box 10223 Off
- Check Box 10224 Off
- Check Box 10225 Off
- Check Box 10226 Off
- Text Field 284
- Check Box 1068 Off
- Check Box 1069 Off
- Check Box 1070 Off
- Check Box 1071 Off
- Check Box 1072 Off
- Check Box 1073 Off
- Check Box 1074 Off
- Check Box 1075 Off
- Check Box 1076 Off
- Check Box 1077 Off
- Check Box 1078 Off
- Check Box 1079 Off
- Check Box 1080 Off
- Check Box 1081 Off
- Check Box 1082 Off
- Text Field 283
- Check Box 1083 Off
- Check Box 1084 Off
- Check Box 1085 Off
- Check Box 102013 Off
- Check Box 102014 Off
- Check Box 102015 Off
- Check Box 102016 Off
- Check Box 102017 Off
- Check Box 102018 Off
- Check Box 102019 Off
- Check Box 10227 Off
- Check Box 10228 Off
- Text Field 285
- Check Box 10229 Off
- Check Box 10230 Off
- Check Box 10231 Off
- Check Box 10232 Off
- Check Box 10233 Off
- Check Box 10234 Off
- Check Box 1098 Off
- Check Box 1099 Off
- Check Box 10100 Off
- Check Box 10101 Off
- Check Box 10102 Off
- Check Box 10103 Off
- Check Box 10107 Off
- Check Box 10108 Off
- Check Box 10109 Off
- Check Box 10110 Off
- Check Box 10111 Off
- Check Box 10112 Off
- Check Box 10113 Off
- Check Box 10114 Off
- Check Box 10115 Off
- Check Box 10116 Off
- Check Box 10117 Off
- Check Box 10118 Off
- Text Field 287
- Text Field 288
- Check Box 10119 Off
- Check Box 10120 Off
- Check Box 101010 Off
- Check Box 101011 Off
- Check Box 101012 Off
- Check Box 101013 Off
- Check Box 101014 Off
- Check Box 101015 Off
- Check Box 101019 Off
- Check Box 10121 Off
- Check Box 10122 Off
- Check Box 10123 Off
- Check Box 10124 Off
- Check Box 10125 Off
- Check Box 10126 Off
- Text Field 289
- Check Box 101020 Off
- Check Box 101021 Off
- Check Box 101022 Off
- Check Box 101023 Off
- Check Box 101024 Off
- Check Box 101025 Off
- Check Box 10127 Off
- Check Box 10128 Off
- Check Box 10129 Off
- Check Box 10130 Off
- Check Box 10131 Off
- Check Box 10132 Off
- Text Field 290
- Check Box 101026 Off
- Check Box 101027 Off
- Check Box 101028 Off
- Check Box 101029 Off
- Check Box 101030 Off
- Check Box 101031 Off
- Check Box 10133 Off
- Check Box 10134 Off
- Check Box 10135 Off
- Check Box 10136 Off
- Check Box 10137 Off
- Check Box 10138 Off
- Text Field 291
- Check Box 10139 Off
- Check Box 10140 Off
- Check Box 101016 Off
- Check Box 101017 Off
- Check Box 101018 Off
- Check Box 101032 Off
- Text Field 292
- Check Box 101036 Off
- Check Box 101037 Off
- Check Box 101038 Off
- Check Box 101039 Off
- Check Box 101040 Off
- Check Box 101041 Off
- Check Box 10150 Off
- Check Box 10151 Off
- Check Box 10152 Off
- Check Box 10153 Off
- Check Box 10154 Off
- Check Box 10155 Off
- Check Box 101042 Off
- Check Box 101043 Off
- Check Box 101044 Off
- Check Box 101045 Off
- Check Box 101046 Off
- Check Box 101047 Off
- Text Field 293
- Check Box 10156 Off
- Check Box 10157 Off
- Check Box 10158 Off
- Check Box 10159 Off
- Check Box 10160 Off
- Check Box 10161 Off
- Check Box 101048 Off
- Check Box 101049 Off
- Check Box 101050 Off
- Check Box 10162 Off
- Check Box 10163 Off
- Check Box 10164 Off
- Text Field 294
- Check Box 101052 Off
- Check Box 101053 Off
- Check Box 101054 Off
- Check Box 101055 Off
- Check Box 101056 Off
- Check Box 101057 Off
- Check Box 1010263 Off
- Check Box 1010264 Off
- Check Box 10165 Off
- Check Box 10166 Off
- Check Box 10167 Off
- Check Box 101058 Off
- Check Box 101059 Off
- Check Box 101060 Off
- Check Box 1010269 Off
- Check Box 1010270 Off
- Text Field 357
- Check Box 1010271 Off
- Check Box 1010272 Off
- Check Box 1010273 Off
- Text Field 358
- Check Box 1010274 Off
- Check Box 1010330 Off
- Check Box 1010331 Off
- Text Field 359
- Check Box 1010343 Off
- Check Box 1010344 Off
- Check Box 1010345 Off
- Text Field 360
- Check Box 1010348 Off
- Check Box 1010349 Off
- Check Box 1010350 Off
- Text Field 297
- Check Box 101061 Off
- Check Box 101062 Off
- Check Box 101063 Off
- Check Box 101064 Off
- Check Box 101065 Off
- Check Box 101066 Off
- Check Box 10168 Off
- Check Box 10169 Off
- Check Box 10170 Off
- Check Box 10171 Off
- Check Box 10172 Off
- Check Box 10173 Off
- Check Box 101067 Off
- Check Box 101068 Off
- Check Box 101069 Off
- Check Box 10174 Off
- Check Box 10175 Off
- Check Box 10176 Off
- Check Box 10177 Off
- Check Box 10178 Off
- Check Box 10179 Off
- Check Box 101070 Off
- Check Box 101071 Off
- Check Box 101072 Off
- Check Box 10180 Off
- Check Box 10181 Off
- Check Box 10182 Off
- Check Box 101073 Off
- Check Box 101074 Off
- Check Box 101075 Off
- Check Box 10183 Off
- Check Box 10184 Off
- Check Box 10185 Off
- Check Box 10186 Off
- Check Box 10187 Off
- Check Box 10235 Off
- Check Box 101076 Off
- Check Box 101077 Off
- Check Box 101078 Off
- Text Field 298
- Check Box 101079 Off
- Check Box 101080 Off
- Check Box 101081 Off
- Check Box 101082 Off
- Check Box 101083 Off
- Check Box 101084 Off
- Text Field 299
- Check Box 101088 Off
- Check Box 101089 Off
- Check Box 101090 Off
- Text Field 300
- Check Box 101091 Off
- Check Box 101092 Off
- Check Box 101093 Off
- Check Box 1010351 Off
- Check Box 1010352 Off
- Check Box 1010353 Off
- Text Field 301
- Check Box 10242 Off
- Check Box 10243 Off
- Check Box 10244 Off
- Check Box 101094 Off
- Check Box 101095 Off
- Check Box 101096 Off
- Check Box 101097 Off
- Check Box 101098 Off
- Check Box 101099 Off
- Text Field 302
- Check Box 1010103 Off
- Check Box 1010104 Off
- Check Box 1010105 Off
- Check Box 10245 Off
- Check Box 10246 Off
- Check Box 10247 Off
- Check Box 10248 Off
- Check Box 10249 Off
- Check Box 10250 Off
- Check Box 1010106 Off
- Check Box 1010107 Off
- Check Box 1010108 Off
- Check Box 1010109 Off
- Check Box 1010110 Off
- Check Box 1010111 Off
- Check Box 1010112 Off
- Check Box 1010113 Off
- Check Box 1010114 Off
- Check Box 10251 Off
- Check Box 10252 Off
- Check Box 10253 Off
- Check Box 1010115 Off
- Check Box 1010116 Off
- Check Box 1010117 Off
- Text Field 303
- Check Box 10260 Off
- Check Box 10261 Off
- Check Box 10262 Off
- Check Box 10101017 Off
- Check Box 10101018 Off
- Check Box 10101019 Off
- Check Box 10101020 Off
- Check Box 1010118 Off
- Check Box 1010119 Off
- Check Box 1010120 Off
- Check Box 1010126 Off
- Check Box 1010127 Off
- Check Box 10263 Off
- Check Box 10264 Off
- Check Box 10265 Off
- Check Box 10269 Off
- Check Box 10270 Off
- Check Box 10271 Off
- Check Box 10101025 Off
- Check Box 10101026 Off
- Check Box 10101027 Off
- Text Field 306
- Check Box 10266 Off
- Check Box 10267 Off
- Check Box 10268 Off
- Check Box 10101021 Off
- Check Box 10101022 Off
- Check Box 10101023 Off
- Check Box 10101024 Off
- Check Box 1010131 Off
- Check Box 1010132 Off
- Check Box 1010133 Off
- Check Box 1010134 Off
- Check Box 1010135 Off
- Check Box 1010136 Off
- Check Box 1010137 Off
- Check Box 1010138 Off
- Text Field 3025
- Check Box 10367 Off
- Check Box 10368 Off
- Check Box 10369 Off
- Check Box 10407 Off
- Check Box 10431 Off
- Check Box 10432 Off
- Text Field 3059
- Check Box 104010 Off
- Check Box 10433 Off
- Check Box 10465 Off
- Check Box 104011 Off
- Check Box 10466 Off
- Check Box 10527 Off
- Text Field 3060
- Check Box 104012 Off
- Check Box 10528 Off
- Check Box 10529 Off
- Text Field 3063
- Check Box 10101037 Off
- Check Box 10101038 Off
- Check Box 10101039 Off
- Text Field 309
- Check Box 10275 Off
- Check Box 10276 Off
- Check Box 10277 Off
- Check Box 10101040 Off
- Check Box 10101041 Off
- Check Box 10101042 Off
- Text Field 3010
- Check Box 10278 Off
- Check Box 10279 Off
- Check Box 10280 Off
- Check Box 10101044 Off
- Check Box 10101045 Off
- Check Box 10101046 Off
- Check Box 10101047 Off
- Check Box 1010141 Off
- Check Box 1010142 Off
- Text Field 3011
- Check Box 10281 Off
- Check Box 10282 Off
- Check Box 10283 Off
- Check Box 10101048 Off
- Check Box 10101049 Off
- Check Box 10101050 Off
- Check Box 10101051 Off
- Check Box 10101052 Off
- Check Box 10101053 Off
- Check Box 10101054 Off
- Check Box 10101055 Off
- Check Box 10101056 Off
- Check Box 10101057 Off
- Check Box 10101058 Off
- Check Box 10101059 Off
- Check Box 10101060 Off
- Check Box 10101061 Off
- Check Box 10101062 Off
- Check Box 10101063 Off
- Check Box 10101064 Off
- Check Box 10101065 Off
- Check Box 10101066 Off
- Check Box 10101067 Off
- Check Box 10101068 Off
- Check Box 10101069 Off
- Check Box 10101070 Off
- Check Box 10101071 Off
- Check Box 10101072 Off
- Check Box 10101073 Off
- Check Box 10101074 Off
- Text Field 3012
- Check Box 10284 Off
- Check Box 10285 Off
- Check Box 10286 Off
- Text Field 3013
- Check Box 10101075 Off
- Check Box 10101076 Off
- Check Box 10101077 Off
- Text Field 3014
- Check Box 10101078 Off
- Check Box 1010143 Off
- Check Box 1010144 Off
- Text Field 3015
- Check Box 10287 Off
- Check Box 10288 Off
- Check Box 10289 Off
- Check Box 10334 Off
- Check Box 10335 Off
- Check Box 10336 Off
- Check Box 10371 Off
- Check Box 10372 Off
- Check Box 10436 Off
- Check Box 10437 Off
- Check Box 10438 Off
- Check Box 10447 Off
- Text Field 3016
- Check Box 10401 Off
- Check Box 10402 Off
- Check Box 10403 Off
- Check Box 10291 Off
- Check Box 10292 Off
- Check Box 10337 Off
- Check Box 10448 Off
- Check Box 10449 Off
- Check Box 10456 Off
- Check Box 10457 Off
- Check Box 10458 Off
- Check Box 10533 Off
- Check Box 10534 Off
- Check Box 10535 Off
- Check Box 10543 Off
- Check Box 10544 Off
- Check Box 10740 Off
- Check Box 10741 Off
- Text Field 3017
- Check Box 10101079 Off
- Check Box 10101080 Off
- Check Box 10101081 Off
- Check Box 10101082 Off
- Check Box 1010145 Off
- Check Box 1010146 Off
- Check Box 10293 Off
- Check Box 10294 Off
- Check Box 10295 Off
- Check Box 10338 Off
- Check Box 10339 Off
- Check Box 10370 Off
- Check Box 10101083 Off
- Check Box 10101084 Off
- Check Box 10101085 Off
- Check Box 10101086 Off
- Check Box 1010147 Off
- Check Box 1010148 Off
- Check Box 10296 Off
- Check Box 10297 Off
- Check Box 10298 Off
- Text Field 3018
- Check Box 10299 Off
- Check Box 10300 Off
- Check Box 10301 Off
- Check Box 10101087 Off
- Check Box 10101088 Off
- Check Box 10101089 Off
- Check Box 10101090 Off
- Check Box 1010149 Off
- Check Box 1010150 Off
- Check Box 10302 Off
- Check Box 10303 Off
- Check Box 10304 Off
- Text Field 3019
- Check Box 10305 Off
- Check Box 10306 Off
- Check Box 10307 Off
- Text Field 3020
- Check Box 10308 Off
- Check Box 10309 Off
- Check Box 103010 Off
- Text Field 311
- Check Box 10141 Off
- Check Box 10142 Off
- Check Box 10143 Off
- Check Box 10144 Off
- Check Box 10145 Off
- Check Box 10149 Off
- Check Box 10257 Off
- Check Box 10258 Off
- Check Box 10259 Off
- Check Box 10310 Off
- Check Box 10311 Off
- Check Box 10312 Off
- Check Box 10331 Off
- Check Box 10332 Off
- Check Box 10333 Off
- Check Box 10313 Off
- Check Box 10314 Off
- Check Box 10315 Off
- Check Box 10316 Off
- Check Box 10317 Off
- Check Box 10318 Off
- Check Box 10319 Off
- Check Box 10320 Off
- Check Box 10321 Off
- Check Box 10322 Off
- Check Box 10323 Off
- Check Box 10324 Off
- Check Box 10325 Off
- Check Box 10326 Off
- Check Box 10327 Off
- Check Box 10399 Off
- Check Box 10400 Off
- Check Box 10530 Off
- Text Field 335
- Check Box 10567 Off
- Check Box 10568 Off
- Check Box 10569 Off
- Check Box 10570 Off
- Check Box 10571 Off
- Check Box 10572 Off
- Check Box 10573 Off
- Check Box 10574 Off
- Check Box 10575 Off
- Check Box 10576 Off
- Check Box 10577 Off
- Check Box 10578 Off
- Check Box 10597 Off
- Check Box 10598 Off
- Check Box 10599 Off
- Check Box 10579 Off
- Check Box 10580 Off
- Check Box 10581 Off
- Check Box 10582 Off
- Check Box 10583 Off
- Check Box 10584 Off
- Check Box 10585 Off
- Check Box 10586 Off
- Check Box 10587 Off
- Check Box 10588 Off
- Check Box 10589 Off
- Check Box 10590 Off
- Check Box 10591 Off
- Check Box 10592 Off
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- Check Box 10594 Off
- Check Box 10595 Off
- Check Box 10596 Off
- Check Box 10600 Off
- Check Box 10601 Off
- Check Box 10602 Off
- Check Box 10603 Off
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- Check Box 10605 Off
- Check Box 10606 Off
- Check Box 10607 Off
- Check Box 10608 Off
- Check Box 10609 Off
- Check Box 106010 Off
- Check Box 106011 Off
- Check Box 106012 Off
- Check Box 106013 Off
- Check Box 106014 Off
- Check Box 106015 Off
- Check Box 106016 Off
- Check Box 106017 Off
- Text Field 315
- Check Box 10340 Off
- Check Box 10341 Off
- Check Box 10342 Off
- Check Box 10343 Off
- Check Box 10344 Off
- Check Box 10345 Off
- Check Box 10346 Off
- Check Box 10347 Off
- Check Box 10348 Off
- Check Box 10349 Off
- Check Box 10350 Off
- Check Box 10351 Off
- Check Box 10531 Off
- Check Box 10532 Off
- Check Box 10542 Off
- Text Field 313
- Check Box 10352 Off
- Check Box 10353 Off
- Check Box 10354 Off
- Text Field 316
- Check Box 10355 Off
- Check Box 10356 Off
- Check Box 10357 Off
- Check Box 10358 Off
- Check Box 10359 Off
- Check Box 10360 Off
- Check Box 10361 Off
- Check Box 10362 Off
- Check Box 10363 Off
- Check Box 10364 Off
- Check Box 10365 Off
- Check Box 10366 Off
- Check Box 10404 Off
- Check Box 10405 Off
- Check Box 10406 Off
- Text Field 352
- Check Box 102021 Off
- Check Box 102022 Off
- Check Box 102040 Off
- Check Box 102041 Off
- Check Box 102042 Off
- Check Box 102043 Off
- Check Box 102044 Off
- Check Box 102045 Off
- Check Box 102046 Off
- Check Box 102047 Off
- Check Box 102048 Off
- Check Box 102049 Off
- Check Box 102050 Off
- Check Box 102051 Off
- Check Box 102052 Off
- Check Box 102065 Off
- Check Box 102066 Off
- Check Box 102067 Off
- Check Box 102053 Off
- Check Box 102054 Off
- Check Box 102055 Off
- Text Field 351
- Check Box 102056 Off
- Check Box 102057 Off
- Check Box 102058 Off
- Check Box 102059 Off
- Check Box 102060 Off
- Check Box 102061 Off
- Check Box 102062 Off
- Check Box 102063 Off
- Check Box 102064 Off
- Check Box 102068 Off
- Check Box 102069 Off
- Check Box 102070 Off
- Text Field 318
- Check Box 10373 Off
- Check Box 10374 Off
- Check Box 10375 Off
- Check Box 10376 Off
- Check Box 10377 Off
- Check Box 10378 Off
- Check Box 10379 Off
- Check Box 10380 Off
- Check Box 10381 Off
- Check Box 10382 Off
- Check Box 10383 Off
- Check Box 10384 Off
- Check Box 10385 Off
- Check Box 10386 Off
- Check Box 10387 Off
- Text Field 317
- Check Box 10388 Off
- Check Box 10389 Off
- Check Box 10390 Off
- Check Box 102023 Off
- Check Box 102024 Off
- Check Box 102025 Off
- Check Box 102026 Off
- Check Box 102027 Off
- Check Box 102028 Off
- Check Box 102071 Off
- Check Box 102072 Off
- Check Box 102073 Off
- Check Box 102029 Off
- Check Box 10391 Off
- Check Box 10392 Off
- Check Box 10393 Off
- Check Box 10394 Off
- Check Box 10395 Off
- Check Box 10396 Off
- Check Box 10397 Off
- Check Box 10398 Off
- Check Box 102030 Off
- Check Box 102031 Off
- Check Box 102032 Off
- Text Field 319
- Text Field 322
- Check Box 10408 Off
- Check Box 10409 Off
- Check Box 10410 Off
- Check Box 10411 Off
- Check Box 10412 Off
- Check Box 10413 Off
- Check Box 10414 Off
- Check Box 10415 Off
- Check Box 10416 Off
- Check Box 10417 Off
- Check Box 10418 Off
- Check Box 10419 Off
- Text Field 321
- Check Box 10420 Off
- Check Box 10421 Off
- Check Box 10422 Off
- Check Box 10423 Off
- Check Box 10424 Off
- Check Box 10425 Off
- Text Field 337
- Check Box 102033 Off
- Check Box 102034 Off
- Check Box 102035 Off
- Check Box 102036 Off
- Check Box 102037 Off
- Check Box 102038 Off
- Text Field 338
- Check Box 102039 Off
- Check Box 10426 Off
- Check Box 10427 Off
- Check Box 10428 Off
- Check Box 10429 Off
- Check Box 10430 Off
- Text Field 324
- Check Box 10434 Off
- Check Box 10435 Off
- Check Box 101051 Off
- Check Box 1010100 Off
- Check Box 1010101 Off
- Check Box 1010102 Off
- Check Box 1010128 Off
- Check Box 1010129 Off
- Check Box 1010130 Off
- Check Box 10439 Off
- Check Box 10440 Off
- Check Box 10441 Off
- Check Box 10442 Off
- Check Box 10443 Off
- Check Box 10444 Off
- Text Field 350
- Check Box 10742 Off
- Check Box 10743 Off
- Check Box 10744 Off
- Text Field 325
- Check Box 10445 Off
- Check Box 10446 Off
- Check Box 1010151 Off
- Check Box 1010152 Off
- Check Box 1010153 Off
- Check Box 1010154 Off
- Check Box 1010155 Off
- Check Box 1010156 Off
- Check Box 1010157 Off
- Check Box 10450 Off
- Check Box 10451 Off
- Check Box 10452 Off
- Text Field 326
- Check Box 1010158 Off
- Check Box 1010159 Off
- Check Box 1010160 Off
- Check Box 1010161 Off
- Check Box 1010162 Off
- Check Box 1010163 Off
- Check Box 10453 Off
- Check Box 10454 Off
- Check Box 10455 Off
- Check Box 10745 Off
- Check Box 10746 Off
- Check Box 10747 Off
- Check Box 10748 Off
- Check Box 10749 Off
- Check Box 10750 Off
- Check Box 1010167 Off
- Check Box 1010168 Off
- Check Box 1010169 Off
- Check Box 10459 Off
- Check Box 10460 Off
- Check Box 10461 Off
- Check Box 10462 Off
- Check Box 10463 Off
- Check Box 10464 Off
- Check Box 10611 Off
- Check Box 10612 Off
- Check Box 10613 Off
- Text Field 329
- Check Box 1010171 Off
- Check Box 1010172 Off
- Check Box 1010173 Off
- Check Box 1010174 Off
- Check Box 1010175 Off
- Check Box 1010176 Off
- Check Box 1010177 Off
- Check Box 1010178 Off
- Check Box 1010179 Off
- Check Box 10467 Off
- Check Box 10468 Off
- Check Box 10469 Off
- Check Box 10470 Off
- Check Box 10471 Off
- Check Box 10472 Off
- Check Box 1010180 Off
- Check Box 1010181 Off
- Check Box 1010182 Off
- Text Field 330
- Check Box 1010183 Off
- Check Box 1010184 Off
- Check Box 1010185 Off
- Check Box 10473 Off
- Check Box 10474 Off
- Check Box 10475 Off
- Check Box 10476 Off
- Check Box 10477 Off
- Check Box 10478 Off
- Check Box 1010186 Off
- Check Box 1010187 Off
- Check Box 1010188 Off
- Check Box 1010275 Off
- Check Box 1010276 Off
- Check Box 1010277 Off
- Text Field 331
- Check Box 1010189 Off
- Check Box 1010190 Off
- Check Box 1010191 Off
- Check Box 1010192 Off
- Check Box 1010193 Off
- Check Box 1010194 Off
- Check Box 1010354 Off
- Check Box 1010355 Off
- Check Box 1010356 Off
- Check Box 10479 Off
- Check Box 10480 Off
- Check Box 10481 Off
- Check Box 10482 Off
- Check Box 10483 Off
- Check Box 10484 Off
- Check Box 1010195 Off
- Check Box 1010196 Off
- Check Box 1010197 Off
- Check Box 1010278 Off
- Check Box 1010279 Off
- Check Box 1010280 Off
- Text Field 339
- Check Box 10614 Off
- Check Box 10615 Off
- Check Box 10616 Off
- Check Box 10617 Off
- Check Box 10618 Off
- Check Box 10619 Off
- Check Box 1010281 Off
- Check Box 1010282 Off
- Check Box 1010283 Off
- Text Field 340
- Check Box 1010284 Off
- Check Box 1010285 Off
- Check Box 1010286 Off
- Check Box 1010287 Off
- Check Box 1010288 Off
- Check Box 1010289 Off
- Check Box 10620 Off
- Check Box 10621 Off
- Check Box 10622 Off
- Check Box 10623 Off
- Check Box 10624 Off
- Check Box 10625 Off
- Check Box 1010290 Off
- Check Box 1010291 Off
- Check Box 1010292 Off
- Check Box 1010293 Off
- Check Box 1010294 Off
- Check Box 1010295 Off
- Check Box 10626 Off
- Check Box 10627 Off
- Check Box 10628 Off
- Check Box 10751 Off
- Check Box 10752 Off
- Check Box 10753 Off
- Text Field 342
- Check Box 1010296 Off
- Check Box 1010297 Off
- Check Box 1010298 Off
- Check Box 10632 Off
- Check Box 10633 Off
- Check Box 10634 Off
- Check Box 10635 Off
- Check Box 10636 Off
- Check Box 10637 Off
- Text Field 349
- Check Box 1010305 Off
- Check Box 1010306 Off
- Check Box 1010307 Off
- Check Box 1010308 Off
- Check Box 1010309 Off
- Check Box 10103010 Off
- Check Box 10641 Off
- Check Box 10642 Off
- Check Box 10643 Off
- Text Field 343
- Check Box 1010299 Off
- Check Box 1010300 Off
- Check Box 1010301 Off
- Check Box 1010302 Off
- Check Box 1010303 Off
- Check Box 1010304 Off
- Check Box 10638 Off
- Check Box 10639 Off
- Check Box 10640 Off
- Check Box 10644 Off
- Check Box 10645 Off
- Check Box 10646 Off
- Check Box 1010328 Off
- Check Box 10103012 Off
- Check Box 10103013 Off
- Check Box 10103014 Off
- Check Box 10103015 Off
- Check Box 10103016 Off
- Check Box 10648 Off
- Check Box 10649 Off
- Check Box 10650 Off
- Check Box 10651 Off
- Check Box 10652 Off
- Check Box 10653 Off
- Check Box 10654 Off
- Check Box 10755 Off
- Check Box 10756 Off
- Check Box 10757 Off
- Check Box 10758 Off
- Check Box 10759 Off
- Check Box 10760 Off
- Check Box 10761 Off
- Check Box 10762 Off
- Check Box 10763 Off
- Check Box 10764 Off
- Check Box 10765 Off
- Check Box 10766 Off
- Check Box 10767 Off
- Check Box 10768 Off
- Text Field 361
- Check Box 10103020 Off
- Check Box 10103021 Off
- Check Box 10103022 Off
- Text Field 362
- Text Field 371
- Check Box 10103018 Off
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- Check Box 10737 Off
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- Check Box 10739 Off
2
In order to help us develop the highest quality resources we are undertaking a continuous programme of review not only to measure the success of our resources but also to highlight areas for improvement and to identify new development needs
We invite you to complete our survey by visiting the website below Your comments on the quality and relevance of our resources are very important to us
wwwsurveymonkeycoukrGL6ZNJB
Copyright copy UCLES 2018 Cambridge Assessment International Education is part of the Cambridge Assessment Group Cambridge Assessment is the brand name of the University of Cambridge Local Examinations Syndicate (UCLES) which itself is a department of the University of Cambridge
UCLES retains the copyright on all its publications Registered Centres are permitted to copy material from this booklet for their own internal use However we cannot give permission to Centres to photocopy any material that is acknowledged to a third party even for internal use within a Centre
Would you like to become a Cambridge consultant and help us develop support materials
Please follow the link below to register your interest
wwwcambridgeinternationalorgcambridge-forteachersteacherconsultants
3
About this guide 4
Section 1 Syllabus content ndash what you need to know about 5
Section 2 How you will be assessed 6
Section 3 What skills will be assessed 11
Section 4 Example candidate response 13
Section 5 Revision 24
Contents
4
This guide introduces you to your Cambridge IGCSE Mathematics course and how you will be assessed You should use this guide alongside the support of your teacher
It will help you to
9 understand what skills you should develop by taking this course
9 understand how you will be assessed
9 understand what we are looking for in the answers you write
9 plan your revision programme
9 revise by providing revision tips and an interactive revision checklist (Section 6)
About this guide
Key benefits
The course will help you to build your skills and knowledge across a range of mathematical techniques You will be able to develop your problem solving and reasoning skills in a variety of situations
The Extended course will provide you with a strong foundation to continue to study mathematics qualifications beyond IGCSE The Core course will equip you with skills needed to support your learning in other subjects and in your general working life
5
This section gives you an outline of the syllabus content for this course Only the top-level topics of the syllabus have been included here which are the same for both the Core and Extended courses In the lsquooverviewrsquo column you are given a very basic idea of what each topic covers Highlighted cells show Extended-only content
Learners taking the Extended course need to know all of the Core content as well as some extra content This extra content requires learners to explore topics and sub-topics of the Core syllabus in more detail to cover some more complex techniques and to learn new sub-topics
Ask your teacher for more detail about each topic including the differences between the Core and Extended courses You can also find more detail in the revision checklists in Section 6 of this guide
Topic Overview
Number Number sets and Venn diagrams squares and cubes directed numbers fractions decimals and percentages ordering indices lsquofour rulesrsquo estimates bounds ratio proportion rate percentage time money and finance Growth and decay (Extended only)
Algebra and graphs Basic algebra algebraic manipulation equations formulae sequences drawing sketching and interpreting graphs of functionsAlgebraic fractions harder simultaneous equations proportion linear programming functions gradients of curves derived functions and differentiation (Extended only)
Co-ordinate geometry Straight-line graphs
Vectors and transformations Vectors (column) transformations
Magnitude of a vector represent vectors by directed line segments position vectors (Extended only)
Geometry Language construction symmetry angle properties congruence similarity
Mensuration Measures mensuration
Trigonometry Bearings trigonometry in right-angled triangles
Sine rule cosine rule trig graphs solving simple trig equations (Extended only)
Probability Probability
Conditional probability (Extended only)
Statistics Statistics
Section 1 Syllabus content ndash what you need to know about
Make sure you always check the latest syllabus which is available at wwwcambridgeinternationalorg
6
You will be assessed at the end of the course using two written examinations The papers that you will sit are different for the Core and Extended courses
bull Paper 1 ndash Short-answer questionsbull Paper 3 ndash Structured questions
bull Paper 2 ndash Short-answer questionsbull Paper 4 ndash Structured questions
Components at a glanceThe table summarises the key information about each component
Component How long and how many marks Skills assessed Percentage of the
qualificationCore Paper 1
(Short-answer questions)
1 hour
56 marks Mathematical techniques as listed in the Core syllabus and applying those techniques to solve problems
35
Paper 3 (Structured questions)
2 hours
104 marks 65
Extended Paper 2 (Short-answer questions)
1 hour 30 minutes
70 marksMathematical techniques as listed in the Core and Extended syllabus and applying those techniques to solve problems
35
Paper 4 (Structured questions)
2 hours 30 minutes
130 marks 65
Section 2 How you will be assessed
Core Extended
Make sure you find out from your teacher which course you will be following
7
About the componentsIt is important that you understand the different types of question in each paper so you know what to expect
Core Paper 1 (Short-answer questions) and Paper 3 (Structured questions)
You need to answer all questions on each paper
Paper 3Paper 1
You can use an electronic calculator in both papers Ask your teacher to recommend a suitable calculator
Paper 1 contains lots of short-answer questions These are usually worth 1ndash3 marks each Some might be broken up into two parts
Write your working and answers in the spaces provided
The number of marks for each part is shown
Paper 3 contains structured questions Each question is split into many parts with each part usually being worth 1ndash4 marks Here for example question 1 is split over two pages
Often the answers to later parts will depend on the answers to earlier parts
8
Extended Paper 2 (Shortndashanswer questions) and Paper 4 (Structured questions)
You need to answer all questions on both papers
Paper 2 questions are short-answer questions Most questions are worth 1ndash3 marks with some being worth 4 or 5 marks Some questions might be broken up into two parts
Write your working and answers in the spaces provided
The number of marks for each part is shown
Paper 4Paper 2
You can use an electronic calculator in both papers Ask your teacher to recommend a suitable calculator
Paper 4 contains structured questions Each question is split into many parts with each part usually being worth 1ndash6 marks Here for example question 2 is split over two pages
Often the answers to later parts will depend on the answers to earlier parts
9
Equipment for the examMake sure you have
bull a blue or black pen (a spare pen is always a good idea)bull a pencil (for graphs and diagrams)bull an electronic calculatorbull a protractorbull a pair of compassesbull a ruler
1 Read the questions carefully to make sure that you understand what is being asked
2 Give your answers to the accuracy indicated in the question If none is given and the answer isnrsquot exact then
bull give your answer to three significant figures 123 9 12298 x
bull if the answer is in degrees then give it to one decimal place 231deg 9 23deg x
3 Include units with your answers if they are not given on the paper For example 1 kg of apples costs hellip pound120 9 120 x
4 Show your working Show as much working as you can for all your questions
5 If you make a mistake clearly cross out any working or answers that you do not want the examiner to mark
Use the value of π from your calculator or use 3142 which is given on the front page of the question paper
Timingbull If you are stuck on a question dont waste too much time trying to answer it ndash go on to the next question and
come back to the one you are stuck on at the endbull Use any time that you have left at the end of the exam to go back and check your answers and working
Make sure that you give your answer in the form asked for in the question eg some questions ask for answers to be given in terms of π For lengths areas and volumes give answers in decimals (not in surds or in terms of π) unless you are told to given an exact answer
You can gain marks for the correct working even if you have an incorrect answer or cannot complete the whole question
If you need more space ask for extra of paper and clearly indicate where the rest of the answer is written On the additional paper make it clear which questions(s) you are answering
General advice for all Papers
10
The areas of knowledge understanding and skills that you will be assessed on are called assessment objectives (AOs) There are two AOs for this course
AO1 Demonstrate knowledge and
understanding of mathematical techniques
AO2 Reason interpret and communicate
mathematically when solving problems
AO1 Demonstrate knowledge and understanding of mathematical techniquesYou need to show that you can recall and apply mathematical knowledge terminology and definitions to carry out single or multi-step solutions in mathematical and everyday situations
Section 3 What skills will be assessed
This means that you need to show that you can
bull organise process and present information accurately in written tabular graphical and diagrammatic forms
bull use and interpret mathematical notation correctly
bull perform calculations and procedures by suitable methods including using a calculator
bull understand systems of measurement in everyday use and make use of these
bull estimate approximate and work to degrees of accuracy appropriate to the context and convert between equivalent numerical forms
bull use geometrical instruments to measure and to draw to an acceptable degree of accuracy
bull recognise and use spatial relationships in two and three dimensions
AO1 is assessed in all papers
Use tables graphs and diagrams
An example of degress of accuracy include significant figures or decimal places
An example of converting between equivalent numerical forms include between fractions decimals and percentages or between normal numbers and standard form
eg a pair of compasses a protractor and a ruler
11
AO2 Reason interpret and communicate mathematically when solving problemsYou need to demonstrate that you can analyse a problem select a suitable strategy and apply appropriate techniques to obtain a solution
This means that you need to show that you can
bull make logical deductions make inferences and draw conclusions from given mathematical data
bull recognise patterns and structures in a variety of situations and form generalisations
bull present arguments and chains of reasoning in a logical and structured way
bull interprete and communicate information accurately and change from one form of presentation to another
bull assesses the validity of an argument and critically evaluate a given way of presenting information
bull solve unstructured problems by putting them into a structured form involving a series of processes
bull apply combinations of mathematical skills and techniques using connections between different areas of mathematics in problem solving
bull interprete results in the context of a given problem and evaluate the methods used and solutions obtained
AO2 is assessed in all papers
Recognise and extent patterns
Take information and organise it to answer a problem
12
Section 4 Command wordsA command word is the part of the question that tells you what you need to do with your knowledge For example you might need to describe something explain something argue a point of view or list what you know The table below includes command words used in the assessment for this syllabus The use of the command word(s) within an question will relate to the context
Cambridge IGCSE Mathematics 0580 syllabus for 2020 2021 and 2022 Details of the assessment
37wwwcambridgeinternationalorgigcseBack to contents page
Command wordsThe table below includes command words used in the assessment for this syllabus The use of the command word will relate to the subject context
Command word What it means
Calculate work out from given facts figures or information generally using a calculator
Construct make an accurate drawing
Describe state the points of a topicgive characteristics and main features
Determine establish with certainty
Explain set out purposes or reasons make the relationships between things evident provide why andor how and support with relevant evidence
Give produce an answer from a given source or recallmemory
Plot mark point(s) on a graph
Show (that) provide structured evidence that leads to a given result
Sketch make a simple freehand drawing showing the key features
Work out calculate from given facts figures or information with or without the use of a calculator
Write give an answer in a specific form
Write down give an answer without significant working
The question below is taken from Paper 4 and illustrates the use of two command words
The command words lsquoWrite downrsquo indicates that you do not need to show your working and the answer should just be written down The mark allocation [1] also supports this
The command words lsquoShow thatrsquo indicate that you need to provide evidence in the form of a clear mathematical explanation to demonstrate that you know how to obtain the given result In other words you need to show a method that leads to the result
The answer space in this case does not contain a dotted answer line as there is no single lsquoanswerrsquo to be found Your working that leads to the given result should be written in the blank working space
13
This section takes you through an example question and learner response from one of the 2020 specimen papers for this course It will help you to identify the command words and other key instructions within questions and to understand what is required in your response
This section is structured as follows
QuestionThe command words and instructions in the question have
been highlighted and explained This should help you to understand clearly what is required by the question
Mark schemeThis tells you as clearly as possible what an examiner expects
from an answer to award marks
Example candidate responseThis an exemplar answer written in the style of
a high level candidate
How the answer could have been improvedThis summarises what could be done to gain more marks
All information and advice in this section is specific to the example question and response being demonstrated It should give you an idea of how your responses might be viewed by an examiner but it is not a list of what to do in all questions In your own examination you will need to pay careful attention to what each question is asking you to do
Common mistakesThis will help you to avoid common mistakes made by
candidates So often candidates lose marks in their exams because they misread or misinterpret the questions
Section 5 Example candidate response
14
QuestionThe question used in this example is from Specimen Paper 3 (Core) It represents the type of structured question you will see in both Paper 3 (Core) and Paper 4 (Extended) A structured question means that it is broken into several parts Often later parts will depend on your answers to earlier parts
This means that you cannot find the answer by
measuring the diagramWork out indicates that the answer should be calculated from the given information so measurement will not score marks
The allocation of 1 mark indicates that the answer can be obtained with minimum working
Give reasons for your answer indicates that your answer should be supported with reasons using the correct mathematical terminology You must justify your answer
Use trigonometry to calculate indicates that you should use this method with the given information to find the answer and that a calculator is needed to solve the problem If you did not use trigonometry you would not be awarded any marks
15
Show that indicates the answer is given and you need to write down all of the steps in a method that leads to the given answer You need to provide evidence that you understand and know how the answer is reached
Work out indicates that you should calculate the answer from the given information The mark allocation of 4 marks suggests that you will need to include several steps of working in order to get to the answer
Learner Guide
16
Answer Mark Notes(a)(i) 35 1 This is the only acceptable answer for this part of the question
(a)(ii) 74 1 This is the only acceptable answer for this part of the question
(b) 43deg and correct mathematical reasons
3 Two marks are awarded for the final answer of 43deg
The third mark is awarded for a fully correct reason for example angles on a straight line add up to 180deg and angles in a triangle add up to 180deg There are other correct reasons that could be also be used
If 43deg is not obtained one method mark can be awarded if the following calculation is seen in the working
180 ndash 128 or 128 ndash 85
(c) 322 or 3223hellip 2 This is the only acceptable answer for this part of the question
The answer has to be rounded correct to three significant figures or can be given with more figures in the answer
Those that did not get this answer can score one method mark for showing the following in their working
sin = 8 divide 15
(d)(i) 2 2300 225+2 This does not have to be shown in one step as long as the method shown is the same as this overall Those that do not
show this can have one method mark for showing the following in their working
300deg + 225deg
(d)(ii) 15 35 4 The answer 3 35pm is also acceptable for 4 marks
If the correct answer is not found one method mark is available for showing 375 divide 450 in their working and a second method mark can be awarded for sight of them multiplying their answer to this by 60 to change it to hours A third method mark can be awarded for adding their answer in hours to 14 45 ndash this shows the correct method so only one mark is lost for an incorrect final answers
Mark schemeYour examination papers will be marked and the overall number of marks for each paper will be recorded Your marks across all papers will then be converted to a grade
Final answer This value is what the examiner expects to see The answer has to be exactly as given in the mark scheme unless there are acceptable alternatives The mark scheme will always make it clear if there are acceptable alternative answers
Method marks Sometimes method marks are awarded for lines of working as well as for the final answer This means that you could get the final answer incorrect but still get some marks if you include the correct working The mark scheme does not include all possible methods so if you use a method not included in the mark scheme but it is accurate and relevant then the examiner will still award marks for the appropriate parts of the working ndash unless the questions asks you to use a specific method
example of a final answer
example of a method mark
17
Example candidate responseNow letrsquos look at the sample candidatersquos response to question 8 The examiners comments are in the orange boxes The candidate was awarded 8 marks out of 13
180 ndash 74 + 71 = 177
177
74
0 out of 1
The candidates working suggests they understand that the angle sum of a triangle is 180deg but they did not include brackets around 74 + 71 The answer 177deg is not sensible for this question
1 out of 1
The candidate recognises that there are parallel lines and that angle y is a corresponding angle to angle 74deg
180 ndash 128 = 52 180 ndash 85 ndash 52 = 43
43 angles on a straight line add up to 180deg
2 out of 3
The candidate has given a correct answer for w and shown correct working in two steps They have given a correct reason for 52deg using correct mathematical languge But they have not provided a reason to explain the angle 43deg They lose a mark for not also stating angle sum of a triangle is 180deg
sin p = 8 divide 15 = 053
p = sinndash1 (053)
p = 32005 320
1 out of 2
The candidate has correctly used trigonometry in their method They are awarded one method mark for the first line of working However they have rounded 05333333hellip (the result of 8 divide 15) to 052 and then calculated the inverse sin of 052 rather than 05333333 This has resulted in an inaccurate final answer This is called lsquopremature approximationrsquo and it is a very common error to make
18
AB2 = 3002 + 2252
= 140625
AB = 375
1 out of 2
The candidate has recognised the right-angled triangle and correctly used Pythagorasrsquo theorem in the first line of working However they have missed out an important step by not showing that you need to take the square root of 140625 to get 375 As this is a lsquoshow thatrsquo question and they missed a key step in the method they cannot be awarded full marks as the complete working is not shown One method mark is earned for the first line
T = = = 08333333hellip
08333333 hours = 08333333 times 60 minutes = 50 minutes
arrives at 14 45 + 50 mins = 3 35
DS
375450
3 35
3 out of 4
The candidate has found the time by correctly dividing the distance by the speed and recognised that this is in hours When converting the answer to a decimal they have not rounded the decimal but left its full value on the calculator to get 50 mins which is the correct approach Unfortunately after converting the time from 24 hour clock to 12 hour clock they did not include lsquopmrsquo to indicate that the time is in the afternoon and so the final answer is not quite right So 3 marks are awarded for all of a correct method but a mark is lost due to the accuracy of the final answer
19
How the answer could have been improvedThis answer could have been improved by
bull In part (a)(i) the answer of 177deg was not sensible given the diagram in the question If the candidate had checked their answer for sense they would have realised they had made a mistake It is always a good idea to check that your answer seems sensible before you move on to another question
bull In part (b) the candidate did all the correct steps but failed to provide both reasons There were two steps to the method which should have indicated to the candidate that there were two steps to justify and therefore two reasons should have been provided The mark allocation for the question [3] also indicates that more than one reason would be required one mark for the value of 43deg leaving two marks one mark for each of two reasons The candidate should have read the question carefully and again checked their response seemed reasonable
bull In part (c) the candidate rounded an intermediate answer which affected the accuracy of the final answer This caused them to lose a mark despite using a correct method You should only ever round the final answer do not round intermediate values If you can store the intermediate values in your calculator and so that you can use the full value in your calcuations If youre not able to do this and you have to round the intermediate values do not round them to less than three significant figures
bull In part (d)(i) the candidate missed out a step in the method As this was a show that question they needed to show all the steps in the method Its important to show all steps even if they seem obvious
bull In part (d)(ii) the candidate made a silly error by not stating that the time was pm When working with time answers are accepted in either 24 clock or 12 clock time but if you give your answer in the 12 hour clock then it must include am or pm as well
Common mistakesThere were a number of common mistakes made by other candidates on this question
bull Accuracy of answers
In parts (c) and (d)(ii) a common error was premature rounding ndash rounding intermediate values in the method before the final answer which resulted in their final answer not being accurate Other candidates gave the final answer to less than three significant figures ignoring the instruction on the front of the paper to round to three significant figures
bull Using incorrect terminology when giving reasons
In part (b) the most common error was to not give full reasons to support the answer Another common error was to provide a reason that did not use the correct mathematical language such as lsquoThey add up to 180degrsquo and lsquoIt is a straight linersquo which could not be awarded marks
bull Lack of knowledge
In part (c) a number of candidates had limited knowledge of trigonometry and did not choose the correct trig ratio which was the sine ratio This is why good revision is important
bull Not checking answers
In part (a)(i) even though the diagram is drawn NOT TO SCALE it is possible to see that the angle is an acute angle and should therefore not be bigger than 90deg This should alert candidate that if their answer is over 90deg it is not a sensible answer and they should go back and check their working
20
bull Inefficient method shown
In part (c) the lsquoShow thatrsquo question a number of candidates omitted an important step from the method this is often common in lsquoShow thatrsquo questions where every step must be shown no matter how obvious them seem
General adviceIn order to do your best when answering a mathematics question make sure you
bull revise all of the topics for the syllabus you are studying before the exam
bull understand what all the key terms and command words in the question mean
bull read the questions carefully and consider what you need to do before you do it
bull only round the final answer not intermediate values
bull show all steps in your working and show them clearly
bull round to the correct degree of accuracy
bull use the correct mathematical terminology
bull check your answers seem reasonable given the context or details of the question
21
It is important that you plan your revision in plenty of time for the examinations and that you develop a revision technique that works for you The advice in this section will help you revise and prepare for the examinations It is divided into general advice for all papers
Use the tick boxes to keep a record of what you have done what you plan to do or what you understand
For more advice on revision see the Cambridge Learner Revision Guide on our website
Section 6 Revision
Find out when the examinations are and plan your revision so you have time to revise Create a revision timetable and divide it into sections to cover each topic
Spend most of your time focussing on specific skills knowledge or issues that you have found more difficult when practicing them either during revision or earlier in the course
Write a summary of all the key information for a topic ndash use the checklists at the end of this section
Know the meaning of the command words used in questions and how to apply them to the information given Look at past examination papers and highlight the command words and check what they mean
Make revision notes and work on practice questions Reading alone does not work you need to be active and practice your maths
Work for shorter periods then have a break Revise small sections of the syllabus at a time but do this regularly
Test yourself by trying out some past exam questions Use the mark schemes to assess yourself and to be familiar with how marks are awarded for different questions
Be organised in advance with your notes texts exercise books revision guides and revision websites so you do not waste valuable revision time trying to find things
Make notes of key mathematical words that you should use in questions that ask you to lsquodescribersquo or give lsquogeometrical reasons forrsquo eg in describing transformations or giving reasons in circle theorem questions Look at the mark schemes for these types of questions from past papers to see how marks are awarded
Make sure you have all of the correct mathematical equipment ready for the exam particularly your calculator Make sure you are familiar with the all of the important functions on your calculator
Practice the areas you can do well not just those that you find more difficult
Take breaks and do things to relax when you take your breaks this will help you to be more productive when you are revising
Before the examination
22
During the examination
Plan your time according to the marks for each question For example a question worth one mark requires less time than a question one worth 4 marks If a question has several parts then the parts with more marks will need more time
Read each question very carefully
Identify the command words ndash you could underline or highlight them
Identify the other key words and information and perhaps underline them too particularly where
questions require reasoning or problem solving
Read the questions careully and make you have answered the question that is being asked
Show your working this is particularly important for questions where you are asked to lsquoshow that helliprsquo
Set your working out clearly so that it is easy to follow this makes it easier to keep track of what you have done and makes checking back through your work easier and it makes it easier for the examiner to mark your work try to write it in a logical order in the answer space
Write answers clearly if you want to change an answer then you should cross the answer out and write a replacement if your answer is on the answer line cross it out and write the replacement answer above it do not try to change numbers on the answer line as this can lead to unclear figures
Check your working and answers to avoid errors
Give your answer to the appropriate level of accuracy either the accuracy indicated in the question or the accuracy given on the front of the paper
Avoid rounding intermediate values part way through your calculation only round the final answer
Check that the answer that you have given is sensible and realistic for what is being asked
Use a pencil when drawing diagrams or completing graphs this means that you can change your answer more easily if you have made a mistake
Take care when reading scales
If you are asked for reasons for your answer then use the correct mathematical terms
Use the mark allocation given with the questionsparts of questions to try to judge how much work is needed to answer each part
23
Top tips for revision of Cambridge IGCSE Mathematics1 Summarise recall and applyMake sure that you can recall and apply the key information and mathematical techniques on each topic that you need for the exam
i Write a summary of the key information of a topicii Collect together some questions that test the knowledge and skills of this topic Ask your teacher for practice
questions or suitable past examination questions or use practice books or textbooksiii Test your recall by covering over the summary and trying to remember the details or use the summary as part of
the lsquoTeach the topicrsquo (Tip 3) or lsquoQuestion and answer cardsrsquo (Tip 4) activities iv After you have spent some time revising and practising the knowledge and skills answer the questions that you
collected together on the topic You might do this later on the same day as revising or a few days later Answer as many questions as you can in order to practise applying your knowledge
v Try creating your own questions by adapting existing ones and use these for practice when you return to a topic
On graph questions straight lines should be ruled and curves should be drawn freehand with a smooth curve
Donrsquot spend too long on any one part of a question If you are really stuck on a question then move on and come back to the question later if you have time As a rough guide each mark on the paper should take about one minute
2 Concept mapsConcept maps are a great way to revise the links between different factors or to explore a larger topic They can also be used to collect together your ideas
i Use a blank sheet of paper and turn it on its side (landscape)ii Put the topic title in the middle of the page and build the concept map outwards using lines called lsquobranchesrsquo
ndash The first branches are from the central topic to sub-topics draw these as thick lines
ndash Add new branches from the sub-topics to include more detail draw these as thinner lines
ndash Add even more detail to a point by adding more branches
This creates a hierarchy of information from lsquooverviewrsquo (the thick branches) to lsquofine detailrsquo (thinnest branches)
iii Write single key words or phrases along a branch and add drawings for visual impactiv Use different colours highlighter pens symbols and arrows to highlight key facts or issuesIt is a good idea to use a large piece of plain A3 (or larger) paper and lots of coloured pens
24
3 Teach the topicThis is a very simple but effective technique that focusses on knowledge recall It tests the brain and rehearses the information you need to know for a certain topic and so will help your revision
i Create some topic cards with key bullet points of information on Leave space for ticksii Give these to your parents family or friends for exampleiii Give yourself 10 minutes maximum to teach your audience the main points of the topic You could use a mini-
whiteboard or flip chart to helpiv Your audience tick off all the points you mention in your presentation and give you a final scoreThe brain loves competition so if you do not score full marks you can try again the next day or compete against friends This system of repeat and rehearsal is very effective especially with more complex topics and doesnt take much preparation
4 Question and answer (QampA) cardsThis is very similar to Teach the topic but less formal and less public for those who dislike performing in front of others It tests knowledge recall and rehearses the information you need to know for a certain topic
i Pick a topic and create two sets of cards question cards and answer cards You might find it helpful to make the question cards a different size or use different coloured card for answers
ii Make sure you have the topic or something appropriate depending on what you are focusing on as a heading on each card The questions should test your knowledge and understanding of key areas of the course
iii A friend or family member uses the cards to test you in short 5 or 10 minute periods at any time during the dayiv You could also do this alone by reading the questions to yourself giving the answer and then checking the
correct answer cardv This game can be adapted by using the cards to find matching pairs turn all cards face down across the space
in front of you Turn over two cards leaving them where they are If they match (one is a question card and the other is the corresponding answer card) pick up the pair and put them to one side If they dont match try to remember where they are and what is on each card then turn them back over Turn over two other cards Continue until you have matched all pairs
5 Question paper and mark schemesLooking at past question papers and the mark scheme helps you to familiarise yourself with what to expect and what the standard is
i Ask your teacher for past paper questions with mark schemes for the course ndash ask your teacher for help to make sure you are answering the correct questions and to simplify the mark scheme
ii Look at the revision checklist and identify which topic a given question relates to ndash you might need to ask your teacher to help you do this
iii Once you have finished revising a topic or unit time yourself answering some appropriate exam questions Check the mark schemes to see how well you would have scored or give the answers to your teacher to check
iv Add details or notes to the mark scheme where you missed out on marks in your original answers using a different coloured pen Use these notes when you revise and try the question again later
You can find plenty of past exam papers and mark schemes on the Cambridge International public website
httpwwwcambridgeinternationalorgprogrammes-and-qualificationscambridge-igcse-mathematics-0580past-papers
25
Other useful revision advice for Cambridge IGCSE Mathematics bull Before the exam make sure that you are familiar with your calculator and confident in using it
bull Look at the Example Candidate Response earlier in this guide Can you identify the strengths of the response andwhere they have made mistakes or lost marks
bull When you are attempting a past paper (or questions from a past paper) complete it without referring to yournotes so that you get a true idea of your strengths and weaknesses Then go back through the paper using yournotes and a different coloured pen to make corrections and changes After you have done as much as you can onthe paper mark it using the mark scheme Take notes of any points that you lost marks on
bull Donrsquot just revise the topics that you enjoy and are confident in If you identify an area that you are weaker inthen try to revisit the topic by reviewing your notes and doing some practice questions then use exam questionsto check whether you now understand
bull Return to topics later in your revision to check that you still remember and understand the topic and to help toensure that you recall more of the material when you get to the examination
Revision checklists for Cambridge IGCSE MathematicsThe tables on the following pages can be used as a revision checklist They do not contain all the detailed knowledge you need to know just an overview For more detail see the syllabus and talk to your teacher
You can use the tick boxes in the checklists to show when you have revised and are happy that you do not need to return to it Tick the lsquoRrsquo lsquoArsquo and lsquoGrsquo column to record your progress as follows
bull R = RED means you are really unsure and lack confidence in that area you might want to focus your revisionhere and possibly talk to your teacher for help
bull A = AMBER means you are reasonably confident in a topic but need some extra practicebull G = GREEN means you are very confident in a topic
As your revision progresses you can concentrate on the RED and AMBER topics in order to turn them into GREEN topics You might find it helpful to highlight each topic in red orange or green to help you prioritise
You can use the lsquoCommentsrsquo column to
bull add more information about the details for each pointbull include a reference to a useful resourcebull include a list of formulae or notationbull add learning aids such as rhymes poems or word playbull highlight areas of difficulty or things that you need to talk to your teacher about
There is a set of checklist for the Core syllabus and a different set for the Extended syllabus
Learner Guide
26
Core syllabus contentCore Number
Category You should be able to R A G CommentsNumber Identify and use
bull natural numbers
bull integers (positive negative and zero)
bull prime numbers
bull write a number as a product of its prime factors
bull square numbers and cube numbers
bull common factors and highest common factor of two numbers
bull common multiples and lowest common multiple of two numbers
bull rational numbers
bull irrational numbers (eg π radic2 )
bull real numbers
bull reciprocals
Learner Guide
27
Core Number
Question type You should be able to R A G CommentsSets and Venn diagrams
Understand notation of Venn diagrams
Definition of sets
eg A = xx is a natural number
B = abchellip
Notation
Number of elements in set A n(A)
Universal set
Union of A and B A cup B
Intersection of A and B A cap B
Squares square roots cubes and cube roots
Calculate
bull squares and cubes of numbers
bull square roots and cube roots of numbers
Learner Guide
28
Core Number
Question type You should be able to R A G CommentsDirected numbers
Use directed numbers in practical situations for example temperature changes
Fractions decimals and percentages
Use the language and notation of simple vulgar and decimal fractions and percentages
Recognise equivalent fractions decimals and percentages
Convert between fractions decimals and percentages
Ordering Order quantities by magnitude and demonstrate familiarity with the symbols = ne gt lt ⩾ ⩽
Indices and standard form (links to Algebraic manipulation)
Evaluate indices eg 25 5ndash2 1000 64frac12 8ndash23
Use the rules of indices for
bull multiplication of indices eg 4ndash3 times 45
bull division of indices eg 57 divide 53
bull index numbers raised to an index eg (23)2 (43)2
Use the standard form A times 10n where n is a positive or negative integer and 1 ⩽ A lt 10
bull convert numbers into and out of standard form
bull calculate with numbers in standard form
Learner Guide
29
Core Number
Question type You should be able to R A G CommentsFour rules
( + ndash times divide )
Use the four rules for calculations with
bull whole numbers
bull decimals
bull vulgar and mixed fractions
bull correct ordering of operations (BIDMAS) and use of bracketsEstimates Make estimates of numbers quantities and lengths
Give approximations to a specified number of
bull significant figures
bull decimal places
Round off answers to reasonable accuracy in the context of a given problem
Bounds Give upper and lower bounds for data given to a specified accuracy eg measured lengths
Ratio proportion rate
Understand ratio
Divide a quantity in a given ratio
Understand direct and inverse proportion
Use scales in practical situations
Use common measures of rate (formulae for other rates eg density and pressure will be given in the question)
Calculate average speed
Learner Guide
30
Core Number
Question type You should be able to R A G CommentsPercentages Calculate a percentage of a quantity
Express one quantity as a percentage of another quantity
Calculate percentage increase or decrease
Use of an electronic calculator
Use a calculator efficiently
Check accuracy of calculations
Time Calculate times in terms of the 24-hour and 12-hour clock
Read
bull clocks
bull dials
bull timetables
Money Calculate using money
Convert from one currency to another
Learner Guide
31
Core Number
Question type You should be able to R A G CommentsPersonal and small business finance
Use given data to solve problems on
bull earnings
bull simple interest
bull compound interest (you will need to know the compound interest formula)
bull discount
bull profit and loss
Extract data from tables and charts
Learner Guide
32
Core Algebra and graphs
Question type You should be able to R A G CommentsBasic algebra Use letters to express generalised numbers
Express basic arithmetic processes algebraically
Substitute numbers in formulae
Construct simple expressions and set up simple equations
Rearrange simple formulae
Algebraic manipulation
Manipulate directed numbers
Use brackets
bull expand a single bracket eg 3x(2x ndash4y)
bull expand a pair of brackets eg (x + 3) (x ndash 7)
Extract common factors eg factorise 9x2 + 15xy
Rules of indices Use and interpret positive negative and zero indices
Use the rules of indices eg to simplify algebra such as
bull 3x4 times 5x
bull 10x3 divide 2x2
bull (x6)2
Learner Guide
33
Core Algebra and graphs
Question type You should be able to R A G CommentsEquations and inequalities
Derive and solve simple linear equations in one unknown
Derive and solve simultaneous linear equations in two unknowns
Number sequences
(links to Squares square roots cubes and cube roots)
Continue a number sequence
Recognise patterns in sequences
Recognise relationships between difference sequences
Find the nth term of sequences for
bull liner sequences
bull simple quadratic sequences
bull cubic sequences
Practical graphs
(links to Mensuration)
Interpret and use graphs in practical situations including
bull travel graphs
bull conversion graphs
Draw graphs from given data
Learner Guide
34
Core Algebra and graphs
Question type You should be able to R A G CommentsGraphs of functions
(links to Co-ordinate geometry)
Construct tables of values for functions of the form
bull ax + b (linear)
bull plusmn x2 + ax + b (quadratic)
bull (x ne 0) (reciprocal)
where a and b are integer constants
Draw and interpret such graphs
Solve linear and quadratic equations approximately by graphical methods
Recognise and sketch the graphs of linear and quadratic functions
ax
Learner Guide
35
Core Co-ordinate geometry
Question type You should be able to R A G CommentsCo-ordinates Work with co-ordinates in two dimensions
Gradients Find the gradient of a straight line graph
Equation of straight line
Interpret and obtain the equation of a straight line graph in the form y = mx + c where the graph is given
Parallel lines Determine the equation of a straight line parallel to a given line eg find the equation of a line parallel to y = 4x ndash 1 that passes through (0 ndash3)
Learner Guide
36
Core Geometry
Question type You should be able to R A G CommentsGeometrical language
Use and interpret the geometrical terms
bull point
bull line
bull parallel
bull perpendicular
bull bearing
bull right angle acute obtuse and reflex angles
bull similar
bull congruent
Use and interpret the vocabulary of
bull triangles right-angled scalene isosceles equilateral
bull quadrilaterals
bull circles
bull polygons
bull simple solid figures including nets
Learner Guide
37
Core Geometry
Question type You should be able to R A G CommentsGeometrical constructions
Measure and draw lines and angles
Construct a triangle given the three sides using a ruler and a pair of compasses only
Scale drawings Read and make scale drawings
Similar figures Calculate lengths of similar figures
Congruent Recognise congruent shapes
Symmetry Recognise symmetry properties for triangles quadrilaterals and circles
Recognise line symmetry in two dimensions
Recognise and find the order of rotational symmetry in two dimensions
Learner Guide
38
Core Geometry
Question type You should be able to R A G CommentsAngle properties Calculate unknown angles explaining the properties that you
are using in geometrical language for angles
bull angles at a point
bull angles on a straight line and intersecting straight lines
bull angles within parallel lines
bull angles in triangles
bull angles in quadrilaterals
bull angles in regular polygons
bull angle in a semi-circle
bull angle between tangent and radius of a circle
Learner Guide
39
Core Mensuration
Question type You should be able to R A G CommentsMeasures bull Use current units of
bull mass
bull length
bull area
bull volume
bull capacity
Express quantities in terms of smaller or larger units including units of area and volume
Convert between units including units of area and volume
Perimiter Carry out calculations involving
bull perimeter and area of a rectangle
bull perimeter and area of a triangle
bull perimeter and area of parallelogram
bull perimeter and area of a trapezium
bull perimeter and area of shapes made by combining
bull rectangles triangles parallelograms andor trapeziums
Learner Guide
40
Core Mensuration
Question type You should be able to R A G CommentsCircles Carry out calculations involving circumference and area of a
circle
Solve simple problems involving the arc length and sector area of a circle where the sector angle is a factor of 360deg
Surface area and volume
Carry out calculations involving
bull surface area and volume of a cuboid prism and cylinder (no formulae will be given for these shapes)
bull surface area and volume of a sphere pyramid and cone (formulae will be given for these shapes)
Areas and volumes of compound shapes
Carry out calculations involving the areas and volumes of compound shapes made from combinations of the shapes in Perimeter or Surface area and volume
Learner Guide
41
Core Trigonometry
Question type You should be able to R A G CommentsBearings Use and interpret three-figure bearings measured clockwise
from the North ie 000degndash360degTrigonometry Find unknown sides andor angles in right-angled triangles by
applying
bull Pythagorasrsquo theorem
bull sine cosine and tangent ratios for acute angles in right-angled triangles
Learner Guide
42
Core Vectors and transformations
Question type You should be able to R A G CommentsVectors in two dimensions (links to Trigonometry)
Describe a translation by using a vector represented by
AB or a
Add and subtract vectors
Multiply a vector by a scalar
Transformations Reflect simple shapes in horizontal or vertical lines
Rotate simple shapes through multiples of 90deg about
bull the origin
bull their vertices
bull the midpoints of their sides
Construct translations of simple shapes
Construct enlargements of simple shapes (positive and fractional scale factors)
Recognise and describe using the correct language
bull reflections
bull rotations
bull translations
bull enlargements (positive and fractional scale factors)
( )x
y
Learner Guide
43
Core Probability
Question type You should be able to R A G CommentsSingle events Calculate the probability of a single event as a fraction decimal
or percentage (not a ratio)Probability scale Understand and use the probability scale from 0 to 1
Sum to 1 Understand that the probability of an event occurring = 1 ndash the probability of the event not occurring
Relative frequency
Understand relative frequency as an estimate of probability
Work out expected frequencies using relative frequencyCombined events Calculate the probability of simple combined events using
bull tree diagrams
bull possibility diagrams (points on a grid)
bull Venn diagrams (2 sets only)
Learner Guide
44
Core Statistics
Question type What I need to do R A G CommentsClassify Collect classify and tabulate data
Interpret and compare
Read interpret and draw simple inferences from tables and statistical diagrams
Compare sets of data using
bull tables
bull graphs
bull statistical measures
Be aware of restrictions when making conclusions from data
Charts Construct and use
bull bar charts
bull pie charts
bull pictograms
bull stem-and-leaf diagrams
bull frequency distributions
bull histograms with equal intervals
bull scatter diagrams
Learner Guide
45
Question type What I need to do R A G CommentsAverages Calculate for individual and discrete data
bull mean
bull median
bull mode
bull range
and distinguish between their useCorrelation Understand what is meant by positive negative and zero
correlation with reference to a scatter diagramLine of best fit Draw interpret and use a ruled line of best fit by eye
Learner Guide
46
Extended syllabus content (includes required Core content)Extended Number
Question type You should be able to R A G CommentsNumber Identify and use
bull natural numbers
bull integers (positive negative and zero)
bull prime numbers
bull write a number as a product of its prime factors
bull square and cube numbers
bull common factors and highest common factor of two or more numbers
bull common multiples and lowest common multiple of two or more numbers
bull rational numbers
bull irrational numbers (eg π radic2 )
bull real numbers
bull reciprocals
Learner Guide
47
Extended Number
Question type You should be able to R A G CommentsSet notation and language
Use language notation and Venn diagrams to describe sets and represent relationships between sets as follows
Definition of sets egA = x x is a natural number
B = (xy) y = mx + c
C = x a ⩽ x ⩽ b
D = a b c hellip
Notation egnumber of elements in set A n(A)
lsquois an element ofrsquo isin
lsquois not an element ofrsquo notin
complement of set A
the empty set empty
the universal set
A is a subset of B A sube B
A is a proper subset of B A sub B
A is not a subset of B A ⊈ B
A is not a proper subset of B A nsub B
union of A and B A cup B
intersection of A and B A cap B
Learner Guide
48
Extended Number
Question type You should be able to R A G CommentsSquares square roots cubes and cube roots
Calculatebull squares of numbers
bull square roots of numbers
bull cubes of numbers
bull cube roots of numbers
bull other powers and roots of numbers
Directed numbers
Use directed numbers in practical situations for example temperature changes
Fractions decimals and percentages
Use the language and notation of simple vulgar and decimal fractions and percentages in appropriate contexts
Recognise equivalent fractions decimals and percentages
Convert between fractions decimals and percentages
Convert recurring decimals to fractions
Ordering Order quantities by magnitude and demonstrate familiarity with the symbols = ne gt lt ⩾ ⩽
Learner Guide
49
Extended Number
Question type You should be able to R A G CommentsIndices and standard form (links to Algebraic manipulation)
Evaluate indices including fractional negative and zero
eg 25 5ndash2 1000 10012 8ndash23
Use the rules of indices forbull multiplication of indices eg 43 times 45
bull division of indices eg 57 divide 53
bull index numbers raised to an index eg (43)2
Use the standard form A times 10n where n is a positive or negative integer and 1 ⩽ A lt 10bull convert into and out of standard form
bull calculate with numbers in standard form
Four rules
( + ndash times divide )
Use the four rules for calculations withbull whole numbers
bull decimals
bull vulgar and mixed fractions
bull correct ordering of operations (BIDMAS) and use of brackets
Learner Guide
50
Extended Number
Question type You should be able to R A G CommentsEstimates Make estimates of numbers quantities and lengths
Give approximations to a specified number of
bull significant figures
bull decimal places
Round off answers to reasonable accuracy in the context of a given problem
Bounds Give upper and lower bounds for data given to a specified accuracy eg measured lengths
Obtain appropriate upper and lower bounds to solutions of simple problems given to a specified accuracy eg the lower and upper bounds for the area of a rectangle
Ratio proportion rate
(links to Direct and inverse proportion)
Understand ratio
Divide quantities in a given ratio
Increase and decrease a quantity by a given ratio
Understand numerical problems involving direct and inverse proportion
Use ratio and scales in practical situations
Use common measures of rate (formulae for other rates eg density and pressure will be given in the question)
Calculate average speed
Learner Guide
51
Extended Number
Question type What I need to do R A G CommentsPercentages Calculate a percentage of a quantity
Express one quantity as a percentage of another quantity
Calculate percentage increase or decrease
Calculate reverse percentages eg finding the cost price given the selling price and the percentage profit
Use of an electronic calculator
Use a calculator efficiently
Check accuracy of calculations
Time Calculate times in terms of the 24-hour and 12-hour clock
Read clocks dials and timetables
Money Calculate using money
Convert from one currency to another
Learner Guide
52
Extended Number
Question type You should be able to R A G CommentsPersonal and small business finance
Use given data to solve problems on
bull earnings
bull simple interest
bull compound interest
ndash you must know the compound interest formula
bull discount
bull profit and loss
Extract data from tables and charts
Exponential growth and decay
Use exponential growth and decay in population and finance eg depreciation bacteria growth
Learner Guide
53
Extended Algebra and graphs
Question type You should be able to R A G CommentsBasic algebra Use letters to express generalised numbers
Express basic arithmetic processes algebraically
Substitute numbers in complicated formulae
Construct and rearrange complicated formulae eg where the subject appears twice
Algebraic manipulation
Manipulate directed numbers
Use bracketsbull expand a single bracket eg expand 3x(2x ndash 4y)
bull expand a pair of brackets eg (x ndash 4)(x + 7)
bull expand products of more than two brackets eg (x + 4)(x ndash 7)(2x + 1)
Extract common factors eg factorise 9x2 + 15xy
Factorise expressions of the formbull ax + bx + kay + kby
bull asup2xsup2 ndash bsup2ysup2
bull asup2 + 2ab + bsup2
bull axsup2 + bx + c
Learner Guide
54
Extended Algebra and graphs
Question type You should be able to R A G CommentsAlgebraic fractions
Manipulate algebraic fractions eg
bull
bull
bull
bull
bull
Factorise and simplify algebraic fractions such as
Rules of indices Use and interpret positive negative and zero indices
Use and interpret fractional indices eg solve 32x = 2
Use the rules of indices to simplify algebra eg
x3 + x ndash 4
22x3 +
3(x ndash 5)2
3a4 +
5ab3
3a4 divide
9a10
1x ndash 2 +
2x ndash 3
x2 ndash 2xx2 ndash 5x + 6
3xndash4 times23
x12
32x5( )
3
2xndash2divide25
x12
Learner Guide
55
Extended Algebra and graphs
Question type You should be able to R A G CommentsEquations and inequalities
bull Derive and solve simple linear equations in one unknown
bull Derive and solve simultaneous linear equations in two unknowns
bull Derive and solve simultaneous equations involving one linear and one quadratic
Solve quadratic equations by
bull factorisation
bull completing the square
bull using the formula
Derive and solve simple linear inequalities including representing solutions on a number line
Linear programming
Represent inequalities graphically including using the conventions of
bull broken lines for strict inequalities
bull shading unwanted regions
Solve simple linear programming problems using graphical representations of inequalities
Learner Guide
56
Extended Algebra and graphs
Question type You should be able to R A G CommentsNumber sequences (links to Squares square roots cubes and cube roots)
Continue a number sequence
Recognise patterns in sequences
Recognise relationships between different sequences
Find the nth term of sequences of
bull linear sequences
bull quadratic sequences
bull cubic sequences
bull exponential sequences
and simple combinations of these
Direct and inverse proportion (links to Ratio proportion rate)
Express direct proportion algebraically
Express inverse proportion algebraically
Use algebraic expressions of direct and inverse proportion to find unknown quantities
Practical graphs
(links to Coordinate geometry)
Interpret and use graphs in practical situations including
bull travel graphs
bull conversion graphs
Draw graphs from given data
Learner Guide
57
Extended Algebra and graphs
Question type You should be able to R A G CommentsPractical graphs (links to Coordinate geometry) continued
Apply the idea of rate of change to simple kinematics involving
bull distancendashtime graphs
bull speedndashtime graphs
bull acceleration and deceleration
This may involve estimation and interpretation of the gradient of a tangent at a point
Calculate distance travelled as an area under a linear speedndash time graph
Learner Guide
58
Extended Algebra and graphs
Question type You should be able to R A G CommentsGraphs of functions (links to Coordinate geometry)
Construct tables of values and draw graphs for functions of the form
bull axn where a is a rational constant and n = minus2 minus1 0 1 2 3 and simple sums of not more than three of these
bull abx + c where a and c are rational constants and b is a positive integer
Solve associated equations approximately by graphical methods including finding and interpreting roots and finding turning points of quadratics by completing the square
Draw and interpret graphs representing exponential growth and decay problems
Recognise sketch and interpret graphs of
bull linear
bull quadratic
bull cubic
bull reciprocal
bull exponential
(knowledge of turning points and asymtotes is required)Tangents Estimate gradients of curves by drawing tangents
Learner Guide
59
Extended Algebra and graphs
Question type You should be able to R A G CommentsFunctions Use function notation eg
f(x) = 3x ndash 5 f x α 3x ndash5 to describe simple functions
Find inverse functions f ndash1 (x)
Form composite functions as defined by gf(x) = g(f(x))
Derivatives Understand the idea of a derived function
Use derivatives of the form axn and simple sums of not more than three of these (a is a rational constant and n is a positive integer or 0)
Apply differentiation to gradients and turning points (stationary points)
Use any method to explain whether the turning point is a maximum or a minimum eg second derivative or gradient of function on either side of turning point
Learner Guide
60
Extended Co-ordinate geometry
Question type You should be able to R A G CommentsStraight line graphs
Work with co-ordinates in two dimensions
Gradient Find the gradient of a straight line graph
Calculate the gradient of a straight line from the co-ordinates of two points on it
Length and midpoint
Calculate the length and the co-ordinates of the midpoint of a straight line segment from the co-ordinates of its end points
Equation of line Interpret and obtain the equation of a straight line graph
Parallel lines Determine the equation of a straight line parallel to a given line eg find the equation of a line parallel to y = 4x ndash 1 that passes through (0 ndash3)
Perpendicular lines
Find the gradient of parallel and perpendicular lines eg
bull find the gradient of a line perpendicular to y = 3x + 1
bull find the equation of a line perpendicular to one passing through the co-ordinates (1 3) and (ndash2 ndash9)
Learner Guide
61
Extended Geometry
Question type You should be able to R A G CommentsGeometrical language
Use and interpret the geometrical terms
bull point
bull line
bull parallel
bull perpendicular
bull bearing
bull right angle acute obtuse and reflex angles
bull similar
bull congruent
Use and interpret the vocabulary of
bull triangles right-angled scalene isosceles equilateral
bull quadrilaterals
bull circles
bull polygons
bull simple solid figures including nets
Learner Guide
62
Extended Geometry
Question type What I need to do R A G CommentsGeometrical constructions
Measure and draw lines and angles
Construct a triangle given the three sides using a ruler and a pair of compasses only
Scale drawings Read and make scale drawings
Similar figures Calculate lengths of similar figures
Use relationships between areas of similar triangles and in similar figures
Use relationships between volumes and surface areas of similar solids
Congruent triangles
Use the congruence criteria for triangles (SSS ASA SAS RHS)
Symmetry Recognise symmetry properties for triangles quadrilaterals and circles
Recognise line symmetry in two dimensions
Recognise and find the order of rotational symmetry in two dimensions
Learner Guide
63
Extended Geometry
Question type You should be able to R A G CommentsSymmetry (continued)
Use the following symmetry properties of circles
bull equal chords are equidistant from the centre
bull perpendicular bisector of a chord passes through the centre
bull tangents from an external point are equal in length
Recognise and use symmetry properties of
bull prism cylinder cone and pyramid
Learner Guide
64
Extended Geometry
Question type You should be able to R A G CommentsAngle properties Calculate unknown angles explaining the properties that
you are using in geometrical language for the following geometrical properties
bull angles at a point
bull angles at a point on a straight line and intersecting straight lines
bull angles formed within parallel lines
bull angle properties of triangles and quadrilaterals
bull angle properties of regular polygons
bull angle in a semi-circle
bull angle between tangent and radius of a circle
bull angles properties of irregular polygons
bull angle at the centre of a circle is twice the angle at the circumference
bull angles in the same segment are equal
bull angles in opposite segments are supplementary cyclic quadrilaterals
bull alternate segment theorem
Learner Guide
65
Extended Mensuration
Question type What I need to do R A G CommentsMeasures Use current units of
bull mass
bull length
bull area
bull volume
bull capacity
Express quantities in terms of smaller or larger units including units of area and volume
Perimeter Carry out calculations involving
bull perimeter and area of a rectangle
bull perimeter and area of a triangle
bull perimeter and area of parallelogram
bull perimeter and area of a trapezium
bull perimeter and area of compound shapes made by combining rectangles triangles parallelograms andor trapeziums
Learner Guide
66
Extended Mensuration
Question type You should be able to R A G CommentsCircles Carry out calculations involving circumference and area of a
circle
Solve problems involving arc length and sector area of a circle
Surface area and volume
Carry out calculations involving
bull surface area and volume of a cuboid prism and cylinder (no formulae will be given for these shapes)
bull surface area and volume of a sphere pyramid and cone (formulae will be given for these shapes)
Compound shapes
Carry out calculations involving
bull area of a shape made by combining cuboids prisms andor cylinders
bull volume of a shape made by combining cuboids prisms andor cylinders
Learner Guide
67
Extended Trigonometry
Question type You should be able to R A G CommentsBearings Use and interpret three-figure bearings measured clockwise
from the North ie 000degndash360degTrigonometry Find unknown sides andor angles in right-angled triangles by
applying
bull Pythagorasrsquo theorem
bull sine cosine and tangent ratios for acute angles in right-angled triangles
Solve problems in two dimensions involving angles of elevation and depression
Know that the perpendicular distance from a point to a line is the shortest distance to the line
Trig graphs and equations
Recognise sketch and interpret graphs of simple trigonometric functions
Graph and know the properties of trigonometric functions
Solve simple trigonometric equations for values between 0deg
and 360deg eg Solve sin x = radic32
for values of x between 0deg and
360degGeneral trig Solve problems using sine and cosine rules for any triangle
Find the area of any triangle using frac12absinC
Trig in 3D Solve simple trigonometrical problems in three dimensions including angle between a line and a plane
Learner Guide
68
Extended Vectors and transformations
Question type You should be able to R A G CommentsVectors in two dimensions (links to Trigonometry)
Describe a translation by using a vector represented by
AB or a
Add and subtract vectors
Multiply a vector by a scalar
Transformations Reflect simple shapes in horizontal or vertical lines
Rotate simple shapes through multiples of 90deg about any point
Construct translations of simple shapes
Construct enlargements of simple shapes (positive fractional and negative scale factors)
Recognise and describe
bull reflections
bull rotations
bull translations
bull enlargements (positive fractional and negative scalefactors)
( )x
y
Learner Guide
69
Extended Vectors and transformations
Question type You should be able to R A G CommentsHarder vectors
Calculate the magnitude of a vector as and
understand that magnitude is denoted by modulus signs |A B| or |a|
Represent vectors by directed line segments
Use the sum and difference of two vectors
Use position vectors
( )x
yradicx2 + y2
Learner Guide
70
Extended Probability
Question type You should be able to R A G CommentsProbability (links to Four rules)
Calculate the probability of a single event as a fraction decimal or percentage (not a ratio)
Probability scale Understand and use the probability scale from 0 to 1
Sum to 1 Understand that the probability of an event occurring = 1 ndash the probability of the event not occurring
Relative frequency
Understand relative frequency as an estimate of probability
Work out expected frequencies using relative frequency
Combined events Calculate the probability of combined events using
bull tree diagrams
bull possibility diagrams
bull tables
Learner Guide
71
Extended Statistics
Question type You should be able to R A G CommentsClassify Collect classify and tabulate data
Interpret and compare
Read interpret and draw simple inferences from tables and statistical diagrams
Compare sets of data using
bull tables
bull graphs
bull statistical measures
Be aware of restrictions when making conclusions from data
Charts Construct and use
bull bar charts
bull pie charts
bull pictograms
bull stem ndash and ndash leaf diagrams
bull frequency distributions
bull histograms with equal and unequal intervals
bull scatter diagrams
Learner Guide
72
Extended Statistics
Question type You should be able to R A G CommentsAverages Calculate for individual and discrete data
bull mean
bull median
bull mode
bull range
and distinguish between their use
Estimated mean Calculate an estimate of the mean for grouped and continuous data
Identify the modal class from a grouped frequency distributionCumulative frequency
Construct and use cumulative frequency diagrams to estimate and interpret
bull the median
bull percentiles
bull quartiles
bull inter-quartile range
Construct and interpret box-and-whisker plots
Correlation Understand what is meant by positive negative and zero correlation with reference to a scatter diagram
Lines of best fit Draw interpret and use a ruled line of best fit by eye
Cambridge Assessment International Education1 Hills Road Cambridge CB1 2EU United Kingdomt +44 1223 553554e infocambridgeinternationalorg wwwcambridgeinternationalorg
Copyright copy UCLES October 2017
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3
About this guide 4
Section 1 Syllabus content ndash what you need to know about 5
Section 2 How you will be assessed 6
Section 3 What skills will be assessed 11
Section 4 Example candidate response 13
Section 5 Revision 24
Contents
4
This guide introduces you to your Cambridge IGCSE Mathematics course and how you will be assessed You should use this guide alongside the support of your teacher
It will help you to
9 understand what skills you should develop by taking this course
9 understand how you will be assessed
9 understand what we are looking for in the answers you write
9 plan your revision programme
9 revise by providing revision tips and an interactive revision checklist (Section 6)
About this guide
Key benefits
The course will help you to build your skills and knowledge across a range of mathematical techniques You will be able to develop your problem solving and reasoning skills in a variety of situations
The Extended course will provide you with a strong foundation to continue to study mathematics qualifications beyond IGCSE The Core course will equip you with skills needed to support your learning in other subjects and in your general working life
5
This section gives you an outline of the syllabus content for this course Only the top-level topics of the syllabus have been included here which are the same for both the Core and Extended courses In the lsquooverviewrsquo column you are given a very basic idea of what each topic covers Highlighted cells show Extended-only content
Learners taking the Extended course need to know all of the Core content as well as some extra content This extra content requires learners to explore topics and sub-topics of the Core syllabus in more detail to cover some more complex techniques and to learn new sub-topics
Ask your teacher for more detail about each topic including the differences between the Core and Extended courses You can also find more detail in the revision checklists in Section 6 of this guide
Topic Overview
Number Number sets and Venn diagrams squares and cubes directed numbers fractions decimals and percentages ordering indices lsquofour rulesrsquo estimates bounds ratio proportion rate percentage time money and finance Growth and decay (Extended only)
Algebra and graphs Basic algebra algebraic manipulation equations formulae sequences drawing sketching and interpreting graphs of functionsAlgebraic fractions harder simultaneous equations proportion linear programming functions gradients of curves derived functions and differentiation (Extended only)
Co-ordinate geometry Straight-line graphs
Vectors and transformations Vectors (column) transformations
Magnitude of a vector represent vectors by directed line segments position vectors (Extended only)
Geometry Language construction symmetry angle properties congruence similarity
Mensuration Measures mensuration
Trigonometry Bearings trigonometry in right-angled triangles
Sine rule cosine rule trig graphs solving simple trig equations (Extended only)
Probability Probability
Conditional probability (Extended only)
Statistics Statistics
Section 1 Syllabus content ndash what you need to know about
Make sure you always check the latest syllabus which is available at wwwcambridgeinternationalorg
6
You will be assessed at the end of the course using two written examinations The papers that you will sit are different for the Core and Extended courses
bull Paper 1 ndash Short-answer questionsbull Paper 3 ndash Structured questions
bull Paper 2 ndash Short-answer questionsbull Paper 4 ndash Structured questions
Components at a glanceThe table summarises the key information about each component
Component How long and how many marks Skills assessed Percentage of the
qualificationCore Paper 1
(Short-answer questions)
1 hour
56 marks Mathematical techniques as listed in the Core syllabus and applying those techniques to solve problems
35
Paper 3 (Structured questions)
2 hours
104 marks 65
Extended Paper 2 (Short-answer questions)
1 hour 30 minutes
70 marksMathematical techniques as listed in the Core and Extended syllabus and applying those techniques to solve problems
35
Paper 4 (Structured questions)
2 hours 30 minutes
130 marks 65
Section 2 How you will be assessed
Core Extended
Make sure you find out from your teacher which course you will be following
7
About the componentsIt is important that you understand the different types of question in each paper so you know what to expect
Core Paper 1 (Short-answer questions) and Paper 3 (Structured questions)
You need to answer all questions on each paper
Paper 3Paper 1
You can use an electronic calculator in both papers Ask your teacher to recommend a suitable calculator
Paper 1 contains lots of short-answer questions These are usually worth 1ndash3 marks each Some might be broken up into two parts
Write your working and answers in the spaces provided
The number of marks for each part is shown
Paper 3 contains structured questions Each question is split into many parts with each part usually being worth 1ndash4 marks Here for example question 1 is split over two pages
Often the answers to later parts will depend on the answers to earlier parts
8
Extended Paper 2 (Shortndashanswer questions) and Paper 4 (Structured questions)
You need to answer all questions on both papers
Paper 2 questions are short-answer questions Most questions are worth 1ndash3 marks with some being worth 4 or 5 marks Some questions might be broken up into two parts
Write your working and answers in the spaces provided
The number of marks for each part is shown
Paper 4Paper 2
You can use an electronic calculator in both papers Ask your teacher to recommend a suitable calculator
Paper 4 contains structured questions Each question is split into many parts with each part usually being worth 1ndash6 marks Here for example question 2 is split over two pages
Often the answers to later parts will depend on the answers to earlier parts
9
Equipment for the examMake sure you have
bull a blue or black pen (a spare pen is always a good idea)bull a pencil (for graphs and diagrams)bull an electronic calculatorbull a protractorbull a pair of compassesbull a ruler
1 Read the questions carefully to make sure that you understand what is being asked
2 Give your answers to the accuracy indicated in the question If none is given and the answer isnrsquot exact then
bull give your answer to three significant figures 123 9 12298 x
bull if the answer is in degrees then give it to one decimal place 231deg 9 23deg x
3 Include units with your answers if they are not given on the paper For example 1 kg of apples costs hellip pound120 9 120 x
4 Show your working Show as much working as you can for all your questions
5 If you make a mistake clearly cross out any working or answers that you do not want the examiner to mark
Use the value of π from your calculator or use 3142 which is given on the front page of the question paper
Timingbull If you are stuck on a question dont waste too much time trying to answer it ndash go on to the next question and
come back to the one you are stuck on at the endbull Use any time that you have left at the end of the exam to go back and check your answers and working
Make sure that you give your answer in the form asked for in the question eg some questions ask for answers to be given in terms of π For lengths areas and volumes give answers in decimals (not in surds or in terms of π) unless you are told to given an exact answer
You can gain marks for the correct working even if you have an incorrect answer or cannot complete the whole question
If you need more space ask for extra of paper and clearly indicate where the rest of the answer is written On the additional paper make it clear which questions(s) you are answering
General advice for all Papers
10
The areas of knowledge understanding and skills that you will be assessed on are called assessment objectives (AOs) There are two AOs for this course
AO1 Demonstrate knowledge and
understanding of mathematical techniques
AO2 Reason interpret and communicate
mathematically when solving problems
AO1 Demonstrate knowledge and understanding of mathematical techniquesYou need to show that you can recall and apply mathematical knowledge terminology and definitions to carry out single or multi-step solutions in mathematical and everyday situations
Section 3 What skills will be assessed
This means that you need to show that you can
bull organise process and present information accurately in written tabular graphical and diagrammatic forms
bull use and interpret mathematical notation correctly
bull perform calculations and procedures by suitable methods including using a calculator
bull understand systems of measurement in everyday use and make use of these
bull estimate approximate and work to degrees of accuracy appropriate to the context and convert between equivalent numerical forms
bull use geometrical instruments to measure and to draw to an acceptable degree of accuracy
bull recognise and use spatial relationships in two and three dimensions
AO1 is assessed in all papers
Use tables graphs and diagrams
An example of degress of accuracy include significant figures or decimal places
An example of converting between equivalent numerical forms include between fractions decimals and percentages or between normal numbers and standard form
eg a pair of compasses a protractor and a ruler
11
AO2 Reason interpret and communicate mathematically when solving problemsYou need to demonstrate that you can analyse a problem select a suitable strategy and apply appropriate techniques to obtain a solution
This means that you need to show that you can
bull make logical deductions make inferences and draw conclusions from given mathematical data
bull recognise patterns and structures in a variety of situations and form generalisations
bull present arguments and chains of reasoning in a logical and structured way
bull interprete and communicate information accurately and change from one form of presentation to another
bull assesses the validity of an argument and critically evaluate a given way of presenting information
bull solve unstructured problems by putting them into a structured form involving a series of processes
bull apply combinations of mathematical skills and techniques using connections between different areas of mathematics in problem solving
bull interprete results in the context of a given problem and evaluate the methods used and solutions obtained
AO2 is assessed in all papers
Recognise and extent patterns
Take information and organise it to answer a problem
12
Section 4 Command wordsA command word is the part of the question that tells you what you need to do with your knowledge For example you might need to describe something explain something argue a point of view or list what you know The table below includes command words used in the assessment for this syllabus The use of the command word(s) within an question will relate to the context
Cambridge IGCSE Mathematics 0580 syllabus for 2020 2021 and 2022 Details of the assessment
37wwwcambridgeinternationalorgigcseBack to contents page
Command wordsThe table below includes command words used in the assessment for this syllabus The use of the command word will relate to the subject context
Command word What it means
Calculate work out from given facts figures or information generally using a calculator
Construct make an accurate drawing
Describe state the points of a topicgive characteristics and main features
Determine establish with certainty
Explain set out purposes or reasons make the relationships between things evident provide why andor how and support with relevant evidence
Give produce an answer from a given source or recallmemory
Plot mark point(s) on a graph
Show (that) provide structured evidence that leads to a given result
Sketch make a simple freehand drawing showing the key features
Work out calculate from given facts figures or information with or without the use of a calculator
Write give an answer in a specific form
Write down give an answer without significant working
The question below is taken from Paper 4 and illustrates the use of two command words
The command words lsquoWrite downrsquo indicates that you do not need to show your working and the answer should just be written down The mark allocation [1] also supports this
The command words lsquoShow thatrsquo indicate that you need to provide evidence in the form of a clear mathematical explanation to demonstrate that you know how to obtain the given result In other words you need to show a method that leads to the result
The answer space in this case does not contain a dotted answer line as there is no single lsquoanswerrsquo to be found Your working that leads to the given result should be written in the blank working space
13
This section takes you through an example question and learner response from one of the 2020 specimen papers for this course It will help you to identify the command words and other key instructions within questions and to understand what is required in your response
This section is structured as follows
QuestionThe command words and instructions in the question have
been highlighted and explained This should help you to understand clearly what is required by the question
Mark schemeThis tells you as clearly as possible what an examiner expects
from an answer to award marks
Example candidate responseThis an exemplar answer written in the style of
a high level candidate
How the answer could have been improvedThis summarises what could be done to gain more marks
All information and advice in this section is specific to the example question and response being demonstrated It should give you an idea of how your responses might be viewed by an examiner but it is not a list of what to do in all questions In your own examination you will need to pay careful attention to what each question is asking you to do
Common mistakesThis will help you to avoid common mistakes made by
candidates So often candidates lose marks in their exams because they misread or misinterpret the questions
Section 5 Example candidate response
14
QuestionThe question used in this example is from Specimen Paper 3 (Core) It represents the type of structured question you will see in both Paper 3 (Core) and Paper 4 (Extended) A structured question means that it is broken into several parts Often later parts will depend on your answers to earlier parts
This means that you cannot find the answer by
measuring the diagramWork out indicates that the answer should be calculated from the given information so measurement will not score marks
The allocation of 1 mark indicates that the answer can be obtained with minimum working
Give reasons for your answer indicates that your answer should be supported with reasons using the correct mathematical terminology You must justify your answer
Use trigonometry to calculate indicates that you should use this method with the given information to find the answer and that a calculator is needed to solve the problem If you did not use trigonometry you would not be awarded any marks
15
Show that indicates the answer is given and you need to write down all of the steps in a method that leads to the given answer You need to provide evidence that you understand and know how the answer is reached
Work out indicates that you should calculate the answer from the given information The mark allocation of 4 marks suggests that you will need to include several steps of working in order to get to the answer
Learner Guide
16
Answer Mark Notes(a)(i) 35 1 This is the only acceptable answer for this part of the question
(a)(ii) 74 1 This is the only acceptable answer for this part of the question
(b) 43deg and correct mathematical reasons
3 Two marks are awarded for the final answer of 43deg
The third mark is awarded for a fully correct reason for example angles on a straight line add up to 180deg and angles in a triangle add up to 180deg There are other correct reasons that could be also be used
If 43deg is not obtained one method mark can be awarded if the following calculation is seen in the working
180 ndash 128 or 128 ndash 85
(c) 322 or 3223hellip 2 This is the only acceptable answer for this part of the question
The answer has to be rounded correct to three significant figures or can be given with more figures in the answer
Those that did not get this answer can score one method mark for showing the following in their working
sin = 8 divide 15
(d)(i) 2 2300 225+2 This does not have to be shown in one step as long as the method shown is the same as this overall Those that do not
show this can have one method mark for showing the following in their working
300deg + 225deg
(d)(ii) 15 35 4 The answer 3 35pm is also acceptable for 4 marks
If the correct answer is not found one method mark is available for showing 375 divide 450 in their working and a second method mark can be awarded for sight of them multiplying their answer to this by 60 to change it to hours A third method mark can be awarded for adding their answer in hours to 14 45 ndash this shows the correct method so only one mark is lost for an incorrect final answers
Mark schemeYour examination papers will be marked and the overall number of marks for each paper will be recorded Your marks across all papers will then be converted to a grade
Final answer This value is what the examiner expects to see The answer has to be exactly as given in the mark scheme unless there are acceptable alternatives The mark scheme will always make it clear if there are acceptable alternative answers
Method marks Sometimes method marks are awarded for lines of working as well as for the final answer This means that you could get the final answer incorrect but still get some marks if you include the correct working The mark scheme does not include all possible methods so if you use a method not included in the mark scheme but it is accurate and relevant then the examiner will still award marks for the appropriate parts of the working ndash unless the questions asks you to use a specific method
example of a final answer
example of a method mark
17
Example candidate responseNow letrsquos look at the sample candidatersquos response to question 8 The examiners comments are in the orange boxes The candidate was awarded 8 marks out of 13
180 ndash 74 + 71 = 177
177
74
0 out of 1
The candidates working suggests they understand that the angle sum of a triangle is 180deg but they did not include brackets around 74 + 71 The answer 177deg is not sensible for this question
1 out of 1
The candidate recognises that there are parallel lines and that angle y is a corresponding angle to angle 74deg
180 ndash 128 = 52 180 ndash 85 ndash 52 = 43
43 angles on a straight line add up to 180deg
2 out of 3
The candidate has given a correct answer for w and shown correct working in two steps They have given a correct reason for 52deg using correct mathematical languge But they have not provided a reason to explain the angle 43deg They lose a mark for not also stating angle sum of a triangle is 180deg
sin p = 8 divide 15 = 053
p = sinndash1 (053)
p = 32005 320
1 out of 2
The candidate has correctly used trigonometry in their method They are awarded one method mark for the first line of working However they have rounded 05333333hellip (the result of 8 divide 15) to 052 and then calculated the inverse sin of 052 rather than 05333333 This has resulted in an inaccurate final answer This is called lsquopremature approximationrsquo and it is a very common error to make
18
AB2 = 3002 + 2252
= 140625
AB = 375
1 out of 2
The candidate has recognised the right-angled triangle and correctly used Pythagorasrsquo theorem in the first line of working However they have missed out an important step by not showing that you need to take the square root of 140625 to get 375 As this is a lsquoshow thatrsquo question and they missed a key step in the method they cannot be awarded full marks as the complete working is not shown One method mark is earned for the first line
T = = = 08333333hellip
08333333 hours = 08333333 times 60 minutes = 50 minutes
arrives at 14 45 + 50 mins = 3 35
DS
375450
3 35
3 out of 4
The candidate has found the time by correctly dividing the distance by the speed and recognised that this is in hours When converting the answer to a decimal they have not rounded the decimal but left its full value on the calculator to get 50 mins which is the correct approach Unfortunately after converting the time from 24 hour clock to 12 hour clock they did not include lsquopmrsquo to indicate that the time is in the afternoon and so the final answer is not quite right So 3 marks are awarded for all of a correct method but a mark is lost due to the accuracy of the final answer
19
How the answer could have been improvedThis answer could have been improved by
bull In part (a)(i) the answer of 177deg was not sensible given the diagram in the question If the candidate had checked their answer for sense they would have realised they had made a mistake It is always a good idea to check that your answer seems sensible before you move on to another question
bull In part (b) the candidate did all the correct steps but failed to provide both reasons There were two steps to the method which should have indicated to the candidate that there were two steps to justify and therefore two reasons should have been provided The mark allocation for the question [3] also indicates that more than one reason would be required one mark for the value of 43deg leaving two marks one mark for each of two reasons The candidate should have read the question carefully and again checked their response seemed reasonable
bull In part (c) the candidate rounded an intermediate answer which affected the accuracy of the final answer This caused them to lose a mark despite using a correct method You should only ever round the final answer do not round intermediate values If you can store the intermediate values in your calculator and so that you can use the full value in your calcuations If youre not able to do this and you have to round the intermediate values do not round them to less than three significant figures
bull In part (d)(i) the candidate missed out a step in the method As this was a show that question they needed to show all the steps in the method Its important to show all steps even if they seem obvious
bull In part (d)(ii) the candidate made a silly error by not stating that the time was pm When working with time answers are accepted in either 24 clock or 12 clock time but if you give your answer in the 12 hour clock then it must include am or pm as well
Common mistakesThere were a number of common mistakes made by other candidates on this question
bull Accuracy of answers
In parts (c) and (d)(ii) a common error was premature rounding ndash rounding intermediate values in the method before the final answer which resulted in their final answer not being accurate Other candidates gave the final answer to less than three significant figures ignoring the instruction on the front of the paper to round to three significant figures
bull Using incorrect terminology when giving reasons
In part (b) the most common error was to not give full reasons to support the answer Another common error was to provide a reason that did not use the correct mathematical language such as lsquoThey add up to 180degrsquo and lsquoIt is a straight linersquo which could not be awarded marks
bull Lack of knowledge
In part (c) a number of candidates had limited knowledge of trigonometry and did not choose the correct trig ratio which was the sine ratio This is why good revision is important
bull Not checking answers
In part (a)(i) even though the diagram is drawn NOT TO SCALE it is possible to see that the angle is an acute angle and should therefore not be bigger than 90deg This should alert candidate that if their answer is over 90deg it is not a sensible answer and they should go back and check their working
20
bull Inefficient method shown
In part (c) the lsquoShow thatrsquo question a number of candidates omitted an important step from the method this is often common in lsquoShow thatrsquo questions where every step must be shown no matter how obvious them seem
General adviceIn order to do your best when answering a mathematics question make sure you
bull revise all of the topics for the syllabus you are studying before the exam
bull understand what all the key terms and command words in the question mean
bull read the questions carefully and consider what you need to do before you do it
bull only round the final answer not intermediate values
bull show all steps in your working and show them clearly
bull round to the correct degree of accuracy
bull use the correct mathematical terminology
bull check your answers seem reasonable given the context or details of the question
21
It is important that you plan your revision in plenty of time for the examinations and that you develop a revision technique that works for you The advice in this section will help you revise and prepare for the examinations It is divided into general advice for all papers
Use the tick boxes to keep a record of what you have done what you plan to do or what you understand
For more advice on revision see the Cambridge Learner Revision Guide on our website
Section 6 Revision
Find out when the examinations are and plan your revision so you have time to revise Create a revision timetable and divide it into sections to cover each topic
Spend most of your time focussing on specific skills knowledge or issues that you have found more difficult when practicing them either during revision or earlier in the course
Write a summary of all the key information for a topic ndash use the checklists at the end of this section
Know the meaning of the command words used in questions and how to apply them to the information given Look at past examination papers and highlight the command words and check what they mean
Make revision notes and work on practice questions Reading alone does not work you need to be active and practice your maths
Work for shorter periods then have a break Revise small sections of the syllabus at a time but do this regularly
Test yourself by trying out some past exam questions Use the mark schemes to assess yourself and to be familiar with how marks are awarded for different questions
Be organised in advance with your notes texts exercise books revision guides and revision websites so you do not waste valuable revision time trying to find things
Make notes of key mathematical words that you should use in questions that ask you to lsquodescribersquo or give lsquogeometrical reasons forrsquo eg in describing transformations or giving reasons in circle theorem questions Look at the mark schemes for these types of questions from past papers to see how marks are awarded
Make sure you have all of the correct mathematical equipment ready for the exam particularly your calculator Make sure you are familiar with the all of the important functions on your calculator
Practice the areas you can do well not just those that you find more difficult
Take breaks and do things to relax when you take your breaks this will help you to be more productive when you are revising
Before the examination
22
During the examination
Plan your time according to the marks for each question For example a question worth one mark requires less time than a question one worth 4 marks If a question has several parts then the parts with more marks will need more time
Read each question very carefully
Identify the command words ndash you could underline or highlight them
Identify the other key words and information and perhaps underline them too particularly where
questions require reasoning or problem solving
Read the questions careully and make you have answered the question that is being asked
Show your working this is particularly important for questions where you are asked to lsquoshow that helliprsquo
Set your working out clearly so that it is easy to follow this makes it easier to keep track of what you have done and makes checking back through your work easier and it makes it easier for the examiner to mark your work try to write it in a logical order in the answer space
Write answers clearly if you want to change an answer then you should cross the answer out and write a replacement if your answer is on the answer line cross it out and write the replacement answer above it do not try to change numbers on the answer line as this can lead to unclear figures
Check your working and answers to avoid errors
Give your answer to the appropriate level of accuracy either the accuracy indicated in the question or the accuracy given on the front of the paper
Avoid rounding intermediate values part way through your calculation only round the final answer
Check that the answer that you have given is sensible and realistic for what is being asked
Use a pencil when drawing diagrams or completing graphs this means that you can change your answer more easily if you have made a mistake
Take care when reading scales
If you are asked for reasons for your answer then use the correct mathematical terms
Use the mark allocation given with the questionsparts of questions to try to judge how much work is needed to answer each part
23
Top tips for revision of Cambridge IGCSE Mathematics1 Summarise recall and applyMake sure that you can recall and apply the key information and mathematical techniques on each topic that you need for the exam
i Write a summary of the key information of a topicii Collect together some questions that test the knowledge and skills of this topic Ask your teacher for practice
questions or suitable past examination questions or use practice books or textbooksiii Test your recall by covering over the summary and trying to remember the details or use the summary as part of
the lsquoTeach the topicrsquo (Tip 3) or lsquoQuestion and answer cardsrsquo (Tip 4) activities iv After you have spent some time revising and practising the knowledge and skills answer the questions that you
collected together on the topic You might do this later on the same day as revising or a few days later Answer as many questions as you can in order to practise applying your knowledge
v Try creating your own questions by adapting existing ones and use these for practice when you return to a topic
On graph questions straight lines should be ruled and curves should be drawn freehand with a smooth curve
Donrsquot spend too long on any one part of a question If you are really stuck on a question then move on and come back to the question later if you have time As a rough guide each mark on the paper should take about one minute
2 Concept mapsConcept maps are a great way to revise the links between different factors or to explore a larger topic They can also be used to collect together your ideas
i Use a blank sheet of paper and turn it on its side (landscape)ii Put the topic title in the middle of the page and build the concept map outwards using lines called lsquobranchesrsquo
ndash The first branches are from the central topic to sub-topics draw these as thick lines
ndash Add new branches from the sub-topics to include more detail draw these as thinner lines
ndash Add even more detail to a point by adding more branches
This creates a hierarchy of information from lsquooverviewrsquo (the thick branches) to lsquofine detailrsquo (thinnest branches)
iii Write single key words or phrases along a branch and add drawings for visual impactiv Use different colours highlighter pens symbols and arrows to highlight key facts or issuesIt is a good idea to use a large piece of plain A3 (or larger) paper and lots of coloured pens
24
3 Teach the topicThis is a very simple but effective technique that focusses on knowledge recall It tests the brain and rehearses the information you need to know for a certain topic and so will help your revision
i Create some topic cards with key bullet points of information on Leave space for ticksii Give these to your parents family or friends for exampleiii Give yourself 10 minutes maximum to teach your audience the main points of the topic You could use a mini-
whiteboard or flip chart to helpiv Your audience tick off all the points you mention in your presentation and give you a final scoreThe brain loves competition so if you do not score full marks you can try again the next day or compete against friends This system of repeat and rehearsal is very effective especially with more complex topics and doesnt take much preparation
4 Question and answer (QampA) cardsThis is very similar to Teach the topic but less formal and less public for those who dislike performing in front of others It tests knowledge recall and rehearses the information you need to know for a certain topic
i Pick a topic and create two sets of cards question cards and answer cards You might find it helpful to make the question cards a different size or use different coloured card for answers
ii Make sure you have the topic or something appropriate depending on what you are focusing on as a heading on each card The questions should test your knowledge and understanding of key areas of the course
iii A friend or family member uses the cards to test you in short 5 or 10 minute periods at any time during the dayiv You could also do this alone by reading the questions to yourself giving the answer and then checking the
correct answer cardv This game can be adapted by using the cards to find matching pairs turn all cards face down across the space
in front of you Turn over two cards leaving them where they are If they match (one is a question card and the other is the corresponding answer card) pick up the pair and put them to one side If they dont match try to remember where they are and what is on each card then turn them back over Turn over two other cards Continue until you have matched all pairs
5 Question paper and mark schemesLooking at past question papers and the mark scheme helps you to familiarise yourself with what to expect and what the standard is
i Ask your teacher for past paper questions with mark schemes for the course ndash ask your teacher for help to make sure you are answering the correct questions and to simplify the mark scheme
ii Look at the revision checklist and identify which topic a given question relates to ndash you might need to ask your teacher to help you do this
iii Once you have finished revising a topic or unit time yourself answering some appropriate exam questions Check the mark schemes to see how well you would have scored or give the answers to your teacher to check
iv Add details or notes to the mark scheme where you missed out on marks in your original answers using a different coloured pen Use these notes when you revise and try the question again later
You can find plenty of past exam papers and mark schemes on the Cambridge International public website
httpwwwcambridgeinternationalorgprogrammes-and-qualificationscambridge-igcse-mathematics-0580past-papers
25
Other useful revision advice for Cambridge IGCSE Mathematics bull Before the exam make sure that you are familiar with your calculator and confident in using it
bull Look at the Example Candidate Response earlier in this guide Can you identify the strengths of the response andwhere they have made mistakes or lost marks
bull When you are attempting a past paper (or questions from a past paper) complete it without referring to yournotes so that you get a true idea of your strengths and weaknesses Then go back through the paper using yournotes and a different coloured pen to make corrections and changes After you have done as much as you can onthe paper mark it using the mark scheme Take notes of any points that you lost marks on
bull Donrsquot just revise the topics that you enjoy and are confident in If you identify an area that you are weaker inthen try to revisit the topic by reviewing your notes and doing some practice questions then use exam questionsto check whether you now understand
bull Return to topics later in your revision to check that you still remember and understand the topic and to help toensure that you recall more of the material when you get to the examination
Revision checklists for Cambridge IGCSE MathematicsThe tables on the following pages can be used as a revision checklist They do not contain all the detailed knowledge you need to know just an overview For more detail see the syllabus and talk to your teacher
You can use the tick boxes in the checklists to show when you have revised and are happy that you do not need to return to it Tick the lsquoRrsquo lsquoArsquo and lsquoGrsquo column to record your progress as follows
bull R = RED means you are really unsure and lack confidence in that area you might want to focus your revisionhere and possibly talk to your teacher for help
bull A = AMBER means you are reasonably confident in a topic but need some extra practicebull G = GREEN means you are very confident in a topic
As your revision progresses you can concentrate on the RED and AMBER topics in order to turn them into GREEN topics You might find it helpful to highlight each topic in red orange or green to help you prioritise
You can use the lsquoCommentsrsquo column to
bull add more information about the details for each pointbull include a reference to a useful resourcebull include a list of formulae or notationbull add learning aids such as rhymes poems or word playbull highlight areas of difficulty or things that you need to talk to your teacher about
There is a set of checklist for the Core syllabus and a different set for the Extended syllabus
Learner Guide
26
Core syllabus contentCore Number
Category You should be able to R A G CommentsNumber Identify and use
bull natural numbers
bull integers (positive negative and zero)
bull prime numbers
bull write a number as a product of its prime factors
bull square numbers and cube numbers
bull common factors and highest common factor of two numbers
bull common multiples and lowest common multiple of two numbers
bull rational numbers
bull irrational numbers (eg π radic2 )
bull real numbers
bull reciprocals
Learner Guide
27
Core Number
Question type You should be able to R A G CommentsSets and Venn diagrams
Understand notation of Venn diagrams
Definition of sets
eg A = xx is a natural number
B = abchellip
Notation
Number of elements in set A n(A)
Universal set
Union of A and B A cup B
Intersection of A and B A cap B
Squares square roots cubes and cube roots
Calculate
bull squares and cubes of numbers
bull square roots and cube roots of numbers
Learner Guide
28
Core Number
Question type You should be able to R A G CommentsDirected numbers
Use directed numbers in practical situations for example temperature changes
Fractions decimals and percentages
Use the language and notation of simple vulgar and decimal fractions and percentages
Recognise equivalent fractions decimals and percentages
Convert between fractions decimals and percentages
Ordering Order quantities by magnitude and demonstrate familiarity with the symbols = ne gt lt ⩾ ⩽
Indices and standard form (links to Algebraic manipulation)
Evaluate indices eg 25 5ndash2 1000 64frac12 8ndash23
Use the rules of indices for
bull multiplication of indices eg 4ndash3 times 45
bull division of indices eg 57 divide 53
bull index numbers raised to an index eg (23)2 (43)2
Use the standard form A times 10n where n is a positive or negative integer and 1 ⩽ A lt 10
bull convert numbers into and out of standard form
bull calculate with numbers in standard form
Learner Guide
29
Core Number
Question type You should be able to R A G CommentsFour rules
( + ndash times divide )
Use the four rules for calculations with
bull whole numbers
bull decimals
bull vulgar and mixed fractions
bull correct ordering of operations (BIDMAS) and use of bracketsEstimates Make estimates of numbers quantities and lengths
Give approximations to a specified number of
bull significant figures
bull decimal places
Round off answers to reasonable accuracy in the context of a given problem
Bounds Give upper and lower bounds for data given to a specified accuracy eg measured lengths
Ratio proportion rate
Understand ratio
Divide a quantity in a given ratio
Understand direct and inverse proportion
Use scales in practical situations
Use common measures of rate (formulae for other rates eg density and pressure will be given in the question)
Calculate average speed
Learner Guide
30
Core Number
Question type You should be able to R A G CommentsPercentages Calculate a percentage of a quantity
Express one quantity as a percentage of another quantity
Calculate percentage increase or decrease
Use of an electronic calculator
Use a calculator efficiently
Check accuracy of calculations
Time Calculate times in terms of the 24-hour and 12-hour clock
Read
bull clocks
bull dials
bull timetables
Money Calculate using money
Convert from one currency to another
Learner Guide
31
Core Number
Question type You should be able to R A G CommentsPersonal and small business finance
Use given data to solve problems on
bull earnings
bull simple interest
bull compound interest (you will need to know the compound interest formula)
bull discount
bull profit and loss
Extract data from tables and charts
Learner Guide
32
Core Algebra and graphs
Question type You should be able to R A G CommentsBasic algebra Use letters to express generalised numbers
Express basic arithmetic processes algebraically
Substitute numbers in formulae
Construct simple expressions and set up simple equations
Rearrange simple formulae
Algebraic manipulation
Manipulate directed numbers
Use brackets
bull expand a single bracket eg 3x(2x ndash4y)
bull expand a pair of brackets eg (x + 3) (x ndash 7)
Extract common factors eg factorise 9x2 + 15xy
Rules of indices Use and interpret positive negative and zero indices
Use the rules of indices eg to simplify algebra such as
bull 3x4 times 5x
bull 10x3 divide 2x2
bull (x6)2
Learner Guide
33
Core Algebra and graphs
Question type You should be able to R A G CommentsEquations and inequalities
Derive and solve simple linear equations in one unknown
Derive and solve simultaneous linear equations in two unknowns
Number sequences
(links to Squares square roots cubes and cube roots)
Continue a number sequence
Recognise patterns in sequences
Recognise relationships between difference sequences
Find the nth term of sequences for
bull liner sequences
bull simple quadratic sequences
bull cubic sequences
Practical graphs
(links to Mensuration)
Interpret and use graphs in practical situations including
bull travel graphs
bull conversion graphs
Draw graphs from given data
Learner Guide
34
Core Algebra and graphs
Question type You should be able to R A G CommentsGraphs of functions
(links to Co-ordinate geometry)
Construct tables of values for functions of the form
bull ax + b (linear)
bull plusmn x2 + ax + b (quadratic)
bull (x ne 0) (reciprocal)
where a and b are integer constants
Draw and interpret such graphs
Solve linear and quadratic equations approximately by graphical methods
Recognise and sketch the graphs of linear and quadratic functions
ax
Learner Guide
35
Core Co-ordinate geometry
Question type You should be able to R A G CommentsCo-ordinates Work with co-ordinates in two dimensions
Gradients Find the gradient of a straight line graph
Equation of straight line
Interpret and obtain the equation of a straight line graph in the form y = mx + c where the graph is given
Parallel lines Determine the equation of a straight line parallel to a given line eg find the equation of a line parallel to y = 4x ndash 1 that passes through (0 ndash3)
Learner Guide
36
Core Geometry
Question type You should be able to R A G CommentsGeometrical language
Use and interpret the geometrical terms
bull point
bull line
bull parallel
bull perpendicular
bull bearing
bull right angle acute obtuse and reflex angles
bull similar
bull congruent
Use and interpret the vocabulary of
bull triangles right-angled scalene isosceles equilateral
bull quadrilaterals
bull circles
bull polygons
bull simple solid figures including nets
Learner Guide
37
Core Geometry
Question type You should be able to R A G CommentsGeometrical constructions
Measure and draw lines and angles
Construct a triangle given the three sides using a ruler and a pair of compasses only
Scale drawings Read and make scale drawings
Similar figures Calculate lengths of similar figures
Congruent Recognise congruent shapes
Symmetry Recognise symmetry properties for triangles quadrilaterals and circles
Recognise line symmetry in two dimensions
Recognise and find the order of rotational symmetry in two dimensions
Learner Guide
38
Core Geometry
Question type You should be able to R A G CommentsAngle properties Calculate unknown angles explaining the properties that you
are using in geometrical language for angles
bull angles at a point
bull angles on a straight line and intersecting straight lines
bull angles within parallel lines
bull angles in triangles
bull angles in quadrilaterals
bull angles in regular polygons
bull angle in a semi-circle
bull angle between tangent and radius of a circle
Learner Guide
39
Core Mensuration
Question type You should be able to R A G CommentsMeasures bull Use current units of
bull mass
bull length
bull area
bull volume
bull capacity
Express quantities in terms of smaller or larger units including units of area and volume
Convert between units including units of area and volume
Perimiter Carry out calculations involving
bull perimeter and area of a rectangle
bull perimeter and area of a triangle
bull perimeter and area of parallelogram
bull perimeter and area of a trapezium
bull perimeter and area of shapes made by combining
bull rectangles triangles parallelograms andor trapeziums
Learner Guide
40
Core Mensuration
Question type You should be able to R A G CommentsCircles Carry out calculations involving circumference and area of a
circle
Solve simple problems involving the arc length and sector area of a circle where the sector angle is a factor of 360deg
Surface area and volume
Carry out calculations involving
bull surface area and volume of a cuboid prism and cylinder (no formulae will be given for these shapes)
bull surface area and volume of a sphere pyramid and cone (formulae will be given for these shapes)
Areas and volumes of compound shapes
Carry out calculations involving the areas and volumes of compound shapes made from combinations of the shapes in Perimeter or Surface area and volume
Learner Guide
41
Core Trigonometry
Question type You should be able to R A G CommentsBearings Use and interpret three-figure bearings measured clockwise
from the North ie 000degndash360degTrigonometry Find unknown sides andor angles in right-angled triangles by
applying
bull Pythagorasrsquo theorem
bull sine cosine and tangent ratios for acute angles in right-angled triangles
Learner Guide
42
Core Vectors and transformations
Question type You should be able to R A G CommentsVectors in two dimensions (links to Trigonometry)
Describe a translation by using a vector represented by
AB or a
Add and subtract vectors
Multiply a vector by a scalar
Transformations Reflect simple shapes in horizontal or vertical lines
Rotate simple shapes through multiples of 90deg about
bull the origin
bull their vertices
bull the midpoints of their sides
Construct translations of simple shapes
Construct enlargements of simple shapes (positive and fractional scale factors)
Recognise and describe using the correct language
bull reflections
bull rotations
bull translations
bull enlargements (positive and fractional scale factors)
( )x
y
Learner Guide
43
Core Probability
Question type You should be able to R A G CommentsSingle events Calculate the probability of a single event as a fraction decimal
or percentage (not a ratio)Probability scale Understand and use the probability scale from 0 to 1
Sum to 1 Understand that the probability of an event occurring = 1 ndash the probability of the event not occurring
Relative frequency
Understand relative frequency as an estimate of probability
Work out expected frequencies using relative frequencyCombined events Calculate the probability of simple combined events using
bull tree diagrams
bull possibility diagrams (points on a grid)
bull Venn diagrams (2 sets only)
Learner Guide
44
Core Statistics
Question type What I need to do R A G CommentsClassify Collect classify and tabulate data
Interpret and compare
Read interpret and draw simple inferences from tables and statistical diagrams
Compare sets of data using
bull tables
bull graphs
bull statistical measures
Be aware of restrictions when making conclusions from data
Charts Construct and use
bull bar charts
bull pie charts
bull pictograms
bull stem-and-leaf diagrams
bull frequency distributions
bull histograms with equal intervals
bull scatter diagrams
Learner Guide
45
Question type What I need to do R A G CommentsAverages Calculate for individual and discrete data
bull mean
bull median
bull mode
bull range
and distinguish between their useCorrelation Understand what is meant by positive negative and zero
correlation with reference to a scatter diagramLine of best fit Draw interpret and use a ruled line of best fit by eye
Learner Guide
46
Extended syllabus content (includes required Core content)Extended Number
Question type You should be able to R A G CommentsNumber Identify and use
bull natural numbers
bull integers (positive negative and zero)
bull prime numbers
bull write a number as a product of its prime factors
bull square and cube numbers
bull common factors and highest common factor of two or more numbers
bull common multiples and lowest common multiple of two or more numbers
bull rational numbers
bull irrational numbers (eg π radic2 )
bull real numbers
bull reciprocals
Learner Guide
47
Extended Number
Question type You should be able to R A G CommentsSet notation and language
Use language notation and Venn diagrams to describe sets and represent relationships between sets as follows
Definition of sets egA = x x is a natural number
B = (xy) y = mx + c
C = x a ⩽ x ⩽ b
D = a b c hellip
Notation egnumber of elements in set A n(A)
lsquois an element ofrsquo isin
lsquois not an element ofrsquo notin
complement of set A
the empty set empty
the universal set
A is a subset of B A sube B
A is a proper subset of B A sub B
A is not a subset of B A ⊈ B
A is not a proper subset of B A nsub B
union of A and B A cup B
intersection of A and B A cap B
Learner Guide
48
Extended Number
Question type You should be able to R A G CommentsSquares square roots cubes and cube roots
Calculatebull squares of numbers
bull square roots of numbers
bull cubes of numbers
bull cube roots of numbers
bull other powers and roots of numbers
Directed numbers
Use directed numbers in practical situations for example temperature changes
Fractions decimals and percentages
Use the language and notation of simple vulgar and decimal fractions and percentages in appropriate contexts
Recognise equivalent fractions decimals and percentages
Convert between fractions decimals and percentages
Convert recurring decimals to fractions
Ordering Order quantities by magnitude and demonstrate familiarity with the symbols = ne gt lt ⩾ ⩽
Learner Guide
49
Extended Number
Question type You should be able to R A G CommentsIndices and standard form (links to Algebraic manipulation)
Evaluate indices including fractional negative and zero
eg 25 5ndash2 1000 10012 8ndash23
Use the rules of indices forbull multiplication of indices eg 43 times 45
bull division of indices eg 57 divide 53
bull index numbers raised to an index eg (43)2
Use the standard form A times 10n where n is a positive or negative integer and 1 ⩽ A lt 10bull convert into and out of standard form
bull calculate with numbers in standard form
Four rules
( + ndash times divide )
Use the four rules for calculations withbull whole numbers
bull decimals
bull vulgar and mixed fractions
bull correct ordering of operations (BIDMAS) and use of brackets
Learner Guide
50
Extended Number
Question type You should be able to R A G CommentsEstimates Make estimates of numbers quantities and lengths
Give approximations to a specified number of
bull significant figures
bull decimal places
Round off answers to reasonable accuracy in the context of a given problem
Bounds Give upper and lower bounds for data given to a specified accuracy eg measured lengths
Obtain appropriate upper and lower bounds to solutions of simple problems given to a specified accuracy eg the lower and upper bounds for the area of a rectangle
Ratio proportion rate
(links to Direct and inverse proportion)
Understand ratio
Divide quantities in a given ratio
Increase and decrease a quantity by a given ratio
Understand numerical problems involving direct and inverse proportion
Use ratio and scales in practical situations
Use common measures of rate (formulae for other rates eg density and pressure will be given in the question)
Calculate average speed
Learner Guide
51
Extended Number
Question type What I need to do R A G CommentsPercentages Calculate a percentage of a quantity
Express one quantity as a percentage of another quantity
Calculate percentage increase or decrease
Calculate reverse percentages eg finding the cost price given the selling price and the percentage profit
Use of an electronic calculator
Use a calculator efficiently
Check accuracy of calculations
Time Calculate times in terms of the 24-hour and 12-hour clock
Read clocks dials and timetables
Money Calculate using money
Convert from one currency to another
Learner Guide
52
Extended Number
Question type You should be able to R A G CommentsPersonal and small business finance
Use given data to solve problems on
bull earnings
bull simple interest
bull compound interest
ndash you must know the compound interest formula
bull discount
bull profit and loss
Extract data from tables and charts
Exponential growth and decay
Use exponential growth and decay in population and finance eg depreciation bacteria growth
Learner Guide
53
Extended Algebra and graphs
Question type You should be able to R A G CommentsBasic algebra Use letters to express generalised numbers
Express basic arithmetic processes algebraically
Substitute numbers in complicated formulae
Construct and rearrange complicated formulae eg where the subject appears twice
Algebraic manipulation
Manipulate directed numbers
Use bracketsbull expand a single bracket eg expand 3x(2x ndash 4y)
bull expand a pair of brackets eg (x ndash 4)(x + 7)
bull expand products of more than two brackets eg (x + 4)(x ndash 7)(2x + 1)
Extract common factors eg factorise 9x2 + 15xy
Factorise expressions of the formbull ax + bx + kay + kby
bull asup2xsup2 ndash bsup2ysup2
bull asup2 + 2ab + bsup2
bull axsup2 + bx + c
Learner Guide
54
Extended Algebra and graphs
Question type You should be able to R A G CommentsAlgebraic fractions
Manipulate algebraic fractions eg
bull
bull
bull
bull
bull
Factorise and simplify algebraic fractions such as
Rules of indices Use and interpret positive negative and zero indices
Use and interpret fractional indices eg solve 32x = 2
Use the rules of indices to simplify algebra eg
x3 + x ndash 4
22x3 +
3(x ndash 5)2
3a4 +
5ab3
3a4 divide
9a10
1x ndash 2 +
2x ndash 3
x2 ndash 2xx2 ndash 5x + 6
3xndash4 times23
x12
32x5( )
3
2xndash2divide25
x12
Learner Guide
55
Extended Algebra and graphs
Question type You should be able to R A G CommentsEquations and inequalities
bull Derive and solve simple linear equations in one unknown
bull Derive and solve simultaneous linear equations in two unknowns
bull Derive and solve simultaneous equations involving one linear and one quadratic
Solve quadratic equations by
bull factorisation
bull completing the square
bull using the formula
Derive and solve simple linear inequalities including representing solutions on a number line
Linear programming
Represent inequalities graphically including using the conventions of
bull broken lines for strict inequalities
bull shading unwanted regions
Solve simple linear programming problems using graphical representations of inequalities
Learner Guide
56
Extended Algebra and graphs
Question type You should be able to R A G CommentsNumber sequences (links to Squares square roots cubes and cube roots)
Continue a number sequence
Recognise patterns in sequences
Recognise relationships between different sequences
Find the nth term of sequences of
bull linear sequences
bull quadratic sequences
bull cubic sequences
bull exponential sequences
and simple combinations of these
Direct and inverse proportion (links to Ratio proportion rate)
Express direct proportion algebraically
Express inverse proportion algebraically
Use algebraic expressions of direct and inverse proportion to find unknown quantities
Practical graphs
(links to Coordinate geometry)
Interpret and use graphs in practical situations including
bull travel graphs
bull conversion graphs
Draw graphs from given data
Learner Guide
57
Extended Algebra and graphs
Question type You should be able to R A G CommentsPractical graphs (links to Coordinate geometry) continued
Apply the idea of rate of change to simple kinematics involving
bull distancendashtime graphs
bull speedndashtime graphs
bull acceleration and deceleration
This may involve estimation and interpretation of the gradient of a tangent at a point
Calculate distance travelled as an area under a linear speedndash time graph
Learner Guide
58
Extended Algebra and graphs
Question type You should be able to R A G CommentsGraphs of functions (links to Coordinate geometry)
Construct tables of values and draw graphs for functions of the form
bull axn where a is a rational constant and n = minus2 minus1 0 1 2 3 and simple sums of not more than three of these
bull abx + c where a and c are rational constants and b is a positive integer
Solve associated equations approximately by graphical methods including finding and interpreting roots and finding turning points of quadratics by completing the square
Draw and interpret graphs representing exponential growth and decay problems
Recognise sketch and interpret graphs of
bull linear
bull quadratic
bull cubic
bull reciprocal
bull exponential
(knowledge of turning points and asymtotes is required)Tangents Estimate gradients of curves by drawing tangents
Learner Guide
59
Extended Algebra and graphs
Question type You should be able to R A G CommentsFunctions Use function notation eg
f(x) = 3x ndash 5 f x α 3x ndash5 to describe simple functions
Find inverse functions f ndash1 (x)
Form composite functions as defined by gf(x) = g(f(x))
Derivatives Understand the idea of a derived function
Use derivatives of the form axn and simple sums of not more than three of these (a is a rational constant and n is a positive integer or 0)
Apply differentiation to gradients and turning points (stationary points)
Use any method to explain whether the turning point is a maximum or a minimum eg second derivative or gradient of function on either side of turning point
Learner Guide
60
Extended Co-ordinate geometry
Question type You should be able to R A G CommentsStraight line graphs
Work with co-ordinates in two dimensions
Gradient Find the gradient of a straight line graph
Calculate the gradient of a straight line from the co-ordinates of two points on it
Length and midpoint
Calculate the length and the co-ordinates of the midpoint of a straight line segment from the co-ordinates of its end points
Equation of line Interpret and obtain the equation of a straight line graph
Parallel lines Determine the equation of a straight line parallel to a given line eg find the equation of a line parallel to y = 4x ndash 1 that passes through (0 ndash3)
Perpendicular lines
Find the gradient of parallel and perpendicular lines eg
bull find the gradient of a line perpendicular to y = 3x + 1
bull find the equation of a line perpendicular to one passing through the co-ordinates (1 3) and (ndash2 ndash9)
Learner Guide
61
Extended Geometry
Question type You should be able to R A G CommentsGeometrical language
Use and interpret the geometrical terms
bull point
bull line
bull parallel
bull perpendicular
bull bearing
bull right angle acute obtuse and reflex angles
bull similar
bull congruent
Use and interpret the vocabulary of
bull triangles right-angled scalene isosceles equilateral
bull quadrilaterals
bull circles
bull polygons
bull simple solid figures including nets
Learner Guide
62
Extended Geometry
Question type What I need to do R A G CommentsGeometrical constructions
Measure and draw lines and angles
Construct a triangle given the three sides using a ruler and a pair of compasses only
Scale drawings Read and make scale drawings
Similar figures Calculate lengths of similar figures
Use relationships between areas of similar triangles and in similar figures
Use relationships between volumes and surface areas of similar solids
Congruent triangles
Use the congruence criteria for triangles (SSS ASA SAS RHS)
Symmetry Recognise symmetry properties for triangles quadrilaterals and circles
Recognise line symmetry in two dimensions
Recognise and find the order of rotational symmetry in two dimensions
Learner Guide
63
Extended Geometry
Question type You should be able to R A G CommentsSymmetry (continued)
Use the following symmetry properties of circles
bull equal chords are equidistant from the centre
bull perpendicular bisector of a chord passes through the centre
bull tangents from an external point are equal in length
Recognise and use symmetry properties of
bull prism cylinder cone and pyramid
Learner Guide
64
Extended Geometry
Question type You should be able to R A G CommentsAngle properties Calculate unknown angles explaining the properties that
you are using in geometrical language for the following geometrical properties
bull angles at a point
bull angles at a point on a straight line and intersecting straight lines
bull angles formed within parallel lines
bull angle properties of triangles and quadrilaterals
bull angle properties of regular polygons
bull angle in a semi-circle
bull angle between tangent and radius of a circle
bull angles properties of irregular polygons
bull angle at the centre of a circle is twice the angle at the circumference
bull angles in the same segment are equal
bull angles in opposite segments are supplementary cyclic quadrilaterals
bull alternate segment theorem
Learner Guide
65
Extended Mensuration
Question type What I need to do R A G CommentsMeasures Use current units of
bull mass
bull length
bull area
bull volume
bull capacity
Express quantities in terms of smaller or larger units including units of area and volume
Perimeter Carry out calculations involving
bull perimeter and area of a rectangle
bull perimeter and area of a triangle
bull perimeter and area of parallelogram
bull perimeter and area of a trapezium
bull perimeter and area of compound shapes made by combining rectangles triangles parallelograms andor trapeziums
Learner Guide
66
Extended Mensuration
Question type You should be able to R A G CommentsCircles Carry out calculations involving circumference and area of a
circle
Solve problems involving arc length and sector area of a circle
Surface area and volume
Carry out calculations involving
bull surface area and volume of a cuboid prism and cylinder (no formulae will be given for these shapes)
bull surface area and volume of a sphere pyramid and cone (formulae will be given for these shapes)
Compound shapes
Carry out calculations involving
bull area of a shape made by combining cuboids prisms andor cylinders
bull volume of a shape made by combining cuboids prisms andor cylinders
Learner Guide
67
Extended Trigonometry
Question type You should be able to R A G CommentsBearings Use and interpret three-figure bearings measured clockwise
from the North ie 000degndash360degTrigonometry Find unknown sides andor angles in right-angled triangles by
applying
bull Pythagorasrsquo theorem
bull sine cosine and tangent ratios for acute angles in right-angled triangles
Solve problems in two dimensions involving angles of elevation and depression
Know that the perpendicular distance from a point to a line is the shortest distance to the line
Trig graphs and equations
Recognise sketch and interpret graphs of simple trigonometric functions
Graph and know the properties of trigonometric functions
Solve simple trigonometric equations for values between 0deg
and 360deg eg Solve sin x = radic32
for values of x between 0deg and
360degGeneral trig Solve problems using sine and cosine rules for any triangle
Find the area of any triangle using frac12absinC
Trig in 3D Solve simple trigonometrical problems in three dimensions including angle between a line and a plane
Learner Guide
68
Extended Vectors and transformations
Question type You should be able to R A G CommentsVectors in two dimensions (links to Trigonometry)
Describe a translation by using a vector represented by
AB or a
Add and subtract vectors
Multiply a vector by a scalar
Transformations Reflect simple shapes in horizontal or vertical lines
Rotate simple shapes through multiples of 90deg about any point
Construct translations of simple shapes
Construct enlargements of simple shapes (positive fractional and negative scale factors)
Recognise and describe
bull reflections
bull rotations
bull translations
bull enlargements (positive fractional and negative scalefactors)
( )x
y
Learner Guide
69
Extended Vectors and transformations
Question type You should be able to R A G CommentsHarder vectors
Calculate the magnitude of a vector as and
understand that magnitude is denoted by modulus signs |A B| or |a|
Represent vectors by directed line segments
Use the sum and difference of two vectors
Use position vectors
( )x
yradicx2 + y2
Learner Guide
70
Extended Probability
Question type You should be able to R A G CommentsProbability (links to Four rules)
Calculate the probability of a single event as a fraction decimal or percentage (not a ratio)
Probability scale Understand and use the probability scale from 0 to 1
Sum to 1 Understand that the probability of an event occurring = 1 ndash the probability of the event not occurring
Relative frequency
Understand relative frequency as an estimate of probability
Work out expected frequencies using relative frequency
Combined events Calculate the probability of combined events using
bull tree diagrams
bull possibility diagrams
bull tables
Learner Guide
71
Extended Statistics
Question type You should be able to R A G CommentsClassify Collect classify and tabulate data
Interpret and compare
Read interpret and draw simple inferences from tables and statistical diagrams
Compare sets of data using
bull tables
bull graphs
bull statistical measures
Be aware of restrictions when making conclusions from data
Charts Construct and use
bull bar charts
bull pie charts
bull pictograms
bull stem ndash and ndash leaf diagrams
bull frequency distributions
bull histograms with equal and unequal intervals
bull scatter diagrams
Learner Guide
72
Extended Statistics
Question type You should be able to R A G CommentsAverages Calculate for individual and discrete data
bull mean
bull median
bull mode
bull range
and distinguish between their use
Estimated mean Calculate an estimate of the mean for grouped and continuous data
Identify the modal class from a grouped frequency distributionCumulative frequency
Construct and use cumulative frequency diagrams to estimate and interpret
bull the median
bull percentiles
bull quartiles
bull inter-quartile range
Construct and interpret box-and-whisker plots
Correlation Understand what is meant by positive negative and zero correlation with reference to a scatter diagram
Lines of best fit Draw interpret and use a ruled line of best fit by eye
Cambridge Assessment International Education1 Hills Road Cambridge CB1 2EU United Kingdomt +44 1223 553554e infocambridgeinternationalorg wwwcambridgeinternationalorg
Copyright copy UCLES October 2017
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- Check Box 10125 Off
- Check Box 10126 Off
- Text Field 289
- Check Box 101020 Off
- Check Box 101021 Off
- Check Box 101022 Off
- Check Box 101023 Off
- Check Box 101024 Off
- Check Box 101025 Off
- Check Box 10127 Off
- Check Box 10128 Off
- Check Box 10129 Off
- Check Box 10130 Off
- Check Box 10131 Off
- Check Box 10132 Off
- Text Field 290
- Check Box 101026 Off
- Check Box 101027 Off
- Check Box 101028 Off
- Check Box 101029 Off
- Check Box 101030 Off
- Check Box 101031 Off
- Check Box 10133 Off
- Check Box 10134 Off
- Check Box 10135 Off
- Check Box 10136 Off
- Check Box 10137 Off
- Check Box 10138 Off
- Text Field 291
- Check Box 10139 Off
- Check Box 10140 Off
- Check Box 101016 Off
- Check Box 101017 Off
- Check Box 101018 Off
- Check Box 101032 Off
- Text Field 292
- Check Box 101036 Off
- Check Box 101037 Off
- Check Box 101038 Off
- Check Box 101039 Off
- Check Box 101040 Off
- Check Box 101041 Off
- Check Box 10150 Off
- Check Box 10151 Off
- Check Box 10152 Off
- Check Box 10153 Off
- Check Box 10154 Off
- Check Box 10155 Off
- Check Box 101042 Off
- Check Box 101043 Off
- Check Box 101044 Off
- Check Box 101045 Off
- Check Box 101046 Off
- Check Box 101047 Off
- Text Field 293
- Check Box 10156 Off
- Check Box 10157 Off
- Check Box 10158 Off
- Check Box 10159 Off
- Check Box 10160 Off
- Check Box 10161 Off
- Check Box 101048 Off
- Check Box 101049 Off
- Check Box 101050 Off
- Check Box 10162 Off
- Check Box 10163 Off
- Check Box 10164 Off
- Text Field 294
- Check Box 101052 Off
- Check Box 101053 Off
- Check Box 101054 Off
- Check Box 101055 Off
- Check Box 101056 Off
- Check Box 101057 Off
- Check Box 1010263 Off
- Check Box 1010264 Off
- Check Box 10165 Off
- Check Box 10166 Off
- Check Box 10167 Off
- Check Box 101058 Off
- Check Box 101059 Off
- Check Box 101060 Off
- Check Box 1010269 Off
- Check Box 1010270 Off
- Text Field 357
- Check Box 1010271 Off
- Check Box 1010272 Off
- Check Box 1010273 Off
- Text Field 358
- Check Box 1010274 Off
- Check Box 1010330 Off
- Check Box 1010331 Off
- Text Field 359
- Check Box 1010343 Off
- Check Box 1010344 Off
- Check Box 1010345 Off
- Text Field 360
- Check Box 1010348 Off
- Check Box 1010349 Off
- Check Box 1010350 Off
- Text Field 297
- Check Box 101061 Off
- Check Box 101062 Off
- Check Box 101063 Off
- Check Box 101064 Off
- Check Box 101065 Off
- Check Box 101066 Off
- Check Box 10168 Off
- Check Box 10169 Off
- Check Box 10170 Off
- Check Box 10171 Off
- Check Box 10172 Off
- Check Box 10173 Off
- Check Box 101067 Off
- Check Box 101068 Off
- Check Box 101069 Off
- Check Box 10174 Off
- Check Box 10175 Off
- Check Box 10176 Off
- Check Box 10177 Off
- Check Box 10178 Off
- Check Box 10179 Off
- Check Box 101070 Off
- Check Box 101071 Off
- Check Box 101072 Off
- Check Box 10180 Off
- Check Box 10181 Off
- Check Box 10182 Off
- Check Box 101073 Off
- Check Box 101074 Off
- Check Box 101075 Off
- Check Box 10183 Off
- Check Box 10184 Off
- Check Box 10185 Off
- Check Box 10186 Off
- Check Box 10187 Off
- Check Box 10235 Off
- Check Box 101076 Off
- Check Box 101077 Off
- Check Box 101078 Off
- Text Field 298
- Check Box 101079 Off
- Check Box 101080 Off
- Check Box 101081 Off
- Check Box 101082 Off
- Check Box 101083 Off
- Check Box 101084 Off
- Text Field 299
- Check Box 101088 Off
- Check Box 101089 Off
- Check Box 101090 Off
- Text Field 300
- Check Box 101091 Off
- Check Box 101092 Off
- Check Box 101093 Off
- Check Box 1010351 Off
- Check Box 1010352 Off
- Check Box 1010353 Off
- Text Field 301
- Check Box 10242 Off
- Check Box 10243 Off
- Check Box 10244 Off
- Check Box 101094 Off
- Check Box 101095 Off
- Check Box 101096 Off
- Check Box 101097 Off
- Check Box 101098 Off
- Check Box 101099 Off
- Text Field 302
- Check Box 1010103 Off
- Check Box 1010104 Off
- Check Box 1010105 Off
- Check Box 10245 Off
- Check Box 10246 Off
- Check Box 10247 Off
- Check Box 10248 Off
- Check Box 10249 Off
- Check Box 10250 Off
- Check Box 1010106 Off
- Check Box 1010107 Off
- Check Box 1010108 Off
- Check Box 1010109 Off
- Check Box 1010110 Off
- Check Box 1010111 Off
- Check Box 1010112 Off
- Check Box 1010113 Off
- Check Box 1010114 Off
- Check Box 10251 Off
- Check Box 10252 Off
- Check Box 10253 Off
- Check Box 1010115 Off
- Check Box 1010116 Off
- Check Box 1010117 Off
- Text Field 303
- Check Box 10260 Off
- Check Box 10261 Off
- Check Box 10262 Off
- Check Box 10101017 Off
- Check Box 10101018 Off
- Check Box 10101019 Off
- Check Box 10101020 Off
- Check Box 1010118 Off
- Check Box 1010119 Off
- Check Box 1010120 Off
- Check Box 1010126 Off
- Check Box 1010127 Off
- Check Box 10263 Off
- Check Box 10264 Off
- Check Box 10265 Off
- Check Box 10269 Off
- Check Box 10270 Off
- Check Box 10271 Off
- Check Box 10101025 Off
- Check Box 10101026 Off
- Check Box 10101027 Off
- Text Field 306
- Check Box 10266 Off
- Check Box 10267 Off
- Check Box 10268 Off
- Check Box 10101021 Off
- Check Box 10101022 Off
- Check Box 10101023 Off
- Check Box 10101024 Off
- Check Box 1010131 Off
- Check Box 1010132 Off
- Check Box 1010133 Off
- Check Box 1010134 Off
- Check Box 1010135 Off
- Check Box 1010136 Off
- Check Box 1010137 Off
- Check Box 1010138 Off
- Text Field 3025
- Check Box 10367 Off
- Check Box 10368 Off
- Check Box 10369 Off
- Check Box 10407 Off
- Check Box 10431 Off
- Check Box 10432 Off
- Text Field 3059
- Check Box 104010 Off
- Check Box 10433 Off
- Check Box 10465 Off
- Check Box 104011 Off
- Check Box 10466 Off
- Check Box 10527 Off
- Text Field 3060
- Check Box 104012 Off
- Check Box 10528 Off
- Check Box 10529 Off
- Text Field 3063
- Check Box 10101037 Off
- Check Box 10101038 Off
- Check Box 10101039 Off
- Text Field 309
- Check Box 10275 Off
- Check Box 10276 Off
- Check Box 10277 Off
- Check Box 10101040 Off
- Check Box 10101041 Off
- Check Box 10101042 Off
- Text Field 3010
- Check Box 10278 Off
- Check Box 10279 Off
- Check Box 10280 Off
- Check Box 10101044 Off
- Check Box 10101045 Off
- Check Box 10101046 Off
- Check Box 10101047 Off
- Check Box 1010141 Off
- Check Box 1010142 Off
- Text Field 3011
- Check Box 10281 Off
- Check Box 10282 Off
- Check Box 10283 Off
- Check Box 10101048 Off
- Check Box 10101049 Off
- Check Box 10101050 Off
- Check Box 10101051 Off
- Check Box 10101052 Off
- Check Box 10101053 Off
- Check Box 10101054 Off
- Check Box 10101055 Off
- Check Box 10101056 Off
- Check Box 10101057 Off
- Check Box 10101058 Off
- Check Box 10101059 Off
- Check Box 10101060 Off
- Check Box 10101061 Off
- Check Box 10101062 Off
- Check Box 10101063 Off
- Check Box 10101064 Off
- Check Box 10101065 Off
- Check Box 10101066 Off
- Check Box 10101067 Off
- Check Box 10101068 Off
- Check Box 10101069 Off
- Check Box 10101070 Off
- Check Box 10101071 Off
- Check Box 10101072 Off
- Check Box 10101073 Off
- Check Box 10101074 Off
- Text Field 3012
- Check Box 10284 Off
- Check Box 10285 Off
- Check Box 10286 Off
- Text Field 3013
- Check Box 10101075 Off
- Check Box 10101076 Off
- Check Box 10101077 Off
- Text Field 3014
- Check Box 10101078 Off
- Check Box 1010143 Off
- Check Box 1010144 Off
- Text Field 3015
- Check Box 10287 Off
- Check Box 10288 Off
- Check Box 10289 Off
- Check Box 10334 Off
- Check Box 10335 Off
- Check Box 10336 Off
- Check Box 10371 Off
- Check Box 10372 Off
- Check Box 10436 Off
- Check Box 10437 Off
- Check Box 10438 Off
- Check Box 10447 Off
- Text Field 3016
- Check Box 10401 Off
- Check Box 10402 Off
- Check Box 10403 Off
- Check Box 10291 Off
- Check Box 10292 Off
- Check Box 10337 Off
- Check Box 10448 Off
- Check Box 10449 Off
- Check Box 10456 Off
- Check Box 10457 Off
- Check Box 10458 Off
- Check Box 10533 Off
- Check Box 10534 Off
- Check Box 10535 Off
- Check Box 10543 Off
- Check Box 10544 Off
- Check Box 10740 Off
- Check Box 10741 Off
- Text Field 3017
- Check Box 10101079 Off
- Check Box 10101080 Off
- Check Box 10101081 Off
- Check Box 10101082 Off
- Check Box 1010145 Off
- Check Box 1010146 Off
- Check Box 10293 Off
- Check Box 10294 Off
- Check Box 10295 Off
- Check Box 10338 Off
- Check Box 10339 Off
- Check Box 10370 Off
- Check Box 10101083 Off
- Check Box 10101084 Off
- Check Box 10101085 Off
- Check Box 10101086 Off
- Check Box 1010147 Off
- Check Box 1010148 Off
- Check Box 10296 Off
- Check Box 10297 Off
- Check Box 10298 Off
- Text Field 3018
- Check Box 10299 Off
- Check Box 10300 Off
- Check Box 10301 Off
- Check Box 10101087 Off
- Check Box 10101088 Off
- Check Box 10101089 Off
- Check Box 10101090 Off
- Check Box 1010149 Off
- Check Box 1010150 Off
- Check Box 10302 Off
- Check Box 10303 Off
- Check Box 10304 Off
- Text Field 3019
- Check Box 10305 Off
- Check Box 10306 Off
- Check Box 10307 Off
- Text Field 3020
- Check Box 10308 Off
- Check Box 10309 Off
- Check Box 103010 Off
- Text Field 311
- Check Box 10141 Off
- Check Box 10142 Off
- Check Box 10143 Off
- Check Box 10144 Off
- Check Box 10145 Off
- Check Box 10149 Off
- Check Box 10257 Off
- Check Box 10258 Off
- Check Box 10259 Off
- Check Box 10310 Off
- Check Box 10311 Off
- Check Box 10312 Off
- Check Box 10331 Off
- Check Box 10332 Off
- Check Box 10333 Off
- Check Box 10313 Off
- Check Box 10314 Off
- Check Box 10315 Off
- Check Box 10316 Off
- Check Box 10317 Off
- Check Box 10318 Off
- Check Box 10319 Off
- Check Box 10320 Off
- Check Box 10321 Off
- Check Box 10322 Off
- Check Box 10323 Off
- Check Box 10324 Off
- Check Box 10325 Off
- Check Box 10326 Off
- Check Box 10327 Off
- Check Box 10399 Off
- Check Box 10400 Off
- Check Box 10530 Off
- Text Field 335
- Check Box 10567 Off
- Check Box 10568 Off
- Check Box 10569 Off
- Check Box 10570 Off
- Check Box 10571 Off
- Check Box 10572 Off
- Check Box 10573 Off
- Check Box 10574 Off
- Check Box 10575 Off
- Check Box 10576 Off
- Check Box 10577 Off
- Check Box 10578 Off
- Check Box 10597 Off
- Check Box 10598 Off
- Check Box 10599 Off
- Check Box 10579 Off
- Check Box 10580 Off
- Check Box 10581 Off
- Check Box 10582 Off
- Check Box 10583 Off
- Check Box 10584 Off
- Check Box 10585 Off
- Check Box 10586 Off
- Check Box 10587 Off
- Check Box 10588 Off
- Check Box 10589 Off
- Check Box 10590 Off
- Check Box 10591 Off
- Check Box 10592 Off
- Check Box 10593 Off
- Check Box 10594 Off
- Check Box 10595 Off
- Check Box 10596 Off
- Check Box 10600 Off
- Check Box 10601 Off
- Check Box 10602 Off
- Check Box 10603 Off
- Check Box 10604 Off
- Check Box 10605 Off
- Check Box 10606 Off
- Check Box 10607 Off
- Check Box 10608 Off
- Check Box 10609 Off
- Check Box 106010 Off
- Check Box 106011 Off
- Check Box 106012 Off
- Check Box 106013 Off
- Check Box 106014 Off
- Check Box 106015 Off
- Check Box 106016 Off
- Check Box 106017 Off
- Text Field 315
- Check Box 10340 Off
- Check Box 10341 Off
- Check Box 10342 Off
- Check Box 10343 Off
- Check Box 10344 Off
- Check Box 10345 Off
- Check Box 10346 Off
- Check Box 10347 Off
- Check Box 10348 Off
- Check Box 10349 Off
- Check Box 10350 Off
- Check Box 10351 Off
- Check Box 10531 Off
- Check Box 10532 Off
- Check Box 10542 Off
- Text Field 313
- Check Box 10352 Off
- Check Box 10353 Off
- Check Box 10354 Off
- Text Field 316
- Check Box 10355 Off
- Check Box 10356 Off
- Check Box 10357 Off
- Check Box 10358 Off
- Check Box 10359 Off
- Check Box 10360 Off
- Check Box 10361 Off
- Check Box 10362 Off
- Check Box 10363 Off
- Check Box 10364 Off
- Check Box 10365 Off
- Check Box 10366 Off
- Check Box 10404 Off
- Check Box 10405 Off
- Check Box 10406 Off
- Text Field 352
- Check Box 102021 Off
- Check Box 102022 Off
- Check Box 102040 Off
- Check Box 102041 Off
- Check Box 102042 Off
- Check Box 102043 Off
- Check Box 102044 Off
- Check Box 102045 Off
- Check Box 102046 Off
- Check Box 102047 Off
- Check Box 102048 Off
- Check Box 102049 Off
- Check Box 102050 Off
- Check Box 102051 Off
- Check Box 102052 Off
- Check Box 102065 Off
- Check Box 102066 Off
- Check Box 102067 Off
- Check Box 102053 Off
- Check Box 102054 Off
- Check Box 102055 Off
- Text Field 351
- Check Box 102056 Off
- Check Box 102057 Off
- Check Box 102058 Off
- Check Box 102059 Off
- Check Box 102060 Off
- Check Box 102061 Off
- Check Box 102062 Off
- Check Box 102063 Off
- Check Box 102064 Off
- Check Box 102068 Off
- Check Box 102069 Off
- Check Box 102070 Off
- Text Field 318
- Check Box 10373 Off
- Check Box 10374 Off
- Check Box 10375 Off
- Check Box 10376 Off
- Check Box 10377 Off
- Check Box 10378 Off
- Check Box 10379 Off
- Check Box 10380 Off
- Check Box 10381 Off
- Check Box 10382 Off
- Check Box 10383 Off
- Check Box 10384 Off
- Check Box 10385 Off
- Check Box 10386 Off
- Check Box 10387 Off
- Text Field 317
- Check Box 10388 Off
- Check Box 10389 Off
- Check Box 10390 Off
- Check Box 102023 Off
- Check Box 102024 Off
- Check Box 102025 Off
- Check Box 102026 Off
- Check Box 102027 Off
- Check Box 102028 Off
- Check Box 102071 Off
- Check Box 102072 Off
- Check Box 102073 Off
- Check Box 102029 Off
- Check Box 10391 Off
- Check Box 10392 Off
- Check Box 10393 Off
- Check Box 10394 Off
- Check Box 10395 Off
- Check Box 10396 Off
- Check Box 10397 Off
- Check Box 10398 Off
- Check Box 102030 Off
- Check Box 102031 Off
- Check Box 102032 Off
- Text Field 319
- Text Field 322
- Check Box 10408 Off
- Check Box 10409 Off
- Check Box 10410 Off
- Check Box 10411 Off
- Check Box 10412 Off
- Check Box 10413 Off
- Check Box 10414 Off
- Check Box 10415 Off
- Check Box 10416 Off
- Check Box 10417 Off
- Check Box 10418 Off
- Check Box 10419 Off
- Text Field 321
- Check Box 10420 Off
- Check Box 10421 Off
- Check Box 10422 Off
- Check Box 10423 Off
- Check Box 10424 Off
- Check Box 10425 Off
- Text Field 337
- Check Box 102033 Off
- Check Box 102034 Off
- Check Box 102035 Off
- Check Box 102036 Off
- Check Box 102037 Off
- Check Box 102038 Off
- Text Field 338
- Check Box 102039 Off
- Check Box 10426 Off
- Check Box 10427 Off
- Check Box 10428 Off
- Check Box 10429 Off
- Check Box 10430 Off
- Text Field 324
- Check Box 10434 Off
- Check Box 10435 Off
- Check Box 101051 Off
- Check Box 1010100 Off
- Check Box 1010101 Off
- Check Box 1010102 Off
- Check Box 1010128 Off
- Check Box 1010129 Off
- Check Box 1010130 Off
- Check Box 10439 Off
- Check Box 10440 Off
- Check Box 10441 Off
- Check Box 10442 Off
- Check Box 10443 Off
- Check Box 10444 Off
- Text Field 350
- Check Box 10742 Off
- Check Box 10743 Off
- Check Box 10744 Off
- Text Field 325
- Check Box 10445 Off
- Check Box 10446 Off
- Check Box 1010151 Off
- Check Box 1010152 Off
- Check Box 1010153 Off
- Check Box 1010154 Off
- Check Box 1010155 Off
- Check Box 1010156 Off
- Check Box 1010157 Off
- Check Box 10450 Off
- Check Box 10451 Off
- Check Box 10452 Off
- Text Field 326
- Check Box 1010158 Off
- Check Box 1010159 Off
- Check Box 1010160 Off
- Check Box 1010161 Off
- Check Box 1010162 Off
- Check Box 1010163 Off
- Check Box 10453 Off
- Check Box 10454 Off
- Check Box 10455 Off
- Check Box 10745 Off
- Check Box 10746 Off
- Check Box 10747 Off
- Check Box 10748 Off
- Check Box 10749 Off
- Check Box 10750 Off
- Check Box 1010167 Off
- Check Box 1010168 Off
- Check Box 1010169 Off
- Check Box 10459 Off
- Check Box 10460 Off
- Check Box 10461 Off
- Check Box 10462 Off
- Check Box 10463 Off
- Check Box 10464 Off
- Check Box 10611 Off
- Check Box 10612 Off
- Check Box 10613 Off
- Text Field 329
- Check Box 1010171 Off
- Check Box 1010172 Off
- Check Box 1010173 Off
- Check Box 1010174 Off
- Check Box 1010175 Off
- Check Box 1010176 Off
- Check Box 1010177 Off
- Check Box 1010178 Off
- Check Box 1010179 Off
- Check Box 10467 Off
- Check Box 10468 Off
- Check Box 10469 Off
- Check Box 10470 Off
- Check Box 10471 Off
- Check Box 10472 Off
- Check Box 1010180 Off
- Check Box 1010181 Off
- Check Box 1010182 Off
- Text Field 330
- Check Box 1010183 Off
- Check Box 1010184 Off
- Check Box 1010185 Off
- Check Box 10473 Off
- Check Box 10474 Off
- Check Box 10475 Off
- Check Box 10476 Off
- Check Box 10477 Off
- Check Box 10478 Off
- Check Box 1010186 Off
- Check Box 1010187 Off
- Check Box 1010188 Off
- Check Box 1010275 Off
- Check Box 1010276 Off
- Check Box 1010277 Off
- Text Field 331
- Check Box 1010189 Off
- Check Box 1010190 Off
- Check Box 1010191 Off
- Check Box 1010192 Off
- Check Box 1010193 Off
- Check Box 1010194 Off
- Check Box 1010354 Off
- Check Box 1010355 Off
- Check Box 1010356 Off
- Check Box 10479 Off
- Check Box 10480 Off
- Check Box 10481 Off
- Check Box 10482 Off
- Check Box 10483 Off
- Check Box 10484 Off
- Check Box 1010195 Off
- Check Box 1010196 Off
- Check Box 1010197 Off
- Check Box 1010278 Off
- Check Box 1010279 Off
- Check Box 1010280 Off
- Text Field 339
- Check Box 10614 Off
- Check Box 10615 Off
- Check Box 10616 Off
- Check Box 10617 Off
- Check Box 10618 Off
- Check Box 10619 Off
- Check Box 1010281 Off
- Check Box 1010282 Off
- Check Box 1010283 Off
- Text Field 340
- Check Box 1010284 Off
- Check Box 1010285 Off
- Check Box 1010286 Off
- Check Box 1010287 Off
- Check Box 1010288 Off
- Check Box 1010289 Off
- Check Box 10620 Off
- Check Box 10621 Off
- Check Box 10622 Off
- Check Box 10623 Off
- Check Box 10624 Off
- Check Box 10625 Off
- Check Box 1010290 Off
- Check Box 1010291 Off
- Check Box 1010292 Off
- Check Box 1010293 Off
- Check Box 1010294 Off
- Check Box 1010295 Off
- Check Box 10626 Off
- Check Box 10627 Off
- Check Box 10628 Off
- Check Box 10751 Off
- Check Box 10752 Off
- Check Box 10753 Off
- Text Field 342
- Check Box 1010296 Off
- Check Box 1010297 Off
- Check Box 1010298 Off
- Check Box 10632 Off
- Check Box 10633 Off
- Check Box 10634 Off
- Check Box 10635 Off
- Check Box 10636 Off
- Check Box 10637 Off
- Text Field 349
- Check Box 1010305 Off
- Check Box 1010306 Off
- Check Box 1010307 Off
- Check Box 1010308 Off
- Check Box 1010309 Off
- Check Box 10103010 Off
- Check Box 10641 Off
- Check Box 10642 Off
- Check Box 10643 Off
- Text Field 343
- Check Box 1010299 Off
- Check Box 1010300 Off
- Check Box 1010301 Off
- Check Box 1010302 Off
- Check Box 1010303 Off
- Check Box 1010304 Off
- Check Box 10638 Off
- Check Box 10639 Off
- Check Box 10640 Off
- Check Box 10644 Off
- Check Box 10645 Off
- Check Box 10646 Off
- Check Box 1010328 Off
- Check Box 10103012 Off
- Check Box 10103013 Off
- Check Box 10103014 Off
- Check Box 10103015 Off
- Check Box 10103016 Off
- Check Box 10648 Off
- Check Box 10649 Off
- Check Box 10650 Off
- Check Box 10651 Off
- Check Box 10652 Off
- Check Box 10653 Off
- Check Box 10654 Off
- Check Box 10755 Off
- Check Box 10756 Off
- Check Box 10757 Off
- Check Box 10758 Off
- Check Box 10759 Off
- Check Box 10760 Off
- Check Box 10761 Off
- Check Box 10762 Off
- Check Box 10763 Off
- Check Box 10764 Off
- Check Box 10765 Off
- Check Box 10766 Off
- Check Box 10767 Off
- Check Box 10768 Off
- Text Field 361
- Check Box 10103020 Off
- Check Box 10103021 Off
- Check Box 10103022 Off
- Text Field 362
- Text Field 371
- Check Box 10103018 Off
- Check Box 10103019 Off
- Check Box 10103059 Off
- Check Box 10655 Off
- Check Box 10656 Off
- Check Box 10657 Off
- Check Box 10658 Off
- Check Box 10673 Off
- Check Box 10754 Off
- Text Field 363
- Check Box 10103023 Off
- Check Box 10103024 Off
- Check Box 10103025 Off
- Check Box 10103026 Off
- Check Box 10103027 Off
- Check Box 10103028 Off
- Check Box 10103029 Off
- Check Box 10103030 Off
- Check Box 10103031 Off
- Check Box 10103032 Off
- Check Box 10103033 Off
- Check Box 10103034 Off
- Text Field 365
- Check Box 10103035 Off
- Check Box 10103036 Off
- Check Box 10103037 Off
- Text Field 366
- Check Box 10103038 Off
- Check Box 10103039 Off
- Check Box 10103040 Off
- Check Box 10103041 Off
- Check Box 10103042 Off
- Check Box 10103043 Off
- Text Field 367
- Check Box 10103044 Off
- Check Box 10103045 Off
- Check Box 10103046 Off
- Text Field 368
- Check Box 10103047 Off
- Check Box 10103048 Off
- Check Box 10103049 Off
- Text Field 369
- Check Box 10103050 Off
- Check Box 10103051 Off
- Check Box 10103052 Off
- Text Field 370
- Check Box 10103053 Off
- Check Box 10103054 Off
- Check Box 10103055 Off
- Check Box 10103056 Off
- Check Box 10103057 Off
- Check Box 10103058 Off
- Text Field 332
- Check Box 1010198 Off
- Check Box 1010199 Off
- Check Box 1010200 Off
- Check Box 1010201 Off
- Check Box 1010202 Off
- Check Box 1010203 Off
- Check Box 10485 Off
- Check Box 10486 Off
- Check Box 10487 Off
- Check Box 10488 Off
- Check Box 10489 Off
- Check Box 10490 Off
- Check Box 1010204 Off
- Check Box 1010205 Off
- Check Box 1010206 Off
- Check Box 10491 Off
- Check Box 10492 Off
- Check Box 10493 Off
- Check Box 10494 Off
- Check Box 10495 Off
- Check Box 10496 Off
- Check Box 1010207 Off
- Check Box 1010208 Off
- Check Box 1010209 Off
- Check Box 10497 Off
- Check Box 10498 Off
- Check Box 10499 Off
- Check Box 1010210 Off
- Check Box 1010211 Off
- Check Box 1010212 Off
- Check Box 10500 Off
- Check Box 10501 Off
- Check Box 10502 Off
- Check Box 10503 Off
- Check Box 10504 Off
- Check Box 10505 Off
- Check Box 1010213 Off
- Check Box 1010214 Off
- Check Box 1010215 Off
- Text Field 333
- Check Box 1010216 Off
- Check Box 1010217 Off
- Check Box 1010218 Off
- Check Box 1010219 Off
- Check Box 1010220 Off
- Check Box 1010221 Off
- Text Field 334
- Check Box 1010225 Off
- Check Box 1010226 Off
- Check Box 1010227 Off
- Text Field 3022
- Text Field 3021
- Check Box 1010228 Off
- Check Box 1010229 Off
- Check Box 1010230 Off
- Check Box 10512 Off
- Check Box 10513 Off
- Check Box 10514 Off
- Check Box 1010231 Off
- Check Box 1010232 Off
- Check Box 1010233 Off
- Check Box 1010310 Off
- Text Field 3044
- Check Box 1010234 Off
- Check Box 1010235 Off
- Check Box 1010236 Off
- Check Box 1010332 Off
- Check Box 1010333 Off
- Check Box 1010334 Off
- Check Box 1010335 Off
- Check Box 1010336 Off
- Check Box 1010337 Off
- Text Field 347
- Check Box 1010311 Off
- Check Box 1010312 Off
- Check Box 1010313 Off
- Check Box 1010314 Off
- Check Box 1010315 Off
- Check Box 1010316 Off
- Check Box 105010 Off
- Check Box 105011 Off
- Check Box 105012 Off
- Check Box 105013 Off
- Check Box 10659 Off
- Check Box 10660 Off
- Text Field 3023
- Check Box 10101014 Off
- Check Box 10101015 Off
- Check Box 10101016 Off
- Check Box 10515 Off
- Check Box 10516 Off
- Check Box 10517 Off
- Check Box 10518 Off
- Check Box 10519 Off
- Check Box 10520 Off
- Check Box 10101091 Off
- Check Box 10101092 Off
- Check Box 10101093 Off
- Check Box 10101094 Off
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- Check Box 101010110 Off
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4
This guide introduces you to your Cambridge IGCSE Mathematics course and how you will be assessed You should use this guide alongside the support of your teacher
It will help you to
9 understand what skills you should develop by taking this course
9 understand how you will be assessed
9 understand what we are looking for in the answers you write
9 plan your revision programme
9 revise by providing revision tips and an interactive revision checklist (Section 6)
About this guide
Key benefits
The course will help you to build your skills and knowledge across a range of mathematical techniques You will be able to develop your problem solving and reasoning skills in a variety of situations
The Extended course will provide you with a strong foundation to continue to study mathematics qualifications beyond IGCSE The Core course will equip you with skills needed to support your learning in other subjects and in your general working life
5
This section gives you an outline of the syllabus content for this course Only the top-level topics of the syllabus have been included here which are the same for both the Core and Extended courses In the lsquooverviewrsquo column you are given a very basic idea of what each topic covers Highlighted cells show Extended-only content
Learners taking the Extended course need to know all of the Core content as well as some extra content This extra content requires learners to explore topics and sub-topics of the Core syllabus in more detail to cover some more complex techniques and to learn new sub-topics
Ask your teacher for more detail about each topic including the differences between the Core and Extended courses You can also find more detail in the revision checklists in Section 6 of this guide
Topic Overview
Number Number sets and Venn diagrams squares and cubes directed numbers fractions decimals and percentages ordering indices lsquofour rulesrsquo estimates bounds ratio proportion rate percentage time money and finance Growth and decay (Extended only)
Algebra and graphs Basic algebra algebraic manipulation equations formulae sequences drawing sketching and interpreting graphs of functionsAlgebraic fractions harder simultaneous equations proportion linear programming functions gradients of curves derived functions and differentiation (Extended only)
Co-ordinate geometry Straight-line graphs
Vectors and transformations Vectors (column) transformations
Magnitude of a vector represent vectors by directed line segments position vectors (Extended only)
Geometry Language construction symmetry angle properties congruence similarity
Mensuration Measures mensuration
Trigonometry Bearings trigonometry in right-angled triangles
Sine rule cosine rule trig graphs solving simple trig equations (Extended only)
Probability Probability
Conditional probability (Extended only)
Statistics Statistics
Section 1 Syllabus content ndash what you need to know about
Make sure you always check the latest syllabus which is available at wwwcambridgeinternationalorg
6
You will be assessed at the end of the course using two written examinations The papers that you will sit are different for the Core and Extended courses
bull Paper 1 ndash Short-answer questionsbull Paper 3 ndash Structured questions
bull Paper 2 ndash Short-answer questionsbull Paper 4 ndash Structured questions
Components at a glanceThe table summarises the key information about each component
Component How long and how many marks Skills assessed Percentage of the
qualificationCore Paper 1
(Short-answer questions)
1 hour
56 marks Mathematical techniques as listed in the Core syllabus and applying those techniques to solve problems
35
Paper 3 (Structured questions)
2 hours
104 marks 65
Extended Paper 2 (Short-answer questions)
1 hour 30 minutes
70 marksMathematical techniques as listed in the Core and Extended syllabus and applying those techniques to solve problems
35
Paper 4 (Structured questions)
2 hours 30 minutes
130 marks 65
Section 2 How you will be assessed
Core Extended
Make sure you find out from your teacher which course you will be following
7
About the componentsIt is important that you understand the different types of question in each paper so you know what to expect
Core Paper 1 (Short-answer questions) and Paper 3 (Structured questions)
You need to answer all questions on each paper
Paper 3Paper 1
You can use an electronic calculator in both papers Ask your teacher to recommend a suitable calculator
Paper 1 contains lots of short-answer questions These are usually worth 1ndash3 marks each Some might be broken up into two parts
Write your working and answers in the spaces provided
The number of marks for each part is shown
Paper 3 contains structured questions Each question is split into many parts with each part usually being worth 1ndash4 marks Here for example question 1 is split over two pages
Often the answers to later parts will depend on the answers to earlier parts
8
Extended Paper 2 (Shortndashanswer questions) and Paper 4 (Structured questions)
You need to answer all questions on both papers
Paper 2 questions are short-answer questions Most questions are worth 1ndash3 marks with some being worth 4 or 5 marks Some questions might be broken up into two parts
Write your working and answers in the spaces provided
The number of marks for each part is shown
Paper 4Paper 2
You can use an electronic calculator in both papers Ask your teacher to recommend a suitable calculator
Paper 4 contains structured questions Each question is split into many parts with each part usually being worth 1ndash6 marks Here for example question 2 is split over two pages
Often the answers to later parts will depend on the answers to earlier parts
9
Equipment for the examMake sure you have
bull a blue or black pen (a spare pen is always a good idea)bull a pencil (for graphs and diagrams)bull an electronic calculatorbull a protractorbull a pair of compassesbull a ruler
1 Read the questions carefully to make sure that you understand what is being asked
2 Give your answers to the accuracy indicated in the question If none is given and the answer isnrsquot exact then
bull give your answer to three significant figures 123 9 12298 x
bull if the answer is in degrees then give it to one decimal place 231deg 9 23deg x
3 Include units with your answers if they are not given on the paper For example 1 kg of apples costs hellip pound120 9 120 x
4 Show your working Show as much working as you can for all your questions
5 If you make a mistake clearly cross out any working or answers that you do not want the examiner to mark
Use the value of π from your calculator or use 3142 which is given on the front page of the question paper
Timingbull If you are stuck on a question dont waste too much time trying to answer it ndash go on to the next question and
come back to the one you are stuck on at the endbull Use any time that you have left at the end of the exam to go back and check your answers and working
Make sure that you give your answer in the form asked for in the question eg some questions ask for answers to be given in terms of π For lengths areas and volumes give answers in decimals (not in surds or in terms of π) unless you are told to given an exact answer
You can gain marks for the correct working even if you have an incorrect answer or cannot complete the whole question
If you need more space ask for extra of paper and clearly indicate where the rest of the answer is written On the additional paper make it clear which questions(s) you are answering
General advice for all Papers
10
The areas of knowledge understanding and skills that you will be assessed on are called assessment objectives (AOs) There are two AOs for this course
AO1 Demonstrate knowledge and
understanding of mathematical techniques
AO2 Reason interpret and communicate
mathematically when solving problems
AO1 Demonstrate knowledge and understanding of mathematical techniquesYou need to show that you can recall and apply mathematical knowledge terminology and definitions to carry out single or multi-step solutions in mathematical and everyday situations
Section 3 What skills will be assessed
This means that you need to show that you can
bull organise process and present information accurately in written tabular graphical and diagrammatic forms
bull use and interpret mathematical notation correctly
bull perform calculations and procedures by suitable methods including using a calculator
bull understand systems of measurement in everyday use and make use of these
bull estimate approximate and work to degrees of accuracy appropriate to the context and convert between equivalent numerical forms
bull use geometrical instruments to measure and to draw to an acceptable degree of accuracy
bull recognise and use spatial relationships in two and three dimensions
AO1 is assessed in all papers
Use tables graphs and diagrams
An example of degress of accuracy include significant figures or decimal places
An example of converting between equivalent numerical forms include between fractions decimals and percentages or between normal numbers and standard form
eg a pair of compasses a protractor and a ruler
11
AO2 Reason interpret and communicate mathematically when solving problemsYou need to demonstrate that you can analyse a problem select a suitable strategy and apply appropriate techniques to obtain a solution
This means that you need to show that you can
bull make logical deductions make inferences and draw conclusions from given mathematical data
bull recognise patterns and structures in a variety of situations and form generalisations
bull present arguments and chains of reasoning in a logical and structured way
bull interprete and communicate information accurately and change from one form of presentation to another
bull assesses the validity of an argument and critically evaluate a given way of presenting information
bull solve unstructured problems by putting them into a structured form involving a series of processes
bull apply combinations of mathematical skills and techniques using connections between different areas of mathematics in problem solving
bull interprete results in the context of a given problem and evaluate the methods used and solutions obtained
AO2 is assessed in all papers
Recognise and extent patterns
Take information and organise it to answer a problem
12
Section 4 Command wordsA command word is the part of the question that tells you what you need to do with your knowledge For example you might need to describe something explain something argue a point of view or list what you know The table below includes command words used in the assessment for this syllabus The use of the command word(s) within an question will relate to the context
Cambridge IGCSE Mathematics 0580 syllabus for 2020 2021 and 2022 Details of the assessment
37wwwcambridgeinternationalorgigcseBack to contents page
Command wordsThe table below includes command words used in the assessment for this syllabus The use of the command word will relate to the subject context
Command word What it means
Calculate work out from given facts figures or information generally using a calculator
Construct make an accurate drawing
Describe state the points of a topicgive characteristics and main features
Determine establish with certainty
Explain set out purposes or reasons make the relationships between things evident provide why andor how and support with relevant evidence
Give produce an answer from a given source or recallmemory
Plot mark point(s) on a graph
Show (that) provide structured evidence that leads to a given result
Sketch make a simple freehand drawing showing the key features
Work out calculate from given facts figures or information with or without the use of a calculator
Write give an answer in a specific form
Write down give an answer without significant working
The question below is taken from Paper 4 and illustrates the use of two command words
The command words lsquoWrite downrsquo indicates that you do not need to show your working and the answer should just be written down The mark allocation [1] also supports this
The command words lsquoShow thatrsquo indicate that you need to provide evidence in the form of a clear mathematical explanation to demonstrate that you know how to obtain the given result In other words you need to show a method that leads to the result
The answer space in this case does not contain a dotted answer line as there is no single lsquoanswerrsquo to be found Your working that leads to the given result should be written in the blank working space
13
This section takes you through an example question and learner response from one of the 2020 specimen papers for this course It will help you to identify the command words and other key instructions within questions and to understand what is required in your response
This section is structured as follows
QuestionThe command words and instructions in the question have
been highlighted and explained This should help you to understand clearly what is required by the question
Mark schemeThis tells you as clearly as possible what an examiner expects
from an answer to award marks
Example candidate responseThis an exemplar answer written in the style of
a high level candidate
How the answer could have been improvedThis summarises what could be done to gain more marks
All information and advice in this section is specific to the example question and response being demonstrated It should give you an idea of how your responses might be viewed by an examiner but it is not a list of what to do in all questions In your own examination you will need to pay careful attention to what each question is asking you to do
Common mistakesThis will help you to avoid common mistakes made by
candidates So often candidates lose marks in their exams because they misread or misinterpret the questions
Section 5 Example candidate response
14
QuestionThe question used in this example is from Specimen Paper 3 (Core) It represents the type of structured question you will see in both Paper 3 (Core) and Paper 4 (Extended) A structured question means that it is broken into several parts Often later parts will depend on your answers to earlier parts
This means that you cannot find the answer by
measuring the diagramWork out indicates that the answer should be calculated from the given information so measurement will not score marks
The allocation of 1 mark indicates that the answer can be obtained with minimum working
Give reasons for your answer indicates that your answer should be supported with reasons using the correct mathematical terminology You must justify your answer
Use trigonometry to calculate indicates that you should use this method with the given information to find the answer and that a calculator is needed to solve the problem If you did not use trigonometry you would not be awarded any marks
15
Show that indicates the answer is given and you need to write down all of the steps in a method that leads to the given answer You need to provide evidence that you understand and know how the answer is reached
Work out indicates that you should calculate the answer from the given information The mark allocation of 4 marks suggests that you will need to include several steps of working in order to get to the answer
Learner Guide
16
Answer Mark Notes(a)(i) 35 1 This is the only acceptable answer for this part of the question
(a)(ii) 74 1 This is the only acceptable answer for this part of the question
(b) 43deg and correct mathematical reasons
3 Two marks are awarded for the final answer of 43deg
The third mark is awarded for a fully correct reason for example angles on a straight line add up to 180deg and angles in a triangle add up to 180deg There are other correct reasons that could be also be used
If 43deg is not obtained one method mark can be awarded if the following calculation is seen in the working
180 ndash 128 or 128 ndash 85
(c) 322 or 3223hellip 2 This is the only acceptable answer for this part of the question
The answer has to be rounded correct to three significant figures or can be given with more figures in the answer
Those that did not get this answer can score one method mark for showing the following in their working
sin = 8 divide 15
(d)(i) 2 2300 225+2 This does not have to be shown in one step as long as the method shown is the same as this overall Those that do not
show this can have one method mark for showing the following in their working
300deg + 225deg
(d)(ii) 15 35 4 The answer 3 35pm is also acceptable for 4 marks
If the correct answer is not found one method mark is available for showing 375 divide 450 in their working and a second method mark can be awarded for sight of them multiplying their answer to this by 60 to change it to hours A third method mark can be awarded for adding their answer in hours to 14 45 ndash this shows the correct method so only one mark is lost for an incorrect final answers
Mark schemeYour examination papers will be marked and the overall number of marks for each paper will be recorded Your marks across all papers will then be converted to a grade
Final answer This value is what the examiner expects to see The answer has to be exactly as given in the mark scheme unless there are acceptable alternatives The mark scheme will always make it clear if there are acceptable alternative answers
Method marks Sometimes method marks are awarded for lines of working as well as for the final answer This means that you could get the final answer incorrect but still get some marks if you include the correct working The mark scheme does not include all possible methods so if you use a method not included in the mark scheme but it is accurate and relevant then the examiner will still award marks for the appropriate parts of the working ndash unless the questions asks you to use a specific method
example of a final answer
example of a method mark
17
Example candidate responseNow letrsquos look at the sample candidatersquos response to question 8 The examiners comments are in the orange boxes The candidate was awarded 8 marks out of 13
180 ndash 74 + 71 = 177
177
74
0 out of 1
The candidates working suggests they understand that the angle sum of a triangle is 180deg but they did not include brackets around 74 + 71 The answer 177deg is not sensible for this question
1 out of 1
The candidate recognises that there are parallel lines and that angle y is a corresponding angle to angle 74deg
180 ndash 128 = 52 180 ndash 85 ndash 52 = 43
43 angles on a straight line add up to 180deg
2 out of 3
The candidate has given a correct answer for w and shown correct working in two steps They have given a correct reason for 52deg using correct mathematical languge But they have not provided a reason to explain the angle 43deg They lose a mark for not also stating angle sum of a triangle is 180deg
sin p = 8 divide 15 = 053
p = sinndash1 (053)
p = 32005 320
1 out of 2
The candidate has correctly used trigonometry in their method They are awarded one method mark for the first line of working However they have rounded 05333333hellip (the result of 8 divide 15) to 052 and then calculated the inverse sin of 052 rather than 05333333 This has resulted in an inaccurate final answer This is called lsquopremature approximationrsquo and it is a very common error to make
18
AB2 = 3002 + 2252
= 140625
AB = 375
1 out of 2
The candidate has recognised the right-angled triangle and correctly used Pythagorasrsquo theorem in the first line of working However they have missed out an important step by not showing that you need to take the square root of 140625 to get 375 As this is a lsquoshow thatrsquo question and they missed a key step in the method they cannot be awarded full marks as the complete working is not shown One method mark is earned for the first line
T = = = 08333333hellip
08333333 hours = 08333333 times 60 minutes = 50 minutes
arrives at 14 45 + 50 mins = 3 35
DS
375450
3 35
3 out of 4
The candidate has found the time by correctly dividing the distance by the speed and recognised that this is in hours When converting the answer to a decimal they have not rounded the decimal but left its full value on the calculator to get 50 mins which is the correct approach Unfortunately after converting the time from 24 hour clock to 12 hour clock they did not include lsquopmrsquo to indicate that the time is in the afternoon and so the final answer is not quite right So 3 marks are awarded for all of a correct method but a mark is lost due to the accuracy of the final answer
19
How the answer could have been improvedThis answer could have been improved by
bull In part (a)(i) the answer of 177deg was not sensible given the diagram in the question If the candidate had checked their answer for sense they would have realised they had made a mistake It is always a good idea to check that your answer seems sensible before you move on to another question
bull In part (b) the candidate did all the correct steps but failed to provide both reasons There were two steps to the method which should have indicated to the candidate that there were two steps to justify and therefore two reasons should have been provided The mark allocation for the question [3] also indicates that more than one reason would be required one mark for the value of 43deg leaving two marks one mark for each of two reasons The candidate should have read the question carefully and again checked their response seemed reasonable
bull In part (c) the candidate rounded an intermediate answer which affected the accuracy of the final answer This caused them to lose a mark despite using a correct method You should only ever round the final answer do not round intermediate values If you can store the intermediate values in your calculator and so that you can use the full value in your calcuations If youre not able to do this and you have to round the intermediate values do not round them to less than three significant figures
bull In part (d)(i) the candidate missed out a step in the method As this was a show that question they needed to show all the steps in the method Its important to show all steps even if they seem obvious
bull In part (d)(ii) the candidate made a silly error by not stating that the time was pm When working with time answers are accepted in either 24 clock or 12 clock time but if you give your answer in the 12 hour clock then it must include am or pm as well
Common mistakesThere were a number of common mistakes made by other candidates on this question
bull Accuracy of answers
In parts (c) and (d)(ii) a common error was premature rounding ndash rounding intermediate values in the method before the final answer which resulted in their final answer not being accurate Other candidates gave the final answer to less than three significant figures ignoring the instruction on the front of the paper to round to three significant figures
bull Using incorrect terminology when giving reasons
In part (b) the most common error was to not give full reasons to support the answer Another common error was to provide a reason that did not use the correct mathematical language such as lsquoThey add up to 180degrsquo and lsquoIt is a straight linersquo which could not be awarded marks
bull Lack of knowledge
In part (c) a number of candidates had limited knowledge of trigonometry and did not choose the correct trig ratio which was the sine ratio This is why good revision is important
bull Not checking answers
In part (a)(i) even though the diagram is drawn NOT TO SCALE it is possible to see that the angle is an acute angle and should therefore not be bigger than 90deg This should alert candidate that if their answer is over 90deg it is not a sensible answer and they should go back and check their working
20
bull Inefficient method shown
In part (c) the lsquoShow thatrsquo question a number of candidates omitted an important step from the method this is often common in lsquoShow thatrsquo questions where every step must be shown no matter how obvious them seem
General adviceIn order to do your best when answering a mathematics question make sure you
bull revise all of the topics for the syllabus you are studying before the exam
bull understand what all the key terms and command words in the question mean
bull read the questions carefully and consider what you need to do before you do it
bull only round the final answer not intermediate values
bull show all steps in your working and show them clearly
bull round to the correct degree of accuracy
bull use the correct mathematical terminology
bull check your answers seem reasonable given the context or details of the question
21
It is important that you plan your revision in plenty of time for the examinations and that you develop a revision technique that works for you The advice in this section will help you revise and prepare for the examinations It is divided into general advice for all papers
Use the tick boxes to keep a record of what you have done what you plan to do or what you understand
For more advice on revision see the Cambridge Learner Revision Guide on our website
Section 6 Revision
Find out when the examinations are and plan your revision so you have time to revise Create a revision timetable and divide it into sections to cover each topic
Spend most of your time focussing on specific skills knowledge or issues that you have found more difficult when practicing them either during revision or earlier in the course
Write a summary of all the key information for a topic ndash use the checklists at the end of this section
Know the meaning of the command words used in questions and how to apply them to the information given Look at past examination papers and highlight the command words and check what they mean
Make revision notes and work on practice questions Reading alone does not work you need to be active and practice your maths
Work for shorter periods then have a break Revise small sections of the syllabus at a time but do this regularly
Test yourself by trying out some past exam questions Use the mark schemes to assess yourself and to be familiar with how marks are awarded for different questions
Be organised in advance with your notes texts exercise books revision guides and revision websites so you do not waste valuable revision time trying to find things
Make notes of key mathematical words that you should use in questions that ask you to lsquodescribersquo or give lsquogeometrical reasons forrsquo eg in describing transformations or giving reasons in circle theorem questions Look at the mark schemes for these types of questions from past papers to see how marks are awarded
Make sure you have all of the correct mathematical equipment ready for the exam particularly your calculator Make sure you are familiar with the all of the important functions on your calculator
Practice the areas you can do well not just those that you find more difficult
Take breaks and do things to relax when you take your breaks this will help you to be more productive when you are revising
Before the examination
22
During the examination
Plan your time according to the marks for each question For example a question worth one mark requires less time than a question one worth 4 marks If a question has several parts then the parts with more marks will need more time
Read each question very carefully
Identify the command words ndash you could underline or highlight them
Identify the other key words and information and perhaps underline them too particularly where
questions require reasoning or problem solving
Read the questions careully and make you have answered the question that is being asked
Show your working this is particularly important for questions where you are asked to lsquoshow that helliprsquo
Set your working out clearly so that it is easy to follow this makes it easier to keep track of what you have done and makes checking back through your work easier and it makes it easier for the examiner to mark your work try to write it in a logical order in the answer space
Write answers clearly if you want to change an answer then you should cross the answer out and write a replacement if your answer is on the answer line cross it out and write the replacement answer above it do not try to change numbers on the answer line as this can lead to unclear figures
Check your working and answers to avoid errors
Give your answer to the appropriate level of accuracy either the accuracy indicated in the question or the accuracy given on the front of the paper
Avoid rounding intermediate values part way through your calculation only round the final answer
Check that the answer that you have given is sensible and realistic for what is being asked
Use a pencil when drawing diagrams or completing graphs this means that you can change your answer more easily if you have made a mistake
Take care when reading scales
If you are asked for reasons for your answer then use the correct mathematical terms
Use the mark allocation given with the questionsparts of questions to try to judge how much work is needed to answer each part
23
Top tips for revision of Cambridge IGCSE Mathematics1 Summarise recall and applyMake sure that you can recall and apply the key information and mathematical techniques on each topic that you need for the exam
i Write a summary of the key information of a topicii Collect together some questions that test the knowledge and skills of this topic Ask your teacher for practice
questions or suitable past examination questions or use practice books or textbooksiii Test your recall by covering over the summary and trying to remember the details or use the summary as part of
the lsquoTeach the topicrsquo (Tip 3) or lsquoQuestion and answer cardsrsquo (Tip 4) activities iv After you have spent some time revising and practising the knowledge and skills answer the questions that you
collected together on the topic You might do this later on the same day as revising or a few days later Answer as many questions as you can in order to practise applying your knowledge
v Try creating your own questions by adapting existing ones and use these for practice when you return to a topic
On graph questions straight lines should be ruled and curves should be drawn freehand with a smooth curve
Donrsquot spend too long on any one part of a question If you are really stuck on a question then move on and come back to the question later if you have time As a rough guide each mark on the paper should take about one minute
2 Concept mapsConcept maps are a great way to revise the links between different factors or to explore a larger topic They can also be used to collect together your ideas
i Use a blank sheet of paper and turn it on its side (landscape)ii Put the topic title in the middle of the page and build the concept map outwards using lines called lsquobranchesrsquo
ndash The first branches are from the central topic to sub-topics draw these as thick lines
ndash Add new branches from the sub-topics to include more detail draw these as thinner lines
ndash Add even more detail to a point by adding more branches
This creates a hierarchy of information from lsquooverviewrsquo (the thick branches) to lsquofine detailrsquo (thinnest branches)
iii Write single key words or phrases along a branch and add drawings for visual impactiv Use different colours highlighter pens symbols and arrows to highlight key facts or issuesIt is a good idea to use a large piece of plain A3 (or larger) paper and lots of coloured pens
24
3 Teach the topicThis is a very simple but effective technique that focusses on knowledge recall It tests the brain and rehearses the information you need to know for a certain topic and so will help your revision
i Create some topic cards with key bullet points of information on Leave space for ticksii Give these to your parents family or friends for exampleiii Give yourself 10 minutes maximum to teach your audience the main points of the topic You could use a mini-
whiteboard or flip chart to helpiv Your audience tick off all the points you mention in your presentation and give you a final scoreThe brain loves competition so if you do not score full marks you can try again the next day or compete against friends This system of repeat and rehearsal is very effective especially with more complex topics and doesnt take much preparation
4 Question and answer (QampA) cardsThis is very similar to Teach the topic but less formal and less public for those who dislike performing in front of others It tests knowledge recall and rehearses the information you need to know for a certain topic
i Pick a topic and create two sets of cards question cards and answer cards You might find it helpful to make the question cards a different size or use different coloured card for answers
ii Make sure you have the topic or something appropriate depending on what you are focusing on as a heading on each card The questions should test your knowledge and understanding of key areas of the course
iii A friend or family member uses the cards to test you in short 5 or 10 minute periods at any time during the dayiv You could also do this alone by reading the questions to yourself giving the answer and then checking the
correct answer cardv This game can be adapted by using the cards to find matching pairs turn all cards face down across the space
in front of you Turn over two cards leaving them where they are If they match (one is a question card and the other is the corresponding answer card) pick up the pair and put them to one side If they dont match try to remember where they are and what is on each card then turn them back over Turn over two other cards Continue until you have matched all pairs
5 Question paper and mark schemesLooking at past question papers and the mark scheme helps you to familiarise yourself with what to expect and what the standard is
i Ask your teacher for past paper questions with mark schemes for the course ndash ask your teacher for help to make sure you are answering the correct questions and to simplify the mark scheme
ii Look at the revision checklist and identify which topic a given question relates to ndash you might need to ask your teacher to help you do this
iii Once you have finished revising a topic or unit time yourself answering some appropriate exam questions Check the mark schemes to see how well you would have scored or give the answers to your teacher to check
iv Add details or notes to the mark scheme where you missed out on marks in your original answers using a different coloured pen Use these notes when you revise and try the question again later
You can find plenty of past exam papers and mark schemes on the Cambridge International public website
httpwwwcambridgeinternationalorgprogrammes-and-qualificationscambridge-igcse-mathematics-0580past-papers
25
Other useful revision advice for Cambridge IGCSE Mathematics bull Before the exam make sure that you are familiar with your calculator and confident in using it
bull Look at the Example Candidate Response earlier in this guide Can you identify the strengths of the response andwhere they have made mistakes or lost marks
bull When you are attempting a past paper (or questions from a past paper) complete it without referring to yournotes so that you get a true idea of your strengths and weaknesses Then go back through the paper using yournotes and a different coloured pen to make corrections and changes After you have done as much as you can onthe paper mark it using the mark scheme Take notes of any points that you lost marks on
bull Donrsquot just revise the topics that you enjoy and are confident in If you identify an area that you are weaker inthen try to revisit the topic by reviewing your notes and doing some practice questions then use exam questionsto check whether you now understand
bull Return to topics later in your revision to check that you still remember and understand the topic and to help toensure that you recall more of the material when you get to the examination
Revision checklists for Cambridge IGCSE MathematicsThe tables on the following pages can be used as a revision checklist They do not contain all the detailed knowledge you need to know just an overview For more detail see the syllabus and talk to your teacher
You can use the tick boxes in the checklists to show when you have revised and are happy that you do not need to return to it Tick the lsquoRrsquo lsquoArsquo and lsquoGrsquo column to record your progress as follows
bull R = RED means you are really unsure and lack confidence in that area you might want to focus your revisionhere and possibly talk to your teacher for help
bull A = AMBER means you are reasonably confident in a topic but need some extra practicebull G = GREEN means you are very confident in a topic
As your revision progresses you can concentrate on the RED and AMBER topics in order to turn them into GREEN topics You might find it helpful to highlight each topic in red orange or green to help you prioritise
You can use the lsquoCommentsrsquo column to
bull add more information about the details for each pointbull include a reference to a useful resourcebull include a list of formulae or notationbull add learning aids such as rhymes poems or word playbull highlight areas of difficulty or things that you need to talk to your teacher about
There is a set of checklist for the Core syllabus and a different set for the Extended syllabus
Learner Guide
26
Core syllabus contentCore Number
Category You should be able to R A G CommentsNumber Identify and use
bull natural numbers
bull integers (positive negative and zero)
bull prime numbers
bull write a number as a product of its prime factors
bull square numbers and cube numbers
bull common factors and highest common factor of two numbers
bull common multiples and lowest common multiple of two numbers
bull rational numbers
bull irrational numbers (eg π radic2 )
bull real numbers
bull reciprocals
Learner Guide
27
Core Number
Question type You should be able to R A G CommentsSets and Venn diagrams
Understand notation of Venn diagrams
Definition of sets
eg A = xx is a natural number
B = abchellip
Notation
Number of elements in set A n(A)
Universal set
Union of A and B A cup B
Intersection of A and B A cap B
Squares square roots cubes and cube roots
Calculate
bull squares and cubes of numbers
bull square roots and cube roots of numbers
Learner Guide
28
Core Number
Question type You should be able to R A G CommentsDirected numbers
Use directed numbers in practical situations for example temperature changes
Fractions decimals and percentages
Use the language and notation of simple vulgar and decimal fractions and percentages
Recognise equivalent fractions decimals and percentages
Convert between fractions decimals and percentages
Ordering Order quantities by magnitude and demonstrate familiarity with the symbols = ne gt lt ⩾ ⩽
Indices and standard form (links to Algebraic manipulation)
Evaluate indices eg 25 5ndash2 1000 64frac12 8ndash23
Use the rules of indices for
bull multiplication of indices eg 4ndash3 times 45
bull division of indices eg 57 divide 53
bull index numbers raised to an index eg (23)2 (43)2
Use the standard form A times 10n where n is a positive or negative integer and 1 ⩽ A lt 10
bull convert numbers into and out of standard form
bull calculate with numbers in standard form
Learner Guide
29
Core Number
Question type You should be able to R A G CommentsFour rules
( + ndash times divide )
Use the four rules for calculations with
bull whole numbers
bull decimals
bull vulgar and mixed fractions
bull correct ordering of operations (BIDMAS) and use of bracketsEstimates Make estimates of numbers quantities and lengths
Give approximations to a specified number of
bull significant figures
bull decimal places
Round off answers to reasonable accuracy in the context of a given problem
Bounds Give upper and lower bounds for data given to a specified accuracy eg measured lengths
Ratio proportion rate
Understand ratio
Divide a quantity in a given ratio
Understand direct and inverse proportion
Use scales in practical situations
Use common measures of rate (formulae for other rates eg density and pressure will be given in the question)
Calculate average speed
Learner Guide
30
Core Number
Question type You should be able to R A G CommentsPercentages Calculate a percentage of a quantity
Express one quantity as a percentage of another quantity
Calculate percentage increase or decrease
Use of an electronic calculator
Use a calculator efficiently
Check accuracy of calculations
Time Calculate times in terms of the 24-hour and 12-hour clock
Read
bull clocks
bull dials
bull timetables
Money Calculate using money
Convert from one currency to another
Learner Guide
31
Core Number
Question type You should be able to R A G CommentsPersonal and small business finance
Use given data to solve problems on
bull earnings
bull simple interest
bull compound interest (you will need to know the compound interest formula)
bull discount
bull profit and loss
Extract data from tables and charts
Learner Guide
32
Core Algebra and graphs
Question type You should be able to R A G CommentsBasic algebra Use letters to express generalised numbers
Express basic arithmetic processes algebraically
Substitute numbers in formulae
Construct simple expressions and set up simple equations
Rearrange simple formulae
Algebraic manipulation
Manipulate directed numbers
Use brackets
bull expand a single bracket eg 3x(2x ndash4y)
bull expand a pair of brackets eg (x + 3) (x ndash 7)
Extract common factors eg factorise 9x2 + 15xy
Rules of indices Use and interpret positive negative and zero indices
Use the rules of indices eg to simplify algebra such as
bull 3x4 times 5x
bull 10x3 divide 2x2
bull (x6)2
Learner Guide
33
Core Algebra and graphs
Question type You should be able to R A G CommentsEquations and inequalities
Derive and solve simple linear equations in one unknown
Derive and solve simultaneous linear equations in two unknowns
Number sequences
(links to Squares square roots cubes and cube roots)
Continue a number sequence
Recognise patterns in sequences
Recognise relationships between difference sequences
Find the nth term of sequences for
bull liner sequences
bull simple quadratic sequences
bull cubic sequences
Practical graphs
(links to Mensuration)
Interpret and use graphs in practical situations including
bull travel graphs
bull conversion graphs
Draw graphs from given data
Learner Guide
34
Core Algebra and graphs
Question type You should be able to R A G CommentsGraphs of functions
(links to Co-ordinate geometry)
Construct tables of values for functions of the form
bull ax + b (linear)
bull plusmn x2 + ax + b (quadratic)
bull (x ne 0) (reciprocal)
where a and b are integer constants
Draw and interpret such graphs
Solve linear and quadratic equations approximately by graphical methods
Recognise and sketch the graphs of linear and quadratic functions
ax
Learner Guide
35
Core Co-ordinate geometry
Question type You should be able to R A G CommentsCo-ordinates Work with co-ordinates in two dimensions
Gradients Find the gradient of a straight line graph
Equation of straight line
Interpret and obtain the equation of a straight line graph in the form y = mx + c where the graph is given
Parallel lines Determine the equation of a straight line parallel to a given line eg find the equation of a line parallel to y = 4x ndash 1 that passes through (0 ndash3)
Learner Guide
36
Core Geometry
Question type You should be able to R A G CommentsGeometrical language
Use and interpret the geometrical terms
bull point
bull line
bull parallel
bull perpendicular
bull bearing
bull right angle acute obtuse and reflex angles
bull similar
bull congruent
Use and interpret the vocabulary of
bull triangles right-angled scalene isosceles equilateral
bull quadrilaterals
bull circles
bull polygons
bull simple solid figures including nets
Learner Guide
37
Core Geometry
Question type You should be able to R A G CommentsGeometrical constructions
Measure and draw lines and angles
Construct a triangle given the three sides using a ruler and a pair of compasses only
Scale drawings Read and make scale drawings
Similar figures Calculate lengths of similar figures
Congruent Recognise congruent shapes
Symmetry Recognise symmetry properties for triangles quadrilaterals and circles
Recognise line symmetry in two dimensions
Recognise and find the order of rotational symmetry in two dimensions
Learner Guide
38
Core Geometry
Question type You should be able to R A G CommentsAngle properties Calculate unknown angles explaining the properties that you
are using in geometrical language for angles
bull angles at a point
bull angles on a straight line and intersecting straight lines
bull angles within parallel lines
bull angles in triangles
bull angles in quadrilaterals
bull angles in regular polygons
bull angle in a semi-circle
bull angle between tangent and radius of a circle
Learner Guide
39
Core Mensuration
Question type You should be able to R A G CommentsMeasures bull Use current units of
bull mass
bull length
bull area
bull volume
bull capacity
Express quantities in terms of smaller or larger units including units of area and volume
Convert between units including units of area and volume
Perimiter Carry out calculations involving
bull perimeter and area of a rectangle
bull perimeter and area of a triangle
bull perimeter and area of parallelogram
bull perimeter and area of a trapezium
bull perimeter and area of shapes made by combining
bull rectangles triangles parallelograms andor trapeziums
Learner Guide
40
Core Mensuration
Question type You should be able to R A G CommentsCircles Carry out calculations involving circumference and area of a
circle
Solve simple problems involving the arc length and sector area of a circle where the sector angle is a factor of 360deg
Surface area and volume
Carry out calculations involving
bull surface area and volume of a cuboid prism and cylinder (no formulae will be given for these shapes)
bull surface area and volume of a sphere pyramid and cone (formulae will be given for these shapes)
Areas and volumes of compound shapes
Carry out calculations involving the areas and volumes of compound shapes made from combinations of the shapes in Perimeter or Surface area and volume
Learner Guide
41
Core Trigonometry
Question type You should be able to R A G CommentsBearings Use and interpret three-figure bearings measured clockwise
from the North ie 000degndash360degTrigonometry Find unknown sides andor angles in right-angled triangles by
applying
bull Pythagorasrsquo theorem
bull sine cosine and tangent ratios for acute angles in right-angled triangles
Learner Guide
42
Core Vectors and transformations
Question type You should be able to R A G CommentsVectors in two dimensions (links to Trigonometry)
Describe a translation by using a vector represented by
AB or a
Add and subtract vectors
Multiply a vector by a scalar
Transformations Reflect simple shapes in horizontal or vertical lines
Rotate simple shapes through multiples of 90deg about
bull the origin
bull their vertices
bull the midpoints of their sides
Construct translations of simple shapes
Construct enlargements of simple shapes (positive and fractional scale factors)
Recognise and describe using the correct language
bull reflections
bull rotations
bull translations
bull enlargements (positive and fractional scale factors)
( )x
y
Learner Guide
43
Core Probability
Question type You should be able to R A G CommentsSingle events Calculate the probability of a single event as a fraction decimal
or percentage (not a ratio)Probability scale Understand and use the probability scale from 0 to 1
Sum to 1 Understand that the probability of an event occurring = 1 ndash the probability of the event not occurring
Relative frequency
Understand relative frequency as an estimate of probability
Work out expected frequencies using relative frequencyCombined events Calculate the probability of simple combined events using
bull tree diagrams
bull possibility diagrams (points on a grid)
bull Venn diagrams (2 sets only)
Learner Guide
44
Core Statistics
Question type What I need to do R A G CommentsClassify Collect classify and tabulate data
Interpret and compare
Read interpret and draw simple inferences from tables and statistical diagrams
Compare sets of data using
bull tables
bull graphs
bull statistical measures
Be aware of restrictions when making conclusions from data
Charts Construct and use
bull bar charts
bull pie charts
bull pictograms
bull stem-and-leaf diagrams
bull frequency distributions
bull histograms with equal intervals
bull scatter diagrams
Learner Guide
45
Question type What I need to do R A G CommentsAverages Calculate for individual and discrete data
bull mean
bull median
bull mode
bull range
and distinguish between their useCorrelation Understand what is meant by positive negative and zero
correlation with reference to a scatter diagramLine of best fit Draw interpret and use a ruled line of best fit by eye
Learner Guide
46
Extended syllabus content (includes required Core content)Extended Number
Question type You should be able to R A G CommentsNumber Identify and use
bull natural numbers
bull integers (positive negative and zero)
bull prime numbers
bull write a number as a product of its prime factors
bull square and cube numbers
bull common factors and highest common factor of two or more numbers
bull common multiples and lowest common multiple of two or more numbers
bull rational numbers
bull irrational numbers (eg π radic2 )
bull real numbers
bull reciprocals
Learner Guide
47
Extended Number
Question type You should be able to R A G CommentsSet notation and language
Use language notation and Venn diagrams to describe sets and represent relationships between sets as follows
Definition of sets egA = x x is a natural number
B = (xy) y = mx + c
C = x a ⩽ x ⩽ b
D = a b c hellip
Notation egnumber of elements in set A n(A)
lsquois an element ofrsquo isin
lsquois not an element ofrsquo notin
complement of set A
the empty set empty
the universal set
A is a subset of B A sube B
A is a proper subset of B A sub B
A is not a subset of B A ⊈ B
A is not a proper subset of B A nsub B
union of A and B A cup B
intersection of A and B A cap B
Learner Guide
48
Extended Number
Question type You should be able to R A G CommentsSquares square roots cubes and cube roots
Calculatebull squares of numbers
bull square roots of numbers
bull cubes of numbers
bull cube roots of numbers
bull other powers and roots of numbers
Directed numbers
Use directed numbers in practical situations for example temperature changes
Fractions decimals and percentages
Use the language and notation of simple vulgar and decimal fractions and percentages in appropriate contexts
Recognise equivalent fractions decimals and percentages
Convert between fractions decimals and percentages
Convert recurring decimals to fractions
Ordering Order quantities by magnitude and demonstrate familiarity with the symbols = ne gt lt ⩾ ⩽
Learner Guide
49
Extended Number
Question type You should be able to R A G CommentsIndices and standard form (links to Algebraic manipulation)
Evaluate indices including fractional negative and zero
eg 25 5ndash2 1000 10012 8ndash23
Use the rules of indices forbull multiplication of indices eg 43 times 45
bull division of indices eg 57 divide 53
bull index numbers raised to an index eg (43)2
Use the standard form A times 10n where n is a positive or negative integer and 1 ⩽ A lt 10bull convert into and out of standard form
bull calculate with numbers in standard form
Four rules
( + ndash times divide )
Use the four rules for calculations withbull whole numbers
bull decimals
bull vulgar and mixed fractions
bull correct ordering of operations (BIDMAS) and use of brackets
Learner Guide
50
Extended Number
Question type You should be able to R A G CommentsEstimates Make estimates of numbers quantities and lengths
Give approximations to a specified number of
bull significant figures
bull decimal places
Round off answers to reasonable accuracy in the context of a given problem
Bounds Give upper and lower bounds for data given to a specified accuracy eg measured lengths
Obtain appropriate upper and lower bounds to solutions of simple problems given to a specified accuracy eg the lower and upper bounds for the area of a rectangle
Ratio proportion rate
(links to Direct and inverse proportion)
Understand ratio
Divide quantities in a given ratio
Increase and decrease a quantity by a given ratio
Understand numerical problems involving direct and inverse proportion
Use ratio and scales in practical situations
Use common measures of rate (formulae for other rates eg density and pressure will be given in the question)
Calculate average speed
Learner Guide
51
Extended Number
Question type What I need to do R A G CommentsPercentages Calculate a percentage of a quantity
Express one quantity as a percentage of another quantity
Calculate percentage increase or decrease
Calculate reverse percentages eg finding the cost price given the selling price and the percentage profit
Use of an electronic calculator
Use a calculator efficiently
Check accuracy of calculations
Time Calculate times in terms of the 24-hour and 12-hour clock
Read clocks dials and timetables
Money Calculate using money
Convert from one currency to another
Learner Guide
52
Extended Number
Question type You should be able to R A G CommentsPersonal and small business finance
Use given data to solve problems on
bull earnings
bull simple interest
bull compound interest
ndash you must know the compound interest formula
bull discount
bull profit and loss
Extract data from tables and charts
Exponential growth and decay
Use exponential growth and decay in population and finance eg depreciation bacteria growth
Learner Guide
53
Extended Algebra and graphs
Question type You should be able to R A G CommentsBasic algebra Use letters to express generalised numbers
Express basic arithmetic processes algebraically
Substitute numbers in complicated formulae
Construct and rearrange complicated formulae eg where the subject appears twice
Algebraic manipulation
Manipulate directed numbers
Use bracketsbull expand a single bracket eg expand 3x(2x ndash 4y)
bull expand a pair of brackets eg (x ndash 4)(x + 7)
bull expand products of more than two brackets eg (x + 4)(x ndash 7)(2x + 1)
Extract common factors eg factorise 9x2 + 15xy
Factorise expressions of the formbull ax + bx + kay + kby
bull asup2xsup2 ndash bsup2ysup2
bull asup2 + 2ab + bsup2
bull axsup2 + bx + c
Learner Guide
54
Extended Algebra and graphs
Question type You should be able to R A G CommentsAlgebraic fractions
Manipulate algebraic fractions eg
bull
bull
bull
bull
bull
Factorise and simplify algebraic fractions such as
Rules of indices Use and interpret positive negative and zero indices
Use and interpret fractional indices eg solve 32x = 2
Use the rules of indices to simplify algebra eg
x3 + x ndash 4
22x3 +
3(x ndash 5)2
3a4 +
5ab3
3a4 divide
9a10
1x ndash 2 +
2x ndash 3
x2 ndash 2xx2 ndash 5x + 6
3xndash4 times23
x12
32x5( )
3
2xndash2divide25
x12
Learner Guide
55
Extended Algebra and graphs
Question type You should be able to R A G CommentsEquations and inequalities
bull Derive and solve simple linear equations in one unknown
bull Derive and solve simultaneous linear equations in two unknowns
bull Derive and solve simultaneous equations involving one linear and one quadratic
Solve quadratic equations by
bull factorisation
bull completing the square
bull using the formula
Derive and solve simple linear inequalities including representing solutions on a number line
Linear programming
Represent inequalities graphically including using the conventions of
bull broken lines for strict inequalities
bull shading unwanted regions
Solve simple linear programming problems using graphical representations of inequalities
Learner Guide
56
Extended Algebra and graphs
Question type You should be able to R A G CommentsNumber sequences (links to Squares square roots cubes and cube roots)
Continue a number sequence
Recognise patterns in sequences
Recognise relationships between different sequences
Find the nth term of sequences of
bull linear sequences
bull quadratic sequences
bull cubic sequences
bull exponential sequences
and simple combinations of these
Direct and inverse proportion (links to Ratio proportion rate)
Express direct proportion algebraically
Express inverse proportion algebraically
Use algebraic expressions of direct and inverse proportion to find unknown quantities
Practical graphs
(links to Coordinate geometry)
Interpret and use graphs in practical situations including
bull travel graphs
bull conversion graphs
Draw graphs from given data
Learner Guide
57
Extended Algebra and graphs
Question type You should be able to R A G CommentsPractical graphs (links to Coordinate geometry) continued
Apply the idea of rate of change to simple kinematics involving
bull distancendashtime graphs
bull speedndashtime graphs
bull acceleration and deceleration
This may involve estimation and interpretation of the gradient of a tangent at a point
Calculate distance travelled as an area under a linear speedndash time graph
Learner Guide
58
Extended Algebra and graphs
Question type You should be able to R A G CommentsGraphs of functions (links to Coordinate geometry)
Construct tables of values and draw graphs for functions of the form
bull axn where a is a rational constant and n = minus2 minus1 0 1 2 3 and simple sums of not more than three of these
bull abx + c where a and c are rational constants and b is a positive integer
Solve associated equations approximately by graphical methods including finding and interpreting roots and finding turning points of quadratics by completing the square
Draw and interpret graphs representing exponential growth and decay problems
Recognise sketch and interpret graphs of
bull linear
bull quadratic
bull cubic
bull reciprocal
bull exponential
(knowledge of turning points and asymtotes is required)Tangents Estimate gradients of curves by drawing tangents
Learner Guide
59
Extended Algebra and graphs
Question type You should be able to R A G CommentsFunctions Use function notation eg
f(x) = 3x ndash 5 f x α 3x ndash5 to describe simple functions
Find inverse functions f ndash1 (x)
Form composite functions as defined by gf(x) = g(f(x))
Derivatives Understand the idea of a derived function
Use derivatives of the form axn and simple sums of not more than three of these (a is a rational constant and n is a positive integer or 0)
Apply differentiation to gradients and turning points (stationary points)
Use any method to explain whether the turning point is a maximum or a minimum eg second derivative or gradient of function on either side of turning point
Learner Guide
60
Extended Co-ordinate geometry
Question type You should be able to R A G CommentsStraight line graphs
Work with co-ordinates in two dimensions
Gradient Find the gradient of a straight line graph
Calculate the gradient of a straight line from the co-ordinates of two points on it
Length and midpoint
Calculate the length and the co-ordinates of the midpoint of a straight line segment from the co-ordinates of its end points
Equation of line Interpret and obtain the equation of a straight line graph
Parallel lines Determine the equation of a straight line parallel to a given line eg find the equation of a line parallel to y = 4x ndash 1 that passes through (0 ndash3)
Perpendicular lines
Find the gradient of parallel and perpendicular lines eg
bull find the gradient of a line perpendicular to y = 3x + 1
bull find the equation of a line perpendicular to one passing through the co-ordinates (1 3) and (ndash2 ndash9)
Learner Guide
61
Extended Geometry
Question type You should be able to R A G CommentsGeometrical language
Use and interpret the geometrical terms
bull point
bull line
bull parallel
bull perpendicular
bull bearing
bull right angle acute obtuse and reflex angles
bull similar
bull congruent
Use and interpret the vocabulary of
bull triangles right-angled scalene isosceles equilateral
bull quadrilaterals
bull circles
bull polygons
bull simple solid figures including nets
Learner Guide
62
Extended Geometry
Question type What I need to do R A G CommentsGeometrical constructions
Measure and draw lines and angles
Construct a triangle given the three sides using a ruler and a pair of compasses only
Scale drawings Read and make scale drawings
Similar figures Calculate lengths of similar figures
Use relationships between areas of similar triangles and in similar figures
Use relationships between volumes and surface areas of similar solids
Congruent triangles
Use the congruence criteria for triangles (SSS ASA SAS RHS)
Symmetry Recognise symmetry properties for triangles quadrilaterals and circles
Recognise line symmetry in two dimensions
Recognise and find the order of rotational symmetry in two dimensions
Learner Guide
63
Extended Geometry
Question type You should be able to R A G CommentsSymmetry (continued)
Use the following symmetry properties of circles
bull equal chords are equidistant from the centre
bull perpendicular bisector of a chord passes through the centre
bull tangents from an external point are equal in length
Recognise and use symmetry properties of
bull prism cylinder cone and pyramid
Learner Guide
64
Extended Geometry
Question type You should be able to R A G CommentsAngle properties Calculate unknown angles explaining the properties that
you are using in geometrical language for the following geometrical properties
bull angles at a point
bull angles at a point on a straight line and intersecting straight lines
bull angles formed within parallel lines
bull angle properties of triangles and quadrilaterals
bull angle properties of regular polygons
bull angle in a semi-circle
bull angle between tangent and radius of a circle
bull angles properties of irregular polygons
bull angle at the centre of a circle is twice the angle at the circumference
bull angles in the same segment are equal
bull angles in opposite segments are supplementary cyclic quadrilaterals
bull alternate segment theorem
Learner Guide
65
Extended Mensuration
Question type What I need to do R A G CommentsMeasures Use current units of
bull mass
bull length
bull area
bull volume
bull capacity
Express quantities in terms of smaller or larger units including units of area and volume
Perimeter Carry out calculations involving
bull perimeter and area of a rectangle
bull perimeter and area of a triangle
bull perimeter and area of parallelogram
bull perimeter and area of a trapezium
bull perimeter and area of compound shapes made by combining rectangles triangles parallelograms andor trapeziums
Learner Guide
66
Extended Mensuration
Question type You should be able to R A G CommentsCircles Carry out calculations involving circumference and area of a
circle
Solve problems involving arc length and sector area of a circle
Surface area and volume
Carry out calculations involving
bull surface area and volume of a cuboid prism and cylinder (no formulae will be given for these shapes)
bull surface area and volume of a sphere pyramid and cone (formulae will be given for these shapes)
Compound shapes
Carry out calculations involving
bull area of a shape made by combining cuboids prisms andor cylinders
bull volume of a shape made by combining cuboids prisms andor cylinders
Learner Guide
67
Extended Trigonometry
Question type You should be able to R A G CommentsBearings Use and interpret three-figure bearings measured clockwise
from the North ie 000degndash360degTrigonometry Find unknown sides andor angles in right-angled triangles by
applying
bull Pythagorasrsquo theorem
bull sine cosine and tangent ratios for acute angles in right-angled triangles
Solve problems in two dimensions involving angles of elevation and depression
Know that the perpendicular distance from a point to a line is the shortest distance to the line
Trig graphs and equations
Recognise sketch and interpret graphs of simple trigonometric functions
Graph and know the properties of trigonometric functions
Solve simple trigonometric equations for values between 0deg
and 360deg eg Solve sin x = radic32
for values of x between 0deg and
360degGeneral trig Solve problems using sine and cosine rules for any triangle
Find the area of any triangle using frac12absinC
Trig in 3D Solve simple trigonometrical problems in three dimensions including angle between a line and a plane
Learner Guide
68
Extended Vectors and transformations
Question type You should be able to R A G CommentsVectors in two dimensions (links to Trigonometry)
Describe a translation by using a vector represented by
AB or a
Add and subtract vectors
Multiply a vector by a scalar
Transformations Reflect simple shapes in horizontal or vertical lines
Rotate simple shapes through multiples of 90deg about any point
Construct translations of simple shapes
Construct enlargements of simple shapes (positive fractional and negative scale factors)
Recognise and describe
bull reflections
bull rotations
bull translations
bull enlargements (positive fractional and negative scalefactors)
( )x
y
Learner Guide
69
Extended Vectors and transformations
Question type You should be able to R A G CommentsHarder vectors
Calculate the magnitude of a vector as and
understand that magnitude is denoted by modulus signs |A B| or |a|
Represent vectors by directed line segments
Use the sum and difference of two vectors
Use position vectors
( )x
yradicx2 + y2
Learner Guide
70
Extended Probability
Question type You should be able to R A G CommentsProbability (links to Four rules)
Calculate the probability of a single event as a fraction decimal or percentage (not a ratio)
Probability scale Understand and use the probability scale from 0 to 1
Sum to 1 Understand that the probability of an event occurring = 1 ndash the probability of the event not occurring
Relative frequency
Understand relative frequency as an estimate of probability
Work out expected frequencies using relative frequency
Combined events Calculate the probability of combined events using
bull tree diagrams
bull possibility diagrams
bull tables
Learner Guide
71
Extended Statistics
Question type You should be able to R A G CommentsClassify Collect classify and tabulate data
Interpret and compare
Read interpret and draw simple inferences from tables and statistical diagrams
Compare sets of data using
bull tables
bull graphs
bull statistical measures
Be aware of restrictions when making conclusions from data
Charts Construct and use
bull bar charts
bull pie charts
bull pictograms
bull stem ndash and ndash leaf diagrams
bull frequency distributions
bull histograms with equal and unequal intervals
bull scatter diagrams
Learner Guide
72
Extended Statistics
Question type You should be able to R A G CommentsAverages Calculate for individual and discrete data
bull mean
bull median
bull mode
bull range
and distinguish between their use
Estimated mean Calculate an estimate of the mean for grouped and continuous data
Identify the modal class from a grouped frequency distributionCumulative frequency
Construct and use cumulative frequency diagrams to estimate and interpret
bull the median
bull percentiles
bull quartiles
bull inter-quartile range
Construct and interpret box-and-whisker plots
Correlation Understand what is meant by positive negative and zero correlation with reference to a scatter diagram
Lines of best fit Draw interpret and use a ruled line of best fit by eye
Cambridge Assessment International Education1 Hills Road Cambridge CB1 2EU United Kingdomt +44 1223 553554e infocambridgeinternationalorg wwwcambridgeinternationalorg
Copyright copy UCLES October 2017
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5
This section gives you an outline of the syllabus content for this course Only the top-level topics of the syllabus have been included here which are the same for both the Core and Extended courses In the lsquooverviewrsquo column you are given a very basic idea of what each topic covers Highlighted cells show Extended-only content
Learners taking the Extended course need to know all of the Core content as well as some extra content This extra content requires learners to explore topics and sub-topics of the Core syllabus in more detail to cover some more complex techniques and to learn new sub-topics
Ask your teacher for more detail about each topic including the differences between the Core and Extended courses You can also find more detail in the revision checklists in Section 6 of this guide
Topic Overview
Number Number sets and Venn diagrams squares and cubes directed numbers fractions decimals and percentages ordering indices lsquofour rulesrsquo estimates bounds ratio proportion rate percentage time money and finance Growth and decay (Extended only)
Algebra and graphs Basic algebra algebraic manipulation equations formulae sequences drawing sketching and interpreting graphs of functionsAlgebraic fractions harder simultaneous equations proportion linear programming functions gradients of curves derived functions and differentiation (Extended only)
Co-ordinate geometry Straight-line graphs
Vectors and transformations Vectors (column) transformations
Magnitude of a vector represent vectors by directed line segments position vectors (Extended only)
Geometry Language construction symmetry angle properties congruence similarity
Mensuration Measures mensuration
Trigonometry Bearings trigonometry in right-angled triangles
Sine rule cosine rule trig graphs solving simple trig equations (Extended only)
Probability Probability
Conditional probability (Extended only)
Statistics Statistics
Section 1 Syllabus content ndash what you need to know about
Make sure you always check the latest syllabus which is available at wwwcambridgeinternationalorg
6
You will be assessed at the end of the course using two written examinations The papers that you will sit are different for the Core and Extended courses
bull Paper 1 ndash Short-answer questionsbull Paper 3 ndash Structured questions
bull Paper 2 ndash Short-answer questionsbull Paper 4 ndash Structured questions
Components at a glanceThe table summarises the key information about each component
Component How long and how many marks Skills assessed Percentage of the
qualificationCore Paper 1
(Short-answer questions)
1 hour
56 marks Mathematical techniques as listed in the Core syllabus and applying those techniques to solve problems
35
Paper 3 (Structured questions)
2 hours
104 marks 65
Extended Paper 2 (Short-answer questions)
1 hour 30 minutes
70 marksMathematical techniques as listed in the Core and Extended syllabus and applying those techniques to solve problems
35
Paper 4 (Structured questions)
2 hours 30 minutes
130 marks 65
Section 2 How you will be assessed
Core Extended
Make sure you find out from your teacher which course you will be following
7
About the componentsIt is important that you understand the different types of question in each paper so you know what to expect
Core Paper 1 (Short-answer questions) and Paper 3 (Structured questions)
You need to answer all questions on each paper
Paper 3Paper 1
You can use an electronic calculator in both papers Ask your teacher to recommend a suitable calculator
Paper 1 contains lots of short-answer questions These are usually worth 1ndash3 marks each Some might be broken up into two parts
Write your working and answers in the spaces provided
The number of marks for each part is shown
Paper 3 contains structured questions Each question is split into many parts with each part usually being worth 1ndash4 marks Here for example question 1 is split over two pages
Often the answers to later parts will depend on the answers to earlier parts
8
Extended Paper 2 (Shortndashanswer questions) and Paper 4 (Structured questions)
You need to answer all questions on both papers
Paper 2 questions are short-answer questions Most questions are worth 1ndash3 marks with some being worth 4 or 5 marks Some questions might be broken up into two parts
Write your working and answers in the spaces provided
The number of marks for each part is shown
Paper 4Paper 2
You can use an electronic calculator in both papers Ask your teacher to recommend a suitable calculator
Paper 4 contains structured questions Each question is split into many parts with each part usually being worth 1ndash6 marks Here for example question 2 is split over two pages
Often the answers to later parts will depend on the answers to earlier parts
9
Equipment for the examMake sure you have
bull a blue or black pen (a spare pen is always a good idea)bull a pencil (for graphs and diagrams)bull an electronic calculatorbull a protractorbull a pair of compassesbull a ruler
1 Read the questions carefully to make sure that you understand what is being asked
2 Give your answers to the accuracy indicated in the question If none is given and the answer isnrsquot exact then
bull give your answer to three significant figures 123 9 12298 x
bull if the answer is in degrees then give it to one decimal place 231deg 9 23deg x
3 Include units with your answers if they are not given on the paper For example 1 kg of apples costs hellip pound120 9 120 x
4 Show your working Show as much working as you can for all your questions
5 If you make a mistake clearly cross out any working or answers that you do not want the examiner to mark
Use the value of π from your calculator or use 3142 which is given on the front page of the question paper
Timingbull If you are stuck on a question dont waste too much time trying to answer it ndash go on to the next question and
come back to the one you are stuck on at the endbull Use any time that you have left at the end of the exam to go back and check your answers and working
Make sure that you give your answer in the form asked for in the question eg some questions ask for answers to be given in terms of π For lengths areas and volumes give answers in decimals (not in surds or in terms of π) unless you are told to given an exact answer
You can gain marks for the correct working even if you have an incorrect answer or cannot complete the whole question
If you need more space ask for extra of paper and clearly indicate where the rest of the answer is written On the additional paper make it clear which questions(s) you are answering
General advice for all Papers
10
The areas of knowledge understanding and skills that you will be assessed on are called assessment objectives (AOs) There are two AOs for this course
AO1 Demonstrate knowledge and
understanding of mathematical techniques
AO2 Reason interpret and communicate
mathematically when solving problems
AO1 Demonstrate knowledge and understanding of mathematical techniquesYou need to show that you can recall and apply mathematical knowledge terminology and definitions to carry out single or multi-step solutions in mathematical and everyday situations
Section 3 What skills will be assessed
This means that you need to show that you can
bull organise process and present information accurately in written tabular graphical and diagrammatic forms
bull use and interpret mathematical notation correctly
bull perform calculations and procedures by suitable methods including using a calculator
bull understand systems of measurement in everyday use and make use of these
bull estimate approximate and work to degrees of accuracy appropriate to the context and convert between equivalent numerical forms
bull use geometrical instruments to measure and to draw to an acceptable degree of accuracy
bull recognise and use spatial relationships in two and three dimensions
AO1 is assessed in all papers
Use tables graphs and diagrams
An example of degress of accuracy include significant figures or decimal places
An example of converting between equivalent numerical forms include between fractions decimals and percentages or between normal numbers and standard form
eg a pair of compasses a protractor and a ruler
11
AO2 Reason interpret and communicate mathematically when solving problemsYou need to demonstrate that you can analyse a problem select a suitable strategy and apply appropriate techniques to obtain a solution
This means that you need to show that you can
bull make logical deductions make inferences and draw conclusions from given mathematical data
bull recognise patterns and structures in a variety of situations and form generalisations
bull present arguments and chains of reasoning in a logical and structured way
bull interprete and communicate information accurately and change from one form of presentation to another
bull assesses the validity of an argument and critically evaluate a given way of presenting information
bull solve unstructured problems by putting them into a structured form involving a series of processes
bull apply combinations of mathematical skills and techniques using connections between different areas of mathematics in problem solving
bull interprete results in the context of a given problem and evaluate the methods used and solutions obtained
AO2 is assessed in all papers
Recognise and extent patterns
Take information and organise it to answer a problem
12
Section 4 Command wordsA command word is the part of the question that tells you what you need to do with your knowledge For example you might need to describe something explain something argue a point of view or list what you know The table below includes command words used in the assessment for this syllabus The use of the command word(s) within an question will relate to the context
Cambridge IGCSE Mathematics 0580 syllabus for 2020 2021 and 2022 Details of the assessment
37wwwcambridgeinternationalorgigcseBack to contents page
Command wordsThe table below includes command words used in the assessment for this syllabus The use of the command word will relate to the subject context
Command word What it means
Calculate work out from given facts figures or information generally using a calculator
Construct make an accurate drawing
Describe state the points of a topicgive characteristics and main features
Determine establish with certainty
Explain set out purposes or reasons make the relationships between things evident provide why andor how and support with relevant evidence
Give produce an answer from a given source or recallmemory
Plot mark point(s) on a graph
Show (that) provide structured evidence that leads to a given result
Sketch make a simple freehand drawing showing the key features
Work out calculate from given facts figures or information with or without the use of a calculator
Write give an answer in a specific form
Write down give an answer without significant working
The question below is taken from Paper 4 and illustrates the use of two command words
The command words lsquoWrite downrsquo indicates that you do not need to show your working and the answer should just be written down The mark allocation [1] also supports this
The command words lsquoShow thatrsquo indicate that you need to provide evidence in the form of a clear mathematical explanation to demonstrate that you know how to obtain the given result In other words you need to show a method that leads to the result
The answer space in this case does not contain a dotted answer line as there is no single lsquoanswerrsquo to be found Your working that leads to the given result should be written in the blank working space
13
This section takes you through an example question and learner response from one of the 2020 specimen papers for this course It will help you to identify the command words and other key instructions within questions and to understand what is required in your response
This section is structured as follows
QuestionThe command words and instructions in the question have
been highlighted and explained This should help you to understand clearly what is required by the question
Mark schemeThis tells you as clearly as possible what an examiner expects
from an answer to award marks
Example candidate responseThis an exemplar answer written in the style of
a high level candidate
How the answer could have been improvedThis summarises what could be done to gain more marks
All information and advice in this section is specific to the example question and response being demonstrated It should give you an idea of how your responses might be viewed by an examiner but it is not a list of what to do in all questions In your own examination you will need to pay careful attention to what each question is asking you to do
Common mistakesThis will help you to avoid common mistakes made by
candidates So often candidates lose marks in their exams because they misread or misinterpret the questions
Section 5 Example candidate response
14
QuestionThe question used in this example is from Specimen Paper 3 (Core) It represents the type of structured question you will see in both Paper 3 (Core) and Paper 4 (Extended) A structured question means that it is broken into several parts Often later parts will depend on your answers to earlier parts
This means that you cannot find the answer by
measuring the diagramWork out indicates that the answer should be calculated from the given information so measurement will not score marks
The allocation of 1 mark indicates that the answer can be obtained with minimum working
Give reasons for your answer indicates that your answer should be supported with reasons using the correct mathematical terminology You must justify your answer
Use trigonometry to calculate indicates that you should use this method with the given information to find the answer and that a calculator is needed to solve the problem If you did not use trigonometry you would not be awarded any marks
15
Show that indicates the answer is given and you need to write down all of the steps in a method that leads to the given answer You need to provide evidence that you understand and know how the answer is reached
Work out indicates that you should calculate the answer from the given information The mark allocation of 4 marks suggests that you will need to include several steps of working in order to get to the answer
Learner Guide
16
Answer Mark Notes(a)(i) 35 1 This is the only acceptable answer for this part of the question
(a)(ii) 74 1 This is the only acceptable answer for this part of the question
(b) 43deg and correct mathematical reasons
3 Two marks are awarded for the final answer of 43deg
The third mark is awarded for a fully correct reason for example angles on a straight line add up to 180deg and angles in a triangle add up to 180deg There are other correct reasons that could be also be used
If 43deg is not obtained one method mark can be awarded if the following calculation is seen in the working
180 ndash 128 or 128 ndash 85
(c) 322 or 3223hellip 2 This is the only acceptable answer for this part of the question
The answer has to be rounded correct to three significant figures or can be given with more figures in the answer
Those that did not get this answer can score one method mark for showing the following in their working
sin = 8 divide 15
(d)(i) 2 2300 225+2 This does not have to be shown in one step as long as the method shown is the same as this overall Those that do not
show this can have one method mark for showing the following in their working
300deg + 225deg
(d)(ii) 15 35 4 The answer 3 35pm is also acceptable for 4 marks
If the correct answer is not found one method mark is available for showing 375 divide 450 in their working and a second method mark can be awarded for sight of them multiplying their answer to this by 60 to change it to hours A third method mark can be awarded for adding their answer in hours to 14 45 ndash this shows the correct method so only one mark is lost for an incorrect final answers
Mark schemeYour examination papers will be marked and the overall number of marks for each paper will be recorded Your marks across all papers will then be converted to a grade
Final answer This value is what the examiner expects to see The answer has to be exactly as given in the mark scheme unless there are acceptable alternatives The mark scheme will always make it clear if there are acceptable alternative answers
Method marks Sometimes method marks are awarded for lines of working as well as for the final answer This means that you could get the final answer incorrect but still get some marks if you include the correct working The mark scheme does not include all possible methods so if you use a method not included in the mark scheme but it is accurate and relevant then the examiner will still award marks for the appropriate parts of the working ndash unless the questions asks you to use a specific method
example of a final answer
example of a method mark
17
Example candidate responseNow letrsquos look at the sample candidatersquos response to question 8 The examiners comments are in the orange boxes The candidate was awarded 8 marks out of 13
180 ndash 74 + 71 = 177
177
74
0 out of 1
The candidates working suggests they understand that the angle sum of a triangle is 180deg but they did not include brackets around 74 + 71 The answer 177deg is not sensible for this question
1 out of 1
The candidate recognises that there are parallel lines and that angle y is a corresponding angle to angle 74deg
180 ndash 128 = 52 180 ndash 85 ndash 52 = 43
43 angles on a straight line add up to 180deg
2 out of 3
The candidate has given a correct answer for w and shown correct working in two steps They have given a correct reason for 52deg using correct mathematical languge But they have not provided a reason to explain the angle 43deg They lose a mark for not also stating angle sum of a triangle is 180deg
sin p = 8 divide 15 = 053
p = sinndash1 (053)
p = 32005 320
1 out of 2
The candidate has correctly used trigonometry in their method They are awarded one method mark for the first line of working However they have rounded 05333333hellip (the result of 8 divide 15) to 052 and then calculated the inverse sin of 052 rather than 05333333 This has resulted in an inaccurate final answer This is called lsquopremature approximationrsquo and it is a very common error to make
18
AB2 = 3002 + 2252
= 140625
AB = 375
1 out of 2
The candidate has recognised the right-angled triangle and correctly used Pythagorasrsquo theorem in the first line of working However they have missed out an important step by not showing that you need to take the square root of 140625 to get 375 As this is a lsquoshow thatrsquo question and they missed a key step in the method they cannot be awarded full marks as the complete working is not shown One method mark is earned for the first line
T = = = 08333333hellip
08333333 hours = 08333333 times 60 minutes = 50 minutes
arrives at 14 45 + 50 mins = 3 35
DS
375450
3 35
3 out of 4
The candidate has found the time by correctly dividing the distance by the speed and recognised that this is in hours When converting the answer to a decimal they have not rounded the decimal but left its full value on the calculator to get 50 mins which is the correct approach Unfortunately after converting the time from 24 hour clock to 12 hour clock they did not include lsquopmrsquo to indicate that the time is in the afternoon and so the final answer is not quite right So 3 marks are awarded for all of a correct method but a mark is lost due to the accuracy of the final answer
19
How the answer could have been improvedThis answer could have been improved by
bull In part (a)(i) the answer of 177deg was not sensible given the diagram in the question If the candidate had checked their answer for sense they would have realised they had made a mistake It is always a good idea to check that your answer seems sensible before you move on to another question
bull In part (b) the candidate did all the correct steps but failed to provide both reasons There were two steps to the method which should have indicated to the candidate that there were two steps to justify and therefore two reasons should have been provided The mark allocation for the question [3] also indicates that more than one reason would be required one mark for the value of 43deg leaving two marks one mark for each of two reasons The candidate should have read the question carefully and again checked their response seemed reasonable
bull In part (c) the candidate rounded an intermediate answer which affected the accuracy of the final answer This caused them to lose a mark despite using a correct method You should only ever round the final answer do not round intermediate values If you can store the intermediate values in your calculator and so that you can use the full value in your calcuations If youre not able to do this and you have to round the intermediate values do not round them to less than three significant figures
bull In part (d)(i) the candidate missed out a step in the method As this was a show that question they needed to show all the steps in the method Its important to show all steps even if they seem obvious
bull In part (d)(ii) the candidate made a silly error by not stating that the time was pm When working with time answers are accepted in either 24 clock or 12 clock time but if you give your answer in the 12 hour clock then it must include am or pm as well
Common mistakesThere were a number of common mistakes made by other candidates on this question
bull Accuracy of answers
In parts (c) and (d)(ii) a common error was premature rounding ndash rounding intermediate values in the method before the final answer which resulted in their final answer not being accurate Other candidates gave the final answer to less than three significant figures ignoring the instruction on the front of the paper to round to three significant figures
bull Using incorrect terminology when giving reasons
In part (b) the most common error was to not give full reasons to support the answer Another common error was to provide a reason that did not use the correct mathematical language such as lsquoThey add up to 180degrsquo and lsquoIt is a straight linersquo which could not be awarded marks
bull Lack of knowledge
In part (c) a number of candidates had limited knowledge of trigonometry and did not choose the correct trig ratio which was the sine ratio This is why good revision is important
bull Not checking answers
In part (a)(i) even though the diagram is drawn NOT TO SCALE it is possible to see that the angle is an acute angle and should therefore not be bigger than 90deg This should alert candidate that if their answer is over 90deg it is not a sensible answer and they should go back and check their working
20
bull Inefficient method shown
In part (c) the lsquoShow thatrsquo question a number of candidates omitted an important step from the method this is often common in lsquoShow thatrsquo questions where every step must be shown no matter how obvious them seem
General adviceIn order to do your best when answering a mathematics question make sure you
bull revise all of the topics for the syllabus you are studying before the exam
bull understand what all the key terms and command words in the question mean
bull read the questions carefully and consider what you need to do before you do it
bull only round the final answer not intermediate values
bull show all steps in your working and show them clearly
bull round to the correct degree of accuracy
bull use the correct mathematical terminology
bull check your answers seem reasonable given the context or details of the question
21
It is important that you plan your revision in plenty of time for the examinations and that you develop a revision technique that works for you The advice in this section will help you revise and prepare for the examinations It is divided into general advice for all papers
Use the tick boxes to keep a record of what you have done what you plan to do or what you understand
For more advice on revision see the Cambridge Learner Revision Guide on our website
Section 6 Revision
Find out when the examinations are and plan your revision so you have time to revise Create a revision timetable and divide it into sections to cover each topic
Spend most of your time focussing on specific skills knowledge or issues that you have found more difficult when practicing them either during revision or earlier in the course
Write a summary of all the key information for a topic ndash use the checklists at the end of this section
Know the meaning of the command words used in questions and how to apply them to the information given Look at past examination papers and highlight the command words and check what they mean
Make revision notes and work on practice questions Reading alone does not work you need to be active and practice your maths
Work for shorter periods then have a break Revise small sections of the syllabus at a time but do this regularly
Test yourself by trying out some past exam questions Use the mark schemes to assess yourself and to be familiar with how marks are awarded for different questions
Be organised in advance with your notes texts exercise books revision guides and revision websites so you do not waste valuable revision time trying to find things
Make notes of key mathematical words that you should use in questions that ask you to lsquodescribersquo or give lsquogeometrical reasons forrsquo eg in describing transformations or giving reasons in circle theorem questions Look at the mark schemes for these types of questions from past papers to see how marks are awarded
Make sure you have all of the correct mathematical equipment ready for the exam particularly your calculator Make sure you are familiar with the all of the important functions on your calculator
Practice the areas you can do well not just those that you find more difficult
Take breaks and do things to relax when you take your breaks this will help you to be more productive when you are revising
Before the examination
22
During the examination
Plan your time according to the marks for each question For example a question worth one mark requires less time than a question one worth 4 marks If a question has several parts then the parts with more marks will need more time
Read each question very carefully
Identify the command words ndash you could underline or highlight them
Identify the other key words and information and perhaps underline them too particularly where
questions require reasoning or problem solving
Read the questions careully and make you have answered the question that is being asked
Show your working this is particularly important for questions where you are asked to lsquoshow that helliprsquo
Set your working out clearly so that it is easy to follow this makes it easier to keep track of what you have done and makes checking back through your work easier and it makes it easier for the examiner to mark your work try to write it in a logical order in the answer space
Write answers clearly if you want to change an answer then you should cross the answer out and write a replacement if your answer is on the answer line cross it out and write the replacement answer above it do not try to change numbers on the answer line as this can lead to unclear figures
Check your working and answers to avoid errors
Give your answer to the appropriate level of accuracy either the accuracy indicated in the question or the accuracy given on the front of the paper
Avoid rounding intermediate values part way through your calculation only round the final answer
Check that the answer that you have given is sensible and realistic for what is being asked
Use a pencil when drawing diagrams or completing graphs this means that you can change your answer more easily if you have made a mistake
Take care when reading scales
If you are asked for reasons for your answer then use the correct mathematical terms
Use the mark allocation given with the questionsparts of questions to try to judge how much work is needed to answer each part
23
Top tips for revision of Cambridge IGCSE Mathematics1 Summarise recall and applyMake sure that you can recall and apply the key information and mathematical techniques on each topic that you need for the exam
i Write a summary of the key information of a topicii Collect together some questions that test the knowledge and skills of this topic Ask your teacher for practice
questions or suitable past examination questions or use practice books or textbooksiii Test your recall by covering over the summary and trying to remember the details or use the summary as part of
the lsquoTeach the topicrsquo (Tip 3) or lsquoQuestion and answer cardsrsquo (Tip 4) activities iv After you have spent some time revising and practising the knowledge and skills answer the questions that you
collected together on the topic You might do this later on the same day as revising or a few days later Answer as many questions as you can in order to practise applying your knowledge
v Try creating your own questions by adapting existing ones and use these for practice when you return to a topic
On graph questions straight lines should be ruled and curves should be drawn freehand with a smooth curve
Donrsquot spend too long on any one part of a question If you are really stuck on a question then move on and come back to the question later if you have time As a rough guide each mark on the paper should take about one minute
2 Concept mapsConcept maps are a great way to revise the links between different factors or to explore a larger topic They can also be used to collect together your ideas
i Use a blank sheet of paper and turn it on its side (landscape)ii Put the topic title in the middle of the page and build the concept map outwards using lines called lsquobranchesrsquo
ndash The first branches are from the central topic to sub-topics draw these as thick lines
ndash Add new branches from the sub-topics to include more detail draw these as thinner lines
ndash Add even more detail to a point by adding more branches
This creates a hierarchy of information from lsquooverviewrsquo (the thick branches) to lsquofine detailrsquo (thinnest branches)
iii Write single key words or phrases along a branch and add drawings for visual impactiv Use different colours highlighter pens symbols and arrows to highlight key facts or issuesIt is a good idea to use a large piece of plain A3 (or larger) paper and lots of coloured pens
24
3 Teach the topicThis is a very simple but effective technique that focusses on knowledge recall It tests the brain and rehearses the information you need to know for a certain topic and so will help your revision
i Create some topic cards with key bullet points of information on Leave space for ticksii Give these to your parents family or friends for exampleiii Give yourself 10 minutes maximum to teach your audience the main points of the topic You could use a mini-
whiteboard or flip chart to helpiv Your audience tick off all the points you mention in your presentation and give you a final scoreThe brain loves competition so if you do not score full marks you can try again the next day or compete against friends This system of repeat and rehearsal is very effective especially with more complex topics and doesnt take much preparation
4 Question and answer (QampA) cardsThis is very similar to Teach the topic but less formal and less public for those who dislike performing in front of others It tests knowledge recall and rehearses the information you need to know for a certain topic
i Pick a topic and create two sets of cards question cards and answer cards You might find it helpful to make the question cards a different size or use different coloured card for answers
ii Make sure you have the topic or something appropriate depending on what you are focusing on as a heading on each card The questions should test your knowledge and understanding of key areas of the course
iii A friend or family member uses the cards to test you in short 5 or 10 minute periods at any time during the dayiv You could also do this alone by reading the questions to yourself giving the answer and then checking the
correct answer cardv This game can be adapted by using the cards to find matching pairs turn all cards face down across the space
in front of you Turn over two cards leaving them where they are If they match (one is a question card and the other is the corresponding answer card) pick up the pair and put them to one side If they dont match try to remember where they are and what is on each card then turn them back over Turn over two other cards Continue until you have matched all pairs
5 Question paper and mark schemesLooking at past question papers and the mark scheme helps you to familiarise yourself with what to expect and what the standard is
i Ask your teacher for past paper questions with mark schemes for the course ndash ask your teacher for help to make sure you are answering the correct questions and to simplify the mark scheme
ii Look at the revision checklist and identify which topic a given question relates to ndash you might need to ask your teacher to help you do this
iii Once you have finished revising a topic or unit time yourself answering some appropriate exam questions Check the mark schemes to see how well you would have scored or give the answers to your teacher to check
iv Add details or notes to the mark scheme where you missed out on marks in your original answers using a different coloured pen Use these notes when you revise and try the question again later
You can find plenty of past exam papers and mark schemes on the Cambridge International public website
httpwwwcambridgeinternationalorgprogrammes-and-qualificationscambridge-igcse-mathematics-0580past-papers
25
Other useful revision advice for Cambridge IGCSE Mathematics bull Before the exam make sure that you are familiar with your calculator and confident in using it
bull Look at the Example Candidate Response earlier in this guide Can you identify the strengths of the response andwhere they have made mistakes or lost marks
bull When you are attempting a past paper (or questions from a past paper) complete it without referring to yournotes so that you get a true idea of your strengths and weaknesses Then go back through the paper using yournotes and a different coloured pen to make corrections and changes After you have done as much as you can onthe paper mark it using the mark scheme Take notes of any points that you lost marks on
bull Donrsquot just revise the topics that you enjoy and are confident in If you identify an area that you are weaker inthen try to revisit the topic by reviewing your notes and doing some practice questions then use exam questionsto check whether you now understand
bull Return to topics later in your revision to check that you still remember and understand the topic and to help toensure that you recall more of the material when you get to the examination
Revision checklists for Cambridge IGCSE MathematicsThe tables on the following pages can be used as a revision checklist They do not contain all the detailed knowledge you need to know just an overview For more detail see the syllabus and talk to your teacher
You can use the tick boxes in the checklists to show when you have revised and are happy that you do not need to return to it Tick the lsquoRrsquo lsquoArsquo and lsquoGrsquo column to record your progress as follows
bull R = RED means you are really unsure and lack confidence in that area you might want to focus your revisionhere and possibly talk to your teacher for help
bull A = AMBER means you are reasonably confident in a topic but need some extra practicebull G = GREEN means you are very confident in a topic
As your revision progresses you can concentrate on the RED and AMBER topics in order to turn them into GREEN topics You might find it helpful to highlight each topic in red orange or green to help you prioritise
You can use the lsquoCommentsrsquo column to
bull add more information about the details for each pointbull include a reference to a useful resourcebull include a list of formulae or notationbull add learning aids such as rhymes poems or word playbull highlight areas of difficulty or things that you need to talk to your teacher about
There is a set of checklist for the Core syllabus and a different set for the Extended syllabus
Learner Guide
26
Core syllabus contentCore Number
Category You should be able to R A G CommentsNumber Identify and use
bull natural numbers
bull integers (positive negative and zero)
bull prime numbers
bull write a number as a product of its prime factors
bull square numbers and cube numbers
bull common factors and highest common factor of two numbers
bull common multiples and lowest common multiple of two numbers
bull rational numbers
bull irrational numbers (eg π radic2 )
bull real numbers
bull reciprocals
Learner Guide
27
Core Number
Question type You should be able to R A G CommentsSets and Venn diagrams
Understand notation of Venn diagrams
Definition of sets
eg A = xx is a natural number
B = abchellip
Notation
Number of elements in set A n(A)
Universal set
Union of A and B A cup B
Intersection of A and B A cap B
Squares square roots cubes and cube roots
Calculate
bull squares and cubes of numbers
bull square roots and cube roots of numbers
Learner Guide
28
Core Number
Question type You should be able to R A G CommentsDirected numbers
Use directed numbers in practical situations for example temperature changes
Fractions decimals and percentages
Use the language and notation of simple vulgar and decimal fractions and percentages
Recognise equivalent fractions decimals and percentages
Convert between fractions decimals and percentages
Ordering Order quantities by magnitude and demonstrate familiarity with the symbols = ne gt lt ⩾ ⩽
Indices and standard form (links to Algebraic manipulation)
Evaluate indices eg 25 5ndash2 1000 64frac12 8ndash23
Use the rules of indices for
bull multiplication of indices eg 4ndash3 times 45
bull division of indices eg 57 divide 53
bull index numbers raised to an index eg (23)2 (43)2
Use the standard form A times 10n where n is a positive or negative integer and 1 ⩽ A lt 10
bull convert numbers into and out of standard form
bull calculate with numbers in standard form
Learner Guide
29
Core Number
Question type You should be able to R A G CommentsFour rules
( + ndash times divide )
Use the four rules for calculations with
bull whole numbers
bull decimals
bull vulgar and mixed fractions
bull correct ordering of operations (BIDMAS) and use of bracketsEstimates Make estimates of numbers quantities and lengths
Give approximations to a specified number of
bull significant figures
bull decimal places
Round off answers to reasonable accuracy in the context of a given problem
Bounds Give upper and lower bounds for data given to a specified accuracy eg measured lengths
Ratio proportion rate
Understand ratio
Divide a quantity in a given ratio
Understand direct and inverse proportion
Use scales in practical situations
Use common measures of rate (formulae for other rates eg density and pressure will be given in the question)
Calculate average speed
Learner Guide
30
Core Number
Question type You should be able to R A G CommentsPercentages Calculate a percentage of a quantity
Express one quantity as a percentage of another quantity
Calculate percentage increase or decrease
Use of an electronic calculator
Use a calculator efficiently
Check accuracy of calculations
Time Calculate times in terms of the 24-hour and 12-hour clock
Read
bull clocks
bull dials
bull timetables
Money Calculate using money
Convert from one currency to another
Learner Guide
31
Core Number
Question type You should be able to R A G CommentsPersonal and small business finance
Use given data to solve problems on
bull earnings
bull simple interest
bull compound interest (you will need to know the compound interest formula)
bull discount
bull profit and loss
Extract data from tables and charts
Learner Guide
32
Core Algebra and graphs
Question type You should be able to R A G CommentsBasic algebra Use letters to express generalised numbers
Express basic arithmetic processes algebraically
Substitute numbers in formulae
Construct simple expressions and set up simple equations
Rearrange simple formulae
Algebraic manipulation
Manipulate directed numbers
Use brackets
bull expand a single bracket eg 3x(2x ndash4y)
bull expand a pair of brackets eg (x + 3) (x ndash 7)
Extract common factors eg factorise 9x2 + 15xy
Rules of indices Use and interpret positive negative and zero indices
Use the rules of indices eg to simplify algebra such as
bull 3x4 times 5x
bull 10x3 divide 2x2
bull (x6)2
Learner Guide
33
Core Algebra and graphs
Question type You should be able to R A G CommentsEquations and inequalities
Derive and solve simple linear equations in one unknown
Derive and solve simultaneous linear equations in two unknowns
Number sequences
(links to Squares square roots cubes and cube roots)
Continue a number sequence
Recognise patterns in sequences
Recognise relationships between difference sequences
Find the nth term of sequences for
bull liner sequences
bull simple quadratic sequences
bull cubic sequences
Practical graphs
(links to Mensuration)
Interpret and use graphs in practical situations including
bull travel graphs
bull conversion graphs
Draw graphs from given data
Learner Guide
34
Core Algebra and graphs
Question type You should be able to R A G CommentsGraphs of functions
(links to Co-ordinate geometry)
Construct tables of values for functions of the form
bull ax + b (linear)
bull plusmn x2 + ax + b (quadratic)
bull (x ne 0) (reciprocal)
where a and b are integer constants
Draw and interpret such graphs
Solve linear and quadratic equations approximately by graphical methods
Recognise and sketch the graphs of linear and quadratic functions
ax
Learner Guide
35
Core Co-ordinate geometry
Question type You should be able to R A G CommentsCo-ordinates Work with co-ordinates in two dimensions
Gradients Find the gradient of a straight line graph
Equation of straight line
Interpret and obtain the equation of a straight line graph in the form y = mx + c where the graph is given
Parallel lines Determine the equation of a straight line parallel to a given line eg find the equation of a line parallel to y = 4x ndash 1 that passes through (0 ndash3)
Learner Guide
36
Core Geometry
Question type You should be able to R A G CommentsGeometrical language
Use and interpret the geometrical terms
bull point
bull line
bull parallel
bull perpendicular
bull bearing
bull right angle acute obtuse and reflex angles
bull similar
bull congruent
Use and interpret the vocabulary of
bull triangles right-angled scalene isosceles equilateral
bull quadrilaterals
bull circles
bull polygons
bull simple solid figures including nets
Learner Guide
37
Core Geometry
Question type You should be able to R A G CommentsGeometrical constructions
Measure and draw lines and angles
Construct a triangle given the three sides using a ruler and a pair of compasses only
Scale drawings Read and make scale drawings
Similar figures Calculate lengths of similar figures
Congruent Recognise congruent shapes
Symmetry Recognise symmetry properties for triangles quadrilaterals and circles
Recognise line symmetry in two dimensions
Recognise and find the order of rotational symmetry in two dimensions
Learner Guide
38
Core Geometry
Question type You should be able to R A G CommentsAngle properties Calculate unknown angles explaining the properties that you
are using in geometrical language for angles
bull angles at a point
bull angles on a straight line and intersecting straight lines
bull angles within parallel lines
bull angles in triangles
bull angles in quadrilaterals
bull angles in regular polygons
bull angle in a semi-circle
bull angle between tangent and radius of a circle
Learner Guide
39
Core Mensuration
Question type You should be able to R A G CommentsMeasures bull Use current units of
bull mass
bull length
bull area
bull volume
bull capacity
Express quantities in terms of smaller or larger units including units of area and volume
Convert between units including units of area and volume
Perimiter Carry out calculations involving
bull perimeter and area of a rectangle
bull perimeter and area of a triangle
bull perimeter and area of parallelogram
bull perimeter and area of a trapezium
bull perimeter and area of shapes made by combining
bull rectangles triangles parallelograms andor trapeziums
Learner Guide
40
Core Mensuration
Question type You should be able to R A G CommentsCircles Carry out calculations involving circumference and area of a
circle
Solve simple problems involving the arc length and sector area of a circle where the sector angle is a factor of 360deg
Surface area and volume
Carry out calculations involving
bull surface area and volume of a cuboid prism and cylinder (no formulae will be given for these shapes)
bull surface area and volume of a sphere pyramid and cone (formulae will be given for these shapes)
Areas and volumes of compound shapes
Carry out calculations involving the areas and volumes of compound shapes made from combinations of the shapes in Perimeter or Surface area and volume
Learner Guide
41
Core Trigonometry
Question type You should be able to R A G CommentsBearings Use and interpret three-figure bearings measured clockwise
from the North ie 000degndash360degTrigonometry Find unknown sides andor angles in right-angled triangles by
applying
bull Pythagorasrsquo theorem
bull sine cosine and tangent ratios for acute angles in right-angled triangles
Learner Guide
42
Core Vectors and transformations
Question type You should be able to R A G CommentsVectors in two dimensions (links to Trigonometry)
Describe a translation by using a vector represented by
AB or a
Add and subtract vectors
Multiply a vector by a scalar
Transformations Reflect simple shapes in horizontal or vertical lines
Rotate simple shapes through multiples of 90deg about
bull the origin
bull their vertices
bull the midpoints of their sides
Construct translations of simple shapes
Construct enlargements of simple shapes (positive and fractional scale factors)
Recognise and describe using the correct language
bull reflections
bull rotations
bull translations
bull enlargements (positive and fractional scale factors)
( )x
y
Learner Guide
43
Core Probability
Question type You should be able to R A G CommentsSingle events Calculate the probability of a single event as a fraction decimal
or percentage (not a ratio)Probability scale Understand and use the probability scale from 0 to 1
Sum to 1 Understand that the probability of an event occurring = 1 ndash the probability of the event not occurring
Relative frequency
Understand relative frequency as an estimate of probability
Work out expected frequencies using relative frequencyCombined events Calculate the probability of simple combined events using
bull tree diagrams
bull possibility diagrams (points on a grid)
bull Venn diagrams (2 sets only)
Learner Guide
44
Core Statistics
Question type What I need to do R A G CommentsClassify Collect classify and tabulate data
Interpret and compare
Read interpret and draw simple inferences from tables and statistical diagrams
Compare sets of data using
bull tables
bull graphs
bull statistical measures
Be aware of restrictions when making conclusions from data
Charts Construct and use
bull bar charts
bull pie charts
bull pictograms
bull stem-and-leaf diagrams
bull frequency distributions
bull histograms with equal intervals
bull scatter diagrams
Learner Guide
45
Question type What I need to do R A G CommentsAverages Calculate for individual and discrete data
bull mean
bull median
bull mode
bull range
and distinguish between their useCorrelation Understand what is meant by positive negative and zero
correlation with reference to a scatter diagramLine of best fit Draw interpret and use a ruled line of best fit by eye
Learner Guide
46
Extended syllabus content (includes required Core content)Extended Number
Question type You should be able to R A G CommentsNumber Identify and use
bull natural numbers
bull integers (positive negative and zero)
bull prime numbers
bull write a number as a product of its prime factors
bull square and cube numbers
bull common factors and highest common factor of two or more numbers
bull common multiples and lowest common multiple of two or more numbers
bull rational numbers
bull irrational numbers (eg π radic2 )
bull real numbers
bull reciprocals
Learner Guide
47
Extended Number
Question type You should be able to R A G CommentsSet notation and language
Use language notation and Venn diagrams to describe sets and represent relationships between sets as follows
Definition of sets egA = x x is a natural number
B = (xy) y = mx + c
C = x a ⩽ x ⩽ b
D = a b c hellip
Notation egnumber of elements in set A n(A)
lsquois an element ofrsquo isin
lsquois not an element ofrsquo notin
complement of set A
the empty set empty
the universal set
A is a subset of B A sube B
A is a proper subset of B A sub B
A is not a subset of B A ⊈ B
A is not a proper subset of B A nsub B
union of A and B A cup B
intersection of A and B A cap B
Learner Guide
48
Extended Number
Question type You should be able to R A G CommentsSquares square roots cubes and cube roots
Calculatebull squares of numbers
bull square roots of numbers
bull cubes of numbers
bull cube roots of numbers
bull other powers and roots of numbers
Directed numbers
Use directed numbers in practical situations for example temperature changes
Fractions decimals and percentages
Use the language and notation of simple vulgar and decimal fractions and percentages in appropriate contexts
Recognise equivalent fractions decimals and percentages
Convert between fractions decimals and percentages
Convert recurring decimals to fractions
Ordering Order quantities by magnitude and demonstrate familiarity with the symbols = ne gt lt ⩾ ⩽
Learner Guide
49
Extended Number
Question type You should be able to R A G CommentsIndices and standard form (links to Algebraic manipulation)
Evaluate indices including fractional negative and zero
eg 25 5ndash2 1000 10012 8ndash23
Use the rules of indices forbull multiplication of indices eg 43 times 45
bull division of indices eg 57 divide 53
bull index numbers raised to an index eg (43)2
Use the standard form A times 10n where n is a positive or negative integer and 1 ⩽ A lt 10bull convert into and out of standard form
bull calculate with numbers in standard form
Four rules
( + ndash times divide )
Use the four rules for calculations withbull whole numbers
bull decimals
bull vulgar and mixed fractions
bull correct ordering of operations (BIDMAS) and use of brackets
Learner Guide
50
Extended Number
Question type You should be able to R A G CommentsEstimates Make estimates of numbers quantities and lengths
Give approximations to a specified number of
bull significant figures
bull decimal places
Round off answers to reasonable accuracy in the context of a given problem
Bounds Give upper and lower bounds for data given to a specified accuracy eg measured lengths
Obtain appropriate upper and lower bounds to solutions of simple problems given to a specified accuracy eg the lower and upper bounds for the area of a rectangle
Ratio proportion rate
(links to Direct and inverse proportion)
Understand ratio
Divide quantities in a given ratio
Increase and decrease a quantity by a given ratio
Understand numerical problems involving direct and inverse proportion
Use ratio and scales in practical situations
Use common measures of rate (formulae for other rates eg density and pressure will be given in the question)
Calculate average speed
Learner Guide
51
Extended Number
Question type What I need to do R A G CommentsPercentages Calculate a percentage of a quantity
Express one quantity as a percentage of another quantity
Calculate percentage increase or decrease
Calculate reverse percentages eg finding the cost price given the selling price and the percentage profit
Use of an electronic calculator
Use a calculator efficiently
Check accuracy of calculations
Time Calculate times in terms of the 24-hour and 12-hour clock
Read clocks dials and timetables
Money Calculate using money
Convert from one currency to another
Learner Guide
52
Extended Number
Question type You should be able to R A G CommentsPersonal and small business finance
Use given data to solve problems on
bull earnings
bull simple interest
bull compound interest
ndash you must know the compound interest formula
bull discount
bull profit and loss
Extract data from tables and charts
Exponential growth and decay
Use exponential growth and decay in population and finance eg depreciation bacteria growth
Learner Guide
53
Extended Algebra and graphs
Question type You should be able to R A G CommentsBasic algebra Use letters to express generalised numbers
Express basic arithmetic processes algebraically
Substitute numbers in complicated formulae
Construct and rearrange complicated formulae eg where the subject appears twice
Algebraic manipulation
Manipulate directed numbers
Use bracketsbull expand a single bracket eg expand 3x(2x ndash 4y)
bull expand a pair of brackets eg (x ndash 4)(x + 7)
bull expand products of more than two brackets eg (x + 4)(x ndash 7)(2x + 1)
Extract common factors eg factorise 9x2 + 15xy
Factorise expressions of the formbull ax + bx + kay + kby
bull asup2xsup2 ndash bsup2ysup2
bull asup2 + 2ab + bsup2
bull axsup2 + bx + c
Learner Guide
54
Extended Algebra and graphs
Question type You should be able to R A G CommentsAlgebraic fractions
Manipulate algebraic fractions eg
bull
bull
bull
bull
bull
Factorise and simplify algebraic fractions such as
Rules of indices Use and interpret positive negative and zero indices
Use and interpret fractional indices eg solve 32x = 2
Use the rules of indices to simplify algebra eg
x3 + x ndash 4
22x3 +
3(x ndash 5)2
3a4 +
5ab3
3a4 divide
9a10
1x ndash 2 +
2x ndash 3
x2 ndash 2xx2 ndash 5x + 6
3xndash4 times23
x12
32x5( )
3
2xndash2divide25
x12
Learner Guide
55
Extended Algebra and graphs
Question type You should be able to R A G CommentsEquations and inequalities
bull Derive and solve simple linear equations in one unknown
bull Derive and solve simultaneous linear equations in two unknowns
bull Derive and solve simultaneous equations involving one linear and one quadratic
Solve quadratic equations by
bull factorisation
bull completing the square
bull using the formula
Derive and solve simple linear inequalities including representing solutions on a number line
Linear programming
Represent inequalities graphically including using the conventions of
bull broken lines for strict inequalities
bull shading unwanted regions
Solve simple linear programming problems using graphical representations of inequalities
Learner Guide
56
Extended Algebra and graphs
Question type You should be able to R A G CommentsNumber sequences (links to Squares square roots cubes and cube roots)
Continue a number sequence
Recognise patterns in sequences
Recognise relationships between different sequences
Find the nth term of sequences of
bull linear sequences
bull quadratic sequences
bull cubic sequences
bull exponential sequences
and simple combinations of these
Direct and inverse proportion (links to Ratio proportion rate)
Express direct proportion algebraically
Express inverse proportion algebraically
Use algebraic expressions of direct and inverse proportion to find unknown quantities
Practical graphs
(links to Coordinate geometry)
Interpret and use graphs in practical situations including
bull travel graphs
bull conversion graphs
Draw graphs from given data
Learner Guide
57
Extended Algebra and graphs
Question type You should be able to R A G CommentsPractical graphs (links to Coordinate geometry) continued
Apply the idea of rate of change to simple kinematics involving
bull distancendashtime graphs
bull speedndashtime graphs
bull acceleration and deceleration
This may involve estimation and interpretation of the gradient of a tangent at a point
Calculate distance travelled as an area under a linear speedndash time graph
Learner Guide
58
Extended Algebra and graphs
Question type You should be able to R A G CommentsGraphs of functions (links to Coordinate geometry)
Construct tables of values and draw graphs for functions of the form
bull axn where a is a rational constant and n = minus2 minus1 0 1 2 3 and simple sums of not more than three of these
bull abx + c where a and c are rational constants and b is a positive integer
Solve associated equations approximately by graphical methods including finding and interpreting roots and finding turning points of quadratics by completing the square
Draw and interpret graphs representing exponential growth and decay problems
Recognise sketch and interpret graphs of
bull linear
bull quadratic
bull cubic
bull reciprocal
bull exponential
(knowledge of turning points and asymtotes is required)Tangents Estimate gradients of curves by drawing tangents
Learner Guide
59
Extended Algebra and graphs
Question type You should be able to R A G CommentsFunctions Use function notation eg
f(x) = 3x ndash 5 f x α 3x ndash5 to describe simple functions
Find inverse functions f ndash1 (x)
Form composite functions as defined by gf(x) = g(f(x))
Derivatives Understand the idea of a derived function
Use derivatives of the form axn and simple sums of not more than three of these (a is a rational constant and n is a positive integer or 0)
Apply differentiation to gradients and turning points (stationary points)
Use any method to explain whether the turning point is a maximum or a minimum eg second derivative or gradient of function on either side of turning point
Learner Guide
60
Extended Co-ordinate geometry
Question type You should be able to R A G CommentsStraight line graphs
Work with co-ordinates in two dimensions
Gradient Find the gradient of a straight line graph
Calculate the gradient of a straight line from the co-ordinates of two points on it
Length and midpoint
Calculate the length and the co-ordinates of the midpoint of a straight line segment from the co-ordinates of its end points
Equation of line Interpret and obtain the equation of a straight line graph
Parallel lines Determine the equation of a straight line parallel to a given line eg find the equation of a line parallel to y = 4x ndash 1 that passes through (0 ndash3)
Perpendicular lines
Find the gradient of parallel and perpendicular lines eg
bull find the gradient of a line perpendicular to y = 3x + 1
bull find the equation of a line perpendicular to one passing through the co-ordinates (1 3) and (ndash2 ndash9)
Learner Guide
61
Extended Geometry
Question type You should be able to R A G CommentsGeometrical language
Use and interpret the geometrical terms
bull point
bull line
bull parallel
bull perpendicular
bull bearing
bull right angle acute obtuse and reflex angles
bull similar
bull congruent
Use and interpret the vocabulary of
bull triangles right-angled scalene isosceles equilateral
bull quadrilaterals
bull circles
bull polygons
bull simple solid figures including nets
Learner Guide
62
Extended Geometry
Question type What I need to do R A G CommentsGeometrical constructions
Measure and draw lines and angles
Construct a triangle given the three sides using a ruler and a pair of compasses only
Scale drawings Read and make scale drawings
Similar figures Calculate lengths of similar figures
Use relationships between areas of similar triangles and in similar figures
Use relationships between volumes and surface areas of similar solids
Congruent triangles
Use the congruence criteria for triangles (SSS ASA SAS RHS)
Symmetry Recognise symmetry properties for triangles quadrilaterals and circles
Recognise line symmetry in two dimensions
Recognise and find the order of rotational symmetry in two dimensions
Learner Guide
63
Extended Geometry
Question type You should be able to R A G CommentsSymmetry (continued)
Use the following symmetry properties of circles
bull equal chords are equidistant from the centre
bull perpendicular bisector of a chord passes through the centre
bull tangents from an external point are equal in length
Recognise and use symmetry properties of
bull prism cylinder cone and pyramid
Learner Guide
64
Extended Geometry
Question type You should be able to R A G CommentsAngle properties Calculate unknown angles explaining the properties that
you are using in geometrical language for the following geometrical properties
bull angles at a point
bull angles at a point on a straight line and intersecting straight lines
bull angles formed within parallel lines
bull angle properties of triangles and quadrilaterals
bull angle properties of regular polygons
bull angle in a semi-circle
bull angle between tangent and radius of a circle
bull angles properties of irregular polygons
bull angle at the centre of a circle is twice the angle at the circumference
bull angles in the same segment are equal
bull angles in opposite segments are supplementary cyclic quadrilaterals
bull alternate segment theorem
Learner Guide
65
Extended Mensuration
Question type What I need to do R A G CommentsMeasures Use current units of
bull mass
bull length
bull area
bull volume
bull capacity
Express quantities in terms of smaller or larger units including units of area and volume
Perimeter Carry out calculations involving
bull perimeter and area of a rectangle
bull perimeter and area of a triangle
bull perimeter and area of parallelogram
bull perimeter and area of a trapezium
bull perimeter and area of compound shapes made by combining rectangles triangles parallelograms andor trapeziums
Learner Guide
66
Extended Mensuration
Question type You should be able to R A G CommentsCircles Carry out calculations involving circumference and area of a
circle
Solve problems involving arc length and sector area of a circle
Surface area and volume
Carry out calculations involving
bull surface area and volume of a cuboid prism and cylinder (no formulae will be given for these shapes)
bull surface area and volume of a sphere pyramid and cone (formulae will be given for these shapes)
Compound shapes
Carry out calculations involving
bull area of a shape made by combining cuboids prisms andor cylinders
bull volume of a shape made by combining cuboids prisms andor cylinders
Learner Guide
67
Extended Trigonometry
Question type You should be able to R A G CommentsBearings Use and interpret three-figure bearings measured clockwise
from the North ie 000degndash360degTrigonometry Find unknown sides andor angles in right-angled triangles by
applying
bull Pythagorasrsquo theorem
bull sine cosine and tangent ratios for acute angles in right-angled triangles
Solve problems in two dimensions involving angles of elevation and depression
Know that the perpendicular distance from a point to a line is the shortest distance to the line
Trig graphs and equations
Recognise sketch and interpret graphs of simple trigonometric functions
Graph and know the properties of trigonometric functions
Solve simple trigonometric equations for values between 0deg
and 360deg eg Solve sin x = radic32
for values of x between 0deg and
360degGeneral trig Solve problems using sine and cosine rules for any triangle
Find the area of any triangle using frac12absinC
Trig in 3D Solve simple trigonometrical problems in three dimensions including angle between a line and a plane
Learner Guide
68
Extended Vectors and transformations
Question type You should be able to R A G CommentsVectors in two dimensions (links to Trigonometry)
Describe a translation by using a vector represented by
AB or a
Add and subtract vectors
Multiply a vector by a scalar
Transformations Reflect simple shapes in horizontal or vertical lines
Rotate simple shapes through multiples of 90deg about any point
Construct translations of simple shapes
Construct enlargements of simple shapes (positive fractional and negative scale factors)
Recognise and describe
bull reflections
bull rotations
bull translations
bull enlargements (positive fractional and negative scalefactors)
( )x
y
Learner Guide
69
Extended Vectors and transformations
Question type You should be able to R A G CommentsHarder vectors
Calculate the magnitude of a vector as and
understand that magnitude is denoted by modulus signs |A B| or |a|
Represent vectors by directed line segments
Use the sum and difference of two vectors
Use position vectors
( )x
yradicx2 + y2
Learner Guide
70
Extended Probability
Question type You should be able to R A G CommentsProbability (links to Four rules)
Calculate the probability of a single event as a fraction decimal or percentage (not a ratio)
Probability scale Understand and use the probability scale from 0 to 1
Sum to 1 Understand that the probability of an event occurring = 1 ndash the probability of the event not occurring
Relative frequency
Understand relative frequency as an estimate of probability
Work out expected frequencies using relative frequency
Combined events Calculate the probability of combined events using
bull tree diagrams
bull possibility diagrams
bull tables
Learner Guide
71
Extended Statistics
Question type You should be able to R A G CommentsClassify Collect classify and tabulate data
Interpret and compare
Read interpret and draw simple inferences from tables and statistical diagrams
Compare sets of data using
bull tables
bull graphs
bull statistical measures
Be aware of restrictions when making conclusions from data
Charts Construct and use
bull bar charts
bull pie charts
bull pictograms
bull stem ndash and ndash leaf diagrams
bull frequency distributions
bull histograms with equal and unequal intervals
bull scatter diagrams
Learner Guide
72
Extended Statistics
Question type You should be able to R A G CommentsAverages Calculate for individual and discrete data
bull mean
bull median
bull mode
bull range
and distinguish between their use
Estimated mean Calculate an estimate of the mean for grouped and continuous data
Identify the modal class from a grouped frequency distributionCumulative frequency
Construct and use cumulative frequency diagrams to estimate and interpret
bull the median
bull percentiles
bull quartiles
bull inter-quartile range
Construct and interpret box-and-whisker plots
Correlation Understand what is meant by positive negative and zero correlation with reference to a scatter diagram
Lines of best fit Draw interpret and use a ruled line of best fit by eye
Cambridge Assessment International Education1 Hills Road Cambridge CB1 2EU United Kingdomt +44 1223 553554e infocambridgeinternationalorg wwwcambridgeinternationalorg
Copyright copy UCLES October 2017
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- Check Box 1010137 Off
- Check Box 1010138 Off
- Text Field 3025
- Check Box 10367 Off
- Check Box 10368 Off
- Check Box 10369 Off
- Check Box 10407 Off
- Check Box 10431 Off
- Check Box 10432 Off
- Text Field 3059
- Check Box 104010 Off
- Check Box 10433 Off
- Check Box 10465 Off
- Check Box 104011 Off
- Check Box 10466 Off
- Check Box 10527 Off
- Text Field 3060
- Check Box 104012 Off
- Check Box 10528 Off
- Check Box 10529 Off
- Text Field 3063
- Check Box 10101037 Off
- Check Box 10101038 Off
- Check Box 10101039 Off
- Text Field 309
- Check Box 10275 Off
- Check Box 10276 Off
- Check Box 10277 Off
- Check Box 10101040 Off
- Check Box 10101041 Off
- Check Box 10101042 Off
- Text Field 3010
- Check Box 10278 Off
- Check Box 10279 Off
- Check Box 10280 Off
- Check Box 10101044 Off
- Check Box 10101045 Off
- Check Box 10101046 Off
- Check Box 10101047 Off
- Check Box 1010141 Off
- Check Box 1010142 Off
- Text Field 3011
- Check Box 10281 Off
- Check Box 10282 Off
- Check Box 10283 Off
- Check Box 10101048 Off
- Check Box 10101049 Off
- Check Box 10101050 Off
- Check Box 10101051 Off
- Check Box 10101052 Off
- Check Box 10101053 Off
- Check Box 10101054 Off
- Check Box 10101055 Off
- Check Box 10101056 Off
- Check Box 10101057 Off
- Check Box 10101058 Off
- Check Box 10101059 Off
- Check Box 10101060 Off
- Check Box 10101061 Off
- Check Box 10101062 Off
- Check Box 10101063 Off
- Check Box 10101064 Off
- Check Box 10101065 Off
- Check Box 10101066 Off
- Check Box 10101067 Off
- Check Box 10101068 Off
- Check Box 10101069 Off
- Check Box 10101070 Off
- Check Box 10101071 Off
- Check Box 10101072 Off
- Check Box 10101073 Off
- Check Box 10101074 Off
- Text Field 3012
- Check Box 10284 Off
- Check Box 10285 Off
- Check Box 10286 Off
- Text Field 3013
- Check Box 10101075 Off
- Check Box 10101076 Off
- Check Box 10101077 Off
- Text Field 3014
- Check Box 10101078 Off
- Check Box 1010143 Off
- Check Box 1010144 Off
- Text Field 3015
- Check Box 10287 Off
- Check Box 10288 Off
- Check Box 10289 Off
- Check Box 10334 Off
- Check Box 10335 Off
- Check Box 10336 Off
- Check Box 10371 Off
- Check Box 10372 Off
- Check Box 10436 Off
- Check Box 10437 Off
- Check Box 10438 Off
- Check Box 10447 Off
- Text Field 3016
- Check Box 10401 Off
- Check Box 10402 Off
- Check Box 10403 Off
- Check Box 10291 Off
- Check Box 10292 Off
- Check Box 10337 Off
- Check Box 10448 Off
- Check Box 10449 Off
- Check Box 10456 Off
- Check Box 10457 Off
- Check Box 10458 Off
- Check Box 10533 Off
- Check Box 10534 Off
- Check Box 10535 Off
- Check Box 10543 Off
- Check Box 10544 Off
- Check Box 10740 Off
- Check Box 10741 Off
- Text Field 3017
- Check Box 10101079 Off
- Check Box 10101080 Off
- Check Box 10101081 Off
- Check Box 10101082 Off
- Check Box 1010145 Off
- Check Box 1010146 Off
- Check Box 10293 Off
- Check Box 10294 Off
- Check Box 10295 Off
- Check Box 10338 Off
- Check Box 10339 Off
- Check Box 10370 Off
- Check Box 10101083 Off
- Check Box 10101084 Off
- Check Box 10101085 Off
- Check Box 10101086 Off
- Check Box 1010147 Off
- Check Box 1010148 Off
- Check Box 10296 Off
- Check Box 10297 Off
- Check Box 10298 Off
- Text Field 3018
- Check Box 10299 Off
- Check Box 10300 Off
- Check Box 10301 Off
- Check Box 10101087 Off
- Check Box 10101088 Off
- Check Box 10101089 Off
- Check Box 10101090 Off
- Check Box 1010149 Off
- Check Box 1010150 Off
- Check Box 10302 Off
- Check Box 10303 Off
- Check Box 10304 Off
- Text Field 3019
- Check Box 10305 Off
- Check Box 10306 Off
- Check Box 10307 Off
- Text Field 3020
- Check Box 10308 Off
- Check Box 10309 Off
- Check Box 103010 Off
- Text Field 311
- Check Box 10141 Off
- Check Box 10142 Off
- Check Box 10143 Off
- Check Box 10144 Off
- Check Box 10145 Off
- Check Box 10149 Off
- Check Box 10257 Off
- Check Box 10258 Off
- Check Box 10259 Off
- Check Box 10310 Off
- Check Box 10311 Off
- Check Box 10312 Off
- Check Box 10331 Off
- Check Box 10332 Off
- Check Box 10333 Off
- Check Box 10313 Off
- Check Box 10314 Off
- Check Box 10315 Off
- Check Box 10316 Off
- Check Box 10317 Off
- Check Box 10318 Off
- Check Box 10319 Off
- Check Box 10320 Off
- Check Box 10321 Off
- Check Box 10322 Off
- Check Box 10323 Off
- Check Box 10324 Off
- Check Box 10325 Off
- Check Box 10326 Off
- Check Box 10327 Off
- Check Box 10399 Off
- Check Box 10400 Off
- Check Box 10530 Off
- Text Field 335
- Check Box 10567 Off
- Check Box 10568 Off
- Check Box 10569 Off
- Check Box 10570 Off
- Check Box 10571 Off
- Check Box 10572 Off
- Check Box 10573 Off
- Check Box 10574 Off
- Check Box 10575 Off
- Check Box 10576 Off
- Check Box 10577 Off
- Check Box 10578 Off
- Check Box 10597 Off
- Check Box 10598 Off
- Check Box 10599 Off
- Check Box 10579 Off
- Check Box 10580 Off
- Check Box 10581 Off
- Check Box 10582 Off
- Check Box 10583 Off
- Check Box 10584 Off
- Check Box 10585 Off
- Check Box 10586 Off
- Check Box 10587 Off
- Check Box 10588 Off
- Check Box 10589 Off
- Check Box 10590 Off
- Check Box 10591 Off
- Check Box 10592 Off
- Check Box 10593 Off
- Check Box 10594 Off
- Check Box 10595 Off
- Check Box 10596 Off
- Check Box 10600 Off
- Check Box 10601 Off
- Check Box 10602 Off
- Check Box 10603 Off
- Check Box 10604 Off
- Check Box 10605 Off
- Check Box 10606 Off
- Check Box 10607 Off
- Check Box 10608 Off
- Check Box 10609 Off
- Check Box 106010 Off
- Check Box 106011 Off
- Check Box 106012 Off
- Check Box 106013 Off
- Check Box 106014 Off
- Check Box 106015 Off
- Check Box 106016 Off
- Check Box 106017 Off
- Text Field 315
- Check Box 10340 Off
- Check Box 10341 Off
- Check Box 10342 Off
- Check Box 10343 Off
- Check Box 10344 Off
- Check Box 10345 Off
- Check Box 10346 Off
- Check Box 10347 Off
- Check Box 10348 Off
- Check Box 10349 Off
- Check Box 10350 Off
- Check Box 10351 Off
- Check Box 10531 Off
- Check Box 10532 Off
- Check Box 10542 Off
- Text Field 313
- Check Box 10352 Off
- Check Box 10353 Off
- Check Box 10354 Off
- Text Field 316
- Check Box 10355 Off
- Check Box 10356 Off
- Check Box 10357 Off
- Check Box 10358 Off
- Check Box 10359 Off
- Check Box 10360 Off
- Check Box 10361 Off
- Check Box 10362 Off
- Check Box 10363 Off
- Check Box 10364 Off
- Check Box 10365 Off
- Check Box 10366 Off
- Check Box 10404 Off
- Check Box 10405 Off
- Check Box 10406 Off
- Text Field 352
- Check Box 102021 Off
- Check Box 102022 Off
- Check Box 102040 Off
- Check Box 102041 Off
- Check Box 102042 Off
- Check Box 102043 Off
- Check Box 102044 Off
- Check Box 102045 Off
- Check Box 102046 Off
- Check Box 102047 Off
- Check Box 102048 Off
- Check Box 102049 Off
- Check Box 102050 Off
- Check Box 102051 Off
- Check Box 102052 Off
- Check Box 102065 Off
- Check Box 102066 Off
- Check Box 102067 Off
- Check Box 102053 Off
- Check Box 102054 Off
- Check Box 102055 Off
- Text Field 351
- Check Box 102056 Off
- Check Box 102057 Off
- Check Box 102058 Off
- Check Box 102059 Off
- Check Box 102060 Off
- Check Box 102061 Off
- Check Box 102062 Off
- Check Box 102063 Off
- Check Box 102064 Off
- Check Box 102068 Off
- Check Box 102069 Off
- Check Box 102070 Off
- Text Field 318
- Check Box 10373 Off
- Check Box 10374 Off
- Check Box 10375 Off
- Check Box 10376 Off
- Check Box 10377 Off
- Check Box 10378 Off
- Check Box 10379 Off
- Check Box 10380 Off
- Check Box 10381 Off
- Check Box 10382 Off
- Check Box 10383 Off
- Check Box 10384 Off
- Check Box 10385 Off
- Check Box 10386 Off
- Check Box 10387 Off
- Text Field 317
- Check Box 10388 Off
- Check Box 10389 Off
- Check Box 10390 Off
- Check Box 102023 Off
- Check Box 102024 Off
- Check Box 102025 Off
- Check Box 102026 Off
- Check Box 102027 Off
- Check Box 102028 Off
- Check Box 102071 Off
- Check Box 102072 Off
- Check Box 102073 Off
- Check Box 102029 Off
- Check Box 10391 Off
- Check Box 10392 Off
- Check Box 10393 Off
- Check Box 10394 Off
- Check Box 10395 Off
- Check Box 10396 Off
- Check Box 10397 Off
- Check Box 10398 Off
- Check Box 102030 Off
- Check Box 102031 Off
- Check Box 102032 Off
- Text Field 319
- Text Field 322
- Check Box 10408 Off
- Check Box 10409 Off
- Check Box 10410 Off
- Check Box 10411 Off
- Check Box 10412 Off
- Check Box 10413 Off
- Check Box 10414 Off
- Check Box 10415 Off
- Check Box 10416 Off
- Check Box 10417 Off
- Check Box 10418 Off
- Check Box 10419 Off
- Text Field 321
- Check Box 10420 Off
- Check Box 10421 Off
- Check Box 10422 Off
- Check Box 10423 Off
- Check Box 10424 Off
- Check Box 10425 Off
- Text Field 337
- Check Box 102033 Off
- Check Box 102034 Off
- Check Box 102035 Off
- Check Box 102036 Off
- Check Box 102037 Off
- Check Box 102038 Off
- Text Field 338
- Check Box 102039 Off
- Check Box 10426 Off
- Check Box 10427 Off
- Check Box 10428 Off
- Check Box 10429 Off
- Check Box 10430 Off
- Text Field 324
- Check Box 10434 Off
- Check Box 10435 Off
- Check Box 101051 Off
- Check Box 1010100 Off
- Check Box 1010101 Off
- Check Box 1010102 Off
- Check Box 1010128 Off
- Check Box 1010129 Off
- Check Box 1010130 Off
- Check Box 10439 Off
- Check Box 10440 Off
- Check Box 10441 Off
- Check Box 10442 Off
- Check Box 10443 Off
- Check Box 10444 Off
- Text Field 350
- Check Box 10742 Off
- Check Box 10743 Off
- Check Box 10744 Off
- Text Field 325
- Check Box 10445 Off
- Check Box 10446 Off
- Check Box 1010151 Off
- Check Box 1010152 Off
- Check Box 1010153 Off
- Check Box 1010154 Off
- Check Box 1010155 Off
- Check Box 1010156 Off
- Check Box 1010157 Off
- Check Box 10450 Off
- Check Box 10451 Off
- Check Box 10452 Off
- Text Field 326
- Check Box 1010158 Off
- Check Box 1010159 Off
- Check Box 1010160 Off
- Check Box 1010161 Off
- Check Box 1010162 Off
- Check Box 1010163 Off
- Check Box 10453 Off
- Check Box 10454 Off
- Check Box 10455 Off
- Check Box 10745 Off
- Check Box 10746 Off
- Check Box 10747 Off
- Check Box 10748 Off
- Check Box 10749 Off
- Check Box 10750 Off
- Check Box 1010167 Off
- Check Box 1010168 Off
- Check Box 1010169 Off
- Check Box 10459 Off
- Check Box 10460 Off
- Check Box 10461 Off
- Check Box 10462 Off
- Check Box 10463 Off
- Check Box 10464 Off
- Check Box 10611 Off
- Check Box 10612 Off
- Check Box 10613 Off
- Text Field 329
- Check Box 1010171 Off
- Check Box 1010172 Off
- Check Box 1010173 Off
- Check Box 1010174 Off
- Check Box 1010175 Off
- Check Box 1010176 Off
- Check Box 1010177 Off
- Check Box 1010178 Off
- Check Box 1010179 Off
- Check Box 10467 Off
- Check Box 10468 Off
- Check Box 10469 Off
- Check Box 10470 Off
- Check Box 10471 Off
- Check Box 10472 Off
- Check Box 1010180 Off
- Check Box 1010181 Off
- Check Box 1010182 Off
- Text Field 330
- Check Box 1010183 Off
- Check Box 1010184 Off
- Check Box 1010185 Off
- Check Box 10473 Off
- Check Box 10474 Off
- Check Box 10475 Off
- Check Box 10476 Off
- Check Box 10477 Off
- Check Box 10478 Off
- Check Box 1010186 Off
- Check Box 1010187 Off
- Check Box 1010188 Off
- Check Box 1010275 Off
- Check Box 1010276 Off
- Check Box 1010277 Off
- Text Field 331
- Check Box 1010189 Off
- Check Box 1010190 Off
- Check Box 1010191 Off
- Check Box 1010192 Off
- Check Box 1010193 Off
- Check Box 1010194 Off
- Check Box 1010354 Off
- Check Box 1010355 Off
- Check Box 1010356 Off
- Check Box 10479 Off
- Check Box 10480 Off
- Check Box 10481 Off
- Check Box 10482 Off
- Check Box 10483 Off
- Check Box 10484 Off
- Check Box 1010195 Off
- Check Box 1010196 Off
- Check Box 1010197 Off
- Check Box 1010278 Off
- Check Box 1010279 Off
- Check Box 1010280 Off
- Text Field 339
- Check Box 10614 Off
- Check Box 10615 Off
- Check Box 10616 Off
- Check Box 10617 Off
- Check Box 10618 Off
- Check Box 10619 Off
- Check Box 1010281 Off
- Check Box 1010282 Off
- Check Box 1010283 Off
- Text Field 340
- Check Box 1010284 Off
- Check Box 1010285 Off
- Check Box 1010286 Off
- Check Box 1010287 Off
- Check Box 1010288 Off
- Check Box 1010289 Off
- Check Box 10620 Off
- Check Box 10621 Off
- Check Box 10622 Off
- Check Box 10623 Off
- Check Box 10624 Off
- Check Box 10625 Off
- Check Box 1010290 Off
- Check Box 1010291 Off
- Check Box 1010292 Off
- Check Box 1010293 Off
- Check Box 1010294 Off
- Check Box 1010295 Off
- Check Box 10626 Off
- Check Box 10627 Off
- Check Box 10628 Off
- Check Box 10751 Off
- Check Box 10752 Off
- Check Box 10753 Off
- Text Field 342
- Check Box 1010296 Off
- Check Box 1010297 Off
- Check Box 1010298 Off
- Check Box 10632 Off
- Check Box 10633 Off
- Check Box 10634 Off
- Check Box 10635 Off
- Check Box 10636 Off
- Check Box 10637 Off
- Text Field 349
- Check Box 1010305 Off
- Check Box 1010306 Off
- Check Box 1010307 Off
- Check Box 1010308 Off
- Check Box 1010309 Off
- Check Box 10103010 Off
- Check Box 10641 Off
- Check Box 10642 Off
- Check Box 10643 Off
- Text Field 343
- Check Box 1010299 Off
- Check Box 1010300 Off
- Check Box 1010301 Off
- Check Box 1010302 Off
- Check Box 1010303 Off
- Check Box 1010304 Off
- Check Box 10638 Off
- Check Box 10639 Off
- Check Box 10640 Off
- Check Box 10644 Off
- Check Box 10645 Off
- Check Box 10646 Off
- Check Box 1010328 Off
- Check Box 10103012 Off
- Check Box 10103013 Off
- Check Box 10103014 Off
- Check Box 10103015 Off
- Check Box 10103016 Off
- Check Box 10648 Off
- Check Box 10649 Off
- Check Box 10650 Off
- Check Box 10651 Off
- Check Box 10652 Off
- Check Box 10653 Off
- Check Box 10654 Off
- Check Box 10755 Off
- Check Box 10756 Off
- Check Box 10757 Off
- Check Box 10758 Off
- Check Box 10759 Off
- Check Box 10760 Off
- Check Box 10761 Off
- Check Box 10762 Off
- Check Box 10763 Off
- Check Box 10764 Off
- Check Box 10765 Off
- Check Box 10766 Off
- Check Box 10767 Off
- Check Box 10768 Off
- Text Field 361
- Check Box 10103020 Off
- Check Box 10103021 Off
- Check Box 10103022 Off
- Text Field 362
- Text Field 371
- Check Box 10103018 Off
- Check Box 10103019 Off
- Check Box 10103059 Off
- Check Box 10655 Off
- Check Box 10656 Off
- Check Box 10657 Off
- Check Box 10658 Off
- Check Box 10673 Off
- Check Box 10754 Off
- Text Field 363
- Check Box 10103023 Off
- Check Box 10103024 Off
- Check Box 10103025 Off
- Check Box 10103026 Off
- Check Box 10103027 Off
- Check Box 10103028 Off
- Check Box 10103029 Off
- Check Box 10103030 Off
- Check Box 10103031 Off
- Check Box 10103032 Off
- Check Box 10103033 Off
- Check Box 10103034 Off
- Text Field 365
- Check Box 10103035 Off
- Check Box 10103036 Off
- Check Box 10103037 Off
- Text Field 366
- Check Box 10103038 Off
- Check Box 10103039 Off
- Check Box 10103040 Off
- Check Box 10103041 Off
- Check Box 10103042 Off
- Check Box 10103043 Off
- Text Field 367
- Check Box 10103044 Off
- Check Box 10103045 Off
- Check Box 10103046 Off
- Text Field 368
- Check Box 10103047 Off
- Check Box 10103048 Off
- Check Box 10103049 Off
- Text Field 369
- Check Box 10103050 Off
- Check Box 10103051 Off
- Check Box 10103052 Off
- Text Field 370
- Check Box 10103053 Off
- Check Box 10103054 Off
- Check Box 10103055 Off
- Check Box 10103056 Off
- Check Box 10103057 Off
- Check Box 10103058 Off
- Text Field 332
- Check Box 1010198 Off
- Check Box 1010199 Off
- Check Box 1010200 Off
- Check Box 1010201 Off
- Check Box 1010202 Off
- Check Box 1010203 Off
- Check Box 10485 Off
- Check Box 10486 Off
- Check Box 10487 Off
- Check Box 10488 Off
- Check Box 10489 Off
- Check Box 10490 Off
- Check Box 1010204 Off
- Check Box 1010205 Off
- Check Box 1010206 Off
- Check Box 10491 Off
- Check Box 10492 Off
- Check Box 10493 Off
- Check Box 10494 Off
- Check Box 10495 Off
- Check Box 10496 Off
- Check Box 1010207 Off
- Check Box 1010208 Off
- Check Box 1010209 Off
- Check Box 10497 Off
- Check Box 10498 Off
- Check Box 10499 Off
- Check Box 1010210 Off
- Check Box 1010211 Off
- Check Box 1010212 Off
- Check Box 10500 Off
- Check Box 10501 Off
- Check Box 10502 Off
- Check Box 10503 Off
- Check Box 10504 Off
- Check Box 10505 Off
- Check Box 1010213 Off
- Check Box 1010214 Off
- Check Box 1010215 Off
- Text Field 333
- Check Box 1010216 Off
- Check Box 1010217 Off
- Check Box 1010218 Off
- Check Box 1010219 Off
- Check Box 1010220 Off
- Check Box 1010221 Off
- Text Field 334
- Check Box 1010225 Off
- Check Box 1010226 Off
- Check Box 1010227 Off
- Text Field 3022
- Text Field 3021
- Check Box 1010228 Off
- Check Box 1010229 Off
- Check Box 1010230 Off
- Check Box 10512 Off
- Check Box 10513 Off
- Check Box 10514 Off
- Check Box 1010231 Off
- Check Box 1010232 Off
- Check Box 1010233 Off
- Check Box 1010310 Off
- Text Field 3044
- Check Box 1010234 Off
- Check Box 1010235 Off
- Check Box 1010236 Off
- Check Box 1010332 Off
- Check Box 1010333 Off
- Check Box 1010334 Off
- Check Box 1010335 Off
- Check Box 1010336 Off
- Check Box 1010337 Off
- Text Field 347
- Check Box 1010311 Off
- Check Box 1010312 Off
- Check Box 1010313 Off
- Check Box 1010314 Off
- Check Box 1010315 Off
- Check Box 1010316 Off
- Check Box 105010 Off
- Check Box 105011 Off
- Check Box 105012 Off
- Check Box 105013 Off
- Check Box 10659 Off
- Check Box 10660 Off
- Text Field 3023
- Check Box 10101014 Off
- Check Box 10101015 Off
- Check Box 10101016 Off
- Check Box 10515 Off
- Check Box 10516 Off
- Check Box 10517 Off
- Check Box 10518 Off
- Check Box 10519 Off
- Check Box 10520 Off
- Check Box 10101091 Off
- Check Box 10101092 Off
- Check Box 10101093 Off
- Check Box 10101094 Off
- Check Box 1010237 Off
- Check Box 1010238 Off
- Check Box 1010239 Off
- Check Box 1010240 Off
- Check Box 1010241 Off
- Check Box 10521 Off
- Check Box 10522 Off
- Check Box 10523 Off
- Check Box 1010242 Off
- Check Box 1010243 Off
- Check Box 1010244 Off
- Check Box 10524 Off
- Check Box 10525 Off
- Check Box 10526 Off
- Check Box 10101095 Off
- Check Box 10101096 Off
- Check Box 10101097 Off
- Check Box 10101098 Off
- Check Box 1010245 Off
- Check Box 1010246 Off
- Check Box 1010247 Off
- Check Box 1010248 Off
- Check Box 1010249 Off
- Text Field 3045
- Check Box 101010194 Off
- Check Box 101010195 Off
- Check Box 101010196 Off
- Check Box 10676 Off
- Check Box 10677 Off
- Check Box 10678 Off
- Check Box 10679 Off
- Check Box 10680 Off
- Check Box 10681 Off
- Check Box 101010197 Off
- Check Box 101010198 Off
- Check Box 101010199 Off
- Check Box 101010200 Off
- Check Box 101010201 Off
- Check Box 101010202 Off
- Check Box 101010203 Off
- Check Box 101010204 Off
- Check Box 101010205 Off
- Text Field 3046
- Check Box 101010209 Off
- Check Box 101010210 Off
- Check Box 101010211 Off
- Check Box 10682 Off
- Check Box 10683 Off
- Check Box 10684 Off
- Check Box 10685 Off
- Check Box 10686 Off
- Check Box 10687 Off
- Check Box 101010212 Off
- Check Box 101010213 Off
- Check Box 101010214 Off
- Check Box 1010102010 Off
- Check Box 1010102011 Off
- Check Box 1010102012 Off
- Text Field 3026
- Check Box 10536 Off
- Check Box 10537 Off
- Check Box 10538 Off
- Check Box 101010107 Off
- Check Box 101010108 Off
- Check Box 101010109 Off
- Text Field 3047
- Check Box 1010101010 Off
- Check Box 1010101011 Off
- Check Box 1010101012 Off
- Check Box 1010101013 Off
- Check Box 1010101023 Off
- Check Box 1010101024 Off
- Text Field 3048
- Check Box 1010101025 Off
- Check Box 1010101026 Off
- Check Box 1010101027 Off
- Check Box 1010101028 Off
- Check Box 1010101029 Off
- Check Box 1010101030 Off
- Text Field 3027
- Check Box 10539 Off
- Check Box 10540 Off
- Check Box 10541 Off
- Text Field 3028
- Check Box 101010110 Off
- Check Box 101010111 Off
- Check Box 101010112 Off
- Check Box 101010113 Off
- Check Box 101010114 Off
- Check Box 101010115 Off
- Check Box 101010215 Off
- Check Box 101010216 Off
- Check Box 101010217 Off
- Check Box 101010116 Off
- Check Box 101010117 Off
- Check Box 101010118 Off
- Text Field 3029
- Check Box 101010119 Off
- Check Box 101010120 Off
- Check Box 101010121 Off
- Check Box 101010122 Off
- Check Box 101010123 Off
- Check Box 101010124 Off
- Check Box 101010125 Off
- Text Field 3030
- Check Box 101010161 Off
- Check Box 101010162 Off
- Check Box 101010163 Off
- Check Box 101010164 Off
- Check Box 101010165 Off
- Check Box 101010166 Off
- Check Box 101010167 Off
- Text Field 3031
- Check Box 10545 Off
- Check Box 10546 Off
- Check Box 10547 Off
- Check Box 101010126 Off
- Check Box 101010127 Off
- Check Box 101010128 Off
- Check Box 101010129 Off
- Check Box 1010265 Off
- Check Box 1010266 Off
- Text Field 3032
- Check Box 10548 Off
- Check Box 10549 Off
- Check Box 10550 Off
- Check Box 101010130 Off
- Check Box 101010131 Off
- Check Box 101010132 Off
- Check Box 101010139 Off
- Check Box 101010140 Off
- Check Box 101010141 Off
- Check Box 101010142 Off
- Check Box 101010143 Off
- Check Box 101010144 Off
- Check Box 101010145 Off
- Check Box 101010146 Off
- Check Box 101010147 Off
- Check Box 101010148 Off
- Check Box 101010149 Off
- Check Box 101010150 Off
- Check Box 101010151 Off
- Check Box 101010152 Off
- Check Box 101010153 Off
- Check Box 101010154 Off
- Check Box 101010155 Off
- Check Box 101010156 Off
- Text Field 3042
- Check Box 10661 Off
- Check Box 10662 Off
- Check Box 10663 Off
- Check Box 101010184 Off
- Check Box 101010185 Off
- Check Box 101010186 Off
- Check Box 101010187 Off
- Check Box 1010326 Off
- Check Box 1010327 Off
- Check Box 10670 Off
- Check Box 10671 Off
- Check Box 10672 Off
- Check Box 101010188 Off
- Check Box 101010189 Off
- Check Box 101010190 Off
- Text Field 3033
- Check Box 10551 Off
- Check Box 10552 Off
- Check Box 10553 Off
- Text Field 3034
- Check Box 101010157 Off
- Check Box 101010158 Off
- Check Box 101010159 Off
- Text Field 3035
- Check Box 101010168 Off
- Check Box 101010169 Off
- Check Box 101010170 Off
- Text Field 3036
- Check Box 101010171 Off
- Check Box 101010172 Off
- Check Box 101010174 Off
- Check Box 101010175 Off
- Check Box 101010176 Off
- Check Box 101010177 Off
- Text Field 3056
- Check Box 101010173 Off
- Check Box 1010317 Off
- Check Box 1010318 Off
- Check Box 101010160 Off
- Check Box 1010267 Off
- Check Box 1010268 Off
- Check Box 10554 Off
- Check Box 10555 Off
- Check Box 10556 Off
- Text Field 3057
- Check Box 10557 Off
- Check Box 10558 Off
- Check Box 10559 Off
- Text Field 3058
- Check Box 10560 Off
- Check Box 10561 Off
- Check Box 10562 Off
- Check Box 10563 Off
- Check Box 10564 Off
- Check Box 10565 Off
- Check Box 10566 Off
- Check Box 10610 Off
- Check Box 10629 Off
- Check Box 10630 Off
- Check Box 10631 Off
- Check Box 10647 Off
- Check Box 10664 Off
- Check Box 10665 Off
- Check Box 10666 Off
- Text Field 3061
- Check Box 10667 Off
- Check Box 10668 Off
- Check Box 10669 Off
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- Text Field 3062
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6
You will be assessed at the end of the course using two written examinations The papers that you will sit are different for the Core and Extended courses
bull Paper 1 ndash Short-answer questionsbull Paper 3 ndash Structured questions
bull Paper 2 ndash Short-answer questionsbull Paper 4 ndash Structured questions
Components at a glanceThe table summarises the key information about each component
Component How long and how many marks Skills assessed Percentage of the
qualificationCore Paper 1
(Short-answer questions)
1 hour
56 marks Mathematical techniques as listed in the Core syllabus and applying those techniques to solve problems
35
Paper 3 (Structured questions)
2 hours
104 marks 65
Extended Paper 2 (Short-answer questions)
1 hour 30 minutes
70 marksMathematical techniques as listed in the Core and Extended syllabus and applying those techniques to solve problems
35
Paper 4 (Structured questions)
2 hours 30 minutes
130 marks 65
Section 2 How you will be assessed
Core Extended
Make sure you find out from your teacher which course you will be following
7
About the componentsIt is important that you understand the different types of question in each paper so you know what to expect
Core Paper 1 (Short-answer questions) and Paper 3 (Structured questions)
You need to answer all questions on each paper
Paper 3Paper 1
You can use an electronic calculator in both papers Ask your teacher to recommend a suitable calculator
Paper 1 contains lots of short-answer questions These are usually worth 1ndash3 marks each Some might be broken up into two parts
Write your working and answers in the spaces provided
The number of marks for each part is shown
Paper 3 contains structured questions Each question is split into many parts with each part usually being worth 1ndash4 marks Here for example question 1 is split over two pages
Often the answers to later parts will depend on the answers to earlier parts
8
Extended Paper 2 (Shortndashanswer questions) and Paper 4 (Structured questions)
You need to answer all questions on both papers
Paper 2 questions are short-answer questions Most questions are worth 1ndash3 marks with some being worth 4 or 5 marks Some questions might be broken up into two parts
Write your working and answers in the spaces provided
The number of marks for each part is shown
Paper 4Paper 2
You can use an electronic calculator in both papers Ask your teacher to recommend a suitable calculator
Paper 4 contains structured questions Each question is split into many parts with each part usually being worth 1ndash6 marks Here for example question 2 is split over two pages
Often the answers to later parts will depend on the answers to earlier parts
9
Equipment for the examMake sure you have
bull a blue or black pen (a spare pen is always a good idea)bull a pencil (for graphs and diagrams)bull an electronic calculatorbull a protractorbull a pair of compassesbull a ruler
1 Read the questions carefully to make sure that you understand what is being asked
2 Give your answers to the accuracy indicated in the question If none is given and the answer isnrsquot exact then
bull give your answer to three significant figures 123 9 12298 x
bull if the answer is in degrees then give it to one decimal place 231deg 9 23deg x
3 Include units with your answers if they are not given on the paper For example 1 kg of apples costs hellip pound120 9 120 x
4 Show your working Show as much working as you can for all your questions
5 If you make a mistake clearly cross out any working or answers that you do not want the examiner to mark
Use the value of π from your calculator or use 3142 which is given on the front page of the question paper
Timingbull If you are stuck on a question dont waste too much time trying to answer it ndash go on to the next question and
come back to the one you are stuck on at the endbull Use any time that you have left at the end of the exam to go back and check your answers and working
Make sure that you give your answer in the form asked for in the question eg some questions ask for answers to be given in terms of π For lengths areas and volumes give answers in decimals (not in surds or in terms of π) unless you are told to given an exact answer
You can gain marks for the correct working even if you have an incorrect answer or cannot complete the whole question
If you need more space ask for extra of paper and clearly indicate where the rest of the answer is written On the additional paper make it clear which questions(s) you are answering
General advice for all Papers
10
The areas of knowledge understanding and skills that you will be assessed on are called assessment objectives (AOs) There are two AOs for this course
AO1 Demonstrate knowledge and
understanding of mathematical techniques
AO2 Reason interpret and communicate
mathematically when solving problems
AO1 Demonstrate knowledge and understanding of mathematical techniquesYou need to show that you can recall and apply mathematical knowledge terminology and definitions to carry out single or multi-step solutions in mathematical and everyday situations
Section 3 What skills will be assessed
This means that you need to show that you can
bull organise process and present information accurately in written tabular graphical and diagrammatic forms
bull use and interpret mathematical notation correctly
bull perform calculations and procedures by suitable methods including using a calculator
bull understand systems of measurement in everyday use and make use of these
bull estimate approximate and work to degrees of accuracy appropriate to the context and convert between equivalent numerical forms
bull use geometrical instruments to measure and to draw to an acceptable degree of accuracy
bull recognise and use spatial relationships in two and three dimensions
AO1 is assessed in all papers
Use tables graphs and diagrams
An example of degress of accuracy include significant figures or decimal places
An example of converting between equivalent numerical forms include between fractions decimals and percentages or between normal numbers and standard form
eg a pair of compasses a protractor and a ruler
11
AO2 Reason interpret and communicate mathematically when solving problemsYou need to demonstrate that you can analyse a problem select a suitable strategy and apply appropriate techniques to obtain a solution
This means that you need to show that you can
bull make logical deductions make inferences and draw conclusions from given mathematical data
bull recognise patterns and structures in a variety of situations and form generalisations
bull present arguments and chains of reasoning in a logical and structured way
bull interprete and communicate information accurately and change from one form of presentation to another
bull assesses the validity of an argument and critically evaluate a given way of presenting information
bull solve unstructured problems by putting them into a structured form involving a series of processes
bull apply combinations of mathematical skills and techniques using connections between different areas of mathematics in problem solving
bull interprete results in the context of a given problem and evaluate the methods used and solutions obtained
AO2 is assessed in all papers
Recognise and extent patterns
Take information and organise it to answer a problem
12
Section 4 Command wordsA command word is the part of the question that tells you what you need to do with your knowledge For example you might need to describe something explain something argue a point of view or list what you know The table below includes command words used in the assessment for this syllabus The use of the command word(s) within an question will relate to the context
Cambridge IGCSE Mathematics 0580 syllabus for 2020 2021 and 2022 Details of the assessment
37wwwcambridgeinternationalorgigcseBack to contents page
Command wordsThe table below includes command words used in the assessment for this syllabus The use of the command word will relate to the subject context
Command word What it means
Calculate work out from given facts figures or information generally using a calculator
Construct make an accurate drawing
Describe state the points of a topicgive characteristics and main features
Determine establish with certainty
Explain set out purposes or reasons make the relationships between things evident provide why andor how and support with relevant evidence
Give produce an answer from a given source or recallmemory
Plot mark point(s) on a graph
Show (that) provide structured evidence that leads to a given result
Sketch make a simple freehand drawing showing the key features
Work out calculate from given facts figures or information with or without the use of a calculator
Write give an answer in a specific form
Write down give an answer without significant working
The question below is taken from Paper 4 and illustrates the use of two command words
The command words lsquoWrite downrsquo indicates that you do not need to show your working and the answer should just be written down The mark allocation [1] also supports this
The command words lsquoShow thatrsquo indicate that you need to provide evidence in the form of a clear mathematical explanation to demonstrate that you know how to obtain the given result In other words you need to show a method that leads to the result
The answer space in this case does not contain a dotted answer line as there is no single lsquoanswerrsquo to be found Your working that leads to the given result should be written in the blank working space
13
This section takes you through an example question and learner response from one of the 2020 specimen papers for this course It will help you to identify the command words and other key instructions within questions and to understand what is required in your response
This section is structured as follows
QuestionThe command words and instructions in the question have
been highlighted and explained This should help you to understand clearly what is required by the question
Mark schemeThis tells you as clearly as possible what an examiner expects
from an answer to award marks
Example candidate responseThis an exemplar answer written in the style of
a high level candidate
How the answer could have been improvedThis summarises what could be done to gain more marks
All information and advice in this section is specific to the example question and response being demonstrated It should give you an idea of how your responses might be viewed by an examiner but it is not a list of what to do in all questions In your own examination you will need to pay careful attention to what each question is asking you to do
Common mistakesThis will help you to avoid common mistakes made by
candidates So often candidates lose marks in their exams because they misread or misinterpret the questions
Section 5 Example candidate response
14
QuestionThe question used in this example is from Specimen Paper 3 (Core) It represents the type of structured question you will see in both Paper 3 (Core) and Paper 4 (Extended) A structured question means that it is broken into several parts Often later parts will depend on your answers to earlier parts
This means that you cannot find the answer by
measuring the diagramWork out indicates that the answer should be calculated from the given information so measurement will not score marks
The allocation of 1 mark indicates that the answer can be obtained with minimum working
Give reasons for your answer indicates that your answer should be supported with reasons using the correct mathematical terminology You must justify your answer
Use trigonometry to calculate indicates that you should use this method with the given information to find the answer and that a calculator is needed to solve the problem If you did not use trigonometry you would not be awarded any marks
15
Show that indicates the answer is given and you need to write down all of the steps in a method that leads to the given answer You need to provide evidence that you understand and know how the answer is reached
Work out indicates that you should calculate the answer from the given information The mark allocation of 4 marks suggests that you will need to include several steps of working in order to get to the answer
Learner Guide
16
Answer Mark Notes(a)(i) 35 1 This is the only acceptable answer for this part of the question
(a)(ii) 74 1 This is the only acceptable answer for this part of the question
(b) 43deg and correct mathematical reasons
3 Two marks are awarded for the final answer of 43deg
The third mark is awarded for a fully correct reason for example angles on a straight line add up to 180deg and angles in a triangle add up to 180deg There are other correct reasons that could be also be used
If 43deg is not obtained one method mark can be awarded if the following calculation is seen in the working
180 ndash 128 or 128 ndash 85
(c) 322 or 3223hellip 2 This is the only acceptable answer for this part of the question
The answer has to be rounded correct to three significant figures or can be given with more figures in the answer
Those that did not get this answer can score one method mark for showing the following in their working
sin = 8 divide 15
(d)(i) 2 2300 225+2 This does not have to be shown in one step as long as the method shown is the same as this overall Those that do not
show this can have one method mark for showing the following in their working
300deg + 225deg
(d)(ii) 15 35 4 The answer 3 35pm is also acceptable for 4 marks
If the correct answer is not found one method mark is available for showing 375 divide 450 in their working and a second method mark can be awarded for sight of them multiplying their answer to this by 60 to change it to hours A third method mark can be awarded for adding their answer in hours to 14 45 ndash this shows the correct method so only one mark is lost for an incorrect final answers
Mark schemeYour examination papers will be marked and the overall number of marks for each paper will be recorded Your marks across all papers will then be converted to a grade
Final answer This value is what the examiner expects to see The answer has to be exactly as given in the mark scheme unless there are acceptable alternatives The mark scheme will always make it clear if there are acceptable alternative answers
Method marks Sometimes method marks are awarded for lines of working as well as for the final answer This means that you could get the final answer incorrect but still get some marks if you include the correct working The mark scheme does not include all possible methods so if you use a method not included in the mark scheme but it is accurate and relevant then the examiner will still award marks for the appropriate parts of the working ndash unless the questions asks you to use a specific method
example of a final answer
example of a method mark
17
Example candidate responseNow letrsquos look at the sample candidatersquos response to question 8 The examiners comments are in the orange boxes The candidate was awarded 8 marks out of 13
180 ndash 74 + 71 = 177
177
74
0 out of 1
The candidates working suggests they understand that the angle sum of a triangle is 180deg but they did not include brackets around 74 + 71 The answer 177deg is not sensible for this question
1 out of 1
The candidate recognises that there are parallel lines and that angle y is a corresponding angle to angle 74deg
180 ndash 128 = 52 180 ndash 85 ndash 52 = 43
43 angles on a straight line add up to 180deg
2 out of 3
The candidate has given a correct answer for w and shown correct working in two steps They have given a correct reason for 52deg using correct mathematical languge But they have not provided a reason to explain the angle 43deg They lose a mark for not also stating angle sum of a triangle is 180deg
sin p = 8 divide 15 = 053
p = sinndash1 (053)
p = 32005 320
1 out of 2
The candidate has correctly used trigonometry in their method They are awarded one method mark for the first line of working However they have rounded 05333333hellip (the result of 8 divide 15) to 052 and then calculated the inverse sin of 052 rather than 05333333 This has resulted in an inaccurate final answer This is called lsquopremature approximationrsquo and it is a very common error to make
18
AB2 = 3002 + 2252
= 140625
AB = 375
1 out of 2
The candidate has recognised the right-angled triangle and correctly used Pythagorasrsquo theorem in the first line of working However they have missed out an important step by not showing that you need to take the square root of 140625 to get 375 As this is a lsquoshow thatrsquo question and they missed a key step in the method they cannot be awarded full marks as the complete working is not shown One method mark is earned for the first line
T = = = 08333333hellip
08333333 hours = 08333333 times 60 minutes = 50 minutes
arrives at 14 45 + 50 mins = 3 35
DS
375450
3 35
3 out of 4
The candidate has found the time by correctly dividing the distance by the speed and recognised that this is in hours When converting the answer to a decimal they have not rounded the decimal but left its full value on the calculator to get 50 mins which is the correct approach Unfortunately after converting the time from 24 hour clock to 12 hour clock they did not include lsquopmrsquo to indicate that the time is in the afternoon and so the final answer is not quite right So 3 marks are awarded for all of a correct method but a mark is lost due to the accuracy of the final answer
19
How the answer could have been improvedThis answer could have been improved by
bull In part (a)(i) the answer of 177deg was not sensible given the diagram in the question If the candidate had checked their answer for sense they would have realised they had made a mistake It is always a good idea to check that your answer seems sensible before you move on to another question
bull In part (b) the candidate did all the correct steps but failed to provide both reasons There were two steps to the method which should have indicated to the candidate that there were two steps to justify and therefore two reasons should have been provided The mark allocation for the question [3] also indicates that more than one reason would be required one mark for the value of 43deg leaving two marks one mark for each of two reasons The candidate should have read the question carefully and again checked their response seemed reasonable
bull In part (c) the candidate rounded an intermediate answer which affected the accuracy of the final answer This caused them to lose a mark despite using a correct method You should only ever round the final answer do not round intermediate values If you can store the intermediate values in your calculator and so that you can use the full value in your calcuations If youre not able to do this and you have to round the intermediate values do not round them to less than three significant figures
bull In part (d)(i) the candidate missed out a step in the method As this was a show that question they needed to show all the steps in the method Its important to show all steps even if they seem obvious
bull In part (d)(ii) the candidate made a silly error by not stating that the time was pm When working with time answers are accepted in either 24 clock or 12 clock time but if you give your answer in the 12 hour clock then it must include am or pm as well
Common mistakesThere were a number of common mistakes made by other candidates on this question
bull Accuracy of answers
In parts (c) and (d)(ii) a common error was premature rounding ndash rounding intermediate values in the method before the final answer which resulted in their final answer not being accurate Other candidates gave the final answer to less than three significant figures ignoring the instruction on the front of the paper to round to three significant figures
bull Using incorrect terminology when giving reasons
In part (b) the most common error was to not give full reasons to support the answer Another common error was to provide a reason that did not use the correct mathematical language such as lsquoThey add up to 180degrsquo and lsquoIt is a straight linersquo which could not be awarded marks
bull Lack of knowledge
In part (c) a number of candidates had limited knowledge of trigonometry and did not choose the correct trig ratio which was the sine ratio This is why good revision is important
bull Not checking answers
In part (a)(i) even though the diagram is drawn NOT TO SCALE it is possible to see that the angle is an acute angle and should therefore not be bigger than 90deg This should alert candidate that if their answer is over 90deg it is not a sensible answer and they should go back and check their working
20
bull Inefficient method shown
In part (c) the lsquoShow thatrsquo question a number of candidates omitted an important step from the method this is often common in lsquoShow thatrsquo questions where every step must be shown no matter how obvious them seem
General adviceIn order to do your best when answering a mathematics question make sure you
bull revise all of the topics for the syllabus you are studying before the exam
bull understand what all the key terms and command words in the question mean
bull read the questions carefully and consider what you need to do before you do it
bull only round the final answer not intermediate values
bull show all steps in your working and show them clearly
bull round to the correct degree of accuracy
bull use the correct mathematical terminology
bull check your answers seem reasonable given the context or details of the question
21
It is important that you plan your revision in plenty of time for the examinations and that you develop a revision technique that works for you The advice in this section will help you revise and prepare for the examinations It is divided into general advice for all papers
Use the tick boxes to keep a record of what you have done what you plan to do or what you understand
For more advice on revision see the Cambridge Learner Revision Guide on our website
Section 6 Revision
Find out when the examinations are and plan your revision so you have time to revise Create a revision timetable and divide it into sections to cover each topic
Spend most of your time focussing on specific skills knowledge or issues that you have found more difficult when practicing them either during revision or earlier in the course
Write a summary of all the key information for a topic ndash use the checklists at the end of this section
Know the meaning of the command words used in questions and how to apply them to the information given Look at past examination papers and highlight the command words and check what they mean
Make revision notes and work on practice questions Reading alone does not work you need to be active and practice your maths
Work for shorter periods then have a break Revise small sections of the syllabus at a time but do this regularly
Test yourself by trying out some past exam questions Use the mark schemes to assess yourself and to be familiar with how marks are awarded for different questions
Be organised in advance with your notes texts exercise books revision guides and revision websites so you do not waste valuable revision time trying to find things
Make notes of key mathematical words that you should use in questions that ask you to lsquodescribersquo or give lsquogeometrical reasons forrsquo eg in describing transformations or giving reasons in circle theorem questions Look at the mark schemes for these types of questions from past papers to see how marks are awarded
Make sure you have all of the correct mathematical equipment ready for the exam particularly your calculator Make sure you are familiar with the all of the important functions on your calculator
Practice the areas you can do well not just those that you find more difficult
Take breaks and do things to relax when you take your breaks this will help you to be more productive when you are revising
Before the examination
22
During the examination
Plan your time according to the marks for each question For example a question worth one mark requires less time than a question one worth 4 marks If a question has several parts then the parts with more marks will need more time
Read each question very carefully
Identify the command words ndash you could underline or highlight them
Identify the other key words and information and perhaps underline them too particularly where
questions require reasoning or problem solving
Read the questions careully and make you have answered the question that is being asked
Show your working this is particularly important for questions where you are asked to lsquoshow that helliprsquo
Set your working out clearly so that it is easy to follow this makes it easier to keep track of what you have done and makes checking back through your work easier and it makes it easier for the examiner to mark your work try to write it in a logical order in the answer space
Write answers clearly if you want to change an answer then you should cross the answer out and write a replacement if your answer is on the answer line cross it out and write the replacement answer above it do not try to change numbers on the answer line as this can lead to unclear figures
Check your working and answers to avoid errors
Give your answer to the appropriate level of accuracy either the accuracy indicated in the question or the accuracy given on the front of the paper
Avoid rounding intermediate values part way through your calculation only round the final answer
Check that the answer that you have given is sensible and realistic for what is being asked
Use a pencil when drawing diagrams or completing graphs this means that you can change your answer more easily if you have made a mistake
Take care when reading scales
If you are asked for reasons for your answer then use the correct mathematical terms
Use the mark allocation given with the questionsparts of questions to try to judge how much work is needed to answer each part
23
Top tips for revision of Cambridge IGCSE Mathematics1 Summarise recall and applyMake sure that you can recall and apply the key information and mathematical techniques on each topic that you need for the exam
i Write a summary of the key information of a topicii Collect together some questions that test the knowledge and skills of this topic Ask your teacher for practice
questions or suitable past examination questions or use practice books or textbooksiii Test your recall by covering over the summary and trying to remember the details or use the summary as part of
the lsquoTeach the topicrsquo (Tip 3) or lsquoQuestion and answer cardsrsquo (Tip 4) activities iv After you have spent some time revising and practising the knowledge and skills answer the questions that you
collected together on the topic You might do this later on the same day as revising or a few days later Answer as many questions as you can in order to practise applying your knowledge
v Try creating your own questions by adapting existing ones and use these for practice when you return to a topic
On graph questions straight lines should be ruled and curves should be drawn freehand with a smooth curve
Donrsquot spend too long on any one part of a question If you are really stuck on a question then move on and come back to the question later if you have time As a rough guide each mark on the paper should take about one minute
2 Concept mapsConcept maps are a great way to revise the links between different factors or to explore a larger topic They can also be used to collect together your ideas
i Use a blank sheet of paper and turn it on its side (landscape)ii Put the topic title in the middle of the page and build the concept map outwards using lines called lsquobranchesrsquo
ndash The first branches are from the central topic to sub-topics draw these as thick lines
ndash Add new branches from the sub-topics to include more detail draw these as thinner lines
ndash Add even more detail to a point by adding more branches
This creates a hierarchy of information from lsquooverviewrsquo (the thick branches) to lsquofine detailrsquo (thinnest branches)
iii Write single key words or phrases along a branch and add drawings for visual impactiv Use different colours highlighter pens symbols and arrows to highlight key facts or issuesIt is a good idea to use a large piece of plain A3 (or larger) paper and lots of coloured pens
24
3 Teach the topicThis is a very simple but effective technique that focusses on knowledge recall It tests the brain and rehearses the information you need to know for a certain topic and so will help your revision
i Create some topic cards with key bullet points of information on Leave space for ticksii Give these to your parents family or friends for exampleiii Give yourself 10 minutes maximum to teach your audience the main points of the topic You could use a mini-
whiteboard or flip chart to helpiv Your audience tick off all the points you mention in your presentation and give you a final scoreThe brain loves competition so if you do not score full marks you can try again the next day or compete against friends This system of repeat and rehearsal is very effective especially with more complex topics and doesnt take much preparation
4 Question and answer (QampA) cardsThis is very similar to Teach the topic but less formal and less public for those who dislike performing in front of others It tests knowledge recall and rehearses the information you need to know for a certain topic
i Pick a topic and create two sets of cards question cards and answer cards You might find it helpful to make the question cards a different size or use different coloured card for answers
ii Make sure you have the topic or something appropriate depending on what you are focusing on as a heading on each card The questions should test your knowledge and understanding of key areas of the course
iii A friend or family member uses the cards to test you in short 5 or 10 minute periods at any time during the dayiv You could also do this alone by reading the questions to yourself giving the answer and then checking the
correct answer cardv This game can be adapted by using the cards to find matching pairs turn all cards face down across the space
in front of you Turn over two cards leaving them where they are If they match (one is a question card and the other is the corresponding answer card) pick up the pair and put them to one side If they dont match try to remember where they are and what is on each card then turn them back over Turn over two other cards Continue until you have matched all pairs
5 Question paper and mark schemesLooking at past question papers and the mark scheme helps you to familiarise yourself with what to expect and what the standard is
i Ask your teacher for past paper questions with mark schemes for the course ndash ask your teacher for help to make sure you are answering the correct questions and to simplify the mark scheme
ii Look at the revision checklist and identify which topic a given question relates to ndash you might need to ask your teacher to help you do this
iii Once you have finished revising a topic or unit time yourself answering some appropriate exam questions Check the mark schemes to see how well you would have scored or give the answers to your teacher to check
iv Add details or notes to the mark scheme where you missed out on marks in your original answers using a different coloured pen Use these notes when you revise and try the question again later
You can find plenty of past exam papers and mark schemes on the Cambridge International public website
httpwwwcambridgeinternationalorgprogrammes-and-qualificationscambridge-igcse-mathematics-0580past-papers
25
Other useful revision advice for Cambridge IGCSE Mathematics bull Before the exam make sure that you are familiar with your calculator and confident in using it
bull Look at the Example Candidate Response earlier in this guide Can you identify the strengths of the response andwhere they have made mistakes or lost marks
bull When you are attempting a past paper (or questions from a past paper) complete it without referring to yournotes so that you get a true idea of your strengths and weaknesses Then go back through the paper using yournotes and a different coloured pen to make corrections and changes After you have done as much as you can onthe paper mark it using the mark scheme Take notes of any points that you lost marks on
bull Donrsquot just revise the topics that you enjoy and are confident in If you identify an area that you are weaker inthen try to revisit the topic by reviewing your notes and doing some practice questions then use exam questionsto check whether you now understand
bull Return to topics later in your revision to check that you still remember and understand the topic and to help toensure that you recall more of the material when you get to the examination
Revision checklists for Cambridge IGCSE MathematicsThe tables on the following pages can be used as a revision checklist They do not contain all the detailed knowledge you need to know just an overview For more detail see the syllabus and talk to your teacher
You can use the tick boxes in the checklists to show when you have revised and are happy that you do not need to return to it Tick the lsquoRrsquo lsquoArsquo and lsquoGrsquo column to record your progress as follows
bull R = RED means you are really unsure and lack confidence in that area you might want to focus your revisionhere and possibly talk to your teacher for help
bull A = AMBER means you are reasonably confident in a topic but need some extra practicebull G = GREEN means you are very confident in a topic
As your revision progresses you can concentrate on the RED and AMBER topics in order to turn them into GREEN topics You might find it helpful to highlight each topic in red orange or green to help you prioritise
You can use the lsquoCommentsrsquo column to
bull add more information about the details for each pointbull include a reference to a useful resourcebull include a list of formulae or notationbull add learning aids such as rhymes poems or word playbull highlight areas of difficulty or things that you need to talk to your teacher about
There is a set of checklist for the Core syllabus and a different set for the Extended syllabus
Learner Guide
26
Core syllabus contentCore Number
Category You should be able to R A G CommentsNumber Identify and use
bull natural numbers
bull integers (positive negative and zero)
bull prime numbers
bull write a number as a product of its prime factors
bull square numbers and cube numbers
bull common factors and highest common factor of two numbers
bull common multiples and lowest common multiple of two numbers
bull rational numbers
bull irrational numbers (eg π radic2 )
bull real numbers
bull reciprocals
Learner Guide
27
Core Number
Question type You should be able to R A G CommentsSets and Venn diagrams
Understand notation of Venn diagrams
Definition of sets
eg A = xx is a natural number
B = abchellip
Notation
Number of elements in set A n(A)
Universal set
Union of A and B A cup B
Intersection of A and B A cap B
Squares square roots cubes and cube roots
Calculate
bull squares and cubes of numbers
bull square roots and cube roots of numbers
Learner Guide
28
Core Number
Question type You should be able to R A G CommentsDirected numbers
Use directed numbers in practical situations for example temperature changes
Fractions decimals and percentages
Use the language and notation of simple vulgar and decimal fractions and percentages
Recognise equivalent fractions decimals and percentages
Convert between fractions decimals and percentages
Ordering Order quantities by magnitude and demonstrate familiarity with the symbols = ne gt lt ⩾ ⩽
Indices and standard form (links to Algebraic manipulation)
Evaluate indices eg 25 5ndash2 1000 64frac12 8ndash23
Use the rules of indices for
bull multiplication of indices eg 4ndash3 times 45
bull division of indices eg 57 divide 53
bull index numbers raised to an index eg (23)2 (43)2
Use the standard form A times 10n where n is a positive or negative integer and 1 ⩽ A lt 10
bull convert numbers into and out of standard form
bull calculate with numbers in standard form
Learner Guide
29
Core Number
Question type You should be able to R A G CommentsFour rules
( + ndash times divide )
Use the four rules for calculations with
bull whole numbers
bull decimals
bull vulgar and mixed fractions
bull correct ordering of operations (BIDMAS) and use of bracketsEstimates Make estimates of numbers quantities and lengths
Give approximations to a specified number of
bull significant figures
bull decimal places
Round off answers to reasonable accuracy in the context of a given problem
Bounds Give upper and lower bounds for data given to a specified accuracy eg measured lengths
Ratio proportion rate
Understand ratio
Divide a quantity in a given ratio
Understand direct and inverse proportion
Use scales in practical situations
Use common measures of rate (formulae for other rates eg density and pressure will be given in the question)
Calculate average speed
Learner Guide
30
Core Number
Question type You should be able to R A G CommentsPercentages Calculate a percentage of a quantity
Express one quantity as a percentage of another quantity
Calculate percentage increase or decrease
Use of an electronic calculator
Use a calculator efficiently
Check accuracy of calculations
Time Calculate times in terms of the 24-hour and 12-hour clock
Read
bull clocks
bull dials
bull timetables
Money Calculate using money
Convert from one currency to another
Learner Guide
31
Core Number
Question type You should be able to R A G CommentsPersonal and small business finance
Use given data to solve problems on
bull earnings
bull simple interest
bull compound interest (you will need to know the compound interest formula)
bull discount
bull profit and loss
Extract data from tables and charts
Learner Guide
32
Core Algebra and graphs
Question type You should be able to R A G CommentsBasic algebra Use letters to express generalised numbers
Express basic arithmetic processes algebraically
Substitute numbers in formulae
Construct simple expressions and set up simple equations
Rearrange simple formulae
Algebraic manipulation
Manipulate directed numbers
Use brackets
bull expand a single bracket eg 3x(2x ndash4y)
bull expand a pair of brackets eg (x + 3) (x ndash 7)
Extract common factors eg factorise 9x2 + 15xy
Rules of indices Use and interpret positive negative and zero indices
Use the rules of indices eg to simplify algebra such as
bull 3x4 times 5x
bull 10x3 divide 2x2
bull (x6)2
Learner Guide
33
Core Algebra and graphs
Question type You should be able to R A G CommentsEquations and inequalities
Derive and solve simple linear equations in one unknown
Derive and solve simultaneous linear equations in two unknowns
Number sequences
(links to Squares square roots cubes and cube roots)
Continue a number sequence
Recognise patterns in sequences
Recognise relationships between difference sequences
Find the nth term of sequences for
bull liner sequences
bull simple quadratic sequences
bull cubic sequences
Practical graphs
(links to Mensuration)
Interpret and use graphs in practical situations including
bull travel graphs
bull conversion graphs
Draw graphs from given data
Learner Guide
34
Core Algebra and graphs
Question type You should be able to R A G CommentsGraphs of functions
(links to Co-ordinate geometry)
Construct tables of values for functions of the form
bull ax + b (linear)
bull plusmn x2 + ax + b (quadratic)
bull (x ne 0) (reciprocal)
where a and b are integer constants
Draw and interpret such graphs
Solve linear and quadratic equations approximately by graphical methods
Recognise and sketch the graphs of linear and quadratic functions
ax
Learner Guide
35
Core Co-ordinate geometry
Question type You should be able to R A G CommentsCo-ordinates Work with co-ordinates in two dimensions
Gradients Find the gradient of a straight line graph
Equation of straight line
Interpret and obtain the equation of a straight line graph in the form y = mx + c where the graph is given
Parallel lines Determine the equation of a straight line parallel to a given line eg find the equation of a line parallel to y = 4x ndash 1 that passes through (0 ndash3)
Learner Guide
36
Core Geometry
Question type You should be able to R A G CommentsGeometrical language
Use and interpret the geometrical terms
bull point
bull line
bull parallel
bull perpendicular
bull bearing
bull right angle acute obtuse and reflex angles
bull similar
bull congruent
Use and interpret the vocabulary of
bull triangles right-angled scalene isosceles equilateral
bull quadrilaterals
bull circles
bull polygons
bull simple solid figures including nets
Learner Guide
37
Core Geometry
Question type You should be able to R A G CommentsGeometrical constructions
Measure and draw lines and angles
Construct a triangle given the three sides using a ruler and a pair of compasses only
Scale drawings Read and make scale drawings
Similar figures Calculate lengths of similar figures
Congruent Recognise congruent shapes
Symmetry Recognise symmetry properties for triangles quadrilaterals and circles
Recognise line symmetry in two dimensions
Recognise and find the order of rotational symmetry in two dimensions
Learner Guide
38
Core Geometry
Question type You should be able to R A G CommentsAngle properties Calculate unknown angles explaining the properties that you
are using in geometrical language for angles
bull angles at a point
bull angles on a straight line and intersecting straight lines
bull angles within parallel lines
bull angles in triangles
bull angles in quadrilaterals
bull angles in regular polygons
bull angle in a semi-circle
bull angle between tangent and radius of a circle
Learner Guide
39
Core Mensuration
Question type You should be able to R A G CommentsMeasures bull Use current units of
bull mass
bull length
bull area
bull volume
bull capacity
Express quantities in terms of smaller or larger units including units of area and volume
Convert between units including units of area and volume
Perimiter Carry out calculations involving
bull perimeter and area of a rectangle
bull perimeter and area of a triangle
bull perimeter and area of parallelogram
bull perimeter and area of a trapezium
bull perimeter and area of shapes made by combining
bull rectangles triangles parallelograms andor trapeziums
Learner Guide
40
Core Mensuration
Question type You should be able to R A G CommentsCircles Carry out calculations involving circumference and area of a
circle
Solve simple problems involving the arc length and sector area of a circle where the sector angle is a factor of 360deg
Surface area and volume
Carry out calculations involving
bull surface area and volume of a cuboid prism and cylinder (no formulae will be given for these shapes)
bull surface area and volume of a sphere pyramid and cone (formulae will be given for these shapes)
Areas and volumes of compound shapes
Carry out calculations involving the areas and volumes of compound shapes made from combinations of the shapes in Perimeter or Surface area and volume
Learner Guide
41
Core Trigonometry
Question type You should be able to R A G CommentsBearings Use and interpret three-figure bearings measured clockwise
from the North ie 000degndash360degTrigonometry Find unknown sides andor angles in right-angled triangles by
applying
bull Pythagorasrsquo theorem
bull sine cosine and tangent ratios for acute angles in right-angled triangles
Learner Guide
42
Core Vectors and transformations
Question type You should be able to R A G CommentsVectors in two dimensions (links to Trigonometry)
Describe a translation by using a vector represented by
AB or a
Add and subtract vectors
Multiply a vector by a scalar
Transformations Reflect simple shapes in horizontal or vertical lines
Rotate simple shapes through multiples of 90deg about
bull the origin
bull their vertices
bull the midpoints of their sides
Construct translations of simple shapes
Construct enlargements of simple shapes (positive and fractional scale factors)
Recognise and describe using the correct language
bull reflections
bull rotations
bull translations
bull enlargements (positive and fractional scale factors)
( )x
y
Learner Guide
43
Core Probability
Question type You should be able to R A G CommentsSingle events Calculate the probability of a single event as a fraction decimal
or percentage (not a ratio)Probability scale Understand and use the probability scale from 0 to 1
Sum to 1 Understand that the probability of an event occurring = 1 ndash the probability of the event not occurring
Relative frequency
Understand relative frequency as an estimate of probability
Work out expected frequencies using relative frequencyCombined events Calculate the probability of simple combined events using
bull tree diagrams
bull possibility diagrams (points on a grid)
bull Venn diagrams (2 sets only)
Learner Guide
44
Core Statistics
Question type What I need to do R A G CommentsClassify Collect classify and tabulate data
Interpret and compare
Read interpret and draw simple inferences from tables and statistical diagrams
Compare sets of data using
bull tables
bull graphs
bull statistical measures
Be aware of restrictions when making conclusions from data
Charts Construct and use
bull bar charts
bull pie charts
bull pictograms
bull stem-and-leaf diagrams
bull frequency distributions
bull histograms with equal intervals
bull scatter diagrams
Learner Guide
45
Question type What I need to do R A G CommentsAverages Calculate for individual and discrete data
bull mean
bull median
bull mode
bull range
and distinguish between their useCorrelation Understand what is meant by positive negative and zero
correlation with reference to a scatter diagramLine of best fit Draw interpret and use a ruled line of best fit by eye
Learner Guide
46
Extended syllabus content (includes required Core content)Extended Number
Question type You should be able to R A G CommentsNumber Identify and use
bull natural numbers
bull integers (positive negative and zero)
bull prime numbers
bull write a number as a product of its prime factors
bull square and cube numbers
bull common factors and highest common factor of two or more numbers
bull common multiples and lowest common multiple of two or more numbers
bull rational numbers
bull irrational numbers (eg π radic2 )
bull real numbers
bull reciprocals
Learner Guide
47
Extended Number
Question type You should be able to R A G CommentsSet notation and language
Use language notation and Venn diagrams to describe sets and represent relationships between sets as follows
Definition of sets egA = x x is a natural number
B = (xy) y = mx + c
C = x a ⩽ x ⩽ b
D = a b c hellip
Notation egnumber of elements in set A n(A)
lsquois an element ofrsquo isin
lsquois not an element ofrsquo notin
complement of set A
the empty set empty
the universal set
A is a subset of B A sube B
A is a proper subset of B A sub B
A is not a subset of B A ⊈ B
A is not a proper subset of B A nsub B
union of A and B A cup B
intersection of A and B A cap B
Learner Guide
48
Extended Number
Question type You should be able to R A G CommentsSquares square roots cubes and cube roots
Calculatebull squares of numbers
bull square roots of numbers
bull cubes of numbers
bull cube roots of numbers
bull other powers and roots of numbers
Directed numbers
Use directed numbers in practical situations for example temperature changes
Fractions decimals and percentages
Use the language and notation of simple vulgar and decimal fractions and percentages in appropriate contexts
Recognise equivalent fractions decimals and percentages
Convert between fractions decimals and percentages
Convert recurring decimals to fractions
Ordering Order quantities by magnitude and demonstrate familiarity with the symbols = ne gt lt ⩾ ⩽
Learner Guide
49
Extended Number
Question type You should be able to R A G CommentsIndices and standard form (links to Algebraic manipulation)
Evaluate indices including fractional negative and zero
eg 25 5ndash2 1000 10012 8ndash23
Use the rules of indices forbull multiplication of indices eg 43 times 45
bull division of indices eg 57 divide 53
bull index numbers raised to an index eg (43)2
Use the standard form A times 10n where n is a positive or negative integer and 1 ⩽ A lt 10bull convert into and out of standard form
bull calculate with numbers in standard form
Four rules
( + ndash times divide )
Use the four rules for calculations withbull whole numbers
bull decimals
bull vulgar and mixed fractions
bull correct ordering of operations (BIDMAS) and use of brackets
Learner Guide
50
Extended Number
Question type You should be able to R A G CommentsEstimates Make estimates of numbers quantities and lengths
Give approximations to a specified number of
bull significant figures
bull decimal places
Round off answers to reasonable accuracy in the context of a given problem
Bounds Give upper and lower bounds for data given to a specified accuracy eg measured lengths
Obtain appropriate upper and lower bounds to solutions of simple problems given to a specified accuracy eg the lower and upper bounds for the area of a rectangle
Ratio proportion rate
(links to Direct and inverse proportion)
Understand ratio
Divide quantities in a given ratio
Increase and decrease a quantity by a given ratio
Understand numerical problems involving direct and inverse proportion
Use ratio and scales in practical situations
Use common measures of rate (formulae for other rates eg density and pressure will be given in the question)
Calculate average speed
Learner Guide
51
Extended Number
Question type What I need to do R A G CommentsPercentages Calculate a percentage of a quantity
Express one quantity as a percentage of another quantity
Calculate percentage increase or decrease
Calculate reverse percentages eg finding the cost price given the selling price and the percentage profit
Use of an electronic calculator
Use a calculator efficiently
Check accuracy of calculations
Time Calculate times in terms of the 24-hour and 12-hour clock
Read clocks dials and timetables
Money Calculate using money
Convert from one currency to another
Learner Guide
52
Extended Number
Question type You should be able to R A G CommentsPersonal and small business finance
Use given data to solve problems on
bull earnings
bull simple interest
bull compound interest
ndash you must know the compound interest formula
bull discount
bull profit and loss
Extract data from tables and charts
Exponential growth and decay
Use exponential growth and decay in population and finance eg depreciation bacteria growth
Learner Guide
53
Extended Algebra and graphs
Question type You should be able to R A G CommentsBasic algebra Use letters to express generalised numbers
Express basic arithmetic processes algebraically
Substitute numbers in complicated formulae
Construct and rearrange complicated formulae eg where the subject appears twice
Algebraic manipulation
Manipulate directed numbers
Use bracketsbull expand a single bracket eg expand 3x(2x ndash 4y)
bull expand a pair of brackets eg (x ndash 4)(x + 7)
bull expand products of more than two brackets eg (x + 4)(x ndash 7)(2x + 1)
Extract common factors eg factorise 9x2 + 15xy
Factorise expressions of the formbull ax + bx + kay + kby
bull asup2xsup2 ndash bsup2ysup2
bull asup2 + 2ab + bsup2
bull axsup2 + bx + c
Learner Guide
54
Extended Algebra and graphs
Question type You should be able to R A G CommentsAlgebraic fractions
Manipulate algebraic fractions eg
bull
bull
bull
bull
bull
Factorise and simplify algebraic fractions such as
Rules of indices Use and interpret positive negative and zero indices
Use and interpret fractional indices eg solve 32x = 2
Use the rules of indices to simplify algebra eg
x3 + x ndash 4
22x3 +
3(x ndash 5)2
3a4 +
5ab3
3a4 divide
9a10
1x ndash 2 +
2x ndash 3
x2 ndash 2xx2 ndash 5x + 6
3xndash4 times23
x12
32x5( )
3
2xndash2divide25
x12
Learner Guide
55
Extended Algebra and graphs
Question type You should be able to R A G CommentsEquations and inequalities
bull Derive and solve simple linear equations in one unknown
bull Derive and solve simultaneous linear equations in two unknowns
bull Derive and solve simultaneous equations involving one linear and one quadratic
Solve quadratic equations by
bull factorisation
bull completing the square
bull using the formula
Derive and solve simple linear inequalities including representing solutions on a number line
Linear programming
Represent inequalities graphically including using the conventions of
bull broken lines for strict inequalities
bull shading unwanted regions
Solve simple linear programming problems using graphical representations of inequalities
Learner Guide
56
Extended Algebra and graphs
Question type You should be able to R A G CommentsNumber sequences (links to Squares square roots cubes and cube roots)
Continue a number sequence
Recognise patterns in sequences
Recognise relationships between different sequences
Find the nth term of sequences of
bull linear sequences
bull quadratic sequences
bull cubic sequences
bull exponential sequences
and simple combinations of these
Direct and inverse proportion (links to Ratio proportion rate)
Express direct proportion algebraically
Express inverse proportion algebraically
Use algebraic expressions of direct and inverse proportion to find unknown quantities
Practical graphs
(links to Coordinate geometry)
Interpret and use graphs in practical situations including
bull travel graphs
bull conversion graphs
Draw graphs from given data
Learner Guide
57
Extended Algebra and graphs
Question type You should be able to R A G CommentsPractical graphs (links to Coordinate geometry) continued
Apply the idea of rate of change to simple kinematics involving
bull distancendashtime graphs
bull speedndashtime graphs
bull acceleration and deceleration
This may involve estimation and interpretation of the gradient of a tangent at a point
Calculate distance travelled as an area under a linear speedndash time graph
Learner Guide
58
Extended Algebra and graphs
Question type You should be able to R A G CommentsGraphs of functions (links to Coordinate geometry)
Construct tables of values and draw graphs for functions of the form
bull axn where a is a rational constant and n = minus2 minus1 0 1 2 3 and simple sums of not more than three of these
bull abx + c where a and c are rational constants and b is a positive integer
Solve associated equations approximately by graphical methods including finding and interpreting roots and finding turning points of quadratics by completing the square
Draw and interpret graphs representing exponential growth and decay problems
Recognise sketch and interpret graphs of
bull linear
bull quadratic
bull cubic
bull reciprocal
bull exponential
(knowledge of turning points and asymtotes is required)Tangents Estimate gradients of curves by drawing tangents
Learner Guide
59
Extended Algebra and graphs
Question type You should be able to R A G CommentsFunctions Use function notation eg
f(x) = 3x ndash 5 f x α 3x ndash5 to describe simple functions
Find inverse functions f ndash1 (x)
Form composite functions as defined by gf(x) = g(f(x))
Derivatives Understand the idea of a derived function
Use derivatives of the form axn and simple sums of not more than three of these (a is a rational constant and n is a positive integer or 0)
Apply differentiation to gradients and turning points (stationary points)
Use any method to explain whether the turning point is a maximum or a minimum eg second derivative or gradient of function on either side of turning point
Learner Guide
60
Extended Co-ordinate geometry
Question type You should be able to R A G CommentsStraight line graphs
Work with co-ordinates in two dimensions
Gradient Find the gradient of a straight line graph
Calculate the gradient of a straight line from the co-ordinates of two points on it
Length and midpoint
Calculate the length and the co-ordinates of the midpoint of a straight line segment from the co-ordinates of its end points
Equation of line Interpret and obtain the equation of a straight line graph
Parallel lines Determine the equation of a straight line parallel to a given line eg find the equation of a line parallel to y = 4x ndash 1 that passes through (0 ndash3)
Perpendicular lines
Find the gradient of parallel and perpendicular lines eg
bull find the gradient of a line perpendicular to y = 3x + 1
bull find the equation of a line perpendicular to one passing through the co-ordinates (1 3) and (ndash2 ndash9)
Learner Guide
61
Extended Geometry
Question type You should be able to R A G CommentsGeometrical language
Use and interpret the geometrical terms
bull point
bull line
bull parallel
bull perpendicular
bull bearing
bull right angle acute obtuse and reflex angles
bull similar
bull congruent
Use and interpret the vocabulary of
bull triangles right-angled scalene isosceles equilateral
bull quadrilaterals
bull circles
bull polygons
bull simple solid figures including nets
Learner Guide
62
Extended Geometry
Question type What I need to do R A G CommentsGeometrical constructions
Measure and draw lines and angles
Construct a triangle given the three sides using a ruler and a pair of compasses only
Scale drawings Read and make scale drawings
Similar figures Calculate lengths of similar figures
Use relationships between areas of similar triangles and in similar figures
Use relationships between volumes and surface areas of similar solids
Congruent triangles
Use the congruence criteria for triangles (SSS ASA SAS RHS)
Symmetry Recognise symmetry properties for triangles quadrilaterals and circles
Recognise line symmetry in two dimensions
Recognise and find the order of rotational symmetry in two dimensions
Learner Guide
63
Extended Geometry
Question type You should be able to R A G CommentsSymmetry (continued)
Use the following symmetry properties of circles
bull equal chords are equidistant from the centre
bull perpendicular bisector of a chord passes through the centre
bull tangents from an external point are equal in length
Recognise and use symmetry properties of
bull prism cylinder cone and pyramid
Learner Guide
64
Extended Geometry
Question type You should be able to R A G CommentsAngle properties Calculate unknown angles explaining the properties that
you are using in geometrical language for the following geometrical properties
bull angles at a point
bull angles at a point on a straight line and intersecting straight lines
bull angles formed within parallel lines
bull angle properties of triangles and quadrilaterals
bull angle properties of regular polygons
bull angle in a semi-circle
bull angle between tangent and radius of a circle
bull angles properties of irregular polygons
bull angle at the centre of a circle is twice the angle at the circumference
bull angles in the same segment are equal
bull angles in opposite segments are supplementary cyclic quadrilaterals
bull alternate segment theorem
Learner Guide
65
Extended Mensuration
Question type What I need to do R A G CommentsMeasures Use current units of
bull mass
bull length
bull area
bull volume
bull capacity
Express quantities in terms of smaller or larger units including units of area and volume
Perimeter Carry out calculations involving
bull perimeter and area of a rectangle
bull perimeter and area of a triangle
bull perimeter and area of parallelogram
bull perimeter and area of a trapezium
bull perimeter and area of compound shapes made by combining rectangles triangles parallelograms andor trapeziums
Learner Guide
66
Extended Mensuration
Question type You should be able to R A G CommentsCircles Carry out calculations involving circumference and area of a
circle
Solve problems involving arc length and sector area of a circle
Surface area and volume
Carry out calculations involving
bull surface area and volume of a cuboid prism and cylinder (no formulae will be given for these shapes)
bull surface area and volume of a sphere pyramid and cone (formulae will be given for these shapes)
Compound shapes
Carry out calculations involving
bull area of a shape made by combining cuboids prisms andor cylinders
bull volume of a shape made by combining cuboids prisms andor cylinders
Learner Guide
67
Extended Trigonometry
Question type You should be able to R A G CommentsBearings Use and interpret three-figure bearings measured clockwise
from the North ie 000degndash360degTrigonometry Find unknown sides andor angles in right-angled triangles by
applying
bull Pythagorasrsquo theorem
bull sine cosine and tangent ratios for acute angles in right-angled triangles
Solve problems in two dimensions involving angles of elevation and depression
Know that the perpendicular distance from a point to a line is the shortest distance to the line
Trig graphs and equations
Recognise sketch and interpret graphs of simple trigonometric functions
Graph and know the properties of trigonometric functions
Solve simple trigonometric equations for values between 0deg
and 360deg eg Solve sin x = radic32
for values of x between 0deg and
360degGeneral trig Solve problems using sine and cosine rules for any triangle
Find the area of any triangle using frac12absinC
Trig in 3D Solve simple trigonometrical problems in three dimensions including angle between a line and a plane
Learner Guide
68
Extended Vectors and transformations
Question type You should be able to R A G CommentsVectors in two dimensions (links to Trigonometry)
Describe a translation by using a vector represented by
AB or a
Add and subtract vectors
Multiply a vector by a scalar
Transformations Reflect simple shapes in horizontal or vertical lines
Rotate simple shapes through multiples of 90deg about any point
Construct translations of simple shapes
Construct enlargements of simple shapes (positive fractional and negative scale factors)
Recognise and describe
bull reflections
bull rotations
bull translations
bull enlargements (positive fractional and negative scalefactors)
( )x
y
Learner Guide
69
Extended Vectors and transformations
Question type You should be able to R A G CommentsHarder vectors
Calculate the magnitude of a vector as and
understand that magnitude is denoted by modulus signs |A B| or |a|
Represent vectors by directed line segments
Use the sum and difference of two vectors
Use position vectors
( )x
yradicx2 + y2
Learner Guide
70
Extended Probability
Question type You should be able to R A G CommentsProbability (links to Four rules)
Calculate the probability of a single event as a fraction decimal or percentage (not a ratio)
Probability scale Understand and use the probability scale from 0 to 1
Sum to 1 Understand that the probability of an event occurring = 1 ndash the probability of the event not occurring
Relative frequency
Understand relative frequency as an estimate of probability
Work out expected frequencies using relative frequency
Combined events Calculate the probability of combined events using
bull tree diagrams
bull possibility diagrams
bull tables
Learner Guide
71
Extended Statistics
Question type You should be able to R A G CommentsClassify Collect classify and tabulate data
Interpret and compare
Read interpret and draw simple inferences from tables and statistical diagrams
Compare sets of data using
bull tables
bull graphs
bull statistical measures
Be aware of restrictions when making conclusions from data
Charts Construct and use
bull bar charts
bull pie charts
bull pictograms
bull stem ndash and ndash leaf diagrams
bull frequency distributions
bull histograms with equal and unequal intervals
bull scatter diagrams
Learner Guide
72
Extended Statistics
Question type You should be able to R A G CommentsAverages Calculate for individual and discrete data
bull mean
bull median
bull mode
bull range
and distinguish between their use
Estimated mean Calculate an estimate of the mean for grouped and continuous data
Identify the modal class from a grouped frequency distributionCumulative frequency
Construct and use cumulative frequency diagrams to estimate and interpret
bull the median
bull percentiles
bull quartiles
bull inter-quartile range
Construct and interpret box-and-whisker plots
Correlation Understand what is meant by positive negative and zero correlation with reference to a scatter diagram
Lines of best fit Draw interpret and use a ruled line of best fit by eye
Cambridge Assessment International Education1 Hills Road Cambridge CB1 2EU United Kingdomt +44 1223 553554e infocambridgeinternationalorg wwwcambridgeinternationalorg
Copyright copy UCLES October 2017
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- Check Box 1067 Off
- Check Box 10203 Off
- Check Box 10204 Off
- Check Box 10205 Off
- Check Box 10206 Off
- Check Box 10207 Off
- Check Box 10208 Off
- Text Field 281
- Check Box 10209 Off
- Check Box 10210 Off
- Check Box 10211 Off
- Text Field 282
- Check Box 10212 Off
- Check Box 10213 Off
- Check Box 10214 Off
- Check Box 10215 Off
- Check Box 10216 Off
- Check Box 10217 Off
- Check Box 102010 Off
- Check Box 102011 Off
- Check Box 102012 Off
- Check Box 10218 Off
- Check Box 10219 Off
- Check Box 10220 Off
- Check Box 10221 Off
- Check Box 10222 Off
- Check Box 10223 Off
- Check Box 10224 Off
- Check Box 10225 Off
- Check Box 10226 Off
- Text Field 284
- Check Box 1068 Off
- Check Box 1069 Off
- Check Box 1070 Off
- Check Box 1071 Off
- Check Box 1072 Off
- Check Box 1073 Off
- Check Box 1074 Off
- Check Box 1075 Off
- Check Box 1076 Off
- Check Box 1077 Off
- Check Box 1078 Off
- Check Box 1079 Off
- Check Box 1080 Off
- Check Box 1081 Off
- Check Box 1082 Off
- Text Field 283
- Check Box 1083 Off
- Check Box 1084 Off
- Check Box 1085 Off
- Check Box 102013 Off
- Check Box 102014 Off
- Check Box 102015 Off
- Check Box 102016 Off
- Check Box 102017 Off
- Check Box 102018 Off
- Check Box 102019 Off
- Check Box 10227 Off
- Check Box 10228 Off
- Text Field 285
- Check Box 10229 Off
- Check Box 10230 Off
- Check Box 10231 Off
- Check Box 10232 Off
- Check Box 10233 Off
- Check Box 10234 Off
- Check Box 1098 Off
- Check Box 1099 Off
- Check Box 10100 Off
- Check Box 10101 Off
- Check Box 10102 Off
- Check Box 10103 Off
- Check Box 10107 Off
- Check Box 10108 Off
- Check Box 10109 Off
- Check Box 10110 Off
- Check Box 10111 Off
- Check Box 10112 Off
- Check Box 10113 Off
- Check Box 10114 Off
- Check Box 10115 Off
- Check Box 10116 Off
- Check Box 10117 Off
- Check Box 10118 Off
- Text Field 287
- Text Field 288
- Check Box 10119 Off
- Check Box 10120 Off
- Check Box 101010 Off
- Check Box 101011 Off
- Check Box 101012 Off
- Check Box 101013 Off
- Check Box 101014 Off
- Check Box 101015 Off
- Check Box 101019 Off
- Check Box 10121 Off
- Check Box 10122 Off
- Check Box 10123 Off
- Check Box 10124 Off
- Check Box 10125 Off
- Check Box 10126 Off
- Text Field 289
- Check Box 101020 Off
- Check Box 101021 Off
- Check Box 101022 Off
- Check Box 101023 Off
- Check Box 101024 Off
- Check Box 101025 Off
- Check Box 10127 Off
- Check Box 10128 Off
- Check Box 10129 Off
- Check Box 10130 Off
- Check Box 10131 Off
- Check Box 10132 Off
- Text Field 290
- Check Box 101026 Off
- Check Box 101027 Off
- Check Box 101028 Off
- Check Box 101029 Off
- Check Box 101030 Off
- Check Box 101031 Off
- Check Box 10133 Off
- Check Box 10134 Off
- Check Box 10135 Off
- Check Box 10136 Off
- Check Box 10137 Off
- Check Box 10138 Off
- Text Field 291
- Check Box 10139 Off
- Check Box 10140 Off
- Check Box 101016 Off
- Check Box 101017 Off
- Check Box 101018 Off
- Check Box 101032 Off
- Text Field 292
- Check Box 101036 Off
- Check Box 101037 Off
- Check Box 101038 Off
- Check Box 101039 Off
- Check Box 101040 Off
- Check Box 101041 Off
- Check Box 10150 Off
- Check Box 10151 Off
- Check Box 10152 Off
- Check Box 10153 Off
- Check Box 10154 Off
- Check Box 10155 Off
- Check Box 101042 Off
- Check Box 101043 Off
- Check Box 101044 Off
- Check Box 101045 Off
- Check Box 101046 Off
- Check Box 101047 Off
- Text Field 293
- Check Box 10156 Off
- Check Box 10157 Off
- Check Box 10158 Off
- Check Box 10159 Off
- Check Box 10160 Off
- Check Box 10161 Off
- Check Box 101048 Off
- Check Box 101049 Off
- Check Box 101050 Off
- Check Box 10162 Off
- Check Box 10163 Off
- Check Box 10164 Off
- Text Field 294
- Check Box 101052 Off
- Check Box 101053 Off
- Check Box 101054 Off
- Check Box 101055 Off
- Check Box 101056 Off
- Check Box 101057 Off
- Check Box 1010263 Off
- Check Box 1010264 Off
- Check Box 10165 Off
- Check Box 10166 Off
- Check Box 10167 Off
- Check Box 101058 Off
- Check Box 101059 Off
- Check Box 101060 Off
- Check Box 1010269 Off
- Check Box 1010270 Off
- Text Field 357
- Check Box 1010271 Off
- Check Box 1010272 Off
- Check Box 1010273 Off
- Text Field 358
- Check Box 1010274 Off
- Check Box 1010330 Off
- Check Box 1010331 Off
- Text Field 359
- Check Box 1010343 Off
- Check Box 1010344 Off
- Check Box 1010345 Off
- Text Field 360
- Check Box 1010348 Off
- Check Box 1010349 Off
- Check Box 1010350 Off
- Text Field 297
- Check Box 101061 Off
- Check Box 101062 Off
- Check Box 101063 Off
- Check Box 101064 Off
- Check Box 101065 Off
- Check Box 101066 Off
- Check Box 10168 Off
- Check Box 10169 Off
- Check Box 10170 Off
- Check Box 10171 Off
- Check Box 10172 Off
- Check Box 10173 Off
- Check Box 101067 Off
- Check Box 101068 Off
- Check Box 101069 Off
- Check Box 10174 Off
- Check Box 10175 Off
- Check Box 10176 Off
- Check Box 10177 Off
- Check Box 10178 Off
- Check Box 10179 Off
- Check Box 101070 Off
- Check Box 101071 Off
- Check Box 101072 Off
- Check Box 10180 Off
- Check Box 10181 Off
- Check Box 10182 Off
- Check Box 101073 Off
- Check Box 101074 Off
- Check Box 101075 Off
- Check Box 10183 Off
- Check Box 10184 Off
- Check Box 10185 Off
- Check Box 10186 Off
- Check Box 10187 Off
- Check Box 10235 Off
- Check Box 101076 Off
- Check Box 101077 Off
- Check Box 101078 Off
- Text Field 298
- Check Box 101079 Off
- Check Box 101080 Off
- Check Box 101081 Off
- Check Box 101082 Off
- Check Box 101083 Off
- Check Box 101084 Off
- Text Field 299
- Check Box 101088 Off
- Check Box 101089 Off
- Check Box 101090 Off
- Text Field 300
- Check Box 101091 Off
- Check Box 101092 Off
- Check Box 101093 Off
- Check Box 1010351 Off
- Check Box 1010352 Off
- Check Box 1010353 Off
- Text Field 301
- Check Box 10242 Off
- Check Box 10243 Off
- Check Box 10244 Off
- Check Box 101094 Off
- Check Box 101095 Off
- Check Box 101096 Off
- Check Box 101097 Off
- Check Box 101098 Off
- Check Box 101099 Off
- Text Field 302
- Check Box 1010103 Off
- Check Box 1010104 Off
- Check Box 1010105 Off
- Check Box 10245 Off
- Check Box 10246 Off
- Check Box 10247 Off
- Check Box 10248 Off
- Check Box 10249 Off
- Check Box 10250 Off
- Check Box 1010106 Off
- Check Box 1010107 Off
- Check Box 1010108 Off
- Check Box 1010109 Off
- Check Box 1010110 Off
- Check Box 1010111 Off
- Check Box 1010112 Off
- Check Box 1010113 Off
- Check Box 1010114 Off
- Check Box 10251 Off
- Check Box 10252 Off
- Check Box 10253 Off
- Check Box 1010115 Off
- Check Box 1010116 Off
- Check Box 1010117 Off
- Text Field 303
- Check Box 10260 Off
- Check Box 10261 Off
- Check Box 10262 Off
- Check Box 10101017 Off
- Check Box 10101018 Off
- Check Box 10101019 Off
- Check Box 10101020 Off
- Check Box 1010118 Off
- Check Box 1010119 Off
- Check Box 1010120 Off
- Check Box 1010126 Off
- Check Box 1010127 Off
- Check Box 10263 Off
- Check Box 10264 Off
- Check Box 10265 Off
- Check Box 10269 Off
- Check Box 10270 Off
- Check Box 10271 Off
- Check Box 10101025 Off
- Check Box 10101026 Off
- Check Box 10101027 Off
- Text Field 306
- Check Box 10266 Off
- Check Box 10267 Off
- Check Box 10268 Off
- Check Box 10101021 Off
- Check Box 10101022 Off
- Check Box 10101023 Off
- Check Box 10101024 Off
- Check Box 1010131 Off
- Check Box 1010132 Off
- Check Box 1010133 Off
- Check Box 1010134 Off
- Check Box 1010135 Off
- Check Box 1010136 Off
- Check Box 1010137 Off
- Check Box 1010138 Off
- Text Field 3025
- Check Box 10367 Off
- Check Box 10368 Off
- Check Box 10369 Off
- Check Box 10407 Off
- Check Box 10431 Off
- Check Box 10432 Off
- Text Field 3059
- Check Box 104010 Off
- Check Box 10433 Off
- Check Box 10465 Off
- Check Box 104011 Off
- Check Box 10466 Off
- Check Box 10527 Off
- Text Field 3060
- Check Box 104012 Off
- Check Box 10528 Off
- Check Box 10529 Off
- Text Field 3063
- Check Box 10101037 Off
- Check Box 10101038 Off
- Check Box 10101039 Off
- Text Field 309
- Check Box 10275 Off
- Check Box 10276 Off
- Check Box 10277 Off
- Check Box 10101040 Off
- Check Box 10101041 Off
- Check Box 10101042 Off
- Text Field 3010
- Check Box 10278 Off
- Check Box 10279 Off
- Check Box 10280 Off
- Check Box 10101044 Off
- Check Box 10101045 Off
- Check Box 10101046 Off
- Check Box 10101047 Off
- Check Box 1010141 Off
- Check Box 1010142 Off
- Text Field 3011
- Check Box 10281 Off
- Check Box 10282 Off
- Check Box 10283 Off
- Check Box 10101048 Off
- Check Box 10101049 Off
- Check Box 10101050 Off
- Check Box 10101051 Off
- Check Box 10101052 Off
- Check Box 10101053 Off
- Check Box 10101054 Off
- Check Box 10101055 Off
- Check Box 10101056 Off
- Check Box 10101057 Off
- Check Box 10101058 Off
- Check Box 10101059 Off
- Check Box 10101060 Off
- Check Box 10101061 Off
- Check Box 10101062 Off
- Check Box 10101063 Off
- Check Box 10101064 Off
- Check Box 10101065 Off
- Check Box 10101066 Off
- Check Box 10101067 Off
- Check Box 10101068 Off
- Check Box 10101069 Off
- Check Box 10101070 Off
- Check Box 10101071 Off
- Check Box 10101072 Off
- Check Box 10101073 Off
- Check Box 10101074 Off
- Text Field 3012
- Check Box 10284 Off
- Check Box 10285 Off
- Check Box 10286 Off
- Text Field 3013
- Check Box 10101075 Off
- Check Box 10101076 Off
- Check Box 10101077 Off
- Text Field 3014
- Check Box 10101078 Off
- Check Box 1010143 Off
- Check Box 1010144 Off
- Text Field 3015
- Check Box 10287 Off
- Check Box 10288 Off
- Check Box 10289 Off
- Check Box 10334 Off
- Check Box 10335 Off
- Check Box 10336 Off
- Check Box 10371 Off
- Check Box 10372 Off
- Check Box 10436 Off
- Check Box 10437 Off
- Check Box 10438 Off
- Check Box 10447 Off
- Text Field 3016
- Check Box 10401 Off
- Check Box 10402 Off
- Check Box 10403 Off
- Check Box 10291 Off
- Check Box 10292 Off
- Check Box 10337 Off
- Check Box 10448 Off
- Check Box 10449 Off
- Check Box 10456 Off
- Check Box 10457 Off
- Check Box 10458 Off
- Check Box 10533 Off
- Check Box 10534 Off
- Check Box 10535 Off
- Check Box 10543 Off
- Check Box 10544 Off
- Check Box 10740 Off
- Check Box 10741 Off
- Text Field 3017
- Check Box 10101079 Off
- Check Box 10101080 Off
- Check Box 10101081 Off
- Check Box 10101082 Off
- Check Box 1010145 Off
- Check Box 1010146 Off
- Check Box 10293 Off
- Check Box 10294 Off
- Check Box 10295 Off
- Check Box 10338 Off
- Check Box 10339 Off
- Check Box 10370 Off
- Check Box 10101083 Off
- Check Box 10101084 Off
- Check Box 10101085 Off
- Check Box 10101086 Off
- Check Box 1010147 Off
- Check Box 1010148 Off
- Check Box 10296 Off
- Check Box 10297 Off
- Check Box 10298 Off
- Text Field 3018
- Check Box 10299 Off
- Check Box 10300 Off
- Check Box 10301 Off
- Check Box 10101087 Off
- Check Box 10101088 Off
- Check Box 10101089 Off
- Check Box 10101090 Off
- Check Box 1010149 Off
- Check Box 1010150 Off
- Check Box 10302 Off
- Check Box 10303 Off
- Check Box 10304 Off
- Text Field 3019
- Check Box 10305 Off
- Check Box 10306 Off
- Check Box 10307 Off
- Text Field 3020
- Check Box 10308 Off
- Check Box 10309 Off
- Check Box 103010 Off
- Text Field 311
- Check Box 10141 Off
- Check Box 10142 Off
- Check Box 10143 Off
- Check Box 10144 Off
- Check Box 10145 Off
- Check Box 10149 Off
- Check Box 10257 Off
- Check Box 10258 Off
- Check Box 10259 Off
- Check Box 10310 Off
- Check Box 10311 Off
- Check Box 10312 Off
- Check Box 10331 Off
- Check Box 10332 Off
- Check Box 10333 Off
- Check Box 10313 Off
- Check Box 10314 Off
- Check Box 10315 Off
- Check Box 10316 Off
- Check Box 10317 Off
- Check Box 10318 Off
- Check Box 10319 Off
- Check Box 10320 Off
- Check Box 10321 Off
- Check Box 10322 Off
- Check Box 10323 Off
- Check Box 10324 Off
- Check Box 10325 Off
- Check Box 10326 Off
- Check Box 10327 Off
- Check Box 10399 Off
- Check Box 10400 Off
- Check Box 10530 Off
- Text Field 335
- Check Box 10567 Off
- Check Box 10568 Off
- Check Box 10569 Off
- Check Box 10570 Off
- Check Box 10571 Off
- Check Box 10572 Off
- Check Box 10573 Off
- Check Box 10574 Off
- Check Box 10575 Off
- Check Box 10576 Off
- Check Box 10577 Off
- Check Box 10578 Off
- Check Box 10597 Off
- Check Box 10598 Off
- Check Box 10599 Off
- Check Box 10579 Off
- Check Box 10580 Off
- Check Box 10581 Off
- Check Box 10582 Off
- Check Box 10583 Off
- Check Box 10584 Off
- Check Box 10585 Off
- Check Box 10586 Off
- Check Box 10587 Off
- Check Box 10588 Off
- Check Box 10589 Off
- Check Box 10590 Off
- Check Box 10591 Off
- Check Box 10592 Off
- Check Box 10593 Off
- Check Box 10594 Off
- Check Box 10595 Off
- Check Box 10596 Off
- Check Box 10600 Off
- Check Box 10601 Off
- Check Box 10602 Off
- Check Box 10603 Off
- Check Box 10604 Off
- Check Box 10605 Off
- Check Box 10606 Off
- Check Box 10607 Off
- Check Box 10608 Off
- Check Box 10609 Off
- Check Box 106010 Off
- Check Box 106011 Off
- Check Box 106012 Off
- Check Box 106013 Off
- Check Box 106014 Off
- Check Box 106015 Off
- Check Box 106016 Off
- Check Box 106017 Off
- Text Field 315
- Check Box 10340 Off
- Check Box 10341 Off
- Check Box 10342 Off
- Check Box 10343 Off
- Check Box 10344 Off
- Check Box 10345 Off
- Check Box 10346 Off
- Check Box 10347 Off
- Check Box 10348 Off
- Check Box 10349 Off
- Check Box 10350 Off
- Check Box 10351 Off
- Check Box 10531 Off
- Check Box 10532 Off
- Check Box 10542 Off
- Text Field 313
- Check Box 10352 Off
- Check Box 10353 Off
- Check Box 10354 Off
- Text Field 316
- Check Box 10355 Off
- Check Box 10356 Off
- Check Box 10357 Off
- Check Box 10358 Off
- Check Box 10359 Off
- Check Box 10360 Off
- Check Box 10361 Off
- Check Box 10362 Off
- Check Box 10363 Off
- Check Box 10364 Off
- Check Box 10365 Off
- Check Box 10366 Off
- Check Box 10404 Off
- Check Box 10405 Off
- Check Box 10406 Off
- Text Field 352
- Check Box 102021 Off
- Check Box 102022 Off
- Check Box 102040 Off
- Check Box 102041 Off
- Check Box 102042 Off
- Check Box 102043 Off
- Check Box 102044 Off
- Check Box 102045 Off
- Check Box 102046 Off
- Check Box 102047 Off
- Check Box 102048 Off
- Check Box 102049 Off
- Check Box 102050 Off
- Check Box 102051 Off
- Check Box 102052 Off
- Check Box 102065 Off
- Check Box 102066 Off
- Check Box 102067 Off
- Check Box 102053 Off
- Check Box 102054 Off
- Check Box 102055 Off
- Text Field 351
- Check Box 102056 Off
- Check Box 102057 Off
- Check Box 102058 Off
- Check Box 102059 Off
- Check Box 102060 Off
- Check Box 102061 Off
- Check Box 102062 Off
- Check Box 102063 Off
- Check Box 102064 Off
- Check Box 102068 Off
- Check Box 102069 Off
- Check Box 102070 Off
- Text Field 318
- Check Box 10373 Off
- Check Box 10374 Off
- Check Box 10375 Off
- Check Box 10376 Off
- Check Box 10377 Off
- Check Box 10378 Off
- Check Box 10379 Off
- Check Box 10380 Off
- Check Box 10381 Off
- Check Box 10382 Off
- Check Box 10383 Off
- Check Box 10384 Off
- Check Box 10385 Off
- Check Box 10386 Off
- Check Box 10387 Off
- Text Field 317
- Check Box 10388 Off
- Check Box 10389 Off
- Check Box 10390 Off
- Check Box 102023 Off
- Check Box 102024 Off
- Check Box 102025 Off
- Check Box 102026 Off
- Check Box 102027 Off
- Check Box 102028 Off
- Check Box 102071 Off
- Check Box 102072 Off
- Check Box 102073 Off
- Check Box 102029 Off
- Check Box 10391 Off
- Check Box 10392 Off
- Check Box 10393 Off
- Check Box 10394 Off
- Check Box 10395 Off
- Check Box 10396 Off
- Check Box 10397 Off
- Check Box 10398 Off
- Check Box 102030 Off
- Check Box 102031 Off
- Check Box 102032 Off
- Text Field 319
- Text Field 322
- Check Box 10408 Off
- Check Box 10409 Off
- Check Box 10410 Off
- Check Box 10411 Off
- Check Box 10412 Off
- Check Box 10413 Off
- Check Box 10414 Off
- Check Box 10415 Off
- Check Box 10416 Off
- Check Box 10417 Off
- Check Box 10418 Off
- Check Box 10419 Off
- Text Field 321
- Check Box 10420 Off
- Check Box 10421 Off
- Check Box 10422 Off
- Check Box 10423 Off
- Check Box 10424 Off
- Check Box 10425 Off
- Text Field 337
- Check Box 102033 Off
- Check Box 102034 Off
- Check Box 102035 Off
- Check Box 102036 Off
- Check Box 102037 Off
- Check Box 102038 Off
- Text Field 338
- Check Box 102039 Off
- Check Box 10426 Off
- Check Box 10427 Off
- Check Box 10428 Off
- Check Box 10429 Off
- Check Box 10430 Off
- Text Field 324
- Check Box 10434 Off
- Check Box 10435 Off
- Check Box 101051 Off
- Check Box 1010100 Off
- Check Box 1010101 Off
- Check Box 1010102 Off
- Check Box 1010128 Off
- Check Box 1010129 Off
- Check Box 1010130 Off
- Check Box 10439 Off
- Check Box 10440 Off
- Check Box 10441 Off
- Check Box 10442 Off
- Check Box 10443 Off
- Check Box 10444 Off
- Text Field 350
- Check Box 10742 Off
- Check Box 10743 Off
- Check Box 10744 Off
- Text Field 325
- Check Box 10445 Off
- Check Box 10446 Off
- Check Box 1010151 Off
- Check Box 1010152 Off
- Check Box 1010153 Off
- Check Box 1010154 Off
- Check Box 1010155 Off
- Check Box 1010156 Off
- Check Box 1010157 Off
- Check Box 10450 Off
- Check Box 10451 Off
- Check Box 10452 Off
- Text Field 326
- Check Box 1010158 Off
- Check Box 1010159 Off
- Check Box 1010160 Off
- Check Box 1010161 Off
- Check Box 1010162 Off
- Check Box 1010163 Off
- Check Box 10453 Off
- Check Box 10454 Off
- Check Box 10455 Off
- Check Box 10745 Off
- Check Box 10746 Off
- Check Box 10747 Off
- Check Box 10748 Off
- Check Box 10749 Off
- Check Box 10750 Off
- Check Box 1010167 Off
- Check Box 1010168 Off
- Check Box 1010169 Off
- Check Box 10459 Off
- Check Box 10460 Off
- Check Box 10461 Off
- Check Box 10462 Off
- Check Box 10463 Off
- Check Box 10464 Off
- Check Box 10611 Off
- Check Box 10612 Off
- Check Box 10613 Off
- Text Field 329
- Check Box 1010171 Off
- Check Box 1010172 Off
- Check Box 1010173 Off
- Check Box 1010174 Off
- Check Box 1010175 Off
- Check Box 1010176 Off
- Check Box 1010177 Off
- Check Box 1010178 Off
- Check Box 1010179 Off
- Check Box 10467 Off
- Check Box 10468 Off
- Check Box 10469 Off
- Check Box 10470 Off
- Check Box 10471 Off
- Check Box 10472 Off
- Check Box 1010180 Off
- Check Box 1010181 Off
- Check Box 1010182 Off
- Text Field 330
- Check Box 1010183 Off
- Check Box 1010184 Off
- Check Box 1010185 Off
- Check Box 10473 Off
- Check Box 10474 Off
- Check Box 10475 Off
- Check Box 10476 Off
- Check Box 10477 Off
- Check Box 10478 Off
- Check Box 1010186 Off
- Check Box 1010187 Off
- Check Box 1010188 Off
- Check Box 1010275 Off
- Check Box 1010276 Off
- Check Box 1010277 Off
- Text Field 331
- Check Box 1010189 Off
- Check Box 1010190 Off
- Check Box 1010191 Off
- Check Box 1010192 Off
- Check Box 1010193 Off
- Check Box 1010194 Off
- Check Box 1010354 Off
- Check Box 1010355 Off
- Check Box 1010356 Off
- Check Box 10479 Off
- Check Box 10480 Off
- Check Box 10481 Off
- Check Box 10482 Off
- Check Box 10483 Off
- Check Box 10484 Off
- Check Box 1010195 Off
- Check Box 1010196 Off
- Check Box 1010197 Off
- Check Box 1010278 Off
- Check Box 1010279 Off
- Check Box 1010280 Off
- Text Field 339
- Check Box 10614 Off
- Check Box 10615 Off
- Check Box 10616 Off
- Check Box 10617 Off
- Check Box 10618 Off
- Check Box 10619 Off
- Check Box 1010281 Off
- Check Box 1010282 Off
- Check Box 1010283 Off
- Text Field 340
- Check Box 1010284 Off
- Check Box 1010285 Off
- Check Box 1010286 Off
- Check Box 1010287 Off
- Check Box 1010288 Off
- Check Box 1010289 Off
- Check Box 10620 Off
- Check Box 10621 Off
- Check Box 10622 Off
- Check Box 10623 Off
- Check Box 10624 Off
- Check Box 10625 Off
- Check Box 1010290 Off
- Check Box 1010291 Off
- Check Box 1010292 Off
- Check Box 1010293 Off
- Check Box 1010294 Off
- Check Box 1010295 Off
- Check Box 10626 Off
- Check Box 10627 Off
- Check Box 10628 Off
- Check Box 10751 Off
- Check Box 10752 Off
- Check Box 10753 Off
- Text Field 342
- Check Box 1010296 Off
- Check Box 1010297 Off
- Check Box 1010298 Off
- Check Box 10632 Off
- Check Box 10633 Off
- Check Box 10634 Off
- Check Box 10635 Off
- Check Box 10636 Off
- Check Box 10637 Off
- Text Field 349
- Check Box 1010305 Off
- Check Box 1010306 Off
- Check Box 1010307 Off
- Check Box 1010308 Off
- Check Box 1010309 Off
- Check Box 10103010 Off
- Check Box 10641 Off
- Check Box 10642 Off
- Check Box 10643 Off
- Text Field 343
- Check Box 1010299 Off
- Check Box 1010300 Off
- Check Box 1010301 Off
- Check Box 1010302 Off
- Check Box 1010303 Off
- Check Box 1010304 Off
- Check Box 10638 Off
- Check Box 10639 Off
- Check Box 10640 Off
- Check Box 10644 Off
- Check Box 10645 Off
- Check Box 10646 Off
- Check Box 1010328 Off
- Check Box 10103012 Off
- Check Box 10103013 Off
- Check Box 10103014 Off
- Check Box 10103015 Off
- Check Box 10103016 Off
- Check Box 10648 Off
- Check Box 10649 Off
- Check Box 10650 Off
- Check Box 10651 Off
- Check Box 10652 Off
- Check Box 10653 Off
- Check Box 10654 Off
- Check Box 10755 Off
- Check Box 10756 Off
- Check Box 10757 Off
- Check Box 10758 Off
- Check Box 10759 Off
- Check Box 10760 Off
- Check Box 10761 Off
- Check Box 10762 Off
- Check Box 10763 Off
- Check Box 10764 Off
- Check Box 10765 Off
- Check Box 10766 Off
- Check Box 10767 Off
- Check Box 10768 Off
- Text Field 361
- Check Box 10103020 Off
- Check Box 10103021 Off
- Check Box 10103022 Off
- Text Field 362
- Text Field 371
- Check Box 10103018 Off
- Check Box 10103019 Off
- Check Box 10103059 Off
- Check Box 10655 Off
- Check Box 10656 Off
- Check Box 10657 Off
- Check Box 10658 Off
- Check Box 10673 Off
- Check Box 10754 Off
- Text Field 363
- Check Box 10103023 Off
- Check Box 10103024 Off
- Check Box 10103025 Off
- Check Box 10103026 Off
- Check Box 10103027 Off
- Check Box 10103028 Off
- Check Box 10103029 Off
- Check Box 10103030 Off
- Check Box 10103031 Off
- Check Box 10103032 Off
- Check Box 10103033 Off
- Check Box 10103034 Off
- Text Field 365
- Check Box 10103035 Off
- Check Box 10103036 Off
- Check Box 10103037 Off
- Text Field 366
- Check Box 10103038 Off
- Check Box 10103039 Off
- Check Box 10103040 Off
- Check Box 10103041 Off
- Check Box 10103042 Off
- Check Box 10103043 Off
- Text Field 367
- Check Box 10103044 Off
- Check Box 10103045 Off
- Check Box 10103046 Off
- Text Field 368
- Check Box 10103047 Off
- Check Box 10103048 Off
- Check Box 10103049 Off
- Text Field 369
- Check Box 10103050 Off
- Check Box 10103051 Off
- Check Box 10103052 Off
- Text Field 370
- Check Box 10103053 Off
- Check Box 10103054 Off
- Check Box 10103055 Off
- Check Box 10103056 Off
- Check Box 10103057 Off
- Check Box 10103058 Off
- Text Field 332
- Check Box 1010198 Off
- Check Box 1010199 Off
- Check Box 1010200 Off
- Check Box 1010201 Off
- Check Box 1010202 Off
- Check Box 1010203 Off
- Check Box 10485 Off
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- Text Field 3045
- Check Box 101010194 Off
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- Text Field 3046
- Check Box 101010209 Off
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- Text Field 3026
- Check Box 10536 Off
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- Text Field 3047
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- Text Field 3048
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- Text Field 3027
- Check Box 10539 Off
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- Text Field 3028
- Check Box 101010110 Off
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7
About the componentsIt is important that you understand the different types of question in each paper so you know what to expect
Core Paper 1 (Short-answer questions) and Paper 3 (Structured questions)
You need to answer all questions on each paper
Paper 3Paper 1
You can use an electronic calculator in both papers Ask your teacher to recommend a suitable calculator
Paper 1 contains lots of short-answer questions These are usually worth 1ndash3 marks each Some might be broken up into two parts
Write your working and answers in the spaces provided
The number of marks for each part is shown
Paper 3 contains structured questions Each question is split into many parts with each part usually being worth 1ndash4 marks Here for example question 1 is split over two pages
Often the answers to later parts will depend on the answers to earlier parts
8
Extended Paper 2 (Shortndashanswer questions) and Paper 4 (Structured questions)
You need to answer all questions on both papers
Paper 2 questions are short-answer questions Most questions are worth 1ndash3 marks with some being worth 4 or 5 marks Some questions might be broken up into two parts
Write your working and answers in the spaces provided
The number of marks for each part is shown
Paper 4Paper 2
You can use an electronic calculator in both papers Ask your teacher to recommend a suitable calculator
Paper 4 contains structured questions Each question is split into many parts with each part usually being worth 1ndash6 marks Here for example question 2 is split over two pages
Often the answers to later parts will depend on the answers to earlier parts
9
Equipment for the examMake sure you have
bull a blue or black pen (a spare pen is always a good idea)bull a pencil (for graphs and diagrams)bull an electronic calculatorbull a protractorbull a pair of compassesbull a ruler
1 Read the questions carefully to make sure that you understand what is being asked
2 Give your answers to the accuracy indicated in the question If none is given and the answer isnrsquot exact then
bull give your answer to three significant figures 123 9 12298 x
bull if the answer is in degrees then give it to one decimal place 231deg 9 23deg x
3 Include units with your answers if they are not given on the paper For example 1 kg of apples costs hellip pound120 9 120 x
4 Show your working Show as much working as you can for all your questions
5 If you make a mistake clearly cross out any working or answers that you do not want the examiner to mark
Use the value of π from your calculator or use 3142 which is given on the front page of the question paper
Timingbull If you are stuck on a question dont waste too much time trying to answer it ndash go on to the next question and
come back to the one you are stuck on at the endbull Use any time that you have left at the end of the exam to go back and check your answers and working
Make sure that you give your answer in the form asked for in the question eg some questions ask for answers to be given in terms of π For lengths areas and volumes give answers in decimals (not in surds or in terms of π) unless you are told to given an exact answer
You can gain marks for the correct working even if you have an incorrect answer or cannot complete the whole question
If you need more space ask for extra of paper and clearly indicate where the rest of the answer is written On the additional paper make it clear which questions(s) you are answering
General advice for all Papers
10
The areas of knowledge understanding and skills that you will be assessed on are called assessment objectives (AOs) There are two AOs for this course
AO1 Demonstrate knowledge and
understanding of mathematical techniques
AO2 Reason interpret and communicate
mathematically when solving problems
AO1 Demonstrate knowledge and understanding of mathematical techniquesYou need to show that you can recall and apply mathematical knowledge terminology and definitions to carry out single or multi-step solutions in mathematical and everyday situations
Section 3 What skills will be assessed
This means that you need to show that you can
bull organise process and present information accurately in written tabular graphical and diagrammatic forms
bull use and interpret mathematical notation correctly
bull perform calculations and procedures by suitable methods including using a calculator
bull understand systems of measurement in everyday use and make use of these
bull estimate approximate and work to degrees of accuracy appropriate to the context and convert between equivalent numerical forms
bull use geometrical instruments to measure and to draw to an acceptable degree of accuracy
bull recognise and use spatial relationships in two and three dimensions
AO1 is assessed in all papers
Use tables graphs and diagrams
An example of degress of accuracy include significant figures or decimal places
An example of converting between equivalent numerical forms include between fractions decimals and percentages or between normal numbers and standard form
eg a pair of compasses a protractor and a ruler
11
AO2 Reason interpret and communicate mathematically when solving problemsYou need to demonstrate that you can analyse a problem select a suitable strategy and apply appropriate techniques to obtain a solution
This means that you need to show that you can
bull make logical deductions make inferences and draw conclusions from given mathematical data
bull recognise patterns and structures in a variety of situations and form generalisations
bull present arguments and chains of reasoning in a logical and structured way
bull interprete and communicate information accurately and change from one form of presentation to another
bull assesses the validity of an argument and critically evaluate a given way of presenting information
bull solve unstructured problems by putting them into a structured form involving a series of processes
bull apply combinations of mathematical skills and techniques using connections between different areas of mathematics in problem solving
bull interprete results in the context of a given problem and evaluate the methods used and solutions obtained
AO2 is assessed in all papers
Recognise and extent patterns
Take information and organise it to answer a problem
12
Section 4 Command wordsA command word is the part of the question that tells you what you need to do with your knowledge For example you might need to describe something explain something argue a point of view or list what you know The table below includes command words used in the assessment for this syllabus The use of the command word(s) within an question will relate to the context
Cambridge IGCSE Mathematics 0580 syllabus for 2020 2021 and 2022 Details of the assessment
37wwwcambridgeinternationalorgigcseBack to contents page
Command wordsThe table below includes command words used in the assessment for this syllabus The use of the command word will relate to the subject context
Command word What it means
Calculate work out from given facts figures or information generally using a calculator
Construct make an accurate drawing
Describe state the points of a topicgive characteristics and main features
Determine establish with certainty
Explain set out purposes or reasons make the relationships between things evident provide why andor how and support with relevant evidence
Give produce an answer from a given source or recallmemory
Plot mark point(s) on a graph
Show (that) provide structured evidence that leads to a given result
Sketch make a simple freehand drawing showing the key features
Work out calculate from given facts figures or information with or without the use of a calculator
Write give an answer in a specific form
Write down give an answer without significant working
The question below is taken from Paper 4 and illustrates the use of two command words
The command words lsquoWrite downrsquo indicates that you do not need to show your working and the answer should just be written down The mark allocation [1] also supports this
The command words lsquoShow thatrsquo indicate that you need to provide evidence in the form of a clear mathematical explanation to demonstrate that you know how to obtain the given result In other words you need to show a method that leads to the result
The answer space in this case does not contain a dotted answer line as there is no single lsquoanswerrsquo to be found Your working that leads to the given result should be written in the blank working space
13
This section takes you through an example question and learner response from one of the 2020 specimen papers for this course It will help you to identify the command words and other key instructions within questions and to understand what is required in your response
This section is structured as follows
QuestionThe command words and instructions in the question have
been highlighted and explained This should help you to understand clearly what is required by the question
Mark schemeThis tells you as clearly as possible what an examiner expects
from an answer to award marks
Example candidate responseThis an exemplar answer written in the style of
a high level candidate
How the answer could have been improvedThis summarises what could be done to gain more marks
All information and advice in this section is specific to the example question and response being demonstrated It should give you an idea of how your responses might be viewed by an examiner but it is not a list of what to do in all questions In your own examination you will need to pay careful attention to what each question is asking you to do
Common mistakesThis will help you to avoid common mistakes made by
candidates So often candidates lose marks in their exams because they misread or misinterpret the questions
Section 5 Example candidate response
14
QuestionThe question used in this example is from Specimen Paper 3 (Core) It represents the type of structured question you will see in both Paper 3 (Core) and Paper 4 (Extended) A structured question means that it is broken into several parts Often later parts will depend on your answers to earlier parts
This means that you cannot find the answer by
measuring the diagramWork out indicates that the answer should be calculated from the given information so measurement will not score marks
The allocation of 1 mark indicates that the answer can be obtained with minimum working
Give reasons for your answer indicates that your answer should be supported with reasons using the correct mathematical terminology You must justify your answer
Use trigonometry to calculate indicates that you should use this method with the given information to find the answer and that a calculator is needed to solve the problem If you did not use trigonometry you would not be awarded any marks
15
Show that indicates the answer is given and you need to write down all of the steps in a method that leads to the given answer You need to provide evidence that you understand and know how the answer is reached
Work out indicates that you should calculate the answer from the given information The mark allocation of 4 marks suggests that you will need to include several steps of working in order to get to the answer
Learner Guide
16
Answer Mark Notes(a)(i) 35 1 This is the only acceptable answer for this part of the question
(a)(ii) 74 1 This is the only acceptable answer for this part of the question
(b) 43deg and correct mathematical reasons
3 Two marks are awarded for the final answer of 43deg
The third mark is awarded for a fully correct reason for example angles on a straight line add up to 180deg and angles in a triangle add up to 180deg There are other correct reasons that could be also be used
If 43deg is not obtained one method mark can be awarded if the following calculation is seen in the working
180 ndash 128 or 128 ndash 85
(c) 322 or 3223hellip 2 This is the only acceptable answer for this part of the question
The answer has to be rounded correct to three significant figures or can be given with more figures in the answer
Those that did not get this answer can score one method mark for showing the following in their working
sin = 8 divide 15
(d)(i) 2 2300 225+2 This does not have to be shown in one step as long as the method shown is the same as this overall Those that do not
show this can have one method mark for showing the following in their working
300deg + 225deg
(d)(ii) 15 35 4 The answer 3 35pm is also acceptable for 4 marks
If the correct answer is not found one method mark is available for showing 375 divide 450 in their working and a second method mark can be awarded for sight of them multiplying their answer to this by 60 to change it to hours A third method mark can be awarded for adding their answer in hours to 14 45 ndash this shows the correct method so only one mark is lost for an incorrect final answers
Mark schemeYour examination papers will be marked and the overall number of marks for each paper will be recorded Your marks across all papers will then be converted to a grade
Final answer This value is what the examiner expects to see The answer has to be exactly as given in the mark scheme unless there are acceptable alternatives The mark scheme will always make it clear if there are acceptable alternative answers
Method marks Sometimes method marks are awarded for lines of working as well as for the final answer This means that you could get the final answer incorrect but still get some marks if you include the correct working The mark scheme does not include all possible methods so if you use a method not included in the mark scheme but it is accurate and relevant then the examiner will still award marks for the appropriate parts of the working ndash unless the questions asks you to use a specific method
example of a final answer
example of a method mark
17
Example candidate responseNow letrsquos look at the sample candidatersquos response to question 8 The examiners comments are in the orange boxes The candidate was awarded 8 marks out of 13
180 ndash 74 + 71 = 177
177
74
0 out of 1
The candidates working suggests they understand that the angle sum of a triangle is 180deg but they did not include brackets around 74 + 71 The answer 177deg is not sensible for this question
1 out of 1
The candidate recognises that there are parallel lines and that angle y is a corresponding angle to angle 74deg
180 ndash 128 = 52 180 ndash 85 ndash 52 = 43
43 angles on a straight line add up to 180deg
2 out of 3
The candidate has given a correct answer for w and shown correct working in two steps They have given a correct reason for 52deg using correct mathematical languge But they have not provided a reason to explain the angle 43deg They lose a mark for not also stating angle sum of a triangle is 180deg
sin p = 8 divide 15 = 053
p = sinndash1 (053)
p = 32005 320
1 out of 2
The candidate has correctly used trigonometry in their method They are awarded one method mark for the first line of working However they have rounded 05333333hellip (the result of 8 divide 15) to 052 and then calculated the inverse sin of 052 rather than 05333333 This has resulted in an inaccurate final answer This is called lsquopremature approximationrsquo and it is a very common error to make
18
AB2 = 3002 + 2252
= 140625
AB = 375
1 out of 2
The candidate has recognised the right-angled triangle and correctly used Pythagorasrsquo theorem in the first line of working However they have missed out an important step by not showing that you need to take the square root of 140625 to get 375 As this is a lsquoshow thatrsquo question and they missed a key step in the method they cannot be awarded full marks as the complete working is not shown One method mark is earned for the first line
T = = = 08333333hellip
08333333 hours = 08333333 times 60 minutes = 50 minutes
arrives at 14 45 + 50 mins = 3 35
DS
375450
3 35
3 out of 4
The candidate has found the time by correctly dividing the distance by the speed and recognised that this is in hours When converting the answer to a decimal they have not rounded the decimal but left its full value on the calculator to get 50 mins which is the correct approach Unfortunately after converting the time from 24 hour clock to 12 hour clock they did not include lsquopmrsquo to indicate that the time is in the afternoon and so the final answer is not quite right So 3 marks are awarded for all of a correct method but a mark is lost due to the accuracy of the final answer
19
How the answer could have been improvedThis answer could have been improved by
bull In part (a)(i) the answer of 177deg was not sensible given the diagram in the question If the candidate had checked their answer for sense they would have realised they had made a mistake It is always a good idea to check that your answer seems sensible before you move on to another question
bull In part (b) the candidate did all the correct steps but failed to provide both reasons There were two steps to the method which should have indicated to the candidate that there were two steps to justify and therefore two reasons should have been provided The mark allocation for the question [3] also indicates that more than one reason would be required one mark for the value of 43deg leaving two marks one mark for each of two reasons The candidate should have read the question carefully and again checked their response seemed reasonable
bull In part (c) the candidate rounded an intermediate answer which affected the accuracy of the final answer This caused them to lose a mark despite using a correct method You should only ever round the final answer do not round intermediate values If you can store the intermediate values in your calculator and so that you can use the full value in your calcuations If youre not able to do this and you have to round the intermediate values do not round them to less than three significant figures
bull In part (d)(i) the candidate missed out a step in the method As this was a show that question they needed to show all the steps in the method Its important to show all steps even if they seem obvious
bull In part (d)(ii) the candidate made a silly error by not stating that the time was pm When working with time answers are accepted in either 24 clock or 12 clock time but if you give your answer in the 12 hour clock then it must include am or pm as well
Common mistakesThere were a number of common mistakes made by other candidates on this question
bull Accuracy of answers
In parts (c) and (d)(ii) a common error was premature rounding ndash rounding intermediate values in the method before the final answer which resulted in their final answer not being accurate Other candidates gave the final answer to less than three significant figures ignoring the instruction on the front of the paper to round to three significant figures
bull Using incorrect terminology when giving reasons
In part (b) the most common error was to not give full reasons to support the answer Another common error was to provide a reason that did not use the correct mathematical language such as lsquoThey add up to 180degrsquo and lsquoIt is a straight linersquo which could not be awarded marks
bull Lack of knowledge
In part (c) a number of candidates had limited knowledge of trigonometry and did not choose the correct trig ratio which was the sine ratio This is why good revision is important
bull Not checking answers
In part (a)(i) even though the diagram is drawn NOT TO SCALE it is possible to see that the angle is an acute angle and should therefore not be bigger than 90deg This should alert candidate that if their answer is over 90deg it is not a sensible answer and they should go back and check their working
20
bull Inefficient method shown
In part (c) the lsquoShow thatrsquo question a number of candidates omitted an important step from the method this is often common in lsquoShow thatrsquo questions where every step must be shown no matter how obvious them seem
General adviceIn order to do your best when answering a mathematics question make sure you
bull revise all of the topics for the syllabus you are studying before the exam
bull understand what all the key terms and command words in the question mean
bull read the questions carefully and consider what you need to do before you do it
bull only round the final answer not intermediate values
bull show all steps in your working and show them clearly
bull round to the correct degree of accuracy
bull use the correct mathematical terminology
bull check your answers seem reasonable given the context or details of the question
21
It is important that you plan your revision in plenty of time for the examinations and that you develop a revision technique that works for you The advice in this section will help you revise and prepare for the examinations It is divided into general advice for all papers
Use the tick boxes to keep a record of what you have done what you plan to do or what you understand
For more advice on revision see the Cambridge Learner Revision Guide on our website
Section 6 Revision
Find out when the examinations are and plan your revision so you have time to revise Create a revision timetable and divide it into sections to cover each topic
Spend most of your time focussing on specific skills knowledge or issues that you have found more difficult when practicing them either during revision or earlier in the course
Write a summary of all the key information for a topic ndash use the checklists at the end of this section
Know the meaning of the command words used in questions and how to apply them to the information given Look at past examination papers and highlight the command words and check what they mean
Make revision notes and work on practice questions Reading alone does not work you need to be active and practice your maths
Work for shorter periods then have a break Revise small sections of the syllabus at a time but do this regularly
Test yourself by trying out some past exam questions Use the mark schemes to assess yourself and to be familiar with how marks are awarded for different questions
Be organised in advance with your notes texts exercise books revision guides and revision websites so you do not waste valuable revision time trying to find things
Make notes of key mathematical words that you should use in questions that ask you to lsquodescribersquo or give lsquogeometrical reasons forrsquo eg in describing transformations or giving reasons in circle theorem questions Look at the mark schemes for these types of questions from past papers to see how marks are awarded
Make sure you have all of the correct mathematical equipment ready for the exam particularly your calculator Make sure you are familiar with the all of the important functions on your calculator
Practice the areas you can do well not just those that you find more difficult
Take breaks and do things to relax when you take your breaks this will help you to be more productive when you are revising
Before the examination
22
During the examination
Plan your time according to the marks for each question For example a question worth one mark requires less time than a question one worth 4 marks If a question has several parts then the parts with more marks will need more time
Read each question very carefully
Identify the command words ndash you could underline or highlight them
Identify the other key words and information and perhaps underline them too particularly where
questions require reasoning or problem solving
Read the questions careully and make you have answered the question that is being asked
Show your working this is particularly important for questions where you are asked to lsquoshow that helliprsquo
Set your working out clearly so that it is easy to follow this makes it easier to keep track of what you have done and makes checking back through your work easier and it makes it easier for the examiner to mark your work try to write it in a logical order in the answer space
Write answers clearly if you want to change an answer then you should cross the answer out and write a replacement if your answer is on the answer line cross it out and write the replacement answer above it do not try to change numbers on the answer line as this can lead to unclear figures
Check your working and answers to avoid errors
Give your answer to the appropriate level of accuracy either the accuracy indicated in the question or the accuracy given on the front of the paper
Avoid rounding intermediate values part way through your calculation only round the final answer
Check that the answer that you have given is sensible and realistic for what is being asked
Use a pencil when drawing diagrams or completing graphs this means that you can change your answer more easily if you have made a mistake
Take care when reading scales
If you are asked for reasons for your answer then use the correct mathematical terms
Use the mark allocation given with the questionsparts of questions to try to judge how much work is needed to answer each part
23
Top tips for revision of Cambridge IGCSE Mathematics1 Summarise recall and applyMake sure that you can recall and apply the key information and mathematical techniques on each topic that you need for the exam
i Write a summary of the key information of a topicii Collect together some questions that test the knowledge and skills of this topic Ask your teacher for practice
questions or suitable past examination questions or use practice books or textbooksiii Test your recall by covering over the summary and trying to remember the details or use the summary as part of
the lsquoTeach the topicrsquo (Tip 3) or lsquoQuestion and answer cardsrsquo (Tip 4) activities iv After you have spent some time revising and practising the knowledge and skills answer the questions that you
collected together on the topic You might do this later on the same day as revising or a few days later Answer as many questions as you can in order to practise applying your knowledge
v Try creating your own questions by adapting existing ones and use these for practice when you return to a topic
On graph questions straight lines should be ruled and curves should be drawn freehand with a smooth curve
Donrsquot spend too long on any one part of a question If you are really stuck on a question then move on and come back to the question later if you have time As a rough guide each mark on the paper should take about one minute
2 Concept mapsConcept maps are a great way to revise the links between different factors or to explore a larger topic They can also be used to collect together your ideas
i Use a blank sheet of paper and turn it on its side (landscape)ii Put the topic title in the middle of the page and build the concept map outwards using lines called lsquobranchesrsquo
ndash The first branches are from the central topic to sub-topics draw these as thick lines
ndash Add new branches from the sub-topics to include more detail draw these as thinner lines
ndash Add even more detail to a point by adding more branches
This creates a hierarchy of information from lsquooverviewrsquo (the thick branches) to lsquofine detailrsquo (thinnest branches)
iii Write single key words or phrases along a branch and add drawings for visual impactiv Use different colours highlighter pens symbols and arrows to highlight key facts or issuesIt is a good idea to use a large piece of plain A3 (or larger) paper and lots of coloured pens
24
3 Teach the topicThis is a very simple but effective technique that focusses on knowledge recall It tests the brain and rehearses the information you need to know for a certain topic and so will help your revision
i Create some topic cards with key bullet points of information on Leave space for ticksii Give these to your parents family or friends for exampleiii Give yourself 10 minutes maximum to teach your audience the main points of the topic You could use a mini-
whiteboard or flip chart to helpiv Your audience tick off all the points you mention in your presentation and give you a final scoreThe brain loves competition so if you do not score full marks you can try again the next day or compete against friends This system of repeat and rehearsal is very effective especially with more complex topics and doesnt take much preparation
4 Question and answer (QampA) cardsThis is very similar to Teach the topic but less formal and less public for those who dislike performing in front of others It tests knowledge recall and rehearses the information you need to know for a certain topic
i Pick a topic and create two sets of cards question cards and answer cards You might find it helpful to make the question cards a different size or use different coloured card for answers
ii Make sure you have the topic or something appropriate depending on what you are focusing on as a heading on each card The questions should test your knowledge and understanding of key areas of the course
iii A friend or family member uses the cards to test you in short 5 or 10 minute periods at any time during the dayiv You could also do this alone by reading the questions to yourself giving the answer and then checking the
correct answer cardv This game can be adapted by using the cards to find matching pairs turn all cards face down across the space
in front of you Turn over two cards leaving them where they are If they match (one is a question card and the other is the corresponding answer card) pick up the pair and put them to one side If they dont match try to remember where they are and what is on each card then turn them back over Turn over two other cards Continue until you have matched all pairs
5 Question paper and mark schemesLooking at past question papers and the mark scheme helps you to familiarise yourself with what to expect and what the standard is
i Ask your teacher for past paper questions with mark schemes for the course ndash ask your teacher for help to make sure you are answering the correct questions and to simplify the mark scheme
ii Look at the revision checklist and identify which topic a given question relates to ndash you might need to ask your teacher to help you do this
iii Once you have finished revising a topic or unit time yourself answering some appropriate exam questions Check the mark schemes to see how well you would have scored or give the answers to your teacher to check
iv Add details or notes to the mark scheme where you missed out on marks in your original answers using a different coloured pen Use these notes when you revise and try the question again later
You can find plenty of past exam papers and mark schemes on the Cambridge International public website
httpwwwcambridgeinternationalorgprogrammes-and-qualificationscambridge-igcse-mathematics-0580past-papers
25
Other useful revision advice for Cambridge IGCSE Mathematics bull Before the exam make sure that you are familiar with your calculator and confident in using it
bull Look at the Example Candidate Response earlier in this guide Can you identify the strengths of the response andwhere they have made mistakes or lost marks
bull When you are attempting a past paper (or questions from a past paper) complete it without referring to yournotes so that you get a true idea of your strengths and weaknesses Then go back through the paper using yournotes and a different coloured pen to make corrections and changes After you have done as much as you can onthe paper mark it using the mark scheme Take notes of any points that you lost marks on
bull Donrsquot just revise the topics that you enjoy and are confident in If you identify an area that you are weaker inthen try to revisit the topic by reviewing your notes and doing some practice questions then use exam questionsto check whether you now understand
bull Return to topics later in your revision to check that you still remember and understand the topic and to help toensure that you recall more of the material when you get to the examination
Revision checklists for Cambridge IGCSE MathematicsThe tables on the following pages can be used as a revision checklist They do not contain all the detailed knowledge you need to know just an overview For more detail see the syllabus and talk to your teacher
You can use the tick boxes in the checklists to show when you have revised and are happy that you do not need to return to it Tick the lsquoRrsquo lsquoArsquo and lsquoGrsquo column to record your progress as follows
bull R = RED means you are really unsure and lack confidence in that area you might want to focus your revisionhere and possibly talk to your teacher for help
bull A = AMBER means you are reasonably confident in a topic but need some extra practicebull G = GREEN means you are very confident in a topic
As your revision progresses you can concentrate on the RED and AMBER topics in order to turn them into GREEN topics You might find it helpful to highlight each topic in red orange or green to help you prioritise
You can use the lsquoCommentsrsquo column to
bull add more information about the details for each pointbull include a reference to a useful resourcebull include a list of formulae or notationbull add learning aids such as rhymes poems or word playbull highlight areas of difficulty or things that you need to talk to your teacher about
There is a set of checklist for the Core syllabus and a different set for the Extended syllabus
Learner Guide
26
Core syllabus contentCore Number
Category You should be able to R A G CommentsNumber Identify and use
bull natural numbers
bull integers (positive negative and zero)
bull prime numbers
bull write a number as a product of its prime factors
bull square numbers and cube numbers
bull common factors and highest common factor of two numbers
bull common multiples and lowest common multiple of two numbers
bull rational numbers
bull irrational numbers (eg π radic2 )
bull real numbers
bull reciprocals
Learner Guide
27
Core Number
Question type You should be able to R A G CommentsSets and Venn diagrams
Understand notation of Venn diagrams
Definition of sets
eg A = xx is a natural number
B = abchellip
Notation
Number of elements in set A n(A)
Universal set
Union of A and B A cup B
Intersection of A and B A cap B
Squares square roots cubes and cube roots
Calculate
bull squares and cubes of numbers
bull square roots and cube roots of numbers
Learner Guide
28
Core Number
Question type You should be able to R A G CommentsDirected numbers
Use directed numbers in practical situations for example temperature changes
Fractions decimals and percentages
Use the language and notation of simple vulgar and decimal fractions and percentages
Recognise equivalent fractions decimals and percentages
Convert between fractions decimals and percentages
Ordering Order quantities by magnitude and demonstrate familiarity with the symbols = ne gt lt ⩾ ⩽
Indices and standard form (links to Algebraic manipulation)
Evaluate indices eg 25 5ndash2 1000 64frac12 8ndash23
Use the rules of indices for
bull multiplication of indices eg 4ndash3 times 45
bull division of indices eg 57 divide 53
bull index numbers raised to an index eg (23)2 (43)2
Use the standard form A times 10n where n is a positive or negative integer and 1 ⩽ A lt 10
bull convert numbers into and out of standard form
bull calculate with numbers in standard form
Learner Guide
29
Core Number
Question type You should be able to R A G CommentsFour rules
( + ndash times divide )
Use the four rules for calculations with
bull whole numbers
bull decimals
bull vulgar and mixed fractions
bull correct ordering of operations (BIDMAS) and use of bracketsEstimates Make estimates of numbers quantities and lengths
Give approximations to a specified number of
bull significant figures
bull decimal places
Round off answers to reasonable accuracy in the context of a given problem
Bounds Give upper and lower bounds for data given to a specified accuracy eg measured lengths
Ratio proportion rate
Understand ratio
Divide a quantity in a given ratio
Understand direct and inverse proportion
Use scales in practical situations
Use common measures of rate (formulae for other rates eg density and pressure will be given in the question)
Calculate average speed
Learner Guide
30
Core Number
Question type You should be able to R A G CommentsPercentages Calculate a percentage of a quantity
Express one quantity as a percentage of another quantity
Calculate percentage increase or decrease
Use of an electronic calculator
Use a calculator efficiently
Check accuracy of calculations
Time Calculate times in terms of the 24-hour and 12-hour clock
Read
bull clocks
bull dials
bull timetables
Money Calculate using money
Convert from one currency to another
Learner Guide
31
Core Number
Question type You should be able to R A G CommentsPersonal and small business finance
Use given data to solve problems on
bull earnings
bull simple interest
bull compound interest (you will need to know the compound interest formula)
bull discount
bull profit and loss
Extract data from tables and charts
Learner Guide
32
Core Algebra and graphs
Question type You should be able to R A G CommentsBasic algebra Use letters to express generalised numbers
Express basic arithmetic processes algebraically
Substitute numbers in formulae
Construct simple expressions and set up simple equations
Rearrange simple formulae
Algebraic manipulation
Manipulate directed numbers
Use brackets
bull expand a single bracket eg 3x(2x ndash4y)
bull expand a pair of brackets eg (x + 3) (x ndash 7)
Extract common factors eg factorise 9x2 + 15xy
Rules of indices Use and interpret positive negative and zero indices
Use the rules of indices eg to simplify algebra such as
bull 3x4 times 5x
bull 10x3 divide 2x2
bull (x6)2
Learner Guide
33
Core Algebra and graphs
Question type You should be able to R A G CommentsEquations and inequalities
Derive and solve simple linear equations in one unknown
Derive and solve simultaneous linear equations in two unknowns
Number sequences
(links to Squares square roots cubes and cube roots)
Continue a number sequence
Recognise patterns in sequences
Recognise relationships between difference sequences
Find the nth term of sequences for
bull liner sequences
bull simple quadratic sequences
bull cubic sequences
Practical graphs
(links to Mensuration)
Interpret and use graphs in practical situations including
bull travel graphs
bull conversion graphs
Draw graphs from given data
Learner Guide
34
Core Algebra and graphs
Question type You should be able to R A G CommentsGraphs of functions
(links to Co-ordinate geometry)
Construct tables of values for functions of the form
bull ax + b (linear)
bull plusmn x2 + ax + b (quadratic)
bull (x ne 0) (reciprocal)
where a and b are integer constants
Draw and interpret such graphs
Solve linear and quadratic equations approximately by graphical methods
Recognise and sketch the graphs of linear and quadratic functions
ax
Learner Guide
35
Core Co-ordinate geometry
Question type You should be able to R A G CommentsCo-ordinates Work with co-ordinates in two dimensions
Gradients Find the gradient of a straight line graph
Equation of straight line
Interpret and obtain the equation of a straight line graph in the form y = mx + c where the graph is given
Parallel lines Determine the equation of a straight line parallel to a given line eg find the equation of a line parallel to y = 4x ndash 1 that passes through (0 ndash3)
Learner Guide
36
Core Geometry
Question type You should be able to R A G CommentsGeometrical language
Use and interpret the geometrical terms
bull point
bull line
bull parallel
bull perpendicular
bull bearing
bull right angle acute obtuse and reflex angles
bull similar
bull congruent
Use and interpret the vocabulary of
bull triangles right-angled scalene isosceles equilateral
bull quadrilaterals
bull circles
bull polygons
bull simple solid figures including nets
Learner Guide
37
Core Geometry
Question type You should be able to R A G CommentsGeometrical constructions
Measure and draw lines and angles
Construct a triangle given the three sides using a ruler and a pair of compasses only
Scale drawings Read and make scale drawings
Similar figures Calculate lengths of similar figures
Congruent Recognise congruent shapes
Symmetry Recognise symmetry properties for triangles quadrilaterals and circles
Recognise line symmetry in two dimensions
Recognise and find the order of rotational symmetry in two dimensions
Learner Guide
38
Core Geometry
Question type You should be able to R A G CommentsAngle properties Calculate unknown angles explaining the properties that you
are using in geometrical language for angles
bull angles at a point
bull angles on a straight line and intersecting straight lines
bull angles within parallel lines
bull angles in triangles
bull angles in quadrilaterals
bull angles in regular polygons
bull angle in a semi-circle
bull angle between tangent and radius of a circle
Learner Guide
39
Core Mensuration
Question type You should be able to R A G CommentsMeasures bull Use current units of
bull mass
bull length
bull area
bull volume
bull capacity
Express quantities in terms of smaller or larger units including units of area and volume
Convert between units including units of area and volume
Perimiter Carry out calculations involving
bull perimeter and area of a rectangle
bull perimeter and area of a triangle
bull perimeter and area of parallelogram
bull perimeter and area of a trapezium
bull perimeter and area of shapes made by combining
bull rectangles triangles parallelograms andor trapeziums
Learner Guide
40
Core Mensuration
Question type You should be able to R A G CommentsCircles Carry out calculations involving circumference and area of a
circle
Solve simple problems involving the arc length and sector area of a circle where the sector angle is a factor of 360deg
Surface area and volume
Carry out calculations involving
bull surface area and volume of a cuboid prism and cylinder (no formulae will be given for these shapes)
bull surface area and volume of a sphere pyramid and cone (formulae will be given for these shapes)
Areas and volumes of compound shapes
Carry out calculations involving the areas and volumes of compound shapes made from combinations of the shapes in Perimeter or Surface area and volume
Learner Guide
41
Core Trigonometry
Question type You should be able to R A G CommentsBearings Use and interpret three-figure bearings measured clockwise
from the North ie 000degndash360degTrigonometry Find unknown sides andor angles in right-angled triangles by
applying
bull Pythagorasrsquo theorem
bull sine cosine and tangent ratios for acute angles in right-angled triangles
Learner Guide
42
Core Vectors and transformations
Question type You should be able to R A G CommentsVectors in two dimensions (links to Trigonometry)
Describe a translation by using a vector represented by
AB or a
Add and subtract vectors
Multiply a vector by a scalar
Transformations Reflect simple shapes in horizontal or vertical lines
Rotate simple shapes through multiples of 90deg about
bull the origin
bull their vertices
bull the midpoints of their sides
Construct translations of simple shapes
Construct enlargements of simple shapes (positive and fractional scale factors)
Recognise and describe using the correct language
bull reflections
bull rotations
bull translations
bull enlargements (positive and fractional scale factors)
( )x
y
Learner Guide
43
Core Probability
Question type You should be able to R A G CommentsSingle events Calculate the probability of a single event as a fraction decimal
or percentage (not a ratio)Probability scale Understand and use the probability scale from 0 to 1
Sum to 1 Understand that the probability of an event occurring = 1 ndash the probability of the event not occurring
Relative frequency
Understand relative frequency as an estimate of probability
Work out expected frequencies using relative frequencyCombined events Calculate the probability of simple combined events using
bull tree diagrams
bull possibility diagrams (points on a grid)
bull Venn diagrams (2 sets only)
Learner Guide
44
Core Statistics
Question type What I need to do R A G CommentsClassify Collect classify and tabulate data
Interpret and compare
Read interpret and draw simple inferences from tables and statistical diagrams
Compare sets of data using
bull tables
bull graphs
bull statistical measures
Be aware of restrictions when making conclusions from data
Charts Construct and use
bull bar charts
bull pie charts
bull pictograms
bull stem-and-leaf diagrams
bull frequency distributions
bull histograms with equal intervals
bull scatter diagrams
Learner Guide
45
Question type What I need to do R A G CommentsAverages Calculate for individual and discrete data
bull mean
bull median
bull mode
bull range
and distinguish between their useCorrelation Understand what is meant by positive negative and zero
correlation with reference to a scatter diagramLine of best fit Draw interpret and use a ruled line of best fit by eye
Learner Guide
46
Extended syllabus content (includes required Core content)Extended Number
Question type You should be able to R A G CommentsNumber Identify and use
bull natural numbers
bull integers (positive negative and zero)
bull prime numbers
bull write a number as a product of its prime factors
bull square and cube numbers
bull common factors and highest common factor of two or more numbers
bull common multiples and lowest common multiple of two or more numbers
bull rational numbers
bull irrational numbers (eg π radic2 )
bull real numbers
bull reciprocals
Learner Guide
47
Extended Number
Question type You should be able to R A G CommentsSet notation and language
Use language notation and Venn diagrams to describe sets and represent relationships between sets as follows
Definition of sets egA = x x is a natural number
B = (xy) y = mx + c
C = x a ⩽ x ⩽ b
D = a b c hellip
Notation egnumber of elements in set A n(A)
lsquois an element ofrsquo isin
lsquois not an element ofrsquo notin
complement of set A
the empty set empty
the universal set
A is a subset of B A sube B
A is a proper subset of B A sub B
A is not a subset of B A ⊈ B
A is not a proper subset of B A nsub B
union of A and B A cup B
intersection of A and B A cap B
Learner Guide
48
Extended Number
Question type You should be able to R A G CommentsSquares square roots cubes and cube roots
Calculatebull squares of numbers
bull square roots of numbers
bull cubes of numbers
bull cube roots of numbers
bull other powers and roots of numbers
Directed numbers
Use directed numbers in practical situations for example temperature changes
Fractions decimals and percentages
Use the language and notation of simple vulgar and decimal fractions and percentages in appropriate contexts
Recognise equivalent fractions decimals and percentages
Convert between fractions decimals and percentages
Convert recurring decimals to fractions
Ordering Order quantities by magnitude and demonstrate familiarity with the symbols = ne gt lt ⩾ ⩽
Learner Guide
49
Extended Number
Question type You should be able to R A G CommentsIndices and standard form (links to Algebraic manipulation)
Evaluate indices including fractional negative and zero
eg 25 5ndash2 1000 10012 8ndash23
Use the rules of indices forbull multiplication of indices eg 43 times 45
bull division of indices eg 57 divide 53
bull index numbers raised to an index eg (43)2
Use the standard form A times 10n where n is a positive or negative integer and 1 ⩽ A lt 10bull convert into and out of standard form
bull calculate with numbers in standard form
Four rules
( + ndash times divide )
Use the four rules for calculations withbull whole numbers
bull decimals
bull vulgar and mixed fractions
bull correct ordering of operations (BIDMAS) and use of brackets
Learner Guide
50
Extended Number
Question type You should be able to R A G CommentsEstimates Make estimates of numbers quantities and lengths
Give approximations to a specified number of
bull significant figures
bull decimal places
Round off answers to reasonable accuracy in the context of a given problem
Bounds Give upper and lower bounds for data given to a specified accuracy eg measured lengths
Obtain appropriate upper and lower bounds to solutions of simple problems given to a specified accuracy eg the lower and upper bounds for the area of a rectangle
Ratio proportion rate
(links to Direct and inverse proportion)
Understand ratio
Divide quantities in a given ratio
Increase and decrease a quantity by a given ratio
Understand numerical problems involving direct and inverse proportion
Use ratio and scales in practical situations
Use common measures of rate (formulae for other rates eg density and pressure will be given in the question)
Calculate average speed
Learner Guide
51
Extended Number
Question type What I need to do R A G CommentsPercentages Calculate a percentage of a quantity
Express one quantity as a percentage of another quantity
Calculate percentage increase or decrease
Calculate reverse percentages eg finding the cost price given the selling price and the percentage profit
Use of an electronic calculator
Use a calculator efficiently
Check accuracy of calculations
Time Calculate times in terms of the 24-hour and 12-hour clock
Read clocks dials and timetables
Money Calculate using money
Convert from one currency to another
Learner Guide
52
Extended Number
Question type You should be able to R A G CommentsPersonal and small business finance
Use given data to solve problems on
bull earnings
bull simple interest
bull compound interest
ndash you must know the compound interest formula
bull discount
bull profit and loss
Extract data from tables and charts
Exponential growth and decay
Use exponential growth and decay in population and finance eg depreciation bacteria growth
Learner Guide
53
Extended Algebra and graphs
Question type You should be able to R A G CommentsBasic algebra Use letters to express generalised numbers
Express basic arithmetic processes algebraically
Substitute numbers in complicated formulae
Construct and rearrange complicated formulae eg where the subject appears twice
Algebraic manipulation
Manipulate directed numbers
Use bracketsbull expand a single bracket eg expand 3x(2x ndash 4y)
bull expand a pair of brackets eg (x ndash 4)(x + 7)
bull expand products of more than two brackets eg (x + 4)(x ndash 7)(2x + 1)
Extract common factors eg factorise 9x2 + 15xy
Factorise expressions of the formbull ax + bx + kay + kby
bull asup2xsup2 ndash bsup2ysup2
bull asup2 + 2ab + bsup2
bull axsup2 + bx + c
Learner Guide
54
Extended Algebra and graphs
Question type You should be able to R A G CommentsAlgebraic fractions
Manipulate algebraic fractions eg
bull
bull
bull
bull
bull
Factorise and simplify algebraic fractions such as
Rules of indices Use and interpret positive negative and zero indices
Use and interpret fractional indices eg solve 32x = 2
Use the rules of indices to simplify algebra eg
x3 + x ndash 4
22x3 +
3(x ndash 5)2
3a4 +
5ab3
3a4 divide
9a10
1x ndash 2 +
2x ndash 3
x2 ndash 2xx2 ndash 5x + 6
3xndash4 times23
x12
32x5( )
3
2xndash2divide25
x12
Learner Guide
55
Extended Algebra and graphs
Question type You should be able to R A G CommentsEquations and inequalities
bull Derive and solve simple linear equations in one unknown
bull Derive and solve simultaneous linear equations in two unknowns
bull Derive and solve simultaneous equations involving one linear and one quadratic
Solve quadratic equations by
bull factorisation
bull completing the square
bull using the formula
Derive and solve simple linear inequalities including representing solutions on a number line
Linear programming
Represent inequalities graphically including using the conventions of
bull broken lines for strict inequalities
bull shading unwanted regions
Solve simple linear programming problems using graphical representations of inequalities
Learner Guide
56
Extended Algebra and graphs
Question type You should be able to R A G CommentsNumber sequences (links to Squares square roots cubes and cube roots)
Continue a number sequence
Recognise patterns in sequences
Recognise relationships between different sequences
Find the nth term of sequences of
bull linear sequences
bull quadratic sequences
bull cubic sequences
bull exponential sequences
and simple combinations of these
Direct and inverse proportion (links to Ratio proportion rate)
Express direct proportion algebraically
Express inverse proportion algebraically
Use algebraic expressions of direct and inverse proportion to find unknown quantities
Practical graphs
(links to Coordinate geometry)
Interpret and use graphs in practical situations including
bull travel graphs
bull conversion graphs
Draw graphs from given data
Learner Guide
57
Extended Algebra and graphs
Question type You should be able to R A G CommentsPractical graphs (links to Coordinate geometry) continued
Apply the idea of rate of change to simple kinematics involving
bull distancendashtime graphs
bull speedndashtime graphs
bull acceleration and deceleration
This may involve estimation and interpretation of the gradient of a tangent at a point
Calculate distance travelled as an area under a linear speedndash time graph
Learner Guide
58
Extended Algebra and graphs
Question type You should be able to R A G CommentsGraphs of functions (links to Coordinate geometry)
Construct tables of values and draw graphs for functions of the form
bull axn where a is a rational constant and n = minus2 minus1 0 1 2 3 and simple sums of not more than three of these
bull abx + c where a and c are rational constants and b is a positive integer
Solve associated equations approximately by graphical methods including finding and interpreting roots and finding turning points of quadratics by completing the square
Draw and interpret graphs representing exponential growth and decay problems
Recognise sketch and interpret graphs of
bull linear
bull quadratic
bull cubic
bull reciprocal
bull exponential
(knowledge of turning points and asymtotes is required)Tangents Estimate gradients of curves by drawing tangents
Learner Guide
59
Extended Algebra and graphs
Question type You should be able to R A G CommentsFunctions Use function notation eg
f(x) = 3x ndash 5 f x α 3x ndash5 to describe simple functions
Find inverse functions f ndash1 (x)
Form composite functions as defined by gf(x) = g(f(x))
Derivatives Understand the idea of a derived function
Use derivatives of the form axn and simple sums of not more than three of these (a is a rational constant and n is a positive integer or 0)
Apply differentiation to gradients and turning points (stationary points)
Use any method to explain whether the turning point is a maximum or a minimum eg second derivative or gradient of function on either side of turning point
Learner Guide
60
Extended Co-ordinate geometry
Question type You should be able to R A G CommentsStraight line graphs
Work with co-ordinates in two dimensions
Gradient Find the gradient of a straight line graph
Calculate the gradient of a straight line from the co-ordinates of two points on it
Length and midpoint
Calculate the length and the co-ordinates of the midpoint of a straight line segment from the co-ordinates of its end points
Equation of line Interpret and obtain the equation of a straight line graph
Parallel lines Determine the equation of a straight line parallel to a given line eg find the equation of a line parallel to y = 4x ndash 1 that passes through (0 ndash3)
Perpendicular lines
Find the gradient of parallel and perpendicular lines eg
bull find the gradient of a line perpendicular to y = 3x + 1
bull find the equation of a line perpendicular to one passing through the co-ordinates (1 3) and (ndash2 ndash9)
Learner Guide
61
Extended Geometry
Question type You should be able to R A G CommentsGeometrical language
Use and interpret the geometrical terms
bull point
bull line
bull parallel
bull perpendicular
bull bearing
bull right angle acute obtuse and reflex angles
bull similar
bull congruent
Use and interpret the vocabulary of
bull triangles right-angled scalene isosceles equilateral
bull quadrilaterals
bull circles
bull polygons
bull simple solid figures including nets
Learner Guide
62
Extended Geometry
Question type What I need to do R A G CommentsGeometrical constructions
Measure and draw lines and angles
Construct a triangle given the three sides using a ruler and a pair of compasses only
Scale drawings Read and make scale drawings
Similar figures Calculate lengths of similar figures
Use relationships between areas of similar triangles and in similar figures
Use relationships between volumes and surface areas of similar solids
Congruent triangles
Use the congruence criteria for triangles (SSS ASA SAS RHS)
Symmetry Recognise symmetry properties for triangles quadrilaterals and circles
Recognise line symmetry in two dimensions
Recognise and find the order of rotational symmetry in two dimensions
Learner Guide
63
Extended Geometry
Question type You should be able to R A G CommentsSymmetry (continued)
Use the following symmetry properties of circles
bull equal chords are equidistant from the centre
bull perpendicular bisector of a chord passes through the centre
bull tangents from an external point are equal in length
Recognise and use symmetry properties of
bull prism cylinder cone and pyramid
Learner Guide
64
Extended Geometry
Question type You should be able to R A G CommentsAngle properties Calculate unknown angles explaining the properties that
you are using in geometrical language for the following geometrical properties
bull angles at a point
bull angles at a point on a straight line and intersecting straight lines
bull angles formed within parallel lines
bull angle properties of triangles and quadrilaterals
bull angle properties of regular polygons
bull angle in a semi-circle
bull angle between tangent and radius of a circle
bull angles properties of irregular polygons
bull angle at the centre of a circle is twice the angle at the circumference
bull angles in the same segment are equal
bull angles in opposite segments are supplementary cyclic quadrilaterals
bull alternate segment theorem
Learner Guide
65
Extended Mensuration
Question type What I need to do R A G CommentsMeasures Use current units of
bull mass
bull length
bull area
bull volume
bull capacity
Express quantities in terms of smaller or larger units including units of area and volume
Perimeter Carry out calculations involving
bull perimeter and area of a rectangle
bull perimeter and area of a triangle
bull perimeter and area of parallelogram
bull perimeter and area of a trapezium
bull perimeter and area of compound shapes made by combining rectangles triangles parallelograms andor trapeziums
Learner Guide
66
Extended Mensuration
Question type You should be able to R A G CommentsCircles Carry out calculations involving circumference and area of a
circle
Solve problems involving arc length and sector area of a circle
Surface area and volume
Carry out calculations involving
bull surface area and volume of a cuboid prism and cylinder (no formulae will be given for these shapes)
bull surface area and volume of a sphere pyramid and cone (formulae will be given for these shapes)
Compound shapes
Carry out calculations involving
bull area of a shape made by combining cuboids prisms andor cylinders
bull volume of a shape made by combining cuboids prisms andor cylinders
Learner Guide
67
Extended Trigonometry
Question type You should be able to R A G CommentsBearings Use and interpret three-figure bearings measured clockwise
from the North ie 000degndash360degTrigonometry Find unknown sides andor angles in right-angled triangles by
applying
bull Pythagorasrsquo theorem
bull sine cosine and tangent ratios for acute angles in right-angled triangles
Solve problems in two dimensions involving angles of elevation and depression
Know that the perpendicular distance from a point to a line is the shortest distance to the line
Trig graphs and equations
Recognise sketch and interpret graphs of simple trigonometric functions
Graph and know the properties of trigonometric functions
Solve simple trigonometric equations for values between 0deg
and 360deg eg Solve sin x = radic32
for values of x between 0deg and
360degGeneral trig Solve problems using sine and cosine rules for any triangle
Find the area of any triangle using frac12absinC
Trig in 3D Solve simple trigonometrical problems in three dimensions including angle between a line and a plane
Learner Guide
68
Extended Vectors and transformations
Question type You should be able to R A G CommentsVectors in two dimensions (links to Trigonometry)
Describe a translation by using a vector represented by
AB or a
Add and subtract vectors
Multiply a vector by a scalar
Transformations Reflect simple shapes in horizontal or vertical lines
Rotate simple shapes through multiples of 90deg about any point
Construct translations of simple shapes
Construct enlargements of simple shapes (positive fractional and negative scale factors)
Recognise and describe
bull reflections
bull rotations
bull translations
bull enlargements (positive fractional and negative scalefactors)
( )x
y
Learner Guide
69
Extended Vectors and transformations
Question type You should be able to R A G CommentsHarder vectors
Calculate the magnitude of a vector as and
understand that magnitude is denoted by modulus signs |A B| or |a|
Represent vectors by directed line segments
Use the sum and difference of two vectors
Use position vectors
( )x
yradicx2 + y2
Learner Guide
70
Extended Probability
Question type You should be able to R A G CommentsProbability (links to Four rules)
Calculate the probability of a single event as a fraction decimal or percentage (not a ratio)
Probability scale Understand and use the probability scale from 0 to 1
Sum to 1 Understand that the probability of an event occurring = 1 ndash the probability of the event not occurring
Relative frequency
Understand relative frequency as an estimate of probability
Work out expected frequencies using relative frequency
Combined events Calculate the probability of combined events using
bull tree diagrams
bull possibility diagrams
bull tables
Learner Guide
71
Extended Statistics
Question type You should be able to R A G CommentsClassify Collect classify and tabulate data
Interpret and compare
Read interpret and draw simple inferences from tables and statistical diagrams
Compare sets of data using
bull tables
bull graphs
bull statistical measures
Be aware of restrictions when making conclusions from data
Charts Construct and use
bull bar charts
bull pie charts
bull pictograms
bull stem ndash and ndash leaf diagrams
bull frequency distributions
bull histograms with equal and unequal intervals
bull scatter diagrams
Learner Guide
72
Extended Statistics
Question type You should be able to R A G CommentsAverages Calculate for individual and discrete data
bull mean
bull median
bull mode
bull range
and distinguish between their use
Estimated mean Calculate an estimate of the mean for grouped and continuous data
Identify the modal class from a grouped frequency distributionCumulative frequency
Construct and use cumulative frequency diagrams to estimate and interpret
bull the median
bull percentiles
bull quartiles
bull inter-quartile range
Construct and interpret box-and-whisker plots
Correlation Understand what is meant by positive negative and zero correlation with reference to a scatter diagram
Lines of best fit Draw interpret and use a ruled line of best fit by eye
Cambridge Assessment International Education1 Hills Road Cambridge CB1 2EU United Kingdomt +44 1223 553554e infocambridgeinternationalorg wwwcambridgeinternationalorg
Copyright copy UCLES October 2017
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- Text Field 3045
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- Text Field 3046
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- Text Field 3026
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- Text Field 3047
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- Text Field 3048
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- Text Field 3027
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- Text Field 3029
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- Text Field 3030
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- Text Field 3031
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- Text Field 3032
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- Text Field 3042
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8
Extended Paper 2 (Shortndashanswer questions) and Paper 4 (Structured questions)
You need to answer all questions on both papers
Paper 2 questions are short-answer questions Most questions are worth 1ndash3 marks with some being worth 4 or 5 marks Some questions might be broken up into two parts
Write your working and answers in the spaces provided
The number of marks for each part is shown
Paper 4Paper 2
You can use an electronic calculator in both papers Ask your teacher to recommend a suitable calculator
Paper 4 contains structured questions Each question is split into many parts with each part usually being worth 1ndash6 marks Here for example question 2 is split over two pages
Often the answers to later parts will depend on the answers to earlier parts
9
Equipment for the examMake sure you have
bull a blue or black pen (a spare pen is always a good idea)bull a pencil (for graphs and diagrams)bull an electronic calculatorbull a protractorbull a pair of compassesbull a ruler
1 Read the questions carefully to make sure that you understand what is being asked
2 Give your answers to the accuracy indicated in the question If none is given and the answer isnrsquot exact then
bull give your answer to three significant figures 123 9 12298 x
bull if the answer is in degrees then give it to one decimal place 231deg 9 23deg x
3 Include units with your answers if they are not given on the paper For example 1 kg of apples costs hellip pound120 9 120 x
4 Show your working Show as much working as you can for all your questions
5 If you make a mistake clearly cross out any working or answers that you do not want the examiner to mark
Use the value of π from your calculator or use 3142 which is given on the front page of the question paper
Timingbull If you are stuck on a question dont waste too much time trying to answer it ndash go on to the next question and
come back to the one you are stuck on at the endbull Use any time that you have left at the end of the exam to go back and check your answers and working
Make sure that you give your answer in the form asked for in the question eg some questions ask for answers to be given in terms of π For lengths areas and volumes give answers in decimals (not in surds or in terms of π) unless you are told to given an exact answer
You can gain marks for the correct working even if you have an incorrect answer or cannot complete the whole question
If you need more space ask for extra of paper and clearly indicate where the rest of the answer is written On the additional paper make it clear which questions(s) you are answering
General advice for all Papers
10
The areas of knowledge understanding and skills that you will be assessed on are called assessment objectives (AOs) There are two AOs for this course
AO1 Demonstrate knowledge and
understanding of mathematical techniques
AO2 Reason interpret and communicate
mathematically when solving problems
AO1 Demonstrate knowledge and understanding of mathematical techniquesYou need to show that you can recall and apply mathematical knowledge terminology and definitions to carry out single or multi-step solutions in mathematical and everyday situations
Section 3 What skills will be assessed
This means that you need to show that you can
bull organise process and present information accurately in written tabular graphical and diagrammatic forms
bull use and interpret mathematical notation correctly
bull perform calculations and procedures by suitable methods including using a calculator
bull understand systems of measurement in everyday use and make use of these
bull estimate approximate and work to degrees of accuracy appropriate to the context and convert between equivalent numerical forms
bull use geometrical instruments to measure and to draw to an acceptable degree of accuracy
bull recognise and use spatial relationships in two and three dimensions
AO1 is assessed in all papers
Use tables graphs and diagrams
An example of degress of accuracy include significant figures or decimal places
An example of converting between equivalent numerical forms include between fractions decimals and percentages or between normal numbers and standard form
eg a pair of compasses a protractor and a ruler
11
AO2 Reason interpret and communicate mathematically when solving problemsYou need to demonstrate that you can analyse a problem select a suitable strategy and apply appropriate techniques to obtain a solution
This means that you need to show that you can
bull make logical deductions make inferences and draw conclusions from given mathematical data
bull recognise patterns and structures in a variety of situations and form generalisations
bull present arguments and chains of reasoning in a logical and structured way
bull interprete and communicate information accurately and change from one form of presentation to another
bull assesses the validity of an argument and critically evaluate a given way of presenting information
bull solve unstructured problems by putting them into a structured form involving a series of processes
bull apply combinations of mathematical skills and techniques using connections between different areas of mathematics in problem solving
bull interprete results in the context of a given problem and evaluate the methods used and solutions obtained
AO2 is assessed in all papers
Recognise and extent patterns
Take information and organise it to answer a problem
12
Section 4 Command wordsA command word is the part of the question that tells you what you need to do with your knowledge For example you might need to describe something explain something argue a point of view or list what you know The table below includes command words used in the assessment for this syllabus The use of the command word(s) within an question will relate to the context
Cambridge IGCSE Mathematics 0580 syllabus for 2020 2021 and 2022 Details of the assessment
37wwwcambridgeinternationalorgigcseBack to contents page
Command wordsThe table below includes command words used in the assessment for this syllabus The use of the command word will relate to the subject context
Command word What it means
Calculate work out from given facts figures or information generally using a calculator
Construct make an accurate drawing
Describe state the points of a topicgive characteristics and main features
Determine establish with certainty
Explain set out purposes or reasons make the relationships between things evident provide why andor how and support with relevant evidence
Give produce an answer from a given source or recallmemory
Plot mark point(s) on a graph
Show (that) provide structured evidence that leads to a given result
Sketch make a simple freehand drawing showing the key features
Work out calculate from given facts figures or information with or without the use of a calculator
Write give an answer in a specific form
Write down give an answer without significant working
The question below is taken from Paper 4 and illustrates the use of two command words
The command words lsquoWrite downrsquo indicates that you do not need to show your working and the answer should just be written down The mark allocation [1] also supports this
The command words lsquoShow thatrsquo indicate that you need to provide evidence in the form of a clear mathematical explanation to demonstrate that you know how to obtain the given result In other words you need to show a method that leads to the result
The answer space in this case does not contain a dotted answer line as there is no single lsquoanswerrsquo to be found Your working that leads to the given result should be written in the blank working space
13
This section takes you through an example question and learner response from one of the 2020 specimen papers for this course It will help you to identify the command words and other key instructions within questions and to understand what is required in your response
This section is structured as follows
QuestionThe command words and instructions in the question have
been highlighted and explained This should help you to understand clearly what is required by the question
Mark schemeThis tells you as clearly as possible what an examiner expects
from an answer to award marks
Example candidate responseThis an exemplar answer written in the style of
a high level candidate
How the answer could have been improvedThis summarises what could be done to gain more marks
All information and advice in this section is specific to the example question and response being demonstrated It should give you an idea of how your responses might be viewed by an examiner but it is not a list of what to do in all questions In your own examination you will need to pay careful attention to what each question is asking you to do
Common mistakesThis will help you to avoid common mistakes made by
candidates So often candidates lose marks in their exams because they misread or misinterpret the questions
Section 5 Example candidate response
14
QuestionThe question used in this example is from Specimen Paper 3 (Core) It represents the type of structured question you will see in both Paper 3 (Core) and Paper 4 (Extended) A structured question means that it is broken into several parts Often later parts will depend on your answers to earlier parts
This means that you cannot find the answer by
measuring the diagramWork out indicates that the answer should be calculated from the given information so measurement will not score marks
The allocation of 1 mark indicates that the answer can be obtained with minimum working
Give reasons for your answer indicates that your answer should be supported with reasons using the correct mathematical terminology You must justify your answer
Use trigonometry to calculate indicates that you should use this method with the given information to find the answer and that a calculator is needed to solve the problem If you did not use trigonometry you would not be awarded any marks
15
Show that indicates the answer is given and you need to write down all of the steps in a method that leads to the given answer You need to provide evidence that you understand and know how the answer is reached
Work out indicates that you should calculate the answer from the given information The mark allocation of 4 marks suggests that you will need to include several steps of working in order to get to the answer
Learner Guide
16
Answer Mark Notes(a)(i) 35 1 This is the only acceptable answer for this part of the question
(a)(ii) 74 1 This is the only acceptable answer for this part of the question
(b) 43deg and correct mathematical reasons
3 Two marks are awarded for the final answer of 43deg
The third mark is awarded for a fully correct reason for example angles on a straight line add up to 180deg and angles in a triangle add up to 180deg There are other correct reasons that could be also be used
If 43deg is not obtained one method mark can be awarded if the following calculation is seen in the working
180 ndash 128 or 128 ndash 85
(c) 322 or 3223hellip 2 This is the only acceptable answer for this part of the question
The answer has to be rounded correct to three significant figures or can be given with more figures in the answer
Those that did not get this answer can score one method mark for showing the following in their working
sin = 8 divide 15
(d)(i) 2 2300 225+2 This does not have to be shown in one step as long as the method shown is the same as this overall Those that do not
show this can have one method mark for showing the following in their working
300deg + 225deg
(d)(ii) 15 35 4 The answer 3 35pm is also acceptable for 4 marks
If the correct answer is not found one method mark is available for showing 375 divide 450 in their working and a second method mark can be awarded for sight of them multiplying their answer to this by 60 to change it to hours A third method mark can be awarded for adding their answer in hours to 14 45 ndash this shows the correct method so only one mark is lost for an incorrect final answers
Mark schemeYour examination papers will be marked and the overall number of marks for each paper will be recorded Your marks across all papers will then be converted to a grade
Final answer This value is what the examiner expects to see The answer has to be exactly as given in the mark scheme unless there are acceptable alternatives The mark scheme will always make it clear if there are acceptable alternative answers
Method marks Sometimes method marks are awarded for lines of working as well as for the final answer This means that you could get the final answer incorrect but still get some marks if you include the correct working The mark scheme does not include all possible methods so if you use a method not included in the mark scheme but it is accurate and relevant then the examiner will still award marks for the appropriate parts of the working ndash unless the questions asks you to use a specific method
example of a final answer
example of a method mark
17
Example candidate responseNow letrsquos look at the sample candidatersquos response to question 8 The examiners comments are in the orange boxes The candidate was awarded 8 marks out of 13
180 ndash 74 + 71 = 177
177
74
0 out of 1
The candidates working suggests they understand that the angle sum of a triangle is 180deg but they did not include brackets around 74 + 71 The answer 177deg is not sensible for this question
1 out of 1
The candidate recognises that there are parallel lines and that angle y is a corresponding angle to angle 74deg
180 ndash 128 = 52 180 ndash 85 ndash 52 = 43
43 angles on a straight line add up to 180deg
2 out of 3
The candidate has given a correct answer for w and shown correct working in two steps They have given a correct reason for 52deg using correct mathematical languge But they have not provided a reason to explain the angle 43deg They lose a mark for not also stating angle sum of a triangle is 180deg
sin p = 8 divide 15 = 053
p = sinndash1 (053)
p = 32005 320
1 out of 2
The candidate has correctly used trigonometry in their method They are awarded one method mark for the first line of working However they have rounded 05333333hellip (the result of 8 divide 15) to 052 and then calculated the inverse sin of 052 rather than 05333333 This has resulted in an inaccurate final answer This is called lsquopremature approximationrsquo and it is a very common error to make
18
AB2 = 3002 + 2252
= 140625
AB = 375
1 out of 2
The candidate has recognised the right-angled triangle and correctly used Pythagorasrsquo theorem in the first line of working However they have missed out an important step by not showing that you need to take the square root of 140625 to get 375 As this is a lsquoshow thatrsquo question and they missed a key step in the method they cannot be awarded full marks as the complete working is not shown One method mark is earned for the first line
T = = = 08333333hellip
08333333 hours = 08333333 times 60 minutes = 50 minutes
arrives at 14 45 + 50 mins = 3 35
DS
375450
3 35
3 out of 4
The candidate has found the time by correctly dividing the distance by the speed and recognised that this is in hours When converting the answer to a decimal they have not rounded the decimal but left its full value on the calculator to get 50 mins which is the correct approach Unfortunately after converting the time from 24 hour clock to 12 hour clock they did not include lsquopmrsquo to indicate that the time is in the afternoon and so the final answer is not quite right So 3 marks are awarded for all of a correct method but a mark is lost due to the accuracy of the final answer
19
How the answer could have been improvedThis answer could have been improved by
bull In part (a)(i) the answer of 177deg was not sensible given the diagram in the question If the candidate had checked their answer for sense they would have realised they had made a mistake It is always a good idea to check that your answer seems sensible before you move on to another question
bull In part (b) the candidate did all the correct steps but failed to provide both reasons There were two steps to the method which should have indicated to the candidate that there were two steps to justify and therefore two reasons should have been provided The mark allocation for the question [3] also indicates that more than one reason would be required one mark for the value of 43deg leaving two marks one mark for each of two reasons The candidate should have read the question carefully and again checked their response seemed reasonable
bull In part (c) the candidate rounded an intermediate answer which affected the accuracy of the final answer This caused them to lose a mark despite using a correct method You should only ever round the final answer do not round intermediate values If you can store the intermediate values in your calculator and so that you can use the full value in your calcuations If youre not able to do this and you have to round the intermediate values do not round them to less than three significant figures
bull In part (d)(i) the candidate missed out a step in the method As this was a show that question they needed to show all the steps in the method Its important to show all steps even if they seem obvious
bull In part (d)(ii) the candidate made a silly error by not stating that the time was pm When working with time answers are accepted in either 24 clock or 12 clock time but if you give your answer in the 12 hour clock then it must include am or pm as well
Common mistakesThere were a number of common mistakes made by other candidates on this question
bull Accuracy of answers
In parts (c) and (d)(ii) a common error was premature rounding ndash rounding intermediate values in the method before the final answer which resulted in their final answer not being accurate Other candidates gave the final answer to less than three significant figures ignoring the instruction on the front of the paper to round to three significant figures
bull Using incorrect terminology when giving reasons
In part (b) the most common error was to not give full reasons to support the answer Another common error was to provide a reason that did not use the correct mathematical language such as lsquoThey add up to 180degrsquo and lsquoIt is a straight linersquo which could not be awarded marks
bull Lack of knowledge
In part (c) a number of candidates had limited knowledge of trigonometry and did not choose the correct trig ratio which was the sine ratio This is why good revision is important
bull Not checking answers
In part (a)(i) even though the diagram is drawn NOT TO SCALE it is possible to see that the angle is an acute angle and should therefore not be bigger than 90deg This should alert candidate that if their answer is over 90deg it is not a sensible answer and they should go back and check their working
20
bull Inefficient method shown
In part (c) the lsquoShow thatrsquo question a number of candidates omitted an important step from the method this is often common in lsquoShow thatrsquo questions where every step must be shown no matter how obvious them seem
General adviceIn order to do your best when answering a mathematics question make sure you
bull revise all of the topics for the syllabus you are studying before the exam
bull understand what all the key terms and command words in the question mean
bull read the questions carefully and consider what you need to do before you do it
bull only round the final answer not intermediate values
bull show all steps in your working and show them clearly
bull round to the correct degree of accuracy
bull use the correct mathematical terminology
bull check your answers seem reasonable given the context or details of the question
21
It is important that you plan your revision in plenty of time for the examinations and that you develop a revision technique that works for you The advice in this section will help you revise and prepare for the examinations It is divided into general advice for all papers
Use the tick boxes to keep a record of what you have done what you plan to do or what you understand
For more advice on revision see the Cambridge Learner Revision Guide on our website
Section 6 Revision
Find out when the examinations are and plan your revision so you have time to revise Create a revision timetable and divide it into sections to cover each topic
Spend most of your time focussing on specific skills knowledge or issues that you have found more difficult when practicing them either during revision or earlier in the course
Write a summary of all the key information for a topic ndash use the checklists at the end of this section
Know the meaning of the command words used in questions and how to apply them to the information given Look at past examination papers and highlight the command words and check what they mean
Make revision notes and work on practice questions Reading alone does not work you need to be active and practice your maths
Work for shorter periods then have a break Revise small sections of the syllabus at a time but do this regularly
Test yourself by trying out some past exam questions Use the mark schemes to assess yourself and to be familiar with how marks are awarded for different questions
Be organised in advance with your notes texts exercise books revision guides and revision websites so you do not waste valuable revision time trying to find things
Make notes of key mathematical words that you should use in questions that ask you to lsquodescribersquo or give lsquogeometrical reasons forrsquo eg in describing transformations or giving reasons in circle theorem questions Look at the mark schemes for these types of questions from past papers to see how marks are awarded
Make sure you have all of the correct mathematical equipment ready for the exam particularly your calculator Make sure you are familiar with the all of the important functions on your calculator
Practice the areas you can do well not just those that you find more difficult
Take breaks and do things to relax when you take your breaks this will help you to be more productive when you are revising
Before the examination
22
During the examination
Plan your time according to the marks for each question For example a question worth one mark requires less time than a question one worth 4 marks If a question has several parts then the parts with more marks will need more time
Read each question very carefully
Identify the command words ndash you could underline or highlight them
Identify the other key words and information and perhaps underline them too particularly where
questions require reasoning or problem solving
Read the questions careully and make you have answered the question that is being asked
Show your working this is particularly important for questions where you are asked to lsquoshow that helliprsquo
Set your working out clearly so that it is easy to follow this makes it easier to keep track of what you have done and makes checking back through your work easier and it makes it easier for the examiner to mark your work try to write it in a logical order in the answer space
Write answers clearly if you want to change an answer then you should cross the answer out and write a replacement if your answer is on the answer line cross it out and write the replacement answer above it do not try to change numbers on the answer line as this can lead to unclear figures
Check your working and answers to avoid errors
Give your answer to the appropriate level of accuracy either the accuracy indicated in the question or the accuracy given on the front of the paper
Avoid rounding intermediate values part way through your calculation only round the final answer
Check that the answer that you have given is sensible and realistic for what is being asked
Use a pencil when drawing diagrams or completing graphs this means that you can change your answer more easily if you have made a mistake
Take care when reading scales
If you are asked for reasons for your answer then use the correct mathematical terms
Use the mark allocation given with the questionsparts of questions to try to judge how much work is needed to answer each part
23
Top tips for revision of Cambridge IGCSE Mathematics1 Summarise recall and applyMake sure that you can recall and apply the key information and mathematical techniques on each topic that you need for the exam
i Write a summary of the key information of a topicii Collect together some questions that test the knowledge and skills of this topic Ask your teacher for practice
questions or suitable past examination questions or use practice books or textbooksiii Test your recall by covering over the summary and trying to remember the details or use the summary as part of
the lsquoTeach the topicrsquo (Tip 3) or lsquoQuestion and answer cardsrsquo (Tip 4) activities iv After you have spent some time revising and practising the knowledge and skills answer the questions that you
collected together on the topic You might do this later on the same day as revising or a few days later Answer as many questions as you can in order to practise applying your knowledge
v Try creating your own questions by adapting existing ones and use these for practice when you return to a topic
On graph questions straight lines should be ruled and curves should be drawn freehand with a smooth curve
Donrsquot spend too long on any one part of a question If you are really stuck on a question then move on and come back to the question later if you have time As a rough guide each mark on the paper should take about one minute
2 Concept mapsConcept maps are a great way to revise the links between different factors or to explore a larger topic They can also be used to collect together your ideas
i Use a blank sheet of paper and turn it on its side (landscape)ii Put the topic title in the middle of the page and build the concept map outwards using lines called lsquobranchesrsquo
ndash The first branches are from the central topic to sub-topics draw these as thick lines
ndash Add new branches from the sub-topics to include more detail draw these as thinner lines
ndash Add even more detail to a point by adding more branches
This creates a hierarchy of information from lsquooverviewrsquo (the thick branches) to lsquofine detailrsquo (thinnest branches)
iii Write single key words or phrases along a branch and add drawings for visual impactiv Use different colours highlighter pens symbols and arrows to highlight key facts or issuesIt is a good idea to use a large piece of plain A3 (or larger) paper and lots of coloured pens
24
3 Teach the topicThis is a very simple but effective technique that focusses on knowledge recall It tests the brain and rehearses the information you need to know for a certain topic and so will help your revision
i Create some topic cards with key bullet points of information on Leave space for ticksii Give these to your parents family or friends for exampleiii Give yourself 10 minutes maximum to teach your audience the main points of the topic You could use a mini-
whiteboard or flip chart to helpiv Your audience tick off all the points you mention in your presentation and give you a final scoreThe brain loves competition so if you do not score full marks you can try again the next day or compete against friends This system of repeat and rehearsal is very effective especially with more complex topics and doesnt take much preparation
4 Question and answer (QampA) cardsThis is very similar to Teach the topic but less formal and less public for those who dislike performing in front of others It tests knowledge recall and rehearses the information you need to know for a certain topic
i Pick a topic and create two sets of cards question cards and answer cards You might find it helpful to make the question cards a different size or use different coloured card for answers
ii Make sure you have the topic or something appropriate depending on what you are focusing on as a heading on each card The questions should test your knowledge and understanding of key areas of the course
iii A friend or family member uses the cards to test you in short 5 or 10 minute periods at any time during the dayiv You could also do this alone by reading the questions to yourself giving the answer and then checking the
correct answer cardv This game can be adapted by using the cards to find matching pairs turn all cards face down across the space
in front of you Turn over two cards leaving them where they are If they match (one is a question card and the other is the corresponding answer card) pick up the pair and put them to one side If they dont match try to remember where they are and what is on each card then turn them back over Turn over two other cards Continue until you have matched all pairs
5 Question paper and mark schemesLooking at past question papers and the mark scheme helps you to familiarise yourself with what to expect and what the standard is
i Ask your teacher for past paper questions with mark schemes for the course ndash ask your teacher for help to make sure you are answering the correct questions and to simplify the mark scheme
ii Look at the revision checklist and identify which topic a given question relates to ndash you might need to ask your teacher to help you do this
iii Once you have finished revising a topic or unit time yourself answering some appropriate exam questions Check the mark schemes to see how well you would have scored or give the answers to your teacher to check
iv Add details or notes to the mark scheme where you missed out on marks in your original answers using a different coloured pen Use these notes when you revise and try the question again later
You can find plenty of past exam papers and mark schemes on the Cambridge International public website
httpwwwcambridgeinternationalorgprogrammes-and-qualificationscambridge-igcse-mathematics-0580past-papers
25
Other useful revision advice for Cambridge IGCSE Mathematics bull Before the exam make sure that you are familiar with your calculator and confident in using it
bull Look at the Example Candidate Response earlier in this guide Can you identify the strengths of the response andwhere they have made mistakes or lost marks
bull When you are attempting a past paper (or questions from a past paper) complete it without referring to yournotes so that you get a true idea of your strengths and weaknesses Then go back through the paper using yournotes and a different coloured pen to make corrections and changes After you have done as much as you can onthe paper mark it using the mark scheme Take notes of any points that you lost marks on
bull Donrsquot just revise the topics that you enjoy and are confident in If you identify an area that you are weaker inthen try to revisit the topic by reviewing your notes and doing some practice questions then use exam questionsto check whether you now understand
bull Return to topics later in your revision to check that you still remember and understand the topic and to help toensure that you recall more of the material when you get to the examination
Revision checklists for Cambridge IGCSE MathematicsThe tables on the following pages can be used as a revision checklist They do not contain all the detailed knowledge you need to know just an overview For more detail see the syllabus and talk to your teacher
You can use the tick boxes in the checklists to show when you have revised and are happy that you do not need to return to it Tick the lsquoRrsquo lsquoArsquo and lsquoGrsquo column to record your progress as follows
bull R = RED means you are really unsure and lack confidence in that area you might want to focus your revisionhere and possibly talk to your teacher for help
bull A = AMBER means you are reasonably confident in a topic but need some extra practicebull G = GREEN means you are very confident in a topic
As your revision progresses you can concentrate on the RED and AMBER topics in order to turn them into GREEN topics You might find it helpful to highlight each topic in red orange or green to help you prioritise
You can use the lsquoCommentsrsquo column to
bull add more information about the details for each pointbull include a reference to a useful resourcebull include a list of formulae or notationbull add learning aids such as rhymes poems or word playbull highlight areas of difficulty or things that you need to talk to your teacher about
There is a set of checklist for the Core syllabus and a different set for the Extended syllabus
Learner Guide
26
Core syllabus contentCore Number
Category You should be able to R A G CommentsNumber Identify and use
bull natural numbers
bull integers (positive negative and zero)
bull prime numbers
bull write a number as a product of its prime factors
bull square numbers and cube numbers
bull common factors and highest common factor of two numbers
bull common multiples and lowest common multiple of two numbers
bull rational numbers
bull irrational numbers (eg π radic2 )
bull real numbers
bull reciprocals
Learner Guide
27
Core Number
Question type You should be able to R A G CommentsSets and Venn diagrams
Understand notation of Venn diagrams
Definition of sets
eg A = xx is a natural number
B = abchellip
Notation
Number of elements in set A n(A)
Universal set
Union of A and B A cup B
Intersection of A and B A cap B
Squares square roots cubes and cube roots
Calculate
bull squares and cubes of numbers
bull square roots and cube roots of numbers
Learner Guide
28
Core Number
Question type You should be able to R A G CommentsDirected numbers
Use directed numbers in practical situations for example temperature changes
Fractions decimals and percentages
Use the language and notation of simple vulgar and decimal fractions and percentages
Recognise equivalent fractions decimals and percentages
Convert between fractions decimals and percentages
Ordering Order quantities by magnitude and demonstrate familiarity with the symbols = ne gt lt ⩾ ⩽
Indices and standard form (links to Algebraic manipulation)
Evaluate indices eg 25 5ndash2 1000 64frac12 8ndash23
Use the rules of indices for
bull multiplication of indices eg 4ndash3 times 45
bull division of indices eg 57 divide 53
bull index numbers raised to an index eg (23)2 (43)2
Use the standard form A times 10n where n is a positive or negative integer and 1 ⩽ A lt 10
bull convert numbers into and out of standard form
bull calculate with numbers in standard form
Learner Guide
29
Core Number
Question type You should be able to R A G CommentsFour rules
( + ndash times divide )
Use the four rules for calculations with
bull whole numbers
bull decimals
bull vulgar and mixed fractions
bull correct ordering of operations (BIDMAS) and use of bracketsEstimates Make estimates of numbers quantities and lengths
Give approximations to a specified number of
bull significant figures
bull decimal places
Round off answers to reasonable accuracy in the context of a given problem
Bounds Give upper and lower bounds for data given to a specified accuracy eg measured lengths
Ratio proportion rate
Understand ratio
Divide a quantity in a given ratio
Understand direct and inverse proportion
Use scales in practical situations
Use common measures of rate (formulae for other rates eg density and pressure will be given in the question)
Calculate average speed
Learner Guide
30
Core Number
Question type You should be able to R A G CommentsPercentages Calculate a percentage of a quantity
Express one quantity as a percentage of another quantity
Calculate percentage increase or decrease
Use of an electronic calculator
Use a calculator efficiently
Check accuracy of calculations
Time Calculate times in terms of the 24-hour and 12-hour clock
Read
bull clocks
bull dials
bull timetables
Money Calculate using money
Convert from one currency to another
Learner Guide
31
Core Number
Question type You should be able to R A G CommentsPersonal and small business finance
Use given data to solve problems on
bull earnings
bull simple interest
bull compound interest (you will need to know the compound interest formula)
bull discount
bull profit and loss
Extract data from tables and charts
Learner Guide
32
Core Algebra and graphs
Question type You should be able to R A G CommentsBasic algebra Use letters to express generalised numbers
Express basic arithmetic processes algebraically
Substitute numbers in formulae
Construct simple expressions and set up simple equations
Rearrange simple formulae
Algebraic manipulation
Manipulate directed numbers
Use brackets
bull expand a single bracket eg 3x(2x ndash4y)
bull expand a pair of brackets eg (x + 3) (x ndash 7)
Extract common factors eg factorise 9x2 + 15xy
Rules of indices Use and interpret positive negative and zero indices
Use the rules of indices eg to simplify algebra such as
bull 3x4 times 5x
bull 10x3 divide 2x2
bull (x6)2
Learner Guide
33
Core Algebra and graphs
Question type You should be able to R A G CommentsEquations and inequalities
Derive and solve simple linear equations in one unknown
Derive and solve simultaneous linear equations in two unknowns
Number sequences
(links to Squares square roots cubes and cube roots)
Continue a number sequence
Recognise patterns in sequences
Recognise relationships between difference sequences
Find the nth term of sequences for
bull liner sequences
bull simple quadratic sequences
bull cubic sequences
Practical graphs
(links to Mensuration)
Interpret and use graphs in practical situations including
bull travel graphs
bull conversion graphs
Draw graphs from given data
Learner Guide
34
Core Algebra and graphs
Question type You should be able to R A G CommentsGraphs of functions
(links to Co-ordinate geometry)
Construct tables of values for functions of the form
bull ax + b (linear)
bull plusmn x2 + ax + b (quadratic)
bull (x ne 0) (reciprocal)
where a and b are integer constants
Draw and interpret such graphs
Solve linear and quadratic equations approximately by graphical methods
Recognise and sketch the graphs of linear and quadratic functions
ax
Learner Guide
35
Core Co-ordinate geometry
Question type You should be able to R A G CommentsCo-ordinates Work with co-ordinates in two dimensions
Gradients Find the gradient of a straight line graph
Equation of straight line
Interpret and obtain the equation of a straight line graph in the form y = mx + c where the graph is given
Parallel lines Determine the equation of a straight line parallel to a given line eg find the equation of a line parallel to y = 4x ndash 1 that passes through (0 ndash3)
Learner Guide
36
Core Geometry
Question type You should be able to R A G CommentsGeometrical language
Use and interpret the geometrical terms
bull point
bull line
bull parallel
bull perpendicular
bull bearing
bull right angle acute obtuse and reflex angles
bull similar
bull congruent
Use and interpret the vocabulary of
bull triangles right-angled scalene isosceles equilateral
bull quadrilaterals
bull circles
bull polygons
bull simple solid figures including nets
Learner Guide
37
Core Geometry
Question type You should be able to R A G CommentsGeometrical constructions
Measure and draw lines and angles
Construct a triangle given the three sides using a ruler and a pair of compasses only
Scale drawings Read and make scale drawings
Similar figures Calculate lengths of similar figures
Congruent Recognise congruent shapes
Symmetry Recognise symmetry properties for triangles quadrilaterals and circles
Recognise line symmetry in two dimensions
Recognise and find the order of rotational symmetry in two dimensions
Learner Guide
38
Core Geometry
Question type You should be able to R A G CommentsAngle properties Calculate unknown angles explaining the properties that you
are using in geometrical language for angles
bull angles at a point
bull angles on a straight line and intersecting straight lines
bull angles within parallel lines
bull angles in triangles
bull angles in quadrilaterals
bull angles in regular polygons
bull angle in a semi-circle
bull angle between tangent and radius of a circle
Learner Guide
39
Core Mensuration
Question type You should be able to R A G CommentsMeasures bull Use current units of
bull mass
bull length
bull area
bull volume
bull capacity
Express quantities in terms of smaller or larger units including units of area and volume
Convert between units including units of area and volume
Perimiter Carry out calculations involving
bull perimeter and area of a rectangle
bull perimeter and area of a triangle
bull perimeter and area of parallelogram
bull perimeter and area of a trapezium
bull perimeter and area of shapes made by combining
bull rectangles triangles parallelograms andor trapeziums
Learner Guide
40
Core Mensuration
Question type You should be able to R A G CommentsCircles Carry out calculations involving circumference and area of a
circle
Solve simple problems involving the arc length and sector area of a circle where the sector angle is a factor of 360deg
Surface area and volume
Carry out calculations involving
bull surface area and volume of a cuboid prism and cylinder (no formulae will be given for these shapes)
bull surface area and volume of a sphere pyramid and cone (formulae will be given for these shapes)
Areas and volumes of compound shapes
Carry out calculations involving the areas and volumes of compound shapes made from combinations of the shapes in Perimeter or Surface area and volume
Learner Guide
41
Core Trigonometry
Question type You should be able to R A G CommentsBearings Use and interpret three-figure bearings measured clockwise
from the North ie 000degndash360degTrigonometry Find unknown sides andor angles in right-angled triangles by
applying
bull Pythagorasrsquo theorem
bull sine cosine and tangent ratios for acute angles in right-angled triangles
Learner Guide
42
Core Vectors and transformations
Question type You should be able to R A G CommentsVectors in two dimensions (links to Trigonometry)
Describe a translation by using a vector represented by
AB or a
Add and subtract vectors
Multiply a vector by a scalar
Transformations Reflect simple shapes in horizontal or vertical lines
Rotate simple shapes through multiples of 90deg about
bull the origin
bull their vertices
bull the midpoints of their sides
Construct translations of simple shapes
Construct enlargements of simple shapes (positive and fractional scale factors)
Recognise and describe using the correct language
bull reflections
bull rotations
bull translations
bull enlargements (positive and fractional scale factors)
( )x
y
Learner Guide
43
Core Probability
Question type You should be able to R A G CommentsSingle events Calculate the probability of a single event as a fraction decimal
or percentage (not a ratio)Probability scale Understand and use the probability scale from 0 to 1
Sum to 1 Understand that the probability of an event occurring = 1 ndash the probability of the event not occurring
Relative frequency
Understand relative frequency as an estimate of probability
Work out expected frequencies using relative frequencyCombined events Calculate the probability of simple combined events using
bull tree diagrams
bull possibility diagrams (points on a grid)
bull Venn diagrams (2 sets only)
Learner Guide
44
Core Statistics
Question type What I need to do R A G CommentsClassify Collect classify and tabulate data
Interpret and compare
Read interpret and draw simple inferences from tables and statistical diagrams
Compare sets of data using
bull tables
bull graphs
bull statistical measures
Be aware of restrictions when making conclusions from data
Charts Construct and use
bull bar charts
bull pie charts
bull pictograms
bull stem-and-leaf diagrams
bull frequency distributions
bull histograms with equal intervals
bull scatter diagrams
Learner Guide
45
Question type What I need to do R A G CommentsAverages Calculate for individual and discrete data
bull mean
bull median
bull mode
bull range
and distinguish between their useCorrelation Understand what is meant by positive negative and zero
correlation with reference to a scatter diagramLine of best fit Draw interpret and use a ruled line of best fit by eye
Learner Guide
46
Extended syllabus content (includes required Core content)Extended Number
Question type You should be able to R A G CommentsNumber Identify and use
bull natural numbers
bull integers (positive negative and zero)
bull prime numbers
bull write a number as a product of its prime factors
bull square and cube numbers
bull common factors and highest common factor of two or more numbers
bull common multiples and lowest common multiple of two or more numbers
bull rational numbers
bull irrational numbers (eg π radic2 )
bull real numbers
bull reciprocals
Learner Guide
47
Extended Number
Question type You should be able to R A G CommentsSet notation and language
Use language notation and Venn diagrams to describe sets and represent relationships between sets as follows
Definition of sets egA = x x is a natural number
B = (xy) y = mx + c
C = x a ⩽ x ⩽ b
D = a b c hellip
Notation egnumber of elements in set A n(A)
lsquois an element ofrsquo isin
lsquois not an element ofrsquo notin
complement of set A
the empty set empty
the universal set
A is a subset of B A sube B
A is a proper subset of B A sub B
A is not a subset of B A ⊈ B
A is not a proper subset of B A nsub B
union of A and B A cup B
intersection of A and B A cap B
Learner Guide
48
Extended Number
Question type You should be able to R A G CommentsSquares square roots cubes and cube roots
Calculatebull squares of numbers
bull square roots of numbers
bull cubes of numbers
bull cube roots of numbers
bull other powers and roots of numbers
Directed numbers
Use directed numbers in practical situations for example temperature changes
Fractions decimals and percentages
Use the language and notation of simple vulgar and decimal fractions and percentages in appropriate contexts
Recognise equivalent fractions decimals and percentages
Convert between fractions decimals and percentages
Convert recurring decimals to fractions
Ordering Order quantities by magnitude and demonstrate familiarity with the symbols = ne gt lt ⩾ ⩽
Learner Guide
49
Extended Number
Question type You should be able to R A G CommentsIndices and standard form (links to Algebraic manipulation)
Evaluate indices including fractional negative and zero
eg 25 5ndash2 1000 10012 8ndash23
Use the rules of indices forbull multiplication of indices eg 43 times 45
bull division of indices eg 57 divide 53
bull index numbers raised to an index eg (43)2
Use the standard form A times 10n where n is a positive or negative integer and 1 ⩽ A lt 10bull convert into and out of standard form
bull calculate with numbers in standard form
Four rules
( + ndash times divide )
Use the four rules for calculations withbull whole numbers
bull decimals
bull vulgar and mixed fractions
bull correct ordering of operations (BIDMAS) and use of brackets
Learner Guide
50
Extended Number
Question type You should be able to R A G CommentsEstimates Make estimates of numbers quantities and lengths
Give approximations to a specified number of
bull significant figures
bull decimal places
Round off answers to reasonable accuracy in the context of a given problem
Bounds Give upper and lower bounds for data given to a specified accuracy eg measured lengths
Obtain appropriate upper and lower bounds to solutions of simple problems given to a specified accuracy eg the lower and upper bounds for the area of a rectangle
Ratio proportion rate
(links to Direct and inverse proportion)
Understand ratio
Divide quantities in a given ratio
Increase and decrease a quantity by a given ratio
Understand numerical problems involving direct and inverse proportion
Use ratio and scales in practical situations
Use common measures of rate (formulae for other rates eg density and pressure will be given in the question)
Calculate average speed
Learner Guide
51
Extended Number
Question type What I need to do R A G CommentsPercentages Calculate a percentage of a quantity
Express one quantity as a percentage of another quantity
Calculate percentage increase or decrease
Calculate reverse percentages eg finding the cost price given the selling price and the percentage profit
Use of an electronic calculator
Use a calculator efficiently
Check accuracy of calculations
Time Calculate times in terms of the 24-hour and 12-hour clock
Read clocks dials and timetables
Money Calculate using money
Convert from one currency to another
Learner Guide
52
Extended Number
Question type You should be able to R A G CommentsPersonal and small business finance
Use given data to solve problems on
bull earnings
bull simple interest
bull compound interest
ndash you must know the compound interest formula
bull discount
bull profit and loss
Extract data from tables and charts
Exponential growth and decay
Use exponential growth and decay in population and finance eg depreciation bacteria growth
Learner Guide
53
Extended Algebra and graphs
Question type You should be able to R A G CommentsBasic algebra Use letters to express generalised numbers
Express basic arithmetic processes algebraically
Substitute numbers in complicated formulae
Construct and rearrange complicated formulae eg where the subject appears twice
Algebraic manipulation
Manipulate directed numbers
Use bracketsbull expand a single bracket eg expand 3x(2x ndash 4y)
bull expand a pair of brackets eg (x ndash 4)(x + 7)
bull expand products of more than two brackets eg (x + 4)(x ndash 7)(2x + 1)
Extract common factors eg factorise 9x2 + 15xy
Factorise expressions of the formbull ax + bx + kay + kby
bull asup2xsup2 ndash bsup2ysup2
bull asup2 + 2ab + bsup2
bull axsup2 + bx + c
Learner Guide
54
Extended Algebra and graphs
Question type You should be able to R A G CommentsAlgebraic fractions
Manipulate algebraic fractions eg
bull
bull
bull
bull
bull
Factorise and simplify algebraic fractions such as
Rules of indices Use and interpret positive negative and zero indices
Use and interpret fractional indices eg solve 32x = 2
Use the rules of indices to simplify algebra eg
x3 + x ndash 4
22x3 +
3(x ndash 5)2
3a4 +
5ab3
3a4 divide
9a10
1x ndash 2 +
2x ndash 3
x2 ndash 2xx2 ndash 5x + 6
3xndash4 times23
x12
32x5( )
3
2xndash2divide25
x12
Learner Guide
55
Extended Algebra and graphs
Question type You should be able to R A G CommentsEquations and inequalities
bull Derive and solve simple linear equations in one unknown
bull Derive and solve simultaneous linear equations in two unknowns
bull Derive and solve simultaneous equations involving one linear and one quadratic
Solve quadratic equations by
bull factorisation
bull completing the square
bull using the formula
Derive and solve simple linear inequalities including representing solutions on a number line
Linear programming
Represent inequalities graphically including using the conventions of
bull broken lines for strict inequalities
bull shading unwanted regions
Solve simple linear programming problems using graphical representations of inequalities
Learner Guide
56
Extended Algebra and graphs
Question type You should be able to R A G CommentsNumber sequences (links to Squares square roots cubes and cube roots)
Continue a number sequence
Recognise patterns in sequences
Recognise relationships between different sequences
Find the nth term of sequences of
bull linear sequences
bull quadratic sequences
bull cubic sequences
bull exponential sequences
and simple combinations of these
Direct and inverse proportion (links to Ratio proportion rate)
Express direct proportion algebraically
Express inverse proportion algebraically
Use algebraic expressions of direct and inverse proportion to find unknown quantities
Practical graphs
(links to Coordinate geometry)
Interpret and use graphs in practical situations including
bull travel graphs
bull conversion graphs
Draw graphs from given data
Learner Guide
57
Extended Algebra and graphs
Question type You should be able to R A G CommentsPractical graphs (links to Coordinate geometry) continued
Apply the idea of rate of change to simple kinematics involving
bull distancendashtime graphs
bull speedndashtime graphs
bull acceleration and deceleration
This may involve estimation and interpretation of the gradient of a tangent at a point
Calculate distance travelled as an area under a linear speedndash time graph
Learner Guide
58
Extended Algebra and graphs
Question type You should be able to R A G CommentsGraphs of functions (links to Coordinate geometry)
Construct tables of values and draw graphs for functions of the form
bull axn where a is a rational constant and n = minus2 minus1 0 1 2 3 and simple sums of not more than three of these
bull abx + c where a and c are rational constants and b is a positive integer
Solve associated equations approximately by graphical methods including finding and interpreting roots and finding turning points of quadratics by completing the square
Draw and interpret graphs representing exponential growth and decay problems
Recognise sketch and interpret graphs of
bull linear
bull quadratic
bull cubic
bull reciprocal
bull exponential
(knowledge of turning points and asymtotes is required)Tangents Estimate gradients of curves by drawing tangents
Learner Guide
59
Extended Algebra and graphs
Question type You should be able to R A G CommentsFunctions Use function notation eg
f(x) = 3x ndash 5 f x α 3x ndash5 to describe simple functions
Find inverse functions f ndash1 (x)
Form composite functions as defined by gf(x) = g(f(x))
Derivatives Understand the idea of a derived function
Use derivatives of the form axn and simple sums of not more than three of these (a is a rational constant and n is a positive integer or 0)
Apply differentiation to gradients and turning points (stationary points)
Use any method to explain whether the turning point is a maximum or a minimum eg second derivative or gradient of function on either side of turning point
Learner Guide
60
Extended Co-ordinate geometry
Question type You should be able to R A G CommentsStraight line graphs
Work with co-ordinates in two dimensions
Gradient Find the gradient of a straight line graph
Calculate the gradient of a straight line from the co-ordinates of two points on it
Length and midpoint
Calculate the length and the co-ordinates of the midpoint of a straight line segment from the co-ordinates of its end points
Equation of line Interpret and obtain the equation of a straight line graph
Parallel lines Determine the equation of a straight line parallel to a given line eg find the equation of a line parallel to y = 4x ndash 1 that passes through (0 ndash3)
Perpendicular lines
Find the gradient of parallel and perpendicular lines eg
bull find the gradient of a line perpendicular to y = 3x + 1
bull find the equation of a line perpendicular to one passing through the co-ordinates (1 3) and (ndash2 ndash9)
Learner Guide
61
Extended Geometry
Question type You should be able to R A G CommentsGeometrical language
Use and interpret the geometrical terms
bull point
bull line
bull parallel
bull perpendicular
bull bearing
bull right angle acute obtuse and reflex angles
bull similar
bull congruent
Use and interpret the vocabulary of
bull triangles right-angled scalene isosceles equilateral
bull quadrilaterals
bull circles
bull polygons
bull simple solid figures including nets
Learner Guide
62
Extended Geometry
Question type What I need to do R A G CommentsGeometrical constructions
Measure and draw lines and angles
Construct a triangle given the three sides using a ruler and a pair of compasses only
Scale drawings Read and make scale drawings
Similar figures Calculate lengths of similar figures
Use relationships between areas of similar triangles and in similar figures
Use relationships between volumes and surface areas of similar solids
Congruent triangles
Use the congruence criteria for triangles (SSS ASA SAS RHS)
Symmetry Recognise symmetry properties for triangles quadrilaterals and circles
Recognise line symmetry in two dimensions
Recognise and find the order of rotational symmetry in two dimensions
Learner Guide
63
Extended Geometry
Question type You should be able to R A G CommentsSymmetry (continued)
Use the following symmetry properties of circles
bull equal chords are equidistant from the centre
bull perpendicular bisector of a chord passes through the centre
bull tangents from an external point are equal in length
Recognise and use symmetry properties of
bull prism cylinder cone and pyramid
Learner Guide
64
Extended Geometry
Question type You should be able to R A G CommentsAngle properties Calculate unknown angles explaining the properties that
you are using in geometrical language for the following geometrical properties
bull angles at a point
bull angles at a point on a straight line and intersecting straight lines
bull angles formed within parallel lines
bull angle properties of triangles and quadrilaterals
bull angle properties of regular polygons
bull angle in a semi-circle
bull angle between tangent and radius of a circle
bull angles properties of irregular polygons
bull angle at the centre of a circle is twice the angle at the circumference
bull angles in the same segment are equal
bull angles in opposite segments are supplementary cyclic quadrilaterals
bull alternate segment theorem
Learner Guide
65
Extended Mensuration
Question type What I need to do R A G CommentsMeasures Use current units of
bull mass
bull length
bull area
bull volume
bull capacity
Express quantities in terms of smaller or larger units including units of area and volume
Perimeter Carry out calculations involving
bull perimeter and area of a rectangle
bull perimeter and area of a triangle
bull perimeter and area of parallelogram
bull perimeter and area of a trapezium
bull perimeter and area of compound shapes made by combining rectangles triangles parallelograms andor trapeziums
Learner Guide
66
Extended Mensuration
Question type You should be able to R A G CommentsCircles Carry out calculations involving circumference and area of a
circle
Solve problems involving arc length and sector area of a circle
Surface area and volume
Carry out calculations involving
bull surface area and volume of a cuboid prism and cylinder (no formulae will be given for these shapes)
bull surface area and volume of a sphere pyramid and cone (formulae will be given for these shapes)
Compound shapes
Carry out calculations involving
bull area of a shape made by combining cuboids prisms andor cylinders
bull volume of a shape made by combining cuboids prisms andor cylinders
Learner Guide
67
Extended Trigonometry
Question type You should be able to R A G CommentsBearings Use and interpret three-figure bearings measured clockwise
from the North ie 000degndash360degTrigonometry Find unknown sides andor angles in right-angled triangles by
applying
bull Pythagorasrsquo theorem
bull sine cosine and tangent ratios for acute angles in right-angled triangles
Solve problems in two dimensions involving angles of elevation and depression
Know that the perpendicular distance from a point to a line is the shortest distance to the line
Trig graphs and equations
Recognise sketch and interpret graphs of simple trigonometric functions
Graph and know the properties of trigonometric functions
Solve simple trigonometric equations for values between 0deg
and 360deg eg Solve sin x = radic32
for values of x between 0deg and
360degGeneral trig Solve problems using sine and cosine rules for any triangle
Find the area of any triangle using frac12absinC
Trig in 3D Solve simple trigonometrical problems in three dimensions including angle between a line and a plane
Learner Guide
68
Extended Vectors and transformations
Question type You should be able to R A G CommentsVectors in two dimensions (links to Trigonometry)
Describe a translation by using a vector represented by
AB or a
Add and subtract vectors
Multiply a vector by a scalar
Transformations Reflect simple shapes in horizontal or vertical lines
Rotate simple shapes through multiples of 90deg about any point
Construct translations of simple shapes
Construct enlargements of simple shapes (positive fractional and negative scale factors)
Recognise and describe
bull reflections
bull rotations
bull translations
bull enlargements (positive fractional and negative scalefactors)
( )x
y
Learner Guide
69
Extended Vectors and transformations
Question type You should be able to R A G CommentsHarder vectors
Calculate the magnitude of a vector as and
understand that magnitude is denoted by modulus signs |A B| or |a|
Represent vectors by directed line segments
Use the sum and difference of two vectors
Use position vectors
( )x
yradicx2 + y2
Learner Guide
70
Extended Probability
Question type You should be able to R A G CommentsProbability (links to Four rules)
Calculate the probability of a single event as a fraction decimal or percentage (not a ratio)
Probability scale Understand and use the probability scale from 0 to 1
Sum to 1 Understand that the probability of an event occurring = 1 ndash the probability of the event not occurring
Relative frequency
Understand relative frequency as an estimate of probability
Work out expected frequencies using relative frequency
Combined events Calculate the probability of combined events using
bull tree diagrams
bull possibility diagrams
bull tables
Learner Guide
71
Extended Statistics
Question type You should be able to R A G CommentsClassify Collect classify and tabulate data
Interpret and compare
Read interpret and draw simple inferences from tables and statistical diagrams
Compare sets of data using
bull tables
bull graphs
bull statistical measures
Be aware of restrictions when making conclusions from data
Charts Construct and use
bull bar charts
bull pie charts
bull pictograms
bull stem ndash and ndash leaf diagrams
bull frequency distributions
bull histograms with equal and unequal intervals
bull scatter diagrams
Learner Guide
72
Extended Statistics
Question type You should be able to R A G CommentsAverages Calculate for individual and discrete data
bull mean
bull median
bull mode
bull range
and distinguish between their use
Estimated mean Calculate an estimate of the mean for grouped and continuous data
Identify the modal class from a grouped frequency distributionCumulative frequency
Construct and use cumulative frequency diagrams to estimate and interpret
bull the median
bull percentiles
bull quartiles
bull inter-quartile range
Construct and interpret box-and-whisker plots
Correlation Understand what is meant by positive negative and zero correlation with reference to a scatter diagram
Lines of best fit Draw interpret and use a ruled line of best fit by eye
Cambridge Assessment International Education1 Hills Road Cambridge CB1 2EU United Kingdomt +44 1223 553554e infocambridgeinternationalorg wwwcambridgeinternationalorg
Copyright copy UCLES October 2017
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- Text Field 330
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- Text Field 339
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- Text Field 340
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- Text Field 342
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- Text Field 349
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- Text Field 343
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- Text Field 361
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- Text Field 363
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- Text Field 334
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- Text Field 3022
- Text Field 3021
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- Text Field 3044
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- Text Field 347
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- Text Field 3023
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- Text Field 3045
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- Text Field 3046
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- Text Field 3026
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- Text Field 3047
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- Text Field 3048
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- Text Field 3027
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- Text Field 3028
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- Text Field 3029
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- Text Field 3030
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- Text Field 3031
- Check Box 10545 Off
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- Text Field 3032
- Check Box 10548 Off
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- Text Field 3042
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- Text Field 3033
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- Text Field 3034
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- Text Field 3035
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- Text Field 3036
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- Text Field 3056
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- Text Field 3062
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- Text Field 3064
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- Text Field 3067
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9
Equipment for the examMake sure you have
bull a blue or black pen (a spare pen is always a good idea)bull a pencil (for graphs and diagrams)bull an electronic calculatorbull a protractorbull a pair of compassesbull a ruler
1 Read the questions carefully to make sure that you understand what is being asked
2 Give your answers to the accuracy indicated in the question If none is given and the answer isnrsquot exact then
bull give your answer to three significant figures 123 9 12298 x
bull if the answer is in degrees then give it to one decimal place 231deg 9 23deg x
3 Include units with your answers if they are not given on the paper For example 1 kg of apples costs hellip pound120 9 120 x
4 Show your working Show as much working as you can for all your questions
5 If you make a mistake clearly cross out any working or answers that you do not want the examiner to mark
Use the value of π from your calculator or use 3142 which is given on the front page of the question paper
Timingbull If you are stuck on a question dont waste too much time trying to answer it ndash go on to the next question and
come back to the one you are stuck on at the endbull Use any time that you have left at the end of the exam to go back and check your answers and working
Make sure that you give your answer in the form asked for in the question eg some questions ask for answers to be given in terms of π For lengths areas and volumes give answers in decimals (not in surds or in terms of π) unless you are told to given an exact answer
You can gain marks for the correct working even if you have an incorrect answer or cannot complete the whole question
If you need more space ask for extra of paper and clearly indicate where the rest of the answer is written On the additional paper make it clear which questions(s) you are answering
General advice for all Papers
10
The areas of knowledge understanding and skills that you will be assessed on are called assessment objectives (AOs) There are two AOs for this course
AO1 Demonstrate knowledge and
understanding of mathematical techniques
AO2 Reason interpret and communicate
mathematically when solving problems
AO1 Demonstrate knowledge and understanding of mathematical techniquesYou need to show that you can recall and apply mathematical knowledge terminology and definitions to carry out single or multi-step solutions in mathematical and everyday situations
Section 3 What skills will be assessed
This means that you need to show that you can
bull organise process and present information accurately in written tabular graphical and diagrammatic forms
bull use and interpret mathematical notation correctly
bull perform calculations and procedures by suitable methods including using a calculator
bull understand systems of measurement in everyday use and make use of these
bull estimate approximate and work to degrees of accuracy appropriate to the context and convert between equivalent numerical forms
bull use geometrical instruments to measure and to draw to an acceptable degree of accuracy
bull recognise and use spatial relationships in two and three dimensions
AO1 is assessed in all papers
Use tables graphs and diagrams
An example of degress of accuracy include significant figures or decimal places
An example of converting between equivalent numerical forms include between fractions decimals and percentages or between normal numbers and standard form
eg a pair of compasses a protractor and a ruler
11
AO2 Reason interpret and communicate mathematically when solving problemsYou need to demonstrate that you can analyse a problem select a suitable strategy and apply appropriate techniques to obtain a solution
This means that you need to show that you can
bull make logical deductions make inferences and draw conclusions from given mathematical data
bull recognise patterns and structures in a variety of situations and form generalisations
bull present arguments and chains of reasoning in a logical and structured way
bull interprete and communicate information accurately and change from one form of presentation to another
bull assesses the validity of an argument and critically evaluate a given way of presenting information
bull solve unstructured problems by putting them into a structured form involving a series of processes
bull apply combinations of mathematical skills and techniques using connections between different areas of mathematics in problem solving
bull interprete results in the context of a given problem and evaluate the methods used and solutions obtained
AO2 is assessed in all papers
Recognise and extent patterns
Take information and organise it to answer a problem
12
Section 4 Command wordsA command word is the part of the question that tells you what you need to do with your knowledge For example you might need to describe something explain something argue a point of view or list what you know The table below includes command words used in the assessment for this syllabus The use of the command word(s) within an question will relate to the context
Cambridge IGCSE Mathematics 0580 syllabus for 2020 2021 and 2022 Details of the assessment
37wwwcambridgeinternationalorgigcseBack to contents page
Command wordsThe table below includes command words used in the assessment for this syllabus The use of the command word will relate to the subject context
Command word What it means
Calculate work out from given facts figures or information generally using a calculator
Construct make an accurate drawing
Describe state the points of a topicgive characteristics and main features
Determine establish with certainty
Explain set out purposes or reasons make the relationships between things evident provide why andor how and support with relevant evidence
Give produce an answer from a given source or recallmemory
Plot mark point(s) on a graph
Show (that) provide structured evidence that leads to a given result
Sketch make a simple freehand drawing showing the key features
Work out calculate from given facts figures or information with or without the use of a calculator
Write give an answer in a specific form
Write down give an answer without significant working
The question below is taken from Paper 4 and illustrates the use of two command words
The command words lsquoWrite downrsquo indicates that you do not need to show your working and the answer should just be written down The mark allocation [1] also supports this
The command words lsquoShow thatrsquo indicate that you need to provide evidence in the form of a clear mathematical explanation to demonstrate that you know how to obtain the given result In other words you need to show a method that leads to the result
The answer space in this case does not contain a dotted answer line as there is no single lsquoanswerrsquo to be found Your working that leads to the given result should be written in the blank working space
13
This section takes you through an example question and learner response from one of the 2020 specimen papers for this course It will help you to identify the command words and other key instructions within questions and to understand what is required in your response
This section is structured as follows
QuestionThe command words and instructions in the question have
been highlighted and explained This should help you to understand clearly what is required by the question
Mark schemeThis tells you as clearly as possible what an examiner expects
from an answer to award marks
Example candidate responseThis an exemplar answer written in the style of
a high level candidate
How the answer could have been improvedThis summarises what could be done to gain more marks
All information and advice in this section is specific to the example question and response being demonstrated It should give you an idea of how your responses might be viewed by an examiner but it is not a list of what to do in all questions In your own examination you will need to pay careful attention to what each question is asking you to do
Common mistakesThis will help you to avoid common mistakes made by
candidates So often candidates lose marks in their exams because they misread or misinterpret the questions
Section 5 Example candidate response
14
QuestionThe question used in this example is from Specimen Paper 3 (Core) It represents the type of structured question you will see in both Paper 3 (Core) and Paper 4 (Extended) A structured question means that it is broken into several parts Often later parts will depend on your answers to earlier parts
This means that you cannot find the answer by
measuring the diagramWork out indicates that the answer should be calculated from the given information so measurement will not score marks
The allocation of 1 mark indicates that the answer can be obtained with minimum working
Give reasons for your answer indicates that your answer should be supported with reasons using the correct mathematical terminology You must justify your answer
Use trigonometry to calculate indicates that you should use this method with the given information to find the answer and that a calculator is needed to solve the problem If you did not use trigonometry you would not be awarded any marks
15
Show that indicates the answer is given and you need to write down all of the steps in a method that leads to the given answer You need to provide evidence that you understand and know how the answer is reached
Work out indicates that you should calculate the answer from the given information The mark allocation of 4 marks suggests that you will need to include several steps of working in order to get to the answer
Learner Guide
16
Answer Mark Notes(a)(i) 35 1 This is the only acceptable answer for this part of the question
(a)(ii) 74 1 This is the only acceptable answer for this part of the question
(b) 43deg and correct mathematical reasons
3 Two marks are awarded for the final answer of 43deg
The third mark is awarded for a fully correct reason for example angles on a straight line add up to 180deg and angles in a triangle add up to 180deg There are other correct reasons that could be also be used
If 43deg is not obtained one method mark can be awarded if the following calculation is seen in the working
180 ndash 128 or 128 ndash 85
(c) 322 or 3223hellip 2 This is the only acceptable answer for this part of the question
The answer has to be rounded correct to three significant figures or can be given with more figures in the answer
Those that did not get this answer can score one method mark for showing the following in their working
sin = 8 divide 15
(d)(i) 2 2300 225+2 This does not have to be shown in one step as long as the method shown is the same as this overall Those that do not
show this can have one method mark for showing the following in their working
300deg + 225deg
(d)(ii) 15 35 4 The answer 3 35pm is also acceptable for 4 marks
If the correct answer is not found one method mark is available for showing 375 divide 450 in their working and a second method mark can be awarded for sight of them multiplying their answer to this by 60 to change it to hours A third method mark can be awarded for adding their answer in hours to 14 45 ndash this shows the correct method so only one mark is lost for an incorrect final answers
Mark schemeYour examination papers will be marked and the overall number of marks for each paper will be recorded Your marks across all papers will then be converted to a grade
Final answer This value is what the examiner expects to see The answer has to be exactly as given in the mark scheme unless there are acceptable alternatives The mark scheme will always make it clear if there are acceptable alternative answers
Method marks Sometimes method marks are awarded for lines of working as well as for the final answer This means that you could get the final answer incorrect but still get some marks if you include the correct working The mark scheme does not include all possible methods so if you use a method not included in the mark scheme but it is accurate and relevant then the examiner will still award marks for the appropriate parts of the working ndash unless the questions asks you to use a specific method
example of a final answer
example of a method mark
17
Example candidate responseNow letrsquos look at the sample candidatersquos response to question 8 The examiners comments are in the orange boxes The candidate was awarded 8 marks out of 13
180 ndash 74 + 71 = 177
177
74
0 out of 1
The candidates working suggests they understand that the angle sum of a triangle is 180deg but they did not include brackets around 74 + 71 The answer 177deg is not sensible for this question
1 out of 1
The candidate recognises that there are parallel lines and that angle y is a corresponding angle to angle 74deg
180 ndash 128 = 52 180 ndash 85 ndash 52 = 43
43 angles on a straight line add up to 180deg
2 out of 3
The candidate has given a correct answer for w and shown correct working in two steps They have given a correct reason for 52deg using correct mathematical languge But they have not provided a reason to explain the angle 43deg They lose a mark for not also stating angle sum of a triangle is 180deg
sin p = 8 divide 15 = 053
p = sinndash1 (053)
p = 32005 320
1 out of 2
The candidate has correctly used trigonometry in their method They are awarded one method mark for the first line of working However they have rounded 05333333hellip (the result of 8 divide 15) to 052 and then calculated the inverse sin of 052 rather than 05333333 This has resulted in an inaccurate final answer This is called lsquopremature approximationrsquo and it is a very common error to make
18
AB2 = 3002 + 2252
= 140625
AB = 375
1 out of 2
The candidate has recognised the right-angled triangle and correctly used Pythagorasrsquo theorem in the first line of working However they have missed out an important step by not showing that you need to take the square root of 140625 to get 375 As this is a lsquoshow thatrsquo question and they missed a key step in the method they cannot be awarded full marks as the complete working is not shown One method mark is earned for the first line
T = = = 08333333hellip
08333333 hours = 08333333 times 60 minutes = 50 minutes
arrives at 14 45 + 50 mins = 3 35
DS
375450
3 35
3 out of 4
The candidate has found the time by correctly dividing the distance by the speed and recognised that this is in hours When converting the answer to a decimal they have not rounded the decimal but left its full value on the calculator to get 50 mins which is the correct approach Unfortunately after converting the time from 24 hour clock to 12 hour clock they did not include lsquopmrsquo to indicate that the time is in the afternoon and so the final answer is not quite right So 3 marks are awarded for all of a correct method but a mark is lost due to the accuracy of the final answer
19
How the answer could have been improvedThis answer could have been improved by
bull In part (a)(i) the answer of 177deg was not sensible given the diagram in the question If the candidate had checked their answer for sense they would have realised they had made a mistake It is always a good idea to check that your answer seems sensible before you move on to another question
bull In part (b) the candidate did all the correct steps but failed to provide both reasons There were two steps to the method which should have indicated to the candidate that there were two steps to justify and therefore two reasons should have been provided The mark allocation for the question [3] also indicates that more than one reason would be required one mark for the value of 43deg leaving two marks one mark for each of two reasons The candidate should have read the question carefully and again checked their response seemed reasonable
bull In part (c) the candidate rounded an intermediate answer which affected the accuracy of the final answer This caused them to lose a mark despite using a correct method You should only ever round the final answer do not round intermediate values If you can store the intermediate values in your calculator and so that you can use the full value in your calcuations If youre not able to do this and you have to round the intermediate values do not round them to less than three significant figures
bull In part (d)(i) the candidate missed out a step in the method As this was a show that question they needed to show all the steps in the method Its important to show all steps even if they seem obvious
bull In part (d)(ii) the candidate made a silly error by not stating that the time was pm When working with time answers are accepted in either 24 clock or 12 clock time but if you give your answer in the 12 hour clock then it must include am or pm as well
Common mistakesThere were a number of common mistakes made by other candidates on this question
bull Accuracy of answers
In parts (c) and (d)(ii) a common error was premature rounding ndash rounding intermediate values in the method before the final answer which resulted in their final answer not being accurate Other candidates gave the final answer to less than three significant figures ignoring the instruction on the front of the paper to round to three significant figures
bull Using incorrect terminology when giving reasons
In part (b) the most common error was to not give full reasons to support the answer Another common error was to provide a reason that did not use the correct mathematical language such as lsquoThey add up to 180degrsquo and lsquoIt is a straight linersquo which could not be awarded marks
bull Lack of knowledge
In part (c) a number of candidates had limited knowledge of trigonometry and did not choose the correct trig ratio which was the sine ratio This is why good revision is important
bull Not checking answers
In part (a)(i) even though the diagram is drawn NOT TO SCALE it is possible to see that the angle is an acute angle and should therefore not be bigger than 90deg This should alert candidate that if their answer is over 90deg it is not a sensible answer and they should go back and check their working
20
bull Inefficient method shown
In part (c) the lsquoShow thatrsquo question a number of candidates omitted an important step from the method this is often common in lsquoShow thatrsquo questions where every step must be shown no matter how obvious them seem
General adviceIn order to do your best when answering a mathematics question make sure you
bull revise all of the topics for the syllabus you are studying before the exam
bull understand what all the key terms and command words in the question mean
bull read the questions carefully and consider what you need to do before you do it
bull only round the final answer not intermediate values
bull show all steps in your working and show them clearly
bull round to the correct degree of accuracy
bull use the correct mathematical terminology
bull check your answers seem reasonable given the context or details of the question
21
It is important that you plan your revision in plenty of time for the examinations and that you develop a revision technique that works for you The advice in this section will help you revise and prepare for the examinations It is divided into general advice for all papers
Use the tick boxes to keep a record of what you have done what you plan to do or what you understand
For more advice on revision see the Cambridge Learner Revision Guide on our website
Section 6 Revision
Find out when the examinations are and plan your revision so you have time to revise Create a revision timetable and divide it into sections to cover each topic
Spend most of your time focussing on specific skills knowledge or issues that you have found more difficult when practicing them either during revision or earlier in the course
Write a summary of all the key information for a topic ndash use the checklists at the end of this section
Know the meaning of the command words used in questions and how to apply them to the information given Look at past examination papers and highlight the command words and check what they mean
Make revision notes and work on practice questions Reading alone does not work you need to be active and practice your maths
Work for shorter periods then have a break Revise small sections of the syllabus at a time but do this regularly
Test yourself by trying out some past exam questions Use the mark schemes to assess yourself and to be familiar with how marks are awarded for different questions
Be organised in advance with your notes texts exercise books revision guides and revision websites so you do not waste valuable revision time trying to find things
Make notes of key mathematical words that you should use in questions that ask you to lsquodescribersquo or give lsquogeometrical reasons forrsquo eg in describing transformations or giving reasons in circle theorem questions Look at the mark schemes for these types of questions from past papers to see how marks are awarded
Make sure you have all of the correct mathematical equipment ready for the exam particularly your calculator Make sure you are familiar with the all of the important functions on your calculator
Practice the areas you can do well not just those that you find more difficult
Take breaks and do things to relax when you take your breaks this will help you to be more productive when you are revising
Before the examination
22
During the examination
Plan your time according to the marks for each question For example a question worth one mark requires less time than a question one worth 4 marks If a question has several parts then the parts with more marks will need more time
Read each question very carefully
Identify the command words ndash you could underline or highlight them
Identify the other key words and information and perhaps underline them too particularly where
questions require reasoning or problem solving
Read the questions careully and make you have answered the question that is being asked
Show your working this is particularly important for questions where you are asked to lsquoshow that helliprsquo
Set your working out clearly so that it is easy to follow this makes it easier to keep track of what you have done and makes checking back through your work easier and it makes it easier for the examiner to mark your work try to write it in a logical order in the answer space
Write answers clearly if you want to change an answer then you should cross the answer out and write a replacement if your answer is on the answer line cross it out and write the replacement answer above it do not try to change numbers on the answer line as this can lead to unclear figures
Check your working and answers to avoid errors
Give your answer to the appropriate level of accuracy either the accuracy indicated in the question or the accuracy given on the front of the paper
Avoid rounding intermediate values part way through your calculation only round the final answer
Check that the answer that you have given is sensible and realistic for what is being asked
Use a pencil when drawing diagrams or completing graphs this means that you can change your answer more easily if you have made a mistake
Take care when reading scales
If you are asked for reasons for your answer then use the correct mathematical terms
Use the mark allocation given with the questionsparts of questions to try to judge how much work is needed to answer each part
23
Top tips for revision of Cambridge IGCSE Mathematics1 Summarise recall and applyMake sure that you can recall and apply the key information and mathematical techniques on each topic that you need for the exam
i Write a summary of the key information of a topicii Collect together some questions that test the knowledge and skills of this topic Ask your teacher for practice
questions or suitable past examination questions or use practice books or textbooksiii Test your recall by covering over the summary and trying to remember the details or use the summary as part of
the lsquoTeach the topicrsquo (Tip 3) or lsquoQuestion and answer cardsrsquo (Tip 4) activities iv After you have spent some time revising and practising the knowledge and skills answer the questions that you
collected together on the topic You might do this later on the same day as revising or a few days later Answer as many questions as you can in order to practise applying your knowledge
v Try creating your own questions by adapting existing ones and use these for practice when you return to a topic
On graph questions straight lines should be ruled and curves should be drawn freehand with a smooth curve
Donrsquot spend too long on any one part of a question If you are really stuck on a question then move on and come back to the question later if you have time As a rough guide each mark on the paper should take about one minute
2 Concept mapsConcept maps are a great way to revise the links between different factors or to explore a larger topic They can also be used to collect together your ideas
i Use a blank sheet of paper and turn it on its side (landscape)ii Put the topic title in the middle of the page and build the concept map outwards using lines called lsquobranchesrsquo
ndash The first branches are from the central topic to sub-topics draw these as thick lines
ndash Add new branches from the sub-topics to include more detail draw these as thinner lines
ndash Add even more detail to a point by adding more branches
This creates a hierarchy of information from lsquooverviewrsquo (the thick branches) to lsquofine detailrsquo (thinnest branches)
iii Write single key words or phrases along a branch and add drawings for visual impactiv Use different colours highlighter pens symbols and arrows to highlight key facts or issuesIt is a good idea to use a large piece of plain A3 (or larger) paper and lots of coloured pens
24
3 Teach the topicThis is a very simple but effective technique that focusses on knowledge recall It tests the brain and rehearses the information you need to know for a certain topic and so will help your revision
i Create some topic cards with key bullet points of information on Leave space for ticksii Give these to your parents family or friends for exampleiii Give yourself 10 minutes maximum to teach your audience the main points of the topic You could use a mini-
whiteboard or flip chart to helpiv Your audience tick off all the points you mention in your presentation and give you a final scoreThe brain loves competition so if you do not score full marks you can try again the next day or compete against friends This system of repeat and rehearsal is very effective especially with more complex topics and doesnt take much preparation
4 Question and answer (QampA) cardsThis is very similar to Teach the topic but less formal and less public for those who dislike performing in front of others It tests knowledge recall and rehearses the information you need to know for a certain topic
i Pick a topic and create two sets of cards question cards and answer cards You might find it helpful to make the question cards a different size or use different coloured card for answers
ii Make sure you have the topic or something appropriate depending on what you are focusing on as a heading on each card The questions should test your knowledge and understanding of key areas of the course
iii A friend or family member uses the cards to test you in short 5 or 10 minute periods at any time during the dayiv You could also do this alone by reading the questions to yourself giving the answer and then checking the
correct answer cardv This game can be adapted by using the cards to find matching pairs turn all cards face down across the space
in front of you Turn over two cards leaving them where they are If they match (one is a question card and the other is the corresponding answer card) pick up the pair and put them to one side If they dont match try to remember where they are and what is on each card then turn them back over Turn over two other cards Continue until you have matched all pairs
5 Question paper and mark schemesLooking at past question papers and the mark scheme helps you to familiarise yourself with what to expect and what the standard is
i Ask your teacher for past paper questions with mark schemes for the course ndash ask your teacher for help to make sure you are answering the correct questions and to simplify the mark scheme
ii Look at the revision checklist and identify which topic a given question relates to ndash you might need to ask your teacher to help you do this
iii Once you have finished revising a topic or unit time yourself answering some appropriate exam questions Check the mark schemes to see how well you would have scored or give the answers to your teacher to check
iv Add details or notes to the mark scheme where you missed out on marks in your original answers using a different coloured pen Use these notes when you revise and try the question again later
You can find plenty of past exam papers and mark schemes on the Cambridge International public website
httpwwwcambridgeinternationalorgprogrammes-and-qualificationscambridge-igcse-mathematics-0580past-papers
25
Other useful revision advice for Cambridge IGCSE Mathematics bull Before the exam make sure that you are familiar with your calculator and confident in using it
bull Look at the Example Candidate Response earlier in this guide Can you identify the strengths of the response andwhere they have made mistakes or lost marks
bull When you are attempting a past paper (or questions from a past paper) complete it without referring to yournotes so that you get a true idea of your strengths and weaknesses Then go back through the paper using yournotes and a different coloured pen to make corrections and changes After you have done as much as you can onthe paper mark it using the mark scheme Take notes of any points that you lost marks on
bull Donrsquot just revise the topics that you enjoy and are confident in If you identify an area that you are weaker inthen try to revisit the topic by reviewing your notes and doing some practice questions then use exam questionsto check whether you now understand
bull Return to topics later in your revision to check that you still remember and understand the topic and to help toensure that you recall more of the material when you get to the examination
Revision checklists for Cambridge IGCSE MathematicsThe tables on the following pages can be used as a revision checklist They do not contain all the detailed knowledge you need to know just an overview For more detail see the syllabus and talk to your teacher
You can use the tick boxes in the checklists to show when you have revised and are happy that you do not need to return to it Tick the lsquoRrsquo lsquoArsquo and lsquoGrsquo column to record your progress as follows
bull R = RED means you are really unsure and lack confidence in that area you might want to focus your revisionhere and possibly talk to your teacher for help
bull A = AMBER means you are reasonably confident in a topic but need some extra practicebull G = GREEN means you are very confident in a topic
As your revision progresses you can concentrate on the RED and AMBER topics in order to turn them into GREEN topics You might find it helpful to highlight each topic in red orange or green to help you prioritise
You can use the lsquoCommentsrsquo column to
bull add more information about the details for each pointbull include a reference to a useful resourcebull include a list of formulae or notationbull add learning aids such as rhymes poems or word playbull highlight areas of difficulty or things that you need to talk to your teacher about
There is a set of checklist for the Core syllabus and a different set for the Extended syllabus
Learner Guide
26
Core syllabus contentCore Number
Category You should be able to R A G CommentsNumber Identify and use
bull natural numbers
bull integers (positive negative and zero)
bull prime numbers
bull write a number as a product of its prime factors
bull square numbers and cube numbers
bull common factors and highest common factor of two numbers
bull common multiples and lowest common multiple of two numbers
bull rational numbers
bull irrational numbers (eg π radic2 )
bull real numbers
bull reciprocals
Learner Guide
27
Core Number
Question type You should be able to R A G CommentsSets and Venn diagrams
Understand notation of Venn diagrams
Definition of sets
eg A = xx is a natural number
B = abchellip
Notation
Number of elements in set A n(A)
Universal set
Union of A and B A cup B
Intersection of A and B A cap B
Squares square roots cubes and cube roots
Calculate
bull squares and cubes of numbers
bull square roots and cube roots of numbers
Learner Guide
28
Core Number
Question type You should be able to R A G CommentsDirected numbers
Use directed numbers in practical situations for example temperature changes
Fractions decimals and percentages
Use the language and notation of simple vulgar and decimal fractions and percentages
Recognise equivalent fractions decimals and percentages
Convert between fractions decimals and percentages
Ordering Order quantities by magnitude and demonstrate familiarity with the symbols = ne gt lt ⩾ ⩽
Indices and standard form (links to Algebraic manipulation)
Evaluate indices eg 25 5ndash2 1000 64frac12 8ndash23
Use the rules of indices for
bull multiplication of indices eg 4ndash3 times 45
bull division of indices eg 57 divide 53
bull index numbers raised to an index eg (23)2 (43)2
Use the standard form A times 10n where n is a positive or negative integer and 1 ⩽ A lt 10
bull convert numbers into and out of standard form
bull calculate with numbers in standard form
Learner Guide
29
Core Number
Question type You should be able to R A G CommentsFour rules
( + ndash times divide )
Use the four rules for calculations with
bull whole numbers
bull decimals
bull vulgar and mixed fractions
bull correct ordering of operations (BIDMAS) and use of bracketsEstimates Make estimates of numbers quantities and lengths
Give approximations to a specified number of
bull significant figures
bull decimal places
Round off answers to reasonable accuracy in the context of a given problem
Bounds Give upper and lower bounds for data given to a specified accuracy eg measured lengths
Ratio proportion rate
Understand ratio
Divide a quantity in a given ratio
Understand direct and inverse proportion
Use scales in practical situations
Use common measures of rate (formulae for other rates eg density and pressure will be given in the question)
Calculate average speed
Learner Guide
30
Core Number
Question type You should be able to R A G CommentsPercentages Calculate a percentage of a quantity
Express one quantity as a percentage of another quantity
Calculate percentage increase or decrease
Use of an electronic calculator
Use a calculator efficiently
Check accuracy of calculations
Time Calculate times in terms of the 24-hour and 12-hour clock
Read
bull clocks
bull dials
bull timetables
Money Calculate using money
Convert from one currency to another
Learner Guide
31
Core Number
Question type You should be able to R A G CommentsPersonal and small business finance
Use given data to solve problems on
bull earnings
bull simple interest
bull compound interest (you will need to know the compound interest formula)
bull discount
bull profit and loss
Extract data from tables and charts
Learner Guide
32
Core Algebra and graphs
Question type You should be able to R A G CommentsBasic algebra Use letters to express generalised numbers
Express basic arithmetic processes algebraically
Substitute numbers in formulae
Construct simple expressions and set up simple equations
Rearrange simple formulae
Algebraic manipulation
Manipulate directed numbers
Use brackets
bull expand a single bracket eg 3x(2x ndash4y)
bull expand a pair of brackets eg (x + 3) (x ndash 7)
Extract common factors eg factorise 9x2 + 15xy
Rules of indices Use and interpret positive negative and zero indices
Use the rules of indices eg to simplify algebra such as
bull 3x4 times 5x
bull 10x3 divide 2x2
bull (x6)2
Learner Guide
33
Core Algebra and graphs
Question type You should be able to R A G CommentsEquations and inequalities
Derive and solve simple linear equations in one unknown
Derive and solve simultaneous linear equations in two unknowns
Number sequences
(links to Squares square roots cubes and cube roots)
Continue a number sequence
Recognise patterns in sequences
Recognise relationships between difference sequences
Find the nth term of sequences for
bull liner sequences
bull simple quadratic sequences
bull cubic sequences
Practical graphs
(links to Mensuration)
Interpret and use graphs in practical situations including
bull travel graphs
bull conversion graphs
Draw graphs from given data
Learner Guide
34
Core Algebra and graphs
Question type You should be able to R A G CommentsGraphs of functions
(links to Co-ordinate geometry)
Construct tables of values for functions of the form
bull ax + b (linear)
bull plusmn x2 + ax + b (quadratic)
bull (x ne 0) (reciprocal)
where a and b are integer constants
Draw and interpret such graphs
Solve linear and quadratic equations approximately by graphical methods
Recognise and sketch the graphs of linear and quadratic functions
ax
Learner Guide
35
Core Co-ordinate geometry
Question type You should be able to R A G CommentsCo-ordinates Work with co-ordinates in two dimensions
Gradients Find the gradient of a straight line graph
Equation of straight line
Interpret and obtain the equation of a straight line graph in the form y = mx + c where the graph is given
Parallel lines Determine the equation of a straight line parallel to a given line eg find the equation of a line parallel to y = 4x ndash 1 that passes through (0 ndash3)
Learner Guide
36
Core Geometry
Question type You should be able to R A G CommentsGeometrical language
Use and interpret the geometrical terms
bull point
bull line
bull parallel
bull perpendicular
bull bearing
bull right angle acute obtuse and reflex angles
bull similar
bull congruent
Use and interpret the vocabulary of
bull triangles right-angled scalene isosceles equilateral
bull quadrilaterals
bull circles
bull polygons
bull simple solid figures including nets
Learner Guide
37
Core Geometry
Question type You should be able to R A G CommentsGeometrical constructions
Measure and draw lines and angles
Construct a triangle given the three sides using a ruler and a pair of compasses only
Scale drawings Read and make scale drawings
Similar figures Calculate lengths of similar figures
Congruent Recognise congruent shapes
Symmetry Recognise symmetry properties for triangles quadrilaterals and circles
Recognise line symmetry in two dimensions
Recognise and find the order of rotational symmetry in two dimensions
Learner Guide
38
Core Geometry
Question type You should be able to R A G CommentsAngle properties Calculate unknown angles explaining the properties that you
are using in geometrical language for angles
bull angles at a point
bull angles on a straight line and intersecting straight lines
bull angles within parallel lines
bull angles in triangles
bull angles in quadrilaterals
bull angles in regular polygons
bull angle in a semi-circle
bull angle between tangent and radius of a circle
Learner Guide
39
Core Mensuration
Question type You should be able to R A G CommentsMeasures bull Use current units of
bull mass
bull length
bull area
bull volume
bull capacity
Express quantities in terms of smaller or larger units including units of area and volume
Convert between units including units of area and volume
Perimiter Carry out calculations involving
bull perimeter and area of a rectangle
bull perimeter and area of a triangle
bull perimeter and area of parallelogram
bull perimeter and area of a trapezium
bull perimeter and area of shapes made by combining
bull rectangles triangles parallelograms andor trapeziums
Learner Guide
40
Core Mensuration
Question type You should be able to R A G CommentsCircles Carry out calculations involving circumference and area of a
circle
Solve simple problems involving the arc length and sector area of a circle where the sector angle is a factor of 360deg
Surface area and volume
Carry out calculations involving
bull surface area and volume of a cuboid prism and cylinder (no formulae will be given for these shapes)
bull surface area and volume of a sphere pyramid and cone (formulae will be given for these shapes)
Areas and volumes of compound shapes
Carry out calculations involving the areas and volumes of compound shapes made from combinations of the shapes in Perimeter or Surface area and volume
Learner Guide
41
Core Trigonometry
Question type You should be able to R A G CommentsBearings Use and interpret three-figure bearings measured clockwise
from the North ie 000degndash360degTrigonometry Find unknown sides andor angles in right-angled triangles by
applying
bull Pythagorasrsquo theorem
bull sine cosine and tangent ratios for acute angles in right-angled triangles
Learner Guide
42
Core Vectors and transformations
Question type You should be able to R A G CommentsVectors in two dimensions (links to Trigonometry)
Describe a translation by using a vector represented by
AB or a
Add and subtract vectors
Multiply a vector by a scalar
Transformations Reflect simple shapes in horizontal or vertical lines
Rotate simple shapes through multiples of 90deg about
bull the origin
bull their vertices
bull the midpoints of their sides
Construct translations of simple shapes
Construct enlargements of simple shapes (positive and fractional scale factors)
Recognise and describe using the correct language
bull reflections
bull rotations
bull translations
bull enlargements (positive and fractional scale factors)
( )x
y
Learner Guide
43
Core Probability
Question type You should be able to R A G CommentsSingle events Calculate the probability of a single event as a fraction decimal
or percentage (not a ratio)Probability scale Understand and use the probability scale from 0 to 1
Sum to 1 Understand that the probability of an event occurring = 1 ndash the probability of the event not occurring
Relative frequency
Understand relative frequency as an estimate of probability
Work out expected frequencies using relative frequencyCombined events Calculate the probability of simple combined events using
bull tree diagrams
bull possibility diagrams (points on a grid)
bull Venn diagrams (2 sets only)
Learner Guide
44
Core Statistics
Question type What I need to do R A G CommentsClassify Collect classify and tabulate data
Interpret and compare
Read interpret and draw simple inferences from tables and statistical diagrams
Compare sets of data using
bull tables
bull graphs
bull statistical measures
Be aware of restrictions when making conclusions from data
Charts Construct and use
bull bar charts
bull pie charts
bull pictograms
bull stem-and-leaf diagrams
bull frequency distributions
bull histograms with equal intervals
bull scatter diagrams
Learner Guide
45
Question type What I need to do R A G CommentsAverages Calculate for individual and discrete data
bull mean
bull median
bull mode
bull range
and distinguish between their useCorrelation Understand what is meant by positive negative and zero
correlation with reference to a scatter diagramLine of best fit Draw interpret and use a ruled line of best fit by eye
Learner Guide
46
Extended syllabus content (includes required Core content)Extended Number
Question type You should be able to R A G CommentsNumber Identify and use
bull natural numbers
bull integers (positive negative and zero)
bull prime numbers
bull write a number as a product of its prime factors
bull square and cube numbers
bull common factors and highest common factor of two or more numbers
bull common multiples and lowest common multiple of two or more numbers
bull rational numbers
bull irrational numbers (eg π radic2 )
bull real numbers
bull reciprocals
Learner Guide
47
Extended Number
Question type You should be able to R A G CommentsSet notation and language
Use language notation and Venn diagrams to describe sets and represent relationships between sets as follows
Definition of sets egA = x x is a natural number
B = (xy) y = mx + c
C = x a ⩽ x ⩽ b
D = a b c hellip
Notation egnumber of elements in set A n(A)
lsquois an element ofrsquo isin
lsquois not an element ofrsquo notin
complement of set A
the empty set empty
the universal set
A is a subset of B A sube B
A is a proper subset of B A sub B
A is not a subset of B A ⊈ B
A is not a proper subset of B A nsub B
union of A and B A cup B
intersection of A and B A cap B
Learner Guide
48
Extended Number
Question type You should be able to R A G CommentsSquares square roots cubes and cube roots
Calculatebull squares of numbers
bull square roots of numbers
bull cubes of numbers
bull cube roots of numbers
bull other powers and roots of numbers
Directed numbers
Use directed numbers in practical situations for example temperature changes
Fractions decimals and percentages
Use the language and notation of simple vulgar and decimal fractions and percentages in appropriate contexts
Recognise equivalent fractions decimals and percentages
Convert between fractions decimals and percentages
Convert recurring decimals to fractions
Ordering Order quantities by magnitude and demonstrate familiarity with the symbols = ne gt lt ⩾ ⩽
Learner Guide
49
Extended Number
Question type You should be able to R A G CommentsIndices and standard form (links to Algebraic manipulation)
Evaluate indices including fractional negative and zero
eg 25 5ndash2 1000 10012 8ndash23
Use the rules of indices forbull multiplication of indices eg 43 times 45
bull division of indices eg 57 divide 53
bull index numbers raised to an index eg (43)2
Use the standard form A times 10n where n is a positive or negative integer and 1 ⩽ A lt 10bull convert into and out of standard form
bull calculate with numbers in standard form
Four rules
( + ndash times divide )
Use the four rules for calculations withbull whole numbers
bull decimals
bull vulgar and mixed fractions
bull correct ordering of operations (BIDMAS) and use of brackets
Learner Guide
50
Extended Number
Question type You should be able to R A G CommentsEstimates Make estimates of numbers quantities and lengths
Give approximations to a specified number of
bull significant figures
bull decimal places
Round off answers to reasonable accuracy in the context of a given problem
Bounds Give upper and lower bounds for data given to a specified accuracy eg measured lengths
Obtain appropriate upper and lower bounds to solutions of simple problems given to a specified accuracy eg the lower and upper bounds for the area of a rectangle
Ratio proportion rate
(links to Direct and inverse proportion)
Understand ratio
Divide quantities in a given ratio
Increase and decrease a quantity by a given ratio
Understand numerical problems involving direct and inverse proportion
Use ratio and scales in practical situations
Use common measures of rate (formulae for other rates eg density and pressure will be given in the question)
Calculate average speed
Learner Guide
51
Extended Number
Question type What I need to do R A G CommentsPercentages Calculate a percentage of a quantity
Express one quantity as a percentage of another quantity
Calculate percentage increase or decrease
Calculate reverse percentages eg finding the cost price given the selling price and the percentage profit
Use of an electronic calculator
Use a calculator efficiently
Check accuracy of calculations
Time Calculate times in terms of the 24-hour and 12-hour clock
Read clocks dials and timetables
Money Calculate using money
Convert from one currency to another
Learner Guide
52
Extended Number
Question type You should be able to R A G CommentsPersonal and small business finance
Use given data to solve problems on
bull earnings
bull simple interest
bull compound interest
ndash you must know the compound interest formula
bull discount
bull profit and loss
Extract data from tables and charts
Exponential growth and decay
Use exponential growth and decay in population and finance eg depreciation bacteria growth
Learner Guide
53
Extended Algebra and graphs
Question type You should be able to R A G CommentsBasic algebra Use letters to express generalised numbers
Express basic arithmetic processes algebraically
Substitute numbers in complicated formulae
Construct and rearrange complicated formulae eg where the subject appears twice
Algebraic manipulation
Manipulate directed numbers
Use bracketsbull expand a single bracket eg expand 3x(2x ndash 4y)
bull expand a pair of brackets eg (x ndash 4)(x + 7)
bull expand products of more than two brackets eg (x + 4)(x ndash 7)(2x + 1)
Extract common factors eg factorise 9x2 + 15xy
Factorise expressions of the formbull ax + bx + kay + kby
bull asup2xsup2 ndash bsup2ysup2
bull asup2 + 2ab + bsup2
bull axsup2 + bx + c
Learner Guide
54
Extended Algebra and graphs
Question type You should be able to R A G CommentsAlgebraic fractions
Manipulate algebraic fractions eg
bull
bull
bull
bull
bull
Factorise and simplify algebraic fractions such as
Rules of indices Use and interpret positive negative and zero indices
Use and interpret fractional indices eg solve 32x = 2
Use the rules of indices to simplify algebra eg
x3 + x ndash 4
22x3 +
3(x ndash 5)2
3a4 +
5ab3
3a4 divide
9a10
1x ndash 2 +
2x ndash 3
x2 ndash 2xx2 ndash 5x + 6
3xndash4 times23
x12
32x5( )
3
2xndash2divide25
x12
Learner Guide
55
Extended Algebra and graphs
Question type You should be able to R A G CommentsEquations and inequalities
bull Derive and solve simple linear equations in one unknown
bull Derive and solve simultaneous linear equations in two unknowns
bull Derive and solve simultaneous equations involving one linear and one quadratic
Solve quadratic equations by
bull factorisation
bull completing the square
bull using the formula
Derive and solve simple linear inequalities including representing solutions on a number line
Linear programming
Represent inequalities graphically including using the conventions of
bull broken lines for strict inequalities
bull shading unwanted regions
Solve simple linear programming problems using graphical representations of inequalities
Learner Guide
56
Extended Algebra and graphs
Question type You should be able to R A G CommentsNumber sequences (links to Squares square roots cubes and cube roots)
Continue a number sequence
Recognise patterns in sequences
Recognise relationships between different sequences
Find the nth term of sequences of
bull linear sequences
bull quadratic sequences
bull cubic sequences
bull exponential sequences
and simple combinations of these
Direct and inverse proportion (links to Ratio proportion rate)
Express direct proportion algebraically
Express inverse proportion algebraically
Use algebraic expressions of direct and inverse proportion to find unknown quantities
Practical graphs
(links to Coordinate geometry)
Interpret and use graphs in practical situations including
bull travel graphs
bull conversion graphs
Draw graphs from given data
Learner Guide
57
Extended Algebra and graphs
Question type You should be able to R A G CommentsPractical graphs (links to Coordinate geometry) continued
Apply the idea of rate of change to simple kinematics involving
bull distancendashtime graphs
bull speedndashtime graphs
bull acceleration and deceleration
This may involve estimation and interpretation of the gradient of a tangent at a point
Calculate distance travelled as an area under a linear speedndash time graph
Learner Guide
58
Extended Algebra and graphs
Question type You should be able to R A G CommentsGraphs of functions (links to Coordinate geometry)
Construct tables of values and draw graphs for functions of the form
bull axn where a is a rational constant and n = minus2 minus1 0 1 2 3 and simple sums of not more than three of these
bull abx + c where a and c are rational constants and b is a positive integer
Solve associated equations approximately by graphical methods including finding and interpreting roots and finding turning points of quadratics by completing the square
Draw and interpret graphs representing exponential growth and decay problems
Recognise sketch and interpret graphs of
bull linear
bull quadratic
bull cubic
bull reciprocal
bull exponential
(knowledge of turning points and asymtotes is required)Tangents Estimate gradients of curves by drawing tangents
Learner Guide
59
Extended Algebra and graphs
Question type You should be able to R A G CommentsFunctions Use function notation eg
f(x) = 3x ndash 5 f x α 3x ndash5 to describe simple functions
Find inverse functions f ndash1 (x)
Form composite functions as defined by gf(x) = g(f(x))
Derivatives Understand the idea of a derived function
Use derivatives of the form axn and simple sums of not more than three of these (a is a rational constant and n is a positive integer or 0)
Apply differentiation to gradients and turning points (stationary points)
Use any method to explain whether the turning point is a maximum or a minimum eg second derivative or gradient of function on either side of turning point
Learner Guide
60
Extended Co-ordinate geometry
Question type You should be able to R A G CommentsStraight line graphs
Work with co-ordinates in two dimensions
Gradient Find the gradient of a straight line graph
Calculate the gradient of a straight line from the co-ordinates of two points on it
Length and midpoint
Calculate the length and the co-ordinates of the midpoint of a straight line segment from the co-ordinates of its end points
Equation of line Interpret and obtain the equation of a straight line graph
Parallel lines Determine the equation of a straight line parallel to a given line eg find the equation of a line parallel to y = 4x ndash 1 that passes through (0 ndash3)
Perpendicular lines
Find the gradient of parallel and perpendicular lines eg
bull find the gradient of a line perpendicular to y = 3x + 1
bull find the equation of a line perpendicular to one passing through the co-ordinates (1 3) and (ndash2 ndash9)
Learner Guide
61
Extended Geometry
Question type You should be able to R A G CommentsGeometrical language
Use and interpret the geometrical terms
bull point
bull line
bull parallel
bull perpendicular
bull bearing
bull right angle acute obtuse and reflex angles
bull similar
bull congruent
Use and interpret the vocabulary of
bull triangles right-angled scalene isosceles equilateral
bull quadrilaterals
bull circles
bull polygons
bull simple solid figures including nets
Learner Guide
62
Extended Geometry
Question type What I need to do R A G CommentsGeometrical constructions
Measure and draw lines and angles
Construct a triangle given the three sides using a ruler and a pair of compasses only
Scale drawings Read and make scale drawings
Similar figures Calculate lengths of similar figures
Use relationships between areas of similar triangles and in similar figures
Use relationships between volumes and surface areas of similar solids
Congruent triangles
Use the congruence criteria for triangles (SSS ASA SAS RHS)
Symmetry Recognise symmetry properties for triangles quadrilaterals and circles
Recognise line symmetry in two dimensions
Recognise and find the order of rotational symmetry in two dimensions
Learner Guide
63
Extended Geometry
Question type You should be able to R A G CommentsSymmetry (continued)
Use the following symmetry properties of circles
bull equal chords are equidistant from the centre
bull perpendicular bisector of a chord passes through the centre
bull tangents from an external point are equal in length
Recognise and use symmetry properties of
bull prism cylinder cone and pyramid
Learner Guide
64
Extended Geometry
Question type You should be able to R A G CommentsAngle properties Calculate unknown angles explaining the properties that
you are using in geometrical language for the following geometrical properties
bull angles at a point
bull angles at a point on a straight line and intersecting straight lines
bull angles formed within parallel lines
bull angle properties of triangles and quadrilaterals
bull angle properties of regular polygons
bull angle in a semi-circle
bull angle between tangent and radius of a circle
bull angles properties of irregular polygons
bull angle at the centre of a circle is twice the angle at the circumference
bull angles in the same segment are equal
bull angles in opposite segments are supplementary cyclic quadrilaterals
bull alternate segment theorem
Learner Guide
65
Extended Mensuration
Question type What I need to do R A G CommentsMeasures Use current units of
bull mass
bull length
bull area
bull volume
bull capacity
Express quantities in terms of smaller or larger units including units of area and volume
Perimeter Carry out calculations involving
bull perimeter and area of a rectangle
bull perimeter and area of a triangle
bull perimeter and area of parallelogram
bull perimeter and area of a trapezium
bull perimeter and area of compound shapes made by combining rectangles triangles parallelograms andor trapeziums
Learner Guide
66
Extended Mensuration
Question type You should be able to R A G CommentsCircles Carry out calculations involving circumference and area of a
circle
Solve problems involving arc length and sector area of a circle
Surface area and volume
Carry out calculations involving
bull surface area and volume of a cuboid prism and cylinder (no formulae will be given for these shapes)
bull surface area and volume of a sphere pyramid and cone (formulae will be given for these shapes)
Compound shapes
Carry out calculations involving
bull area of a shape made by combining cuboids prisms andor cylinders
bull volume of a shape made by combining cuboids prisms andor cylinders
Learner Guide
67
Extended Trigonometry
Question type You should be able to R A G CommentsBearings Use and interpret three-figure bearings measured clockwise
from the North ie 000degndash360degTrigonometry Find unknown sides andor angles in right-angled triangles by
applying
bull Pythagorasrsquo theorem
bull sine cosine and tangent ratios for acute angles in right-angled triangles
Solve problems in two dimensions involving angles of elevation and depression
Know that the perpendicular distance from a point to a line is the shortest distance to the line
Trig graphs and equations
Recognise sketch and interpret graphs of simple trigonometric functions
Graph and know the properties of trigonometric functions
Solve simple trigonometric equations for values between 0deg
and 360deg eg Solve sin x = radic32
for values of x between 0deg and
360degGeneral trig Solve problems using sine and cosine rules for any triangle
Find the area of any triangle using frac12absinC
Trig in 3D Solve simple trigonometrical problems in three dimensions including angle between a line and a plane
Learner Guide
68
Extended Vectors and transformations
Question type You should be able to R A G CommentsVectors in two dimensions (links to Trigonometry)
Describe a translation by using a vector represented by
AB or a
Add and subtract vectors
Multiply a vector by a scalar
Transformations Reflect simple shapes in horizontal or vertical lines
Rotate simple shapes through multiples of 90deg about any point
Construct translations of simple shapes
Construct enlargements of simple shapes (positive fractional and negative scale factors)
Recognise and describe
bull reflections
bull rotations
bull translations
bull enlargements (positive fractional and negative scalefactors)
( )x
y
Learner Guide
69
Extended Vectors and transformations
Question type You should be able to R A G CommentsHarder vectors
Calculate the magnitude of a vector as and
understand that magnitude is denoted by modulus signs |A B| or |a|
Represent vectors by directed line segments
Use the sum and difference of two vectors
Use position vectors
( )x
yradicx2 + y2
Learner Guide
70
Extended Probability
Question type You should be able to R A G CommentsProbability (links to Four rules)
Calculate the probability of a single event as a fraction decimal or percentage (not a ratio)
Probability scale Understand and use the probability scale from 0 to 1
Sum to 1 Understand that the probability of an event occurring = 1 ndash the probability of the event not occurring
Relative frequency
Understand relative frequency as an estimate of probability
Work out expected frequencies using relative frequency
Combined events Calculate the probability of combined events using
bull tree diagrams
bull possibility diagrams
bull tables
Learner Guide
71
Extended Statistics
Question type You should be able to R A G CommentsClassify Collect classify and tabulate data
Interpret and compare
Read interpret and draw simple inferences from tables and statistical diagrams
Compare sets of data using
bull tables
bull graphs
bull statistical measures
Be aware of restrictions when making conclusions from data
Charts Construct and use
bull bar charts
bull pie charts
bull pictograms
bull stem ndash and ndash leaf diagrams
bull frequency distributions
bull histograms with equal and unequal intervals
bull scatter diagrams
Learner Guide
72
Extended Statistics
Question type You should be able to R A G CommentsAverages Calculate for individual and discrete data
bull mean
bull median
bull mode
bull range
and distinguish between their use
Estimated mean Calculate an estimate of the mean for grouped and continuous data
Identify the modal class from a grouped frequency distributionCumulative frequency
Construct and use cumulative frequency diagrams to estimate and interpret
bull the median
bull percentiles
bull quartiles
bull inter-quartile range
Construct and interpret box-and-whisker plots
Correlation Understand what is meant by positive negative and zero correlation with reference to a scatter diagram
Lines of best fit Draw interpret and use a ruled line of best fit by eye
Cambridge Assessment International Education1 Hills Road Cambridge CB1 2EU United Kingdomt +44 1223 553554e infocambridgeinternationalorg wwwcambridgeinternationalorg
Copyright copy UCLES October 2017
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- Check Box 101058 Off
- Check Box 101059 Off
- Check Box 101060 Off
- Check Box 1010269 Off
- Check Box 1010270 Off
- Text Field 357
- Check Box 1010271 Off
- Check Box 1010272 Off
- Check Box 1010273 Off
- Text Field 358
- Check Box 1010274 Off
- Check Box 1010330 Off
- Check Box 1010331 Off
- Text Field 359
- Check Box 1010343 Off
- Check Box 1010344 Off
- Check Box 1010345 Off
- Text Field 360
- Check Box 1010348 Off
- Check Box 1010349 Off
- Check Box 1010350 Off
- Text Field 297
- Check Box 101061 Off
- Check Box 101062 Off
- Check Box 101063 Off
- Check Box 101064 Off
- Check Box 101065 Off
- Check Box 101066 Off
- Check Box 10168 Off
- Check Box 10169 Off
- Check Box 10170 Off
- Check Box 10171 Off
- Check Box 10172 Off
- Check Box 10173 Off
- Check Box 101067 Off
- Check Box 101068 Off
- Check Box 101069 Off
- Check Box 10174 Off
- Check Box 10175 Off
- Check Box 10176 Off
- Check Box 10177 Off
- Check Box 10178 Off
- Check Box 10179 Off
- Check Box 101070 Off
- Check Box 101071 Off
- Check Box 101072 Off
- Check Box 10180 Off
- Check Box 10181 Off
- Check Box 10182 Off
- Check Box 101073 Off
- Check Box 101074 Off
- Check Box 101075 Off
- Check Box 10183 Off
- Check Box 10184 Off
- Check Box 10185 Off
- Check Box 10186 Off
- Check Box 10187 Off
- Check Box 10235 Off
- Check Box 101076 Off
- Check Box 101077 Off
- Check Box 101078 Off
- Text Field 298
- Check Box 101079 Off
- Check Box 101080 Off
- Check Box 101081 Off
- Check Box 101082 Off
- Check Box 101083 Off
- Check Box 101084 Off
- Text Field 299
- Check Box 101088 Off
- Check Box 101089 Off
- Check Box 101090 Off
- Text Field 300
- Check Box 101091 Off
- Check Box 101092 Off
- Check Box 101093 Off
- Check Box 1010351 Off
- Check Box 1010352 Off
- Check Box 1010353 Off
- Text Field 301
- Check Box 10242 Off
- Check Box 10243 Off
- Check Box 10244 Off
- Check Box 101094 Off
- Check Box 101095 Off
- Check Box 101096 Off
- Check Box 101097 Off
- Check Box 101098 Off
- Check Box 101099 Off
- Text Field 302
- Check Box 1010103 Off
- Check Box 1010104 Off
- Check Box 1010105 Off
- Check Box 10245 Off
- Check Box 10246 Off
- Check Box 10247 Off
- Check Box 10248 Off
- Check Box 10249 Off
- Check Box 10250 Off
- Check Box 1010106 Off
- Check Box 1010107 Off
- Check Box 1010108 Off
- Check Box 1010109 Off
- Check Box 1010110 Off
- Check Box 1010111 Off
- Check Box 1010112 Off
- Check Box 1010113 Off
- Check Box 1010114 Off
- Check Box 10251 Off
- Check Box 10252 Off
- Check Box 10253 Off
- Check Box 1010115 Off
- Check Box 1010116 Off
- Check Box 1010117 Off
- Text Field 303
- Check Box 10260 Off
- Check Box 10261 Off
- Check Box 10262 Off
- Check Box 10101017 Off
- Check Box 10101018 Off
- Check Box 10101019 Off
- Check Box 10101020 Off
- Check Box 1010118 Off
- Check Box 1010119 Off
- Check Box 1010120 Off
- Check Box 1010126 Off
- Check Box 1010127 Off
- Check Box 10263 Off
- Check Box 10264 Off
- Check Box 10265 Off
- Check Box 10269 Off
- Check Box 10270 Off
- Check Box 10271 Off
- Check Box 10101025 Off
- Check Box 10101026 Off
- Check Box 10101027 Off
- Text Field 306
- Check Box 10266 Off
- Check Box 10267 Off
- Check Box 10268 Off
- Check Box 10101021 Off
- Check Box 10101022 Off
- Check Box 10101023 Off
- Check Box 10101024 Off
- Check Box 1010131 Off
- Check Box 1010132 Off
- Check Box 1010133 Off
- Check Box 1010134 Off
- Check Box 1010135 Off
- Check Box 1010136 Off
- Check Box 1010137 Off
- Check Box 1010138 Off
- Text Field 3025
- Check Box 10367 Off
- Check Box 10368 Off
- Check Box 10369 Off
- Check Box 10407 Off
- Check Box 10431 Off
- Check Box 10432 Off
- Text Field 3059
- Check Box 104010 Off
- Check Box 10433 Off
- Check Box 10465 Off
- Check Box 104011 Off
- Check Box 10466 Off
- Check Box 10527 Off
- Text Field 3060
- Check Box 104012 Off
- Check Box 10528 Off
- Check Box 10529 Off
- Text Field 3063
- Check Box 10101037 Off
- Check Box 10101038 Off
- Check Box 10101039 Off
- Text Field 309
- Check Box 10275 Off
- Check Box 10276 Off
- Check Box 10277 Off
- Check Box 10101040 Off
- Check Box 10101041 Off
- Check Box 10101042 Off
- Text Field 3010
- Check Box 10278 Off
- Check Box 10279 Off
- Check Box 10280 Off
- Check Box 10101044 Off
- Check Box 10101045 Off
- Check Box 10101046 Off
- Check Box 10101047 Off
- Check Box 1010141 Off
- Check Box 1010142 Off
- Text Field 3011
- Check Box 10281 Off
- Check Box 10282 Off
- Check Box 10283 Off
- Check Box 10101048 Off
- Check Box 10101049 Off
- Check Box 10101050 Off
- Check Box 10101051 Off
- Check Box 10101052 Off
- Check Box 10101053 Off
- Check Box 10101054 Off
- Check Box 10101055 Off
- Check Box 10101056 Off
- Check Box 10101057 Off
- Check Box 10101058 Off
- Check Box 10101059 Off
- Check Box 10101060 Off
- Check Box 10101061 Off
- Check Box 10101062 Off
- Check Box 10101063 Off
- Check Box 10101064 Off
- Check Box 10101065 Off
- Check Box 10101066 Off
- Check Box 10101067 Off
- Check Box 10101068 Off
- Check Box 10101069 Off
- Check Box 10101070 Off
- Check Box 10101071 Off
- Check Box 10101072 Off
- Check Box 10101073 Off
- Check Box 10101074 Off
- Text Field 3012
- Check Box 10284 Off
- Check Box 10285 Off
- Check Box 10286 Off
- Text Field 3013
- Check Box 10101075 Off
- Check Box 10101076 Off
- Check Box 10101077 Off
- Text Field 3014
- Check Box 10101078 Off
- Check Box 1010143 Off
- Check Box 1010144 Off
- Text Field 3015
- Check Box 10287 Off
- Check Box 10288 Off
- Check Box 10289 Off
- Check Box 10334 Off
- Check Box 10335 Off
- Check Box 10336 Off
- Check Box 10371 Off
- Check Box 10372 Off
- Check Box 10436 Off
- Check Box 10437 Off
- Check Box 10438 Off
- Check Box 10447 Off
- Text Field 3016
- Check Box 10401 Off
- Check Box 10402 Off
- Check Box 10403 Off
- Check Box 10291 Off
- Check Box 10292 Off
- Check Box 10337 Off
- Check Box 10448 Off
- Check Box 10449 Off
- Check Box 10456 Off
- Check Box 10457 Off
- Check Box 10458 Off
- Check Box 10533 Off
- Check Box 10534 Off
- Check Box 10535 Off
- Check Box 10543 Off
- Check Box 10544 Off
- Check Box 10740 Off
- Check Box 10741 Off
- Text Field 3017
- Check Box 10101079 Off
- Check Box 10101080 Off
- Check Box 10101081 Off
- Check Box 10101082 Off
- Check Box 1010145 Off
- Check Box 1010146 Off
- Check Box 10293 Off
- Check Box 10294 Off
- Check Box 10295 Off
- Check Box 10338 Off
- Check Box 10339 Off
- Check Box 10370 Off
- Check Box 10101083 Off
- Check Box 10101084 Off
- Check Box 10101085 Off
- Check Box 10101086 Off
- Check Box 1010147 Off
- Check Box 1010148 Off
- Check Box 10296 Off
- Check Box 10297 Off
- Check Box 10298 Off
- Text Field 3018
- Check Box 10299 Off
- Check Box 10300 Off
- Check Box 10301 Off
- Check Box 10101087 Off
- Check Box 10101088 Off
- Check Box 10101089 Off
- Check Box 10101090 Off
- Check Box 1010149 Off
- Check Box 1010150 Off
- Check Box 10302 Off
- Check Box 10303 Off
- Check Box 10304 Off
- Text Field 3019
- Check Box 10305 Off
- Check Box 10306 Off
- Check Box 10307 Off
- Text Field 3020
- Check Box 10308 Off
- Check Box 10309 Off
- Check Box 103010 Off
- Text Field 311
- Check Box 10141 Off
- Check Box 10142 Off
- Check Box 10143 Off
- Check Box 10144 Off
- Check Box 10145 Off
- Check Box 10149 Off
- Check Box 10257 Off
- Check Box 10258 Off
- Check Box 10259 Off
- Check Box 10310 Off
- Check Box 10311 Off
- Check Box 10312 Off
- Check Box 10331 Off
- Check Box 10332 Off
- Check Box 10333 Off
- Check Box 10313 Off
- Check Box 10314 Off
- Check Box 10315 Off
- Check Box 10316 Off
- Check Box 10317 Off
- Check Box 10318 Off
- Check Box 10319 Off
- Check Box 10320 Off
- Check Box 10321 Off
- Check Box 10322 Off
- Check Box 10323 Off
- Check Box 10324 Off
- Check Box 10325 Off
- Check Box 10326 Off
- Check Box 10327 Off
- Check Box 10399 Off
- Check Box 10400 Off
- Check Box 10530 Off
- Text Field 335
- Check Box 10567 Off
- Check Box 10568 Off
- Check Box 10569 Off
- Check Box 10570 Off
- Check Box 10571 Off
- Check Box 10572 Off
- Check Box 10573 Off
- Check Box 10574 Off
- Check Box 10575 Off
- Check Box 10576 Off
- Check Box 10577 Off
- Check Box 10578 Off
- Check Box 10597 Off
- Check Box 10598 Off
- Check Box 10599 Off
- Check Box 10579 Off
- Check Box 10580 Off
- Check Box 10581 Off
- Check Box 10582 Off
- Check Box 10583 Off
- Check Box 10584 Off
- Check Box 10585 Off
- Check Box 10586 Off
- Check Box 10587 Off
- Check Box 10588 Off
- Check Box 10589 Off
- Check Box 10590 Off
- Check Box 10591 Off
- Check Box 10592 Off
- Check Box 10593 Off
- Check Box 10594 Off
- Check Box 10595 Off
- Check Box 10596 Off
- Check Box 10600 Off
- Check Box 10601 Off
- Check Box 10602 Off
- Check Box 10603 Off
- Check Box 10604 Off
- Check Box 10605 Off
- Check Box 10606 Off
- Check Box 10607 Off
- Check Box 10608 Off
- Check Box 10609 Off
- Check Box 106010 Off
- Check Box 106011 Off
- Check Box 106012 Off
- Check Box 106013 Off
- Check Box 106014 Off
- Check Box 106015 Off
- Check Box 106016 Off
- Check Box 106017 Off
- Text Field 315
- Check Box 10340 Off
- Check Box 10341 Off
- Check Box 10342 Off
- Check Box 10343 Off
- Check Box 10344 Off
- Check Box 10345 Off
- Check Box 10346 Off
- Check Box 10347 Off
- Check Box 10348 Off
- Check Box 10349 Off
- Check Box 10350 Off
- Check Box 10351 Off
- Check Box 10531 Off
- Check Box 10532 Off
- Check Box 10542 Off
- Text Field 313
- Check Box 10352 Off
- Check Box 10353 Off
- Check Box 10354 Off
- Text Field 316
- Check Box 10355 Off
- Check Box 10356 Off
- Check Box 10357 Off
- Check Box 10358 Off
- Check Box 10359 Off
- Check Box 10360 Off
- Check Box 10361 Off
- Check Box 10362 Off
- Check Box 10363 Off
- Check Box 10364 Off
- Check Box 10365 Off
- Check Box 10366 Off
- Check Box 10404 Off
- Check Box 10405 Off
- Check Box 10406 Off
- Text Field 352
- Check Box 102021 Off
- Check Box 102022 Off
- Check Box 102040 Off
- Check Box 102041 Off
- Check Box 102042 Off
- Check Box 102043 Off
- Check Box 102044 Off
- Check Box 102045 Off
- Check Box 102046 Off
- Check Box 102047 Off
- Check Box 102048 Off
- Check Box 102049 Off
- Check Box 102050 Off
- Check Box 102051 Off
- Check Box 102052 Off
- Check Box 102065 Off
- Check Box 102066 Off
- Check Box 102067 Off
- Check Box 102053 Off
- Check Box 102054 Off
- Check Box 102055 Off
- Text Field 351
- Check Box 102056 Off
- Check Box 102057 Off
- Check Box 102058 Off
- Check Box 102059 Off
- Check Box 102060 Off
- Check Box 102061 Off
- Check Box 102062 Off
- Check Box 102063 Off
- Check Box 102064 Off
- Check Box 102068 Off
- Check Box 102069 Off
- Check Box 102070 Off
- Text Field 318
- Check Box 10373 Off
- Check Box 10374 Off
- Check Box 10375 Off
- Check Box 10376 Off
- Check Box 10377 Off
- Check Box 10378 Off
- Check Box 10379 Off
- Check Box 10380 Off
- Check Box 10381 Off
- Check Box 10382 Off
- Check Box 10383 Off
- Check Box 10384 Off
- Check Box 10385 Off
- Check Box 10386 Off
- Check Box 10387 Off
- Text Field 317
- Check Box 10388 Off
- Check Box 10389 Off
- Check Box 10390 Off
- Check Box 102023 Off
- Check Box 102024 Off
- Check Box 102025 Off
- Check Box 102026 Off
- Check Box 102027 Off
- Check Box 102028 Off
- Check Box 102071 Off
- Check Box 102072 Off
- Check Box 102073 Off
- Check Box 102029 Off
- Check Box 10391 Off
- Check Box 10392 Off
- Check Box 10393 Off
- Check Box 10394 Off
- Check Box 10395 Off
- Check Box 10396 Off
- Check Box 10397 Off
- Check Box 10398 Off
- Check Box 102030 Off
- Check Box 102031 Off
- Check Box 102032 Off
- Text Field 319
- Text Field 322
- Check Box 10408 Off
- Check Box 10409 Off
- Check Box 10410 Off
- Check Box 10411 Off
- Check Box 10412 Off
- Check Box 10413 Off
- Check Box 10414 Off
- Check Box 10415 Off
- Check Box 10416 Off
- Check Box 10417 Off
- Check Box 10418 Off
- Check Box 10419 Off
- Text Field 321
- Check Box 10420 Off
- Check Box 10421 Off
- Check Box 10422 Off
- Check Box 10423 Off
- Check Box 10424 Off
- Check Box 10425 Off
- Text Field 337
- Check Box 102033 Off
- Check Box 102034 Off
- Check Box 102035 Off
- Check Box 102036 Off
- Check Box 102037 Off
- Check Box 102038 Off
- Text Field 338
- Check Box 102039 Off
- Check Box 10426 Off
- Check Box 10427 Off
- Check Box 10428 Off
- Check Box 10429 Off
- Check Box 10430 Off
- Text Field 324
- Check Box 10434 Off
- Check Box 10435 Off
- Check Box 101051 Off
- Check Box 1010100 Off
- Check Box 1010101 Off
- Check Box 1010102 Off
- Check Box 1010128 Off
- Check Box 1010129 Off
- Check Box 1010130 Off
- Check Box 10439 Off
- Check Box 10440 Off
- Check Box 10441 Off
- Check Box 10442 Off
- Check Box 10443 Off
- Check Box 10444 Off
- Text Field 350
- Check Box 10742 Off
- Check Box 10743 Off
- Check Box 10744 Off
- Text Field 325
- Check Box 10445 Off
- Check Box 10446 Off
- Check Box 1010151 Off
- Check Box 1010152 Off
- Check Box 1010153 Off
- Check Box 1010154 Off
- Check Box 1010155 Off
- Check Box 1010156 Off
- Check Box 1010157 Off
- Check Box 10450 Off
- Check Box 10451 Off
- Check Box 10452 Off
- Text Field 326
- Check Box 1010158 Off
- Check Box 1010159 Off
- Check Box 1010160 Off
- Check Box 1010161 Off
- Check Box 1010162 Off
- Check Box 1010163 Off
- Check Box 10453 Off
- Check Box 10454 Off
- Check Box 10455 Off
- Check Box 10745 Off
- Check Box 10746 Off
- Check Box 10747 Off
- Check Box 10748 Off
- Check Box 10749 Off
- Check Box 10750 Off
- Check Box 1010167 Off
- Check Box 1010168 Off
- Check Box 1010169 Off
- Check Box 10459 Off
- Check Box 10460 Off
- Check Box 10461 Off
- Check Box 10462 Off
- Check Box 10463 Off
- Check Box 10464 Off
- Check Box 10611 Off
- Check Box 10612 Off
- Check Box 10613 Off
- Text Field 329
- Check Box 1010171 Off
- Check Box 1010172 Off
- Check Box 1010173 Off
- Check Box 1010174 Off
- Check Box 1010175 Off
- Check Box 1010176 Off
- Check Box 1010177 Off
- Check Box 1010178 Off
- Check Box 1010179 Off
- Check Box 10467 Off
- Check Box 10468 Off
- Check Box 10469 Off
- Check Box 10470 Off
- Check Box 10471 Off
- Check Box 10472 Off
- Check Box 1010180 Off
- Check Box 1010181 Off
- Check Box 1010182 Off
- Text Field 330
- Check Box 1010183 Off
- Check Box 1010184 Off
- Check Box 1010185 Off
- Check Box 10473 Off
- Check Box 10474 Off
- Check Box 10475 Off
- Check Box 10476 Off
- Check Box 10477 Off
- Check Box 10478 Off
- Check Box 1010186 Off
- Check Box 1010187 Off
- Check Box 1010188 Off
- Check Box 1010275 Off
- Check Box 1010276 Off
- Check Box 1010277 Off
- Text Field 331
- Check Box 1010189 Off
- Check Box 1010190 Off
- Check Box 1010191 Off
- Check Box 1010192 Off
- Check Box 1010193 Off
- Check Box 1010194 Off
- Check Box 1010354 Off
- Check Box 1010355 Off
- Check Box 1010356 Off
- Check Box 10479 Off
- Check Box 10480 Off
- Check Box 10481 Off
- Check Box 10482 Off
- Check Box 10483 Off
- Check Box 10484 Off
- Check Box 1010195 Off
- Check Box 1010196 Off
- Check Box 1010197 Off
- Check Box 1010278 Off
- Check Box 1010279 Off
- Check Box 1010280 Off
- Text Field 339
- Check Box 10614 Off
- Check Box 10615 Off
- Check Box 10616 Off
- Check Box 10617 Off
- Check Box 10618 Off
- Check Box 10619 Off
- Check Box 1010281 Off
- Check Box 1010282 Off
- Check Box 1010283 Off
- Text Field 340
- Check Box 1010284 Off
- Check Box 1010285 Off
- Check Box 1010286 Off
- Check Box 1010287 Off
- Check Box 1010288 Off
- Check Box 1010289 Off
- Check Box 10620 Off
- Check Box 10621 Off
- Check Box 10622 Off
- Check Box 10623 Off
- Check Box 10624 Off
- Check Box 10625 Off
- Check Box 1010290 Off
- Check Box 1010291 Off
- Check Box 1010292 Off
- Check Box 1010293 Off
- Check Box 1010294 Off
- Check Box 1010295 Off
- Check Box 10626 Off
- Check Box 10627 Off
- Check Box 10628 Off
- Check Box 10751 Off
- Check Box 10752 Off
- Check Box 10753 Off
- Text Field 342
- Check Box 1010296 Off
- Check Box 1010297 Off
- Check Box 1010298 Off
- Check Box 10632 Off
- Check Box 10633 Off
- Check Box 10634 Off
- Check Box 10635 Off
- Check Box 10636 Off
- Check Box 10637 Off
- Text Field 349
- Check Box 1010305 Off
- Check Box 1010306 Off
- Check Box 1010307 Off
- Check Box 1010308 Off
- Check Box 1010309 Off
- Check Box 10103010 Off
- Check Box 10641 Off
- Check Box 10642 Off
- Check Box 10643 Off
- Text Field 343
- Check Box 1010299 Off
- Check Box 1010300 Off
- Check Box 1010301 Off
- Check Box 1010302 Off
- Check Box 1010303 Off
- Check Box 1010304 Off
- Check Box 10638 Off
- Check Box 10639 Off
- Check Box 10640 Off
- Check Box 10644 Off
- Check Box 10645 Off
- Check Box 10646 Off
- Check Box 1010328 Off
- Check Box 10103012 Off
- Check Box 10103013 Off
- Check Box 10103014 Off
- Check Box 10103015 Off
- Check Box 10103016 Off
- Check Box 10648 Off
- Check Box 10649 Off
- Check Box 10650 Off
- Check Box 10651 Off
- Check Box 10652 Off
- Check Box 10653 Off
- Check Box 10654 Off
- Check Box 10755 Off
- Check Box 10756 Off
- Check Box 10757 Off
- Check Box 10758 Off
- Check Box 10759 Off
- Check Box 10760 Off
- Check Box 10761 Off
- Check Box 10762 Off
- Check Box 10763 Off
- Check Box 10764 Off
- Check Box 10765 Off
- Check Box 10766 Off
- Check Box 10767 Off
- Check Box 10768 Off
- Text Field 361
- Check Box 10103020 Off
- Check Box 10103021 Off
- Check Box 10103022 Off
- Text Field 362
- Text Field 371
- Check Box 10103018 Off
- Check Box 10103019 Off
- Check Box 10103059 Off
- Check Box 10655 Off
- Check Box 10656 Off
- Check Box 10657 Off
- Check Box 10658 Off
- Check Box 10673 Off
- Check Box 10754 Off
- Text Field 363
- Check Box 10103023 Off
- Check Box 10103024 Off
- Check Box 10103025 Off
- Check Box 10103026 Off
- Check Box 10103027 Off
- Check Box 10103028 Off
- Check Box 10103029 Off
- Check Box 10103030 Off
- Check Box 10103031 Off
- Check Box 10103032 Off
- Check Box 10103033 Off
- Check Box 10103034 Off
- Text Field 365
- Check Box 10103035 Off
- Check Box 10103036 Off
- Check Box 10103037 Off
- Text Field 366
- Check Box 10103038 Off
- Check Box 10103039 Off
- Check Box 10103040 Off
- Check Box 10103041 Off
- Check Box 10103042 Off
- Check Box 10103043 Off
- Text Field 367
- Check Box 10103044 Off
- Check Box 10103045 Off
- Check Box 10103046 Off
- Text Field 368
- Check Box 10103047 Off
- Check Box 10103048 Off
- Check Box 10103049 Off
- Text Field 369
- Check Box 10103050 Off
- Check Box 10103051 Off
- Check Box 10103052 Off
- Text Field 370
- Check Box 10103053 Off
- Check Box 10103054 Off
- Check Box 10103055 Off
- Check Box 10103056 Off
- Check Box 10103057 Off
- Check Box 10103058 Off
- Text Field 332
- Check Box 1010198 Off
- Check Box 1010199 Off
- Check Box 1010200 Off
- Check Box 1010201 Off
- Check Box 1010202 Off
- Check Box 1010203 Off
- Check Box 10485 Off
- Check Box 10486 Off
- Check Box 10487 Off
- Check Box 10488 Off
- Check Box 10489 Off
- Check Box 10490 Off
- Check Box 1010204 Off
- Check Box 1010205 Off
- Check Box 1010206 Off
- Check Box 10491 Off
- Check Box 10492 Off
- Check Box 10493 Off
- Check Box 10494 Off
- Check Box 10495 Off
- Check Box 10496 Off
- Check Box 1010207 Off
- Check Box 1010208 Off
- Check Box 1010209 Off
- Check Box 10497 Off
- Check Box 10498 Off
- Check Box 10499 Off
- Check Box 1010210 Off
- Check Box 1010211 Off
- Check Box 1010212 Off
- Check Box 10500 Off
- Check Box 10501 Off
- Check Box 10502 Off
- Check Box 10503 Off
- Check Box 10504 Off
- Check Box 10505 Off
- Check Box 1010213 Off
- Check Box 1010214 Off
- Check Box 1010215 Off
- Text Field 333
- Check Box 1010216 Off
- Check Box 1010217 Off
- Check Box 1010218 Off
- Check Box 1010219 Off
- Check Box 1010220 Off
- Check Box 1010221 Off
- Text Field 334
- Check Box 1010225 Off
- Check Box 1010226 Off
- Check Box 1010227 Off
- Text Field 3022
- Text Field 3021
- Check Box 1010228 Off
- Check Box 1010229 Off
- Check Box 1010230 Off
- Check Box 10512 Off
- Check Box 10513 Off
- Check Box 10514 Off
- Check Box 1010231 Off
- Check Box 1010232 Off
- Check Box 1010233 Off
- Check Box 1010310 Off
- Text Field 3044
- Check Box 1010234 Off
- Check Box 1010235 Off
- Check Box 1010236 Off
- Check Box 1010332 Off
- Check Box 1010333 Off
- Check Box 1010334 Off
- Check Box 1010335 Off
- Check Box 1010336 Off
- Check Box 1010337 Off
- Text Field 347
- Check Box 1010311 Off
- Check Box 1010312 Off
- Check Box 1010313 Off
- Check Box 1010314 Off
- Check Box 1010315 Off
- Check Box 1010316 Off
- Check Box 105010 Off
- Check Box 105011 Off
- Check Box 105012 Off
- Check Box 105013 Off
- Check Box 10659 Off
- Check Box 10660 Off
- Text Field 3023
- Check Box 10101014 Off
- Check Box 10101015 Off
- Check Box 10101016 Off
- Check Box 10515 Off
- Check Box 10516 Off
- Check Box 10517 Off
- Check Box 10518 Off
- Check Box 10519 Off
- Check Box 10520 Off
- Check Box 10101091 Off
- Check Box 10101092 Off
- Check Box 10101093 Off
- Check Box 10101094 Off
- Check Box 1010237 Off
- Check Box 1010238 Off
- Check Box 1010239 Off
- Check Box 1010240 Off
- Check Box 1010241 Off
- Check Box 10521 Off
- Check Box 10522 Off
- Check Box 10523 Off
- Check Box 1010242 Off
- Check Box 1010243 Off
- Check Box 1010244 Off
- Check Box 10524 Off
- Check Box 10525 Off
- Check Box 10526 Off
- Check Box 10101095 Off
- Check Box 10101096 Off
- Check Box 10101097 Off
- Check Box 10101098 Off
- Check Box 1010245 Off
- Check Box 1010246 Off
- Check Box 1010247 Off
- Check Box 1010248 Off
- Check Box 1010249 Off
- Text Field 3045
- Check Box 101010194 Off
- Check Box 101010195 Off
- Check Box 101010196 Off
- Check Box 10676 Off
- Check Box 10677 Off
- Check Box 10678 Off
- Check Box 10679 Off
- Check Box 10680 Off
- Check Box 10681 Off
- Check Box 101010197 Off
- Check Box 101010198 Off
- Check Box 101010199 Off
- Check Box 101010200 Off
- Check Box 101010201 Off
- Check Box 101010202 Off
- Check Box 101010203 Off
- Check Box 101010204 Off
- Check Box 101010205 Off
- Text Field 3046
- Check Box 101010209 Off
- Check Box 101010210 Off
- Check Box 101010211 Off
- Check Box 10682 Off
- Check Box 10683 Off
- Check Box 10684 Off
- Check Box 10685 Off
- Check Box 10686 Off
- Check Box 10687 Off
- Check Box 101010212 Off
- Check Box 101010213 Off
- Check Box 101010214 Off
- Check Box 1010102010 Off
- Check Box 1010102011 Off
- Check Box 1010102012 Off
- Text Field 3026
- Check Box 10536 Off
- Check Box 10537 Off
- Check Box 10538 Off
- Check Box 101010107 Off
- Check Box 101010108 Off
- Check Box 101010109 Off
- Text Field 3047
- Check Box 1010101010 Off
- Check Box 1010101011 Off
- Check Box 1010101012 Off
- Check Box 1010101013 Off
- Check Box 1010101023 Off
- Check Box 1010101024 Off
- Text Field 3048
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10
The areas of knowledge understanding and skills that you will be assessed on are called assessment objectives (AOs) There are two AOs for this course
AO1 Demonstrate knowledge and
understanding of mathematical techniques
AO2 Reason interpret and communicate
mathematically when solving problems
AO1 Demonstrate knowledge and understanding of mathematical techniquesYou need to show that you can recall and apply mathematical knowledge terminology and definitions to carry out single or multi-step solutions in mathematical and everyday situations
Section 3 What skills will be assessed
This means that you need to show that you can
bull organise process and present information accurately in written tabular graphical and diagrammatic forms
bull use and interpret mathematical notation correctly
bull perform calculations and procedures by suitable methods including using a calculator
bull understand systems of measurement in everyday use and make use of these
bull estimate approximate and work to degrees of accuracy appropriate to the context and convert between equivalent numerical forms
bull use geometrical instruments to measure and to draw to an acceptable degree of accuracy
bull recognise and use spatial relationships in two and three dimensions
AO1 is assessed in all papers
Use tables graphs and diagrams
An example of degress of accuracy include significant figures or decimal places
An example of converting between equivalent numerical forms include between fractions decimals and percentages or between normal numbers and standard form
eg a pair of compasses a protractor and a ruler
11
AO2 Reason interpret and communicate mathematically when solving problemsYou need to demonstrate that you can analyse a problem select a suitable strategy and apply appropriate techniques to obtain a solution
This means that you need to show that you can
bull make logical deductions make inferences and draw conclusions from given mathematical data
bull recognise patterns and structures in a variety of situations and form generalisations
bull present arguments and chains of reasoning in a logical and structured way
bull interprete and communicate information accurately and change from one form of presentation to another
bull assesses the validity of an argument and critically evaluate a given way of presenting information
bull solve unstructured problems by putting them into a structured form involving a series of processes
bull apply combinations of mathematical skills and techniques using connections between different areas of mathematics in problem solving
bull interprete results in the context of a given problem and evaluate the methods used and solutions obtained
AO2 is assessed in all papers
Recognise and extent patterns
Take information and organise it to answer a problem
12
Section 4 Command wordsA command word is the part of the question that tells you what you need to do with your knowledge For example you might need to describe something explain something argue a point of view or list what you know The table below includes command words used in the assessment for this syllabus The use of the command word(s) within an question will relate to the context
Cambridge IGCSE Mathematics 0580 syllabus for 2020 2021 and 2022 Details of the assessment
37wwwcambridgeinternationalorgigcseBack to contents page
Command wordsThe table below includes command words used in the assessment for this syllabus The use of the command word will relate to the subject context
Command word What it means
Calculate work out from given facts figures or information generally using a calculator
Construct make an accurate drawing
Describe state the points of a topicgive characteristics and main features
Determine establish with certainty
Explain set out purposes or reasons make the relationships between things evident provide why andor how and support with relevant evidence
Give produce an answer from a given source or recallmemory
Plot mark point(s) on a graph
Show (that) provide structured evidence that leads to a given result
Sketch make a simple freehand drawing showing the key features
Work out calculate from given facts figures or information with or without the use of a calculator
Write give an answer in a specific form
Write down give an answer without significant working
The question below is taken from Paper 4 and illustrates the use of two command words
The command words lsquoWrite downrsquo indicates that you do not need to show your working and the answer should just be written down The mark allocation [1] also supports this
The command words lsquoShow thatrsquo indicate that you need to provide evidence in the form of a clear mathematical explanation to demonstrate that you know how to obtain the given result In other words you need to show a method that leads to the result
The answer space in this case does not contain a dotted answer line as there is no single lsquoanswerrsquo to be found Your working that leads to the given result should be written in the blank working space
13
This section takes you through an example question and learner response from one of the 2020 specimen papers for this course It will help you to identify the command words and other key instructions within questions and to understand what is required in your response
This section is structured as follows
QuestionThe command words and instructions in the question have
been highlighted and explained This should help you to understand clearly what is required by the question
Mark schemeThis tells you as clearly as possible what an examiner expects
from an answer to award marks
Example candidate responseThis an exemplar answer written in the style of
a high level candidate
How the answer could have been improvedThis summarises what could be done to gain more marks
All information and advice in this section is specific to the example question and response being demonstrated It should give you an idea of how your responses might be viewed by an examiner but it is not a list of what to do in all questions In your own examination you will need to pay careful attention to what each question is asking you to do
Common mistakesThis will help you to avoid common mistakes made by
candidates So often candidates lose marks in their exams because they misread or misinterpret the questions
Section 5 Example candidate response
14
QuestionThe question used in this example is from Specimen Paper 3 (Core) It represents the type of structured question you will see in both Paper 3 (Core) and Paper 4 (Extended) A structured question means that it is broken into several parts Often later parts will depend on your answers to earlier parts
This means that you cannot find the answer by
measuring the diagramWork out indicates that the answer should be calculated from the given information so measurement will not score marks
The allocation of 1 mark indicates that the answer can be obtained with minimum working
Give reasons for your answer indicates that your answer should be supported with reasons using the correct mathematical terminology You must justify your answer
Use trigonometry to calculate indicates that you should use this method with the given information to find the answer and that a calculator is needed to solve the problem If you did not use trigonometry you would not be awarded any marks
15
Show that indicates the answer is given and you need to write down all of the steps in a method that leads to the given answer You need to provide evidence that you understand and know how the answer is reached
Work out indicates that you should calculate the answer from the given information The mark allocation of 4 marks suggests that you will need to include several steps of working in order to get to the answer
Learner Guide
16
Answer Mark Notes(a)(i) 35 1 This is the only acceptable answer for this part of the question
(a)(ii) 74 1 This is the only acceptable answer for this part of the question
(b) 43deg and correct mathematical reasons
3 Two marks are awarded for the final answer of 43deg
The third mark is awarded for a fully correct reason for example angles on a straight line add up to 180deg and angles in a triangle add up to 180deg There are other correct reasons that could be also be used
If 43deg is not obtained one method mark can be awarded if the following calculation is seen in the working
180 ndash 128 or 128 ndash 85
(c) 322 or 3223hellip 2 This is the only acceptable answer for this part of the question
The answer has to be rounded correct to three significant figures or can be given with more figures in the answer
Those that did not get this answer can score one method mark for showing the following in their working
sin = 8 divide 15
(d)(i) 2 2300 225+2 This does not have to be shown in one step as long as the method shown is the same as this overall Those that do not
show this can have one method mark for showing the following in their working
300deg + 225deg
(d)(ii) 15 35 4 The answer 3 35pm is also acceptable for 4 marks
If the correct answer is not found one method mark is available for showing 375 divide 450 in their working and a second method mark can be awarded for sight of them multiplying their answer to this by 60 to change it to hours A third method mark can be awarded for adding their answer in hours to 14 45 ndash this shows the correct method so only one mark is lost for an incorrect final answers
Mark schemeYour examination papers will be marked and the overall number of marks for each paper will be recorded Your marks across all papers will then be converted to a grade
Final answer This value is what the examiner expects to see The answer has to be exactly as given in the mark scheme unless there are acceptable alternatives The mark scheme will always make it clear if there are acceptable alternative answers
Method marks Sometimes method marks are awarded for lines of working as well as for the final answer This means that you could get the final answer incorrect but still get some marks if you include the correct working The mark scheme does not include all possible methods so if you use a method not included in the mark scheme but it is accurate and relevant then the examiner will still award marks for the appropriate parts of the working ndash unless the questions asks you to use a specific method
example of a final answer
example of a method mark
17
Example candidate responseNow letrsquos look at the sample candidatersquos response to question 8 The examiners comments are in the orange boxes The candidate was awarded 8 marks out of 13
180 ndash 74 + 71 = 177
177
74
0 out of 1
The candidates working suggests they understand that the angle sum of a triangle is 180deg but they did not include brackets around 74 + 71 The answer 177deg is not sensible for this question
1 out of 1
The candidate recognises that there are parallel lines and that angle y is a corresponding angle to angle 74deg
180 ndash 128 = 52 180 ndash 85 ndash 52 = 43
43 angles on a straight line add up to 180deg
2 out of 3
The candidate has given a correct answer for w and shown correct working in two steps They have given a correct reason for 52deg using correct mathematical languge But they have not provided a reason to explain the angle 43deg They lose a mark for not also stating angle sum of a triangle is 180deg
sin p = 8 divide 15 = 053
p = sinndash1 (053)
p = 32005 320
1 out of 2
The candidate has correctly used trigonometry in their method They are awarded one method mark for the first line of working However they have rounded 05333333hellip (the result of 8 divide 15) to 052 and then calculated the inverse sin of 052 rather than 05333333 This has resulted in an inaccurate final answer This is called lsquopremature approximationrsquo and it is a very common error to make
18
AB2 = 3002 + 2252
= 140625
AB = 375
1 out of 2
The candidate has recognised the right-angled triangle and correctly used Pythagorasrsquo theorem in the first line of working However they have missed out an important step by not showing that you need to take the square root of 140625 to get 375 As this is a lsquoshow thatrsquo question and they missed a key step in the method they cannot be awarded full marks as the complete working is not shown One method mark is earned for the first line
T = = = 08333333hellip
08333333 hours = 08333333 times 60 minutes = 50 minutes
arrives at 14 45 + 50 mins = 3 35
DS
375450
3 35
3 out of 4
The candidate has found the time by correctly dividing the distance by the speed and recognised that this is in hours When converting the answer to a decimal they have not rounded the decimal but left its full value on the calculator to get 50 mins which is the correct approach Unfortunately after converting the time from 24 hour clock to 12 hour clock they did not include lsquopmrsquo to indicate that the time is in the afternoon and so the final answer is not quite right So 3 marks are awarded for all of a correct method but a mark is lost due to the accuracy of the final answer
19
How the answer could have been improvedThis answer could have been improved by
bull In part (a)(i) the answer of 177deg was not sensible given the diagram in the question If the candidate had checked their answer for sense they would have realised they had made a mistake It is always a good idea to check that your answer seems sensible before you move on to another question
bull In part (b) the candidate did all the correct steps but failed to provide both reasons There were two steps to the method which should have indicated to the candidate that there were two steps to justify and therefore two reasons should have been provided The mark allocation for the question [3] also indicates that more than one reason would be required one mark for the value of 43deg leaving two marks one mark for each of two reasons The candidate should have read the question carefully and again checked their response seemed reasonable
bull In part (c) the candidate rounded an intermediate answer which affected the accuracy of the final answer This caused them to lose a mark despite using a correct method You should only ever round the final answer do not round intermediate values If you can store the intermediate values in your calculator and so that you can use the full value in your calcuations If youre not able to do this and you have to round the intermediate values do not round them to less than three significant figures
bull In part (d)(i) the candidate missed out a step in the method As this was a show that question they needed to show all the steps in the method Its important to show all steps even if they seem obvious
bull In part (d)(ii) the candidate made a silly error by not stating that the time was pm When working with time answers are accepted in either 24 clock or 12 clock time but if you give your answer in the 12 hour clock then it must include am or pm as well
Common mistakesThere were a number of common mistakes made by other candidates on this question
bull Accuracy of answers
In parts (c) and (d)(ii) a common error was premature rounding ndash rounding intermediate values in the method before the final answer which resulted in their final answer not being accurate Other candidates gave the final answer to less than three significant figures ignoring the instruction on the front of the paper to round to three significant figures
bull Using incorrect terminology when giving reasons
In part (b) the most common error was to not give full reasons to support the answer Another common error was to provide a reason that did not use the correct mathematical language such as lsquoThey add up to 180degrsquo and lsquoIt is a straight linersquo which could not be awarded marks
bull Lack of knowledge
In part (c) a number of candidates had limited knowledge of trigonometry and did not choose the correct trig ratio which was the sine ratio This is why good revision is important
bull Not checking answers
In part (a)(i) even though the diagram is drawn NOT TO SCALE it is possible to see that the angle is an acute angle and should therefore not be bigger than 90deg This should alert candidate that if their answer is over 90deg it is not a sensible answer and they should go back and check their working
20
bull Inefficient method shown
In part (c) the lsquoShow thatrsquo question a number of candidates omitted an important step from the method this is often common in lsquoShow thatrsquo questions where every step must be shown no matter how obvious them seem
General adviceIn order to do your best when answering a mathematics question make sure you
bull revise all of the topics for the syllabus you are studying before the exam
bull understand what all the key terms and command words in the question mean
bull read the questions carefully and consider what you need to do before you do it
bull only round the final answer not intermediate values
bull show all steps in your working and show them clearly
bull round to the correct degree of accuracy
bull use the correct mathematical terminology
bull check your answers seem reasonable given the context or details of the question
21
It is important that you plan your revision in plenty of time for the examinations and that you develop a revision technique that works for you The advice in this section will help you revise and prepare for the examinations It is divided into general advice for all papers
Use the tick boxes to keep a record of what you have done what you plan to do or what you understand
For more advice on revision see the Cambridge Learner Revision Guide on our website
Section 6 Revision
Find out when the examinations are and plan your revision so you have time to revise Create a revision timetable and divide it into sections to cover each topic
Spend most of your time focussing on specific skills knowledge or issues that you have found more difficult when practicing them either during revision or earlier in the course
Write a summary of all the key information for a topic ndash use the checklists at the end of this section
Know the meaning of the command words used in questions and how to apply them to the information given Look at past examination papers and highlight the command words and check what they mean
Make revision notes and work on practice questions Reading alone does not work you need to be active and practice your maths
Work for shorter periods then have a break Revise small sections of the syllabus at a time but do this regularly
Test yourself by trying out some past exam questions Use the mark schemes to assess yourself and to be familiar with how marks are awarded for different questions
Be organised in advance with your notes texts exercise books revision guides and revision websites so you do not waste valuable revision time trying to find things
Make notes of key mathematical words that you should use in questions that ask you to lsquodescribersquo or give lsquogeometrical reasons forrsquo eg in describing transformations or giving reasons in circle theorem questions Look at the mark schemes for these types of questions from past papers to see how marks are awarded
Make sure you have all of the correct mathematical equipment ready for the exam particularly your calculator Make sure you are familiar with the all of the important functions on your calculator
Practice the areas you can do well not just those that you find more difficult
Take breaks and do things to relax when you take your breaks this will help you to be more productive when you are revising
Before the examination
22
During the examination
Plan your time according to the marks for each question For example a question worth one mark requires less time than a question one worth 4 marks If a question has several parts then the parts with more marks will need more time
Read each question very carefully
Identify the command words ndash you could underline or highlight them
Identify the other key words and information and perhaps underline them too particularly where
questions require reasoning or problem solving
Read the questions careully and make you have answered the question that is being asked
Show your working this is particularly important for questions where you are asked to lsquoshow that helliprsquo
Set your working out clearly so that it is easy to follow this makes it easier to keep track of what you have done and makes checking back through your work easier and it makes it easier for the examiner to mark your work try to write it in a logical order in the answer space
Write answers clearly if you want to change an answer then you should cross the answer out and write a replacement if your answer is on the answer line cross it out and write the replacement answer above it do not try to change numbers on the answer line as this can lead to unclear figures
Check your working and answers to avoid errors
Give your answer to the appropriate level of accuracy either the accuracy indicated in the question or the accuracy given on the front of the paper
Avoid rounding intermediate values part way through your calculation only round the final answer
Check that the answer that you have given is sensible and realistic for what is being asked
Use a pencil when drawing diagrams or completing graphs this means that you can change your answer more easily if you have made a mistake
Take care when reading scales
If you are asked for reasons for your answer then use the correct mathematical terms
Use the mark allocation given with the questionsparts of questions to try to judge how much work is needed to answer each part
23
Top tips for revision of Cambridge IGCSE Mathematics1 Summarise recall and applyMake sure that you can recall and apply the key information and mathematical techniques on each topic that you need for the exam
i Write a summary of the key information of a topicii Collect together some questions that test the knowledge and skills of this topic Ask your teacher for practice
questions or suitable past examination questions or use practice books or textbooksiii Test your recall by covering over the summary and trying to remember the details or use the summary as part of
the lsquoTeach the topicrsquo (Tip 3) or lsquoQuestion and answer cardsrsquo (Tip 4) activities iv After you have spent some time revising and practising the knowledge and skills answer the questions that you
collected together on the topic You might do this later on the same day as revising or a few days later Answer as many questions as you can in order to practise applying your knowledge
v Try creating your own questions by adapting existing ones and use these for practice when you return to a topic
On graph questions straight lines should be ruled and curves should be drawn freehand with a smooth curve
Donrsquot spend too long on any one part of a question If you are really stuck on a question then move on and come back to the question later if you have time As a rough guide each mark on the paper should take about one minute
2 Concept mapsConcept maps are a great way to revise the links between different factors or to explore a larger topic They can also be used to collect together your ideas
i Use a blank sheet of paper and turn it on its side (landscape)ii Put the topic title in the middle of the page and build the concept map outwards using lines called lsquobranchesrsquo
ndash The first branches are from the central topic to sub-topics draw these as thick lines
ndash Add new branches from the sub-topics to include more detail draw these as thinner lines
ndash Add even more detail to a point by adding more branches
This creates a hierarchy of information from lsquooverviewrsquo (the thick branches) to lsquofine detailrsquo (thinnest branches)
iii Write single key words or phrases along a branch and add drawings for visual impactiv Use different colours highlighter pens symbols and arrows to highlight key facts or issuesIt is a good idea to use a large piece of plain A3 (or larger) paper and lots of coloured pens
24
3 Teach the topicThis is a very simple but effective technique that focusses on knowledge recall It tests the brain and rehearses the information you need to know for a certain topic and so will help your revision
i Create some topic cards with key bullet points of information on Leave space for ticksii Give these to your parents family or friends for exampleiii Give yourself 10 minutes maximum to teach your audience the main points of the topic You could use a mini-
whiteboard or flip chart to helpiv Your audience tick off all the points you mention in your presentation and give you a final scoreThe brain loves competition so if you do not score full marks you can try again the next day or compete against friends This system of repeat and rehearsal is very effective especially with more complex topics and doesnt take much preparation
4 Question and answer (QampA) cardsThis is very similar to Teach the topic but less formal and less public for those who dislike performing in front of others It tests knowledge recall and rehearses the information you need to know for a certain topic
i Pick a topic and create two sets of cards question cards and answer cards You might find it helpful to make the question cards a different size or use different coloured card for answers
ii Make sure you have the topic or something appropriate depending on what you are focusing on as a heading on each card The questions should test your knowledge and understanding of key areas of the course
iii A friend or family member uses the cards to test you in short 5 or 10 minute periods at any time during the dayiv You could also do this alone by reading the questions to yourself giving the answer and then checking the
correct answer cardv This game can be adapted by using the cards to find matching pairs turn all cards face down across the space
in front of you Turn over two cards leaving them where they are If they match (one is a question card and the other is the corresponding answer card) pick up the pair and put them to one side If they dont match try to remember where they are and what is on each card then turn them back over Turn over two other cards Continue until you have matched all pairs
5 Question paper and mark schemesLooking at past question papers and the mark scheme helps you to familiarise yourself with what to expect and what the standard is
i Ask your teacher for past paper questions with mark schemes for the course ndash ask your teacher for help to make sure you are answering the correct questions and to simplify the mark scheme
ii Look at the revision checklist and identify which topic a given question relates to ndash you might need to ask your teacher to help you do this
iii Once you have finished revising a topic or unit time yourself answering some appropriate exam questions Check the mark schemes to see how well you would have scored or give the answers to your teacher to check
iv Add details or notes to the mark scheme where you missed out on marks in your original answers using a different coloured pen Use these notes when you revise and try the question again later
You can find plenty of past exam papers and mark schemes on the Cambridge International public website
httpwwwcambridgeinternationalorgprogrammes-and-qualificationscambridge-igcse-mathematics-0580past-papers
25
Other useful revision advice for Cambridge IGCSE Mathematics bull Before the exam make sure that you are familiar with your calculator and confident in using it
bull Look at the Example Candidate Response earlier in this guide Can you identify the strengths of the response andwhere they have made mistakes or lost marks
bull When you are attempting a past paper (or questions from a past paper) complete it without referring to yournotes so that you get a true idea of your strengths and weaknesses Then go back through the paper using yournotes and a different coloured pen to make corrections and changes After you have done as much as you can onthe paper mark it using the mark scheme Take notes of any points that you lost marks on
bull Donrsquot just revise the topics that you enjoy and are confident in If you identify an area that you are weaker inthen try to revisit the topic by reviewing your notes and doing some practice questions then use exam questionsto check whether you now understand
bull Return to topics later in your revision to check that you still remember and understand the topic and to help toensure that you recall more of the material when you get to the examination
Revision checklists for Cambridge IGCSE MathematicsThe tables on the following pages can be used as a revision checklist They do not contain all the detailed knowledge you need to know just an overview For more detail see the syllabus and talk to your teacher
You can use the tick boxes in the checklists to show when you have revised and are happy that you do not need to return to it Tick the lsquoRrsquo lsquoArsquo and lsquoGrsquo column to record your progress as follows
bull R = RED means you are really unsure and lack confidence in that area you might want to focus your revisionhere and possibly talk to your teacher for help
bull A = AMBER means you are reasonably confident in a topic but need some extra practicebull G = GREEN means you are very confident in a topic
As your revision progresses you can concentrate on the RED and AMBER topics in order to turn them into GREEN topics You might find it helpful to highlight each topic in red orange or green to help you prioritise
You can use the lsquoCommentsrsquo column to
bull add more information about the details for each pointbull include a reference to a useful resourcebull include a list of formulae or notationbull add learning aids such as rhymes poems or word playbull highlight areas of difficulty or things that you need to talk to your teacher about
There is a set of checklist for the Core syllabus and a different set for the Extended syllabus
Learner Guide
26
Core syllabus contentCore Number
Category You should be able to R A G CommentsNumber Identify and use
bull natural numbers
bull integers (positive negative and zero)
bull prime numbers
bull write a number as a product of its prime factors
bull square numbers and cube numbers
bull common factors and highest common factor of two numbers
bull common multiples and lowest common multiple of two numbers
bull rational numbers
bull irrational numbers (eg π radic2 )
bull real numbers
bull reciprocals
Learner Guide
27
Core Number
Question type You should be able to R A G CommentsSets and Venn diagrams
Understand notation of Venn diagrams
Definition of sets
eg A = xx is a natural number
B = abchellip
Notation
Number of elements in set A n(A)
Universal set
Union of A and B A cup B
Intersection of A and B A cap B
Squares square roots cubes and cube roots
Calculate
bull squares and cubes of numbers
bull square roots and cube roots of numbers
Learner Guide
28
Core Number
Question type You should be able to R A G CommentsDirected numbers
Use directed numbers in practical situations for example temperature changes
Fractions decimals and percentages
Use the language and notation of simple vulgar and decimal fractions and percentages
Recognise equivalent fractions decimals and percentages
Convert between fractions decimals and percentages
Ordering Order quantities by magnitude and demonstrate familiarity with the symbols = ne gt lt ⩾ ⩽
Indices and standard form (links to Algebraic manipulation)
Evaluate indices eg 25 5ndash2 1000 64frac12 8ndash23
Use the rules of indices for
bull multiplication of indices eg 4ndash3 times 45
bull division of indices eg 57 divide 53
bull index numbers raised to an index eg (23)2 (43)2
Use the standard form A times 10n where n is a positive or negative integer and 1 ⩽ A lt 10
bull convert numbers into and out of standard form
bull calculate with numbers in standard form
Learner Guide
29
Core Number
Question type You should be able to R A G CommentsFour rules
( + ndash times divide )
Use the four rules for calculations with
bull whole numbers
bull decimals
bull vulgar and mixed fractions
bull correct ordering of operations (BIDMAS) and use of bracketsEstimates Make estimates of numbers quantities and lengths
Give approximations to a specified number of
bull significant figures
bull decimal places
Round off answers to reasonable accuracy in the context of a given problem
Bounds Give upper and lower bounds for data given to a specified accuracy eg measured lengths
Ratio proportion rate
Understand ratio
Divide a quantity in a given ratio
Understand direct and inverse proportion
Use scales in practical situations
Use common measures of rate (formulae for other rates eg density and pressure will be given in the question)
Calculate average speed
Learner Guide
30
Core Number
Question type You should be able to R A G CommentsPercentages Calculate a percentage of a quantity
Express one quantity as a percentage of another quantity
Calculate percentage increase or decrease
Use of an electronic calculator
Use a calculator efficiently
Check accuracy of calculations
Time Calculate times in terms of the 24-hour and 12-hour clock
Read
bull clocks
bull dials
bull timetables
Money Calculate using money
Convert from one currency to another
Learner Guide
31
Core Number
Question type You should be able to R A G CommentsPersonal and small business finance
Use given data to solve problems on
bull earnings
bull simple interest
bull compound interest (you will need to know the compound interest formula)
bull discount
bull profit and loss
Extract data from tables and charts
Learner Guide
32
Core Algebra and graphs
Question type You should be able to R A G CommentsBasic algebra Use letters to express generalised numbers
Express basic arithmetic processes algebraically
Substitute numbers in formulae
Construct simple expressions and set up simple equations
Rearrange simple formulae
Algebraic manipulation
Manipulate directed numbers
Use brackets
bull expand a single bracket eg 3x(2x ndash4y)
bull expand a pair of brackets eg (x + 3) (x ndash 7)
Extract common factors eg factorise 9x2 + 15xy
Rules of indices Use and interpret positive negative and zero indices
Use the rules of indices eg to simplify algebra such as
bull 3x4 times 5x
bull 10x3 divide 2x2
bull (x6)2
Learner Guide
33
Core Algebra and graphs
Question type You should be able to R A G CommentsEquations and inequalities
Derive and solve simple linear equations in one unknown
Derive and solve simultaneous linear equations in two unknowns
Number sequences
(links to Squares square roots cubes and cube roots)
Continue a number sequence
Recognise patterns in sequences
Recognise relationships between difference sequences
Find the nth term of sequences for
bull liner sequences
bull simple quadratic sequences
bull cubic sequences
Practical graphs
(links to Mensuration)
Interpret and use graphs in practical situations including
bull travel graphs
bull conversion graphs
Draw graphs from given data
Learner Guide
34
Core Algebra and graphs
Question type You should be able to R A G CommentsGraphs of functions
(links to Co-ordinate geometry)
Construct tables of values for functions of the form
bull ax + b (linear)
bull plusmn x2 + ax + b (quadratic)
bull (x ne 0) (reciprocal)
where a and b are integer constants
Draw and interpret such graphs
Solve linear and quadratic equations approximately by graphical methods
Recognise and sketch the graphs of linear and quadratic functions
ax
Learner Guide
35
Core Co-ordinate geometry
Question type You should be able to R A G CommentsCo-ordinates Work with co-ordinates in two dimensions
Gradients Find the gradient of a straight line graph
Equation of straight line
Interpret and obtain the equation of a straight line graph in the form y = mx + c where the graph is given
Parallel lines Determine the equation of a straight line parallel to a given line eg find the equation of a line parallel to y = 4x ndash 1 that passes through (0 ndash3)
Learner Guide
36
Core Geometry
Question type You should be able to R A G CommentsGeometrical language
Use and interpret the geometrical terms
bull point
bull line
bull parallel
bull perpendicular
bull bearing
bull right angle acute obtuse and reflex angles
bull similar
bull congruent
Use and interpret the vocabulary of
bull triangles right-angled scalene isosceles equilateral
bull quadrilaterals
bull circles
bull polygons
bull simple solid figures including nets
Learner Guide
37
Core Geometry
Question type You should be able to R A G CommentsGeometrical constructions
Measure and draw lines and angles
Construct a triangle given the three sides using a ruler and a pair of compasses only
Scale drawings Read and make scale drawings
Similar figures Calculate lengths of similar figures
Congruent Recognise congruent shapes
Symmetry Recognise symmetry properties for triangles quadrilaterals and circles
Recognise line symmetry in two dimensions
Recognise and find the order of rotational symmetry in two dimensions
Learner Guide
38
Core Geometry
Question type You should be able to R A G CommentsAngle properties Calculate unknown angles explaining the properties that you
are using in geometrical language for angles
bull angles at a point
bull angles on a straight line and intersecting straight lines
bull angles within parallel lines
bull angles in triangles
bull angles in quadrilaterals
bull angles in regular polygons
bull angle in a semi-circle
bull angle between tangent and radius of a circle
Learner Guide
39
Core Mensuration
Question type You should be able to R A G CommentsMeasures bull Use current units of
bull mass
bull length
bull area
bull volume
bull capacity
Express quantities in terms of smaller or larger units including units of area and volume
Convert between units including units of area and volume
Perimiter Carry out calculations involving
bull perimeter and area of a rectangle
bull perimeter and area of a triangle
bull perimeter and area of parallelogram
bull perimeter and area of a trapezium
bull perimeter and area of shapes made by combining
bull rectangles triangles parallelograms andor trapeziums
Learner Guide
40
Core Mensuration
Question type You should be able to R A G CommentsCircles Carry out calculations involving circumference and area of a
circle
Solve simple problems involving the arc length and sector area of a circle where the sector angle is a factor of 360deg
Surface area and volume
Carry out calculations involving
bull surface area and volume of a cuboid prism and cylinder (no formulae will be given for these shapes)
bull surface area and volume of a sphere pyramid and cone (formulae will be given for these shapes)
Areas and volumes of compound shapes
Carry out calculations involving the areas and volumes of compound shapes made from combinations of the shapes in Perimeter or Surface area and volume
Learner Guide
41
Core Trigonometry
Question type You should be able to R A G CommentsBearings Use and interpret three-figure bearings measured clockwise
from the North ie 000degndash360degTrigonometry Find unknown sides andor angles in right-angled triangles by
applying
bull Pythagorasrsquo theorem
bull sine cosine and tangent ratios for acute angles in right-angled triangles
Learner Guide
42
Core Vectors and transformations
Question type You should be able to R A G CommentsVectors in two dimensions (links to Trigonometry)
Describe a translation by using a vector represented by
AB or a
Add and subtract vectors
Multiply a vector by a scalar
Transformations Reflect simple shapes in horizontal or vertical lines
Rotate simple shapes through multiples of 90deg about
bull the origin
bull their vertices
bull the midpoints of their sides
Construct translations of simple shapes
Construct enlargements of simple shapes (positive and fractional scale factors)
Recognise and describe using the correct language
bull reflections
bull rotations
bull translations
bull enlargements (positive and fractional scale factors)
( )x
y
Learner Guide
43
Core Probability
Question type You should be able to R A G CommentsSingle events Calculate the probability of a single event as a fraction decimal
or percentage (not a ratio)Probability scale Understand and use the probability scale from 0 to 1
Sum to 1 Understand that the probability of an event occurring = 1 ndash the probability of the event not occurring
Relative frequency
Understand relative frequency as an estimate of probability
Work out expected frequencies using relative frequencyCombined events Calculate the probability of simple combined events using
bull tree diagrams
bull possibility diagrams (points on a grid)
bull Venn diagrams (2 sets only)
Learner Guide
44
Core Statistics
Question type What I need to do R A G CommentsClassify Collect classify and tabulate data
Interpret and compare
Read interpret and draw simple inferences from tables and statistical diagrams
Compare sets of data using
bull tables
bull graphs
bull statistical measures
Be aware of restrictions when making conclusions from data
Charts Construct and use
bull bar charts
bull pie charts
bull pictograms
bull stem-and-leaf diagrams
bull frequency distributions
bull histograms with equal intervals
bull scatter diagrams
Learner Guide
45
Question type What I need to do R A G CommentsAverages Calculate for individual and discrete data
bull mean
bull median
bull mode
bull range
and distinguish between their useCorrelation Understand what is meant by positive negative and zero
correlation with reference to a scatter diagramLine of best fit Draw interpret and use a ruled line of best fit by eye
Learner Guide
46
Extended syllabus content (includes required Core content)Extended Number
Question type You should be able to R A G CommentsNumber Identify and use
bull natural numbers
bull integers (positive negative and zero)
bull prime numbers
bull write a number as a product of its prime factors
bull square and cube numbers
bull common factors and highest common factor of two or more numbers
bull common multiples and lowest common multiple of two or more numbers
bull rational numbers
bull irrational numbers (eg π radic2 )
bull real numbers
bull reciprocals
Learner Guide
47
Extended Number
Question type You should be able to R A G CommentsSet notation and language
Use language notation and Venn diagrams to describe sets and represent relationships between sets as follows
Definition of sets egA = x x is a natural number
B = (xy) y = mx + c
C = x a ⩽ x ⩽ b
D = a b c hellip
Notation egnumber of elements in set A n(A)
lsquois an element ofrsquo isin
lsquois not an element ofrsquo notin
complement of set A
the empty set empty
the universal set
A is a subset of B A sube B
A is a proper subset of B A sub B
A is not a subset of B A ⊈ B
A is not a proper subset of B A nsub B
union of A and B A cup B
intersection of A and B A cap B
Learner Guide
48
Extended Number
Question type You should be able to R A G CommentsSquares square roots cubes and cube roots
Calculatebull squares of numbers
bull square roots of numbers
bull cubes of numbers
bull cube roots of numbers
bull other powers and roots of numbers
Directed numbers
Use directed numbers in practical situations for example temperature changes
Fractions decimals and percentages
Use the language and notation of simple vulgar and decimal fractions and percentages in appropriate contexts
Recognise equivalent fractions decimals and percentages
Convert between fractions decimals and percentages
Convert recurring decimals to fractions
Ordering Order quantities by magnitude and demonstrate familiarity with the symbols = ne gt lt ⩾ ⩽
Learner Guide
49
Extended Number
Question type You should be able to R A G CommentsIndices and standard form (links to Algebraic manipulation)
Evaluate indices including fractional negative and zero
eg 25 5ndash2 1000 10012 8ndash23
Use the rules of indices forbull multiplication of indices eg 43 times 45
bull division of indices eg 57 divide 53
bull index numbers raised to an index eg (43)2
Use the standard form A times 10n where n is a positive or negative integer and 1 ⩽ A lt 10bull convert into and out of standard form
bull calculate with numbers in standard form
Four rules
( + ndash times divide )
Use the four rules for calculations withbull whole numbers
bull decimals
bull vulgar and mixed fractions
bull correct ordering of operations (BIDMAS) and use of brackets
Learner Guide
50
Extended Number
Question type You should be able to R A G CommentsEstimates Make estimates of numbers quantities and lengths
Give approximations to a specified number of
bull significant figures
bull decimal places
Round off answers to reasonable accuracy in the context of a given problem
Bounds Give upper and lower bounds for data given to a specified accuracy eg measured lengths
Obtain appropriate upper and lower bounds to solutions of simple problems given to a specified accuracy eg the lower and upper bounds for the area of a rectangle
Ratio proportion rate
(links to Direct and inverse proportion)
Understand ratio
Divide quantities in a given ratio
Increase and decrease a quantity by a given ratio
Understand numerical problems involving direct and inverse proportion
Use ratio and scales in practical situations
Use common measures of rate (formulae for other rates eg density and pressure will be given in the question)
Calculate average speed
Learner Guide
51
Extended Number
Question type What I need to do R A G CommentsPercentages Calculate a percentage of a quantity
Express one quantity as a percentage of another quantity
Calculate percentage increase or decrease
Calculate reverse percentages eg finding the cost price given the selling price and the percentage profit
Use of an electronic calculator
Use a calculator efficiently
Check accuracy of calculations
Time Calculate times in terms of the 24-hour and 12-hour clock
Read clocks dials and timetables
Money Calculate using money
Convert from one currency to another
Learner Guide
52
Extended Number
Question type You should be able to R A G CommentsPersonal and small business finance
Use given data to solve problems on
bull earnings
bull simple interest
bull compound interest
ndash you must know the compound interest formula
bull discount
bull profit and loss
Extract data from tables and charts
Exponential growth and decay
Use exponential growth and decay in population and finance eg depreciation bacteria growth
Learner Guide
53
Extended Algebra and graphs
Question type You should be able to R A G CommentsBasic algebra Use letters to express generalised numbers
Express basic arithmetic processes algebraically
Substitute numbers in complicated formulae
Construct and rearrange complicated formulae eg where the subject appears twice
Algebraic manipulation
Manipulate directed numbers
Use bracketsbull expand a single bracket eg expand 3x(2x ndash 4y)
bull expand a pair of brackets eg (x ndash 4)(x + 7)
bull expand products of more than two brackets eg (x + 4)(x ndash 7)(2x + 1)
Extract common factors eg factorise 9x2 + 15xy
Factorise expressions of the formbull ax + bx + kay + kby
bull asup2xsup2 ndash bsup2ysup2
bull asup2 + 2ab + bsup2
bull axsup2 + bx + c
Learner Guide
54
Extended Algebra and graphs
Question type You should be able to R A G CommentsAlgebraic fractions
Manipulate algebraic fractions eg
bull
bull
bull
bull
bull
Factorise and simplify algebraic fractions such as
Rules of indices Use and interpret positive negative and zero indices
Use and interpret fractional indices eg solve 32x = 2
Use the rules of indices to simplify algebra eg
x3 + x ndash 4
22x3 +
3(x ndash 5)2
3a4 +
5ab3
3a4 divide
9a10
1x ndash 2 +
2x ndash 3
x2 ndash 2xx2 ndash 5x + 6
3xndash4 times23
x12
32x5( )
3
2xndash2divide25
x12
Learner Guide
55
Extended Algebra and graphs
Question type You should be able to R A G CommentsEquations and inequalities
bull Derive and solve simple linear equations in one unknown
bull Derive and solve simultaneous linear equations in two unknowns
bull Derive and solve simultaneous equations involving one linear and one quadratic
Solve quadratic equations by
bull factorisation
bull completing the square
bull using the formula
Derive and solve simple linear inequalities including representing solutions on a number line
Linear programming
Represent inequalities graphically including using the conventions of
bull broken lines for strict inequalities
bull shading unwanted regions
Solve simple linear programming problems using graphical representations of inequalities
Learner Guide
56
Extended Algebra and graphs
Question type You should be able to R A G CommentsNumber sequences (links to Squares square roots cubes and cube roots)
Continue a number sequence
Recognise patterns in sequences
Recognise relationships between different sequences
Find the nth term of sequences of
bull linear sequences
bull quadratic sequences
bull cubic sequences
bull exponential sequences
and simple combinations of these
Direct and inverse proportion (links to Ratio proportion rate)
Express direct proportion algebraically
Express inverse proportion algebraically
Use algebraic expressions of direct and inverse proportion to find unknown quantities
Practical graphs
(links to Coordinate geometry)
Interpret and use graphs in practical situations including
bull travel graphs
bull conversion graphs
Draw graphs from given data
Learner Guide
57
Extended Algebra and graphs
Question type You should be able to R A G CommentsPractical graphs (links to Coordinate geometry) continued
Apply the idea of rate of change to simple kinematics involving
bull distancendashtime graphs
bull speedndashtime graphs
bull acceleration and deceleration
This may involve estimation and interpretation of the gradient of a tangent at a point
Calculate distance travelled as an area under a linear speedndash time graph
Learner Guide
58
Extended Algebra and graphs
Question type You should be able to R A G CommentsGraphs of functions (links to Coordinate geometry)
Construct tables of values and draw graphs for functions of the form
bull axn where a is a rational constant and n = minus2 minus1 0 1 2 3 and simple sums of not more than three of these
bull abx + c where a and c are rational constants and b is a positive integer
Solve associated equations approximately by graphical methods including finding and interpreting roots and finding turning points of quadratics by completing the square
Draw and interpret graphs representing exponential growth and decay problems
Recognise sketch and interpret graphs of
bull linear
bull quadratic
bull cubic
bull reciprocal
bull exponential
(knowledge of turning points and asymtotes is required)Tangents Estimate gradients of curves by drawing tangents
Learner Guide
59
Extended Algebra and graphs
Question type You should be able to R A G CommentsFunctions Use function notation eg
f(x) = 3x ndash 5 f x α 3x ndash5 to describe simple functions
Find inverse functions f ndash1 (x)
Form composite functions as defined by gf(x) = g(f(x))
Derivatives Understand the idea of a derived function
Use derivatives of the form axn and simple sums of not more than three of these (a is a rational constant and n is a positive integer or 0)
Apply differentiation to gradients and turning points (stationary points)
Use any method to explain whether the turning point is a maximum or a minimum eg second derivative or gradient of function on either side of turning point
Learner Guide
60
Extended Co-ordinate geometry
Question type You should be able to R A G CommentsStraight line graphs
Work with co-ordinates in two dimensions
Gradient Find the gradient of a straight line graph
Calculate the gradient of a straight line from the co-ordinates of two points on it
Length and midpoint
Calculate the length and the co-ordinates of the midpoint of a straight line segment from the co-ordinates of its end points
Equation of line Interpret and obtain the equation of a straight line graph
Parallel lines Determine the equation of a straight line parallel to a given line eg find the equation of a line parallel to y = 4x ndash 1 that passes through (0 ndash3)
Perpendicular lines
Find the gradient of parallel and perpendicular lines eg
bull find the gradient of a line perpendicular to y = 3x + 1
bull find the equation of a line perpendicular to one passing through the co-ordinates (1 3) and (ndash2 ndash9)
Learner Guide
61
Extended Geometry
Question type You should be able to R A G CommentsGeometrical language
Use and interpret the geometrical terms
bull point
bull line
bull parallel
bull perpendicular
bull bearing
bull right angle acute obtuse and reflex angles
bull similar
bull congruent
Use and interpret the vocabulary of
bull triangles right-angled scalene isosceles equilateral
bull quadrilaterals
bull circles
bull polygons
bull simple solid figures including nets
Learner Guide
62
Extended Geometry
Question type What I need to do R A G CommentsGeometrical constructions
Measure and draw lines and angles
Construct a triangle given the three sides using a ruler and a pair of compasses only
Scale drawings Read and make scale drawings
Similar figures Calculate lengths of similar figures
Use relationships between areas of similar triangles and in similar figures
Use relationships between volumes and surface areas of similar solids
Congruent triangles
Use the congruence criteria for triangles (SSS ASA SAS RHS)
Symmetry Recognise symmetry properties for triangles quadrilaterals and circles
Recognise line symmetry in two dimensions
Recognise and find the order of rotational symmetry in two dimensions
Learner Guide
63
Extended Geometry
Question type You should be able to R A G CommentsSymmetry (continued)
Use the following symmetry properties of circles
bull equal chords are equidistant from the centre
bull perpendicular bisector of a chord passes through the centre
bull tangents from an external point are equal in length
Recognise and use symmetry properties of
bull prism cylinder cone and pyramid
Learner Guide
64
Extended Geometry
Question type You should be able to R A G CommentsAngle properties Calculate unknown angles explaining the properties that
you are using in geometrical language for the following geometrical properties
bull angles at a point
bull angles at a point on a straight line and intersecting straight lines
bull angles formed within parallel lines
bull angle properties of triangles and quadrilaterals
bull angle properties of regular polygons
bull angle in a semi-circle
bull angle between tangent and radius of a circle
bull angles properties of irregular polygons
bull angle at the centre of a circle is twice the angle at the circumference
bull angles in the same segment are equal
bull angles in opposite segments are supplementary cyclic quadrilaterals
bull alternate segment theorem
Learner Guide
65
Extended Mensuration
Question type What I need to do R A G CommentsMeasures Use current units of
bull mass
bull length
bull area
bull volume
bull capacity
Express quantities in terms of smaller or larger units including units of area and volume
Perimeter Carry out calculations involving
bull perimeter and area of a rectangle
bull perimeter and area of a triangle
bull perimeter and area of parallelogram
bull perimeter and area of a trapezium
bull perimeter and area of compound shapes made by combining rectangles triangles parallelograms andor trapeziums
Learner Guide
66
Extended Mensuration
Question type You should be able to R A G CommentsCircles Carry out calculations involving circumference and area of a
circle
Solve problems involving arc length and sector area of a circle
Surface area and volume
Carry out calculations involving
bull surface area and volume of a cuboid prism and cylinder (no formulae will be given for these shapes)
bull surface area and volume of a sphere pyramid and cone (formulae will be given for these shapes)
Compound shapes
Carry out calculations involving
bull area of a shape made by combining cuboids prisms andor cylinders
bull volume of a shape made by combining cuboids prisms andor cylinders
Learner Guide
67
Extended Trigonometry
Question type You should be able to R A G CommentsBearings Use and interpret three-figure bearings measured clockwise
from the North ie 000degndash360degTrigonometry Find unknown sides andor angles in right-angled triangles by
applying
bull Pythagorasrsquo theorem
bull sine cosine and tangent ratios for acute angles in right-angled triangles
Solve problems in two dimensions involving angles of elevation and depression
Know that the perpendicular distance from a point to a line is the shortest distance to the line
Trig graphs and equations
Recognise sketch and interpret graphs of simple trigonometric functions
Graph and know the properties of trigonometric functions
Solve simple trigonometric equations for values between 0deg
and 360deg eg Solve sin x = radic32
for values of x between 0deg and
360degGeneral trig Solve problems using sine and cosine rules for any triangle
Find the area of any triangle using frac12absinC
Trig in 3D Solve simple trigonometrical problems in three dimensions including angle between a line and a plane
Learner Guide
68
Extended Vectors and transformations
Question type You should be able to R A G CommentsVectors in two dimensions (links to Trigonometry)
Describe a translation by using a vector represented by
AB or a
Add and subtract vectors
Multiply a vector by a scalar
Transformations Reflect simple shapes in horizontal or vertical lines
Rotate simple shapes through multiples of 90deg about any point
Construct translations of simple shapes
Construct enlargements of simple shapes (positive fractional and negative scale factors)
Recognise and describe
bull reflections
bull rotations
bull translations
bull enlargements (positive fractional and negative scalefactors)
( )x
y
Learner Guide
69
Extended Vectors and transformations
Question type You should be able to R A G CommentsHarder vectors
Calculate the magnitude of a vector as and
understand that magnitude is denoted by modulus signs |A B| or |a|
Represent vectors by directed line segments
Use the sum and difference of two vectors
Use position vectors
( )x
yradicx2 + y2
Learner Guide
70
Extended Probability
Question type You should be able to R A G CommentsProbability (links to Four rules)
Calculate the probability of a single event as a fraction decimal or percentage (not a ratio)
Probability scale Understand and use the probability scale from 0 to 1
Sum to 1 Understand that the probability of an event occurring = 1 ndash the probability of the event not occurring
Relative frequency
Understand relative frequency as an estimate of probability
Work out expected frequencies using relative frequency
Combined events Calculate the probability of combined events using
bull tree diagrams
bull possibility diagrams
bull tables
Learner Guide
71
Extended Statistics
Question type You should be able to R A G CommentsClassify Collect classify and tabulate data
Interpret and compare
Read interpret and draw simple inferences from tables and statistical diagrams
Compare sets of data using
bull tables
bull graphs
bull statistical measures
Be aware of restrictions when making conclusions from data
Charts Construct and use
bull bar charts
bull pie charts
bull pictograms
bull stem ndash and ndash leaf diagrams
bull frequency distributions
bull histograms with equal and unequal intervals
bull scatter diagrams
Learner Guide
72
Extended Statistics
Question type You should be able to R A G CommentsAverages Calculate for individual and discrete data
bull mean
bull median
bull mode
bull range
and distinguish between their use
Estimated mean Calculate an estimate of the mean for grouped and continuous data
Identify the modal class from a grouped frequency distributionCumulative frequency
Construct and use cumulative frequency diagrams to estimate and interpret
bull the median
bull percentiles
bull quartiles
bull inter-quartile range
Construct and interpret box-and-whisker plots
Correlation Understand what is meant by positive negative and zero correlation with reference to a scatter diagram
Lines of best fit Draw interpret and use a ruled line of best fit by eye
Cambridge Assessment International Education1 Hills Road Cambridge CB1 2EU United Kingdomt +44 1223 553554e infocambridgeinternationalorg wwwcambridgeinternationalorg
Copyright copy UCLES October 2017
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- Check Box 10198 Off
- Check Box 10199 Off
- Check Box 10200 Off
- Check Box 10201 Off
- Check Box 10202 Off
- Text Field 278
- Check Box 1050 Off
- Check Box 1051 Off
- Check Box 1052 Off
- Check Box 1053 Off
- Check Box 1054 Off
- Check Box 1055 Off
- Check Box 1056 Off
- Check Box 1057 Off
- Check Box 1058 Off
- Check Box 1059 Off
- Check Box 1060 Off
- Check Box 1061 Off
- Text Field 277
- Check Box 1062 Off
- Check Box 1063 Off
- Check Box 1064 Off
- Check Box 1065 Off
- Check Box 1066 Off
- Check Box 1067 Off
- Check Box 10203 Off
- Check Box 10204 Off
- Check Box 10205 Off
- Check Box 10206 Off
- Check Box 10207 Off
- Check Box 10208 Off
- Text Field 281
- Check Box 10209 Off
- Check Box 10210 Off
- Check Box 10211 Off
- Text Field 282
- Check Box 10212 Off
- Check Box 10213 Off
- Check Box 10214 Off
- Check Box 10215 Off
- Check Box 10216 Off
- Check Box 10217 Off
- Check Box 102010 Off
- Check Box 102011 Off
- Check Box 102012 Off
- Check Box 10218 Off
- Check Box 10219 Off
- Check Box 10220 Off
- Check Box 10221 Off
- Check Box 10222 Off
- Check Box 10223 Off
- Check Box 10224 Off
- Check Box 10225 Off
- Check Box 10226 Off
- Text Field 284
- Check Box 1068 Off
- Check Box 1069 Off
- Check Box 1070 Off
- Check Box 1071 Off
- Check Box 1072 Off
- Check Box 1073 Off
- Check Box 1074 Off
- Check Box 1075 Off
- Check Box 1076 Off
- Check Box 1077 Off
- Check Box 1078 Off
- Check Box 1079 Off
- Check Box 1080 Off
- Check Box 1081 Off
- Check Box 1082 Off
- Text Field 283
- Check Box 1083 Off
- Check Box 1084 Off
- Check Box 1085 Off
- Check Box 102013 Off
- Check Box 102014 Off
- Check Box 102015 Off
- Check Box 102016 Off
- Check Box 102017 Off
- Check Box 102018 Off
- Check Box 102019 Off
- Check Box 10227 Off
- Check Box 10228 Off
- Text Field 285
- Check Box 10229 Off
- Check Box 10230 Off
- Check Box 10231 Off
- Check Box 10232 Off
- Check Box 10233 Off
- Check Box 10234 Off
- Check Box 1098 Off
- Check Box 1099 Off
- Check Box 10100 Off
- Check Box 10101 Off
- Check Box 10102 Off
- Check Box 10103 Off
- Check Box 10107 Off
- Check Box 10108 Off
- Check Box 10109 Off
- Check Box 10110 Off
- Check Box 10111 Off
- Check Box 10112 Off
- Check Box 10113 Off
- Check Box 10114 Off
- Check Box 10115 Off
- Check Box 10116 Off
- Check Box 10117 Off
- Check Box 10118 Off
- Text Field 287
- Text Field 288
- Check Box 10119 Off
- Check Box 10120 Off
- Check Box 101010 Off
- Check Box 101011 Off
- Check Box 101012 Off
- Check Box 101013 Off
- Check Box 101014 Off
- Check Box 101015 Off
- Check Box 101019 Off
- Check Box 10121 Off
- Check Box 10122 Off
- Check Box 10123 Off
- Check Box 10124 Off
- Check Box 10125 Off
- Check Box 10126 Off
- Text Field 289
- Check Box 101020 Off
- Check Box 101021 Off
- Check Box 101022 Off
- Check Box 101023 Off
- Check Box 101024 Off
- Check Box 101025 Off
- Check Box 10127 Off
- Check Box 10128 Off
- Check Box 10129 Off
- Check Box 10130 Off
- Check Box 10131 Off
- Check Box 10132 Off
- Text Field 290
- Check Box 101026 Off
- Check Box 101027 Off
- Check Box 101028 Off
- Check Box 101029 Off
- Check Box 101030 Off
- Check Box 101031 Off
- Check Box 10133 Off
- Check Box 10134 Off
- Check Box 10135 Off
- Check Box 10136 Off
- Check Box 10137 Off
- Check Box 10138 Off
- Text Field 291
- Check Box 10139 Off
- Check Box 10140 Off
- Check Box 101016 Off
- Check Box 101017 Off
- Check Box 101018 Off
- Check Box 101032 Off
- Text Field 292
- Check Box 101036 Off
- Check Box 101037 Off
- Check Box 101038 Off
- Check Box 101039 Off
- Check Box 101040 Off
- Check Box 101041 Off
- Check Box 10150 Off
- Check Box 10151 Off
- Check Box 10152 Off
- Check Box 10153 Off
- Check Box 10154 Off
- Check Box 10155 Off
- Check Box 101042 Off
- Check Box 101043 Off
- Check Box 101044 Off
- Check Box 101045 Off
- Check Box 101046 Off
- Check Box 101047 Off
- Text Field 293
- Check Box 10156 Off
- Check Box 10157 Off
- Check Box 10158 Off
- Check Box 10159 Off
- Check Box 10160 Off
- Check Box 10161 Off
- Check Box 101048 Off
- Check Box 101049 Off
- Check Box 101050 Off
- Check Box 10162 Off
- Check Box 10163 Off
- Check Box 10164 Off
- Text Field 294
- Check Box 101052 Off
- Check Box 101053 Off
- Check Box 101054 Off
- Check Box 101055 Off
- Check Box 101056 Off
- Check Box 101057 Off
- Check Box 1010263 Off
- Check Box 1010264 Off
- Check Box 10165 Off
- Check Box 10166 Off
- Check Box 10167 Off
- Check Box 101058 Off
- Check Box 101059 Off
- Check Box 101060 Off
- Check Box 1010269 Off
- Check Box 1010270 Off
- Text Field 357
- Check Box 1010271 Off
- Check Box 1010272 Off
- Check Box 1010273 Off
- Text Field 358
- Check Box 1010274 Off
- Check Box 1010330 Off
- Check Box 1010331 Off
- Text Field 359
- Check Box 1010343 Off
- Check Box 1010344 Off
- Check Box 1010345 Off
- Text Field 360
- Check Box 1010348 Off
- Check Box 1010349 Off
- Check Box 1010350 Off
- Text Field 297
- Check Box 101061 Off
- Check Box 101062 Off
- Check Box 101063 Off
- Check Box 101064 Off
- Check Box 101065 Off
- Check Box 101066 Off
- Check Box 10168 Off
- Check Box 10169 Off
- Check Box 10170 Off
- Check Box 10171 Off
- Check Box 10172 Off
- Check Box 10173 Off
- Check Box 101067 Off
- Check Box 101068 Off
- Check Box 101069 Off
- Check Box 10174 Off
- Check Box 10175 Off
- Check Box 10176 Off
- Check Box 10177 Off
- Check Box 10178 Off
- Check Box 10179 Off
- Check Box 101070 Off
- Check Box 101071 Off
- Check Box 101072 Off
- Check Box 10180 Off
- Check Box 10181 Off
- Check Box 10182 Off
- Check Box 101073 Off
- Check Box 101074 Off
- Check Box 101075 Off
- Check Box 10183 Off
- Check Box 10184 Off
- Check Box 10185 Off
- Check Box 10186 Off
- Check Box 10187 Off
- Check Box 10235 Off
- Check Box 101076 Off
- Check Box 101077 Off
- Check Box 101078 Off
- Text Field 298
- Check Box 101079 Off
- Check Box 101080 Off
- Check Box 101081 Off
- Check Box 101082 Off
- Check Box 101083 Off
- Check Box 101084 Off
- Text Field 299
- Check Box 101088 Off
- Check Box 101089 Off
- Check Box 101090 Off
- Text Field 300
- Check Box 101091 Off
- Check Box 101092 Off
- Check Box 101093 Off
- Check Box 1010351 Off
- Check Box 1010352 Off
- Check Box 1010353 Off
- Text Field 301
- Check Box 10242 Off
- Check Box 10243 Off
- Check Box 10244 Off
- Check Box 101094 Off
- Check Box 101095 Off
- Check Box 101096 Off
- Check Box 101097 Off
- Check Box 101098 Off
- Check Box 101099 Off
- Text Field 302
- Check Box 1010103 Off
- Check Box 1010104 Off
- Check Box 1010105 Off
- Check Box 10245 Off
- Check Box 10246 Off
- Check Box 10247 Off
- Check Box 10248 Off
- Check Box 10249 Off
- Check Box 10250 Off
- Check Box 1010106 Off
- Check Box 1010107 Off
- Check Box 1010108 Off
- Check Box 1010109 Off
- Check Box 1010110 Off
- Check Box 1010111 Off
- Check Box 1010112 Off
- Check Box 1010113 Off
- Check Box 1010114 Off
- Check Box 10251 Off
- Check Box 10252 Off
- Check Box 10253 Off
- Check Box 1010115 Off
- Check Box 1010116 Off
- Check Box 1010117 Off
- Text Field 303
- Check Box 10260 Off
- Check Box 10261 Off
- Check Box 10262 Off
- Check Box 10101017 Off
- Check Box 10101018 Off
- Check Box 10101019 Off
- Check Box 10101020 Off
- Check Box 1010118 Off
- Check Box 1010119 Off
- Check Box 1010120 Off
- Check Box 1010126 Off
- Check Box 1010127 Off
- Check Box 10263 Off
- Check Box 10264 Off
- Check Box 10265 Off
- Check Box 10269 Off
- Check Box 10270 Off
- Check Box 10271 Off
- Check Box 10101025 Off
- Check Box 10101026 Off
- Check Box 10101027 Off
- Text Field 306
- Check Box 10266 Off
- Check Box 10267 Off
- Check Box 10268 Off
- Check Box 10101021 Off
- Check Box 10101022 Off
- Check Box 10101023 Off
- Check Box 10101024 Off
- Check Box 1010131 Off
- Check Box 1010132 Off
- Check Box 1010133 Off
- Check Box 1010134 Off
- Check Box 1010135 Off
- Check Box 1010136 Off
- Check Box 1010137 Off
- Check Box 1010138 Off
- Text Field 3025
- Check Box 10367 Off
- Check Box 10368 Off
- Check Box 10369 Off
- Check Box 10407 Off
- Check Box 10431 Off
- Check Box 10432 Off
- Text Field 3059
- Check Box 104010 Off
- Check Box 10433 Off
- Check Box 10465 Off
- Check Box 104011 Off
- Check Box 10466 Off
- Check Box 10527 Off
- Text Field 3060
- Check Box 104012 Off
- Check Box 10528 Off
- Check Box 10529 Off
- Text Field 3063
- Check Box 10101037 Off
- Check Box 10101038 Off
- Check Box 10101039 Off
- Text Field 309
- Check Box 10275 Off
- Check Box 10276 Off
- Check Box 10277 Off
- Check Box 10101040 Off
- Check Box 10101041 Off
- Check Box 10101042 Off
- Text Field 3010
- Check Box 10278 Off
- Check Box 10279 Off
- Check Box 10280 Off
- Check Box 10101044 Off
- Check Box 10101045 Off
- Check Box 10101046 Off
- Check Box 10101047 Off
- Check Box 1010141 Off
- Check Box 1010142 Off
- Text Field 3011
- Check Box 10281 Off
- Check Box 10282 Off
- Check Box 10283 Off
- Check Box 10101048 Off
- Check Box 10101049 Off
- Check Box 10101050 Off
- Check Box 10101051 Off
- Check Box 10101052 Off
- Check Box 10101053 Off
- Check Box 10101054 Off
- Check Box 10101055 Off
- Check Box 10101056 Off
- Check Box 10101057 Off
- Check Box 10101058 Off
- Check Box 10101059 Off
- Check Box 10101060 Off
- Check Box 10101061 Off
- Check Box 10101062 Off
- Check Box 10101063 Off
- Check Box 10101064 Off
- Check Box 10101065 Off
- Check Box 10101066 Off
- Check Box 10101067 Off
- Check Box 10101068 Off
- Check Box 10101069 Off
- Check Box 10101070 Off
- Check Box 10101071 Off
- Check Box 10101072 Off
- Check Box 10101073 Off
- Check Box 10101074 Off
- Text Field 3012
- Check Box 10284 Off
- Check Box 10285 Off
- Check Box 10286 Off
- Text Field 3013
- Check Box 10101075 Off
- Check Box 10101076 Off
- Check Box 10101077 Off
- Text Field 3014
- Check Box 10101078 Off
- Check Box 1010143 Off
- Check Box 1010144 Off
- Text Field 3015
- Check Box 10287 Off
- Check Box 10288 Off
- Check Box 10289 Off
- Check Box 10334 Off
- Check Box 10335 Off
- Check Box 10336 Off
- Check Box 10371 Off
- Check Box 10372 Off
- Check Box 10436 Off
- Check Box 10437 Off
- Check Box 10438 Off
- Check Box 10447 Off
- Text Field 3016
- Check Box 10401 Off
- Check Box 10402 Off
- Check Box 10403 Off
- Check Box 10291 Off
- Check Box 10292 Off
- Check Box 10337 Off
- Check Box 10448 Off
- Check Box 10449 Off
- Check Box 10456 Off
- Check Box 10457 Off
- Check Box 10458 Off
- Check Box 10533 Off
- Check Box 10534 Off
- Check Box 10535 Off
- Check Box 10543 Off
- Check Box 10544 Off
- Check Box 10740 Off
- Check Box 10741 Off
- Text Field 3017
- Check Box 10101079 Off
- Check Box 10101080 Off
- Check Box 10101081 Off
- Check Box 10101082 Off
- Check Box 1010145 Off
- Check Box 1010146 Off
- Check Box 10293 Off
- Check Box 10294 Off
- Check Box 10295 Off
- Check Box 10338 Off
- Check Box 10339 Off
- Check Box 10370 Off
- Check Box 10101083 Off
- Check Box 10101084 Off
- Check Box 10101085 Off
- Check Box 10101086 Off
- Check Box 1010147 Off
- Check Box 1010148 Off
- Check Box 10296 Off
- Check Box 10297 Off
- Check Box 10298 Off
- Text Field 3018
- Check Box 10299 Off
- Check Box 10300 Off
- Check Box 10301 Off
- Check Box 10101087 Off
- Check Box 10101088 Off
- Check Box 10101089 Off
- Check Box 10101090 Off
- Check Box 1010149 Off
- Check Box 1010150 Off
- Check Box 10302 Off
- Check Box 10303 Off
- Check Box 10304 Off
- Text Field 3019
- Check Box 10305 Off
- Check Box 10306 Off
- Check Box 10307 Off
- Text Field 3020
- Check Box 10308 Off
- Check Box 10309 Off
- Check Box 103010 Off
- Text Field 311
- Check Box 10141 Off
- Check Box 10142 Off
- Check Box 10143 Off
- Check Box 10144 Off
- Check Box 10145 Off
- Check Box 10149 Off
- Check Box 10257 Off
- Check Box 10258 Off
- Check Box 10259 Off
- Check Box 10310 Off
- Check Box 10311 Off
- Check Box 10312 Off
- Check Box 10331 Off
- Check Box 10332 Off
- Check Box 10333 Off
- Check Box 10313 Off
- Check Box 10314 Off
- Check Box 10315 Off
- Check Box 10316 Off
- Check Box 10317 Off
- Check Box 10318 Off
- Check Box 10319 Off
- Check Box 10320 Off
- Check Box 10321 Off
- Check Box 10322 Off
- Check Box 10323 Off
- Check Box 10324 Off
- Check Box 10325 Off
- Check Box 10326 Off
- Check Box 10327 Off
- Check Box 10399 Off
- Check Box 10400 Off
- Check Box 10530 Off
- Text Field 335
- Check Box 10567 Off
- Check Box 10568 Off
- Check Box 10569 Off
- Check Box 10570 Off
- Check Box 10571 Off
- Check Box 10572 Off
- Check Box 10573 Off
- Check Box 10574 Off
- Check Box 10575 Off
- Check Box 10576 Off
- Check Box 10577 Off
- Check Box 10578 Off
- Check Box 10597 Off
- Check Box 10598 Off
- Check Box 10599 Off
- Check Box 10579 Off
- Check Box 10580 Off
- Check Box 10581 Off
- Check Box 10582 Off
- Check Box 10583 Off
- Check Box 10584 Off
- Check Box 10585 Off
- Check Box 10586 Off
- Check Box 10587 Off
- Check Box 10588 Off
- Check Box 10589 Off
- Check Box 10590 Off
- Check Box 10591 Off
- Check Box 10592 Off
- Check Box 10593 Off
- Check Box 10594 Off
- Check Box 10595 Off
- Check Box 10596 Off
- Check Box 10600 Off
- Check Box 10601 Off
- Check Box 10602 Off
- Check Box 10603 Off
- Check Box 10604 Off
- Check Box 10605 Off
- Check Box 10606 Off
- Check Box 10607 Off
- Check Box 10608 Off
- Check Box 10609 Off
- Check Box 106010 Off
- Check Box 106011 Off
- Check Box 106012 Off
- Check Box 106013 Off
- Check Box 106014 Off
- Check Box 106015 Off
- Check Box 106016 Off
- Check Box 106017 Off
- Text Field 315
- Check Box 10340 Off
- Check Box 10341 Off
- Check Box 10342 Off
- Check Box 10343 Off
- Check Box 10344 Off
- Check Box 10345 Off
- Check Box 10346 Off
- Check Box 10347 Off
- Check Box 10348 Off
- Check Box 10349 Off
- Check Box 10350 Off
- Check Box 10351 Off
- Check Box 10531 Off
- Check Box 10532 Off
- Check Box 10542 Off
- Text Field 313
- Check Box 10352 Off
- Check Box 10353 Off
- Check Box 10354 Off
- Text Field 316
- Check Box 10355 Off
- Check Box 10356 Off
- Check Box 10357 Off
- Check Box 10358 Off
- Check Box 10359 Off
- Check Box 10360 Off
- Check Box 10361 Off
- Check Box 10362 Off
- Check Box 10363 Off
- Check Box 10364 Off
- Check Box 10365 Off
- Check Box 10366 Off
- Check Box 10404 Off
- Check Box 10405 Off
- Check Box 10406 Off
- Text Field 352
- Check Box 102021 Off
- Check Box 102022 Off
- Check Box 102040 Off
- Check Box 102041 Off
- Check Box 102042 Off
- Check Box 102043 Off
- Check Box 102044 Off
- Check Box 102045 Off
- Check Box 102046 Off
- Check Box 102047 Off
- Check Box 102048 Off
- Check Box 102049 Off
- Check Box 102050 Off
- Check Box 102051 Off
- Check Box 102052 Off
- Check Box 102065 Off
- Check Box 102066 Off
- Check Box 102067 Off
- Check Box 102053 Off
- Check Box 102054 Off
- Check Box 102055 Off
- Text Field 351
- Check Box 102056 Off
- Check Box 102057 Off
- Check Box 102058 Off
- Check Box 102059 Off
- Check Box 102060 Off
- Check Box 102061 Off
- Check Box 102062 Off
- Check Box 102063 Off
- Check Box 102064 Off
- Check Box 102068 Off
- Check Box 102069 Off
- Check Box 102070 Off
- Text Field 318
- Check Box 10373 Off
- Check Box 10374 Off
- Check Box 10375 Off
- Check Box 10376 Off
- Check Box 10377 Off
- Check Box 10378 Off
- Check Box 10379 Off
- Check Box 10380 Off
- Check Box 10381 Off
- Check Box 10382 Off
- Check Box 10383 Off
- Check Box 10384 Off
- Check Box 10385 Off
- Check Box 10386 Off
- Check Box 10387 Off
- Text Field 317
- Check Box 10388 Off
- Check Box 10389 Off
- Check Box 10390 Off
- Check Box 102023 Off
- Check Box 102024 Off
- Check Box 102025 Off
- Check Box 102026 Off
- Check Box 102027 Off
- Check Box 102028 Off
- Check Box 102071 Off
- Check Box 102072 Off
- Check Box 102073 Off
- Check Box 102029 Off
- Check Box 10391 Off
- Check Box 10392 Off
- Check Box 10393 Off
- Check Box 10394 Off
- Check Box 10395 Off
- Check Box 10396 Off
- Check Box 10397 Off
- Check Box 10398 Off
- Check Box 102030 Off
- Check Box 102031 Off
- Check Box 102032 Off
- Text Field 319
- Text Field 322
- Check Box 10408 Off
- Check Box 10409 Off
- Check Box 10410 Off
- Check Box 10411 Off
- Check Box 10412 Off
- Check Box 10413 Off
- Check Box 10414 Off
- Check Box 10415 Off
- Check Box 10416 Off
- Check Box 10417 Off
- Check Box 10418 Off
- Check Box 10419 Off
- Text Field 321
- Check Box 10420 Off
- Check Box 10421 Off
- Check Box 10422 Off
- Check Box 10423 Off
- Check Box 10424 Off
- Check Box 10425 Off
- Text Field 337
- Check Box 102033 Off
- Check Box 102034 Off
- Check Box 102035 Off
- Check Box 102036 Off
- Check Box 102037 Off
- Check Box 102038 Off
- Text Field 338
- Check Box 102039 Off
- Check Box 10426 Off
- Check Box 10427 Off
- Check Box 10428 Off
- Check Box 10429 Off
- Check Box 10430 Off
- Text Field 324
- Check Box 10434 Off
- Check Box 10435 Off
- Check Box 101051 Off
- Check Box 1010100 Off
- Check Box 1010101 Off
- Check Box 1010102 Off
- Check Box 1010128 Off
- Check Box 1010129 Off
- Check Box 1010130 Off
- Check Box 10439 Off
- Check Box 10440 Off
- Check Box 10441 Off
- Check Box 10442 Off
- Check Box 10443 Off
- Check Box 10444 Off
- Text Field 350
- Check Box 10742 Off
- Check Box 10743 Off
- Check Box 10744 Off
- Text Field 325
- Check Box 10445 Off
- Check Box 10446 Off
- Check Box 1010151 Off
- Check Box 1010152 Off
- Check Box 1010153 Off
- Check Box 1010154 Off
- Check Box 1010155 Off
- Check Box 1010156 Off
- Check Box 1010157 Off
- Check Box 10450 Off
- Check Box 10451 Off
- Check Box 10452 Off
- Text Field 326
- Check Box 1010158 Off
- Check Box 1010159 Off
- Check Box 1010160 Off
- Check Box 1010161 Off
- Check Box 1010162 Off
- Check Box 1010163 Off
- Check Box 10453 Off
- Check Box 10454 Off
- Check Box 10455 Off
- Check Box 10745 Off
- Check Box 10746 Off
- Check Box 10747 Off
- Check Box 10748 Off
- Check Box 10749 Off
- Check Box 10750 Off
- Check Box 1010167 Off
- Check Box 1010168 Off
- Check Box 1010169 Off
- Check Box 10459 Off
- Check Box 10460 Off
- Check Box 10461 Off
- Check Box 10462 Off
- Check Box 10463 Off
- Check Box 10464 Off
- Check Box 10611 Off
- Check Box 10612 Off
- Check Box 10613 Off
- Text Field 329
- Check Box 1010171 Off
- Check Box 1010172 Off
- Check Box 1010173 Off
- Check Box 1010174 Off
- Check Box 1010175 Off
- Check Box 1010176 Off
- Check Box 1010177 Off
- Check Box 1010178 Off
- Check Box 1010179 Off
- Check Box 10467 Off
- Check Box 10468 Off
- Check Box 10469 Off
- Check Box 10470 Off
- Check Box 10471 Off
- Check Box 10472 Off
- Check Box 1010180 Off
- Check Box 1010181 Off
- Check Box 1010182 Off
- Text Field 330
- Check Box 1010183 Off
- Check Box 1010184 Off
- Check Box 1010185 Off
- Check Box 10473 Off
- Check Box 10474 Off
- Check Box 10475 Off
- Check Box 10476 Off
- Check Box 10477 Off
- Check Box 10478 Off
- Check Box 1010186 Off
- Check Box 1010187 Off
- Check Box 1010188 Off
- Check Box 1010275 Off
- Check Box 1010276 Off
- Check Box 1010277 Off
- Text Field 331
- Check Box 1010189 Off
- Check Box 1010190 Off
- Check Box 1010191 Off
- Check Box 1010192 Off
- Check Box 1010193 Off
- Check Box 1010194 Off
- Check Box 1010354 Off
- Check Box 1010355 Off
- Check Box 1010356 Off
- Check Box 10479 Off
- Check Box 10480 Off
- Check Box 10481 Off
- Check Box 10482 Off
- Check Box 10483 Off
- Check Box 10484 Off
- Check Box 1010195 Off
- Check Box 1010196 Off
- Check Box 1010197 Off
- Check Box 1010278 Off
- Check Box 1010279 Off
- Check Box 1010280 Off
- Text Field 339
- Check Box 10614 Off
- Check Box 10615 Off
- Check Box 10616 Off
- Check Box 10617 Off
- Check Box 10618 Off
- Check Box 10619 Off
- Check Box 1010281 Off
- Check Box 1010282 Off
- Check Box 1010283 Off
- Text Field 340
- Check Box 1010284 Off
- Check Box 1010285 Off
- Check Box 1010286 Off
- Check Box 1010287 Off
- Check Box 1010288 Off
- Check Box 1010289 Off
- Check Box 10620 Off
- Check Box 10621 Off
- Check Box 10622 Off
- Check Box 10623 Off
- Check Box 10624 Off
- Check Box 10625 Off
- Check Box 1010290 Off
- Check Box 1010291 Off
- Check Box 1010292 Off
- Check Box 1010293 Off
- Check Box 1010294 Off
- Check Box 1010295 Off
- Check Box 10626 Off
- Check Box 10627 Off
- Check Box 10628 Off
- Check Box 10751 Off
- Check Box 10752 Off
- Check Box 10753 Off
- Text Field 342
- Check Box 1010296 Off
- Check Box 1010297 Off
- Check Box 1010298 Off
- Check Box 10632 Off
- Check Box 10633 Off
- Check Box 10634 Off
- Check Box 10635 Off
- Check Box 10636 Off
- Check Box 10637 Off
- Text Field 349
- Check Box 1010305 Off
- Check Box 1010306 Off
- Check Box 1010307 Off
- Check Box 1010308 Off
- Check Box 1010309 Off
- Check Box 10103010 Off
- Check Box 10641 Off
- Check Box 10642 Off
- Check Box 10643 Off
- Text Field 343
- Check Box 1010299 Off
- Check Box 1010300 Off
- Check Box 1010301 Off
- Check Box 1010302 Off
- Check Box 1010303 Off
- Check Box 1010304 Off
- Check Box 10638 Off
- Check Box 10639 Off
- Check Box 10640 Off
- Check Box 10644 Off
- Check Box 10645 Off
- Check Box 10646 Off
- Check Box 1010328 Off
- Check Box 10103012 Off
- Check Box 10103013 Off
- Check Box 10103014 Off
- Check Box 10103015 Off
- Check Box 10103016 Off
- Check Box 10648 Off
- Check Box 10649 Off
- Check Box 10650 Off
- Check Box 10651 Off
- Check Box 10652 Off
- Check Box 10653 Off
- Check Box 10654 Off
- Check Box 10755 Off
- Check Box 10756 Off
- Check Box 10757 Off
- Check Box 10758 Off
- Check Box 10759 Off
- Check Box 10760 Off
- Check Box 10761 Off
- Check Box 10762 Off
- Check Box 10763 Off
- Check Box 10764 Off
- Check Box 10765 Off
- Check Box 10766 Off
- Check Box 10767 Off
- Check Box 10768 Off
- Text Field 361
- Check Box 10103020 Off
- Check Box 10103021 Off
- Check Box 10103022 Off
- Text Field 362
- Text Field 371
- Check Box 10103018 Off
- Check Box 10103019 Off
- Check Box 10103059 Off
- Check Box 10655 Off
- Check Box 10656 Off
- Check Box 10657 Off
- Check Box 10658 Off
- Check Box 10673 Off
- Check Box 10754 Off
- Text Field 363
- Check Box 10103023 Off
- Check Box 10103024 Off
- Check Box 10103025 Off
- Check Box 10103026 Off
- Check Box 10103027 Off
- Check Box 10103028 Off
- Check Box 10103029 Off
- Check Box 10103030 Off
- Check Box 10103031 Off
- Check Box 10103032 Off
- Check Box 10103033 Off
- Check Box 10103034 Off
- Text Field 365
- Check Box 10103035 Off
- Check Box 10103036 Off
- Check Box 10103037 Off
- Text Field 366
- Check Box 10103038 Off
- Check Box 10103039 Off
- Check Box 10103040 Off
- Check Box 10103041 Off
- Check Box 10103042 Off
- Check Box 10103043 Off
- Text Field 367
- Check Box 10103044 Off
- Check Box 10103045 Off
- Check Box 10103046 Off
- Text Field 368
- Check Box 10103047 Off
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- Check Box 1010311 Off
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- Text Field 3027
- Check Box 10539 Off
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- Text Field 3028
- Check Box 101010110 Off
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- Text Field 3029
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- Text Field 3030
- Check Box 101010161 Off
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- Text Field 3031
- Check Box 10545 Off
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- Text Field 3032
- Check Box 10548 Off
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- Text Field 3042
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- Text Field 3033
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- Check Box 101010157 Off
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- Text Field 3056
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- Text Field 3057
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- Text Field 3061
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- Text Field 3064
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- Text Field 3067
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11
AO2 Reason interpret and communicate mathematically when solving problemsYou need to demonstrate that you can analyse a problem select a suitable strategy and apply appropriate techniques to obtain a solution
This means that you need to show that you can
bull make logical deductions make inferences and draw conclusions from given mathematical data
bull recognise patterns and structures in a variety of situations and form generalisations
bull present arguments and chains of reasoning in a logical and structured way
bull interprete and communicate information accurately and change from one form of presentation to another
bull assesses the validity of an argument and critically evaluate a given way of presenting information
bull solve unstructured problems by putting them into a structured form involving a series of processes
bull apply combinations of mathematical skills and techniques using connections between different areas of mathematics in problem solving
bull interprete results in the context of a given problem and evaluate the methods used and solutions obtained
AO2 is assessed in all papers
Recognise and extent patterns
Take information and organise it to answer a problem
12
Section 4 Command wordsA command word is the part of the question that tells you what you need to do with your knowledge For example you might need to describe something explain something argue a point of view or list what you know The table below includes command words used in the assessment for this syllabus The use of the command word(s) within an question will relate to the context
Cambridge IGCSE Mathematics 0580 syllabus for 2020 2021 and 2022 Details of the assessment
37wwwcambridgeinternationalorgigcseBack to contents page
Command wordsThe table below includes command words used in the assessment for this syllabus The use of the command word will relate to the subject context
Command word What it means
Calculate work out from given facts figures or information generally using a calculator
Construct make an accurate drawing
Describe state the points of a topicgive characteristics and main features
Determine establish with certainty
Explain set out purposes or reasons make the relationships between things evident provide why andor how and support with relevant evidence
Give produce an answer from a given source or recallmemory
Plot mark point(s) on a graph
Show (that) provide structured evidence that leads to a given result
Sketch make a simple freehand drawing showing the key features
Work out calculate from given facts figures or information with or without the use of a calculator
Write give an answer in a specific form
Write down give an answer without significant working
The question below is taken from Paper 4 and illustrates the use of two command words
The command words lsquoWrite downrsquo indicates that you do not need to show your working and the answer should just be written down The mark allocation [1] also supports this
The command words lsquoShow thatrsquo indicate that you need to provide evidence in the form of a clear mathematical explanation to demonstrate that you know how to obtain the given result In other words you need to show a method that leads to the result
The answer space in this case does not contain a dotted answer line as there is no single lsquoanswerrsquo to be found Your working that leads to the given result should be written in the blank working space
13
This section takes you through an example question and learner response from one of the 2020 specimen papers for this course It will help you to identify the command words and other key instructions within questions and to understand what is required in your response
This section is structured as follows
QuestionThe command words and instructions in the question have
been highlighted and explained This should help you to understand clearly what is required by the question
Mark schemeThis tells you as clearly as possible what an examiner expects
from an answer to award marks
Example candidate responseThis an exemplar answer written in the style of
a high level candidate
How the answer could have been improvedThis summarises what could be done to gain more marks
All information and advice in this section is specific to the example question and response being demonstrated It should give you an idea of how your responses might be viewed by an examiner but it is not a list of what to do in all questions In your own examination you will need to pay careful attention to what each question is asking you to do
Common mistakesThis will help you to avoid common mistakes made by
candidates So often candidates lose marks in their exams because they misread or misinterpret the questions
Section 5 Example candidate response
14
QuestionThe question used in this example is from Specimen Paper 3 (Core) It represents the type of structured question you will see in both Paper 3 (Core) and Paper 4 (Extended) A structured question means that it is broken into several parts Often later parts will depend on your answers to earlier parts
This means that you cannot find the answer by
measuring the diagramWork out indicates that the answer should be calculated from the given information so measurement will not score marks
The allocation of 1 mark indicates that the answer can be obtained with minimum working
Give reasons for your answer indicates that your answer should be supported with reasons using the correct mathematical terminology You must justify your answer
Use trigonometry to calculate indicates that you should use this method with the given information to find the answer and that a calculator is needed to solve the problem If you did not use trigonometry you would not be awarded any marks
15
Show that indicates the answer is given and you need to write down all of the steps in a method that leads to the given answer You need to provide evidence that you understand and know how the answer is reached
Work out indicates that you should calculate the answer from the given information The mark allocation of 4 marks suggests that you will need to include several steps of working in order to get to the answer
Learner Guide
16
Answer Mark Notes(a)(i) 35 1 This is the only acceptable answer for this part of the question
(a)(ii) 74 1 This is the only acceptable answer for this part of the question
(b) 43deg and correct mathematical reasons
3 Two marks are awarded for the final answer of 43deg
The third mark is awarded for a fully correct reason for example angles on a straight line add up to 180deg and angles in a triangle add up to 180deg There are other correct reasons that could be also be used
If 43deg is not obtained one method mark can be awarded if the following calculation is seen in the working
180 ndash 128 or 128 ndash 85
(c) 322 or 3223hellip 2 This is the only acceptable answer for this part of the question
The answer has to be rounded correct to three significant figures or can be given with more figures in the answer
Those that did not get this answer can score one method mark for showing the following in their working
sin = 8 divide 15
(d)(i) 2 2300 225+2 This does not have to be shown in one step as long as the method shown is the same as this overall Those that do not
show this can have one method mark for showing the following in their working
300deg + 225deg
(d)(ii) 15 35 4 The answer 3 35pm is also acceptable for 4 marks
If the correct answer is not found one method mark is available for showing 375 divide 450 in their working and a second method mark can be awarded for sight of them multiplying their answer to this by 60 to change it to hours A third method mark can be awarded for adding their answer in hours to 14 45 ndash this shows the correct method so only one mark is lost for an incorrect final answers
Mark schemeYour examination papers will be marked and the overall number of marks for each paper will be recorded Your marks across all papers will then be converted to a grade
Final answer This value is what the examiner expects to see The answer has to be exactly as given in the mark scheme unless there are acceptable alternatives The mark scheme will always make it clear if there are acceptable alternative answers
Method marks Sometimes method marks are awarded for lines of working as well as for the final answer This means that you could get the final answer incorrect but still get some marks if you include the correct working The mark scheme does not include all possible methods so if you use a method not included in the mark scheme but it is accurate and relevant then the examiner will still award marks for the appropriate parts of the working ndash unless the questions asks you to use a specific method
example of a final answer
example of a method mark
17
Example candidate responseNow letrsquos look at the sample candidatersquos response to question 8 The examiners comments are in the orange boxes The candidate was awarded 8 marks out of 13
180 ndash 74 + 71 = 177
177
74
0 out of 1
The candidates working suggests they understand that the angle sum of a triangle is 180deg but they did not include brackets around 74 + 71 The answer 177deg is not sensible for this question
1 out of 1
The candidate recognises that there are parallel lines and that angle y is a corresponding angle to angle 74deg
180 ndash 128 = 52 180 ndash 85 ndash 52 = 43
43 angles on a straight line add up to 180deg
2 out of 3
The candidate has given a correct answer for w and shown correct working in two steps They have given a correct reason for 52deg using correct mathematical languge But they have not provided a reason to explain the angle 43deg They lose a mark for not also stating angle sum of a triangle is 180deg
sin p = 8 divide 15 = 053
p = sinndash1 (053)
p = 32005 320
1 out of 2
The candidate has correctly used trigonometry in their method They are awarded one method mark for the first line of working However they have rounded 05333333hellip (the result of 8 divide 15) to 052 and then calculated the inverse sin of 052 rather than 05333333 This has resulted in an inaccurate final answer This is called lsquopremature approximationrsquo and it is a very common error to make
18
AB2 = 3002 + 2252
= 140625
AB = 375
1 out of 2
The candidate has recognised the right-angled triangle and correctly used Pythagorasrsquo theorem in the first line of working However they have missed out an important step by not showing that you need to take the square root of 140625 to get 375 As this is a lsquoshow thatrsquo question and they missed a key step in the method they cannot be awarded full marks as the complete working is not shown One method mark is earned for the first line
T = = = 08333333hellip
08333333 hours = 08333333 times 60 minutes = 50 minutes
arrives at 14 45 + 50 mins = 3 35
DS
375450
3 35
3 out of 4
The candidate has found the time by correctly dividing the distance by the speed and recognised that this is in hours When converting the answer to a decimal they have not rounded the decimal but left its full value on the calculator to get 50 mins which is the correct approach Unfortunately after converting the time from 24 hour clock to 12 hour clock they did not include lsquopmrsquo to indicate that the time is in the afternoon and so the final answer is not quite right So 3 marks are awarded for all of a correct method but a mark is lost due to the accuracy of the final answer
19
How the answer could have been improvedThis answer could have been improved by
bull In part (a)(i) the answer of 177deg was not sensible given the diagram in the question If the candidate had checked their answer for sense they would have realised they had made a mistake It is always a good idea to check that your answer seems sensible before you move on to another question
bull In part (b) the candidate did all the correct steps but failed to provide both reasons There were two steps to the method which should have indicated to the candidate that there were two steps to justify and therefore two reasons should have been provided The mark allocation for the question [3] also indicates that more than one reason would be required one mark for the value of 43deg leaving two marks one mark for each of two reasons The candidate should have read the question carefully and again checked their response seemed reasonable
bull In part (c) the candidate rounded an intermediate answer which affected the accuracy of the final answer This caused them to lose a mark despite using a correct method You should only ever round the final answer do not round intermediate values If you can store the intermediate values in your calculator and so that you can use the full value in your calcuations If youre not able to do this and you have to round the intermediate values do not round them to less than three significant figures
bull In part (d)(i) the candidate missed out a step in the method As this was a show that question they needed to show all the steps in the method Its important to show all steps even if they seem obvious
bull In part (d)(ii) the candidate made a silly error by not stating that the time was pm When working with time answers are accepted in either 24 clock or 12 clock time but if you give your answer in the 12 hour clock then it must include am or pm as well
Common mistakesThere were a number of common mistakes made by other candidates on this question
bull Accuracy of answers
In parts (c) and (d)(ii) a common error was premature rounding ndash rounding intermediate values in the method before the final answer which resulted in their final answer not being accurate Other candidates gave the final answer to less than three significant figures ignoring the instruction on the front of the paper to round to three significant figures
bull Using incorrect terminology when giving reasons
In part (b) the most common error was to not give full reasons to support the answer Another common error was to provide a reason that did not use the correct mathematical language such as lsquoThey add up to 180degrsquo and lsquoIt is a straight linersquo which could not be awarded marks
bull Lack of knowledge
In part (c) a number of candidates had limited knowledge of trigonometry and did not choose the correct trig ratio which was the sine ratio This is why good revision is important
bull Not checking answers
In part (a)(i) even though the diagram is drawn NOT TO SCALE it is possible to see that the angle is an acute angle and should therefore not be bigger than 90deg This should alert candidate that if their answer is over 90deg it is not a sensible answer and they should go back and check their working
20
bull Inefficient method shown
In part (c) the lsquoShow thatrsquo question a number of candidates omitted an important step from the method this is often common in lsquoShow thatrsquo questions where every step must be shown no matter how obvious them seem
General adviceIn order to do your best when answering a mathematics question make sure you
bull revise all of the topics for the syllabus you are studying before the exam
bull understand what all the key terms and command words in the question mean
bull read the questions carefully and consider what you need to do before you do it
bull only round the final answer not intermediate values
bull show all steps in your working and show them clearly
bull round to the correct degree of accuracy
bull use the correct mathematical terminology
bull check your answers seem reasonable given the context or details of the question
21
It is important that you plan your revision in plenty of time for the examinations and that you develop a revision technique that works for you The advice in this section will help you revise and prepare for the examinations It is divided into general advice for all papers
Use the tick boxes to keep a record of what you have done what you plan to do or what you understand
For more advice on revision see the Cambridge Learner Revision Guide on our website
Section 6 Revision
Find out when the examinations are and plan your revision so you have time to revise Create a revision timetable and divide it into sections to cover each topic
Spend most of your time focussing on specific skills knowledge or issues that you have found more difficult when practicing them either during revision or earlier in the course
Write a summary of all the key information for a topic ndash use the checklists at the end of this section
Know the meaning of the command words used in questions and how to apply them to the information given Look at past examination papers and highlight the command words and check what they mean
Make revision notes and work on practice questions Reading alone does not work you need to be active and practice your maths
Work for shorter periods then have a break Revise small sections of the syllabus at a time but do this regularly
Test yourself by trying out some past exam questions Use the mark schemes to assess yourself and to be familiar with how marks are awarded for different questions
Be organised in advance with your notes texts exercise books revision guides and revision websites so you do not waste valuable revision time trying to find things
Make notes of key mathematical words that you should use in questions that ask you to lsquodescribersquo or give lsquogeometrical reasons forrsquo eg in describing transformations or giving reasons in circle theorem questions Look at the mark schemes for these types of questions from past papers to see how marks are awarded
Make sure you have all of the correct mathematical equipment ready for the exam particularly your calculator Make sure you are familiar with the all of the important functions on your calculator
Practice the areas you can do well not just those that you find more difficult
Take breaks and do things to relax when you take your breaks this will help you to be more productive when you are revising
Before the examination
22
During the examination
Plan your time according to the marks for each question For example a question worth one mark requires less time than a question one worth 4 marks If a question has several parts then the parts with more marks will need more time
Read each question very carefully
Identify the command words ndash you could underline or highlight them
Identify the other key words and information and perhaps underline them too particularly where
questions require reasoning or problem solving
Read the questions careully and make you have answered the question that is being asked
Show your working this is particularly important for questions where you are asked to lsquoshow that helliprsquo
Set your working out clearly so that it is easy to follow this makes it easier to keep track of what you have done and makes checking back through your work easier and it makes it easier for the examiner to mark your work try to write it in a logical order in the answer space
Write answers clearly if you want to change an answer then you should cross the answer out and write a replacement if your answer is on the answer line cross it out and write the replacement answer above it do not try to change numbers on the answer line as this can lead to unclear figures
Check your working and answers to avoid errors
Give your answer to the appropriate level of accuracy either the accuracy indicated in the question or the accuracy given on the front of the paper
Avoid rounding intermediate values part way through your calculation only round the final answer
Check that the answer that you have given is sensible and realistic for what is being asked
Use a pencil when drawing diagrams or completing graphs this means that you can change your answer more easily if you have made a mistake
Take care when reading scales
If you are asked for reasons for your answer then use the correct mathematical terms
Use the mark allocation given with the questionsparts of questions to try to judge how much work is needed to answer each part
23
Top tips for revision of Cambridge IGCSE Mathematics1 Summarise recall and applyMake sure that you can recall and apply the key information and mathematical techniques on each topic that you need for the exam
i Write a summary of the key information of a topicii Collect together some questions that test the knowledge and skills of this topic Ask your teacher for practice
questions or suitable past examination questions or use practice books or textbooksiii Test your recall by covering over the summary and trying to remember the details or use the summary as part of
the lsquoTeach the topicrsquo (Tip 3) or lsquoQuestion and answer cardsrsquo (Tip 4) activities iv After you have spent some time revising and practising the knowledge and skills answer the questions that you
collected together on the topic You might do this later on the same day as revising or a few days later Answer as many questions as you can in order to practise applying your knowledge
v Try creating your own questions by adapting existing ones and use these for practice when you return to a topic
On graph questions straight lines should be ruled and curves should be drawn freehand with a smooth curve
Donrsquot spend too long on any one part of a question If you are really stuck on a question then move on and come back to the question later if you have time As a rough guide each mark on the paper should take about one minute
2 Concept mapsConcept maps are a great way to revise the links between different factors or to explore a larger topic They can also be used to collect together your ideas
i Use a blank sheet of paper and turn it on its side (landscape)ii Put the topic title in the middle of the page and build the concept map outwards using lines called lsquobranchesrsquo
ndash The first branches are from the central topic to sub-topics draw these as thick lines
ndash Add new branches from the sub-topics to include more detail draw these as thinner lines
ndash Add even more detail to a point by adding more branches
This creates a hierarchy of information from lsquooverviewrsquo (the thick branches) to lsquofine detailrsquo (thinnest branches)
iii Write single key words or phrases along a branch and add drawings for visual impactiv Use different colours highlighter pens symbols and arrows to highlight key facts or issuesIt is a good idea to use a large piece of plain A3 (or larger) paper and lots of coloured pens
24
3 Teach the topicThis is a very simple but effective technique that focusses on knowledge recall It tests the brain and rehearses the information you need to know for a certain topic and so will help your revision
i Create some topic cards with key bullet points of information on Leave space for ticksii Give these to your parents family or friends for exampleiii Give yourself 10 minutes maximum to teach your audience the main points of the topic You could use a mini-
whiteboard or flip chart to helpiv Your audience tick off all the points you mention in your presentation and give you a final scoreThe brain loves competition so if you do not score full marks you can try again the next day or compete against friends This system of repeat and rehearsal is very effective especially with more complex topics and doesnt take much preparation
4 Question and answer (QampA) cardsThis is very similar to Teach the topic but less formal and less public for those who dislike performing in front of others It tests knowledge recall and rehearses the information you need to know for a certain topic
i Pick a topic and create two sets of cards question cards and answer cards You might find it helpful to make the question cards a different size or use different coloured card for answers
ii Make sure you have the topic or something appropriate depending on what you are focusing on as a heading on each card The questions should test your knowledge and understanding of key areas of the course
iii A friend or family member uses the cards to test you in short 5 or 10 minute periods at any time during the dayiv You could also do this alone by reading the questions to yourself giving the answer and then checking the
correct answer cardv This game can be adapted by using the cards to find matching pairs turn all cards face down across the space
in front of you Turn over two cards leaving them where they are If they match (one is a question card and the other is the corresponding answer card) pick up the pair and put them to one side If they dont match try to remember where they are and what is on each card then turn them back over Turn over two other cards Continue until you have matched all pairs
5 Question paper and mark schemesLooking at past question papers and the mark scheme helps you to familiarise yourself with what to expect and what the standard is
i Ask your teacher for past paper questions with mark schemes for the course ndash ask your teacher for help to make sure you are answering the correct questions and to simplify the mark scheme
ii Look at the revision checklist and identify which topic a given question relates to ndash you might need to ask your teacher to help you do this
iii Once you have finished revising a topic or unit time yourself answering some appropriate exam questions Check the mark schemes to see how well you would have scored or give the answers to your teacher to check
iv Add details or notes to the mark scheme where you missed out on marks in your original answers using a different coloured pen Use these notes when you revise and try the question again later
You can find plenty of past exam papers and mark schemes on the Cambridge International public website
httpwwwcambridgeinternationalorgprogrammes-and-qualificationscambridge-igcse-mathematics-0580past-papers
25
Other useful revision advice for Cambridge IGCSE Mathematics bull Before the exam make sure that you are familiar with your calculator and confident in using it
bull Look at the Example Candidate Response earlier in this guide Can you identify the strengths of the response andwhere they have made mistakes or lost marks
bull When you are attempting a past paper (or questions from a past paper) complete it without referring to yournotes so that you get a true idea of your strengths and weaknesses Then go back through the paper using yournotes and a different coloured pen to make corrections and changes After you have done as much as you can onthe paper mark it using the mark scheme Take notes of any points that you lost marks on
bull Donrsquot just revise the topics that you enjoy and are confident in If you identify an area that you are weaker inthen try to revisit the topic by reviewing your notes and doing some practice questions then use exam questionsto check whether you now understand
bull Return to topics later in your revision to check that you still remember and understand the topic and to help toensure that you recall more of the material when you get to the examination
Revision checklists for Cambridge IGCSE MathematicsThe tables on the following pages can be used as a revision checklist They do not contain all the detailed knowledge you need to know just an overview For more detail see the syllabus and talk to your teacher
You can use the tick boxes in the checklists to show when you have revised and are happy that you do not need to return to it Tick the lsquoRrsquo lsquoArsquo and lsquoGrsquo column to record your progress as follows
bull R = RED means you are really unsure and lack confidence in that area you might want to focus your revisionhere and possibly talk to your teacher for help
bull A = AMBER means you are reasonably confident in a topic but need some extra practicebull G = GREEN means you are very confident in a topic
As your revision progresses you can concentrate on the RED and AMBER topics in order to turn them into GREEN topics You might find it helpful to highlight each topic in red orange or green to help you prioritise
You can use the lsquoCommentsrsquo column to
bull add more information about the details for each pointbull include a reference to a useful resourcebull include a list of formulae or notationbull add learning aids such as rhymes poems or word playbull highlight areas of difficulty or things that you need to talk to your teacher about
There is a set of checklist for the Core syllabus and a different set for the Extended syllabus
Learner Guide
26
Core syllabus contentCore Number
Category You should be able to R A G CommentsNumber Identify and use
bull natural numbers
bull integers (positive negative and zero)
bull prime numbers
bull write a number as a product of its prime factors
bull square numbers and cube numbers
bull common factors and highest common factor of two numbers
bull common multiples and lowest common multiple of two numbers
bull rational numbers
bull irrational numbers (eg π radic2 )
bull real numbers
bull reciprocals
Learner Guide
27
Core Number
Question type You should be able to R A G CommentsSets and Venn diagrams
Understand notation of Venn diagrams
Definition of sets
eg A = xx is a natural number
B = abchellip
Notation
Number of elements in set A n(A)
Universal set
Union of A and B A cup B
Intersection of A and B A cap B
Squares square roots cubes and cube roots
Calculate
bull squares and cubes of numbers
bull square roots and cube roots of numbers
Learner Guide
28
Core Number
Question type You should be able to R A G CommentsDirected numbers
Use directed numbers in practical situations for example temperature changes
Fractions decimals and percentages
Use the language and notation of simple vulgar and decimal fractions and percentages
Recognise equivalent fractions decimals and percentages
Convert between fractions decimals and percentages
Ordering Order quantities by magnitude and demonstrate familiarity with the symbols = ne gt lt ⩾ ⩽
Indices and standard form (links to Algebraic manipulation)
Evaluate indices eg 25 5ndash2 1000 64frac12 8ndash23
Use the rules of indices for
bull multiplication of indices eg 4ndash3 times 45
bull division of indices eg 57 divide 53
bull index numbers raised to an index eg (23)2 (43)2
Use the standard form A times 10n where n is a positive or negative integer and 1 ⩽ A lt 10
bull convert numbers into and out of standard form
bull calculate with numbers in standard form
Learner Guide
29
Core Number
Question type You should be able to R A G CommentsFour rules
( + ndash times divide )
Use the four rules for calculations with
bull whole numbers
bull decimals
bull vulgar and mixed fractions
bull correct ordering of operations (BIDMAS) and use of bracketsEstimates Make estimates of numbers quantities and lengths
Give approximations to a specified number of
bull significant figures
bull decimal places
Round off answers to reasonable accuracy in the context of a given problem
Bounds Give upper and lower bounds for data given to a specified accuracy eg measured lengths
Ratio proportion rate
Understand ratio
Divide a quantity in a given ratio
Understand direct and inverse proportion
Use scales in practical situations
Use common measures of rate (formulae for other rates eg density and pressure will be given in the question)
Calculate average speed
Learner Guide
30
Core Number
Question type You should be able to R A G CommentsPercentages Calculate a percentage of a quantity
Express one quantity as a percentage of another quantity
Calculate percentage increase or decrease
Use of an electronic calculator
Use a calculator efficiently
Check accuracy of calculations
Time Calculate times in terms of the 24-hour and 12-hour clock
Read
bull clocks
bull dials
bull timetables
Money Calculate using money
Convert from one currency to another
Learner Guide
31
Core Number
Question type You should be able to R A G CommentsPersonal and small business finance
Use given data to solve problems on
bull earnings
bull simple interest
bull compound interest (you will need to know the compound interest formula)
bull discount
bull profit and loss
Extract data from tables and charts
Learner Guide
32
Core Algebra and graphs
Question type You should be able to R A G CommentsBasic algebra Use letters to express generalised numbers
Express basic arithmetic processes algebraically
Substitute numbers in formulae
Construct simple expressions and set up simple equations
Rearrange simple formulae
Algebraic manipulation
Manipulate directed numbers
Use brackets
bull expand a single bracket eg 3x(2x ndash4y)
bull expand a pair of brackets eg (x + 3) (x ndash 7)
Extract common factors eg factorise 9x2 + 15xy
Rules of indices Use and interpret positive negative and zero indices
Use the rules of indices eg to simplify algebra such as
bull 3x4 times 5x
bull 10x3 divide 2x2
bull (x6)2
Learner Guide
33
Core Algebra and graphs
Question type You should be able to R A G CommentsEquations and inequalities
Derive and solve simple linear equations in one unknown
Derive and solve simultaneous linear equations in two unknowns
Number sequences
(links to Squares square roots cubes and cube roots)
Continue a number sequence
Recognise patterns in sequences
Recognise relationships between difference sequences
Find the nth term of sequences for
bull liner sequences
bull simple quadratic sequences
bull cubic sequences
Practical graphs
(links to Mensuration)
Interpret and use graphs in practical situations including
bull travel graphs
bull conversion graphs
Draw graphs from given data
Learner Guide
34
Core Algebra and graphs
Question type You should be able to R A G CommentsGraphs of functions
(links to Co-ordinate geometry)
Construct tables of values for functions of the form
bull ax + b (linear)
bull plusmn x2 + ax + b (quadratic)
bull (x ne 0) (reciprocal)
where a and b are integer constants
Draw and interpret such graphs
Solve linear and quadratic equations approximately by graphical methods
Recognise and sketch the graphs of linear and quadratic functions
ax
Learner Guide
35
Core Co-ordinate geometry
Question type You should be able to R A G CommentsCo-ordinates Work with co-ordinates in two dimensions
Gradients Find the gradient of a straight line graph
Equation of straight line
Interpret and obtain the equation of a straight line graph in the form y = mx + c where the graph is given
Parallel lines Determine the equation of a straight line parallel to a given line eg find the equation of a line parallel to y = 4x ndash 1 that passes through (0 ndash3)
Learner Guide
36
Core Geometry
Question type You should be able to R A G CommentsGeometrical language
Use and interpret the geometrical terms
bull point
bull line
bull parallel
bull perpendicular
bull bearing
bull right angle acute obtuse and reflex angles
bull similar
bull congruent
Use and interpret the vocabulary of
bull triangles right-angled scalene isosceles equilateral
bull quadrilaterals
bull circles
bull polygons
bull simple solid figures including nets
Learner Guide
37
Core Geometry
Question type You should be able to R A G CommentsGeometrical constructions
Measure and draw lines and angles
Construct a triangle given the three sides using a ruler and a pair of compasses only
Scale drawings Read and make scale drawings
Similar figures Calculate lengths of similar figures
Congruent Recognise congruent shapes
Symmetry Recognise symmetry properties for triangles quadrilaterals and circles
Recognise line symmetry in two dimensions
Recognise and find the order of rotational symmetry in two dimensions
Learner Guide
38
Core Geometry
Question type You should be able to R A G CommentsAngle properties Calculate unknown angles explaining the properties that you
are using in geometrical language for angles
bull angles at a point
bull angles on a straight line and intersecting straight lines
bull angles within parallel lines
bull angles in triangles
bull angles in quadrilaterals
bull angles in regular polygons
bull angle in a semi-circle
bull angle between tangent and radius of a circle
Learner Guide
39
Core Mensuration
Question type You should be able to R A G CommentsMeasures bull Use current units of
bull mass
bull length
bull area
bull volume
bull capacity
Express quantities in terms of smaller or larger units including units of area and volume
Convert between units including units of area and volume
Perimiter Carry out calculations involving
bull perimeter and area of a rectangle
bull perimeter and area of a triangle
bull perimeter and area of parallelogram
bull perimeter and area of a trapezium
bull perimeter and area of shapes made by combining
bull rectangles triangles parallelograms andor trapeziums
Learner Guide
40
Core Mensuration
Question type You should be able to R A G CommentsCircles Carry out calculations involving circumference and area of a
circle
Solve simple problems involving the arc length and sector area of a circle where the sector angle is a factor of 360deg
Surface area and volume
Carry out calculations involving
bull surface area and volume of a cuboid prism and cylinder (no formulae will be given for these shapes)
bull surface area and volume of a sphere pyramid and cone (formulae will be given for these shapes)
Areas and volumes of compound shapes
Carry out calculations involving the areas and volumes of compound shapes made from combinations of the shapes in Perimeter or Surface area and volume
Learner Guide
41
Core Trigonometry
Question type You should be able to R A G CommentsBearings Use and interpret three-figure bearings measured clockwise
from the North ie 000degndash360degTrigonometry Find unknown sides andor angles in right-angled triangles by
applying
bull Pythagorasrsquo theorem
bull sine cosine and tangent ratios for acute angles in right-angled triangles
Learner Guide
42
Core Vectors and transformations
Question type You should be able to R A G CommentsVectors in two dimensions (links to Trigonometry)
Describe a translation by using a vector represented by
AB or a
Add and subtract vectors
Multiply a vector by a scalar
Transformations Reflect simple shapes in horizontal or vertical lines
Rotate simple shapes through multiples of 90deg about
bull the origin
bull their vertices
bull the midpoints of their sides
Construct translations of simple shapes
Construct enlargements of simple shapes (positive and fractional scale factors)
Recognise and describe using the correct language
bull reflections
bull rotations
bull translations
bull enlargements (positive and fractional scale factors)
( )x
y
Learner Guide
43
Core Probability
Question type You should be able to R A G CommentsSingle events Calculate the probability of a single event as a fraction decimal
or percentage (not a ratio)Probability scale Understand and use the probability scale from 0 to 1
Sum to 1 Understand that the probability of an event occurring = 1 ndash the probability of the event not occurring
Relative frequency
Understand relative frequency as an estimate of probability
Work out expected frequencies using relative frequencyCombined events Calculate the probability of simple combined events using
bull tree diagrams
bull possibility diagrams (points on a grid)
bull Venn diagrams (2 sets only)
Learner Guide
44
Core Statistics
Question type What I need to do R A G CommentsClassify Collect classify and tabulate data
Interpret and compare
Read interpret and draw simple inferences from tables and statistical diagrams
Compare sets of data using
bull tables
bull graphs
bull statistical measures
Be aware of restrictions when making conclusions from data
Charts Construct and use
bull bar charts
bull pie charts
bull pictograms
bull stem-and-leaf diagrams
bull frequency distributions
bull histograms with equal intervals
bull scatter diagrams
Learner Guide
45
Question type What I need to do R A G CommentsAverages Calculate for individual and discrete data
bull mean
bull median
bull mode
bull range
and distinguish between their useCorrelation Understand what is meant by positive negative and zero
correlation with reference to a scatter diagramLine of best fit Draw interpret and use a ruled line of best fit by eye
Learner Guide
46
Extended syllabus content (includes required Core content)Extended Number
Question type You should be able to R A G CommentsNumber Identify and use
bull natural numbers
bull integers (positive negative and zero)
bull prime numbers
bull write a number as a product of its prime factors
bull square and cube numbers
bull common factors and highest common factor of two or more numbers
bull common multiples and lowest common multiple of two or more numbers
bull rational numbers
bull irrational numbers (eg π radic2 )
bull real numbers
bull reciprocals
Learner Guide
47
Extended Number
Question type You should be able to R A G CommentsSet notation and language
Use language notation and Venn diagrams to describe sets and represent relationships between sets as follows
Definition of sets egA = x x is a natural number
B = (xy) y = mx + c
C = x a ⩽ x ⩽ b
D = a b c hellip
Notation egnumber of elements in set A n(A)
lsquois an element ofrsquo isin
lsquois not an element ofrsquo notin
complement of set A
the empty set empty
the universal set
A is a subset of B A sube B
A is a proper subset of B A sub B
A is not a subset of B A ⊈ B
A is not a proper subset of B A nsub B
union of A and B A cup B
intersection of A and B A cap B
Learner Guide
48
Extended Number
Question type You should be able to R A G CommentsSquares square roots cubes and cube roots
Calculatebull squares of numbers
bull square roots of numbers
bull cubes of numbers
bull cube roots of numbers
bull other powers and roots of numbers
Directed numbers
Use directed numbers in practical situations for example temperature changes
Fractions decimals and percentages
Use the language and notation of simple vulgar and decimal fractions and percentages in appropriate contexts
Recognise equivalent fractions decimals and percentages
Convert between fractions decimals and percentages
Convert recurring decimals to fractions
Ordering Order quantities by magnitude and demonstrate familiarity with the symbols = ne gt lt ⩾ ⩽
Learner Guide
49
Extended Number
Question type You should be able to R A G CommentsIndices and standard form (links to Algebraic manipulation)
Evaluate indices including fractional negative and zero
eg 25 5ndash2 1000 10012 8ndash23
Use the rules of indices forbull multiplication of indices eg 43 times 45
bull division of indices eg 57 divide 53
bull index numbers raised to an index eg (43)2
Use the standard form A times 10n where n is a positive or negative integer and 1 ⩽ A lt 10bull convert into and out of standard form
bull calculate with numbers in standard form
Four rules
( + ndash times divide )
Use the four rules for calculations withbull whole numbers
bull decimals
bull vulgar and mixed fractions
bull correct ordering of operations (BIDMAS) and use of brackets
Learner Guide
50
Extended Number
Question type You should be able to R A G CommentsEstimates Make estimates of numbers quantities and lengths
Give approximations to a specified number of
bull significant figures
bull decimal places
Round off answers to reasonable accuracy in the context of a given problem
Bounds Give upper and lower bounds for data given to a specified accuracy eg measured lengths
Obtain appropriate upper and lower bounds to solutions of simple problems given to a specified accuracy eg the lower and upper bounds for the area of a rectangle
Ratio proportion rate
(links to Direct and inverse proportion)
Understand ratio
Divide quantities in a given ratio
Increase and decrease a quantity by a given ratio
Understand numerical problems involving direct and inverse proportion
Use ratio and scales in practical situations
Use common measures of rate (formulae for other rates eg density and pressure will be given in the question)
Calculate average speed
Learner Guide
51
Extended Number
Question type What I need to do R A G CommentsPercentages Calculate a percentage of a quantity
Express one quantity as a percentage of another quantity
Calculate percentage increase or decrease
Calculate reverse percentages eg finding the cost price given the selling price and the percentage profit
Use of an electronic calculator
Use a calculator efficiently
Check accuracy of calculations
Time Calculate times in terms of the 24-hour and 12-hour clock
Read clocks dials and timetables
Money Calculate using money
Convert from one currency to another
Learner Guide
52
Extended Number
Question type You should be able to R A G CommentsPersonal and small business finance
Use given data to solve problems on
bull earnings
bull simple interest
bull compound interest
ndash you must know the compound interest formula
bull discount
bull profit and loss
Extract data from tables and charts
Exponential growth and decay
Use exponential growth and decay in population and finance eg depreciation bacteria growth
Learner Guide
53
Extended Algebra and graphs
Question type You should be able to R A G CommentsBasic algebra Use letters to express generalised numbers
Express basic arithmetic processes algebraically
Substitute numbers in complicated formulae
Construct and rearrange complicated formulae eg where the subject appears twice
Algebraic manipulation
Manipulate directed numbers
Use bracketsbull expand a single bracket eg expand 3x(2x ndash 4y)
bull expand a pair of brackets eg (x ndash 4)(x + 7)
bull expand products of more than two brackets eg (x + 4)(x ndash 7)(2x + 1)
Extract common factors eg factorise 9x2 + 15xy
Factorise expressions of the formbull ax + bx + kay + kby
bull asup2xsup2 ndash bsup2ysup2
bull asup2 + 2ab + bsup2
bull axsup2 + bx + c
Learner Guide
54
Extended Algebra and graphs
Question type You should be able to R A G CommentsAlgebraic fractions
Manipulate algebraic fractions eg
bull
bull
bull
bull
bull
Factorise and simplify algebraic fractions such as
Rules of indices Use and interpret positive negative and zero indices
Use and interpret fractional indices eg solve 32x = 2
Use the rules of indices to simplify algebra eg
x3 + x ndash 4
22x3 +
3(x ndash 5)2
3a4 +
5ab3
3a4 divide
9a10
1x ndash 2 +
2x ndash 3
x2 ndash 2xx2 ndash 5x + 6
3xndash4 times23
x12
32x5( )
3
2xndash2divide25
x12
Learner Guide
55
Extended Algebra and graphs
Question type You should be able to R A G CommentsEquations and inequalities
bull Derive and solve simple linear equations in one unknown
bull Derive and solve simultaneous linear equations in two unknowns
bull Derive and solve simultaneous equations involving one linear and one quadratic
Solve quadratic equations by
bull factorisation
bull completing the square
bull using the formula
Derive and solve simple linear inequalities including representing solutions on a number line
Linear programming
Represent inequalities graphically including using the conventions of
bull broken lines for strict inequalities
bull shading unwanted regions
Solve simple linear programming problems using graphical representations of inequalities
Learner Guide
56
Extended Algebra and graphs
Question type You should be able to R A G CommentsNumber sequences (links to Squares square roots cubes and cube roots)
Continue a number sequence
Recognise patterns in sequences
Recognise relationships between different sequences
Find the nth term of sequences of
bull linear sequences
bull quadratic sequences
bull cubic sequences
bull exponential sequences
and simple combinations of these
Direct and inverse proportion (links to Ratio proportion rate)
Express direct proportion algebraically
Express inverse proportion algebraically
Use algebraic expressions of direct and inverse proportion to find unknown quantities
Practical graphs
(links to Coordinate geometry)
Interpret and use graphs in practical situations including
bull travel graphs
bull conversion graphs
Draw graphs from given data
Learner Guide
57
Extended Algebra and graphs
Question type You should be able to R A G CommentsPractical graphs (links to Coordinate geometry) continued
Apply the idea of rate of change to simple kinematics involving
bull distancendashtime graphs
bull speedndashtime graphs
bull acceleration and deceleration
This may involve estimation and interpretation of the gradient of a tangent at a point
Calculate distance travelled as an area under a linear speedndash time graph
Learner Guide
58
Extended Algebra and graphs
Question type You should be able to R A G CommentsGraphs of functions (links to Coordinate geometry)
Construct tables of values and draw graphs for functions of the form
bull axn where a is a rational constant and n = minus2 minus1 0 1 2 3 and simple sums of not more than three of these
bull abx + c where a and c are rational constants and b is a positive integer
Solve associated equations approximately by graphical methods including finding and interpreting roots and finding turning points of quadratics by completing the square
Draw and interpret graphs representing exponential growth and decay problems
Recognise sketch and interpret graphs of
bull linear
bull quadratic
bull cubic
bull reciprocal
bull exponential
(knowledge of turning points and asymtotes is required)Tangents Estimate gradients of curves by drawing tangents
Learner Guide
59
Extended Algebra and graphs
Question type You should be able to R A G CommentsFunctions Use function notation eg
f(x) = 3x ndash 5 f x α 3x ndash5 to describe simple functions
Find inverse functions f ndash1 (x)
Form composite functions as defined by gf(x) = g(f(x))
Derivatives Understand the idea of a derived function
Use derivatives of the form axn and simple sums of not more than three of these (a is a rational constant and n is a positive integer or 0)
Apply differentiation to gradients and turning points (stationary points)
Use any method to explain whether the turning point is a maximum or a minimum eg second derivative or gradient of function on either side of turning point
Learner Guide
60
Extended Co-ordinate geometry
Question type You should be able to R A G CommentsStraight line graphs
Work with co-ordinates in two dimensions
Gradient Find the gradient of a straight line graph
Calculate the gradient of a straight line from the co-ordinates of two points on it
Length and midpoint
Calculate the length and the co-ordinates of the midpoint of a straight line segment from the co-ordinates of its end points
Equation of line Interpret and obtain the equation of a straight line graph
Parallel lines Determine the equation of a straight line parallel to a given line eg find the equation of a line parallel to y = 4x ndash 1 that passes through (0 ndash3)
Perpendicular lines
Find the gradient of parallel and perpendicular lines eg
bull find the gradient of a line perpendicular to y = 3x + 1
bull find the equation of a line perpendicular to one passing through the co-ordinates (1 3) and (ndash2 ndash9)
Learner Guide
61
Extended Geometry
Question type You should be able to R A G CommentsGeometrical language
Use and interpret the geometrical terms
bull point
bull line
bull parallel
bull perpendicular
bull bearing
bull right angle acute obtuse and reflex angles
bull similar
bull congruent
Use and interpret the vocabulary of
bull triangles right-angled scalene isosceles equilateral
bull quadrilaterals
bull circles
bull polygons
bull simple solid figures including nets
Learner Guide
62
Extended Geometry
Question type What I need to do R A G CommentsGeometrical constructions
Measure and draw lines and angles
Construct a triangle given the three sides using a ruler and a pair of compasses only
Scale drawings Read and make scale drawings
Similar figures Calculate lengths of similar figures
Use relationships between areas of similar triangles and in similar figures
Use relationships between volumes and surface areas of similar solids
Congruent triangles
Use the congruence criteria for triangles (SSS ASA SAS RHS)
Symmetry Recognise symmetry properties for triangles quadrilaterals and circles
Recognise line symmetry in two dimensions
Recognise and find the order of rotational symmetry in two dimensions
Learner Guide
63
Extended Geometry
Question type You should be able to R A G CommentsSymmetry (continued)
Use the following symmetry properties of circles
bull equal chords are equidistant from the centre
bull perpendicular bisector of a chord passes through the centre
bull tangents from an external point are equal in length
Recognise and use symmetry properties of
bull prism cylinder cone and pyramid
Learner Guide
64
Extended Geometry
Question type You should be able to R A G CommentsAngle properties Calculate unknown angles explaining the properties that
you are using in geometrical language for the following geometrical properties
bull angles at a point
bull angles at a point on a straight line and intersecting straight lines
bull angles formed within parallel lines
bull angle properties of triangles and quadrilaterals
bull angle properties of regular polygons
bull angle in a semi-circle
bull angle between tangent and radius of a circle
bull angles properties of irregular polygons
bull angle at the centre of a circle is twice the angle at the circumference
bull angles in the same segment are equal
bull angles in opposite segments are supplementary cyclic quadrilaterals
bull alternate segment theorem
Learner Guide
65
Extended Mensuration
Question type What I need to do R A G CommentsMeasures Use current units of
bull mass
bull length
bull area
bull volume
bull capacity
Express quantities in terms of smaller or larger units including units of area and volume
Perimeter Carry out calculations involving
bull perimeter and area of a rectangle
bull perimeter and area of a triangle
bull perimeter and area of parallelogram
bull perimeter and area of a trapezium
bull perimeter and area of compound shapes made by combining rectangles triangles parallelograms andor trapeziums
Learner Guide
66
Extended Mensuration
Question type You should be able to R A G CommentsCircles Carry out calculations involving circumference and area of a
circle
Solve problems involving arc length and sector area of a circle
Surface area and volume
Carry out calculations involving
bull surface area and volume of a cuboid prism and cylinder (no formulae will be given for these shapes)
bull surface area and volume of a sphere pyramid and cone (formulae will be given for these shapes)
Compound shapes
Carry out calculations involving
bull area of a shape made by combining cuboids prisms andor cylinders
bull volume of a shape made by combining cuboids prisms andor cylinders
Learner Guide
67
Extended Trigonometry
Question type You should be able to R A G CommentsBearings Use and interpret three-figure bearings measured clockwise
from the North ie 000degndash360degTrigonometry Find unknown sides andor angles in right-angled triangles by
applying
bull Pythagorasrsquo theorem
bull sine cosine and tangent ratios for acute angles in right-angled triangles
Solve problems in two dimensions involving angles of elevation and depression
Know that the perpendicular distance from a point to a line is the shortest distance to the line
Trig graphs and equations
Recognise sketch and interpret graphs of simple trigonometric functions
Graph and know the properties of trigonometric functions
Solve simple trigonometric equations for values between 0deg
and 360deg eg Solve sin x = radic32
for values of x between 0deg and
360degGeneral trig Solve problems using sine and cosine rules for any triangle
Find the area of any triangle using frac12absinC
Trig in 3D Solve simple trigonometrical problems in three dimensions including angle between a line and a plane
Learner Guide
68
Extended Vectors and transformations
Question type You should be able to R A G CommentsVectors in two dimensions (links to Trigonometry)
Describe a translation by using a vector represented by
AB or a
Add and subtract vectors
Multiply a vector by a scalar
Transformations Reflect simple shapes in horizontal or vertical lines
Rotate simple shapes through multiples of 90deg about any point
Construct translations of simple shapes
Construct enlargements of simple shapes (positive fractional and negative scale factors)
Recognise and describe
bull reflections
bull rotations
bull translations
bull enlargements (positive fractional and negative scalefactors)
( )x
y
Learner Guide
69
Extended Vectors and transformations
Question type You should be able to R A G CommentsHarder vectors
Calculate the magnitude of a vector as and
understand that magnitude is denoted by modulus signs |A B| or |a|
Represent vectors by directed line segments
Use the sum and difference of two vectors
Use position vectors
( )x
yradicx2 + y2
Learner Guide
70
Extended Probability
Question type You should be able to R A G CommentsProbability (links to Four rules)
Calculate the probability of a single event as a fraction decimal or percentage (not a ratio)
Probability scale Understand and use the probability scale from 0 to 1
Sum to 1 Understand that the probability of an event occurring = 1 ndash the probability of the event not occurring
Relative frequency
Understand relative frequency as an estimate of probability
Work out expected frequencies using relative frequency
Combined events Calculate the probability of combined events using
bull tree diagrams
bull possibility diagrams
bull tables
Learner Guide
71
Extended Statistics
Question type You should be able to R A G CommentsClassify Collect classify and tabulate data
Interpret and compare
Read interpret and draw simple inferences from tables and statistical diagrams
Compare sets of data using
bull tables
bull graphs
bull statistical measures
Be aware of restrictions when making conclusions from data
Charts Construct and use
bull bar charts
bull pie charts
bull pictograms
bull stem ndash and ndash leaf diagrams
bull frequency distributions
bull histograms with equal and unequal intervals
bull scatter diagrams
Learner Guide
72
Extended Statistics
Question type You should be able to R A G CommentsAverages Calculate for individual and discrete data
bull mean
bull median
bull mode
bull range
and distinguish between their use
Estimated mean Calculate an estimate of the mean for grouped and continuous data
Identify the modal class from a grouped frequency distributionCumulative frequency
Construct and use cumulative frequency diagrams to estimate and interpret
bull the median
bull percentiles
bull quartiles
bull inter-quartile range
Construct and interpret box-and-whisker plots
Correlation Understand what is meant by positive negative and zero correlation with reference to a scatter diagram
Lines of best fit Draw interpret and use a ruled line of best fit by eye
Cambridge Assessment International Education1 Hills Road Cambridge CB1 2EU United Kingdomt +44 1223 553554e infocambridgeinternationalorg wwwcambridgeinternationalorg
Copyright copy UCLES October 2017
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- Text Field 339
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- Text Field 342
- Check Box 1010296 Off
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- Text Field 349
- Check Box 1010305 Off
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- Text Field 343
- Check Box 1010299 Off
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- Text Field 361
- Check Box 10103020 Off
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- Text Field 362
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- Check Box 10103018 Off
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- Text Field 363
- Check Box 10103023 Off
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- Text Field 365
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- Text Field 367
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- Check Box 10103047 Off
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- Text Field 332
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- Text Field 347
- Check Box 1010311 Off
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- Text Field 3023
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- Text Field 3045
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- Text Field 3046
- Check Box 101010209 Off
- Check Box 101010210 Off
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- Check Box 101010212 Off
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- Text Field 3026
- Check Box 10536 Off
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- Text Field 3047
- Check Box 1010101010 Off
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- Text Field 3048
- Check Box 1010101025 Off
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- Text Field 3027
- Check Box 10539 Off
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- Text Field 3028
- Check Box 101010110 Off
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- Text Field 3029
- Check Box 101010119 Off
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- Text Field 3030
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- Text Field 3031
- Check Box 10545 Off
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- Text Field 3032
- Check Box 10548 Off
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- Text Field 3042
- Check Box 10661 Off
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- Text Field 3033
- Check Box 10551 Off
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- Text Field 3034
- Check Box 101010157 Off
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- Text Field 3035
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- Text Field 3036
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- Text Field 3056
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- Check Box 10557 Off
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- Check Box 10560 Off
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- Text Field 3061
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- Text Field 3062
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- Text Field 3064
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- Text Field 3067
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- Check Box 10737 Off
- Check Box 10738 Off
- Check Box 10739 Off
12
Section 4 Command wordsA command word is the part of the question that tells you what you need to do with your knowledge For example you might need to describe something explain something argue a point of view or list what you know The table below includes command words used in the assessment for this syllabus The use of the command word(s) within an question will relate to the context
Cambridge IGCSE Mathematics 0580 syllabus for 2020 2021 and 2022 Details of the assessment
37wwwcambridgeinternationalorgigcseBack to contents page
Command wordsThe table below includes command words used in the assessment for this syllabus The use of the command word will relate to the subject context
Command word What it means
Calculate work out from given facts figures or information generally using a calculator
Construct make an accurate drawing
Describe state the points of a topicgive characteristics and main features
Determine establish with certainty
Explain set out purposes or reasons make the relationships between things evident provide why andor how and support with relevant evidence
Give produce an answer from a given source or recallmemory
Plot mark point(s) on a graph
Show (that) provide structured evidence that leads to a given result
Sketch make a simple freehand drawing showing the key features
Work out calculate from given facts figures or information with or without the use of a calculator
Write give an answer in a specific form
Write down give an answer without significant working
The question below is taken from Paper 4 and illustrates the use of two command words
The command words lsquoWrite downrsquo indicates that you do not need to show your working and the answer should just be written down The mark allocation [1] also supports this
The command words lsquoShow thatrsquo indicate that you need to provide evidence in the form of a clear mathematical explanation to demonstrate that you know how to obtain the given result In other words you need to show a method that leads to the result
The answer space in this case does not contain a dotted answer line as there is no single lsquoanswerrsquo to be found Your working that leads to the given result should be written in the blank working space
13
This section takes you through an example question and learner response from one of the 2020 specimen papers for this course It will help you to identify the command words and other key instructions within questions and to understand what is required in your response
This section is structured as follows
QuestionThe command words and instructions in the question have
been highlighted and explained This should help you to understand clearly what is required by the question
Mark schemeThis tells you as clearly as possible what an examiner expects
from an answer to award marks
Example candidate responseThis an exemplar answer written in the style of
a high level candidate
How the answer could have been improvedThis summarises what could be done to gain more marks
All information and advice in this section is specific to the example question and response being demonstrated It should give you an idea of how your responses might be viewed by an examiner but it is not a list of what to do in all questions In your own examination you will need to pay careful attention to what each question is asking you to do
Common mistakesThis will help you to avoid common mistakes made by
candidates So often candidates lose marks in their exams because they misread or misinterpret the questions
Section 5 Example candidate response
14
QuestionThe question used in this example is from Specimen Paper 3 (Core) It represents the type of structured question you will see in both Paper 3 (Core) and Paper 4 (Extended) A structured question means that it is broken into several parts Often later parts will depend on your answers to earlier parts
This means that you cannot find the answer by
measuring the diagramWork out indicates that the answer should be calculated from the given information so measurement will not score marks
The allocation of 1 mark indicates that the answer can be obtained with minimum working
Give reasons for your answer indicates that your answer should be supported with reasons using the correct mathematical terminology You must justify your answer
Use trigonometry to calculate indicates that you should use this method with the given information to find the answer and that a calculator is needed to solve the problem If you did not use trigonometry you would not be awarded any marks
15
Show that indicates the answer is given and you need to write down all of the steps in a method that leads to the given answer You need to provide evidence that you understand and know how the answer is reached
Work out indicates that you should calculate the answer from the given information The mark allocation of 4 marks suggests that you will need to include several steps of working in order to get to the answer
Learner Guide
16
Answer Mark Notes(a)(i) 35 1 This is the only acceptable answer for this part of the question
(a)(ii) 74 1 This is the only acceptable answer for this part of the question
(b) 43deg and correct mathematical reasons
3 Two marks are awarded for the final answer of 43deg
The third mark is awarded for a fully correct reason for example angles on a straight line add up to 180deg and angles in a triangle add up to 180deg There are other correct reasons that could be also be used
If 43deg is not obtained one method mark can be awarded if the following calculation is seen in the working
180 ndash 128 or 128 ndash 85
(c) 322 or 3223hellip 2 This is the only acceptable answer for this part of the question
The answer has to be rounded correct to three significant figures or can be given with more figures in the answer
Those that did not get this answer can score one method mark for showing the following in their working
sin = 8 divide 15
(d)(i) 2 2300 225+2 This does not have to be shown in one step as long as the method shown is the same as this overall Those that do not
show this can have one method mark for showing the following in their working
300deg + 225deg
(d)(ii) 15 35 4 The answer 3 35pm is also acceptable for 4 marks
If the correct answer is not found one method mark is available for showing 375 divide 450 in their working and a second method mark can be awarded for sight of them multiplying their answer to this by 60 to change it to hours A third method mark can be awarded for adding their answer in hours to 14 45 ndash this shows the correct method so only one mark is lost for an incorrect final answers
Mark schemeYour examination papers will be marked and the overall number of marks for each paper will be recorded Your marks across all papers will then be converted to a grade
Final answer This value is what the examiner expects to see The answer has to be exactly as given in the mark scheme unless there are acceptable alternatives The mark scheme will always make it clear if there are acceptable alternative answers
Method marks Sometimes method marks are awarded for lines of working as well as for the final answer This means that you could get the final answer incorrect but still get some marks if you include the correct working The mark scheme does not include all possible methods so if you use a method not included in the mark scheme but it is accurate and relevant then the examiner will still award marks for the appropriate parts of the working ndash unless the questions asks you to use a specific method
example of a final answer
example of a method mark
17
Example candidate responseNow letrsquos look at the sample candidatersquos response to question 8 The examiners comments are in the orange boxes The candidate was awarded 8 marks out of 13
180 ndash 74 + 71 = 177
177
74
0 out of 1
The candidates working suggests they understand that the angle sum of a triangle is 180deg but they did not include brackets around 74 + 71 The answer 177deg is not sensible for this question
1 out of 1
The candidate recognises that there are parallel lines and that angle y is a corresponding angle to angle 74deg
180 ndash 128 = 52 180 ndash 85 ndash 52 = 43
43 angles on a straight line add up to 180deg
2 out of 3
The candidate has given a correct answer for w and shown correct working in two steps They have given a correct reason for 52deg using correct mathematical languge But they have not provided a reason to explain the angle 43deg They lose a mark for not also stating angle sum of a triangle is 180deg
sin p = 8 divide 15 = 053
p = sinndash1 (053)
p = 32005 320
1 out of 2
The candidate has correctly used trigonometry in their method They are awarded one method mark for the first line of working However they have rounded 05333333hellip (the result of 8 divide 15) to 052 and then calculated the inverse sin of 052 rather than 05333333 This has resulted in an inaccurate final answer This is called lsquopremature approximationrsquo and it is a very common error to make
18
AB2 = 3002 + 2252
= 140625
AB = 375
1 out of 2
The candidate has recognised the right-angled triangle and correctly used Pythagorasrsquo theorem in the first line of working However they have missed out an important step by not showing that you need to take the square root of 140625 to get 375 As this is a lsquoshow thatrsquo question and they missed a key step in the method they cannot be awarded full marks as the complete working is not shown One method mark is earned for the first line
T = = = 08333333hellip
08333333 hours = 08333333 times 60 minutes = 50 minutes
arrives at 14 45 + 50 mins = 3 35
DS
375450
3 35
3 out of 4
The candidate has found the time by correctly dividing the distance by the speed and recognised that this is in hours When converting the answer to a decimal they have not rounded the decimal but left its full value on the calculator to get 50 mins which is the correct approach Unfortunately after converting the time from 24 hour clock to 12 hour clock they did not include lsquopmrsquo to indicate that the time is in the afternoon and so the final answer is not quite right So 3 marks are awarded for all of a correct method but a mark is lost due to the accuracy of the final answer
19
How the answer could have been improvedThis answer could have been improved by
bull In part (a)(i) the answer of 177deg was not sensible given the diagram in the question If the candidate had checked their answer for sense they would have realised they had made a mistake It is always a good idea to check that your answer seems sensible before you move on to another question
bull In part (b) the candidate did all the correct steps but failed to provide both reasons There were two steps to the method which should have indicated to the candidate that there were two steps to justify and therefore two reasons should have been provided The mark allocation for the question [3] also indicates that more than one reason would be required one mark for the value of 43deg leaving two marks one mark for each of two reasons The candidate should have read the question carefully and again checked their response seemed reasonable
bull In part (c) the candidate rounded an intermediate answer which affected the accuracy of the final answer This caused them to lose a mark despite using a correct method You should only ever round the final answer do not round intermediate values If you can store the intermediate values in your calculator and so that you can use the full value in your calcuations If youre not able to do this and you have to round the intermediate values do not round them to less than three significant figures
bull In part (d)(i) the candidate missed out a step in the method As this was a show that question they needed to show all the steps in the method Its important to show all steps even if they seem obvious
bull In part (d)(ii) the candidate made a silly error by not stating that the time was pm When working with time answers are accepted in either 24 clock or 12 clock time but if you give your answer in the 12 hour clock then it must include am or pm as well
Common mistakesThere were a number of common mistakes made by other candidates on this question
bull Accuracy of answers
In parts (c) and (d)(ii) a common error was premature rounding ndash rounding intermediate values in the method before the final answer which resulted in their final answer not being accurate Other candidates gave the final answer to less than three significant figures ignoring the instruction on the front of the paper to round to three significant figures
bull Using incorrect terminology when giving reasons
In part (b) the most common error was to not give full reasons to support the answer Another common error was to provide a reason that did not use the correct mathematical language such as lsquoThey add up to 180degrsquo and lsquoIt is a straight linersquo which could not be awarded marks
bull Lack of knowledge
In part (c) a number of candidates had limited knowledge of trigonometry and did not choose the correct trig ratio which was the sine ratio This is why good revision is important
bull Not checking answers
In part (a)(i) even though the diagram is drawn NOT TO SCALE it is possible to see that the angle is an acute angle and should therefore not be bigger than 90deg This should alert candidate that if their answer is over 90deg it is not a sensible answer and they should go back and check their working
20
bull Inefficient method shown
In part (c) the lsquoShow thatrsquo question a number of candidates omitted an important step from the method this is often common in lsquoShow thatrsquo questions where every step must be shown no matter how obvious them seem
General adviceIn order to do your best when answering a mathematics question make sure you
bull revise all of the topics for the syllabus you are studying before the exam
bull understand what all the key terms and command words in the question mean
bull read the questions carefully and consider what you need to do before you do it
bull only round the final answer not intermediate values
bull show all steps in your working and show them clearly
bull round to the correct degree of accuracy
bull use the correct mathematical terminology
bull check your answers seem reasonable given the context or details of the question
21
It is important that you plan your revision in plenty of time for the examinations and that you develop a revision technique that works for you The advice in this section will help you revise and prepare for the examinations It is divided into general advice for all papers
Use the tick boxes to keep a record of what you have done what you plan to do or what you understand
For more advice on revision see the Cambridge Learner Revision Guide on our website
Section 6 Revision
Find out when the examinations are and plan your revision so you have time to revise Create a revision timetable and divide it into sections to cover each topic
Spend most of your time focussing on specific skills knowledge or issues that you have found more difficult when practicing them either during revision or earlier in the course
Write a summary of all the key information for a topic ndash use the checklists at the end of this section
Know the meaning of the command words used in questions and how to apply them to the information given Look at past examination papers and highlight the command words and check what they mean
Make revision notes and work on practice questions Reading alone does not work you need to be active and practice your maths
Work for shorter periods then have a break Revise small sections of the syllabus at a time but do this regularly
Test yourself by trying out some past exam questions Use the mark schemes to assess yourself and to be familiar with how marks are awarded for different questions
Be organised in advance with your notes texts exercise books revision guides and revision websites so you do not waste valuable revision time trying to find things
Make notes of key mathematical words that you should use in questions that ask you to lsquodescribersquo or give lsquogeometrical reasons forrsquo eg in describing transformations or giving reasons in circle theorem questions Look at the mark schemes for these types of questions from past papers to see how marks are awarded
Make sure you have all of the correct mathematical equipment ready for the exam particularly your calculator Make sure you are familiar with the all of the important functions on your calculator
Practice the areas you can do well not just those that you find more difficult
Take breaks and do things to relax when you take your breaks this will help you to be more productive when you are revising
Before the examination
22
During the examination
Plan your time according to the marks for each question For example a question worth one mark requires less time than a question one worth 4 marks If a question has several parts then the parts with more marks will need more time
Read each question very carefully
Identify the command words ndash you could underline or highlight them
Identify the other key words and information and perhaps underline them too particularly where
questions require reasoning or problem solving
Read the questions careully and make you have answered the question that is being asked
Show your working this is particularly important for questions where you are asked to lsquoshow that helliprsquo
Set your working out clearly so that it is easy to follow this makes it easier to keep track of what you have done and makes checking back through your work easier and it makes it easier for the examiner to mark your work try to write it in a logical order in the answer space
Write answers clearly if you want to change an answer then you should cross the answer out and write a replacement if your answer is on the answer line cross it out and write the replacement answer above it do not try to change numbers on the answer line as this can lead to unclear figures
Check your working and answers to avoid errors
Give your answer to the appropriate level of accuracy either the accuracy indicated in the question or the accuracy given on the front of the paper
Avoid rounding intermediate values part way through your calculation only round the final answer
Check that the answer that you have given is sensible and realistic for what is being asked
Use a pencil when drawing diagrams or completing graphs this means that you can change your answer more easily if you have made a mistake
Take care when reading scales
If you are asked for reasons for your answer then use the correct mathematical terms
Use the mark allocation given with the questionsparts of questions to try to judge how much work is needed to answer each part
23
Top tips for revision of Cambridge IGCSE Mathematics1 Summarise recall and applyMake sure that you can recall and apply the key information and mathematical techniques on each topic that you need for the exam
i Write a summary of the key information of a topicii Collect together some questions that test the knowledge and skills of this topic Ask your teacher for practice
questions or suitable past examination questions or use practice books or textbooksiii Test your recall by covering over the summary and trying to remember the details or use the summary as part of
the lsquoTeach the topicrsquo (Tip 3) or lsquoQuestion and answer cardsrsquo (Tip 4) activities iv After you have spent some time revising and practising the knowledge and skills answer the questions that you
collected together on the topic You might do this later on the same day as revising or a few days later Answer as many questions as you can in order to practise applying your knowledge
v Try creating your own questions by adapting existing ones and use these for practice when you return to a topic
On graph questions straight lines should be ruled and curves should be drawn freehand with a smooth curve
Donrsquot spend too long on any one part of a question If you are really stuck on a question then move on and come back to the question later if you have time As a rough guide each mark on the paper should take about one minute
2 Concept mapsConcept maps are a great way to revise the links between different factors or to explore a larger topic They can also be used to collect together your ideas
i Use a blank sheet of paper and turn it on its side (landscape)ii Put the topic title in the middle of the page and build the concept map outwards using lines called lsquobranchesrsquo
ndash The first branches are from the central topic to sub-topics draw these as thick lines
ndash Add new branches from the sub-topics to include more detail draw these as thinner lines
ndash Add even more detail to a point by adding more branches
This creates a hierarchy of information from lsquooverviewrsquo (the thick branches) to lsquofine detailrsquo (thinnest branches)
iii Write single key words or phrases along a branch and add drawings for visual impactiv Use different colours highlighter pens symbols and arrows to highlight key facts or issuesIt is a good idea to use a large piece of plain A3 (or larger) paper and lots of coloured pens
24
3 Teach the topicThis is a very simple but effective technique that focusses on knowledge recall It tests the brain and rehearses the information you need to know for a certain topic and so will help your revision
i Create some topic cards with key bullet points of information on Leave space for ticksii Give these to your parents family or friends for exampleiii Give yourself 10 minutes maximum to teach your audience the main points of the topic You could use a mini-
whiteboard or flip chart to helpiv Your audience tick off all the points you mention in your presentation and give you a final scoreThe brain loves competition so if you do not score full marks you can try again the next day or compete against friends This system of repeat and rehearsal is very effective especially with more complex topics and doesnt take much preparation
4 Question and answer (QampA) cardsThis is very similar to Teach the topic but less formal and less public for those who dislike performing in front of others It tests knowledge recall and rehearses the information you need to know for a certain topic
i Pick a topic and create two sets of cards question cards and answer cards You might find it helpful to make the question cards a different size or use different coloured card for answers
ii Make sure you have the topic or something appropriate depending on what you are focusing on as a heading on each card The questions should test your knowledge and understanding of key areas of the course
iii A friend or family member uses the cards to test you in short 5 or 10 minute periods at any time during the dayiv You could also do this alone by reading the questions to yourself giving the answer and then checking the
correct answer cardv This game can be adapted by using the cards to find matching pairs turn all cards face down across the space
in front of you Turn over two cards leaving them where they are If they match (one is a question card and the other is the corresponding answer card) pick up the pair and put them to one side If they dont match try to remember where they are and what is on each card then turn them back over Turn over two other cards Continue until you have matched all pairs
5 Question paper and mark schemesLooking at past question papers and the mark scheme helps you to familiarise yourself with what to expect and what the standard is
i Ask your teacher for past paper questions with mark schemes for the course ndash ask your teacher for help to make sure you are answering the correct questions and to simplify the mark scheme
ii Look at the revision checklist and identify which topic a given question relates to ndash you might need to ask your teacher to help you do this
iii Once you have finished revising a topic or unit time yourself answering some appropriate exam questions Check the mark schemes to see how well you would have scored or give the answers to your teacher to check
iv Add details or notes to the mark scheme where you missed out on marks in your original answers using a different coloured pen Use these notes when you revise and try the question again later
You can find plenty of past exam papers and mark schemes on the Cambridge International public website
httpwwwcambridgeinternationalorgprogrammes-and-qualificationscambridge-igcse-mathematics-0580past-papers
25
Other useful revision advice for Cambridge IGCSE Mathematics bull Before the exam make sure that you are familiar with your calculator and confident in using it
bull Look at the Example Candidate Response earlier in this guide Can you identify the strengths of the response andwhere they have made mistakes or lost marks
bull When you are attempting a past paper (or questions from a past paper) complete it without referring to yournotes so that you get a true idea of your strengths and weaknesses Then go back through the paper using yournotes and a different coloured pen to make corrections and changes After you have done as much as you can onthe paper mark it using the mark scheme Take notes of any points that you lost marks on
bull Donrsquot just revise the topics that you enjoy and are confident in If you identify an area that you are weaker inthen try to revisit the topic by reviewing your notes and doing some practice questions then use exam questionsto check whether you now understand
bull Return to topics later in your revision to check that you still remember and understand the topic and to help toensure that you recall more of the material when you get to the examination
Revision checklists for Cambridge IGCSE MathematicsThe tables on the following pages can be used as a revision checklist They do not contain all the detailed knowledge you need to know just an overview For more detail see the syllabus and talk to your teacher
You can use the tick boxes in the checklists to show when you have revised and are happy that you do not need to return to it Tick the lsquoRrsquo lsquoArsquo and lsquoGrsquo column to record your progress as follows
bull R = RED means you are really unsure and lack confidence in that area you might want to focus your revisionhere and possibly talk to your teacher for help
bull A = AMBER means you are reasonably confident in a topic but need some extra practicebull G = GREEN means you are very confident in a topic
As your revision progresses you can concentrate on the RED and AMBER topics in order to turn them into GREEN topics You might find it helpful to highlight each topic in red orange or green to help you prioritise
You can use the lsquoCommentsrsquo column to
bull add more information about the details for each pointbull include a reference to a useful resourcebull include a list of formulae or notationbull add learning aids such as rhymes poems or word playbull highlight areas of difficulty or things that you need to talk to your teacher about
There is a set of checklist for the Core syllabus and a different set for the Extended syllabus
Learner Guide
26
Core syllabus contentCore Number
Category You should be able to R A G CommentsNumber Identify and use
bull natural numbers
bull integers (positive negative and zero)
bull prime numbers
bull write a number as a product of its prime factors
bull square numbers and cube numbers
bull common factors and highest common factor of two numbers
bull common multiples and lowest common multiple of two numbers
bull rational numbers
bull irrational numbers (eg π radic2 )
bull real numbers
bull reciprocals
Learner Guide
27
Core Number
Question type You should be able to R A G CommentsSets and Venn diagrams
Understand notation of Venn diagrams
Definition of sets
eg A = xx is a natural number
B = abchellip
Notation
Number of elements in set A n(A)
Universal set
Union of A and B A cup B
Intersection of A and B A cap B
Squares square roots cubes and cube roots
Calculate
bull squares and cubes of numbers
bull square roots and cube roots of numbers
Learner Guide
28
Core Number
Question type You should be able to R A G CommentsDirected numbers
Use directed numbers in practical situations for example temperature changes
Fractions decimals and percentages
Use the language and notation of simple vulgar and decimal fractions and percentages
Recognise equivalent fractions decimals and percentages
Convert between fractions decimals and percentages
Ordering Order quantities by magnitude and demonstrate familiarity with the symbols = ne gt lt ⩾ ⩽
Indices and standard form (links to Algebraic manipulation)
Evaluate indices eg 25 5ndash2 1000 64frac12 8ndash23
Use the rules of indices for
bull multiplication of indices eg 4ndash3 times 45
bull division of indices eg 57 divide 53
bull index numbers raised to an index eg (23)2 (43)2
Use the standard form A times 10n where n is a positive or negative integer and 1 ⩽ A lt 10
bull convert numbers into and out of standard form
bull calculate with numbers in standard form
Learner Guide
29
Core Number
Question type You should be able to R A G CommentsFour rules
( + ndash times divide )
Use the four rules for calculations with
bull whole numbers
bull decimals
bull vulgar and mixed fractions
bull correct ordering of operations (BIDMAS) and use of bracketsEstimates Make estimates of numbers quantities and lengths
Give approximations to a specified number of
bull significant figures
bull decimal places
Round off answers to reasonable accuracy in the context of a given problem
Bounds Give upper and lower bounds for data given to a specified accuracy eg measured lengths
Ratio proportion rate
Understand ratio
Divide a quantity in a given ratio
Understand direct and inverse proportion
Use scales in practical situations
Use common measures of rate (formulae for other rates eg density and pressure will be given in the question)
Calculate average speed
Learner Guide
30
Core Number
Question type You should be able to R A G CommentsPercentages Calculate a percentage of a quantity
Express one quantity as a percentage of another quantity
Calculate percentage increase or decrease
Use of an electronic calculator
Use a calculator efficiently
Check accuracy of calculations
Time Calculate times in terms of the 24-hour and 12-hour clock
Read
bull clocks
bull dials
bull timetables
Money Calculate using money
Convert from one currency to another
Learner Guide
31
Core Number
Question type You should be able to R A G CommentsPersonal and small business finance
Use given data to solve problems on
bull earnings
bull simple interest
bull compound interest (you will need to know the compound interest formula)
bull discount
bull profit and loss
Extract data from tables and charts
Learner Guide
32
Core Algebra and graphs
Question type You should be able to R A G CommentsBasic algebra Use letters to express generalised numbers
Express basic arithmetic processes algebraically
Substitute numbers in formulae
Construct simple expressions and set up simple equations
Rearrange simple formulae
Algebraic manipulation
Manipulate directed numbers
Use brackets
bull expand a single bracket eg 3x(2x ndash4y)
bull expand a pair of brackets eg (x + 3) (x ndash 7)
Extract common factors eg factorise 9x2 + 15xy
Rules of indices Use and interpret positive negative and zero indices
Use the rules of indices eg to simplify algebra such as
bull 3x4 times 5x
bull 10x3 divide 2x2
bull (x6)2
Learner Guide
33
Core Algebra and graphs
Question type You should be able to R A G CommentsEquations and inequalities
Derive and solve simple linear equations in one unknown
Derive and solve simultaneous linear equations in two unknowns
Number sequences
(links to Squares square roots cubes and cube roots)
Continue a number sequence
Recognise patterns in sequences
Recognise relationships between difference sequences
Find the nth term of sequences for
bull liner sequences
bull simple quadratic sequences
bull cubic sequences
Practical graphs
(links to Mensuration)
Interpret and use graphs in practical situations including
bull travel graphs
bull conversion graphs
Draw graphs from given data
Learner Guide
34
Core Algebra and graphs
Question type You should be able to R A G CommentsGraphs of functions
(links to Co-ordinate geometry)
Construct tables of values for functions of the form
bull ax + b (linear)
bull plusmn x2 + ax + b (quadratic)
bull (x ne 0) (reciprocal)
where a and b are integer constants
Draw and interpret such graphs
Solve linear and quadratic equations approximately by graphical methods
Recognise and sketch the graphs of linear and quadratic functions
ax
Learner Guide
35
Core Co-ordinate geometry
Question type You should be able to R A G CommentsCo-ordinates Work with co-ordinates in two dimensions
Gradients Find the gradient of a straight line graph
Equation of straight line
Interpret and obtain the equation of a straight line graph in the form y = mx + c where the graph is given
Parallel lines Determine the equation of a straight line parallel to a given line eg find the equation of a line parallel to y = 4x ndash 1 that passes through (0 ndash3)
Learner Guide
36
Core Geometry
Question type You should be able to R A G CommentsGeometrical language
Use and interpret the geometrical terms
bull point
bull line
bull parallel
bull perpendicular
bull bearing
bull right angle acute obtuse and reflex angles
bull similar
bull congruent
Use and interpret the vocabulary of
bull triangles right-angled scalene isosceles equilateral
bull quadrilaterals
bull circles
bull polygons
bull simple solid figures including nets
Learner Guide
37
Core Geometry
Question type You should be able to R A G CommentsGeometrical constructions
Measure and draw lines and angles
Construct a triangle given the three sides using a ruler and a pair of compasses only
Scale drawings Read and make scale drawings
Similar figures Calculate lengths of similar figures
Congruent Recognise congruent shapes
Symmetry Recognise symmetry properties for triangles quadrilaterals and circles
Recognise line symmetry in two dimensions
Recognise and find the order of rotational symmetry in two dimensions
Learner Guide
38
Core Geometry
Question type You should be able to R A G CommentsAngle properties Calculate unknown angles explaining the properties that you
are using in geometrical language for angles
bull angles at a point
bull angles on a straight line and intersecting straight lines
bull angles within parallel lines
bull angles in triangles
bull angles in quadrilaterals
bull angles in regular polygons
bull angle in a semi-circle
bull angle between tangent and radius of a circle
Learner Guide
39
Core Mensuration
Question type You should be able to R A G CommentsMeasures bull Use current units of
bull mass
bull length
bull area
bull volume
bull capacity
Express quantities in terms of smaller or larger units including units of area and volume
Convert between units including units of area and volume
Perimiter Carry out calculations involving
bull perimeter and area of a rectangle
bull perimeter and area of a triangle
bull perimeter and area of parallelogram
bull perimeter and area of a trapezium
bull perimeter and area of shapes made by combining
bull rectangles triangles parallelograms andor trapeziums
Learner Guide
40
Core Mensuration
Question type You should be able to R A G CommentsCircles Carry out calculations involving circumference and area of a
circle
Solve simple problems involving the arc length and sector area of a circle where the sector angle is a factor of 360deg
Surface area and volume
Carry out calculations involving
bull surface area and volume of a cuboid prism and cylinder (no formulae will be given for these shapes)
bull surface area and volume of a sphere pyramid and cone (formulae will be given for these shapes)
Areas and volumes of compound shapes
Carry out calculations involving the areas and volumes of compound shapes made from combinations of the shapes in Perimeter or Surface area and volume
Learner Guide
41
Core Trigonometry
Question type You should be able to R A G CommentsBearings Use and interpret three-figure bearings measured clockwise
from the North ie 000degndash360degTrigonometry Find unknown sides andor angles in right-angled triangles by
applying
bull Pythagorasrsquo theorem
bull sine cosine and tangent ratios for acute angles in right-angled triangles
Learner Guide
42
Core Vectors and transformations
Question type You should be able to R A G CommentsVectors in two dimensions (links to Trigonometry)
Describe a translation by using a vector represented by
AB or a
Add and subtract vectors
Multiply a vector by a scalar
Transformations Reflect simple shapes in horizontal or vertical lines
Rotate simple shapes through multiples of 90deg about
bull the origin
bull their vertices
bull the midpoints of their sides
Construct translations of simple shapes
Construct enlargements of simple shapes (positive and fractional scale factors)
Recognise and describe using the correct language
bull reflections
bull rotations
bull translations
bull enlargements (positive and fractional scale factors)
( )x
y
Learner Guide
43
Core Probability
Question type You should be able to R A G CommentsSingle events Calculate the probability of a single event as a fraction decimal
or percentage (not a ratio)Probability scale Understand and use the probability scale from 0 to 1
Sum to 1 Understand that the probability of an event occurring = 1 ndash the probability of the event not occurring
Relative frequency
Understand relative frequency as an estimate of probability
Work out expected frequencies using relative frequencyCombined events Calculate the probability of simple combined events using
bull tree diagrams
bull possibility diagrams (points on a grid)
bull Venn diagrams (2 sets only)
Learner Guide
44
Core Statistics
Question type What I need to do R A G CommentsClassify Collect classify and tabulate data
Interpret and compare
Read interpret and draw simple inferences from tables and statistical diagrams
Compare sets of data using
bull tables
bull graphs
bull statistical measures
Be aware of restrictions when making conclusions from data
Charts Construct and use
bull bar charts
bull pie charts
bull pictograms
bull stem-and-leaf diagrams
bull frequency distributions
bull histograms with equal intervals
bull scatter diagrams
Learner Guide
45
Question type What I need to do R A G CommentsAverages Calculate for individual and discrete data
bull mean
bull median
bull mode
bull range
and distinguish between their useCorrelation Understand what is meant by positive negative and zero
correlation with reference to a scatter diagramLine of best fit Draw interpret and use a ruled line of best fit by eye
Learner Guide
46
Extended syllabus content (includes required Core content)Extended Number
Question type You should be able to R A G CommentsNumber Identify and use
bull natural numbers
bull integers (positive negative and zero)
bull prime numbers
bull write a number as a product of its prime factors
bull square and cube numbers
bull common factors and highest common factor of two or more numbers
bull common multiples and lowest common multiple of two or more numbers
bull rational numbers
bull irrational numbers (eg π radic2 )
bull real numbers
bull reciprocals
Learner Guide
47
Extended Number
Question type You should be able to R A G CommentsSet notation and language
Use language notation and Venn diagrams to describe sets and represent relationships between sets as follows
Definition of sets egA = x x is a natural number
B = (xy) y = mx + c
C = x a ⩽ x ⩽ b
D = a b c hellip
Notation egnumber of elements in set A n(A)
lsquois an element ofrsquo isin
lsquois not an element ofrsquo notin
complement of set A
the empty set empty
the universal set
A is a subset of B A sube B
A is a proper subset of B A sub B
A is not a subset of B A ⊈ B
A is not a proper subset of B A nsub B
union of A and B A cup B
intersection of A and B A cap B
Learner Guide
48
Extended Number
Question type You should be able to R A G CommentsSquares square roots cubes and cube roots
Calculatebull squares of numbers
bull square roots of numbers
bull cubes of numbers
bull cube roots of numbers
bull other powers and roots of numbers
Directed numbers
Use directed numbers in practical situations for example temperature changes
Fractions decimals and percentages
Use the language and notation of simple vulgar and decimal fractions and percentages in appropriate contexts
Recognise equivalent fractions decimals and percentages
Convert between fractions decimals and percentages
Convert recurring decimals to fractions
Ordering Order quantities by magnitude and demonstrate familiarity with the symbols = ne gt lt ⩾ ⩽
Learner Guide
49
Extended Number
Question type You should be able to R A G CommentsIndices and standard form (links to Algebraic manipulation)
Evaluate indices including fractional negative and zero
eg 25 5ndash2 1000 10012 8ndash23
Use the rules of indices forbull multiplication of indices eg 43 times 45
bull division of indices eg 57 divide 53
bull index numbers raised to an index eg (43)2
Use the standard form A times 10n where n is a positive or negative integer and 1 ⩽ A lt 10bull convert into and out of standard form
bull calculate with numbers in standard form
Four rules
( + ndash times divide )
Use the four rules for calculations withbull whole numbers
bull decimals
bull vulgar and mixed fractions
bull correct ordering of operations (BIDMAS) and use of brackets
Learner Guide
50
Extended Number
Question type You should be able to R A G CommentsEstimates Make estimates of numbers quantities and lengths
Give approximations to a specified number of
bull significant figures
bull decimal places
Round off answers to reasonable accuracy in the context of a given problem
Bounds Give upper and lower bounds for data given to a specified accuracy eg measured lengths
Obtain appropriate upper and lower bounds to solutions of simple problems given to a specified accuracy eg the lower and upper bounds for the area of a rectangle
Ratio proportion rate
(links to Direct and inverse proportion)
Understand ratio
Divide quantities in a given ratio
Increase and decrease a quantity by a given ratio
Understand numerical problems involving direct and inverse proportion
Use ratio and scales in practical situations
Use common measures of rate (formulae for other rates eg density and pressure will be given in the question)
Calculate average speed
Learner Guide
51
Extended Number
Question type What I need to do R A G CommentsPercentages Calculate a percentage of a quantity
Express one quantity as a percentage of another quantity
Calculate percentage increase or decrease
Calculate reverse percentages eg finding the cost price given the selling price and the percentage profit
Use of an electronic calculator
Use a calculator efficiently
Check accuracy of calculations
Time Calculate times in terms of the 24-hour and 12-hour clock
Read clocks dials and timetables
Money Calculate using money
Convert from one currency to another
Learner Guide
52
Extended Number
Question type You should be able to R A G CommentsPersonal and small business finance
Use given data to solve problems on
bull earnings
bull simple interest
bull compound interest
ndash you must know the compound interest formula
bull discount
bull profit and loss
Extract data from tables and charts
Exponential growth and decay
Use exponential growth and decay in population and finance eg depreciation bacteria growth
Learner Guide
53
Extended Algebra and graphs
Question type You should be able to R A G CommentsBasic algebra Use letters to express generalised numbers
Express basic arithmetic processes algebraically
Substitute numbers in complicated formulae
Construct and rearrange complicated formulae eg where the subject appears twice
Algebraic manipulation
Manipulate directed numbers
Use bracketsbull expand a single bracket eg expand 3x(2x ndash 4y)
bull expand a pair of brackets eg (x ndash 4)(x + 7)
bull expand products of more than two brackets eg (x + 4)(x ndash 7)(2x + 1)
Extract common factors eg factorise 9x2 + 15xy
Factorise expressions of the formbull ax + bx + kay + kby
bull asup2xsup2 ndash bsup2ysup2
bull asup2 + 2ab + bsup2
bull axsup2 + bx + c
Learner Guide
54
Extended Algebra and graphs
Question type You should be able to R A G CommentsAlgebraic fractions
Manipulate algebraic fractions eg
bull
bull
bull
bull
bull
Factorise and simplify algebraic fractions such as
Rules of indices Use and interpret positive negative and zero indices
Use and interpret fractional indices eg solve 32x = 2
Use the rules of indices to simplify algebra eg
x3 + x ndash 4
22x3 +
3(x ndash 5)2
3a4 +
5ab3
3a4 divide
9a10
1x ndash 2 +
2x ndash 3
x2 ndash 2xx2 ndash 5x + 6
3xndash4 times23
x12
32x5( )
3
2xndash2divide25
x12
Learner Guide
55
Extended Algebra and graphs
Question type You should be able to R A G CommentsEquations and inequalities
bull Derive and solve simple linear equations in one unknown
bull Derive and solve simultaneous linear equations in two unknowns
bull Derive and solve simultaneous equations involving one linear and one quadratic
Solve quadratic equations by
bull factorisation
bull completing the square
bull using the formula
Derive and solve simple linear inequalities including representing solutions on a number line
Linear programming
Represent inequalities graphically including using the conventions of
bull broken lines for strict inequalities
bull shading unwanted regions
Solve simple linear programming problems using graphical representations of inequalities
Learner Guide
56
Extended Algebra and graphs
Question type You should be able to R A G CommentsNumber sequences (links to Squares square roots cubes and cube roots)
Continue a number sequence
Recognise patterns in sequences
Recognise relationships between different sequences
Find the nth term of sequences of
bull linear sequences
bull quadratic sequences
bull cubic sequences
bull exponential sequences
and simple combinations of these
Direct and inverse proportion (links to Ratio proportion rate)
Express direct proportion algebraically
Express inverse proportion algebraically
Use algebraic expressions of direct and inverse proportion to find unknown quantities
Practical graphs
(links to Coordinate geometry)
Interpret and use graphs in practical situations including
bull travel graphs
bull conversion graphs
Draw graphs from given data
Learner Guide
57
Extended Algebra and graphs
Question type You should be able to R A G CommentsPractical graphs (links to Coordinate geometry) continued
Apply the idea of rate of change to simple kinematics involving
bull distancendashtime graphs
bull speedndashtime graphs
bull acceleration and deceleration
This may involve estimation and interpretation of the gradient of a tangent at a point
Calculate distance travelled as an area under a linear speedndash time graph
Learner Guide
58
Extended Algebra and graphs
Question type You should be able to R A G CommentsGraphs of functions (links to Coordinate geometry)
Construct tables of values and draw graphs for functions of the form
bull axn where a is a rational constant and n = minus2 minus1 0 1 2 3 and simple sums of not more than three of these
bull abx + c where a and c are rational constants and b is a positive integer
Solve associated equations approximately by graphical methods including finding and interpreting roots and finding turning points of quadratics by completing the square
Draw and interpret graphs representing exponential growth and decay problems
Recognise sketch and interpret graphs of
bull linear
bull quadratic
bull cubic
bull reciprocal
bull exponential
(knowledge of turning points and asymtotes is required)Tangents Estimate gradients of curves by drawing tangents
Learner Guide
59
Extended Algebra and graphs
Question type You should be able to R A G CommentsFunctions Use function notation eg
f(x) = 3x ndash 5 f x α 3x ndash5 to describe simple functions
Find inverse functions f ndash1 (x)
Form composite functions as defined by gf(x) = g(f(x))
Derivatives Understand the idea of a derived function
Use derivatives of the form axn and simple sums of not more than three of these (a is a rational constant and n is a positive integer or 0)
Apply differentiation to gradients and turning points (stationary points)
Use any method to explain whether the turning point is a maximum or a minimum eg second derivative or gradient of function on either side of turning point
Learner Guide
60
Extended Co-ordinate geometry
Question type You should be able to R A G CommentsStraight line graphs
Work with co-ordinates in two dimensions
Gradient Find the gradient of a straight line graph
Calculate the gradient of a straight line from the co-ordinates of two points on it
Length and midpoint
Calculate the length and the co-ordinates of the midpoint of a straight line segment from the co-ordinates of its end points
Equation of line Interpret and obtain the equation of a straight line graph
Parallel lines Determine the equation of a straight line parallel to a given line eg find the equation of a line parallel to y = 4x ndash 1 that passes through (0 ndash3)
Perpendicular lines
Find the gradient of parallel and perpendicular lines eg
bull find the gradient of a line perpendicular to y = 3x + 1
bull find the equation of a line perpendicular to one passing through the co-ordinates (1 3) and (ndash2 ndash9)
Learner Guide
61
Extended Geometry
Question type You should be able to R A G CommentsGeometrical language
Use and interpret the geometrical terms
bull point
bull line
bull parallel
bull perpendicular
bull bearing
bull right angle acute obtuse and reflex angles
bull similar
bull congruent
Use and interpret the vocabulary of
bull triangles right-angled scalene isosceles equilateral
bull quadrilaterals
bull circles
bull polygons
bull simple solid figures including nets
Learner Guide
62
Extended Geometry
Question type What I need to do R A G CommentsGeometrical constructions
Measure and draw lines and angles
Construct a triangle given the three sides using a ruler and a pair of compasses only
Scale drawings Read and make scale drawings
Similar figures Calculate lengths of similar figures
Use relationships between areas of similar triangles and in similar figures
Use relationships between volumes and surface areas of similar solids
Congruent triangles
Use the congruence criteria for triangles (SSS ASA SAS RHS)
Symmetry Recognise symmetry properties for triangles quadrilaterals and circles
Recognise line symmetry in two dimensions
Recognise and find the order of rotational symmetry in two dimensions
Learner Guide
63
Extended Geometry
Question type You should be able to R A G CommentsSymmetry (continued)
Use the following symmetry properties of circles
bull equal chords are equidistant from the centre
bull perpendicular bisector of a chord passes through the centre
bull tangents from an external point are equal in length
Recognise and use symmetry properties of
bull prism cylinder cone and pyramid
Learner Guide
64
Extended Geometry
Question type You should be able to R A G CommentsAngle properties Calculate unknown angles explaining the properties that
you are using in geometrical language for the following geometrical properties
bull angles at a point
bull angles at a point on a straight line and intersecting straight lines
bull angles formed within parallel lines
bull angle properties of triangles and quadrilaterals
bull angle properties of regular polygons
bull angle in a semi-circle
bull angle between tangent and radius of a circle
bull angles properties of irregular polygons
bull angle at the centre of a circle is twice the angle at the circumference
bull angles in the same segment are equal
bull angles in opposite segments are supplementary cyclic quadrilaterals
bull alternate segment theorem
Learner Guide
65
Extended Mensuration
Question type What I need to do R A G CommentsMeasures Use current units of
bull mass
bull length
bull area
bull volume
bull capacity
Express quantities in terms of smaller or larger units including units of area and volume
Perimeter Carry out calculations involving
bull perimeter and area of a rectangle
bull perimeter and area of a triangle
bull perimeter and area of parallelogram
bull perimeter and area of a trapezium
bull perimeter and area of compound shapes made by combining rectangles triangles parallelograms andor trapeziums
Learner Guide
66
Extended Mensuration
Question type You should be able to R A G CommentsCircles Carry out calculations involving circumference and area of a
circle
Solve problems involving arc length and sector area of a circle
Surface area and volume
Carry out calculations involving
bull surface area and volume of a cuboid prism and cylinder (no formulae will be given for these shapes)
bull surface area and volume of a sphere pyramid and cone (formulae will be given for these shapes)
Compound shapes
Carry out calculations involving
bull area of a shape made by combining cuboids prisms andor cylinders
bull volume of a shape made by combining cuboids prisms andor cylinders
Learner Guide
67
Extended Trigonometry
Question type You should be able to R A G CommentsBearings Use and interpret three-figure bearings measured clockwise
from the North ie 000degndash360degTrigonometry Find unknown sides andor angles in right-angled triangles by
applying
bull Pythagorasrsquo theorem
bull sine cosine and tangent ratios for acute angles in right-angled triangles
Solve problems in two dimensions involving angles of elevation and depression
Know that the perpendicular distance from a point to a line is the shortest distance to the line
Trig graphs and equations
Recognise sketch and interpret graphs of simple trigonometric functions
Graph and know the properties of trigonometric functions
Solve simple trigonometric equations for values between 0deg
and 360deg eg Solve sin x = radic32
for values of x between 0deg and
360degGeneral trig Solve problems using sine and cosine rules for any triangle
Find the area of any triangle using frac12absinC
Trig in 3D Solve simple trigonometrical problems in three dimensions including angle between a line and a plane
Learner Guide
68
Extended Vectors and transformations
Question type You should be able to R A G CommentsVectors in two dimensions (links to Trigonometry)
Describe a translation by using a vector represented by
AB or a
Add and subtract vectors
Multiply a vector by a scalar
Transformations Reflect simple shapes in horizontal or vertical lines
Rotate simple shapes through multiples of 90deg about any point
Construct translations of simple shapes
Construct enlargements of simple shapes (positive fractional and negative scale factors)
Recognise and describe
bull reflections
bull rotations
bull translations
bull enlargements (positive fractional and negative scalefactors)
( )x
y
Learner Guide
69
Extended Vectors and transformations
Question type You should be able to R A G CommentsHarder vectors
Calculate the magnitude of a vector as and
understand that magnitude is denoted by modulus signs |A B| or |a|
Represent vectors by directed line segments
Use the sum and difference of two vectors
Use position vectors
( )x
yradicx2 + y2
Learner Guide
70
Extended Probability
Question type You should be able to R A G CommentsProbability (links to Four rules)
Calculate the probability of a single event as a fraction decimal or percentage (not a ratio)
Probability scale Understand and use the probability scale from 0 to 1
Sum to 1 Understand that the probability of an event occurring = 1 ndash the probability of the event not occurring
Relative frequency
Understand relative frequency as an estimate of probability
Work out expected frequencies using relative frequency
Combined events Calculate the probability of combined events using
bull tree diagrams
bull possibility diagrams
bull tables
Learner Guide
71
Extended Statistics
Question type You should be able to R A G CommentsClassify Collect classify and tabulate data
Interpret and compare
Read interpret and draw simple inferences from tables and statistical diagrams
Compare sets of data using
bull tables
bull graphs
bull statistical measures
Be aware of restrictions when making conclusions from data
Charts Construct and use
bull bar charts
bull pie charts
bull pictograms
bull stem ndash and ndash leaf diagrams
bull frequency distributions
bull histograms with equal and unequal intervals
bull scatter diagrams
Learner Guide
72
Extended Statistics
Question type You should be able to R A G CommentsAverages Calculate for individual and discrete data
bull mean
bull median
bull mode
bull range
and distinguish between their use
Estimated mean Calculate an estimate of the mean for grouped and continuous data
Identify the modal class from a grouped frequency distributionCumulative frequency
Construct and use cumulative frequency diagrams to estimate and interpret
bull the median
bull percentiles
bull quartiles
bull inter-quartile range
Construct and interpret box-and-whisker plots
Correlation Understand what is meant by positive negative and zero correlation with reference to a scatter diagram
Lines of best fit Draw interpret and use a ruled line of best fit by eye
Cambridge Assessment International Education1 Hills Road Cambridge CB1 2EU United Kingdomt +44 1223 553554e infocambridgeinternationalorg wwwcambridgeinternationalorg
Copyright copy UCLES October 2017
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- Text Field 363
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- Text Field 365
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- Text Field 347
- Check Box 1010311 Off
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- Text Field 3023
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- Text Field 3045
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- Text Field 3046
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- Text Field 3026
- Check Box 10536 Off
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- Text Field 3047
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- Text Field 3048
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- Text Field 3027
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- Text Field 3030
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- Text Field 3031
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- Text Field 3032
- Check Box 10548 Off
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- Text Field 3042
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- Text Field 3033
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- Text Field 3056
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- Text Field 3057
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- Text Field 3064
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- Text Field 3067
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13
This section takes you through an example question and learner response from one of the 2020 specimen papers for this course It will help you to identify the command words and other key instructions within questions and to understand what is required in your response
This section is structured as follows
QuestionThe command words and instructions in the question have
been highlighted and explained This should help you to understand clearly what is required by the question
Mark schemeThis tells you as clearly as possible what an examiner expects
from an answer to award marks
Example candidate responseThis an exemplar answer written in the style of
a high level candidate
How the answer could have been improvedThis summarises what could be done to gain more marks
All information and advice in this section is specific to the example question and response being demonstrated It should give you an idea of how your responses might be viewed by an examiner but it is not a list of what to do in all questions In your own examination you will need to pay careful attention to what each question is asking you to do
Common mistakesThis will help you to avoid common mistakes made by
candidates So often candidates lose marks in their exams because they misread or misinterpret the questions
Section 5 Example candidate response
14
QuestionThe question used in this example is from Specimen Paper 3 (Core) It represents the type of structured question you will see in both Paper 3 (Core) and Paper 4 (Extended) A structured question means that it is broken into several parts Often later parts will depend on your answers to earlier parts
This means that you cannot find the answer by
measuring the diagramWork out indicates that the answer should be calculated from the given information so measurement will not score marks
The allocation of 1 mark indicates that the answer can be obtained with minimum working
Give reasons for your answer indicates that your answer should be supported with reasons using the correct mathematical terminology You must justify your answer
Use trigonometry to calculate indicates that you should use this method with the given information to find the answer and that a calculator is needed to solve the problem If you did not use trigonometry you would not be awarded any marks
15
Show that indicates the answer is given and you need to write down all of the steps in a method that leads to the given answer You need to provide evidence that you understand and know how the answer is reached
Work out indicates that you should calculate the answer from the given information The mark allocation of 4 marks suggests that you will need to include several steps of working in order to get to the answer
Learner Guide
16
Answer Mark Notes(a)(i) 35 1 This is the only acceptable answer for this part of the question
(a)(ii) 74 1 This is the only acceptable answer for this part of the question
(b) 43deg and correct mathematical reasons
3 Two marks are awarded for the final answer of 43deg
The third mark is awarded for a fully correct reason for example angles on a straight line add up to 180deg and angles in a triangle add up to 180deg There are other correct reasons that could be also be used
If 43deg is not obtained one method mark can be awarded if the following calculation is seen in the working
180 ndash 128 or 128 ndash 85
(c) 322 or 3223hellip 2 This is the only acceptable answer for this part of the question
The answer has to be rounded correct to three significant figures or can be given with more figures in the answer
Those that did not get this answer can score one method mark for showing the following in their working
sin = 8 divide 15
(d)(i) 2 2300 225+2 This does not have to be shown in one step as long as the method shown is the same as this overall Those that do not
show this can have one method mark for showing the following in their working
300deg + 225deg
(d)(ii) 15 35 4 The answer 3 35pm is also acceptable for 4 marks
If the correct answer is not found one method mark is available for showing 375 divide 450 in their working and a second method mark can be awarded for sight of them multiplying their answer to this by 60 to change it to hours A third method mark can be awarded for adding their answer in hours to 14 45 ndash this shows the correct method so only one mark is lost for an incorrect final answers
Mark schemeYour examination papers will be marked and the overall number of marks for each paper will be recorded Your marks across all papers will then be converted to a grade
Final answer This value is what the examiner expects to see The answer has to be exactly as given in the mark scheme unless there are acceptable alternatives The mark scheme will always make it clear if there are acceptable alternative answers
Method marks Sometimes method marks are awarded for lines of working as well as for the final answer This means that you could get the final answer incorrect but still get some marks if you include the correct working The mark scheme does not include all possible methods so if you use a method not included in the mark scheme but it is accurate and relevant then the examiner will still award marks for the appropriate parts of the working ndash unless the questions asks you to use a specific method
example of a final answer
example of a method mark
17
Example candidate responseNow letrsquos look at the sample candidatersquos response to question 8 The examiners comments are in the orange boxes The candidate was awarded 8 marks out of 13
180 ndash 74 + 71 = 177
177
74
0 out of 1
The candidates working suggests they understand that the angle sum of a triangle is 180deg but they did not include brackets around 74 + 71 The answer 177deg is not sensible for this question
1 out of 1
The candidate recognises that there are parallel lines and that angle y is a corresponding angle to angle 74deg
180 ndash 128 = 52 180 ndash 85 ndash 52 = 43
43 angles on a straight line add up to 180deg
2 out of 3
The candidate has given a correct answer for w and shown correct working in two steps They have given a correct reason for 52deg using correct mathematical languge But they have not provided a reason to explain the angle 43deg They lose a mark for not also stating angle sum of a triangle is 180deg
sin p = 8 divide 15 = 053
p = sinndash1 (053)
p = 32005 320
1 out of 2
The candidate has correctly used trigonometry in their method They are awarded one method mark for the first line of working However they have rounded 05333333hellip (the result of 8 divide 15) to 052 and then calculated the inverse sin of 052 rather than 05333333 This has resulted in an inaccurate final answer This is called lsquopremature approximationrsquo and it is a very common error to make
18
AB2 = 3002 + 2252
= 140625
AB = 375
1 out of 2
The candidate has recognised the right-angled triangle and correctly used Pythagorasrsquo theorem in the first line of working However they have missed out an important step by not showing that you need to take the square root of 140625 to get 375 As this is a lsquoshow thatrsquo question and they missed a key step in the method they cannot be awarded full marks as the complete working is not shown One method mark is earned for the first line
T = = = 08333333hellip
08333333 hours = 08333333 times 60 minutes = 50 minutes
arrives at 14 45 + 50 mins = 3 35
DS
375450
3 35
3 out of 4
The candidate has found the time by correctly dividing the distance by the speed and recognised that this is in hours When converting the answer to a decimal they have not rounded the decimal but left its full value on the calculator to get 50 mins which is the correct approach Unfortunately after converting the time from 24 hour clock to 12 hour clock they did not include lsquopmrsquo to indicate that the time is in the afternoon and so the final answer is not quite right So 3 marks are awarded for all of a correct method but a mark is lost due to the accuracy of the final answer
19
How the answer could have been improvedThis answer could have been improved by
bull In part (a)(i) the answer of 177deg was not sensible given the diagram in the question If the candidate had checked their answer for sense they would have realised they had made a mistake It is always a good idea to check that your answer seems sensible before you move on to another question
bull In part (b) the candidate did all the correct steps but failed to provide both reasons There were two steps to the method which should have indicated to the candidate that there were two steps to justify and therefore two reasons should have been provided The mark allocation for the question [3] also indicates that more than one reason would be required one mark for the value of 43deg leaving two marks one mark for each of two reasons The candidate should have read the question carefully and again checked their response seemed reasonable
bull In part (c) the candidate rounded an intermediate answer which affected the accuracy of the final answer This caused them to lose a mark despite using a correct method You should only ever round the final answer do not round intermediate values If you can store the intermediate values in your calculator and so that you can use the full value in your calcuations If youre not able to do this and you have to round the intermediate values do not round them to less than three significant figures
bull In part (d)(i) the candidate missed out a step in the method As this was a show that question they needed to show all the steps in the method Its important to show all steps even if they seem obvious
bull In part (d)(ii) the candidate made a silly error by not stating that the time was pm When working with time answers are accepted in either 24 clock or 12 clock time but if you give your answer in the 12 hour clock then it must include am or pm as well
Common mistakesThere were a number of common mistakes made by other candidates on this question
bull Accuracy of answers
In parts (c) and (d)(ii) a common error was premature rounding ndash rounding intermediate values in the method before the final answer which resulted in their final answer not being accurate Other candidates gave the final answer to less than three significant figures ignoring the instruction on the front of the paper to round to three significant figures
bull Using incorrect terminology when giving reasons
In part (b) the most common error was to not give full reasons to support the answer Another common error was to provide a reason that did not use the correct mathematical language such as lsquoThey add up to 180degrsquo and lsquoIt is a straight linersquo which could not be awarded marks
bull Lack of knowledge
In part (c) a number of candidates had limited knowledge of trigonometry and did not choose the correct trig ratio which was the sine ratio This is why good revision is important
bull Not checking answers
In part (a)(i) even though the diagram is drawn NOT TO SCALE it is possible to see that the angle is an acute angle and should therefore not be bigger than 90deg This should alert candidate that if their answer is over 90deg it is not a sensible answer and they should go back and check their working
20
bull Inefficient method shown
In part (c) the lsquoShow thatrsquo question a number of candidates omitted an important step from the method this is often common in lsquoShow thatrsquo questions where every step must be shown no matter how obvious them seem
General adviceIn order to do your best when answering a mathematics question make sure you
bull revise all of the topics for the syllabus you are studying before the exam
bull understand what all the key terms and command words in the question mean
bull read the questions carefully and consider what you need to do before you do it
bull only round the final answer not intermediate values
bull show all steps in your working and show them clearly
bull round to the correct degree of accuracy
bull use the correct mathematical terminology
bull check your answers seem reasonable given the context or details of the question
21
It is important that you plan your revision in plenty of time for the examinations and that you develop a revision technique that works for you The advice in this section will help you revise and prepare for the examinations It is divided into general advice for all papers
Use the tick boxes to keep a record of what you have done what you plan to do or what you understand
For more advice on revision see the Cambridge Learner Revision Guide on our website
Section 6 Revision
Find out when the examinations are and plan your revision so you have time to revise Create a revision timetable and divide it into sections to cover each topic
Spend most of your time focussing on specific skills knowledge or issues that you have found more difficult when practicing them either during revision or earlier in the course
Write a summary of all the key information for a topic ndash use the checklists at the end of this section
Know the meaning of the command words used in questions and how to apply them to the information given Look at past examination papers and highlight the command words and check what they mean
Make revision notes and work on practice questions Reading alone does not work you need to be active and practice your maths
Work for shorter periods then have a break Revise small sections of the syllabus at a time but do this regularly
Test yourself by trying out some past exam questions Use the mark schemes to assess yourself and to be familiar with how marks are awarded for different questions
Be organised in advance with your notes texts exercise books revision guides and revision websites so you do not waste valuable revision time trying to find things
Make notes of key mathematical words that you should use in questions that ask you to lsquodescribersquo or give lsquogeometrical reasons forrsquo eg in describing transformations or giving reasons in circle theorem questions Look at the mark schemes for these types of questions from past papers to see how marks are awarded
Make sure you have all of the correct mathematical equipment ready for the exam particularly your calculator Make sure you are familiar with the all of the important functions on your calculator
Practice the areas you can do well not just those that you find more difficult
Take breaks and do things to relax when you take your breaks this will help you to be more productive when you are revising
Before the examination
22
During the examination
Plan your time according to the marks for each question For example a question worth one mark requires less time than a question one worth 4 marks If a question has several parts then the parts with more marks will need more time
Read each question very carefully
Identify the command words ndash you could underline or highlight them
Identify the other key words and information and perhaps underline them too particularly where
questions require reasoning or problem solving
Read the questions careully and make you have answered the question that is being asked
Show your working this is particularly important for questions where you are asked to lsquoshow that helliprsquo
Set your working out clearly so that it is easy to follow this makes it easier to keep track of what you have done and makes checking back through your work easier and it makes it easier for the examiner to mark your work try to write it in a logical order in the answer space
Write answers clearly if you want to change an answer then you should cross the answer out and write a replacement if your answer is on the answer line cross it out and write the replacement answer above it do not try to change numbers on the answer line as this can lead to unclear figures
Check your working and answers to avoid errors
Give your answer to the appropriate level of accuracy either the accuracy indicated in the question or the accuracy given on the front of the paper
Avoid rounding intermediate values part way through your calculation only round the final answer
Check that the answer that you have given is sensible and realistic for what is being asked
Use a pencil when drawing diagrams or completing graphs this means that you can change your answer more easily if you have made a mistake
Take care when reading scales
If you are asked for reasons for your answer then use the correct mathematical terms
Use the mark allocation given with the questionsparts of questions to try to judge how much work is needed to answer each part
23
Top tips for revision of Cambridge IGCSE Mathematics1 Summarise recall and applyMake sure that you can recall and apply the key information and mathematical techniques on each topic that you need for the exam
i Write a summary of the key information of a topicii Collect together some questions that test the knowledge and skills of this topic Ask your teacher for practice
questions or suitable past examination questions or use practice books or textbooksiii Test your recall by covering over the summary and trying to remember the details or use the summary as part of
the lsquoTeach the topicrsquo (Tip 3) or lsquoQuestion and answer cardsrsquo (Tip 4) activities iv After you have spent some time revising and practising the knowledge and skills answer the questions that you
collected together on the topic You might do this later on the same day as revising or a few days later Answer as many questions as you can in order to practise applying your knowledge
v Try creating your own questions by adapting existing ones and use these for practice when you return to a topic
On graph questions straight lines should be ruled and curves should be drawn freehand with a smooth curve
Donrsquot spend too long on any one part of a question If you are really stuck on a question then move on and come back to the question later if you have time As a rough guide each mark on the paper should take about one minute
2 Concept mapsConcept maps are a great way to revise the links between different factors or to explore a larger topic They can also be used to collect together your ideas
i Use a blank sheet of paper and turn it on its side (landscape)ii Put the topic title in the middle of the page and build the concept map outwards using lines called lsquobranchesrsquo
ndash The first branches are from the central topic to sub-topics draw these as thick lines
ndash Add new branches from the sub-topics to include more detail draw these as thinner lines
ndash Add even more detail to a point by adding more branches
This creates a hierarchy of information from lsquooverviewrsquo (the thick branches) to lsquofine detailrsquo (thinnest branches)
iii Write single key words or phrases along a branch and add drawings for visual impactiv Use different colours highlighter pens symbols and arrows to highlight key facts or issuesIt is a good idea to use a large piece of plain A3 (or larger) paper and lots of coloured pens
24
3 Teach the topicThis is a very simple but effective technique that focusses on knowledge recall It tests the brain and rehearses the information you need to know for a certain topic and so will help your revision
i Create some topic cards with key bullet points of information on Leave space for ticksii Give these to your parents family or friends for exampleiii Give yourself 10 minutes maximum to teach your audience the main points of the topic You could use a mini-
whiteboard or flip chart to helpiv Your audience tick off all the points you mention in your presentation and give you a final scoreThe brain loves competition so if you do not score full marks you can try again the next day or compete against friends This system of repeat and rehearsal is very effective especially with more complex topics and doesnt take much preparation
4 Question and answer (QampA) cardsThis is very similar to Teach the topic but less formal and less public for those who dislike performing in front of others It tests knowledge recall and rehearses the information you need to know for a certain topic
i Pick a topic and create two sets of cards question cards and answer cards You might find it helpful to make the question cards a different size or use different coloured card for answers
ii Make sure you have the topic or something appropriate depending on what you are focusing on as a heading on each card The questions should test your knowledge and understanding of key areas of the course
iii A friend or family member uses the cards to test you in short 5 or 10 minute periods at any time during the dayiv You could also do this alone by reading the questions to yourself giving the answer and then checking the
correct answer cardv This game can be adapted by using the cards to find matching pairs turn all cards face down across the space
in front of you Turn over two cards leaving them where they are If they match (one is a question card and the other is the corresponding answer card) pick up the pair and put them to one side If they dont match try to remember where they are and what is on each card then turn them back over Turn over two other cards Continue until you have matched all pairs
5 Question paper and mark schemesLooking at past question papers and the mark scheme helps you to familiarise yourself with what to expect and what the standard is
i Ask your teacher for past paper questions with mark schemes for the course ndash ask your teacher for help to make sure you are answering the correct questions and to simplify the mark scheme
ii Look at the revision checklist and identify which topic a given question relates to ndash you might need to ask your teacher to help you do this
iii Once you have finished revising a topic or unit time yourself answering some appropriate exam questions Check the mark schemes to see how well you would have scored or give the answers to your teacher to check
iv Add details or notes to the mark scheme where you missed out on marks in your original answers using a different coloured pen Use these notes when you revise and try the question again later
You can find plenty of past exam papers and mark schemes on the Cambridge International public website
httpwwwcambridgeinternationalorgprogrammes-and-qualificationscambridge-igcse-mathematics-0580past-papers
25
Other useful revision advice for Cambridge IGCSE Mathematics bull Before the exam make sure that you are familiar with your calculator and confident in using it
bull Look at the Example Candidate Response earlier in this guide Can you identify the strengths of the response andwhere they have made mistakes or lost marks
bull When you are attempting a past paper (or questions from a past paper) complete it without referring to yournotes so that you get a true idea of your strengths and weaknesses Then go back through the paper using yournotes and a different coloured pen to make corrections and changes After you have done as much as you can onthe paper mark it using the mark scheme Take notes of any points that you lost marks on
bull Donrsquot just revise the topics that you enjoy and are confident in If you identify an area that you are weaker inthen try to revisit the topic by reviewing your notes and doing some practice questions then use exam questionsto check whether you now understand
bull Return to topics later in your revision to check that you still remember and understand the topic and to help toensure that you recall more of the material when you get to the examination
Revision checklists for Cambridge IGCSE MathematicsThe tables on the following pages can be used as a revision checklist They do not contain all the detailed knowledge you need to know just an overview For more detail see the syllabus and talk to your teacher
You can use the tick boxes in the checklists to show when you have revised and are happy that you do not need to return to it Tick the lsquoRrsquo lsquoArsquo and lsquoGrsquo column to record your progress as follows
bull R = RED means you are really unsure and lack confidence in that area you might want to focus your revisionhere and possibly talk to your teacher for help
bull A = AMBER means you are reasonably confident in a topic but need some extra practicebull G = GREEN means you are very confident in a topic
As your revision progresses you can concentrate on the RED and AMBER topics in order to turn them into GREEN topics You might find it helpful to highlight each topic in red orange or green to help you prioritise
You can use the lsquoCommentsrsquo column to
bull add more information about the details for each pointbull include a reference to a useful resourcebull include a list of formulae or notationbull add learning aids such as rhymes poems or word playbull highlight areas of difficulty or things that you need to talk to your teacher about
There is a set of checklist for the Core syllabus and a different set for the Extended syllabus
Learner Guide
26
Core syllabus contentCore Number
Category You should be able to R A G CommentsNumber Identify and use
bull natural numbers
bull integers (positive negative and zero)
bull prime numbers
bull write a number as a product of its prime factors
bull square numbers and cube numbers
bull common factors and highest common factor of two numbers
bull common multiples and lowest common multiple of two numbers
bull rational numbers
bull irrational numbers (eg π radic2 )
bull real numbers
bull reciprocals
Learner Guide
27
Core Number
Question type You should be able to R A G CommentsSets and Venn diagrams
Understand notation of Venn diagrams
Definition of sets
eg A = xx is a natural number
B = abchellip
Notation
Number of elements in set A n(A)
Universal set
Union of A and B A cup B
Intersection of A and B A cap B
Squares square roots cubes and cube roots
Calculate
bull squares and cubes of numbers
bull square roots and cube roots of numbers
Learner Guide
28
Core Number
Question type You should be able to R A G CommentsDirected numbers
Use directed numbers in practical situations for example temperature changes
Fractions decimals and percentages
Use the language and notation of simple vulgar and decimal fractions and percentages
Recognise equivalent fractions decimals and percentages
Convert between fractions decimals and percentages
Ordering Order quantities by magnitude and demonstrate familiarity with the symbols = ne gt lt ⩾ ⩽
Indices and standard form (links to Algebraic manipulation)
Evaluate indices eg 25 5ndash2 1000 64frac12 8ndash23
Use the rules of indices for
bull multiplication of indices eg 4ndash3 times 45
bull division of indices eg 57 divide 53
bull index numbers raised to an index eg (23)2 (43)2
Use the standard form A times 10n where n is a positive or negative integer and 1 ⩽ A lt 10
bull convert numbers into and out of standard form
bull calculate with numbers in standard form
Learner Guide
29
Core Number
Question type You should be able to R A G CommentsFour rules
( + ndash times divide )
Use the four rules for calculations with
bull whole numbers
bull decimals
bull vulgar and mixed fractions
bull correct ordering of operations (BIDMAS) and use of bracketsEstimates Make estimates of numbers quantities and lengths
Give approximations to a specified number of
bull significant figures
bull decimal places
Round off answers to reasonable accuracy in the context of a given problem
Bounds Give upper and lower bounds for data given to a specified accuracy eg measured lengths
Ratio proportion rate
Understand ratio
Divide a quantity in a given ratio
Understand direct and inverse proportion
Use scales in practical situations
Use common measures of rate (formulae for other rates eg density and pressure will be given in the question)
Calculate average speed
Learner Guide
30
Core Number
Question type You should be able to R A G CommentsPercentages Calculate a percentage of a quantity
Express one quantity as a percentage of another quantity
Calculate percentage increase or decrease
Use of an electronic calculator
Use a calculator efficiently
Check accuracy of calculations
Time Calculate times in terms of the 24-hour and 12-hour clock
Read
bull clocks
bull dials
bull timetables
Money Calculate using money
Convert from one currency to another
Learner Guide
31
Core Number
Question type You should be able to R A G CommentsPersonal and small business finance
Use given data to solve problems on
bull earnings
bull simple interest
bull compound interest (you will need to know the compound interest formula)
bull discount
bull profit and loss
Extract data from tables and charts
Learner Guide
32
Core Algebra and graphs
Question type You should be able to R A G CommentsBasic algebra Use letters to express generalised numbers
Express basic arithmetic processes algebraically
Substitute numbers in formulae
Construct simple expressions and set up simple equations
Rearrange simple formulae
Algebraic manipulation
Manipulate directed numbers
Use brackets
bull expand a single bracket eg 3x(2x ndash4y)
bull expand a pair of brackets eg (x + 3) (x ndash 7)
Extract common factors eg factorise 9x2 + 15xy
Rules of indices Use and interpret positive negative and zero indices
Use the rules of indices eg to simplify algebra such as
bull 3x4 times 5x
bull 10x3 divide 2x2
bull (x6)2
Learner Guide
33
Core Algebra and graphs
Question type You should be able to R A G CommentsEquations and inequalities
Derive and solve simple linear equations in one unknown
Derive and solve simultaneous linear equations in two unknowns
Number sequences
(links to Squares square roots cubes and cube roots)
Continue a number sequence
Recognise patterns in sequences
Recognise relationships between difference sequences
Find the nth term of sequences for
bull liner sequences
bull simple quadratic sequences
bull cubic sequences
Practical graphs
(links to Mensuration)
Interpret and use graphs in practical situations including
bull travel graphs
bull conversion graphs
Draw graphs from given data
Learner Guide
34
Core Algebra and graphs
Question type You should be able to R A G CommentsGraphs of functions
(links to Co-ordinate geometry)
Construct tables of values for functions of the form
bull ax + b (linear)
bull plusmn x2 + ax + b (quadratic)
bull (x ne 0) (reciprocal)
where a and b are integer constants
Draw and interpret such graphs
Solve linear and quadratic equations approximately by graphical methods
Recognise and sketch the graphs of linear and quadratic functions
ax
Learner Guide
35
Core Co-ordinate geometry
Question type You should be able to R A G CommentsCo-ordinates Work with co-ordinates in two dimensions
Gradients Find the gradient of a straight line graph
Equation of straight line
Interpret and obtain the equation of a straight line graph in the form y = mx + c where the graph is given
Parallel lines Determine the equation of a straight line parallel to a given line eg find the equation of a line parallel to y = 4x ndash 1 that passes through (0 ndash3)
Learner Guide
36
Core Geometry
Question type You should be able to R A G CommentsGeometrical language
Use and interpret the geometrical terms
bull point
bull line
bull parallel
bull perpendicular
bull bearing
bull right angle acute obtuse and reflex angles
bull similar
bull congruent
Use and interpret the vocabulary of
bull triangles right-angled scalene isosceles equilateral
bull quadrilaterals
bull circles
bull polygons
bull simple solid figures including nets
Learner Guide
37
Core Geometry
Question type You should be able to R A G CommentsGeometrical constructions
Measure and draw lines and angles
Construct a triangle given the three sides using a ruler and a pair of compasses only
Scale drawings Read and make scale drawings
Similar figures Calculate lengths of similar figures
Congruent Recognise congruent shapes
Symmetry Recognise symmetry properties for triangles quadrilaterals and circles
Recognise line symmetry in two dimensions
Recognise and find the order of rotational symmetry in two dimensions
Learner Guide
38
Core Geometry
Question type You should be able to R A G CommentsAngle properties Calculate unknown angles explaining the properties that you
are using in geometrical language for angles
bull angles at a point
bull angles on a straight line and intersecting straight lines
bull angles within parallel lines
bull angles in triangles
bull angles in quadrilaterals
bull angles in regular polygons
bull angle in a semi-circle
bull angle between tangent and radius of a circle
Learner Guide
39
Core Mensuration
Question type You should be able to R A G CommentsMeasures bull Use current units of
bull mass
bull length
bull area
bull volume
bull capacity
Express quantities in terms of smaller or larger units including units of area and volume
Convert between units including units of area and volume
Perimiter Carry out calculations involving
bull perimeter and area of a rectangle
bull perimeter and area of a triangle
bull perimeter and area of parallelogram
bull perimeter and area of a trapezium
bull perimeter and area of shapes made by combining
bull rectangles triangles parallelograms andor trapeziums
Learner Guide
40
Core Mensuration
Question type You should be able to R A G CommentsCircles Carry out calculations involving circumference and area of a
circle
Solve simple problems involving the arc length and sector area of a circle where the sector angle is a factor of 360deg
Surface area and volume
Carry out calculations involving
bull surface area and volume of a cuboid prism and cylinder (no formulae will be given for these shapes)
bull surface area and volume of a sphere pyramid and cone (formulae will be given for these shapes)
Areas and volumes of compound shapes
Carry out calculations involving the areas and volumes of compound shapes made from combinations of the shapes in Perimeter or Surface area and volume
Learner Guide
41
Core Trigonometry
Question type You should be able to R A G CommentsBearings Use and interpret three-figure bearings measured clockwise
from the North ie 000degndash360degTrigonometry Find unknown sides andor angles in right-angled triangles by
applying
bull Pythagorasrsquo theorem
bull sine cosine and tangent ratios for acute angles in right-angled triangles
Learner Guide
42
Core Vectors and transformations
Question type You should be able to R A G CommentsVectors in two dimensions (links to Trigonometry)
Describe a translation by using a vector represented by
AB or a
Add and subtract vectors
Multiply a vector by a scalar
Transformations Reflect simple shapes in horizontal or vertical lines
Rotate simple shapes through multiples of 90deg about
bull the origin
bull their vertices
bull the midpoints of their sides
Construct translations of simple shapes
Construct enlargements of simple shapes (positive and fractional scale factors)
Recognise and describe using the correct language
bull reflections
bull rotations
bull translations
bull enlargements (positive and fractional scale factors)
( )x
y
Learner Guide
43
Core Probability
Question type You should be able to R A G CommentsSingle events Calculate the probability of a single event as a fraction decimal
or percentage (not a ratio)Probability scale Understand and use the probability scale from 0 to 1
Sum to 1 Understand that the probability of an event occurring = 1 ndash the probability of the event not occurring
Relative frequency
Understand relative frequency as an estimate of probability
Work out expected frequencies using relative frequencyCombined events Calculate the probability of simple combined events using
bull tree diagrams
bull possibility diagrams (points on a grid)
bull Venn diagrams (2 sets only)
Learner Guide
44
Core Statistics
Question type What I need to do R A G CommentsClassify Collect classify and tabulate data
Interpret and compare
Read interpret and draw simple inferences from tables and statistical diagrams
Compare sets of data using
bull tables
bull graphs
bull statistical measures
Be aware of restrictions when making conclusions from data
Charts Construct and use
bull bar charts
bull pie charts
bull pictograms
bull stem-and-leaf diagrams
bull frequency distributions
bull histograms with equal intervals
bull scatter diagrams
Learner Guide
45
Question type What I need to do R A G CommentsAverages Calculate for individual and discrete data
bull mean
bull median
bull mode
bull range
and distinguish between their useCorrelation Understand what is meant by positive negative and zero
correlation with reference to a scatter diagramLine of best fit Draw interpret and use a ruled line of best fit by eye
Learner Guide
46
Extended syllabus content (includes required Core content)Extended Number
Question type You should be able to R A G CommentsNumber Identify and use
bull natural numbers
bull integers (positive negative and zero)
bull prime numbers
bull write a number as a product of its prime factors
bull square and cube numbers
bull common factors and highest common factor of two or more numbers
bull common multiples and lowest common multiple of two or more numbers
bull rational numbers
bull irrational numbers (eg π radic2 )
bull real numbers
bull reciprocals
Learner Guide
47
Extended Number
Question type You should be able to R A G CommentsSet notation and language
Use language notation and Venn diagrams to describe sets and represent relationships between sets as follows
Definition of sets egA = x x is a natural number
B = (xy) y = mx + c
C = x a ⩽ x ⩽ b
D = a b c hellip
Notation egnumber of elements in set A n(A)
lsquois an element ofrsquo isin
lsquois not an element ofrsquo notin
complement of set A
the empty set empty
the universal set
A is a subset of B A sube B
A is a proper subset of B A sub B
A is not a subset of B A ⊈ B
A is not a proper subset of B A nsub B
union of A and B A cup B
intersection of A and B A cap B
Learner Guide
48
Extended Number
Question type You should be able to R A G CommentsSquares square roots cubes and cube roots
Calculatebull squares of numbers
bull square roots of numbers
bull cubes of numbers
bull cube roots of numbers
bull other powers and roots of numbers
Directed numbers
Use directed numbers in practical situations for example temperature changes
Fractions decimals and percentages
Use the language and notation of simple vulgar and decimal fractions and percentages in appropriate contexts
Recognise equivalent fractions decimals and percentages
Convert between fractions decimals and percentages
Convert recurring decimals to fractions
Ordering Order quantities by magnitude and demonstrate familiarity with the symbols = ne gt lt ⩾ ⩽
Learner Guide
49
Extended Number
Question type You should be able to R A G CommentsIndices and standard form (links to Algebraic manipulation)
Evaluate indices including fractional negative and zero
eg 25 5ndash2 1000 10012 8ndash23
Use the rules of indices forbull multiplication of indices eg 43 times 45
bull division of indices eg 57 divide 53
bull index numbers raised to an index eg (43)2
Use the standard form A times 10n where n is a positive or negative integer and 1 ⩽ A lt 10bull convert into and out of standard form
bull calculate with numbers in standard form
Four rules
( + ndash times divide )
Use the four rules for calculations withbull whole numbers
bull decimals
bull vulgar and mixed fractions
bull correct ordering of operations (BIDMAS) and use of brackets
Learner Guide
50
Extended Number
Question type You should be able to R A G CommentsEstimates Make estimates of numbers quantities and lengths
Give approximations to a specified number of
bull significant figures
bull decimal places
Round off answers to reasonable accuracy in the context of a given problem
Bounds Give upper and lower bounds for data given to a specified accuracy eg measured lengths
Obtain appropriate upper and lower bounds to solutions of simple problems given to a specified accuracy eg the lower and upper bounds for the area of a rectangle
Ratio proportion rate
(links to Direct and inverse proportion)
Understand ratio
Divide quantities in a given ratio
Increase and decrease a quantity by a given ratio
Understand numerical problems involving direct and inverse proportion
Use ratio and scales in practical situations
Use common measures of rate (formulae for other rates eg density and pressure will be given in the question)
Calculate average speed
Learner Guide
51
Extended Number
Question type What I need to do R A G CommentsPercentages Calculate a percentage of a quantity
Express one quantity as a percentage of another quantity
Calculate percentage increase or decrease
Calculate reverse percentages eg finding the cost price given the selling price and the percentage profit
Use of an electronic calculator
Use a calculator efficiently
Check accuracy of calculations
Time Calculate times in terms of the 24-hour and 12-hour clock
Read clocks dials and timetables
Money Calculate using money
Convert from one currency to another
Learner Guide
52
Extended Number
Question type You should be able to R A G CommentsPersonal and small business finance
Use given data to solve problems on
bull earnings
bull simple interest
bull compound interest
ndash you must know the compound interest formula
bull discount
bull profit and loss
Extract data from tables and charts
Exponential growth and decay
Use exponential growth and decay in population and finance eg depreciation bacteria growth
Learner Guide
53
Extended Algebra and graphs
Question type You should be able to R A G CommentsBasic algebra Use letters to express generalised numbers
Express basic arithmetic processes algebraically
Substitute numbers in complicated formulae
Construct and rearrange complicated formulae eg where the subject appears twice
Algebraic manipulation
Manipulate directed numbers
Use bracketsbull expand a single bracket eg expand 3x(2x ndash 4y)
bull expand a pair of brackets eg (x ndash 4)(x + 7)
bull expand products of more than two brackets eg (x + 4)(x ndash 7)(2x + 1)
Extract common factors eg factorise 9x2 + 15xy
Factorise expressions of the formbull ax + bx + kay + kby
bull asup2xsup2 ndash bsup2ysup2
bull asup2 + 2ab + bsup2
bull axsup2 + bx + c
Learner Guide
54
Extended Algebra and graphs
Question type You should be able to R A G CommentsAlgebraic fractions
Manipulate algebraic fractions eg
bull
bull
bull
bull
bull
Factorise and simplify algebraic fractions such as
Rules of indices Use and interpret positive negative and zero indices
Use and interpret fractional indices eg solve 32x = 2
Use the rules of indices to simplify algebra eg
x3 + x ndash 4
22x3 +
3(x ndash 5)2
3a4 +
5ab3
3a4 divide
9a10
1x ndash 2 +
2x ndash 3
x2 ndash 2xx2 ndash 5x + 6
3xndash4 times23
x12
32x5( )
3
2xndash2divide25
x12
Learner Guide
55
Extended Algebra and graphs
Question type You should be able to R A G CommentsEquations and inequalities
bull Derive and solve simple linear equations in one unknown
bull Derive and solve simultaneous linear equations in two unknowns
bull Derive and solve simultaneous equations involving one linear and one quadratic
Solve quadratic equations by
bull factorisation
bull completing the square
bull using the formula
Derive and solve simple linear inequalities including representing solutions on a number line
Linear programming
Represent inequalities graphically including using the conventions of
bull broken lines for strict inequalities
bull shading unwanted regions
Solve simple linear programming problems using graphical representations of inequalities
Learner Guide
56
Extended Algebra and graphs
Question type You should be able to R A G CommentsNumber sequences (links to Squares square roots cubes and cube roots)
Continue a number sequence
Recognise patterns in sequences
Recognise relationships between different sequences
Find the nth term of sequences of
bull linear sequences
bull quadratic sequences
bull cubic sequences
bull exponential sequences
and simple combinations of these
Direct and inverse proportion (links to Ratio proportion rate)
Express direct proportion algebraically
Express inverse proportion algebraically
Use algebraic expressions of direct and inverse proportion to find unknown quantities
Practical graphs
(links to Coordinate geometry)
Interpret and use graphs in practical situations including
bull travel graphs
bull conversion graphs
Draw graphs from given data
Learner Guide
57
Extended Algebra and graphs
Question type You should be able to R A G CommentsPractical graphs (links to Coordinate geometry) continued
Apply the idea of rate of change to simple kinematics involving
bull distancendashtime graphs
bull speedndashtime graphs
bull acceleration and deceleration
This may involve estimation and interpretation of the gradient of a tangent at a point
Calculate distance travelled as an area under a linear speedndash time graph
Learner Guide
58
Extended Algebra and graphs
Question type You should be able to R A G CommentsGraphs of functions (links to Coordinate geometry)
Construct tables of values and draw graphs for functions of the form
bull axn where a is a rational constant and n = minus2 minus1 0 1 2 3 and simple sums of not more than three of these
bull abx + c where a and c are rational constants and b is a positive integer
Solve associated equations approximately by graphical methods including finding and interpreting roots and finding turning points of quadratics by completing the square
Draw and interpret graphs representing exponential growth and decay problems
Recognise sketch and interpret graphs of
bull linear
bull quadratic
bull cubic
bull reciprocal
bull exponential
(knowledge of turning points and asymtotes is required)Tangents Estimate gradients of curves by drawing tangents
Learner Guide
59
Extended Algebra and graphs
Question type You should be able to R A G CommentsFunctions Use function notation eg
f(x) = 3x ndash 5 f x α 3x ndash5 to describe simple functions
Find inverse functions f ndash1 (x)
Form composite functions as defined by gf(x) = g(f(x))
Derivatives Understand the idea of a derived function
Use derivatives of the form axn and simple sums of not more than three of these (a is a rational constant and n is a positive integer or 0)
Apply differentiation to gradients and turning points (stationary points)
Use any method to explain whether the turning point is a maximum or a minimum eg second derivative or gradient of function on either side of turning point
Learner Guide
60
Extended Co-ordinate geometry
Question type You should be able to R A G CommentsStraight line graphs
Work with co-ordinates in two dimensions
Gradient Find the gradient of a straight line graph
Calculate the gradient of a straight line from the co-ordinates of two points on it
Length and midpoint
Calculate the length and the co-ordinates of the midpoint of a straight line segment from the co-ordinates of its end points
Equation of line Interpret and obtain the equation of a straight line graph
Parallel lines Determine the equation of a straight line parallel to a given line eg find the equation of a line parallel to y = 4x ndash 1 that passes through (0 ndash3)
Perpendicular lines
Find the gradient of parallel and perpendicular lines eg
bull find the gradient of a line perpendicular to y = 3x + 1
bull find the equation of a line perpendicular to one passing through the co-ordinates (1 3) and (ndash2 ndash9)
Learner Guide
61
Extended Geometry
Question type You should be able to R A G CommentsGeometrical language
Use and interpret the geometrical terms
bull point
bull line
bull parallel
bull perpendicular
bull bearing
bull right angle acute obtuse and reflex angles
bull similar
bull congruent
Use and interpret the vocabulary of
bull triangles right-angled scalene isosceles equilateral
bull quadrilaterals
bull circles
bull polygons
bull simple solid figures including nets
Learner Guide
62
Extended Geometry
Question type What I need to do R A G CommentsGeometrical constructions
Measure and draw lines and angles
Construct a triangle given the three sides using a ruler and a pair of compasses only
Scale drawings Read and make scale drawings
Similar figures Calculate lengths of similar figures
Use relationships between areas of similar triangles and in similar figures
Use relationships between volumes and surface areas of similar solids
Congruent triangles
Use the congruence criteria for triangles (SSS ASA SAS RHS)
Symmetry Recognise symmetry properties for triangles quadrilaterals and circles
Recognise line symmetry in two dimensions
Recognise and find the order of rotational symmetry in two dimensions
Learner Guide
63
Extended Geometry
Question type You should be able to R A G CommentsSymmetry (continued)
Use the following symmetry properties of circles
bull equal chords are equidistant from the centre
bull perpendicular bisector of a chord passes through the centre
bull tangents from an external point are equal in length
Recognise and use symmetry properties of
bull prism cylinder cone and pyramid
Learner Guide
64
Extended Geometry
Question type You should be able to R A G CommentsAngle properties Calculate unknown angles explaining the properties that
you are using in geometrical language for the following geometrical properties
bull angles at a point
bull angles at a point on a straight line and intersecting straight lines
bull angles formed within parallel lines
bull angle properties of triangles and quadrilaterals
bull angle properties of regular polygons
bull angle in a semi-circle
bull angle between tangent and radius of a circle
bull angles properties of irregular polygons
bull angle at the centre of a circle is twice the angle at the circumference
bull angles in the same segment are equal
bull angles in opposite segments are supplementary cyclic quadrilaterals
bull alternate segment theorem
Learner Guide
65
Extended Mensuration
Question type What I need to do R A G CommentsMeasures Use current units of
bull mass
bull length
bull area
bull volume
bull capacity
Express quantities in terms of smaller or larger units including units of area and volume
Perimeter Carry out calculations involving
bull perimeter and area of a rectangle
bull perimeter and area of a triangle
bull perimeter and area of parallelogram
bull perimeter and area of a trapezium
bull perimeter and area of compound shapes made by combining rectangles triangles parallelograms andor trapeziums
Learner Guide
66
Extended Mensuration
Question type You should be able to R A G CommentsCircles Carry out calculations involving circumference and area of a
circle
Solve problems involving arc length and sector area of a circle
Surface area and volume
Carry out calculations involving
bull surface area and volume of a cuboid prism and cylinder (no formulae will be given for these shapes)
bull surface area and volume of a sphere pyramid and cone (formulae will be given for these shapes)
Compound shapes
Carry out calculations involving
bull area of a shape made by combining cuboids prisms andor cylinders
bull volume of a shape made by combining cuboids prisms andor cylinders
Learner Guide
67
Extended Trigonometry
Question type You should be able to R A G CommentsBearings Use and interpret three-figure bearings measured clockwise
from the North ie 000degndash360degTrigonometry Find unknown sides andor angles in right-angled triangles by
applying
bull Pythagorasrsquo theorem
bull sine cosine and tangent ratios for acute angles in right-angled triangles
Solve problems in two dimensions involving angles of elevation and depression
Know that the perpendicular distance from a point to a line is the shortest distance to the line
Trig graphs and equations
Recognise sketch and interpret graphs of simple trigonometric functions
Graph and know the properties of trigonometric functions
Solve simple trigonometric equations for values between 0deg
and 360deg eg Solve sin x = radic32
for values of x between 0deg and
360degGeneral trig Solve problems using sine and cosine rules for any triangle
Find the area of any triangle using frac12absinC
Trig in 3D Solve simple trigonometrical problems in three dimensions including angle between a line and a plane
Learner Guide
68
Extended Vectors and transformations
Question type You should be able to R A G CommentsVectors in two dimensions (links to Trigonometry)
Describe a translation by using a vector represented by
AB or a
Add and subtract vectors
Multiply a vector by a scalar
Transformations Reflect simple shapes in horizontal or vertical lines
Rotate simple shapes through multiples of 90deg about any point
Construct translations of simple shapes
Construct enlargements of simple shapes (positive fractional and negative scale factors)
Recognise and describe
bull reflections
bull rotations
bull translations
bull enlargements (positive fractional and negative scalefactors)
( )x
y
Learner Guide
69
Extended Vectors and transformations
Question type You should be able to R A G CommentsHarder vectors
Calculate the magnitude of a vector as and
understand that magnitude is denoted by modulus signs |A B| or |a|
Represent vectors by directed line segments
Use the sum and difference of two vectors
Use position vectors
( )x
yradicx2 + y2
Learner Guide
70
Extended Probability
Question type You should be able to R A G CommentsProbability (links to Four rules)
Calculate the probability of a single event as a fraction decimal or percentage (not a ratio)
Probability scale Understand and use the probability scale from 0 to 1
Sum to 1 Understand that the probability of an event occurring = 1 ndash the probability of the event not occurring
Relative frequency
Understand relative frequency as an estimate of probability
Work out expected frequencies using relative frequency
Combined events Calculate the probability of combined events using
bull tree diagrams
bull possibility diagrams
bull tables
Learner Guide
71
Extended Statistics
Question type You should be able to R A G CommentsClassify Collect classify and tabulate data
Interpret and compare
Read interpret and draw simple inferences from tables and statistical diagrams
Compare sets of data using
bull tables
bull graphs
bull statistical measures
Be aware of restrictions when making conclusions from data
Charts Construct and use
bull bar charts
bull pie charts
bull pictograms
bull stem ndash and ndash leaf diagrams
bull frequency distributions
bull histograms with equal and unequal intervals
bull scatter diagrams
Learner Guide
72
Extended Statistics
Question type You should be able to R A G CommentsAverages Calculate for individual and discrete data
bull mean
bull median
bull mode
bull range
and distinguish between their use
Estimated mean Calculate an estimate of the mean for grouped and continuous data
Identify the modal class from a grouped frequency distributionCumulative frequency
Construct and use cumulative frequency diagrams to estimate and interpret
bull the median
bull percentiles
bull quartiles
bull inter-quartile range
Construct and interpret box-and-whisker plots
Correlation Understand what is meant by positive negative and zero correlation with reference to a scatter diagram
Lines of best fit Draw interpret and use a ruled line of best fit by eye
Cambridge Assessment International Education1 Hills Road Cambridge CB1 2EU United Kingdomt +44 1223 553554e infocambridgeinternationalorg wwwcambridgeinternationalorg
Copyright copy UCLES October 2017
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14
QuestionThe question used in this example is from Specimen Paper 3 (Core) It represents the type of structured question you will see in both Paper 3 (Core) and Paper 4 (Extended) A structured question means that it is broken into several parts Often later parts will depend on your answers to earlier parts
This means that you cannot find the answer by
measuring the diagramWork out indicates that the answer should be calculated from the given information so measurement will not score marks
The allocation of 1 mark indicates that the answer can be obtained with minimum working
Give reasons for your answer indicates that your answer should be supported with reasons using the correct mathematical terminology You must justify your answer
Use trigonometry to calculate indicates that you should use this method with the given information to find the answer and that a calculator is needed to solve the problem If you did not use trigonometry you would not be awarded any marks
15
Show that indicates the answer is given and you need to write down all of the steps in a method that leads to the given answer You need to provide evidence that you understand and know how the answer is reached
Work out indicates that you should calculate the answer from the given information The mark allocation of 4 marks suggests that you will need to include several steps of working in order to get to the answer
Learner Guide
16
Answer Mark Notes(a)(i) 35 1 This is the only acceptable answer for this part of the question
(a)(ii) 74 1 This is the only acceptable answer for this part of the question
(b) 43deg and correct mathematical reasons
3 Two marks are awarded for the final answer of 43deg
The third mark is awarded for a fully correct reason for example angles on a straight line add up to 180deg and angles in a triangle add up to 180deg There are other correct reasons that could be also be used
If 43deg is not obtained one method mark can be awarded if the following calculation is seen in the working
180 ndash 128 or 128 ndash 85
(c) 322 or 3223hellip 2 This is the only acceptable answer for this part of the question
The answer has to be rounded correct to three significant figures or can be given with more figures in the answer
Those that did not get this answer can score one method mark for showing the following in their working
sin = 8 divide 15
(d)(i) 2 2300 225+2 This does not have to be shown in one step as long as the method shown is the same as this overall Those that do not
show this can have one method mark for showing the following in their working
300deg + 225deg
(d)(ii) 15 35 4 The answer 3 35pm is also acceptable for 4 marks
If the correct answer is not found one method mark is available for showing 375 divide 450 in their working and a second method mark can be awarded for sight of them multiplying their answer to this by 60 to change it to hours A third method mark can be awarded for adding their answer in hours to 14 45 ndash this shows the correct method so only one mark is lost for an incorrect final answers
Mark schemeYour examination papers will be marked and the overall number of marks for each paper will be recorded Your marks across all papers will then be converted to a grade
Final answer This value is what the examiner expects to see The answer has to be exactly as given in the mark scheme unless there are acceptable alternatives The mark scheme will always make it clear if there are acceptable alternative answers
Method marks Sometimes method marks are awarded for lines of working as well as for the final answer This means that you could get the final answer incorrect but still get some marks if you include the correct working The mark scheme does not include all possible methods so if you use a method not included in the mark scheme but it is accurate and relevant then the examiner will still award marks for the appropriate parts of the working ndash unless the questions asks you to use a specific method
example of a final answer
example of a method mark
17
Example candidate responseNow letrsquos look at the sample candidatersquos response to question 8 The examiners comments are in the orange boxes The candidate was awarded 8 marks out of 13
180 ndash 74 + 71 = 177
177
74
0 out of 1
The candidates working suggests they understand that the angle sum of a triangle is 180deg but they did not include brackets around 74 + 71 The answer 177deg is not sensible for this question
1 out of 1
The candidate recognises that there are parallel lines and that angle y is a corresponding angle to angle 74deg
180 ndash 128 = 52 180 ndash 85 ndash 52 = 43
43 angles on a straight line add up to 180deg
2 out of 3
The candidate has given a correct answer for w and shown correct working in two steps They have given a correct reason for 52deg using correct mathematical languge But they have not provided a reason to explain the angle 43deg They lose a mark for not also stating angle sum of a triangle is 180deg
sin p = 8 divide 15 = 053
p = sinndash1 (053)
p = 32005 320
1 out of 2
The candidate has correctly used trigonometry in their method They are awarded one method mark for the first line of working However they have rounded 05333333hellip (the result of 8 divide 15) to 052 and then calculated the inverse sin of 052 rather than 05333333 This has resulted in an inaccurate final answer This is called lsquopremature approximationrsquo and it is a very common error to make
18
AB2 = 3002 + 2252
= 140625
AB = 375
1 out of 2
The candidate has recognised the right-angled triangle and correctly used Pythagorasrsquo theorem in the first line of working However they have missed out an important step by not showing that you need to take the square root of 140625 to get 375 As this is a lsquoshow thatrsquo question and they missed a key step in the method they cannot be awarded full marks as the complete working is not shown One method mark is earned for the first line
T = = = 08333333hellip
08333333 hours = 08333333 times 60 minutes = 50 minutes
arrives at 14 45 + 50 mins = 3 35
DS
375450
3 35
3 out of 4
The candidate has found the time by correctly dividing the distance by the speed and recognised that this is in hours When converting the answer to a decimal they have not rounded the decimal but left its full value on the calculator to get 50 mins which is the correct approach Unfortunately after converting the time from 24 hour clock to 12 hour clock they did not include lsquopmrsquo to indicate that the time is in the afternoon and so the final answer is not quite right So 3 marks are awarded for all of a correct method but a mark is lost due to the accuracy of the final answer
19
How the answer could have been improvedThis answer could have been improved by
bull In part (a)(i) the answer of 177deg was not sensible given the diagram in the question If the candidate had checked their answer for sense they would have realised they had made a mistake It is always a good idea to check that your answer seems sensible before you move on to another question
bull In part (b) the candidate did all the correct steps but failed to provide both reasons There were two steps to the method which should have indicated to the candidate that there were two steps to justify and therefore two reasons should have been provided The mark allocation for the question [3] also indicates that more than one reason would be required one mark for the value of 43deg leaving two marks one mark for each of two reasons The candidate should have read the question carefully and again checked their response seemed reasonable
bull In part (c) the candidate rounded an intermediate answer which affected the accuracy of the final answer This caused them to lose a mark despite using a correct method You should only ever round the final answer do not round intermediate values If you can store the intermediate values in your calculator and so that you can use the full value in your calcuations If youre not able to do this and you have to round the intermediate values do not round them to less than three significant figures
bull In part (d)(i) the candidate missed out a step in the method As this was a show that question they needed to show all the steps in the method Its important to show all steps even if they seem obvious
bull In part (d)(ii) the candidate made a silly error by not stating that the time was pm When working with time answers are accepted in either 24 clock or 12 clock time but if you give your answer in the 12 hour clock then it must include am or pm as well
Common mistakesThere were a number of common mistakes made by other candidates on this question
bull Accuracy of answers
In parts (c) and (d)(ii) a common error was premature rounding ndash rounding intermediate values in the method before the final answer which resulted in their final answer not being accurate Other candidates gave the final answer to less than three significant figures ignoring the instruction on the front of the paper to round to three significant figures
bull Using incorrect terminology when giving reasons
In part (b) the most common error was to not give full reasons to support the answer Another common error was to provide a reason that did not use the correct mathematical language such as lsquoThey add up to 180degrsquo and lsquoIt is a straight linersquo which could not be awarded marks
bull Lack of knowledge
In part (c) a number of candidates had limited knowledge of trigonometry and did not choose the correct trig ratio which was the sine ratio This is why good revision is important
bull Not checking answers
In part (a)(i) even though the diagram is drawn NOT TO SCALE it is possible to see that the angle is an acute angle and should therefore not be bigger than 90deg This should alert candidate that if their answer is over 90deg it is not a sensible answer and they should go back and check their working
20
bull Inefficient method shown
In part (c) the lsquoShow thatrsquo question a number of candidates omitted an important step from the method this is often common in lsquoShow thatrsquo questions where every step must be shown no matter how obvious them seem
General adviceIn order to do your best when answering a mathematics question make sure you
bull revise all of the topics for the syllabus you are studying before the exam
bull understand what all the key terms and command words in the question mean
bull read the questions carefully and consider what you need to do before you do it
bull only round the final answer not intermediate values
bull show all steps in your working and show them clearly
bull round to the correct degree of accuracy
bull use the correct mathematical terminology
bull check your answers seem reasonable given the context or details of the question
21
It is important that you plan your revision in plenty of time for the examinations and that you develop a revision technique that works for you The advice in this section will help you revise and prepare for the examinations It is divided into general advice for all papers
Use the tick boxes to keep a record of what you have done what you plan to do or what you understand
For more advice on revision see the Cambridge Learner Revision Guide on our website
Section 6 Revision
Find out when the examinations are and plan your revision so you have time to revise Create a revision timetable and divide it into sections to cover each topic
Spend most of your time focussing on specific skills knowledge or issues that you have found more difficult when practicing them either during revision or earlier in the course
Write a summary of all the key information for a topic ndash use the checklists at the end of this section
Know the meaning of the command words used in questions and how to apply them to the information given Look at past examination papers and highlight the command words and check what they mean
Make revision notes and work on practice questions Reading alone does not work you need to be active and practice your maths
Work for shorter periods then have a break Revise small sections of the syllabus at a time but do this regularly
Test yourself by trying out some past exam questions Use the mark schemes to assess yourself and to be familiar with how marks are awarded for different questions
Be organised in advance with your notes texts exercise books revision guides and revision websites so you do not waste valuable revision time trying to find things
Make notes of key mathematical words that you should use in questions that ask you to lsquodescribersquo or give lsquogeometrical reasons forrsquo eg in describing transformations or giving reasons in circle theorem questions Look at the mark schemes for these types of questions from past papers to see how marks are awarded
Make sure you have all of the correct mathematical equipment ready for the exam particularly your calculator Make sure you are familiar with the all of the important functions on your calculator
Practice the areas you can do well not just those that you find more difficult
Take breaks and do things to relax when you take your breaks this will help you to be more productive when you are revising
Before the examination
22
During the examination
Plan your time according to the marks for each question For example a question worth one mark requires less time than a question one worth 4 marks If a question has several parts then the parts with more marks will need more time
Read each question very carefully
Identify the command words ndash you could underline or highlight them
Identify the other key words and information and perhaps underline them too particularly where
questions require reasoning or problem solving
Read the questions careully and make you have answered the question that is being asked
Show your working this is particularly important for questions where you are asked to lsquoshow that helliprsquo
Set your working out clearly so that it is easy to follow this makes it easier to keep track of what you have done and makes checking back through your work easier and it makes it easier for the examiner to mark your work try to write it in a logical order in the answer space
Write answers clearly if you want to change an answer then you should cross the answer out and write a replacement if your answer is on the answer line cross it out and write the replacement answer above it do not try to change numbers on the answer line as this can lead to unclear figures
Check your working and answers to avoid errors
Give your answer to the appropriate level of accuracy either the accuracy indicated in the question or the accuracy given on the front of the paper
Avoid rounding intermediate values part way through your calculation only round the final answer
Check that the answer that you have given is sensible and realistic for what is being asked
Use a pencil when drawing diagrams or completing graphs this means that you can change your answer more easily if you have made a mistake
Take care when reading scales
If you are asked for reasons for your answer then use the correct mathematical terms
Use the mark allocation given with the questionsparts of questions to try to judge how much work is needed to answer each part
23
Top tips for revision of Cambridge IGCSE Mathematics1 Summarise recall and applyMake sure that you can recall and apply the key information and mathematical techniques on each topic that you need for the exam
i Write a summary of the key information of a topicii Collect together some questions that test the knowledge and skills of this topic Ask your teacher for practice
questions or suitable past examination questions or use practice books or textbooksiii Test your recall by covering over the summary and trying to remember the details or use the summary as part of
the lsquoTeach the topicrsquo (Tip 3) or lsquoQuestion and answer cardsrsquo (Tip 4) activities iv After you have spent some time revising and practising the knowledge and skills answer the questions that you
collected together on the topic You might do this later on the same day as revising or a few days later Answer as many questions as you can in order to practise applying your knowledge
v Try creating your own questions by adapting existing ones and use these for practice when you return to a topic
On graph questions straight lines should be ruled and curves should be drawn freehand with a smooth curve
Donrsquot spend too long on any one part of a question If you are really stuck on a question then move on and come back to the question later if you have time As a rough guide each mark on the paper should take about one minute
2 Concept mapsConcept maps are a great way to revise the links between different factors or to explore a larger topic They can also be used to collect together your ideas
i Use a blank sheet of paper and turn it on its side (landscape)ii Put the topic title in the middle of the page and build the concept map outwards using lines called lsquobranchesrsquo
ndash The first branches are from the central topic to sub-topics draw these as thick lines
ndash Add new branches from the sub-topics to include more detail draw these as thinner lines
ndash Add even more detail to a point by adding more branches
This creates a hierarchy of information from lsquooverviewrsquo (the thick branches) to lsquofine detailrsquo (thinnest branches)
iii Write single key words or phrases along a branch and add drawings for visual impactiv Use different colours highlighter pens symbols and arrows to highlight key facts or issuesIt is a good idea to use a large piece of plain A3 (or larger) paper and lots of coloured pens
24
3 Teach the topicThis is a very simple but effective technique that focusses on knowledge recall It tests the brain and rehearses the information you need to know for a certain topic and so will help your revision
i Create some topic cards with key bullet points of information on Leave space for ticksii Give these to your parents family or friends for exampleiii Give yourself 10 minutes maximum to teach your audience the main points of the topic You could use a mini-
whiteboard or flip chart to helpiv Your audience tick off all the points you mention in your presentation and give you a final scoreThe brain loves competition so if you do not score full marks you can try again the next day or compete against friends This system of repeat and rehearsal is very effective especially with more complex topics and doesnt take much preparation
4 Question and answer (QampA) cardsThis is very similar to Teach the topic but less formal and less public for those who dislike performing in front of others It tests knowledge recall and rehearses the information you need to know for a certain topic
i Pick a topic and create two sets of cards question cards and answer cards You might find it helpful to make the question cards a different size or use different coloured card for answers
ii Make sure you have the topic or something appropriate depending on what you are focusing on as a heading on each card The questions should test your knowledge and understanding of key areas of the course
iii A friend or family member uses the cards to test you in short 5 or 10 minute periods at any time during the dayiv You could also do this alone by reading the questions to yourself giving the answer and then checking the
correct answer cardv This game can be adapted by using the cards to find matching pairs turn all cards face down across the space
in front of you Turn over two cards leaving them where they are If they match (one is a question card and the other is the corresponding answer card) pick up the pair and put them to one side If they dont match try to remember where they are and what is on each card then turn them back over Turn over two other cards Continue until you have matched all pairs
5 Question paper and mark schemesLooking at past question papers and the mark scheme helps you to familiarise yourself with what to expect and what the standard is
i Ask your teacher for past paper questions with mark schemes for the course ndash ask your teacher for help to make sure you are answering the correct questions and to simplify the mark scheme
ii Look at the revision checklist and identify which topic a given question relates to ndash you might need to ask your teacher to help you do this
iii Once you have finished revising a topic or unit time yourself answering some appropriate exam questions Check the mark schemes to see how well you would have scored or give the answers to your teacher to check
iv Add details or notes to the mark scheme where you missed out on marks in your original answers using a different coloured pen Use these notes when you revise and try the question again later
You can find plenty of past exam papers and mark schemes on the Cambridge International public website
httpwwwcambridgeinternationalorgprogrammes-and-qualificationscambridge-igcse-mathematics-0580past-papers
25
Other useful revision advice for Cambridge IGCSE Mathematics bull Before the exam make sure that you are familiar with your calculator and confident in using it
bull Look at the Example Candidate Response earlier in this guide Can you identify the strengths of the response andwhere they have made mistakes or lost marks
bull When you are attempting a past paper (or questions from a past paper) complete it without referring to yournotes so that you get a true idea of your strengths and weaknesses Then go back through the paper using yournotes and a different coloured pen to make corrections and changes After you have done as much as you can onthe paper mark it using the mark scheme Take notes of any points that you lost marks on
bull Donrsquot just revise the topics that you enjoy and are confident in If you identify an area that you are weaker inthen try to revisit the topic by reviewing your notes and doing some practice questions then use exam questionsto check whether you now understand
bull Return to topics later in your revision to check that you still remember and understand the topic and to help toensure that you recall more of the material when you get to the examination
Revision checklists for Cambridge IGCSE MathematicsThe tables on the following pages can be used as a revision checklist They do not contain all the detailed knowledge you need to know just an overview For more detail see the syllabus and talk to your teacher
You can use the tick boxes in the checklists to show when you have revised and are happy that you do not need to return to it Tick the lsquoRrsquo lsquoArsquo and lsquoGrsquo column to record your progress as follows
bull R = RED means you are really unsure and lack confidence in that area you might want to focus your revisionhere and possibly talk to your teacher for help
bull A = AMBER means you are reasonably confident in a topic but need some extra practicebull G = GREEN means you are very confident in a topic
As your revision progresses you can concentrate on the RED and AMBER topics in order to turn them into GREEN topics You might find it helpful to highlight each topic in red orange or green to help you prioritise
You can use the lsquoCommentsrsquo column to
bull add more information about the details for each pointbull include a reference to a useful resourcebull include a list of formulae or notationbull add learning aids such as rhymes poems or word playbull highlight areas of difficulty or things that you need to talk to your teacher about
There is a set of checklist for the Core syllabus and a different set for the Extended syllabus
Learner Guide
26
Core syllabus contentCore Number
Category You should be able to R A G CommentsNumber Identify and use
bull natural numbers
bull integers (positive negative and zero)
bull prime numbers
bull write a number as a product of its prime factors
bull square numbers and cube numbers
bull common factors and highest common factor of two numbers
bull common multiples and lowest common multiple of two numbers
bull rational numbers
bull irrational numbers (eg π radic2 )
bull real numbers
bull reciprocals
Learner Guide
27
Core Number
Question type You should be able to R A G CommentsSets and Venn diagrams
Understand notation of Venn diagrams
Definition of sets
eg A = xx is a natural number
B = abchellip
Notation
Number of elements in set A n(A)
Universal set
Union of A and B A cup B
Intersection of A and B A cap B
Squares square roots cubes and cube roots
Calculate
bull squares and cubes of numbers
bull square roots and cube roots of numbers
Learner Guide
28
Core Number
Question type You should be able to R A G CommentsDirected numbers
Use directed numbers in practical situations for example temperature changes
Fractions decimals and percentages
Use the language and notation of simple vulgar and decimal fractions and percentages
Recognise equivalent fractions decimals and percentages
Convert between fractions decimals and percentages
Ordering Order quantities by magnitude and demonstrate familiarity with the symbols = ne gt lt ⩾ ⩽
Indices and standard form (links to Algebraic manipulation)
Evaluate indices eg 25 5ndash2 1000 64frac12 8ndash23
Use the rules of indices for
bull multiplication of indices eg 4ndash3 times 45
bull division of indices eg 57 divide 53
bull index numbers raised to an index eg (23)2 (43)2
Use the standard form A times 10n where n is a positive or negative integer and 1 ⩽ A lt 10
bull convert numbers into and out of standard form
bull calculate with numbers in standard form
Learner Guide
29
Core Number
Question type You should be able to R A G CommentsFour rules
( + ndash times divide )
Use the four rules for calculations with
bull whole numbers
bull decimals
bull vulgar and mixed fractions
bull correct ordering of operations (BIDMAS) and use of bracketsEstimates Make estimates of numbers quantities and lengths
Give approximations to a specified number of
bull significant figures
bull decimal places
Round off answers to reasonable accuracy in the context of a given problem
Bounds Give upper and lower bounds for data given to a specified accuracy eg measured lengths
Ratio proportion rate
Understand ratio
Divide a quantity in a given ratio
Understand direct and inverse proportion
Use scales in practical situations
Use common measures of rate (formulae for other rates eg density and pressure will be given in the question)
Calculate average speed
Learner Guide
30
Core Number
Question type You should be able to R A G CommentsPercentages Calculate a percentage of a quantity
Express one quantity as a percentage of another quantity
Calculate percentage increase or decrease
Use of an electronic calculator
Use a calculator efficiently
Check accuracy of calculations
Time Calculate times in terms of the 24-hour and 12-hour clock
Read
bull clocks
bull dials
bull timetables
Money Calculate using money
Convert from one currency to another
Learner Guide
31
Core Number
Question type You should be able to R A G CommentsPersonal and small business finance
Use given data to solve problems on
bull earnings
bull simple interest
bull compound interest (you will need to know the compound interest formula)
bull discount
bull profit and loss
Extract data from tables and charts
Learner Guide
32
Core Algebra and graphs
Question type You should be able to R A G CommentsBasic algebra Use letters to express generalised numbers
Express basic arithmetic processes algebraically
Substitute numbers in formulae
Construct simple expressions and set up simple equations
Rearrange simple formulae
Algebraic manipulation
Manipulate directed numbers
Use brackets
bull expand a single bracket eg 3x(2x ndash4y)
bull expand a pair of brackets eg (x + 3) (x ndash 7)
Extract common factors eg factorise 9x2 + 15xy
Rules of indices Use and interpret positive negative and zero indices
Use the rules of indices eg to simplify algebra such as
bull 3x4 times 5x
bull 10x3 divide 2x2
bull (x6)2
Learner Guide
33
Core Algebra and graphs
Question type You should be able to R A G CommentsEquations and inequalities
Derive and solve simple linear equations in one unknown
Derive and solve simultaneous linear equations in two unknowns
Number sequences
(links to Squares square roots cubes and cube roots)
Continue a number sequence
Recognise patterns in sequences
Recognise relationships between difference sequences
Find the nth term of sequences for
bull liner sequences
bull simple quadratic sequences
bull cubic sequences
Practical graphs
(links to Mensuration)
Interpret and use graphs in practical situations including
bull travel graphs
bull conversion graphs
Draw graphs from given data
Learner Guide
34
Core Algebra and graphs
Question type You should be able to R A G CommentsGraphs of functions
(links to Co-ordinate geometry)
Construct tables of values for functions of the form
bull ax + b (linear)
bull plusmn x2 + ax + b (quadratic)
bull (x ne 0) (reciprocal)
where a and b are integer constants
Draw and interpret such graphs
Solve linear and quadratic equations approximately by graphical methods
Recognise and sketch the graphs of linear and quadratic functions
ax
Learner Guide
35
Core Co-ordinate geometry
Question type You should be able to R A G CommentsCo-ordinates Work with co-ordinates in two dimensions
Gradients Find the gradient of a straight line graph
Equation of straight line
Interpret and obtain the equation of a straight line graph in the form y = mx + c where the graph is given
Parallel lines Determine the equation of a straight line parallel to a given line eg find the equation of a line parallel to y = 4x ndash 1 that passes through (0 ndash3)
Learner Guide
36
Core Geometry
Question type You should be able to R A G CommentsGeometrical language
Use and interpret the geometrical terms
bull point
bull line
bull parallel
bull perpendicular
bull bearing
bull right angle acute obtuse and reflex angles
bull similar
bull congruent
Use and interpret the vocabulary of
bull triangles right-angled scalene isosceles equilateral
bull quadrilaterals
bull circles
bull polygons
bull simple solid figures including nets
Learner Guide
37
Core Geometry
Question type You should be able to R A G CommentsGeometrical constructions
Measure and draw lines and angles
Construct a triangle given the three sides using a ruler and a pair of compasses only
Scale drawings Read and make scale drawings
Similar figures Calculate lengths of similar figures
Congruent Recognise congruent shapes
Symmetry Recognise symmetry properties for triangles quadrilaterals and circles
Recognise line symmetry in two dimensions
Recognise and find the order of rotational symmetry in two dimensions
Learner Guide
38
Core Geometry
Question type You should be able to R A G CommentsAngle properties Calculate unknown angles explaining the properties that you
are using in geometrical language for angles
bull angles at a point
bull angles on a straight line and intersecting straight lines
bull angles within parallel lines
bull angles in triangles
bull angles in quadrilaterals
bull angles in regular polygons
bull angle in a semi-circle
bull angle between tangent and radius of a circle
Learner Guide
39
Core Mensuration
Question type You should be able to R A G CommentsMeasures bull Use current units of
bull mass
bull length
bull area
bull volume
bull capacity
Express quantities in terms of smaller or larger units including units of area and volume
Convert between units including units of area and volume
Perimiter Carry out calculations involving
bull perimeter and area of a rectangle
bull perimeter and area of a triangle
bull perimeter and area of parallelogram
bull perimeter and area of a trapezium
bull perimeter and area of shapes made by combining
bull rectangles triangles parallelograms andor trapeziums
Learner Guide
40
Core Mensuration
Question type You should be able to R A G CommentsCircles Carry out calculations involving circumference and area of a
circle
Solve simple problems involving the arc length and sector area of a circle where the sector angle is a factor of 360deg
Surface area and volume
Carry out calculations involving
bull surface area and volume of a cuboid prism and cylinder (no formulae will be given for these shapes)
bull surface area and volume of a sphere pyramid and cone (formulae will be given for these shapes)
Areas and volumes of compound shapes
Carry out calculations involving the areas and volumes of compound shapes made from combinations of the shapes in Perimeter or Surface area and volume
Learner Guide
41
Core Trigonometry
Question type You should be able to R A G CommentsBearings Use and interpret three-figure bearings measured clockwise
from the North ie 000degndash360degTrigonometry Find unknown sides andor angles in right-angled triangles by
applying
bull Pythagorasrsquo theorem
bull sine cosine and tangent ratios for acute angles in right-angled triangles
Learner Guide
42
Core Vectors and transformations
Question type You should be able to R A G CommentsVectors in two dimensions (links to Trigonometry)
Describe a translation by using a vector represented by
AB or a
Add and subtract vectors
Multiply a vector by a scalar
Transformations Reflect simple shapes in horizontal or vertical lines
Rotate simple shapes through multiples of 90deg about
bull the origin
bull their vertices
bull the midpoints of their sides
Construct translations of simple shapes
Construct enlargements of simple shapes (positive and fractional scale factors)
Recognise and describe using the correct language
bull reflections
bull rotations
bull translations
bull enlargements (positive and fractional scale factors)
( )x
y
Learner Guide
43
Core Probability
Question type You should be able to R A G CommentsSingle events Calculate the probability of a single event as a fraction decimal
or percentage (not a ratio)Probability scale Understand and use the probability scale from 0 to 1
Sum to 1 Understand that the probability of an event occurring = 1 ndash the probability of the event not occurring
Relative frequency
Understand relative frequency as an estimate of probability
Work out expected frequencies using relative frequencyCombined events Calculate the probability of simple combined events using
bull tree diagrams
bull possibility diagrams (points on a grid)
bull Venn diagrams (2 sets only)
Learner Guide
44
Core Statistics
Question type What I need to do R A G CommentsClassify Collect classify and tabulate data
Interpret and compare
Read interpret and draw simple inferences from tables and statistical diagrams
Compare sets of data using
bull tables
bull graphs
bull statistical measures
Be aware of restrictions when making conclusions from data
Charts Construct and use
bull bar charts
bull pie charts
bull pictograms
bull stem-and-leaf diagrams
bull frequency distributions
bull histograms with equal intervals
bull scatter diagrams
Learner Guide
45
Question type What I need to do R A G CommentsAverages Calculate for individual and discrete data
bull mean
bull median
bull mode
bull range
and distinguish between their useCorrelation Understand what is meant by positive negative and zero
correlation with reference to a scatter diagramLine of best fit Draw interpret and use a ruled line of best fit by eye
Learner Guide
46
Extended syllabus content (includes required Core content)Extended Number
Question type You should be able to R A G CommentsNumber Identify and use
bull natural numbers
bull integers (positive negative and zero)
bull prime numbers
bull write a number as a product of its prime factors
bull square and cube numbers
bull common factors and highest common factor of two or more numbers
bull common multiples and lowest common multiple of two or more numbers
bull rational numbers
bull irrational numbers (eg π radic2 )
bull real numbers
bull reciprocals
Learner Guide
47
Extended Number
Question type You should be able to R A G CommentsSet notation and language
Use language notation and Venn diagrams to describe sets and represent relationships between sets as follows
Definition of sets egA = x x is a natural number
B = (xy) y = mx + c
C = x a ⩽ x ⩽ b
D = a b c hellip
Notation egnumber of elements in set A n(A)
lsquois an element ofrsquo isin
lsquois not an element ofrsquo notin
complement of set A
the empty set empty
the universal set
A is a subset of B A sube B
A is a proper subset of B A sub B
A is not a subset of B A ⊈ B
A is not a proper subset of B A nsub B
union of A and B A cup B
intersection of A and B A cap B
Learner Guide
48
Extended Number
Question type You should be able to R A G CommentsSquares square roots cubes and cube roots
Calculatebull squares of numbers
bull square roots of numbers
bull cubes of numbers
bull cube roots of numbers
bull other powers and roots of numbers
Directed numbers
Use directed numbers in practical situations for example temperature changes
Fractions decimals and percentages
Use the language and notation of simple vulgar and decimal fractions and percentages in appropriate contexts
Recognise equivalent fractions decimals and percentages
Convert between fractions decimals and percentages
Convert recurring decimals to fractions
Ordering Order quantities by magnitude and demonstrate familiarity with the symbols = ne gt lt ⩾ ⩽
Learner Guide
49
Extended Number
Question type You should be able to R A G CommentsIndices and standard form (links to Algebraic manipulation)
Evaluate indices including fractional negative and zero
eg 25 5ndash2 1000 10012 8ndash23
Use the rules of indices forbull multiplication of indices eg 43 times 45
bull division of indices eg 57 divide 53
bull index numbers raised to an index eg (43)2
Use the standard form A times 10n where n is a positive or negative integer and 1 ⩽ A lt 10bull convert into and out of standard form
bull calculate with numbers in standard form
Four rules
( + ndash times divide )
Use the four rules for calculations withbull whole numbers
bull decimals
bull vulgar and mixed fractions
bull correct ordering of operations (BIDMAS) and use of brackets
Learner Guide
50
Extended Number
Question type You should be able to R A G CommentsEstimates Make estimates of numbers quantities and lengths
Give approximations to a specified number of
bull significant figures
bull decimal places
Round off answers to reasonable accuracy in the context of a given problem
Bounds Give upper and lower bounds for data given to a specified accuracy eg measured lengths
Obtain appropriate upper and lower bounds to solutions of simple problems given to a specified accuracy eg the lower and upper bounds for the area of a rectangle
Ratio proportion rate
(links to Direct and inverse proportion)
Understand ratio
Divide quantities in a given ratio
Increase and decrease a quantity by a given ratio
Understand numerical problems involving direct and inverse proportion
Use ratio and scales in practical situations
Use common measures of rate (formulae for other rates eg density and pressure will be given in the question)
Calculate average speed
Learner Guide
51
Extended Number
Question type What I need to do R A G CommentsPercentages Calculate a percentage of a quantity
Express one quantity as a percentage of another quantity
Calculate percentage increase or decrease
Calculate reverse percentages eg finding the cost price given the selling price and the percentage profit
Use of an electronic calculator
Use a calculator efficiently
Check accuracy of calculations
Time Calculate times in terms of the 24-hour and 12-hour clock
Read clocks dials and timetables
Money Calculate using money
Convert from one currency to another
Learner Guide
52
Extended Number
Question type You should be able to R A G CommentsPersonal and small business finance
Use given data to solve problems on
bull earnings
bull simple interest
bull compound interest
ndash you must know the compound interest formula
bull discount
bull profit and loss
Extract data from tables and charts
Exponential growth and decay
Use exponential growth and decay in population and finance eg depreciation bacteria growth
Learner Guide
53
Extended Algebra and graphs
Question type You should be able to R A G CommentsBasic algebra Use letters to express generalised numbers
Express basic arithmetic processes algebraically
Substitute numbers in complicated formulae
Construct and rearrange complicated formulae eg where the subject appears twice
Algebraic manipulation
Manipulate directed numbers
Use bracketsbull expand a single bracket eg expand 3x(2x ndash 4y)
bull expand a pair of brackets eg (x ndash 4)(x + 7)
bull expand products of more than two brackets eg (x + 4)(x ndash 7)(2x + 1)
Extract common factors eg factorise 9x2 + 15xy
Factorise expressions of the formbull ax + bx + kay + kby
bull asup2xsup2 ndash bsup2ysup2
bull asup2 + 2ab + bsup2
bull axsup2 + bx + c
Learner Guide
54
Extended Algebra and graphs
Question type You should be able to R A G CommentsAlgebraic fractions
Manipulate algebraic fractions eg
bull
bull
bull
bull
bull
Factorise and simplify algebraic fractions such as
Rules of indices Use and interpret positive negative and zero indices
Use and interpret fractional indices eg solve 32x = 2
Use the rules of indices to simplify algebra eg
x3 + x ndash 4
22x3 +
3(x ndash 5)2
3a4 +
5ab3
3a4 divide
9a10
1x ndash 2 +
2x ndash 3
x2 ndash 2xx2 ndash 5x + 6
3xndash4 times23
x12
32x5( )
3
2xndash2divide25
x12
Learner Guide
55
Extended Algebra and graphs
Question type You should be able to R A G CommentsEquations and inequalities
bull Derive and solve simple linear equations in one unknown
bull Derive and solve simultaneous linear equations in two unknowns
bull Derive and solve simultaneous equations involving one linear and one quadratic
Solve quadratic equations by
bull factorisation
bull completing the square
bull using the formula
Derive and solve simple linear inequalities including representing solutions on a number line
Linear programming
Represent inequalities graphically including using the conventions of
bull broken lines for strict inequalities
bull shading unwanted regions
Solve simple linear programming problems using graphical representations of inequalities
Learner Guide
56
Extended Algebra and graphs
Question type You should be able to R A G CommentsNumber sequences (links to Squares square roots cubes and cube roots)
Continue a number sequence
Recognise patterns in sequences
Recognise relationships between different sequences
Find the nth term of sequences of
bull linear sequences
bull quadratic sequences
bull cubic sequences
bull exponential sequences
and simple combinations of these
Direct and inverse proportion (links to Ratio proportion rate)
Express direct proportion algebraically
Express inverse proportion algebraically
Use algebraic expressions of direct and inverse proportion to find unknown quantities
Practical graphs
(links to Coordinate geometry)
Interpret and use graphs in practical situations including
bull travel graphs
bull conversion graphs
Draw graphs from given data
Learner Guide
57
Extended Algebra and graphs
Question type You should be able to R A G CommentsPractical graphs (links to Coordinate geometry) continued
Apply the idea of rate of change to simple kinematics involving
bull distancendashtime graphs
bull speedndashtime graphs
bull acceleration and deceleration
This may involve estimation and interpretation of the gradient of a tangent at a point
Calculate distance travelled as an area under a linear speedndash time graph
Learner Guide
58
Extended Algebra and graphs
Question type You should be able to R A G CommentsGraphs of functions (links to Coordinate geometry)
Construct tables of values and draw graphs for functions of the form
bull axn where a is a rational constant and n = minus2 minus1 0 1 2 3 and simple sums of not more than three of these
bull abx + c where a and c are rational constants and b is a positive integer
Solve associated equations approximately by graphical methods including finding and interpreting roots and finding turning points of quadratics by completing the square
Draw and interpret graphs representing exponential growth and decay problems
Recognise sketch and interpret graphs of
bull linear
bull quadratic
bull cubic
bull reciprocal
bull exponential
(knowledge of turning points and asymtotes is required)Tangents Estimate gradients of curves by drawing tangents
Learner Guide
59
Extended Algebra and graphs
Question type You should be able to R A G CommentsFunctions Use function notation eg
f(x) = 3x ndash 5 f x α 3x ndash5 to describe simple functions
Find inverse functions f ndash1 (x)
Form composite functions as defined by gf(x) = g(f(x))
Derivatives Understand the idea of a derived function
Use derivatives of the form axn and simple sums of not more than three of these (a is a rational constant and n is a positive integer or 0)
Apply differentiation to gradients and turning points (stationary points)
Use any method to explain whether the turning point is a maximum or a minimum eg second derivative or gradient of function on either side of turning point
Learner Guide
60
Extended Co-ordinate geometry
Question type You should be able to R A G CommentsStraight line graphs
Work with co-ordinates in two dimensions
Gradient Find the gradient of a straight line graph
Calculate the gradient of a straight line from the co-ordinates of two points on it
Length and midpoint
Calculate the length and the co-ordinates of the midpoint of a straight line segment from the co-ordinates of its end points
Equation of line Interpret and obtain the equation of a straight line graph
Parallel lines Determine the equation of a straight line parallel to a given line eg find the equation of a line parallel to y = 4x ndash 1 that passes through (0 ndash3)
Perpendicular lines
Find the gradient of parallel and perpendicular lines eg
bull find the gradient of a line perpendicular to y = 3x + 1
bull find the equation of a line perpendicular to one passing through the co-ordinates (1 3) and (ndash2 ndash9)
Learner Guide
61
Extended Geometry
Question type You should be able to R A G CommentsGeometrical language
Use and interpret the geometrical terms
bull point
bull line
bull parallel
bull perpendicular
bull bearing
bull right angle acute obtuse and reflex angles
bull similar
bull congruent
Use and interpret the vocabulary of
bull triangles right-angled scalene isosceles equilateral
bull quadrilaterals
bull circles
bull polygons
bull simple solid figures including nets
Learner Guide
62
Extended Geometry
Question type What I need to do R A G CommentsGeometrical constructions
Measure and draw lines and angles
Construct a triangle given the three sides using a ruler and a pair of compasses only
Scale drawings Read and make scale drawings
Similar figures Calculate lengths of similar figures
Use relationships between areas of similar triangles and in similar figures
Use relationships between volumes and surface areas of similar solids
Congruent triangles
Use the congruence criteria for triangles (SSS ASA SAS RHS)
Symmetry Recognise symmetry properties for triangles quadrilaterals and circles
Recognise line symmetry in two dimensions
Recognise and find the order of rotational symmetry in two dimensions
Learner Guide
63
Extended Geometry
Question type You should be able to R A G CommentsSymmetry (continued)
Use the following symmetry properties of circles
bull equal chords are equidistant from the centre
bull perpendicular bisector of a chord passes through the centre
bull tangents from an external point are equal in length
Recognise and use symmetry properties of
bull prism cylinder cone and pyramid
Learner Guide
64
Extended Geometry
Question type You should be able to R A G CommentsAngle properties Calculate unknown angles explaining the properties that
you are using in geometrical language for the following geometrical properties
bull angles at a point
bull angles at a point on a straight line and intersecting straight lines
bull angles formed within parallel lines
bull angle properties of triangles and quadrilaterals
bull angle properties of regular polygons
bull angle in a semi-circle
bull angle between tangent and radius of a circle
bull angles properties of irregular polygons
bull angle at the centre of a circle is twice the angle at the circumference
bull angles in the same segment are equal
bull angles in opposite segments are supplementary cyclic quadrilaterals
bull alternate segment theorem
Learner Guide
65
Extended Mensuration
Question type What I need to do R A G CommentsMeasures Use current units of
bull mass
bull length
bull area
bull volume
bull capacity
Express quantities in terms of smaller or larger units including units of area and volume
Perimeter Carry out calculations involving
bull perimeter and area of a rectangle
bull perimeter and area of a triangle
bull perimeter and area of parallelogram
bull perimeter and area of a trapezium
bull perimeter and area of compound shapes made by combining rectangles triangles parallelograms andor trapeziums
Learner Guide
66
Extended Mensuration
Question type You should be able to R A G CommentsCircles Carry out calculations involving circumference and area of a
circle
Solve problems involving arc length and sector area of a circle
Surface area and volume
Carry out calculations involving
bull surface area and volume of a cuboid prism and cylinder (no formulae will be given for these shapes)
bull surface area and volume of a sphere pyramid and cone (formulae will be given for these shapes)
Compound shapes
Carry out calculations involving
bull area of a shape made by combining cuboids prisms andor cylinders
bull volume of a shape made by combining cuboids prisms andor cylinders
Learner Guide
67
Extended Trigonometry
Question type You should be able to R A G CommentsBearings Use and interpret three-figure bearings measured clockwise
from the North ie 000degndash360degTrigonometry Find unknown sides andor angles in right-angled triangles by
applying
bull Pythagorasrsquo theorem
bull sine cosine and tangent ratios for acute angles in right-angled triangles
Solve problems in two dimensions involving angles of elevation and depression
Know that the perpendicular distance from a point to a line is the shortest distance to the line
Trig graphs and equations
Recognise sketch and interpret graphs of simple trigonometric functions
Graph and know the properties of trigonometric functions
Solve simple trigonometric equations for values between 0deg
and 360deg eg Solve sin x = radic32
for values of x between 0deg and
360degGeneral trig Solve problems using sine and cosine rules for any triangle
Find the area of any triangle using frac12absinC
Trig in 3D Solve simple trigonometrical problems in three dimensions including angle between a line and a plane
Learner Guide
68
Extended Vectors and transformations
Question type You should be able to R A G CommentsVectors in two dimensions (links to Trigonometry)
Describe a translation by using a vector represented by
AB or a
Add and subtract vectors
Multiply a vector by a scalar
Transformations Reflect simple shapes in horizontal or vertical lines
Rotate simple shapes through multiples of 90deg about any point
Construct translations of simple shapes
Construct enlargements of simple shapes (positive fractional and negative scale factors)
Recognise and describe
bull reflections
bull rotations
bull translations
bull enlargements (positive fractional and negative scalefactors)
( )x
y
Learner Guide
69
Extended Vectors and transformations
Question type You should be able to R A G CommentsHarder vectors
Calculate the magnitude of a vector as and
understand that magnitude is denoted by modulus signs |A B| or |a|
Represent vectors by directed line segments
Use the sum and difference of two vectors
Use position vectors
( )x
yradicx2 + y2
Learner Guide
70
Extended Probability
Question type You should be able to R A G CommentsProbability (links to Four rules)
Calculate the probability of a single event as a fraction decimal or percentage (not a ratio)
Probability scale Understand and use the probability scale from 0 to 1
Sum to 1 Understand that the probability of an event occurring = 1 ndash the probability of the event not occurring
Relative frequency
Understand relative frequency as an estimate of probability
Work out expected frequencies using relative frequency
Combined events Calculate the probability of combined events using
bull tree diagrams
bull possibility diagrams
bull tables
Learner Guide
71
Extended Statistics
Question type You should be able to R A G CommentsClassify Collect classify and tabulate data
Interpret and compare
Read interpret and draw simple inferences from tables and statistical diagrams
Compare sets of data using
bull tables
bull graphs
bull statistical measures
Be aware of restrictions when making conclusions from data
Charts Construct and use
bull bar charts
bull pie charts
bull pictograms
bull stem ndash and ndash leaf diagrams
bull frequency distributions
bull histograms with equal and unequal intervals
bull scatter diagrams
Learner Guide
72
Extended Statistics
Question type You should be able to R A G CommentsAverages Calculate for individual and discrete data
bull mean
bull median
bull mode
bull range
and distinguish between their use
Estimated mean Calculate an estimate of the mean for grouped and continuous data
Identify the modal class from a grouped frequency distributionCumulative frequency
Construct and use cumulative frequency diagrams to estimate and interpret
bull the median
bull percentiles
bull quartiles
bull inter-quartile range
Construct and interpret box-and-whisker plots
Correlation Understand what is meant by positive negative and zero correlation with reference to a scatter diagram
Lines of best fit Draw interpret and use a ruled line of best fit by eye
Cambridge Assessment International Education1 Hills Road Cambridge CB1 2EU United Kingdomt +44 1223 553554e infocambridgeinternationalorg wwwcambridgeinternationalorg
Copyright copy UCLES October 2017
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15
Show that indicates the answer is given and you need to write down all of the steps in a method that leads to the given answer You need to provide evidence that you understand and know how the answer is reached
Work out indicates that you should calculate the answer from the given information The mark allocation of 4 marks suggests that you will need to include several steps of working in order to get to the answer
Learner Guide
16
Answer Mark Notes(a)(i) 35 1 This is the only acceptable answer for this part of the question
(a)(ii) 74 1 This is the only acceptable answer for this part of the question
(b) 43deg and correct mathematical reasons
3 Two marks are awarded for the final answer of 43deg
The third mark is awarded for a fully correct reason for example angles on a straight line add up to 180deg and angles in a triangle add up to 180deg There are other correct reasons that could be also be used
If 43deg is not obtained one method mark can be awarded if the following calculation is seen in the working
180 ndash 128 or 128 ndash 85
(c) 322 or 3223hellip 2 This is the only acceptable answer for this part of the question
The answer has to be rounded correct to three significant figures or can be given with more figures in the answer
Those that did not get this answer can score one method mark for showing the following in their working
sin = 8 divide 15
(d)(i) 2 2300 225+2 This does not have to be shown in one step as long as the method shown is the same as this overall Those that do not
show this can have one method mark for showing the following in their working
300deg + 225deg
(d)(ii) 15 35 4 The answer 3 35pm is also acceptable for 4 marks
If the correct answer is not found one method mark is available for showing 375 divide 450 in their working and a second method mark can be awarded for sight of them multiplying their answer to this by 60 to change it to hours A third method mark can be awarded for adding their answer in hours to 14 45 ndash this shows the correct method so only one mark is lost for an incorrect final answers
Mark schemeYour examination papers will be marked and the overall number of marks for each paper will be recorded Your marks across all papers will then be converted to a grade
Final answer This value is what the examiner expects to see The answer has to be exactly as given in the mark scheme unless there are acceptable alternatives The mark scheme will always make it clear if there are acceptable alternative answers
Method marks Sometimes method marks are awarded for lines of working as well as for the final answer This means that you could get the final answer incorrect but still get some marks if you include the correct working The mark scheme does not include all possible methods so if you use a method not included in the mark scheme but it is accurate and relevant then the examiner will still award marks for the appropriate parts of the working ndash unless the questions asks you to use a specific method
example of a final answer
example of a method mark
17
Example candidate responseNow letrsquos look at the sample candidatersquos response to question 8 The examiners comments are in the orange boxes The candidate was awarded 8 marks out of 13
180 ndash 74 + 71 = 177
177
74
0 out of 1
The candidates working suggests they understand that the angle sum of a triangle is 180deg but they did not include brackets around 74 + 71 The answer 177deg is not sensible for this question
1 out of 1
The candidate recognises that there are parallel lines and that angle y is a corresponding angle to angle 74deg
180 ndash 128 = 52 180 ndash 85 ndash 52 = 43
43 angles on a straight line add up to 180deg
2 out of 3
The candidate has given a correct answer for w and shown correct working in two steps They have given a correct reason for 52deg using correct mathematical languge But they have not provided a reason to explain the angle 43deg They lose a mark for not also stating angle sum of a triangle is 180deg
sin p = 8 divide 15 = 053
p = sinndash1 (053)
p = 32005 320
1 out of 2
The candidate has correctly used trigonometry in their method They are awarded one method mark for the first line of working However they have rounded 05333333hellip (the result of 8 divide 15) to 052 and then calculated the inverse sin of 052 rather than 05333333 This has resulted in an inaccurate final answer This is called lsquopremature approximationrsquo and it is a very common error to make
18
AB2 = 3002 + 2252
= 140625
AB = 375
1 out of 2
The candidate has recognised the right-angled triangle and correctly used Pythagorasrsquo theorem in the first line of working However they have missed out an important step by not showing that you need to take the square root of 140625 to get 375 As this is a lsquoshow thatrsquo question and they missed a key step in the method they cannot be awarded full marks as the complete working is not shown One method mark is earned for the first line
T = = = 08333333hellip
08333333 hours = 08333333 times 60 minutes = 50 minutes
arrives at 14 45 + 50 mins = 3 35
DS
375450
3 35
3 out of 4
The candidate has found the time by correctly dividing the distance by the speed and recognised that this is in hours When converting the answer to a decimal they have not rounded the decimal but left its full value on the calculator to get 50 mins which is the correct approach Unfortunately after converting the time from 24 hour clock to 12 hour clock they did not include lsquopmrsquo to indicate that the time is in the afternoon and so the final answer is not quite right So 3 marks are awarded for all of a correct method but a mark is lost due to the accuracy of the final answer
19
How the answer could have been improvedThis answer could have been improved by
bull In part (a)(i) the answer of 177deg was not sensible given the diagram in the question If the candidate had checked their answer for sense they would have realised they had made a mistake It is always a good idea to check that your answer seems sensible before you move on to another question
bull In part (b) the candidate did all the correct steps but failed to provide both reasons There were two steps to the method which should have indicated to the candidate that there were two steps to justify and therefore two reasons should have been provided The mark allocation for the question [3] also indicates that more than one reason would be required one mark for the value of 43deg leaving two marks one mark for each of two reasons The candidate should have read the question carefully and again checked their response seemed reasonable
bull In part (c) the candidate rounded an intermediate answer which affected the accuracy of the final answer This caused them to lose a mark despite using a correct method You should only ever round the final answer do not round intermediate values If you can store the intermediate values in your calculator and so that you can use the full value in your calcuations If youre not able to do this and you have to round the intermediate values do not round them to less than three significant figures
bull In part (d)(i) the candidate missed out a step in the method As this was a show that question they needed to show all the steps in the method Its important to show all steps even if they seem obvious
bull In part (d)(ii) the candidate made a silly error by not stating that the time was pm When working with time answers are accepted in either 24 clock or 12 clock time but if you give your answer in the 12 hour clock then it must include am or pm as well
Common mistakesThere were a number of common mistakes made by other candidates on this question
bull Accuracy of answers
In parts (c) and (d)(ii) a common error was premature rounding ndash rounding intermediate values in the method before the final answer which resulted in their final answer not being accurate Other candidates gave the final answer to less than three significant figures ignoring the instruction on the front of the paper to round to three significant figures
bull Using incorrect terminology when giving reasons
In part (b) the most common error was to not give full reasons to support the answer Another common error was to provide a reason that did not use the correct mathematical language such as lsquoThey add up to 180degrsquo and lsquoIt is a straight linersquo which could not be awarded marks
bull Lack of knowledge
In part (c) a number of candidates had limited knowledge of trigonometry and did not choose the correct trig ratio which was the sine ratio This is why good revision is important
bull Not checking answers
In part (a)(i) even though the diagram is drawn NOT TO SCALE it is possible to see that the angle is an acute angle and should therefore not be bigger than 90deg This should alert candidate that if their answer is over 90deg it is not a sensible answer and they should go back and check their working
20
bull Inefficient method shown
In part (c) the lsquoShow thatrsquo question a number of candidates omitted an important step from the method this is often common in lsquoShow thatrsquo questions where every step must be shown no matter how obvious them seem
General adviceIn order to do your best when answering a mathematics question make sure you
bull revise all of the topics for the syllabus you are studying before the exam
bull understand what all the key terms and command words in the question mean
bull read the questions carefully and consider what you need to do before you do it
bull only round the final answer not intermediate values
bull show all steps in your working and show them clearly
bull round to the correct degree of accuracy
bull use the correct mathematical terminology
bull check your answers seem reasonable given the context or details of the question
21
It is important that you plan your revision in plenty of time for the examinations and that you develop a revision technique that works for you The advice in this section will help you revise and prepare for the examinations It is divided into general advice for all papers
Use the tick boxes to keep a record of what you have done what you plan to do or what you understand
For more advice on revision see the Cambridge Learner Revision Guide on our website
Section 6 Revision
Find out when the examinations are and plan your revision so you have time to revise Create a revision timetable and divide it into sections to cover each topic
Spend most of your time focussing on specific skills knowledge or issues that you have found more difficult when practicing them either during revision or earlier in the course
Write a summary of all the key information for a topic ndash use the checklists at the end of this section
Know the meaning of the command words used in questions and how to apply them to the information given Look at past examination papers and highlight the command words and check what they mean
Make revision notes and work on practice questions Reading alone does not work you need to be active and practice your maths
Work for shorter periods then have a break Revise small sections of the syllabus at a time but do this regularly
Test yourself by trying out some past exam questions Use the mark schemes to assess yourself and to be familiar with how marks are awarded for different questions
Be organised in advance with your notes texts exercise books revision guides and revision websites so you do not waste valuable revision time trying to find things
Make notes of key mathematical words that you should use in questions that ask you to lsquodescribersquo or give lsquogeometrical reasons forrsquo eg in describing transformations or giving reasons in circle theorem questions Look at the mark schemes for these types of questions from past papers to see how marks are awarded
Make sure you have all of the correct mathematical equipment ready for the exam particularly your calculator Make sure you are familiar with the all of the important functions on your calculator
Practice the areas you can do well not just those that you find more difficult
Take breaks and do things to relax when you take your breaks this will help you to be more productive when you are revising
Before the examination
22
During the examination
Plan your time according to the marks for each question For example a question worth one mark requires less time than a question one worth 4 marks If a question has several parts then the parts with more marks will need more time
Read each question very carefully
Identify the command words ndash you could underline or highlight them
Identify the other key words and information and perhaps underline them too particularly where
questions require reasoning or problem solving
Read the questions careully and make you have answered the question that is being asked
Show your working this is particularly important for questions where you are asked to lsquoshow that helliprsquo
Set your working out clearly so that it is easy to follow this makes it easier to keep track of what you have done and makes checking back through your work easier and it makes it easier for the examiner to mark your work try to write it in a logical order in the answer space
Write answers clearly if you want to change an answer then you should cross the answer out and write a replacement if your answer is on the answer line cross it out and write the replacement answer above it do not try to change numbers on the answer line as this can lead to unclear figures
Check your working and answers to avoid errors
Give your answer to the appropriate level of accuracy either the accuracy indicated in the question or the accuracy given on the front of the paper
Avoid rounding intermediate values part way through your calculation only round the final answer
Check that the answer that you have given is sensible and realistic for what is being asked
Use a pencil when drawing diagrams or completing graphs this means that you can change your answer more easily if you have made a mistake
Take care when reading scales
If you are asked for reasons for your answer then use the correct mathematical terms
Use the mark allocation given with the questionsparts of questions to try to judge how much work is needed to answer each part
23
Top tips for revision of Cambridge IGCSE Mathematics1 Summarise recall and applyMake sure that you can recall and apply the key information and mathematical techniques on each topic that you need for the exam
i Write a summary of the key information of a topicii Collect together some questions that test the knowledge and skills of this topic Ask your teacher for practice
questions or suitable past examination questions or use practice books or textbooksiii Test your recall by covering over the summary and trying to remember the details or use the summary as part of
the lsquoTeach the topicrsquo (Tip 3) or lsquoQuestion and answer cardsrsquo (Tip 4) activities iv After you have spent some time revising and practising the knowledge and skills answer the questions that you
collected together on the topic You might do this later on the same day as revising or a few days later Answer as many questions as you can in order to practise applying your knowledge
v Try creating your own questions by adapting existing ones and use these for practice when you return to a topic
On graph questions straight lines should be ruled and curves should be drawn freehand with a smooth curve
Donrsquot spend too long on any one part of a question If you are really stuck on a question then move on and come back to the question later if you have time As a rough guide each mark on the paper should take about one minute
2 Concept mapsConcept maps are a great way to revise the links between different factors or to explore a larger topic They can also be used to collect together your ideas
i Use a blank sheet of paper and turn it on its side (landscape)ii Put the topic title in the middle of the page and build the concept map outwards using lines called lsquobranchesrsquo
ndash The first branches are from the central topic to sub-topics draw these as thick lines
ndash Add new branches from the sub-topics to include more detail draw these as thinner lines
ndash Add even more detail to a point by adding more branches
This creates a hierarchy of information from lsquooverviewrsquo (the thick branches) to lsquofine detailrsquo (thinnest branches)
iii Write single key words or phrases along a branch and add drawings for visual impactiv Use different colours highlighter pens symbols and arrows to highlight key facts or issuesIt is a good idea to use a large piece of plain A3 (or larger) paper and lots of coloured pens
24
3 Teach the topicThis is a very simple but effective technique that focusses on knowledge recall It tests the brain and rehearses the information you need to know for a certain topic and so will help your revision
i Create some topic cards with key bullet points of information on Leave space for ticksii Give these to your parents family or friends for exampleiii Give yourself 10 minutes maximum to teach your audience the main points of the topic You could use a mini-
whiteboard or flip chart to helpiv Your audience tick off all the points you mention in your presentation and give you a final scoreThe brain loves competition so if you do not score full marks you can try again the next day or compete against friends This system of repeat and rehearsal is very effective especially with more complex topics and doesnt take much preparation
4 Question and answer (QampA) cardsThis is very similar to Teach the topic but less formal and less public for those who dislike performing in front of others It tests knowledge recall and rehearses the information you need to know for a certain topic
i Pick a topic and create two sets of cards question cards and answer cards You might find it helpful to make the question cards a different size or use different coloured card for answers
ii Make sure you have the topic or something appropriate depending on what you are focusing on as a heading on each card The questions should test your knowledge and understanding of key areas of the course
iii A friend or family member uses the cards to test you in short 5 or 10 minute periods at any time during the dayiv You could also do this alone by reading the questions to yourself giving the answer and then checking the
correct answer cardv This game can be adapted by using the cards to find matching pairs turn all cards face down across the space
in front of you Turn over two cards leaving them where they are If they match (one is a question card and the other is the corresponding answer card) pick up the pair and put them to one side If they dont match try to remember where they are and what is on each card then turn them back over Turn over two other cards Continue until you have matched all pairs
5 Question paper and mark schemesLooking at past question papers and the mark scheme helps you to familiarise yourself with what to expect and what the standard is
i Ask your teacher for past paper questions with mark schemes for the course ndash ask your teacher for help to make sure you are answering the correct questions and to simplify the mark scheme
ii Look at the revision checklist and identify which topic a given question relates to ndash you might need to ask your teacher to help you do this
iii Once you have finished revising a topic or unit time yourself answering some appropriate exam questions Check the mark schemes to see how well you would have scored or give the answers to your teacher to check
iv Add details or notes to the mark scheme where you missed out on marks in your original answers using a different coloured pen Use these notes when you revise and try the question again later
You can find plenty of past exam papers and mark schemes on the Cambridge International public website
httpwwwcambridgeinternationalorgprogrammes-and-qualificationscambridge-igcse-mathematics-0580past-papers
25
Other useful revision advice for Cambridge IGCSE Mathematics bull Before the exam make sure that you are familiar with your calculator and confident in using it
bull Look at the Example Candidate Response earlier in this guide Can you identify the strengths of the response andwhere they have made mistakes or lost marks
bull When you are attempting a past paper (or questions from a past paper) complete it without referring to yournotes so that you get a true idea of your strengths and weaknesses Then go back through the paper using yournotes and a different coloured pen to make corrections and changes After you have done as much as you can onthe paper mark it using the mark scheme Take notes of any points that you lost marks on
bull Donrsquot just revise the topics that you enjoy and are confident in If you identify an area that you are weaker inthen try to revisit the topic by reviewing your notes and doing some practice questions then use exam questionsto check whether you now understand
bull Return to topics later in your revision to check that you still remember and understand the topic and to help toensure that you recall more of the material when you get to the examination
Revision checklists for Cambridge IGCSE MathematicsThe tables on the following pages can be used as a revision checklist They do not contain all the detailed knowledge you need to know just an overview For more detail see the syllabus and talk to your teacher
You can use the tick boxes in the checklists to show when you have revised and are happy that you do not need to return to it Tick the lsquoRrsquo lsquoArsquo and lsquoGrsquo column to record your progress as follows
bull R = RED means you are really unsure and lack confidence in that area you might want to focus your revisionhere and possibly talk to your teacher for help
bull A = AMBER means you are reasonably confident in a topic but need some extra practicebull G = GREEN means you are very confident in a topic
As your revision progresses you can concentrate on the RED and AMBER topics in order to turn them into GREEN topics You might find it helpful to highlight each topic in red orange or green to help you prioritise
You can use the lsquoCommentsrsquo column to
bull add more information about the details for each pointbull include a reference to a useful resourcebull include a list of formulae or notationbull add learning aids such as rhymes poems or word playbull highlight areas of difficulty or things that you need to talk to your teacher about
There is a set of checklist for the Core syllabus and a different set for the Extended syllabus
Learner Guide
26
Core syllabus contentCore Number
Category You should be able to R A G CommentsNumber Identify and use
bull natural numbers
bull integers (positive negative and zero)
bull prime numbers
bull write a number as a product of its prime factors
bull square numbers and cube numbers
bull common factors and highest common factor of two numbers
bull common multiples and lowest common multiple of two numbers
bull rational numbers
bull irrational numbers (eg π radic2 )
bull real numbers
bull reciprocals
Learner Guide
27
Core Number
Question type You should be able to R A G CommentsSets and Venn diagrams
Understand notation of Venn diagrams
Definition of sets
eg A = xx is a natural number
B = abchellip
Notation
Number of elements in set A n(A)
Universal set
Union of A and B A cup B
Intersection of A and B A cap B
Squares square roots cubes and cube roots
Calculate
bull squares and cubes of numbers
bull square roots and cube roots of numbers
Learner Guide
28
Core Number
Question type You should be able to R A G CommentsDirected numbers
Use directed numbers in practical situations for example temperature changes
Fractions decimals and percentages
Use the language and notation of simple vulgar and decimal fractions and percentages
Recognise equivalent fractions decimals and percentages
Convert between fractions decimals and percentages
Ordering Order quantities by magnitude and demonstrate familiarity with the symbols = ne gt lt ⩾ ⩽
Indices and standard form (links to Algebraic manipulation)
Evaluate indices eg 25 5ndash2 1000 64frac12 8ndash23
Use the rules of indices for
bull multiplication of indices eg 4ndash3 times 45
bull division of indices eg 57 divide 53
bull index numbers raised to an index eg (23)2 (43)2
Use the standard form A times 10n where n is a positive or negative integer and 1 ⩽ A lt 10
bull convert numbers into and out of standard form
bull calculate with numbers in standard form
Learner Guide
29
Core Number
Question type You should be able to R A G CommentsFour rules
( + ndash times divide )
Use the four rules for calculations with
bull whole numbers
bull decimals
bull vulgar and mixed fractions
bull correct ordering of operations (BIDMAS) and use of bracketsEstimates Make estimates of numbers quantities and lengths
Give approximations to a specified number of
bull significant figures
bull decimal places
Round off answers to reasonable accuracy in the context of a given problem
Bounds Give upper and lower bounds for data given to a specified accuracy eg measured lengths
Ratio proportion rate
Understand ratio
Divide a quantity in a given ratio
Understand direct and inverse proportion
Use scales in practical situations
Use common measures of rate (formulae for other rates eg density and pressure will be given in the question)
Calculate average speed
Learner Guide
30
Core Number
Question type You should be able to R A G CommentsPercentages Calculate a percentage of a quantity
Express one quantity as a percentage of another quantity
Calculate percentage increase or decrease
Use of an electronic calculator
Use a calculator efficiently
Check accuracy of calculations
Time Calculate times in terms of the 24-hour and 12-hour clock
Read
bull clocks
bull dials
bull timetables
Money Calculate using money
Convert from one currency to another
Learner Guide
31
Core Number
Question type You should be able to R A G CommentsPersonal and small business finance
Use given data to solve problems on
bull earnings
bull simple interest
bull compound interest (you will need to know the compound interest formula)
bull discount
bull profit and loss
Extract data from tables and charts
Learner Guide
32
Core Algebra and graphs
Question type You should be able to R A G CommentsBasic algebra Use letters to express generalised numbers
Express basic arithmetic processes algebraically
Substitute numbers in formulae
Construct simple expressions and set up simple equations
Rearrange simple formulae
Algebraic manipulation
Manipulate directed numbers
Use brackets
bull expand a single bracket eg 3x(2x ndash4y)
bull expand a pair of brackets eg (x + 3) (x ndash 7)
Extract common factors eg factorise 9x2 + 15xy
Rules of indices Use and interpret positive negative and zero indices
Use the rules of indices eg to simplify algebra such as
bull 3x4 times 5x
bull 10x3 divide 2x2
bull (x6)2
Learner Guide
33
Core Algebra and graphs
Question type You should be able to R A G CommentsEquations and inequalities
Derive and solve simple linear equations in one unknown
Derive and solve simultaneous linear equations in two unknowns
Number sequences
(links to Squares square roots cubes and cube roots)
Continue a number sequence
Recognise patterns in sequences
Recognise relationships between difference sequences
Find the nth term of sequences for
bull liner sequences
bull simple quadratic sequences
bull cubic sequences
Practical graphs
(links to Mensuration)
Interpret and use graphs in practical situations including
bull travel graphs
bull conversion graphs
Draw graphs from given data
Learner Guide
34
Core Algebra and graphs
Question type You should be able to R A G CommentsGraphs of functions
(links to Co-ordinate geometry)
Construct tables of values for functions of the form
bull ax + b (linear)
bull plusmn x2 + ax + b (quadratic)
bull (x ne 0) (reciprocal)
where a and b are integer constants
Draw and interpret such graphs
Solve linear and quadratic equations approximately by graphical methods
Recognise and sketch the graphs of linear and quadratic functions
ax
Learner Guide
35
Core Co-ordinate geometry
Question type You should be able to R A G CommentsCo-ordinates Work with co-ordinates in two dimensions
Gradients Find the gradient of a straight line graph
Equation of straight line
Interpret and obtain the equation of a straight line graph in the form y = mx + c where the graph is given
Parallel lines Determine the equation of a straight line parallel to a given line eg find the equation of a line parallel to y = 4x ndash 1 that passes through (0 ndash3)
Learner Guide
36
Core Geometry
Question type You should be able to R A G CommentsGeometrical language
Use and interpret the geometrical terms
bull point
bull line
bull parallel
bull perpendicular
bull bearing
bull right angle acute obtuse and reflex angles
bull similar
bull congruent
Use and interpret the vocabulary of
bull triangles right-angled scalene isosceles equilateral
bull quadrilaterals
bull circles
bull polygons
bull simple solid figures including nets
Learner Guide
37
Core Geometry
Question type You should be able to R A G CommentsGeometrical constructions
Measure and draw lines and angles
Construct a triangle given the three sides using a ruler and a pair of compasses only
Scale drawings Read and make scale drawings
Similar figures Calculate lengths of similar figures
Congruent Recognise congruent shapes
Symmetry Recognise symmetry properties for triangles quadrilaterals and circles
Recognise line symmetry in two dimensions
Recognise and find the order of rotational symmetry in two dimensions
Learner Guide
38
Core Geometry
Question type You should be able to R A G CommentsAngle properties Calculate unknown angles explaining the properties that you
are using in geometrical language for angles
bull angles at a point
bull angles on a straight line and intersecting straight lines
bull angles within parallel lines
bull angles in triangles
bull angles in quadrilaterals
bull angles in regular polygons
bull angle in a semi-circle
bull angle between tangent and radius of a circle
Learner Guide
39
Core Mensuration
Question type You should be able to R A G CommentsMeasures bull Use current units of
bull mass
bull length
bull area
bull volume
bull capacity
Express quantities in terms of smaller or larger units including units of area and volume
Convert between units including units of area and volume
Perimiter Carry out calculations involving
bull perimeter and area of a rectangle
bull perimeter and area of a triangle
bull perimeter and area of parallelogram
bull perimeter and area of a trapezium
bull perimeter and area of shapes made by combining
bull rectangles triangles parallelograms andor trapeziums
Learner Guide
40
Core Mensuration
Question type You should be able to R A G CommentsCircles Carry out calculations involving circumference and area of a
circle
Solve simple problems involving the arc length and sector area of a circle where the sector angle is a factor of 360deg
Surface area and volume
Carry out calculations involving
bull surface area and volume of a cuboid prism and cylinder (no formulae will be given for these shapes)
bull surface area and volume of a sphere pyramid and cone (formulae will be given for these shapes)
Areas and volumes of compound shapes
Carry out calculations involving the areas and volumes of compound shapes made from combinations of the shapes in Perimeter or Surface area and volume
Learner Guide
41
Core Trigonometry
Question type You should be able to R A G CommentsBearings Use and interpret three-figure bearings measured clockwise
from the North ie 000degndash360degTrigonometry Find unknown sides andor angles in right-angled triangles by
applying
bull Pythagorasrsquo theorem
bull sine cosine and tangent ratios for acute angles in right-angled triangles
Learner Guide
42
Core Vectors and transformations
Question type You should be able to R A G CommentsVectors in two dimensions (links to Trigonometry)
Describe a translation by using a vector represented by
AB or a
Add and subtract vectors
Multiply a vector by a scalar
Transformations Reflect simple shapes in horizontal or vertical lines
Rotate simple shapes through multiples of 90deg about
bull the origin
bull their vertices
bull the midpoints of their sides
Construct translations of simple shapes
Construct enlargements of simple shapes (positive and fractional scale factors)
Recognise and describe using the correct language
bull reflections
bull rotations
bull translations
bull enlargements (positive and fractional scale factors)
( )x
y
Learner Guide
43
Core Probability
Question type You should be able to R A G CommentsSingle events Calculate the probability of a single event as a fraction decimal
or percentage (not a ratio)Probability scale Understand and use the probability scale from 0 to 1
Sum to 1 Understand that the probability of an event occurring = 1 ndash the probability of the event not occurring
Relative frequency
Understand relative frequency as an estimate of probability
Work out expected frequencies using relative frequencyCombined events Calculate the probability of simple combined events using
bull tree diagrams
bull possibility diagrams (points on a grid)
bull Venn diagrams (2 sets only)
Learner Guide
44
Core Statistics
Question type What I need to do R A G CommentsClassify Collect classify and tabulate data
Interpret and compare
Read interpret and draw simple inferences from tables and statistical diagrams
Compare sets of data using
bull tables
bull graphs
bull statistical measures
Be aware of restrictions when making conclusions from data
Charts Construct and use
bull bar charts
bull pie charts
bull pictograms
bull stem-and-leaf diagrams
bull frequency distributions
bull histograms with equal intervals
bull scatter diagrams
Learner Guide
45
Question type What I need to do R A G CommentsAverages Calculate for individual and discrete data
bull mean
bull median
bull mode
bull range
and distinguish between their useCorrelation Understand what is meant by positive negative and zero
correlation with reference to a scatter diagramLine of best fit Draw interpret and use a ruled line of best fit by eye
Learner Guide
46
Extended syllabus content (includes required Core content)Extended Number
Question type You should be able to R A G CommentsNumber Identify and use
bull natural numbers
bull integers (positive negative and zero)
bull prime numbers
bull write a number as a product of its prime factors
bull square and cube numbers
bull common factors and highest common factor of two or more numbers
bull common multiples and lowest common multiple of two or more numbers
bull rational numbers
bull irrational numbers (eg π radic2 )
bull real numbers
bull reciprocals
Learner Guide
47
Extended Number
Question type You should be able to R A G CommentsSet notation and language
Use language notation and Venn diagrams to describe sets and represent relationships between sets as follows
Definition of sets egA = x x is a natural number
B = (xy) y = mx + c
C = x a ⩽ x ⩽ b
D = a b c hellip
Notation egnumber of elements in set A n(A)
lsquois an element ofrsquo isin
lsquois not an element ofrsquo notin
complement of set A
the empty set empty
the universal set
A is a subset of B A sube B
A is a proper subset of B A sub B
A is not a subset of B A ⊈ B
A is not a proper subset of B A nsub B
union of A and B A cup B
intersection of A and B A cap B
Learner Guide
48
Extended Number
Question type You should be able to R A G CommentsSquares square roots cubes and cube roots
Calculatebull squares of numbers
bull square roots of numbers
bull cubes of numbers
bull cube roots of numbers
bull other powers and roots of numbers
Directed numbers
Use directed numbers in practical situations for example temperature changes
Fractions decimals and percentages
Use the language and notation of simple vulgar and decimal fractions and percentages in appropriate contexts
Recognise equivalent fractions decimals and percentages
Convert between fractions decimals and percentages
Convert recurring decimals to fractions
Ordering Order quantities by magnitude and demonstrate familiarity with the symbols = ne gt lt ⩾ ⩽
Learner Guide
49
Extended Number
Question type You should be able to R A G CommentsIndices and standard form (links to Algebraic manipulation)
Evaluate indices including fractional negative and zero
eg 25 5ndash2 1000 10012 8ndash23
Use the rules of indices forbull multiplication of indices eg 43 times 45
bull division of indices eg 57 divide 53
bull index numbers raised to an index eg (43)2
Use the standard form A times 10n where n is a positive or negative integer and 1 ⩽ A lt 10bull convert into and out of standard form
bull calculate with numbers in standard form
Four rules
( + ndash times divide )
Use the four rules for calculations withbull whole numbers
bull decimals
bull vulgar and mixed fractions
bull correct ordering of operations (BIDMAS) and use of brackets
Learner Guide
50
Extended Number
Question type You should be able to R A G CommentsEstimates Make estimates of numbers quantities and lengths
Give approximations to a specified number of
bull significant figures
bull decimal places
Round off answers to reasonable accuracy in the context of a given problem
Bounds Give upper and lower bounds for data given to a specified accuracy eg measured lengths
Obtain appropriate upper and lower bounds to solutions of simple problems given to a specified accuracy eg the lower and upper bounds for the area of a rectangle
Ratio proportion rate
(links to Direct and inverse proportion)
Understand ratio
Divide quantities in a given ratio
Increase and decrease a quantity by a given ratio
Understand numerical problems involving direct and inverse proportion
Use ratio and scales in practical situations
Use common measures of rate (formulae for other rates eg density and pressure will be given in the question)
Calculate average speed
Learner Guide
51
Extended Number
Question type What I need to do R A G CommentsPercentages Calculate a percentage of a quantity
Express one quantity as a percentage of another quantity
Calculate percentage increase or decrease
Calculate reverse percentages eg finding the cost price given the selling price and the percentage profit
Use of an electronic calculator
Use a calculator efficiently
Check accuracy of calculations
Time Calculate times in terms of the 24-hour and 12-hour clock
Read clocks dials and timetables
Money Calculate using money
Convert from one currency to another
Learner Guide
52
Extended Number
Question type You should be able to R A G CommentsPersonal and small business finance
Use given data to solve problems on
bull earnings
bull simple interest
bull compound interest
ndash you must know the compound interest formula
bull discount
bull profit and loss
Extract data from tables and charts
Exponential growth and decay
Use exponential growth and decay in population and finance eg depreciation bacteria growth
Learner Guide
53
Extended Algebra and graphs
Question type You should be able to R A G CommentsBasic algebra Use letters to express generalised numbers
Express basic arithmetic processes algebraically
Substitute numbers in complicated formulae
Construct and rearrange complicated formulae eg where the subject appears twice
Algebraic manipulation
Manipulate directed numbers
Use bracketsbull expand a single bracket eg expand 3x(2x ndash 4y)
bull expand a pair of brackets eg (x ndash 4)(x + 7)
bull expand products of more than two brackets eg (x + 4)(x ndash 7)(2x + 1)
Extract common factors eg factorise 9x2 + 15xy
Factorise expressions of the formbull ax + bx + kay + kby
bull asup2xsup2 ndash bsup2ysup2
bull asup2 + 2ab + bsup2
bull axsup2 + bx + c
Learner Guide
54
Extended Algebra and graphs
Question type You should be able to R A G CommentsAlgebraic fractions
Manipulate algebraic fractions eg
bull
bull
bull
bull
bull
Factorise and simplify algebraic fractions such as
Rules of indices Use and interpret positive negative and zero indices
Use and interpret fractional indices eg solve 32x = 2
Use the rules of indices to simplify algebra eg
x3 + x ndash 4
22x3 +
3(x ndash 5)2
3a4 +
5ab3
3a4 divide
9a10
1x ndash 2 +
2x ndash 3
x2 ndash 2xx2 ndash 5x + 6
3xndash4 times23
x12
32x5( )
3
2xndash2divide25
x12
Learner Guide
55
Extended Algebra and graphs
Question type You should be able to R A G CommentsEquations and inequalities
bull Derive and solve simple linear equations in one unknown
bull Derive and solve simultaneous linear equations in two unknowns
bull Derive and solve simultaneous equations involving one linear and one quadratic
Solve quadratic equations by
bull factorisation
bull completing the square
bull using the formula
Derive and solve simple linear inequalities including representing solutions on a number line
Linear programming
Represent inequalities graphically including using the conventions of
bull broken lines for strict inequalities
bull shading unwanted regions
Solve simple linear programming problems using graphical representations of inequalities
Learner Guide
56
Extended Algebra and graphs
Question type You should be able to R A G CommentsNumber sequences (links to Squares square roots cubes and cube roots)
Continue a number sequence
Recognise patterns in sequences
Recognise relationships between different sequences
Find the nth term of sequences of
bull linear sequences
bull quadratic sequences
bull cubic sequences
bull exponential sequences
and simple combinations of these
Direct and inverse proportion (links to Ratio proportion rate)
Express direct proportion algebraically
Express inverse proportion algebraically
Use algebraic expressions of direct and inverse proportion to find unknown quantities
Practical graphs
(links to Coordinate geometry)
Interpret and use graphs in practical situations including
bull travel graphs
bull conversion graphs
Draw graphs from given data
Learner Guide
57
Extended Algebra and graphs
Question type You should be able to R A G CommentsPractical graphs (links to Coordinate geometry) continued
Apply the idea of rate of change to simple kinematics involving
bull distancendashtime graphs
bull speedndashtime graphs
bull acceleration and deceleration
This may involve estimation and interpretation of the gradient of a tangent at a point
Calculate distance travelled as an area under a linear speedndash time graph
Learner Guide
58
Extended Algebra and graphs
Question type You should be able to R A G CommentsGraphs of functions (links to Coordinate geometry)
Construct tables of values and draw graphs for functions of the form
bull axn where a is a rational constant and n = minus2 minus1 0 1 2 3 and simple sums of not more than three of these
bull abx + c where a and c are rational constants and b is a positive integer
Solve associated equations approximately by graphical methods including finding and interpreting roots and finding turning points of quadratics by completing the square
Draw and interpret graphs representing exponential growth and decay problems
Recognise sketch and interpret graphs of
bull linear
bull quadratic
bull cubic
bull reciprocal
bull exponential
(knowledge of turning points and asymtotes is required)Tangents Estimate gradients of curves by drawing tangents
Learner Guide
59
Extended Algebra and graphs
Question type You should be able to R A G CommentsFunctions Use function notation eg
f(x) = 3x ndash 5 f x α 3x ndash5 to describe simple functions
Find inverse functions f ndash1 (x)
Form composite functions as defined by gf(x) = g(f(x))
Derivatives Understand the idea of a derived function
Use derivatives of the form axn and simple sums of not more than three of these (a is a rational constant and n is a positive integer or 0)
Apply differentiation to gradients and turning points (stationary points)
Use any method to explain whether the turning point is a maximum or a minimum eg second derivative or gradient of function on either side of turning point
Learner Guide
60
Extended Co-ordinate geometry
Question type You should be able to R A G CommentsStraight line graphs
Work with co-ordinates in two dimensions
Gradient Find the gradient of a straight line graph
Calculate the gradient of a straight line from the co-ordinates of two points on it
Length and midpoint
Calculate the length and the co-ordinates of the midpoint of a straight line segment from the co-ordinates of its end points
Equation of line Interpret and obtain the equation of a straight line graph
Parallel lines Determine the equation of a straight line parallel to a given line eg find the equation of a line parallel to y = 4x ndash 1 that passes through (0 ndash3)
Perpendicular lines
Find the gradient of parallel and perpendicular lines eg
bull find the gradient of a line perpendicular to y = 3x + 1
bull find the equation of a line perpendicular to one passing through the co-ordinates (1 3) and (ndash2 ndash9)
Learner Guide
61
Extended Geometry
Question type You should be able to R A G CommentsGeometrical language
Use and interpret the geometrical terms
bull point
bull line
bull parallel
bull perpendicular
bull bearing
bull right angle acute obtuse and reflex angles
bull similar
bull congruent
Use and interpret the vocabulary of
bull triangles right-angled scalene isosceles equilateral
bull quadrilaterals
bull circles
bull polygons
bull simple solid figures including nets
Learner Guide
62
Extended Geometry
Question type What I need to do R A G CommentsGeometrical constructions
Measure and draw lines and angles
Construct a triangle given the three sides using a ruler and a pair of compasses only
Scale drawings Read and make scale drawings
Similar figures Calculate lengths of similar figures
Use relationships between areas of similar triangles and in similar figures
Use relationships between volumes and surface areas of similar solids
Congruent triangles
Use the congruence criteria for triangles (SSS ASA SAS RHS)
Symmetry Recognise symmetry properties for triangles quadrilaterals and circles
Recognise line symmetry in two dimensions
Recognise and find the order of rotational symmetry in two dimensions
Learner Guide
63
Extended Geometry
Question type You should be able to R A G CommentsSymmetry (continued)
Use the following symmetry properties of circles
bull equal chords are equidistant from the centre
bull perpendicular bisector of a chord passes through the centre
bull tangents from an external point are equal in length
Recognise and use symmetry properties of
bull prism cylinder cone and pyramid
Learner Guide
64
Extended Geometry
Question type You should be able to R A G CommentsAngle properties Calculate unknown angles explaining the properties that
you are using in geometrical language for the following geometrical properties
bull angles at a point
bull angles at a point on a straight line and intersecting straight lines
bull angles formed within parallel lines
bull angle properties of triangles and quadrilaterals
bull angle properties of regular polygons
bull angle in a semi-circle
bull angle between tangent and radius of a circle
bull angles properties of irregular polygons
bull angle at the centre of a circle is twice the angle at the circumference
bull angles in the same segment are equal
bull angles in opposite segments are supplementary cyclic quadrilaterals
bull alternate segment theorem
Learner Guide
65
Extended Mensuration
Question type What I need to do R A G CommentsMeasures Use current units of
bull mass
bull length
bull area
bull volume
bull capacity
Express quantities in terms of smaller or larger units including units of area and volume
Perimeter Carry out calculations involving
bull perimeter and area of a rectangle
bull perimeter and area of a triangle
bull perimeter and area of parallelogram
bull perimeter and area of a trapezium
bull perimeter and area of compound shapes made by combining rectangles triangles parallelograms andor trapeziums
Learner Guide
66
Extended Mensuration
Question type You should be able to R A G CommentsCircles Carry out calculations involving circumference and area of a
circle
Solve problems involving arc length and sector area of a circle
Surface area and volume
Carry out calculations involving
bull surface area and volume of a cuboid prism and cylinder (no formulae will be given for these shapes)
bull surface area and volume of a sphere pyramid and cone (formulae will be given for these shapes)
Compound shapes
Carry out calculations involving
bull area of a shape made by combining cuboids prisms andor cylinders
bull volume of a shape made by combining cuboids prisms andor cylinders
Learner Guide
67
Extended Trigonometry
Question type You should be able to R A G CommentsBearings Use and interpret three-figure bearings measured clockwise
from the North ie 000degndash360degTrigonometry Find unknown sides andor angles in right-angled triangles by
applying
bull Pythagorasrsquo theorem
bull sine cosine and tangent ratios for acute angles in right-angled triangles
Solve problems in two dimensions involving angles of elevation and depression
Know that the perpendicular distance from a point to a line is the shortest distance to the line
Trig graphs and equations
Recognise sketch and interpret graphs of simple trigonometric functions
Graph and know the properties of trigonometric functions
Solve simple trigonometric equations for values between 0deg
and 360deg eg Solve sin x = radic32
for values of x between 0deg and
360degGeneral trig Solve problems using sine and cosine rules for any triangle
Find the area of any triangle using frac12absinC
Trig in 3D Solve simple trigonometrical problems in three dimensions including angle between a line and a plane
Learner Guide
68
Extended Vectors and transformations
Question type You should be able to R A G CommentsVectors in two dimensions (links to Trigonometry)
Describe a translation by using a vector represented by
AB or a
Add and subtract vectors
Multiply a vector by a scalar
Transformations Reflect simple shapes in horizontal or vertical lines
Rotate simple shapes through multiples of 90deg about any point
Construct translations of simple shapes
Construct enlargements of simple shapes (positive fractional and negative scale factors)
Recognise and describe
bull reflections
bull rotations
bull translations
bull enlargements (positive fractional and negative scalefactors)
( )x
y
Learner Guide
69
Extended Vectors and transformations
Question type You should be able to R A G CommentsHarder vectors
Calculate the magnitude of a vector as and
understand that magnitude is denoted by modulus signs |A B| or |a|
Represent vectors by directed line segments
Use the sum and difference of two vectors
Use position vectors
( )x
yradicx2 + y2
Learner Guide
70
Extended Probability
Question type You should be able to R A G CommentsProbability (links to Four rules)
Calculate the probability of a single event as a fraction decimal or percentage (not a ratio)
Probability scale Understand and use the probability scale from 0 to 1
Sum to 1 Understand that the probability of an event occurring = 1 ndash the probability of the event not occurring
Relative frequency
Understand relative frequency as an estimate of probability
Work out expected frequencies using relative frequency
Combined events Calculate the probability of combined events using
bull tree diagrams
bull possibility diagrams
bull tables
Learner Guide
71
Extended Statistics
Question type You should be able to R A G CommentsClassify Collect classify and tabulate data
Interpret and compare
Read interpret and draw simple inferences from tables and statistical diagrams
Compare sets of data using
bull tables
bull graphs
bull statistical measures
Be aware of restrictions when making conclusions from data
Charts Construct and use
bull bar charts
bull pie charts
bull pictograms
bull stem ndash and ndash leaf diagrams
bull frequency distributions
bull histograms with equal and unequal intervals
bull scatter diagrams
Learner Guide
72
Extended Statistics
Question type You should be able to R A G CommentsAverages Calculate for individual and discrete data
bull mean
bull median
bull mode
bull range
and distinguish between their use
Estimated mean Calculate an estimate of the mean for grouped and continuous data
Identify the modal class from a grouped frequency distributionCumulative frequency
Construct and use cumulative frequency diagrams to estimate and interpret
bull the median
bull percentiles
bull quartiles
bull inter-quartile range
Construct and interpret box-and-whisker plots
Correlation Understand what is meant by positive negative and zero correlation with reference to a scatter diagram
Lines of best fit Draw interpret and use a ruled line of best fit by eye
Cambridge Assessment International Education1 Hills Road Cambridge CB1 2EU United Kingdomt +44 1223 553554e infocambridgeinternationalorg wwwcambridgeinternationalorg
Copyright copy UCLES October 2017
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- Check Box 10530 Off
- Text Field 335
- Check Box 10567 Off
- Check Box 10568 Off
- Check Box 10569 Off
- Check Box 10570 Off
- Check Box 10571 Off
- Check Box 10572 Off
- Check Box 10573 Off
- Check Box 10574 Off
- Check Box 10575 Off
- Check Box 10576 Off
- Check Box 10577 Off
- Check Box 10578 Off
- Check Box 10597 Off
- Check Box 10598 Off
- Check Box 10599 Off
- Check Box 10579 Off
- Check Box 10580 Off
- Check Box 10581 Off
- Check Box 10582 Off
- Check Box 10583 Off
- Check Box 10584 Off
- Check Box 10585 Off
- Check Box 10586 Off
- Check Box 10587 Off
- Check Box 10588 Off
- Check Box 10589 Off
- Check Box 10590 Off
- Check Box 10591 Off
- Check Box 10592 Off
- Check Box 10593 Off
- Check Box 10594 Off
- Check Box 10595 Off
- Check Box 10596 Off
- Check Box 10600 Off
- Check Box 10601 Off
- Check Box 10602 Off
- Check Box 10603 Off
- Check Box 10604 Off
- Check Box 10605 Off
- Check Box 10606 Off
- Check Box 10607 Off
- Check Box 10608 Off
- Check Box 10609 Off
- Check Box 106010 Off
- Check Box 106011 Off
- Check Box 106012 Off
- Check Box 106013 Off
- Check Box 106014 Off
- Check Box 106015 Off
- Check Box 106016 Off
- Check Box 106017 Off
- Text Field 315
- Check Box 10340 Off
- Check Box 10341 Off
- Check Box 10342 Off
- Check Box 10343 Off
- Check Box 10344 Off
- Check Box 10345 Off
- Check Box 10346 Off
- Check Box 10347 Off
- Check Box 10348 Off
- Check Box 10349 Off
- Check Box 10350 Off
- Check Box 10351 Off
- Check Box 10531 Off
- Check Box 10532 Off
- Check Box 10542 Off
- Text Field 313
- Check Box 10352 Off
- Check Box 10353 Off
- Check Box 10354 Off
- Text Field 316
- Check Box 10355 Off
- Check Box 10356 Off
- Check Box 10357 Off
- Check Box 10358 Off
- Check Box 10359 Off
- Check Box 10360 Off
- Check Box 10361 Off
- Check Box 10362 Off
- Check Box 10363 Off
- Check Box 10364 Off
- Check Box 10365 Off
- Check Box 10366 Off
- Check Box 10404 Off
- Check Box 10405 Off
- Check Box 10406 Off
- Text Field 352
- Check Box 102021 Off
- Check Box 102022 Off
- Check Box 102040 Off
- Check Box 102041 Off
- Check Box 102042 Off
- Check Box 102043 Off
- Check Box 102044 Off
- Check Box 102045 Off
- Check Box 102046 Off
- Check Box 102047 Off
- Check Box 102048 Off
- Check Box 102049 Off
- Check Box 102050 Off
- Check Box 102051 Off
- Check Box 102052 Off
- Check Box 102065 Off
- Check Box 102066 Off
- Check Box 102067 Off
- Check Box 102053 Off
- Check Box 102054 Off
- Check Box 102055 Off
- Text Field 351
- Check Box 102056 Off
- Check Box 102057 Off
- Check Box 102058 Off
- Check Box 102059 Off
- Check Box 102060 Off
- Check Box 102061 Off
- Check Box 102062 Off
- Check Box 102063 Off
- Check Box 102064 Off
- Check Box 102068 Off
- Check Box 102069 Off
- Check Box 102070 Off
- Text Field 318
- Check Box 10373 Off
- Check Box 10374 Off
- Check Box 10375 Off
- Check Box 10376 Off
- Check Box 10377 Off
- Check Box 10378 Off
- Check Box 10379 Off
- Check Box 10380 Off
- Check Box 10381 Off
- Check Box 10382 Off
- Check Box 10383 Off
- Check Box 10384 Off
- Check Box 10385 Off
- Check Box 10386 Off
- Check Box 10387 Off
- Text Field 317
- Check Box 10388 Off
- Check Box 10389 Off
- Check Box 10390 Off
- Check Box 102023 Off
- Check Box 102024 Off
- Check Box 102025 Off
- Check Box 102026 Off
- Check Box 102027 Off
- Check Box 102028 Off
- Check Box 102071 Off
- Check Box 102072 Off
- Check Box 102073 Off
- Check Box 102029 Off
- Check Box 10391 Off
- Check Box 10392 Off
- Check Box 10393 Off
- Check Box 10394 Off
- Check Box 10395 Off
- Check Box 10396 Off
- Check Box 10397 Off
- Check Box 10398 Off
- Check Box 102030 Off
- Check Box 102031 Off
- Check Box 102032 Off
- Text Field 319
- Text Field 322
- Check Box 10408 Off
- Check Box 10409 Off
- Check Box 10410 Off
- Check Box 10411 Off
- Check Box 10412 Off
- Check Box 10413 Off
- Check Box 10414 Off
- Check Box 10415 Off
- Check Box 10416 Off
- Check Box 10417 Off
- Check Box 10418 Off
- Check Box 10419 Off
- Text Field 321
- Check Box 10420 Off
- Check Box 10421 Off
- Check Box 10422 Off
- Check Box 10423 Off
- Check Box 10424 Off
- Check Box 10425 Off
- Text Field 337
- Check Box 102033 Off
- Check Box 102034 Off
- Check Box 102035 Off
- Check Box 102036 Off
- Check Box 102037 Off
- Check Box 102038 Off
- Text Field 338
- Check Box 102039 Off
- Check Box 10426 Off
- Check Box 10427 Off
- Check Box 10428 Off
- Check Box 10429 Off
- Check Box 10430 Off
- Text Field 324
- Check Box 10434 Off
- Check Box 10435 Off
- Check Box 101051 Off
- Check Box 1010100 Off
- Check Box 1010101 Off
- Check Box 1010102 Off
- Check Box 1010128 Off
- Check Box 1010129 Off
- Check Box 1010130 Off
- Check Box 10439 Off
- Check Box 10440 Off
- Check Box 10441 Off
- Check Box 10442 Off
- Check Box 10443 Off
- Check Box 10444 Off
- Text Field 350
- Check Box 10742 Off
- Check Box 10743 Off
- Check Box 10744 Off
- Text Field 325
- Check Box 10445 Off
- Check Box 10446 Off
- Check Box 1010151 Off
- Check Box 1010152 Off
- Check Box 1010153 Off
- Check Box 1010154 Off
- Check Box 1010155 Off
- Check Box 1010156 Off
- Check Box 1010157 Off
- Check Box 10450 Off
- Check Box 10451 Off
- Check Box 10452 Off
- Text Field 326
- Check Box 1010158 Off
- Check Box 1010159 Off
- Check Box 1010160 Off
- Check Box 1010161 Off
- Check Box 1010162 Off
- Check Box 1010163 Off
- Check Box 10453 Off
- Check Box 10454 Off
- Check Box 10455 Off
- Check Box 10745 Off
- Check Box 10746 Off
- Check Box 10747 Off
- Check Box 10748 Off
- Check Box 10749 Off
- Check Box 10750 Off
- Check Box 1010167 Off
- Check Box 1010168 Off
- Check Box 1010169 Off
- Check Box 10459 Off
- Check Box 10460 Off
- Check Box 10461 Off
- Check Box 10462 Off
- Check Box 10463 Off
- Check Box 10464 Off
- Check Box 10611 Off
- Check Box 10612 Off
- Check Box 10613 Off
- Text Field 329
- Check Box 1010171 Off
- Check Box 1010172 Off
- Check Box 1010173 Off
- Check Box 1010174 Off
- Check Box 1010175 Off
- Check Box 1010176 Off
- Check Box 1010177 Off
- Check Box 1010178 Off
- Check Box 1010179 Off
- Check Box 10467 Off
- Check Box 10468 Off
- Check Box 10469 Off
- Check Box 10470 Off
- Check Box 10471 Off
- Check Box 10472 Off
- Check Box 1010180 Off
- Check Box 1010181 Off
- Check Box 1010182 Off
- Text Field 330
- Check Box 1010183 Off
- Check Box 1010184 Off
- Check Box 1010185 Off
- Check Box 10473 Off
- Check Box 10474 Off
- Check Box 10475 Off
- Check Box 10476 Off
- Check Box 10477 Off
- Check Box 10478 Off
- Check Box 1010186 Off
- Check Box 1010187 Off
- Check Box 1010188 Off
- Check Box 1010275 Off
- Check Box 1010276 Off
- Check Box 1010277 Off
- Text Field 331
- Check Box 1010189 Off
- Check Box 1010190 Off
- Check Box 1010191 Off
- Check Box 1010192 Off
- Check Box 1010193 Off
- Check Box 1010194 Off
- Check Box 1010354 Off
- Check Box 1010355 Off
- Check Box 1010356 Off
- Check Box 10479 Off
- Check Box 10480 Off
- Check Box 10481 Off
- Check Box 10482 Off
- Check Box 10483 Off
- Check Box 10484 Off
- Check Box 1010195 Off
- Check Box 1010196 Off
- Check Box 1010197 Off
- Check Box 1010278 Off
- Check Box 1010279 Off
- Check Box 1010280 Off
- Text Field 339
- Check Box 10614 Off
- Check Box 10615 Off
- Check Box 10616 Off
- Check Box 10617 Off
- Check Box 10618 Off
- Check Box 10619 Off
- Check Box 1010281 Off
- Check Box 1010282 Off
- Check Box 1010283 Off
- Text Field 340
- Check Box 1010284 Off
- Check Box 1010285 Off
- Check Box 1010286 Off
- Check Box 1010287 Off
- Check Box 1010288 Off
- Check Box 1010289 Off
- Check Box 10620 Off
- Check Box 10621 Off
- Check Box 10622 Off
- Check Box 10623 Off
- Check Box 10624 Off
- Check Box 10625 Off
- Check Box 1010290 Off
- Check Box 1010291 Off
- Check Box 1010292 Off
- Check Box 1010293 Off
- Check Box 1010294 Off
- Check Box 1010295 Off
- Check Box 10626 Off
- Check Box 10627 Off
- Check Box 10628 Off
- Check Box 10751 Off
- Check Box 10752 Off
- Check Box 10753 Off
- Text Field 342
- Check Box 1010296 Off
- Check Box 1010297 Off
- Check Box 1010298 Off
- Check Box 10632 Off
- Check Box 10633 Off
- Check Box 10634 Off
- Check Box 10635 Off
- Check Box 10636 Off
- Check Box 10637 Off
- Text Field 349
- Check Box 1010305 Off
- Check Box 1010306 Off
- Check Box 1010307 Off
- Check Box 1010308 Off
- Check Box 1010309 Off
- Check Box 10103010 Off
- Check Box 10641 Off
- Check Box 10642 Off
- Check Box 10643 Off
- Text Field 343
- Check Box 1010299 Off
- Check Box 1010300 Off
- Check Box 1010301 Off
- Check Box 1010302 Off
- Check Box 1010303 Off
- Check Box 1010304 Off
- Check Box 10638 Off
- Check Box 10639 Off
- Check Box 10640 Off
- Check Box 10644 Off
- Check Box 10645 Off
- Check Box 10646 Off
- Check Box 1010328 Off
- Check Box 10103012 Off
- Check Box 10103013 Off
- Check Box 10103014 Off
- Check Box 10103015 Off
- Check Box 10103016 Off
- Check Box 10648 Off
- Check Box 10649 Off
- Check Box 10650 Off
- Check Box 10651 Off
- Check Box 10652 Off
- Check Box 10653 Off
- Check Box 10654 Off
- Check Box 10755 Off
- Check Box 10756 Off
- Check Box 10757 Off
- Check Box 10758 Off
- Check Box 10759 Off
- Check Box 10760 Off
- Check Box 10761 Off
- Check Box 10762 Off
- Check Box 10763 Off
- Check Box 10764 Off
- Check Box 10765 Off
- Check Box 10766 Off
- Check Box 10767 Off
- Check Box 10768 Off
- Text Field 361
- Check Box 10103020 Off
- Check Box 10103021 Off
- Check Box 10103022 Off
- Text Field 362
- Text Field 371
- Check Box 10103018 Off
- Check Box 10103019 Off
- Check Box 10103059 Off
- Check Box 10655 Off
- Check Box 10656 Off
- Check Box 10657 Off
- Check Box 10658 Off
- Check Box 10673 Off
- Check Box 10754 Off
- Text Field 363
- Check Box 10103023 Off
- Check Box 10103024 Off
- Check Box 10103025 Off
- Check Box 10103026 Off
- Check Box 10103027 Off
- Check Box 10103028 Off
- Check Box 10103029 Off
- Check Box 10103030 Off
- Check Box 10103031 Off
- Check Box 10103032 Off
- Check Box 10103033 Off
- Check Box 10103034 Off
- Text Field 365
- Check Box 10103035 Off
- Check Box 10103036 Off
- Check Box 10103037 Off
- Text Field 366
- Check Box 10103038 Off
- Check Box 10103039 Off
- Check Box 10103040 Off
- Check Box 10103041 Off
- Check Box 10103042 Off
- Check Box 10103043 Off
- Text Field 367
- Check Box 10103044 Off
- Check Box 10103045 Off
- Check Box 10103046 Off
- Text Field 368
- Check Box 10103047 Off
- Check Box 10103048 Off
- Check Box 10103049 Off
- Text Field 369
- Check Box 10103050 Off
- Check Box 10103051 Off
- Check Box 10103052 Off
- Text Field 370
- Check Box 10103053 Off
- Check Box 10103054 Off
- Check Box 10103055 Off
- Check Box 10103056 Off
- Check Box 10103057 Off
- Check Box 10103058 Off
- Text Field 332
- Check Box 1010198 Off
- Check Box 1010199 Off
- Check Box 1010200 Off
- Check Box 1010201 Off
- Check Box 1010202 Off
- Check Box 1010203 Off
- Check Box 10485 Off
- Check Box 10486 Off
- Check Box 10487 Off
- Check Box 10488 Off
- Check Box 10489 Off
- Check Box 10490 Off
- Check Box 1010204 Off
- Check Box 1010205 Off
- Check Box 1010206 Off
- Check Box 10491 Off
- Check Box 10492 Off
- Check Box 10493 Off
- Check Box 10494 Off
- Check Box 10495 Off
- Check Box 10496 Off
- Check Box 1010207 Off
- Check Box 1010208 Off
- Check Box 1010209 Off
- Check Box 10497 Off
- Check Box 10498 Off
- Check Box 10499 Off
- Check Box 1010210 Off
- Check Box 1010211 Off
- Check Box 1010212 Off
- Check Box 10500 Off
- Check Box 10501 Off
- Check Box 10502 Off
- Check Box 10503 Off
- Check Box 10504 Off
- Check Box 10505 Off
- Check Box 1010213 Off
- Check Box 1010214 Off
- Check Box 1010215 Off
- Text Field 333
- Check Box 1010216 Off
- Check Box 1010217 Off
- Check Box 1010218 Off
- Check Box 1010219 Off
- Check Box 1010220 Off
- Check Box 1010221 Off
- Text Field 334
- Check Box 1010225 Off
- Check Box 1010226 Off
- Check Box 1010227 Off
- Text Field 3022
- Text Field 3021
- Check Box 1010228 Off
- Check Box 1010229 Off
- Check Box 1010230 Off
- Check Box 10512 Off
- Check Box 10513 Off
- Check Box 10514 Off
- Check Box 1010231 Off
- Check Box 1010232 Off
- Check Box 1010233 Off
- Check Box 1010310 Off
- Text Field 3044
- Check Box 1010234 Off
- Check Box 1010235 Off
- Check Box 1010236 Off
- Check Box 1010332 Off
- Check Box 1010333 Off
- Check Box 1010334 Off
- Check Box 1010335 Off
- Check Box 1010336 Off
- Check Box 1010337 Off
- Text Field 347
- Check Box 1010311 Off
- Check Box 1010312 Off
- Check Box 1010313 Off
- Check Box 1010314 Off
- Check Box 1010315 Off
- Check Box 1010316 Off
- Check Box 105010 Off
- Check Box 105011 Off
- Check Box 105012 Off
- Check Box 105013 Off
- Check Box 10659 Off
- Check Box 10660 Off
- Text Field 3023
- Check Box 10101014 Off
- Check Box 10101015 Off
- Check Box 10101016 Off
- Check Box 10515 Off
- Check Box 10516 Off
- Check Box 10517 Off
- Check Box 10518 Off
- Check Box 10519 Off
- Check Box 10520 Off
- Check Box 10101091 Off
- Check Box 10101092 Off
- Check Box 10101093 Off
- Check Box 10101094 Off
- Check Box 1010237 Off
- Check Box 1010238 Off
- Check Box 1010239 Off
- Check Box 1010240 Off
- Check Box 1010241 Off
- Check Box 10521 Off
- Check Box 10522 Off
- Check Box 10523 Off
- Check Box 1010242 Off
- Check Box 1010243 Off
- Check Box 1010244 Off
- Check Box 10524 Off
- Check Box 10525 Off
- Check Box 10526 Off
- Check Box 10101095 Off
- Check Box 10101096 Off
- Check Box 10101097 Off
- Check Box 10101098 Off
- Check Box 1010245 Off
- Check Box 1010246 Off
- Check Box 1010247 Off
- Check Box 1010248 Off
- Check Box 1010249 Off
- Text Field 3045
- Check Box 101010194 Off
- Check Box 101010195 Off
- Check Box 101010196 Off
- Check Box 10676 Off
- Check Box 10677 Off
- Check Box 10678 Off
- Check Box 10679 Off
- Check Box 10680 Off
- Check Box 10681 Off
- Check Box 101010197 Off
- Check Box 101010198 Off
- Check Box 101010199 Off
- Check Box 101010200 Off
- Check Box 101010201 Off
- Check Box 101010202 Off
- Check Box 101010203 Off
- Check Box 101010204 Off
- Check Box 101010205 Off
- Text Field 3046
- Check Box 101010209 Off
- Check Box 101010210 Off
- Check Box 101010211 Off
- Check Box 10682 Off
- Check Box 10683 Off
- Check Box 10684 Off
- Check Box 10685 Off
- Check Box 10686 Off
- Check Box 10687 Off
- Check Box 101010212 Off
- Check Box 101010213 Off
- Check Box 101010214 Off
- Check Box 1010102010 Off
- Check Box 1010102011 Off
- Check Box 1010102012 Off
- Text Field 3026
- Check Box 10536 Off
- Check Box 10537 Off
- Check Box 10538 Off
- Check Box 101010107 Off
- Check Box 101010108 Off
- Check Box 101010109 Off
- Text Field 3047
- Check Box 1010101010 Off
- Check Box 1010101011 Off
- Check Box 1010101012 Off
- Check Box 1010101013 Off
- Check Box 1010101023 Off
- Check Box 1010101024 Off
- Text Field 3048
- Check Box 1010101025 Off
- Check Box 1010101026 Off
- Check Box 1010101027 Off
- Check Box 1010101028 Off
- Check Box 1010101029 Off
- Check Box 1010101030 Off
- Text Field 3027
- Check Box 10539 Off
- Check Box 10540 Off
- Check Box 10541 Off
- Text Field 3028
- Check Box 101010110 Off
- Check Box 101010111 Off
- Check Box 101010112 Off
- Check Box 101010113 Off
- Check Box 101010114 Off
- Check Box 101010115 Off
- Check Box 101010215 Off
- Check Box 101010216 Off
- Check Box 101010217 Off
- Check Box 101010116 Off
- Check Box 101010117 Off
- Check Box 101010118 Off
- Text Field 3029
- Check Box 101010119 Off
- Check Box 101010120 Off
- Check Box 101010121 Off
- Check Box 101010122 Off
- Check Box 101010123 Off
- Check Box 101010124 Off
- Check Box 101010125 Off
- Text Field 3030
- Check Box 101010161 Off
- Check Box 101010162 Off
- Check Box 101010163 Off
- Check Box 101010164 Off
- Check Box 101010165 Off
- Check Box 101010166 Off
- Check Box 101010167 Off
- Text Field 3031
- Check Box 10545 Off
- Check Box 10546 Off
- Check Box 10547 Off
- Check Box 101010126 Off
- Check Box 101010127 Off
- Check Box 101010128 Off
- Check Box 101010129 Off
- Check Box 1010265 Off
- Check Box 1010266 Off
- Text Field 3032
- Check Box 10548 Off
- Check Box 10549 Off
- Check Box 10550 Off
- Check Box 101010130 Off
- Check Box 101010131 Off
- Check Box 101010132 Off
- Check Box 101010139 Off
- Check Box 101010140 Off
- Check Box 101010141 Off
- Check Box 101010142 Off
- Check Box 101010143 Off
- Check Box 101010144 Off
- Check Box 101010145 Off
- Check Box 101010146 Off
- Check Box 101010147 Off
- Check Box 101010148 Off
- Check Box 101010149 Off
- Check Box 101010150 Off
- Check Box 101010151 Off
- Check Box 101010152 Off
- Check Box 101010153 Off
- Check Box 101010154 Off
- Check Box 101010155 Off
- Check Box 101010156 Off
- Text Field 3042
- Check Box 10661 Off
- Check Box 10662 Off
- Check Box 10663 Off
- Check Box 101010184 Off
- Check Box 101010185 Off
- Check Box 101010186 Off
- Check Box 101010187 Off
- Check Box 1010326 Off
- Check Box 1010327 Off
- Check Box 10670 Off
- Check Box 10671 Off
- Check Box 10672 Off
- Check Box 101010188 Off
- Check Box 101010189 Off
- Check Box 101010190 Off
- Text Field 3033
- Check Box 10551 Off
- Check Box 10552 Off
- Check Box 10553 Off
- Text Field 3034
- Check Box 101010157 Off
- Check Box 101010158 Off
- Check Box 101010159 Off
- Text Field 3035
- Check Box 101010168 Off
- Check Box 101010169 Off
- Check Box 101010170 Off
- Text Field 3036
- Check Box 101010171 Off
- Check Box 101010172 Off
- Check Box 101010174 Off
- Check Box 101010175 Off
- Check Box 101010176 Off
- Check Box 101010177 Off
- Text Field 3056
- Check Box 101010173 Off
- Check Box 1010317 Off
- Check Box 1010318 Off
- Check Box 101010160 Off
- Check Box 1010267 Off
- Check Box 1010268 Off
- Check Box 10554 Off
- Check Box 10555 Off
- Check Box 10556 Off
- Text Field 3057
- Check Box 10557 Off
- Check Box 10558 Off
- Check Box 10559 Off
- Text Field 3058
- Check Box 10560 Off
- Check Box 10561 Off
- Check Box 10562 Off
- Check Box 10563 Off
- Check Box 10564 Off
- Check Box 10565 Off
- Check Box 10566 Off
- Check Box 10610 Off
- Check Box 10629 Off
- Check Box 10630 Off
- Check Box 10631 Off
- Check Box 10647 Off
- Check Box 10664 Off
- Check Box 10665 Off
- Check Box 10666 Off
- Text Field 3061
- Check Box 10667 Off
- Check Box 10668 Off
- Check Box 10669 Off
- Check Box 10674 Off
- Check Box 10675 Off
- Check Box 10688 Off
- Check Box 10689 Off
- Check Box 10690 Off
- Check Box 10691 Off
- Check Box 10692 Off
- Check Box 10693 Off
- Check Box 10694 Off
- Check Box 10695 Off
- Check Box 10696 Off
- Check Box 10697 Off
- Check Box 10698 Off
- Check Box 10699 Off
- Check Box 10700 Off
- Check Box 10701 Off
- Check Box 10702 Off
- Check Box 10703 Off
- Text Field 3062
- Check Box 10704 Off
- Check Box 10705 Off
- Check Box 10706 Off
- Check Box 10707 Off
- Check Box 10708 Off
- Check Box 10709 Off
- Check Box 10710 Off
- Check Box 10711 Off
- Check Box 10712 Off
- Check Box 10713 Off
- Check Box 10714 Off
- Check Box 10715 Off
- Check Box 10716 Off
- Check Box 10717 Off
- Check Box 10718 Off
- Text Field 3064
- Check Box 10719 Off
- Check Box 10720 Off
- Check Box 10721 Off
- Check Box 10722 Off
- Check Box 10723 Off
- Check Box 10724 Off
- Text Field 3067
- Check Box 107010 Off
- Check Box 107011 Off
- Check Box 107012 Off
- Check Box 107013 Off
- Check Box 107014 Off
- Check Box 107015 Off
- Check Box 10725 Off
- Check Box 10726 Off
- Check Box 10727 Off
- Check Box 10728 Off
- Check Box 10729 Off
- Check Box 10730 Off
- Check Box 10731 Off
- Check Box 10732 Off
- Check Box 10733 Off
- Text Field 3065
- Check Box 10734 Off
- Check Box 10735 Off
- Check Box 10736 Off
- Text Field 3066
- Check Box 10737 Off
- Check Box 10738 Off
- Check Box 10739 Off