Exploration-HLSL-Subject-Report-comments-2014 (1).pdf

8/17/2019 Exploration-HLSL-Subject-Report-comments-2014 (1).pdf

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May 2014 subject reports

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MATHEMATICS SL TZ1

Overall grade boundaries

Grade: 1 2 3 4 5 6 7

Mark range: 0 - 17 18 - 34 35 - 48 49 - 60 61 - 71 72 - 83 84 - 100

Time zone variants of examination papers

To protect the integrity of the examinations, increasing use is being made of time zone variants of

examination papers. By using variants of the same examination paper candidates in one part of the

world will not always be taking the same examination paper as candidates in other parts of the world.

A rigorous process is applied to ensure that the papers are comparable in terms of difficulty and

syllabus coverage, and measures are taken to guarantee that the same grading standards are applied

to candidates’ scripts for the different versions of the examination papers. For the May 2014

examination session the IB has produced time zone variants of Mathematics SL papers.

Internal assessment

Component grade boundaries

Grade: 1 2 3 4 5 6 7

Mark range: 0 - 2 3 - 5 6 - 8 9 - 11 12 - 14 15 - 17 18 - 20

The range and suitability of the work submitted

A wide range of appropriate topics with mixed quality was submitted. Candidates who had chosen

appropriate topics could attain the upper levels of each criterion. A few others, however, produced

work that was not commensurate with the level of this course.

Examples of popular themes that were received were card games and gambling, demographics,

spread of disease, athletics/sports, and video games. In addition there were many candidates who

attempted explorations on ‘common investigations’ or ‘textbook’ problems, like the Golden Ratio,

Fibonacci numbers, the Birthday paradox, Monty Hall Problem, Pascal’s Triangle. There were also

numerous modelling activities of real life situations that were very similar in style with the old portfolio

modelling tasks. Often in these cases, candidates produced work that was a summary of common

facts and or general history of the topic. This would normally demonstrate a lack of personal

engagement. Nevertheless, explorations which were based on textbook problems sometimes did also


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May 2014 subject reports Group 5, Mathematics SL TZ1

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lead to a good exploration, when the students decided to extend the investigation beyond the original

problems and/or add something of their own in the exploration. However, this was not in abundance.

Most of the explorations based on these common textbook problems or examples revolved around

superficial understanding of the concepts, repetition of methods found on the internet and did not lend

themselves to anything new, and hence, could not reach the highest levels.

The use of technology to develop regression functions in an attempt to model data was very common.

In some cases this was done effectively with suitable mathematical support. However there were

cases where the regression model was simply created and applied via technology with very little

understanding shown. It is recommended that in future, students will justify their choice of regression

model and reflect critically on their choice.

There were a few instances where candidates simply submitted explorations entirely based on old

portfolio tasks, which were specifically designed for the old assessment criteria. As a result, such

explorations would not necessarily provide the candidates with the opportunity to achieve the highest

levels.

The students generally adhered to the recommendation that the exploration be between 6 and 12

pages long. However there were many that were too long. These were often found to be self-penalizing.

Candidate performance against each criterion

Criterion A:

This criterion was addressed well by most of the students, with work being coherent and organized to

different extents. In general, they made an attempt to provide a relevant introduction, a rationale, an

explicit aim and some sort of conclusion. They also tried to explain relevant concepts and took

conciseness into consideration. However, some teachers did miss the subtle differentiation between

level 3 and 4, which is about the conciseness and completeness of student work. For instance, very

lengthy tables of data may be relegated to an appendix, with a summary in the text where theinformation is used. Similarly, pages after pages of repetitive calculations would affect the

conciseness and flow of the paper; one or two sample calculations would suffice and the rest could be

summarized in a table.

Students should be more careful with the stated aim matching what they write and present in their

work, and the conclusion they reach. If they find themselves unable to write a paper originally

intended because of space constraints or any other reasons, then it would be wise for them to adjust

the intended aim accordingly.

In addition, work that depended on a lot of secondary sources tends to have less coherence and is

more difficult to follow.

It is crucial that quoted information be correctly cited at the point in the exploration where it appears,both for the flow of the piece and for academic honesty.

Criterion B:

This criterion was appropriately dealt with in most of the explorations. There were plenty of varieties of

mathematical presentation displayed but it is essential that students are reminded that these are to be

appropriate. Most students were able to use appropriate terminology and notations in their work,

including the use of appropriate ICT tools. However, there were students who still used inappropriate

computer or calculator notation (this is not an issue if generated by the software), did not define key

terms and employed inappropriate presentations, like poorly labelled diagrams or badly scaled

graphs. Graphs copied from the Internet were inserted but without any real purpose. Graphs need a

purpose and not just included to "use multiple forms of mathematical representation". Mathematical


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formulas and theorems just taken from the Internet were often included but did not always really add

to the students’ work.

Criterion C:

This criterion proved to be the most difficult for teachers to assess or interpret and appeared to be theleast understood by both students and teachers. It seems that too many teachers stated that they

‘saw’ engagement but this was not supported by the work submitted. They simply assumed that

interest in the topic chosen by the student meant high personal engagement. High marks should not

be awarded to students who just stated how much they enjoyed the topic or who demonstrated

enthusiasm in class, unless this is seen in the exploration itself. Simply stating, "...it interests me..." is

not personal engagement.

Students who explored a common investigation/textbook problem without any personal input or

extension would not usually achieve the higher achievement levels in this criterion. Nevertheless, a

number of teachers did seem to understand this criterion and were able to transmit that information to

their students effectively. Some explorations do lend themselves more readily to high levels for

personal engagement - for example those where students do their own research and data collection.

With the more descriptive or historical topics it is not particularly easy to score highly here.

It is important to note that this criterion cannot be used to penalize late submission of work .

Criterion D:

This criterion was clearly understood well by many teachers and students and there was a wide range

of achievement here. Many students simply described the results in their explorations. They also

sometimes reflected on why they found the exploration interesting or enjoyed learning about it. Less

often did they reflect on the analytical process of exploring. Many reflections were superficial. There

were also cases where students would undertake explorations similar to the old portfolio tasks using

the same questioning technique to reflect on the process. This did not lend itself to meaningful

reflection.

Many students were under the impression that reflection could only come through in the conclusion

and hence missed out on the opportunity of demonstrating substantial evidence of critical reflection

throughout the exploration.

Higher levels were generally awarded to those students who considered further exploration,

discussed implications of results, compared strengths and weaknesses of mathematical approaches

and contemplated different perspectives.

Criterion E:

There was a wide range of achievement in this criterion from the lowest to the highest. Most students

employed relevant mathematics that was commensurate with the level of the course, since the

ma jority of topics were chosen to allow students to demonstrate at least ‘some’ mathematics.

Students could be seen using many areas of mathematics from sequences to differential equations. In

general, most teachers were able to determine whether or not the work was commensurate with the

level of the course.

Regression analysis was used extensively but not with thorough understanding demonstrated. There

were cases where the regression model was simply created and applied via technology with very little

justification of their choice of regression model.

Teachers occasionally awarded high marks for work with numerous calculations even if no clear

understanding was shown. In addition just showing the correct answer is not the same as showing

understanding; it must be demonstrated. Students who did an excellent job of explaining their

reasoning throughout their papers would gain the higher marks. A considerable number of students

chose topics where the mathematics involved was clearly beyond their understanding. This was often


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because it had been taken from other sources. Although students did reference these sources , it was

clear that many did not understand what they were doing mathematically.

The mathematics used need only be what is required to support the development of the exploration.

This could be a few small topics or even a single topic from the syllabus. It needs to be made clearer

to the students that it is better to do a few things well rather than trying to do more mathematics badly.If the mathematics used is relevant to the topic being explored, commensurate with the course, and

understood by the student, then it can achieve a high level.

Recommendations and guidance for the teaching of future candidates

Teachers need to become familiar with the assessment criteria. There are numerousexamples located in the Teacher Support Material (TSM) on the Online Curriculum Centre(OCC), and they should familiarize themselves with the goals of the exploration, and howachievement levels for the new criteria are awarded by referring to the annotated studentwork in the TSM.

One of the major issues was the lack of annotation and/or comments specific to individual

student work provided by the teachers. In many cases, where comments were provided,these tended to be paraphrased from the descriptors. Teachers are reminded that it states inthe TSM that one of their responsibilities is to assess the work accurately, annotating itappropriately to indicate where achievement levels have been awarded. This includesmarking the mathematics and identifying any errors. These comments greatly help to confirmthe level awarded by the teacher. Without supporting comments, changes are more likely.

Teachers should provide relevant background information about their courses whereappropriate.

Teachers need to follow the procedures in the guide which allows students to submit a firstdraft. This way, teachers can assess the suitability of the topic, check the generalorganization and coherence, orally test the students’ knowledge of the mathematics and mostimportantly, ensure that the work is that of the student and not just a regurgitation of Wolfram,Wikipedia and other math sites.

If students are going to type their work, they need to use an appropriate equation editor toavoid errors in notation. Students should not insert screenshots of equations and formulasfrom Wikipedia or Wolfram. This habit is a good indicator that the work is not their own. Theywould also benefit greatly from explicit instruction in the use of those tools.

Teachers should discourage students from choosing common or textbook topics without aclear plan on how to make them into a proper exploration (with enough relevant mathematicsin it) since these tended to be research based with very little personalization or creativitydemonstrated. Yet teachers should not predefine certain topics for their students or limit themto a certain area of mathematics.

Teachers need to emphasize the importance of clear referencing and proper citation instudent work. Many students provided a bibliography or work cited page at the end of theirdocuments without identifying how these resources have been used in the body of their work.Students should be guided to cite all resources used in the body of their work including all

data and images from secondary sources.

Teachers must annotate and write comments on student work. Those schools where teachersdid this were more likely to have scores confirmed, as would be expected; the reasoningbehind the scores awarded was readily apparent.

Teachers could issue practice explorations to hone/practice certain specific skills.

Students should be reminded of the guidelines that the exploration should be between 6 and12 pages long.

Schools should be strongly discouraged from mandating a particular type of exploration.Rather students should be free to explore an area of their choice.

Further comments

There were instances of potential plagiarism, with many students using sources such as


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Wolfram or Wikipedia to copy content, formulas or ideas.

The mathematical content was often lacking even though the exploration itself was wellwritten and scored well.

The general feeling after seeing the variety of explorations is that this new IA has provided thestudents with a great opportunity to explore what they wished, and given them the opportunityto appreciate mathematics in their own way.

The exemplar materials and the frequently asked questions in the TSM have been/will beupdated after the first live session. Teachers should make sure that they read thesedocuments carefully, along with the updated guidance on applying the criteria.

Paper one


Grade: 1 2 3 4 5 6 7

Mark range: 0 - 17 18 - 34 35 - 46 47 - 56 57 - 65 66 - 75 76 - 90

General comments

The areas of the programme and examination which appeared difficult forthe candidates

Integration, definite and indefinite

Probability, combined and conditional

Application of discriminant Direction vectors of lines

Infinite geometric series in a generalized context

The areas of the programme and examination in which candidatesappeared well prepared

Quadratic functions

Arithmetic sequences and series

Logarithms

Derivatives of polynomials

Intersection of lines in vector form

Probability on a tree diagram

The strengths and weaknesses of the candidates in the treatment ofindividual questions

Question 1: the quadratic function and its graph

Candidates showed great familiarity with the quadratic function and the vertex. A common error was

to give a negative value for h . In solving for a , many found the substitution and subsequent algebra to

be straightforward. Occasionally a candidate would expand the quadratic before substituting the given

values, which led to a more burdensome expression.


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November 2014 subject reports Group 5, Mathematics HL

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Internal assessment


Grade: 1 2 3 4 5 6 7

Mark range: 0 - 2 3 - 5 6 - 8 9 - 11 12 - 14 15 - 16 17 - 20


There was a wide range of interesting topics and some schools are to be commended on the

guidance given to students. Tasks included modelling real life situations and others provideda synopsis of mathematics that was found during the research process. Among the latter,

common explorations included the Birthday Problem, the Buffon needle, game theory, solving

the Rubik’s cube and probabilities in a poker game. Although all these were suitable some

topics did not allow students to show personal engagement apart from understanding the

topic. Some explorations were also far too long, and sometimes too complex for peers to

understand and also for the author to demonstrate good understanding of the mathematics

involved.

It was also noted that some explorations were written in very small font to make them look

concise, whereas others were very short with large diagrams, written in larger font and

double-spaced.


Criterion A

In general students performed well in this criterion; however some explorations were far too

long and therefore not concise. In some cases students had a rationale that was made up

and not genuine. Some students did not write a clear aim and this often led to an incoherent

piece of work that was not complete since they could not write a conclusion to put it all

together.

Criterion B

Language, notation and terminology were generally correctly used. Students also used

technology effectively and included diagrams, graphs and tables in the appropriate places,

along the work. A single notational error can be condoned but repeated use throughout the

exploration should be penalized. Marks were lost when students did a modelling exploration

and did not define key terms.


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Criterion C

More candidates are aware of the requirements for this criterion, and some will give contrived

reasons for choosing the topic thinking that this might give an extra mark. In many cases this

rationale was not supported in the rest of the exploration. A number of explorations were

mere reproductions of papers found on the Internet or common advanced textbook problems.

In this case students would receive some marks for mastering new techniques but it is difficult

to justify top achievement levels. Exploration in a mathematical topic occurs when candidates

use something that has already been explained or systematized as a tool to approaching a

new question that they themselves have come up with. For example, candidates are allowed

to recreate a Koch snowflake as long as they generate their own fractal. Some teachers are

still under the impression that Personal Engagement is a measure of effort so that the choice

of achievement levels becomes subjective.

Criterion D

A number of students did not offer any meaningful or critical reflection but wrote a conclusion

summarizing results. Teachers often marked high on this criterion, which then led to

achievement levels being marked down by the moderator. Students and teachers need to

understand that for high achievement levels reflection needs to take place throughout the

exploration, through candidates isolating themselves from the problem, to see it from another

point of view and to analyse its limits, the connections it may have to other similar problems,

other implications that might arise, aspects that could have been considered but were not,

applications to other real world problems or contexts, discussing the techniques being used,

the validity of the results obtained etc.… Once more, students who reproduced commontextbook problems presented work that contained only superficial reflection.

Criterion E

Mathematical content was varied and while some explorations contained extensive

mathematics others were very descriptive. Most explorations were also in the form of a mini

research paper with mathematical content being reproduced, sometimes without

demonstrating good understanding. In some cases students demonstrated an understanding

of the technique being used but no significant understanding as to why the particular

technique works. Some modelling explorations incorporated fitting data into a model, without

any justification for choosing that model or development of the mathematical model used.Students need to be well guided when choosing their topics. It is sometimes easier to

achieve good levels using simple HL mathematics content than going beyond the syllabus.

Recommendations and guidance for the teaching of futurecandidates

The exploration needs to be introduced early on and referred to frequently with references to

appropriate topics as they arise during the learning experience. Teachers must dedicate the

number of hours specified in the programme to guide the candidates throughout the process.

It is important that teachers highlight the importance of proper referencing and citations.


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Teachers are encouraged to read the new publications on the OCC; i.e., Academic Honesty

in the IB educational context and Effective citing and referencing.

It is recommended that teachers provide candidates with mathematical stimuli in various

forms, including but not limited to texts, web pages, specialized bibliographies, movies, video

clips, photographs, paintings, graphic design, games of chance, board games, experiments,

magic tricks, etc… The investigations that were part of the former internal assessment

component may also serve as a source of ideas for candidates to develop their explorations

creatively and constructively.

Students need to understand the 5 criteria thoroughly before starting to develop their own

exploration. They need to be guided to choose a topic wisely; one that incorporates

Mathematics that allows them to demonstrate full understanding, and which is commensurate

with the course. The topic should allow them to demonstrate personal engagement by

possibly giving them the avenue to be original and creative. The topic should also be focused

and the aim achievable within the set number of pages (6 to 12).

Teachers should refrain from making anecdotal comments about student commitment to the

exploration process, as this has no bearing on criterion C. Personal engagement should be

evident in the students own work. All student work should contain evidence of marking with

errors being pointed out; this makes it easier for the moderator to confirm the teacher’s

marks.

Further comments

Although it is not stated that teachers need to supply information regarding material before

the exploration process was started, it is highly recommended that this background

information be given as it helps the moderator put the development of the exploration into

perspective.

It might be useful for candidates to practice assessing explorations that are available in the

TSM. This gives them an idea of what is expected of them in a project of this nature and it

will ensure that candidates understand all 5 criteria. Class time might even be spent

developing a group exploration with the help of the teacher as a means of understanding the

methodology involved.

Having said all this the moderation of Internal Assessment with the wide variety of creative

and interesting explorations continues to be an enjoyable task for moderators.


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November 2014 subject reports

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MATHEMATICS SL

Overall grade boundaries

Standard level

Grade: 1 2 3 4 5 6 7

Mark range: 0 - 17 18 - 36 37 - 49 50 - 61 62 - 73 74 - 85 86 - 100

Internal assessment


Grade: 1 2 3 4 5 6 7

Mark range: 0 - 2 3 - 5 6 - 8 9 - 11 12 - 14 15 - 17 18 - 20


A wide range of appropriate and engaging topics with mixed quality was submitted, leading to

a range of marks from 1 to 20. Explorations that were suitable tended to have more original

aims that had clear personal relevance and foci. Many students still submit explorations with

research questions similar to textbook problems, or they were not focused enough to be dealt

with adequately within 10 to 12 pages. For instance, there were still many attempts on topics

like the Golden Ratio, Monty Hall Problem, Pascal’s Triangle, Handshake Problem and KochSnowflake. These candidates generally produced work that was a summary of common facts

and/or a general history of the topic. There were also many candidates who produced work

that read like a common textbook example or explanation. In the Koch Snowflake, for

example, student work mirrored the old IB Task, showing no personalization or extension. In

both cases candidates tended to not score well.

The use of technology to develop regression functions in an attempt to model data was very

common. Some schools included samples that were all modelling tasks and generally

following the old portfolio style. Although there is nothing wrong with these tasks, per se, it

would be disappointing if students felt limited to these or were specifically directed to do these

by their teacher. In some cases these tasks were done effectively with suitable mathematical

support. However there were cases where the regression model was simply created and


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November 2014 subject reports Group 5, Mathematics SL

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applied via technology with very little understanding shown. It is hoped that students will be

able to justify their choice of regression model and be able to reflect critically on their choice.

The students generally adhered to the suggestion that the exploration be between 6 and 12

pages long. However there were many that were very long. These were often found to be

self-penalising.


Criterion A

Most students scored well on this criterion. Most of the work was well organized and

systematically presented. They presented some sort of introduction, attempted an aim, made

a conscious effort to organize the work and provided a conclusion at the end. Students whodid poorly in this criterion usually did not have a focused aim and thus could not present a

coherent development for the work. Also some students provided particularly contrived

rationales or simply stated that they found the topic ‘interesting’, which is insufficient for a

rationale. There were quite a few candidates that provided page after page of repetitive

calculations that hurt the conciseness and flow of the paper. Students should provide only

one or two sample calculations in the body and all other similar calculations should be

summarized in a table. Coherence was generally good but at times the work flowed poorly,

with missing explanations and poor linkage between subsections.

Criterion B

Presentation was generally done well. Most students had made a conscious effort to present

their work appropriately and with a variety of mathematical presentations. They used an

equation editor or other mathematical software to enter proper mathematical expressions.

The use of appropriate diagrams with clear labelling was often a problem. It may be that

tables and graphs are more easily generated by computer while diagrams take more effort.

Many graphs and diagrams were cut and pasted from Internet sources and often these were

without any real purpose. Graphs need a purpose and not just included to "use multiple forms

of mathematical representation". Mathematical formulas and theorems just taken from the

Internet were often included but did not always really add to the students’ work.

Criterion C

Many students made an effort to make the work their own by doing their own research,

collecting their own data and providing convincing personal rationales for choosing the topics.

On the other hand, there were quite a few students who did not make the exploration their

own and only did descriptive work. Students who used textbook problems and basically cut-

and-pasted from resources in the public domain often did poorly in this criterion. Similarly,

there were still a good number of teachers awarding high marks for candidates who simply

stated how much they enjoyed the topic or for the enthusiasm they demonstrated even

though there was no evidence in the work of good personal engagement. It is important to

note that this criterion cannot be used to penalise late submission of work.


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Criterion D

Many students could produce some reflections and attempted to make these meaningful.

They would at least consider the relevance of the mathematics they were using or

investigating. Unfortunately, only a few were capable of producing critical and substantial

reflections throughout their explorations. Nevertheless, this did not stop some teachers from

awarding the top level for student work which simply summarized the results.

Criterion E

There was a wide variety of mathematics used in the explorations and a wide range of levels

of understanding. The majority of the students were able to produce explorations that are

commensurate with the mathematics SL syllabus and relevant to the tasks. However often

they were not able to show that they understood the concepts well. For instance, the

mathematics appeared to be regurgitated from textbooks or the internet and not really applied

to the question in hand. Applying it to the student’s own work needs to be encouraged. Only a

few challenged themselves by going beyond the mathematics SL syllabus. The success rates

of these attempts varied.

Students and teachers should be aware that just showing the correct answer is not the same

as showing understanding, it must be demonstrated.

Recommendations and guidance for the teaching of futurecandidates

Teachers should ensure that they are familiar with all the relevant information in the guide and

the Teacher Support Material (TSM), especially the teacher responsibilities in the TSM. In

particular, the following points should be noted.

Teachers should go over some of the exemplars in the TSM and mark them with their

students so that the students will have a better idea on the expectations of each

criterion.

Teachers should encourage originality of work, particularly the idea of “making the

work their own”. They should stress the idea of applying the mathematics that

students have discovered to their own work.

Students should be guided to cite all resources used in the body of the work. Theseinclude images and data that are used. A bibliography is not sufficient because it

does not inform the reader how and where these resources have been used in the

exploration.

Students should be guided to produce explorations that have clear and focused aims,

with evidence supporting their personal engagement.

Teachers need to follow the suggested procedures in the TSM which allows students

to submit a first draft. This way, teachers can assess the suitability of the topic, check

the general organization and coherence, orally test the students’ knowledge of the

mathematics and most importantly, ensure that the work is that of the student and not

just a regurgitation of Wolfram, Wikipedia and other sites.

Schools should be strongly discouraged from mandating a particular type ofexploration. Rather students should be free to explore an area, where this leads to a


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decent exploration, of their choice.

It is extremely helpful to the moderation process if teachers annotate and comment

on the student work as well as on the form 5/EXCS. Teachers must indicate that they

have checked mathematical processes, and noted if they are correct or not.

Where there is more than one teacher, it is essential that internal standardization

between teachers takes place.

Standard level paper one


Grade: 1 2 3 4 5 6 7

Mark range: 0 - 17 18 - 35 36 - 46 47 - 56 57 - 66 67 - 76 77 - 90

The areas of the programme and examination which appeareddifficult for the candidates

Integration using substitution and/or inspection

Expected value of a fair game

Sketching functions, including important features of the graph

Trigonometric ratios of obtuse angles Conditional and binomial probability

Applying properties of logarithms

Vectors and vector equation of a line

The areas of the programme and examination in which candidatesappeared well prepared

Applying formulas for terms and sums of an arithmetic sequence

Sum of a probability distribution

Integration and differentiation of polynomial functions

Solving quadratic equations Simple probability and tree diagrams

The strengths and weaknesses of the candidates in the treatmentof individual questions

Question 1: quadratics

Parts (a) and (b) of this question were answered quite well by nearly all candidates, with only

a few factoring errors in part (b). In part (c), although most candidates were familiar with the

general parabolic shape of the graph, many placed the vertex at the y -intercept (0, -6), andvery few candidates considered the endpoints of the function with the given domain.

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