Mathematics Syllabus SHS 1-3
-
Upload
mensurado-armel -
Category
Documents
-
view
235 -
download
0
Transcript of Mathematics Syllabus SHS 1-3
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 1/66
R E P U B L I C O F G H A N A
MI N I S T R Y O F E D U C A T I O N , S C I E N C E A N D S P O R T S
TEACHING SYLLABUS FOR MATHEMATICS
( SENIOR HIGH SCHOOL 1 – 3 )
Enquiries and comments on this syllabus should be addressed to:
The DirectorCurriculum Research and Development Division (CRDD)
P. O. Box GP 2739,Accra.Ghana.
September, 2007
Republic of Ghana
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 2/66
ii
TEACHING SYLLABUS FOR MATHEMATICS(SENIOR HIGH SCHOOL)
RATIONALE FOR TEACHING MATHEMATICS
Development in almost all areas of life is based on effective knowledge of science and mathematics. There simply cannot be any meaningful
development in virtually any area of life without knowledge of science and mathematics. It is for this reason that the education systems of countriesthat are concerned about their development put great deal of emphases on the study of mathematics. The main rationale for the mathematics syllabus
is focused on attaining one crucial goal: to enable all Ghanaian young persons to acquire the mathematical skills, insights, attitudes and values that
they will need to be successful in their chosen careers and daily lives. The new syllabus is based on the premises that all students can learn
mathematics and that all need to learn mathematics. The syllabus is therefore, designed to meet expected standards of mathematics in many parts of the world. Mathematics at the Senior High school (SHS) in Ghana builds on the knowledge and competencies developed at the Junior High School
level. The student is expected at the SHS level to develop the required mathematical competence to be able to use his/her knowledge in solving real
life problems and secondly, be well equipped to enter into further study and associated vocations in mathematics, science, commerce, industry and a
variety of other professions.
GENERAL AIMS
To meet the demands expressed in the rationale, the SHS Core Mathematics syllabus is designed to help the student to:
1. Develop the skills of selecting and applying criteria for classification and generalization.
2. Communicate effectively using mathematical terms, symbols and explanations through logical reasoning.
3. Use mathematics in daily life by recognizing and applying appropriate mathematical problem-solving strategies.
4. Understand the process of measurement and use appropriate measuring instruments.
5. Develop the ability and willingness to perform investigations using various mathematical ideas and operations.
6. Work co-operatively with other students in carrying out activities and projects in mathematics.
7. Develop the values and personal qualities of diligence, perseverance, confidence, patriotism and tolerance through the study of
mathematics8. Use the calculator and the computer for problem solving and investigations of real life situations
9. Develop interest in studying mathematics to a higher level in preparation for professions and careers in science, technology,
commerce, industry and a variety of work areas.10. Appreciate the connection among ideas within the subject itself and in other disciplines, especially Science, Technology, Economics
and Commerce
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 3/66
iii
GENERAL OBJECTIVES
By the end of the instructional period students will be able to:
1. Develop computational skills by using suitable methods to perform calculations;
2. Recall, apply and interpret mathematical knowledge in the context of everyday situations;3. Develop the ability to translate word problems (story problems) into mathematical language and solve them with related mathematical
knowledge;4. Organize, interpret and present information accurately in written, graphical and diagrammatic forms;
5. Use mathematical and other instruments to measure and construct figures to an acceptable degree of accuracy;6. Develop precise, logical and abstract thinking;
7. Analyze a problem, select a suitable strategy and apply an appropriate technique to obtain it’s solution;
8. Estimate, approximate and work to degrees of accuracy appropriate to the context;
9. Organize and use spatial relationships in two or three dimensions, particularly in solving problems;
10. Respond orally to questions about mathematics, discuss mathematics ideas and carry out mental computations;
11. Carry out practical and investigational works and undertake extended pieces of work;
12. Use the calculator to enhance understanding of numerical computation and solve real life problems
GENERAL OBJECTIVES
The student will:
13. Work co-operatively with other students and develop interest in mathematics.
14. Read and write numbers.
15. Use appropriate strategies to perform number operations.16. Recognize and use patterns, relationships and sequences and make generalizations.
17. Recognize and use functions, formula, equations and inequalities.18. Identify and use arbitrary and standard units of measure.
19. Make and use graphical representations of equations and inequalities.20. Use the appropriate unit to estimate and measure various quantities.
21. Relate solids and plane shapes and appreciate them in the environment.22. Collect, analyze and interpret data and find probability of events.
23. Use the calculator to enhance understanding of numerical computation and solve real life problems.24. Manipulate learning material to enhance understanding of concepts and skills.
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 4/66
iv
SCOPE OF SYLLABUS
This syllabus is based on the notion that an appropriate mathematics curriculum results from a series of critical decisions about three
inseparable linked components: content, instruction and assessment. Consequently, the syllabus is designed to put great deal of emphases onthe development and use of basic mathematical knowledge and skills. The major areas of content covered in all the Senior High School classes
are as follows:
1. Numbers and Numeration.2. Plane Geometry
3. Mensuration4. Algebra
5. Statistics and Probability
6. Trigonometry
7. Vectors and Transformation in a Plane
* Problem solving and application (mathematical processes).
“Numbers and Numeration” covers reading and writing numerals in base two through twelve and the four basic operations on them as well as
ratio, proportion, and parentages. Fractions, integers and rational and irrational numbers and four operations on them are treated extensively.
Plane geometry covers angles of a polygon, Pythagoras’ theorem and its application and circle theorem including tangents. Mensuration covers perimeters and areas of plane shapes, surface areas and volumes of solid shapes. In addition, the earth as a sphere is also treated under
mensuration. “Algebra” – Algebra is a symbolic language used to express mathematical relationships. Students need to understand how
quantities are related to one another, and how algebra can be used to concisely express and analyze those relationships. “Statistics and
Probability” – are important interrelated areas of mathematics. Each provides students with powerful mathematical perspectives on everyday
phenomena and with important examples of how mathematics is used in the modern world. Statistics and probability should involve students in
collecting, organizing, representing and interpreting data gathered from various sources, as well as understanding the fundamental concepts of
probability so that they can apply them in everyday life. Trigonometry covers the trigonometry ratios and their applications to angles of elevation and depression. Drawing and interpretation of graphs of trigonometric functions is also covered under trigonometry.
Topics treated under vectors include, representation, operations on vectors, equal and parallel vectors as well as magnitude of vectors and bearing. Transformation deals with rigid motion and enlargement including scale drawing and its application.
“Problem solving and application” has not been made a topic by itself in the syllabus since nearly all topics include solving word problems as
activities. It is hoped that teachers and textbook developers will incorporate appropriate problems that will require mathematical thinking rather than mere recall and use of standard algorithms. Other aspects of the syllabus should provide opportunity for the students to work co-
operatively in small groups to carry out activities and projects which may require out-of-school time. The level of difficulty of the content of the syllabus has been designed to be within the knowledge and ability range of Senior High School students.
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 5/66
v
STRUCTURE AND ORGANIZATION OF THE SYLLABUS
The syllabus is structured to cover the four years of Senior High School. Each year’s work has been divided into units. SHS 1 has 13 units; S HS 2has 10 units, SHS 3 has 6 units while SHS 4 has 3 units of work. The unit topics for each year have been arranged in a suggested teaching sequence.
No attempt has been made to break the year’s work into terms. This is deliberate because it is difficult to predict, with any degree of certainty, therate of progress of students in each year. Moreover, the syllabus developers wish to discourage teachers from forcing the instructional pace but
would rather advise teachers to ensure that students progressively acquire a good understanding and application of the material specified for eachyear’s class work. It is hoped that no topics will be glossed over for lack of time because it is not desirable to create gaps in students’ knowledge.
The unit topics for the four years' course are indicated on the table below.
SHS 1 2 3 4
UNITS1
2
3
4
5
6
7
8
9
10
11
12
13
Sets and Operations on set
Real number system
Algebraic expressions
Number Bases
Plane Geometry
Linear equations and inequalities
Relations and Functions
Vectors in a plane
Simultaneous linear equation
Rigid motion I
Statistics I
Ratio and Rates
Percentages I
Modular arithmetic
Indices and logarithms
Surds
Percentages II
Variation
Quadratic functions and equations
Plane geometry II (Circles)
Mensuration I
Trigonometry I
Probability
-
-
-
Sequences and Series
Bearings
Constructions
Statistics II
Interpretation of linear and quadratic
graphs
Mensuration II
-
-
-
-
-
-
-
Logical reasoning
Percentage III
Rigid motion IIand Enlargement
Trigonometry II
-
-
-
-
-
-
-
-
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 6/66
vi
TIME ALLOCATION
Mathematics is allocated eight periods a week, each period consisting of thirty (40) minutes. The eight periods should be divided into four double
periods, each of one-hour twenty minutes duration for each day of the week. Suggested time allocation for Core Mathematics and other subjects/items for the four years are as follows:
Year 1 Year 2 Year 3 Year 4
Ø Core Mathematics 8 6 4 3
Ø Physical Education 3 2 2 2
Ø Library Work (Reading and Research) 3 2 2 2
Ø SBA Project 3 2 2 2
Ø Worship 2 2 2 2
Ø Free Period 1 1 1 2
SUGGESTIONS FOR TEACHING THE SYLLABUS
General Objectives
General Objectives for this syllabus have been listed on page iii of the syllabus. The general objectives flow from the general aims of mathematics
teaching listed on the first page of this syllabus. The general objectives form the basis for the selection and organization of the units and their topics.
Read the general objectives very carefully before you start teaching. After teaching all the units for the year, go back and read the general aims and
general objectives again to be sure you have covered both of them adequately in the course of your teaching.
Years and Units
The syllabus has been planned on the basis of Years and Units. Each year's work is covered in a number of units that have been sequentially
arranged to meet the teaching and learning needs of teachers and students.
Syllabus Structure
The syllabus is structured in five columns: Units, Specific Objectives, Content, Teaching and Learning Activities and Evaluation. A description of the contents of each column is as follows:
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 7/66
vii
Column 1 - Units: The units in Column 1 are the major topics for the year. The numbering of the units is different in mathematics from thenumbering adopted in other syllabuses. The unit numbers consist of two digits. The first digit shows the year or class while the second digit shows
the sequential number of the unit. A unit number like 1.2 is interpreted as unit 2 of SHS1. Similarly, a unit number like 3.5 means unit 5 of SHS3.The order in which the units are arranged is to guide you plan your work. However, if you find at some point that teaching and learning in your class
will be more effective if you branched to another unit before coming back to the unit in the sequence, you are encouraged to do so.
Column 2 - Specific Objectives: Column 2 shows the Specific Objectives for each unit. The specific objectives begin with numbers such as1.2.5 or 3.4.1. These numbers are referred to as "Syllabus Reference Numbers". The first digit in the syllabus reference number refers to the
year/class; the second digit refers to the unit, while the third refer to the rank order of the specific objective. For instance 1.2.5 means Year 1 or SHS1, Unit 2 (of SHS1) and Specific Objective 5. In other words 1.2.5 refers to Specific Objective 5 of Unit 2 of SHS1. Using syllabus reference
numbers provides an easy way for communication among teachers and other educators. It further provides an easy way for selecting objectives for test construction. For instance, Unit 4 of SHS3 may have three specific objectives 3.4.1 - 3.4.3. A teacher may want to base his/her test
items/questions on objectives 3.4.2 and 3.4.3 and not use the other first objective. The teacher would hence be able to use the syllabus reference
numbers to sample objectives within units and within the year to be able to develop a test that accurately reflects the importance of the various skills
taught in class.
You will note also that specific objectives have been stated in terms of the students i.e. what the students will be able to do during and after
instruction and learning in the unit. Each specific objective hence starts with the following "The student will be able to", this in effect, means that
you have to address the learning problems of each individual student. It means individualizing your instruction as much as possible such that the
majority of students will be able to master the objectives of each unit of the syllabus.
Column 3 - Content: The "content" in the third column of the syllabus shows the mathematical concepts, and operations required in the teaching
of the specific objectives. In some cases, the content presented is quite exhaustive. In some other cases, you could add some more information
based upon your own training and based also on current knowledge and information.
Column 4 - Teaching/Learning Activities (T/LA): T/LA activities that will ensure maximum student participation in the lessons are presented inColumn 4. The General Aims of the subject can only be most effectively achieved when teachers create learning situations and provide guidedopportunities for students to acquire as much knowledge and understanding of mathematics as possible through their own activities. Students’
questions are as important as teacher's questions. There are times when the teacher must show, demonstrate, and explain. But the major part of astudents’ learning experience should consist of opportunities to explore various mathematical situations in their environment to enable them make
their own observations and discoveries and record them. Avoid rote learning and drill-oriented methods and rather emphasize participatory teachingand learning in your lessons. You are encouraged to re-order the suggested teaching/learning activities and also add to them where necessary in order
to achieve optimum students learning. Emphasize the cognitive, affective and psychomotor domains of knowledge in your instructional systemwherever appropriate.
A suggestion that will help your students acquire the capacity for analytical thinking and the capacity for applying their knowledge to problems and
issues is to begin each lesson with a practical and interesting problem. Select a practical mathematical problem for each lesson. The selection must be made such that students can use knowledge gained in the previous lesson and other types of information not specifically taught in class.
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 8/66
viii
Column 5 - Evaluation: Suggestions and exercises for evaluating the lessons of each unit are indicated in Column 5. Evaluation exercises can be
in the form of oral questions, quizzes, class assignments, essays, project work, etc. Try to ask questions and set tasks and assignments, etc. that willchallenge students to apply their knowledge to issues and problems as we have already said above, and that will engage them in developing solutions,
and in developing observational and investigative skills as a result of having undergone instruction in this subject. The suggested evaluation tasks arenot exhaustive. You are encouraged to develop other creative evaluation tasks to ensure that students have mastered the instruction and behaviours
implied in the specific objectives of each unit.
Lastly, bear in mind that the syllabus cannot be taken as a substitute for lesson plans. It is necessary that you develop a scheme of work and lesson plans for teaching the units of this syllabus.
DEFINITION OF PROFILE DIMENSIONS
The concept of profile dimensions was made central to the syllabuses developed from 1998 onwards. A 'dimension' is a psychological unit for
describing a particular learning behaviour. More than one dimension constitutes a profile of dimensions. A specific objective may be stated with an
action verb as follows: The student will be able to describe….. etc. Being able to "describe" something after the instruction has been completed
means that the student has acquired "knowledge". Being able to explain, summarize, give examples, etc. means that the students has understood the
lesson taught.
Similarly, being able to develop, plan, solve problems, construct, etc. means that the students can "apply" the knowledge acquired in some new
context. Each of the specific objectives in this syllabus contains an "action verb" that describes the behaviour the students will be able to demonstrate
after the instruction. "Knowledge", "Application", etc. are dimensions that should be the prime focus of teaching and learning in schools. It has been
realized unfortunately that schools still teach the low ability thinking skills of knowledge and understanding and ignore the higher ability thinking
skills. Instruction in most cases has tended to stress knowledge acquisition to the detriment of the higher ability behaviours such as application,
analysis, etc. The persistence of this situation in the school system means that students will only do well on recall items and questions and perform
poorly on questions that require higher ability thinking skills such as application of mathematical principles and problem solving. For there to be anychange in the quality of people who go through the school system, students should be encouraged to apply their knowledge, develop analytical
thinking skills, develop plans, generate new and creative ideas and solutions, and use their knowledge in a variety of ways to solve mathematical problems while stil l in school. Each action verb indicates the underlying profile dimension of each particular specific objective. Read each objective
carefully to know the profile dimension toward which you have to teach.
In Mathematics, the two profile dimensions that have been specified for teaching, learning and testing at the SHS level are:
Knowledge and Understanding 30% Application of knowledge 70%
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 9/66
ix
Each of the dimensions has been given a percentage weight that should be reflected in teaching, learning and testing. The weights indicated on theright of the dimensions, show the relative emphasis that the teacher should give in the teaching, learning and testing processes at Senior High School.
Explanation and key words involved in each of the profile dimensions are as follows:
Knowledge and Understanding (KU)
Knowledge the ability to, read, count, identify, define, describe, list, name, locate, match, state principles, facts and concepts. Knowledge
is simply the ability to remember or recall material already learned and constitutes the lowest level of learning.
Understanding the ability to explain, distinguish, factorize, calculate, expand, measure, predict, give examples, generalize, estimate or predictconsequences based upon a trend. Understanding is generally the ability to grasp the meaning of some material that may be
verbal, pictorial, or symbolic.
Application of Knowledge(AK)
The ability to use knowledge or apply knowledge, as implied in this syllabus, has a number of learning/behaviour levels. These levels
include application, analysis, synthesis, and evaluation. These may be considered and taught separately paying attention to reflect each of them
equally in your teaching. The dimension "Application of Knowledge" is a summary dimension for all four learning levels.
Details of each of the four sub-levels are as follows:
Application the ability to apply rules, methods, principles, theories, etc. to concrete situations that are new and unfamiliar. It also involves
the ability to produce, solve, plan, demonstrate, discover, etc.
Analysis the ability to break down material into its component parts; to differentiate, compare, distinguish, outline, separate, identify
significant points, etc.; ability to recognize unstated assumptions and logical fallacies; ability to recognize inferences fromfacts, etc.
Synthesis the ability to put parts together to form a new whole. It involves the ability to combine, compile, compose, devise, plan,
revise, design, organize, create, generate new ideas and solutions, etc.
Evaluation the ability to appraise, compare features of different things and make comments or judgments, compare, contrast criticize, justify, support, discuss, conclude, make recommendations, etc. Evaluation refers to the ability to judge the worth or value of
some material based on some criteria.
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 10/66
x
FORM OF ASSESSMENT
It is important that both instruction and assessment be based on the specified profile dimensions. In developing assessment procedures, first selectspecific objectives in such a way that you will be able to assess a representative sample of the syllabus objectives. Each specific objective in the
syllabus is considered a criterion to be mastered by the students. When you develop a test that consists of items and questions that are based on arepresentative sample of the specific objectives taught, the test is referred to as a “Criterion-Referenced Test”. It is not possible to test all specific
objectives taught in the term or in the year. The assessment procedure you use i.e. class test, homework, projects etc. must be developed in such away that it will consist of a sample of the important objectives taught over the specified period.
End-of-Term Examination
The end-of-term examination is a summative assessment system and should consist of a sample of the knowledge and skills students have acquired inthe term. The end-of-term test for Term 3 should be composed of items/questions based on the specific objectives studied over the three terms, using
a different weighting system such as to reflect the importance of the work done in each term in appropriate proportions. For example, a teacher may
build an end of Term 3 test in such a way that it would consist of the 20% of the objectives studied in Term 1, 20% of the objectives studied in Term
2, and 60% of the objectives studied in Term 3.
The diagram below shows a recommended examination structure for end of term examination in Senior High School following the structure of
WAEC examination papers. The structure consists of two examination papers. Paper 1 is the objective test paper essentially testing knowledge and
understanding. The paper may also contain some items that require application of knowledge. Paper 2 will consist of questions that essentially test
“application of knowledge”. The application dimension should be tested using questions that call for reasoning. Paper 2 could also contain somequestions that require understanding of mathematical principles etc. The SBA should be based on both dimensions. The distribution of marks for
Paper 1, Paper 2 and the SBA should be in line with the weights of the profile dimensions as shown in the last column of the table below.
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 11/66
xi
Distribution of Examination Paper Weights and Marks
Dimensions Paper 1 Paper 2 SBA Total Marks Total Marks
scaled to 100
Knowledge and
Understanding
30 20 10 60 30
Application of knowledge
10 80 50 140 70
Total Marks 40 100 60 200
% Contribution of
Examination Papers
20 50 30 100
Paper 1 or Section A, will be marked out of 40, while Paper 2, the more intellectually demanding paper, will be marked out of 100. The mark
distribution for Paper 2 or Section B, will be 20 marks for “knowledge and understanding” and 80 marks for “application of knowledge”. SBA will
be marked out of 60. The last row shows the percentage contribution of the marks from Paper 1/Section A, Paper 2/Section B, and the School BasedAssessment on total performance in the subject tested.
For testing in schools, the two examination sections could be separate where possible. Where this is not possible, the items/questions for Papers 1 and
2 could be in the same examination paper as two sections; Sections A and B as shown in the example above. Paper 1 or Section A will be an
objective-type paper/section testing knowledge and understanding, while Paper 2 or Section B will consist of application questions with a few
questions on knowledge and understanding.
Combining SBA marks and End-of-Term Examination Marks
The new SBA system is important for raising students’ school performance. For this reason, the 60 marks for the SBA will be scaled to 50. The total
marks for the end of term test will also be scaled to 50 before adding the SBA marks and end-of-term examination marks to determine students’ endof term results. The SBA and the end-of-term test marks will hence be combined in equal proportions of 50:50. The equal proportions will affect onlyassessment in the school system. It will not affect the SBA mark proportion of 30% used by WAEC for determining examination results at the BECE.
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 12/66
xii
GUIDELINES FOR SCHOOL BASED ASSESSMENT
A new School Based Assessment system (SBA), formally referred to as Continuous Assessment, will be introduced into the school system from
September 2008. SBA is a very effective system for teaching and learning if carried out properly. The new SBA system is designed to provideschools with an internal assessment system that will help schools to achieve the following purposes:
o Standardize the practice of internal school-based assessment in all schools in the country
o Provide reduced assessment tasks for each of the primary school subjectso Provide teachers with guidelines for constructing assessment items/questions and other assessment tasks
o Introduce standards of achievement in each subject and in each class of the school system
o Provide guidance in marking and grading of test items/questions and other assessment tasks
o Introduce a system of moderation that will ensure accuracy and reliabili ty of teachers’ marks
o Provide teachers with advice on how to conduct remedial instruction on difficult areas of the syllabus to improve students performance
The new SBA system will consist of 12 assessments a year instead of the 33 assessments in the previous continuous assessment system. This will
mean a reduction by 64% of the work load compared to the previous continuous assessment system. The 12 assessments are labeled as Task 1, Task
2, Task 3 and Task 4. Task 1-4 will be administered in Term 1; Tasks 5-8 will be administered in Term 2, and Tasks 9-12 administered in Term 3.
Task 1 will be administered as an individual test coming at the end of the first month of the term. The equivalent of Task 1 will be Task 5 and Task 9
to the administered in Term 2 and Term 3 respectively. Task 2 will be administered as a Group Exercise and will consist of two or three instructionalobjectives that the teacher considers difficult to teach and learn. The selected objectives could also be those objectives considered very important and
which therefore need students to put in more practice. Task 2 will be administered at the end of the second month in the term. Task 3 will also be
administered as individual test under the supervision of the class teacher at the end of the 11 th or 12 week of the term.
Task 4 (and also Task 8 and Task 12) will be a project to be undertaken throughout the term and submitted at the end of the term. Schools will be
supplied with 9 project topics divided into three topics for each term. A student is expected to select one project topic for each term. Projects for the
second term will be undertaken by teams of students as Group Projects. Projects are intended to encourage students to apply knowledge and skillsacquired in the term to write an analytic or investigative paper, write a poem 9 (as may be required in English and Ghanaian Languages), use science
and mathematics to solve a problem or produce a physical three-dimensional product as may be required in Creative Arts and in Natural Science.
Apart from the SBA, teachers are expected to use class exercises and home work as processes for continually evaluating students’ class performance,and as a means for encouraging improvements in learning performance.
Marking SBA Tasks
At the SHS level, students will be expected to carry out investigations involving use of mathematics as part of their home work assignments and as
part of the SBA. The suggested guideline for marking such assignments and projects is as follows:
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 13/66
xiii
1. Introduction 20%2. Main text – descriptions, analysis, charts etc. 40%
3. Conclusion and evaluation of results/issues 20%4. Acknowledgement and other references 20%
In writing a report on an experiment or any form of investigation, the students has to introduce the main issue in the investigation, project or report. Theintroduction carries a weight of 20%. The actual work, involving description of procedures and processes, use of charts and other forms of diagrammed, andthe analysis of data is given a weight of 40%. Conclusions and generalizations from the investigation, project etc. is weighted 20%. The fourth item, that is,
acknowledgement and references is intended to help teach young people the importance of acknowledging ones source of information and data. The students
should provide a list of at least three sources of references for major work such as the project. The references could be books, magazines, the internet orpersonal communication from teacher or from friends. This component is given a weight of 20%.
The marks derived from projects, the end of month SBA tests and home work specifically designed for the SBA should together constitute the School BasedAssessment component and weighted 60 per cent. The emphasis is to improve students learning by encouraging them to produce essays, poems, and artisticwork and other items of learning using appropriate process skills, analyzing information and other forms of data accurately and make generalizations andconclusions. The SBA will hence consist of:
Ø End-of-month testsØ Home work assignments (specially designed for SBA)Ø
Project
Other regulations for the conduct of SBA will reach schools from GES.
GRADING PROCEDURE
To improve assessment and grading and also introduce uniformity in schools, it is recommended that schools adopt the following grade
boundaries for assigning grades.
Grade A: 80 - 100% - Excellent
Grade B: 70 - 79% - Very GoodGrade C: 60 - 69% - GoodGrade D: 45 - 59% - Credit (Satisfactory)
Grade E: 35 - 44% - PassGrade F: 34% - Fail
In assigning grades to students’ test results, you may apply the above grade boundaries and the descriptors which indicate the meaning of each grade.
For instance, a score of 75% and above is considered "Excellent"; a score of 66% is within the grade boundary of 65-74% and is considered
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 14/66
xiv
"Very Good". Writing 60% for instance, without writing the meaning of the grade does not provide the students with enough information to evaluatehis/her performance on the assessment. It is therefore important to write the meaning of the grade alongside the score you write. The grade
descriptors, Excellent, Very Good etc do not provide enough feedback to students. You should therefore provide short diagnostic information alongside the grade descriptor or write other comments such as:
o Good work, keep it up
o Could do better
o Hard working students
o Not serious in class; more room for improvement etc.
The grade boundaries are also referred to as grade cut-off scores. When you adopt a fixed cut-off score grade system as in this example, you areusing the criterion-referenced grading system. By this system a students must make a specified score to earn the appropriate grade. This system of
grading challenges students to study harder to earn better grades. It is hence very useful for achievement testing and grading.
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 15/66
1
SENIOR HIGH SCHOOL 1
UNIT SPECIFICOBJECTIVES
CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
UNIT 1.1SETS ANDOPERATIONS ON SETS
The student will be able to:
1.1.1 determine and writethe number of subsetsin a set
1.1.2 identify the propertiesof operations on sets.
Finding the number of subsetsin a set with n elements
Properties of Set Operations-Commutativity
Associativity
Distributivity
Review with students description of sets; - words/set builder notation - listing. - Venn diagrams.
Guide students to deduce the number of subsetsin a set with elements. i.e. the number of subsets = 2n
Guide students to determine the commutativeproperty of sets involving given sets A and B
i.e. A B = B A ; A U B = B U A
Guide students to determine the associativeproperty of sets involving three given sets A, Band C,i.e.(A U B) U C = A U (B U C) and (A B) C = A (B C)
Guide students to determine the distributiveproperty of sets involving three given sets A, Band C,i.e. A U (B C) = (A U B) (A U C) A (B U C) = (A B) U (A C)Illustrate the properties with Venn diagrams.
Let students
find the number of subsets in a given set.
verify commutative,associative anddistributive properties of operations on sets
Illustrate properties of set operations usingVenn diagrams
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 16/66
2
UNIT SPECIFICOBJECTIVES
CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
1.1 (CONTD)
SETS ANDOPERATIONS ONSETS
The student will be able to:
1.1.3 describe the regionsof a Venn diagram interms of the setoperations- union,complement
1.1.4 find solution topractical problemsinvolvingclassifications usingVenn diagrams
Description and identification of the regions of Venn diagramsusing set operations
Three-set problems using Venndiagrams
Guide students to develop the concept of thecomplement of a set in a Venn diagram,E.g.
Guide students to(I) describe regions of up to three (3) intersecting sets(ii) shade regions corresponding to given descriptions
Assist students to verify (using Venn diagrams)that given any two intersectingsets, A and B,(A U B)/ = A/
B/
(A B)/ = A/ U B/
Review two-set problems.
Guide students to solve problems involving threesets
Let students
draw 2 intersecting setsand shade givenregions
describe shadedregions of 3intersecting sets
solve 3 set problemsinvolving real lifesituations
A1
A
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 17/66
3
UNIT SPECIFICOBJECTIVES
CONTENT TEACHING AND LEARNING ACTIVITIES EVALUATION
UNIT 1.2REALNUMBERSYSTEM
Students will be able to:
1.2.1 distinguishbetween rational andirrational numbers.
1.2.2 represent realnumbers on thenumber.
Rational andirrational numbers
Real Numbers onthe number line
Guide students to revise natural numbers, whole numbers and integers.
Guide students distinguish between rational and irrational numbers i.e.
rational numbers can be expressed as ba , where a and b are real numbers
and b ≠ 0
Guide students to draw Venn diagrams to illustrate the relationship betweenthe members of the real number system.
i.e.
Assist students to locate points for real numbers onthe number line.E.g. =1, 0, 1, 1, 1.5, , 3.5 2 2Guide students to(i) graph given sets of real numbers on the number line;
(ii) find the range of values for a given graph. E.g. -1≤ x ≤ 2
Let students:
Identify regions representinggiven types of real numbersfrom Venn diagrams.
illustrate a given range of numbers on the number line
R
NZ
Q I
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 18/66
4
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
UNIT 1.2 (CONTD)
REAL NUMBERSYSTEM
Students will be able to:
1.2.1 compare and order
rational numbers
1.2.2 approximate byrounding off decimalnumbers to a givennumber of placevalues
1.2.3 approximate adecimal number to agiven number of significant figures
1.2.4 express recurringdecimals as commonfractions.
Comparing and ordering
rational numbers
Approximating and roundingoff numbers
Significant figures
Recurring decimals
Assist students to compare and order different
types of rational numbers E.g. common fractions,whole numbers, percentages, decimal fractionsand integers using <,> and the number line.
E.g. arrange the fractions; 0.3, 41 , 45% and 28 in
ascending order.
Guide students to approximate decimal numbersto given place valuesE.g. 587.3563 to 2 decimal places (nearesthundredth) is 587.36 and 5873456 rounded to thenearest thousand is 5873000.
Guide students to approximate given decimalnumbers to given number of significant figuresE.g. 46.23067 approximated to 5 significantfigures is 46.231.
Review changing common fractions to decimalsand vice versa.
Guide students to realize that a recurring decimalhas a digit or a block of digits which keeprepeating
E.g. 1.666 or 1..
6
0.727272 or 0...27
Guide students to express recurring decimals as
fractions of the formba where b 0
E.g. 0..
7 =97 and 0.
..
81 =112
9918 =
verify results by using the calculator.
Let students:
arrange sets of rational
numbers in order of magnitude.
round off numbers togiven number of placevalues.
approximate numbers togiven number of significant figures.
express given recurringdecimal fractions ascommon fractions.
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 19/66
5
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
UNIT 1.2(CONTD)
REAL NUMBERSYSTEM
Students will be able to:
1.2.5 express very large or
very small numbers instandard form.
1.2.6 state and use propertiesof operations on realnumbers.
1.2.7 interpret given binaryoperations and apply
them to real numbers
Standard form
Properties of operations
Commutative property
Associative Property
Distributive Property
Binary operations
Guide students to express a very large number in
the form; k x 10n
, where 1 ≤ k <10 and n is aninteger.E.g. 14835 = 1.4835 x 104
0.0034678 = 3.4678 x 10-3
Guide students to investigate the commutativeproperties of addition and multiplication.i.e. a + b = b + a and ab = ba
Guide students to investigate the associativeproperty of addition and multiplication.
i.e. (a + b) + c = a + (b + c), and (ab)c = a(bc)
Guide students to investigate the distributiveproperty of multiplication over addition andsubtraction.i.e. a(b + c) = ab + ac, and
a(b c) = ab ac.
Guide students to interpret and carry out binaryoperations on real numbers such as a * b = 2a + b ab
p * q = p + q 2pq.Use calculator to compute/perform binaryoperations
Let students:
express given numbers
in standard forms andvice versa
State the properties of operations applied ingiven mathematicalsentences.
apply the appropriateproperties to evaluateexpressionsE.g. 18 x 22 = 18 (20+2) 90 x 95 = 90 (100 5).
carry out defined binaryoperations over real
numbersE.g. if m * n = m + n +5,
find 8 * 4
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 20/66
6
UNIT SPECIFICOBJECTIVES
CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
UNIT 1.3ALGEBRAICEXPRESSIONS
The students will be able to:
1.3.1 express statements inmathematical symbols
1.3.2 add and subtractalgebraic
expressions
1.3.3 multiply two binomial Expressions
1.3.4 factorize algebraic expressions
1.3.5 apply difference of twosquares to solveproblems
Algebraic expressions
Operations on algebraicexpressions
Binomial expressions
Factorization
Difference of two squares
Assist students to express simple statementsinvolving algebraic expressions in mathematicalsymbols.
Guide students to add, subtract and simplifyalgebraic expressions involving the four basicoperations.
Assist students to multiply two binomialexpressions and simplifyE.g. (a + b) (c + d) = c (a + b) + d (a + b) = ac + bc + ad + bd
Guide students to identify common factors inalgebraic expressions and factorize (index of thevariable not exceeding 2).
Assist students to develop the rule of differenceof two squares i.e. a2
b2 = (a + b) (a b)
Guide students to apply the idea of difference of two squares to evaluate algebraic expressionsE.g. x² y² = (x + y) (x y) i.e. 52
42
= (5 + 4)(5 4) = 9 x 1 = 9.
Let students
translate statementsinvolving algebraicexpressions inmathematical symbols.
add and subtractalgebraic expressions..
expand and simplifyproduct of two binomialexpressions.
factorize given algebraicexpressions withvariable index notexceeding 2.
apply difference of twosquares to simplifyalgebraic expressions
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 21/66
7
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
UNIT 1.3 (CONTD)
ALGEBRAICEXPRESSIONS
The students will be able to:
1.3.6 perform operations onsimple algebraicfractions.
1.3.7 determine the conditions
under which algebraicfraction is undefined or zero..
Operations on algebraicfractions with monomialdenominators
Operation on algebraicfractions with binomialdenominators
Undefined or Zero algebraic
fractions
Guide students to add and subtract algebraicfractions with monomial denominators.
E.g. axa x
xa+=+ 212
Assist students to add and subtract algebraicfractions with binomial denominators.E.g.
+− b x
1
a x −1
=))((
2
a xb x
ba x
−−−−
,
where x ≠ a, x ≠ b
Discuss with students the condition under which
an algebraic expression is zero.E.g. in 3a 5y , is zero. When 3a = 0 i.e. a = o
Assist students to determine the condition under which an algebraic expression is undefinedE.g. 1 is undefined when 2 2x2 2x = 0. or when x=1
Let students
solve problemsinvolving addition andsubtraction of algebraicfractions with monomialand binomialdenominators.
solve for the value of variables in algebraic
fractions for which thefractions is zero.
find the value of avariable for which analgebraic fraction isundefined.
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 22/66
8
UNIT SPECIFICOBJECTIVES
CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
UNIT 1.4
NUMBER BASES
The student will be able to:
1.4.1 convert base tennumerals to other bases and vice-versa
1.4.2 solve simple equationsinvolving number bases
1.4.3 perform operations onnumber bases other than base ten
Converting base ten numeralsto numerals in other base andvice versa.
Operations on numbersinvolving number bases other than base ten.
• Addition and subtraction
• Multiplication
Guide students to revise number bases byconverting base ten numerals to bases two andfive and vice-versa.
Guide students to convert given numerals frombase ten to numerals in other bases up to basetwelve.
Guide students to solve equations involvingnumber basesE.g. 132x = 42ten
Guide students to add and subtract numbers inbases other than base ten.
Guide students to construct addition tables for bases other than base ten.
Guide students to find the product of twonumbers and construct multiplication table in agiven base other than base ten.
Let students:
convert numerals inbase ten to numerals inother bases and vice-versa.
solve for the base of anumber in equationsinvolving number bases.
construct addition tablein given base other thanbase ten and use it tosolve problems
solve problems onnumber bases (other than base ten) involvingaddition and subtraction
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 23/66
9
∠ ABC + ∠BAC =∠ ACD
UNIT SPECIFICOBJECTIVES
CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
UNIT 1.5PLANE GEOMETRY I
The student will be able to:
1.5.1 calculate the angles ata point
1.5.2 state and use theproperties of parallellines
1.5.3 state and use theexterior angle theoremof a triangles
Angles at a point
Parallel linesRelationships betweencorresponding angles, verticallyopposite angles, alternateangles and adjacent angles,supplementary angles
Exterior angle theorem
Revise with students the sum of angles on astraight line by measuring using a protractor.
Assist students to use protractors to measureangles at a point to verify that they add up to3600.
In groups let students draw parallel lines and atransversal and, measure all the angles todiscover the relationships between;corresponding angles, vertically opposite angles,alternate angles, adjacent angles, andsupplementary angles.
Perform practical activities with students to revisethe sum of the interior and the sum of the exterior angles of a triangle.Guide students to apply this knowledge to find thevalue of missing angles in a triangle
Guide students to perform practical activities toverify the exterior angle theorem of a triangle,students to measure the interior and the exterior angles of a triangle.
E.g.
Let students:
find missing angles ingiven diagrams
find missing anglesbetween parallel linesand a transversal
find missing angles of triangles from givendiagrams
D
A
B C
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 24/66
10
UNIT SPECIFICOBJECTIVES
CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
UNIT 1.5 (CONTD)
PLANE GEOMETRY I
The student will be able to:
1.5.4 identify variousproperties of specialtriangles
Special trianglesIsosceles and equilateraltriangles
Right angled triangle
Revise different types of triangles includingscalene, isosceles equilateral and right-angledtriangles.
Guide students to establish the properties of isosceles and equilateral triangles.
E.g. (i) the line of symmetry of an isoscelestriangle bisects the base and the angle oppositeit, and is perpendicular to the base, (ii) equilateral triangles have three lines of symmetry in the plane and the lines arecongruent
Guide students to use practical activities,including the use of the geoboard to identify the
right-angled triangle and discover the relationshipbetween the hypotenuse and the other two sides.
Let students:
Use properties of special triangles to findmissing angles intriangles
Solve problemsinvolving the application
of the Pythagorastheorem.
use Pythagorastheorem to find amissing side of a right angled triangle whentwo sides are given
c
b
ac
2 = a
2 + b
2
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 25/66
11
UNIT SPECIFICOBJECTIVES
CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
UNIT 1.5 (CONTD)
PLANE GEOMETRY I
The student will be able to:
1.5.5 state the properties of quadrilaterals
1.5.6 calculate the sums of interior angles andexterior angles of apolygon
Quadrilaterals
Polygons
Guide students to use cut-out shapes and fold toestablish congruent sides, congruent angles and,lines of symmetry of quadrilaterals such asparallelograms, kites, rectangles, etc.
Guide students to establish the relation betweenthe number of sides and the number of trianglesin any polygon with sides
. Assist students to complete the table below.
Polygon No. of sides
No. of angles
Sum of angles
Triangle
Quadrilateral
Pentagon
Hexagon...n
3
4
1
2
180º
360º
Guide them to use their results to find the formulafor finding the sum of the interior angles of apolygon.i.e. sum of angles = (n 2)180º
Guide students to perform activities to find thesum of the exterior angles of a polygon.
Let students:
find the number of linesof symmetry of givenquadrilaterals.E.g. Rhombus Parallelogram, etc.
calculate the sum of interior angles of givenpolygon
find an interior or exterior angle of apolygon using the ideasof the sum of interior angles and exterior angles of a polygon.
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 26/66
12
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
UNIT 1.6LINEAR EQUATIONSAND INEQUALITIES
Students will be able to:
1.6.1 find solution sets for linear equations in one variable.
1.6.2 solve word problemsinvolving linear equationsin one variable
1.6.3 solve linear inequalities inone variable and i llustratethe result on the number
line
1.6.4 solve word problemsinvolving linear inequalities in one
variable
Solution sets of linear equations inone variable
Word problems involving linear equations in one variable
Linear inequalities in one variable
Word problems involving linear inequalities in one variable
Guide students to find solution sets of givenlinear equations in one variable
E.g. 5x 2 = 3x + 2 4 2
T = {x : x = - 6}
Guide students to solve word problemsinvolving linear equations in one variable.
Find and illustrate truth sets of linear inequalities in one variable on the number line.E.g. 0 3x 1 2
131 ≤≤ x
Guide students to solve word problemsinvolving linear inequalities in one variable
Let students
find the truth sets of linear equations in one variable.
solve word problemsinvolving linear equationsin one variable.
solve problems involvinglinear inequalities in onevariable and show thesolution on the number
line.
solve real life problemsinvolving linear inequalities
3
1− 03
1
3
2 13
4
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 27/66
13
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
UNIT 1.7RELATIONS ANDFUNCTIONS
The students will be able to:
1.7.1 distinguish between thevarious types of relations.
1.7.2 Identify functions from
other relations.
1.7.3 determine the rule for agiven mapping
Types of relations
Functions
Mapping
Review with students, relations between two sets;arrow diagrams; ordered pairs; domain; co-domain;range.
Guide students to use arrow diagrams to illustratetypes of relations including one-to-one, one-to-many, many- to-one and many-to-manyrelations.
Use expressions of real life relations such as is thefather of , is the wife of to describe relations.
(Encourage students to develop the sense of belongingness)
Use arrow diagrams to guide students to identify the
relations one-to-one and many-to-one asfunctions.
Assist students to determine the rule for a givenmapping on the set of real numbers
The rule is: f(x) = 2x 3.
Let students
determine the type of relation described in agiven arrow diagram.
give reasons why a givenrelation is or is not a
function
determine the rule for agiven function.
-2-10123
-7-5-3-113
X f(x)
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 28/66
14
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
1.7 (CONTD)
RELATIONS ANDFUNCTIONS
The student will be able to:
1.7.4 draw linear and quadratic
graphs for given functions
1.7.5 find the gradient of astraight line, given the co-ordinates of two points onthe line
1.7.6 find the equation of astraight line
.
1.7.7 find the distance betweentwo points
1.7.8 change the subject of arelation
Graphs of Functions
- linear functions
- quadratic functions
Gradient of a straight line
Equation of a straight line
Magnitude of a linesegment
Change of subject of arelation
Guide students to form table of values for a given
linear function defined on the set of real numbers for agiven domain.
Guide students to use completed tables to plot points,draw graphs and read values from the graphs.
Guide students to draw table of values for quadraticfunctions defined on the set of real numbers for agiven domain.
Assist students to use the table of values to drawquadratic graphs and also to read values from thegraphs.
Assist students to develop the ratio12
12 x x y y −− as the
gradient of a straight line joining the points (x1, y1) and(x2, y2)
Guide students to derive the equation of a line from
12
12
1
1
x x
y y
x x
y y
−−
−− =
where (x, y) is an arbitrary point on the line
Discuss with the students different forms of equationof a straight line i.e. (i) y = mx + c
(ii) ax + by + c = 0Guide students to find the distance between twopoints with given coordinates (x1, y1) and (x2, y2) as
d = 212
212 )()( y y x x −+−
Guide students to find one variable in terms of theothers in a relation.
Let students
draw graphs of given
linear functions and readvalues of the function for agiven pre-image and viceversa
draw the graphs of givenquadratic functions
read the value of thefunction for a given pre-image and vice versa
find the gradient of a linefrom given coordinates of points on the line
find the equation of a linefrom given points on theline
find the length of a line joining two given points
change the subject of arelation.
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 29/66
15
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
UNIT 1.8VECTORS IN A PLANE
The student will be able to:
1.8.1 distinguish between scalar and vector quantities
1.8.2 represent vectors invarious forms
1.8.3 add and subtract vectors,
1.8.4 multiply a vector by ascalar
Scalar and vector quantities
Vector notation andrepresentation
Addition and subtraction of vectors
Multiplying a vector by a scalar
Guide students to use diagrams to illustratethe idea of scalar and vector quantities.
Guide students to identify the following:
(a) free vector notation; a, u, etc.
(b) position vector notation; OP , OB ,etc.
(c) representation of vectors in
component form
y
x
(d) in bearing-magnitude form (r, θ0)
Guide students to add and subtract vectors.Eg.
(a)
+
2
2
1
1
y
x
y
x
++
=21
21
y y
x x
(b)
−
2
2
1
1
y
x
y
x =
−−
21
21
y y
x x
Guide students to multiply a vector by a scalar k.
E.g.
y
xk =
ky
kx
Let students
distinguish between scalar and vector quantities
express given vectors withthe appropriate notations
find the sum and differenceof given vectors
multiply given vectors by
given scalars
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 30/66
16
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
1.8 (CONTD)
VECTORS IN A PLANE
The students will be able to:
1.8.5 express the componentsof a vector in column form
1.8.6 add two vectors using thetriangle law of vector addition.
1.8.7 state the conditions for two vectors to be equal or parallel
Column vectors
Triangle law of vectors
Equal and Parallel vectors
Guide students to use graph to determinecomponents of vectors in column form for given coordinates
E.g. A (x1, y1) and B (x2 , y2) in the Oxy plane;
(a)
=
=
2
2
1
1,
y
xOB
y
xOA
(b)
−−
=12
12
y y
x x AB
Using graphs guide students to deduce thetriangle law of vectors addition.
i.e. AB + BC =AC where A, B and C are pointsin the Oxy plane.
Assist students to establish conditions for vectors to be equal or parallel :
i.e. If.
=
2
2
1
1
y
x
y
x
, then x 1 =x 2 and y 1 = y 2 .
If
1
1
y
x is parallel to
2
2
y
x then
=
2
2
1
1
y
xk
y
x, where k is a scalar.
Let students
find the vector AB givencoordinates of A and B
find the coordinates of B, given the vector AB andthe coordinates of A.
find the diagonals of aquadrilateral ABCD invector component form,given the coordinates of the vertices
add two given vectors
use the idea of equal andparallel vectors to solverelated problems
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 31/66
17
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
1.9 (CONTD)VECTORS IN A PLANE
UNIT 1.9
SIMULTANEOUSLINEAR EQUATION
The student will be able to:
1.8.8 find the negative vector of a given vector
.
1.8.9 find the magnitude anddirection of a vector.
1.9.1 find solution sets of twogiven linear equations in
two variables
1.9.2 solve word problemsinvolving simultaneous
linear equations
Negative vectors
Magnitude and direction of avector
Solving Simultaneous linear equations in two variables
Elimination and substitutionmethod
Graphical method
Solving word problems involvingsimultaneous linear equations in
two variables
Assist students to find the negative vector of agiven vector. E.g. the negative vector of
→
B = −2
3
is =− B
→
BA = − 2
3
Guide students to find the magnitude anddirection of a given vector.
i.e. if
=
→
y
x AB , then
→|| AB = ²² y x +
and direction is given by θ = tan-1 )( x
y
Guide students to find the solution sets of twolinear equations in two variables
simultaneously using(i) the elimination method and(ii) the substitution method.
E.g. 2x + 5y = 10 x - 2y = 4
Guide students to use graphical approach tofind the solution sets of two linear equations intwo variables.
Pose word problems involving simultaneouslinear equations in two variables for students
to solve.E.g. A family of three adults and two childrenpaid GH¢8.00 for a journey. Another family of four adults and three children paid GH¢11.00as the fare for the same journey. Calculate thefare for i. an adult ii. a child iii. a family of four adults and five children
Let students
find negative vectors of given vectors incomponent form
find the magnitude anddirection of given vectors.
find the solution set of two
linear equations in twovariables
use graphical method tofind the solution set of twolinear equations in twovariables
solve word problemsinvolving simultaneous
linear equations
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 32/66
18
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
UNIT 1.10
RIGID MOTION I
The student will be able to:
1.10.1 identify and translate an
object or point by atranslating vector anddescribe the image
1.10.2 identify and explain thereflection of an object in amirror line
1.10.3 describe the image pointsof shapes in a reflection
Translation by a vector.
Reflection in a line.
Characteristics of reflection.
Revise congruency through the use of lines of
symmetries of plane figures.Guide students to identify some Ghanaiansymbols that are symmetricalE.g. Gye Nyame symbol.
Guide students to slide shapes todemonstrate translation as movement in astraight line.
Ask students to give real life examples of translation.
Assist students to translate points and planefigures by given vectors on graph sheets and
describe the images.
E.g. Translate P(3, 4) by vector
=
→
1
2 PQ ,
Guide students to carry out different activitieswith concrete objects to identify the images of an object in a given mirror.
Assist students to draw shapes on graphsheets and find their images under reflectionsin given mirror lines.
i.e. x = k y = k y = kx, where k is an integer.
Let students
translate plane figures andpoints by given vectors andstate the image points
draw images of geometricshapes under reflection in
given mirror lines and statethe points
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 33/66
19
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
UNIT 1.11
STATISTICS I
The students will be able to:
1.11.1 draw frequencydistribution tables for
ungrouped and groupeddata
1.11.2 represent data on asuitable graph
1.11.3 calculate the mean usingappropriate formula
1.11.4 estimate the mode from ahistogram
Frequency distribution tables.
Graphical representation of data.
Mean of a distribution.
Estimating the mode from ahistogram.
Guide students to prepare frequency tablesfor grouped and ungrouped distributions.
(exclude unequal class intervals)
Guide students to use appropriate graph torepresent data from real life situations like testscores, rainfall, health records, imports,exports etc.
(Use pie charts and bar charts for ungroupeddata and histograms for grouped data).
Assist students to calculate the mean usingthe formula:
(i)n
x x
∑= _
for ungrouped data
(ii)∑∑=
f
fx x _
for grouped data.
Guide students to use a histogram to estimatethe mode.
Let students:
construct frequency tablesfor grouped and ungrouped
data and represent themon suitable diagrams.
calculate the mean of agiven data using the
appropriate formula
draw histogram for a givendata and use it to estimatethe mode
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 34/66
20
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
UNIT 1.12
RATIO AND RATES
The students will be able to:
1.12.1 divide a quantity in a
given ratio.
1.12.2 interpret scales usedin drawing plans andmaps and use themto calculate distancesbetween two points
1.12.3 convert foreigncurrencies into Ghanacedis and vice versa
Ratio
Scales
Foreign exchange
Guide students to revise the idea of ratio byfinding how many times one quantity is of the
other E.g. 7 and 21 are in the ratio 1 : 3
Assist students to share given quantities ingiven ratios.E.g. Share GH ¢2.5m in the ratio 3 : 2.
Guide students to examine maps, planstoposheets and identify the scales used.E.g. a scale of 1 : 125000 means 1cm on themap represents 125000 cm on the ground.
Guide students to use given scales to drawplans of given areas in the locality or in theschool and let them draw geometric shapesusing scales.
Guide students to use rates obtained fromForex Bureau or banks to convert givenamounts in foreign currencies to Ghana cedisand vice versa.[the use of calculator and spread sheet(Computer) is recommended]E.g. If $1 = GH ¢0.96find in cedis$25.60
Assist students with samples of water bills,electricity bills, telephone bills and populationcharts to explain the idea of rates.
Let students
solve word problemsinvolving division of
quantities in given ratios
draw plans of given placesand shapes
find actual distances
between two points on amap for a given scale
convert given amounts of foreign currencies intoGhana cedis and viceversa
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 35/66
21
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
1.12 (CONTD)
RATIO AND RATES
The students will be able to:
1.12.4 explain and usecommon rates suchas kmh 1, ms 1
1.12.5 draw travel graphsand interpret them..
1.12.6 calculate andcompare populationdensities
Rates.
Travel Graphs.
Population Density.
Guide students to solve problems involving rates, E.g. speed of a vehicles, wages and salaries
Guide students to draw a distance time graph from agiven data and use it to calculate average speed, totaldistance traveled, total time taken, etc.
Assist students to calculate population density aspopulation per square kilometer (collect data fromstatistical services department or the internet).
Students:
solve practical problemsinvolving rates
draw distance time graphfor a given data andinterpret.
calculate and comparepopulation densities incities urban and rural areas
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 36/66
22
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
UNIT 1.13
PERCENTAGES I
The students will be able to:
1.13.1 compare two amounts or
quantities by expressingone as a percentage of the other.
1.13.2 do money makingcalculations that applypercentages.
1.13.3 Do money spendingcalculations that apply hirepurchase.
Comparison by percentages.
Discount, Commission, SimpleInterest.
Hire Purchase.
Assist students to express one quantity as
percentage of another.
Guide students to calculate percentageincrease or decrease on prices of goods andservices.
Guide students to calculate discount asmoney saved on goods bought andcommission as money earned in atransaction.
Assist students calculate the price of goodswhen discount and commission are given.
Guide students to use current bank rates tocalculate interests on savings and loans
Guide students to explain and performcalculations involving Hire Purchase.
NB: the use of calculator to checkcomputation should be encouraged
Let students:
calculate the value of one
quantity as a percentage of another.
solve problems involvingdiscount and commission.
work out hire purchasepayments over givenperiods
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 37/66
23
SENIOR HIGH SCHOOL 2
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
UNIT 2.1
MODULARARITHMETIC
The student will be able to:
2.1.1 calculate the value of numbers for a givenmodulo.
2.1.2 add and multiply numbers ina given modulo.
Calculation of a number for a given modulo.
Addition (⊕) andmultiplication(⊗) tables ingiven modulo.
Guide students to use the clock face todetermine the modulus of a number.
Use the idea of remainders to assiststudents to determine the modulo of anumber.E.g. 27 = 2 mod 5 8 = 2 mod 6
Guide students to construct addition ⊕ andmultiplication (⊗) tables in a given modulo.
Let students:
calculate the value of numbersfor a given modulo.
find the sum and product of anytwo given numbers in givenmodulo
construct addition (⊕) andmultiplication (⊗) tables in givenmodulo; use the tablesconstructed to find the truth setsof statements
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 38/66
24
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
UNIT 2.2
INDICES ANDLOGARITHMS
The student will be able to:
2.2.1 write in exponent form therepeated factors of a number Laws of indices. Revise with students the first two laws of indices
i.e. ax x ay = a(x + y)
a x ÷ ay = a(x-y)
Guide students to discover further rulesgoverning indices
i.e. (am) n = amn
a -m = 1 am
n maa n
m
=
Guide students to deduce the value for anon-zero number with zero exponent
i.e. ao = 1
Let students:
solve problems involvingrepeated factors
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 39/66
25
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
2.2 (CONTD)INDICES ANDLOGARITHMS
The student will be able to:
2.2.2 solve equations involvingindices.
2.2.3 relate indices to logarithms.
.
Solving equationsinvolving indices.
Relating indices tologarithms in base ten
Assist students to solve simple equationsinvolving indices.
E.g. 8x = 32 23x 25
3x = 5
3
5= x
Guide students to express given numbers aspowers of 10.
E.g. 100 = 102
10,000 = 104
Guide students to identify the relationbetween indices and logarithms.
i.e. x = 10n ⇔ log10 x = n
Let students:
solve equations involving indices.
write an expression in indicesusing logarithm
E.g. x = 10y ⇒ log10 x = y
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 40/66
26
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
2.3 (CONTD)
INDICES ANDLOGARITHMS
The student will be able to:
2.2.4 deduce the rules of logarithmsand apply them.
2.2.5 find the anti-logarithm of a givennumber.
Rules of logarithmsand their application.
Find the anti-logarithms of givennumbers.
Guide students to discover the rules of logarithms.
E.g. log10 (A x B) = log10 A + logn B
log10 B A = log10 A - log10 B
log10 Ax = x log10 A
Assist students to use the rules to simplifylogarithmic expressions and solve problems.
Assist students to read the anti-logarithm of given numbers using (i) tables.
(ii) calculators.
Let students:
use the rules to solve logarithmicproblems.
find the anti-logarithms of givennumbers using tables andcalculators.
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 41/66
27
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
UNIT 2.3SURDS.
The student will be able to:
2.3.1 simplify surds
2.3.2 carry out operations involvingsurds
2.3.3 rationalize a surd with monomialdenominator
.Simplifying surds.
Addition, subtractionand multiplication of surds.
Rationalization of surds with monomialdenominators.
Guide students to simplify surds of the form
a
E.g. 8 2 2=
27 3 3=
=72 26
Assist students simplify the product of surds.i.e
a x b = ab
( a )2 = a
b
a =
b
a
Guide students to find sums, differences andproducts of surds.
Guide students to rationalize surds withmonomials denominators.
E.g.3
32
3
3
3
2
3
2=×=
Let students:
simplify surds of the form aand products of surds.
use the relations in surds to solveproblems
solve problems involvingaddition, subtraction andmultiplication of surds
simplify and rationalize thedenominators of surds
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 42/66
28
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
UNIT 2.4PERCENTAGES II
The student will be able to:
2.4.1 solve real life problems involving compound interest
2.4.2 determine the depreciation of an item over a specified period
Compound interestfor a given period.
(up to 4 years)
Depreciation.
Guide the students to revise simple interestand other applications of percentages withstudents
Guide students to calculate compoundinterest of any given amount.(formula is accepted but not required)
Discuss with students examples of thingsthat lose their values with passage of time.E.g. cars, fridges, etc.
calculate the depreciation of an item for agiven period.(Formula is accepted but not required)
Note use of calculator to check computationshould be encouraged
Let students:
calculate the compound intereston a given amount for a givennumber of years
solve practical problems:E.g.
A car bought for GH¢5000.00depreciates at 10% per annum.Calculate the value after 5 years.
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 43/66
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 44/66
30
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
2.5 (CONTD)VARIATION
UNIT 2.6QUADRATIC
FUNCTIONS ANDEQUATIONS.
The student will be able to:
2.5.5 solve problems involving partial variation.
2.6.1 identify and solve quadratic equations by factorization.
Partial variation.
Solving quadraticequations byfactorization.
Discuss with students what partial variationis.
Guide students to write an equationinvolving partial variation.
Guide students to solve problems involvingpartial variations.
Guide the students to identify a quadraticequation as an equation of the formax2 + bx + c = 0 where a, b and c areconstants.
E.g. 2x2 + x - 3 = 0 3x2 - 27 = 0
Guide students to solve quadratic equationsby factorization.
E.g. find the truth set of
2x2 + 5x = 12 = 0
(x + 4) (2x 3) = 0
T = {x : x = -4, 23 }
Let students:
solve problems involving partialvariations.
identify and write quadraticequations
solve given quadratic equationsby factorization.
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 45/66
31
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
2.6 (CONTD)QUADRATICFUNCTIONS ANDEQUATIONS
The student will be able to:
2.6.2 solve quadratic equations by graphical method.
2.6.3 find the minimum and maximum values and points from graphs.
2.6.4 identify the line of symmetry and
write its equation.
Graphical solution of quadratic equations.
Minimum andmaximum values andpoints of quadraticgraphs.
Line of symmetry.
Guide students to complete tables of valuesfor given quadratic functions and draw
graphs of the functions on graph sheets.
Assist students to find the truth sets of quadratic equations from graphs.
Guide students to find the maximum andminimum values from graphs and state thecoordinates of the points where these occurs
Assist students to establish that the
quadratic graph is symmetrical about avertical line and write its equation as x = k,where k is a real number.
Let students:
solve given quadratic equations
graphically.
find and state themaximum/minimum points andvalues of graphs they draw.
find the line of symmetry from a
quadratic graph and write itsequation
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 46/66
32
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
UNIT 2.7
PLANE GEOMETRY II
(CIRCLES)
The student will be able to:
2.7.1 draw circles for given radii.
2.7.2 state and use the circle theorems
2.7.3 identify the tangent as perpendicular to the radius at the point of contact.
2.7.4 verify that the angle between the tangent and the chord at the point of contact is equal to the angle in the alternate segment.
The Circle as a Locus.
Circle Theorems.
Perpendicularity of Tangent and Radius of aCirlce
Angle between Tangentand a Chord.
Guide students to find all points which are a
given distance from a fixed point.E.g. fix a point O and find all points whichare 5cm from O.
Assist students to find the relationshipbetween the angle subtended at the centreand that at the circumference by an arc.
Guide students to find the value of the anglesubtended by a diameter at thecircumference.
Guide students to find the relationshipbetween opposite angles of a cyclicquadrilateral.
Guide students to verify that the tangent isperpendicular to the radius at the point of contact.
Assist students to verify the alternate angletheorem by drawing.
Let students:
draw circles of varying radii.
find missing angles using circletheorems.
construct a tangent to a circleusing the property of the tangentand radius.
find missing angles using thealternate angle theorem
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 47/66
33
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
UNIT 2.7 (CONTD)PLANE GEOMETRY II(CIRCLES)
The student will be able to:
2.7.5 verify that tangents drawn from an external point to
the same circle are equal when measured from their points of contact
Tangents from anExternal Point.
Guide students to verify that two tangentsdrawn from an external point, T, to a circle at
points A and B are equal in length
i.e. |AT| = |BT|
A
B T
Let students:
solve for missing angles in agiven diagram.
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 48/66
34
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
UNIT 2.8
MENSURATION I
The student will be able to:
2.8.1 find the length of an arc of a
circle
2.8.2 calculate the perimeter of planefigures.
Length of an arc.
Perimeter of planefigures.
Revise parts of the circle with students.
Guide students to deduce the formula for thelength of an arc of a circle.
i.e. 2360
×θ
π r
θ = the angle subtended at the centre of thecircle by the arc.r = radius of the circle.
Revise the perimeters of rectangles andsquares with students
Guide students to deduce the formula for the perimeter of sectors
i.e.360
θ× 2πr + 2r
Guide students to find the perimeter of other plane figures with various sides.
Let students:
calculate the lengths of arc of given circles
find the perimeter of given planefigures
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 49/66
35
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
2.8 (CONTD)MENSURATION I
The student will be able to:
2.8.3 calculate the areas of sectorsand segments
2.8.4 find the areas of quadrilaterals.
.
Areas of sectors andsegments.
Areas of quadrilaterals.
Guide students to revise the area of a circleand triangle with students.
Guides students to establish the formulae for the areas of a sector and a segment.
i.e. Area of sector = ×360
θ πr 2
Area of segment = (area of sector area of triangle).
Guide students to find the areas of givenquadrilaterals. E.g. trapezium, rhombus, etc
Let students:
calculate the areas of sectorsand segment of given circles
find the areas of givenquadrilaterals.
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 50/66
36
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
UNIT 2.9
TRIGONOMETRY I
The student will be able to:
2.9.1 define and compute the sine,
cosine and tangent of an acute angle in degrees.
.
Sine, cosine and
tangent of acuteangles.
Guide students to use appropriate diagrams to
define trigonometric ratios.
E.g. B3
B2
B1
B
O A A 1 A2 A3
Sin θ =3
33
2
22
1
11
OB
B A
OB
B A
OB
B A
OB
AB===
Cos θ =3
3
2
2
1
1
OB
OA
OB
OA
OB
OA
OB
OA===
Tan θ =3
33
2
22
1
11
OA
B A
OA
B A
OA
B A
OA
AB===
Guide students to read the values of giventrigonometric ratios of acute angles from tablesand calculators.
Let students:
express the sine, cosine and
tangent in relation to the sides of a given acute angle in a right-angled triangle
read values of giventrigonometric ratios of acuteangles from tables andcalculators
θ
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 51/66
37
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
2.9 (CONTD)TRIGONOMETRY I
The student will be able to:
2.9.2 calculate the values of trigonometric ratios of 30º
45ºand 60º
The trigonometricratios of 30º, 45ºand
60º.
Guide the students to draw an equilateraltriangle of dimensions 2-units and use it to
derive the ratios for 30º and 60º.
E.g.
300 300
2 2
3
600 600
1 1
sin 30º = 2
1
cos 30º= 2
3
sin 60º =2
3 cos 60º =
2
1
Assist students to draw a square of side oneunit, draw one of the diagonals and use thediagonal and two sides to derive the value of trigonometric ratios of 450
450 sin 450 = 1 = √2
√ 2 √2 2 1 Cos 450 = 1 = √2
√2 2 450
1 tan 450 = 1
Let students:
find the trigonometric ratios of theangles 30º ,60ºand 45º
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 52/66
38
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
2.9 (CONTD)TRIGONOMETRY
The student will be able to:
2.9.3 use the calculator to read thevalues of sine, cosine and
tangent of angles up to 360º
2.9.4 find the inverse of trigonometricratios
2.9.5 calculate angles of elevationand angles of depression
.
The use of calculatorsto read sine, cosine
and tangent of anglesbetween 0º and 360º.
Inverse of trigonometric ratios.
Angles of elevationand depression.
Guide the students to use their calculators tofind given angles from 00 and 3600.
Assist students to find the inverse of giventrigonometric ratios using tables or calculators.
Discuss with students what angles of elevation and angles of depression areusing diagrams.E.g.
θ d
α
a a
s α
b
θ is the angle of elevation =
−
b
d 1tan
α is the angle of depression =
−
b
a1tan
Let students:
find the values of sine, cosineand tangent of given angles
using calculators
find the inverse of given angles
explain what angles of elevationand depression are
solve problems involving anglesof elevation and angles of depression.
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 53/66
39
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
2.9 (CONTD)TRIGONOMETRY
UNIT 2.10
PROBABILITY
The student will be able to:
2.9.6 apply the use of trigonometric ratios to calculate distances and heights
2.10.1 determine the sample space of a simple experiment.
2.10.2 determine the sample space of a compound experiment.
2.10.3 calculate the probability of an event
2.10.4 interpret OR in probability as addition.
2.10.5 interpret AND in probability as multiplication.
Application of trigonometric ratios.
Sample Space of simple experiments
Sample Space of compoundexperiment.
Probability of anevent
Addition law for mutually exclusive
events.
Multiplication law for independent events.
Pose problems of real life situationsinvolving trigonometric ratios for students tosolve.
Guide students to perform simpleexperiments such as tossing a coin once,throwing a die once, etc. and list the samplespaces as the set of all possible outcomes,E.g. sample space for throwing a die once isS = {1, 2, 3, 4, 5, 6}
Guide students to perform compoundexperiments such as tossing two coins,tossing a coin and throwing a die, etc. andlist the sample spaces.
Assist students to calculate the probability of an event
i.e. P(E) =)(
)(
S n
E n
Guide students to establish the followingfacts;P(S) = 1P(φ) = 00 P(A) 1P(Á/ ) = 1 P(A)
Guide students to realize that mutuallyexclusive events do not have anything in
common.i.e. P(A or B) = P(A) + P(B)
Guide students to realize that for twoindependent events, the probability of event
A and event B happening together isP(A and B) = P(A) x P(B)
Let students:
apply trigonometric ratios tosolve problems on real lifesituations
make a list of all possibleoutcomes of an experiment
calculate the probability of givenevents
apply the addition law tocalculate probabilities of naturally
exclusive events
apply the multiplication law tocalculate the probability of independent events
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 54/66
40
SENIOR HIGH SCHOOL 3
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNING
ACTIVITIES
EVALUATION
UNIT 3.1
SEQUENCES ANDSERIES
The student will be able to:
3.1.1 continue a sequence with more terms.
3.1.2 recognize an arithmetic progression (AP) and find the nth term or general term
3.1.3 find the sum of n terms of an AP
3.1.4 recognise a geometric
progression(GP)
3.1.5 find an expression for thegeneral term of a GP
Patterns of sequence
Arithmetic Progression
Sum of n terms of an AP.
Geometric Progression
General term of a GP
Guide students to examine and continue asequence of numbers.
Guide students to identify commondifference (or constant) and find the nth termof an A.P.
i.e. Un = a + (n - 1)d
Assist students to deduce and use the rulefor finding the sum (Sn ) of an AP.
i.e. Sn =2n {a + Un }
=2n {2a + (n 1)d}
Guide students to use practical situations toillustrate a GP. E.g. Depreciation
Guide students to deduce the general term
of a GP as Un = ar n-1 ; where a is the first
term and r , the common ratio
Let students:
write the next two or more termsof a given sequence.
write the nth term of givenarithmetic progressions for givenvalues of n.
find the sum of n terms of an AP.
solve everyday problems usingthe concept of GP
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 55/66
41
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
UNIT 3.2
BEARINGS
UNIT 3.3CONSTRUCTION
The student will be able to:
3.2.1 interpret bearing asdirection of one point from
another.
3.2.2 write bearing of one point from another as (r, θ).
3.2.3 find the bearing of a point A from another point B, given the bearing of B from A.
3.3.1 construct 75o 105o 1350and 150o
3.3.2 construct a triangle or quadrilateral under given conditions.
3.3.3 construct a particular loci
Bearing of a point fromanother.
Distance-bearing form
Reverse bearing
Construction of 75o 105o
135o and 150o.
Construction of Trianglesand Quadrilaterals.
Constructing loci
Guide students to measure angles betweenpoints in clockwise direction taking North (N)
as direction of reference.
Guide students to deduce and write thebearing of one point from another in thedistance-bearing form (r, θ).
Assist students to deduce reverse bearingsi.e. if B is θº from A, then A is(i) (180 + θ )0 from B for 00 < θ < 1800
(ii) (θ - 180)0 from B for 1800 < θ < 3600
Review the construction of 30o , 45o , 60o
and 90º with the students.
Guide students to construct angles 75 o ,105 o , and 135 o .
Assist students to use a pair of compassesand ruler only to construct;
1. a triangle, given two sides and anincluded angle;
2. a triangle, given two angles and aside.
3. a quadrilateral under givenconditions.
Guide students to construct the locus of points equidistant from two or more fixedpoints and two or more intersecting straightlines
Let students:
record angle measure in 3-digits.
find the bearing of a point C from A, given the bearing of B from Aand the bearing of C from B.
find the bearing of one point fromanother, given the reversebearing.
construct some given angles.
construct triangles andquadrilaterals under givenconditions
solve loci related problemsthrough construction
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 56/66
42
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
UNIT 3.4STATISTICS II
The student will be able to:
3.4.1 draw a histogram for given
data
3.4.2 use appropriate formulacalculate the mean
3.4.3 draw cumulative frequency curves (ogive) and interpret them.
Histogram.
Mean.
Cumulative FrequencyCurves (ogive).
Guide students to revise the drawing of
frequency table for ungrouped and groupeddata; use it to draw histogram (Restrict togroups of equal intervals) and estimate themode from the histogram.
Guide students to find the mean of ungrouped and grouped data using;
(i) x =n
x∑
(ii) x = ∑∑ f
fx where x is the class
mid-point (in case of grouped data)
(accept assumed mean method but notrequired)
Let students:
represent a given data on a
histogram
estimate the mode from ahistogram
calculate mean of given data
draw a cumulative frequencycurve and use it to estimate;
(i) lower and upper quartiles;
(ii) median;(iii) given deciles and
percentiles;
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 57/66
43
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
3.4 (CONTD)STATISTICS II
The student will be able to:
3.4.4 calculate and interpretstandard deviation andvariance of ungrouped
data.
.
Standard deviation andVariance
Guide students to draw cumulativefrequency curves using data and use thecurves to estimate:
(i) lower and upper quartiles;(ii) median;(iii) deciles and percentiles, etc
Guide students to calculate and interpretstandard deviation and variance of anungrouped data.
Eg method of ungrouped data
Sd = ( )n
x x∑ −2
Variance = Sd2
Eg The scores from an English test are 30,50, 70, 76, 26, 60, 42, 38, 92, and 49. x&& = 53.3: Sd = 21.1
Mathematics scores: 80, 48, 60, 40, 32, 54,62, 31, 86 and 55. x = 53.0 and Sd = 15.7
Therefore, English scores are more spread
around the mean; this implies thatperformance in mathematics is better thanthat of English.
NB: Students may use spreadsheet to drawgraphs and calculate mean, mode, medianand standard deviation
Let student:
Calculate and interpret standarddeviation and variance.
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 58/66
44
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
UNIT 3.5
INTERPRETATION OFLINEAR AND
QUADRATIC GRAPHS.
The student will be able to:
3.5.1 solve simultaneous
equations one linear and one quadratic using graphs
3.5.2 use quadratic graph to solve related equations
3.5.3 find the range of values of x for which y is increasing or decreasing.
3.5.4 find the range of values of x for which y is positive or negative
Solving linear and
quadratic equations usinggraphs.
Solving related quadraticequations.
Increasing/Decreasingvalues of quadraticgraphs.
Positive/Negative valuesof quadratic graph.
Guide students to solve simultaneous
equations, one linear, one quadratic bydrawing the two graphs on the same axes.
Assist students to solve related equationsusing the quadratic graph;
i.e. use the graph of y = ax2 + bx + c to solve ax2 + dx + k = 0 where a, b, c, d and k are constants.
Assist students to determine the range of values of x for which the graph is increasingor decreasing.
Guide students to determine the range of values of x for which a quadratic graph ispositive or negative. (i.e. above or below thex-axis)
Let students:
draw a quadratic and linear
graphs on the same axes andfind the values of x which satisfythe two equations simultaneouslyand find the correspondingvalues of y
use graph of y = ax2 + bx + c tosolve ax2 + dx + k = 0 for various values of k
find the range of values of x for which a given graph is increasingor decreasing.
find the range of values of x for which y is positive or negative.
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 59/66
45
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
UNIT 3.6
MENSURATION II
(SURFACE AREA,VOLUME OF SOLIDSAND THE EARTH AS AEARTH)
The student will be able to:
3.6.1 draw nets of prisms
3.6.2 calculate the surfacearea of prisms
3.6.3 calculate the volume of prisms
3.6.4 calculate the totalsurface area of cone.
Nets of prisms.
Surface Area of Prisms.
Volume of prisms
Surface Area of Cone
Guide students to identify solids with uniform
cross-section as prisms E.g. triangular prisms, rectangular prism, square prism, etc.
Guide students to use cut-out shapes toform the nets of open/close prisms andidentify the faces.
Guide students to discover that the totalsurface area is the sum of the areas of allthe faces.E.g. Cuboid - Area = 2bl + 2bh + 2lh Closed cylinder - A = 2πr (r + h)
Assist students to calculate volume of prisms by multiplying the area of uniformcross-section by the height or length.
Let students open a cone and examine thenet.
Guide students to draw the net and measurethe angle of the sector.
Guide students to deduce the formula for finding the surface area of a cone as
A = Curved Surface + Base Area
×360θ πl
2 +πl
2
= π
+× 22
360r l
θ
Let students:
draw nets of given prisms
calculate the total surface Area of prisms of given dimensions.
calculate the volume of prisms of given dimensions.
use the formula to calculate thetotal surface area of given coneof given dimensions.
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 60/66
46
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
3.5 (CONTD)
MENSURATION II
The student will be able to:
3.6.5 calculate the volume of a cone
3.6.6 calculate the totalsurface area of apyramid
3.6.7 calculate the volumesof Pyramids
3.6.8 calculate surface area of a sphere
3.6.9 calculate the volume of a Sphere
3.6.10 calculate distance along a given latitude and longitude
Volume of a Cone.
Surface Area of aPyramid.
Volume of a pyramid.
Surface area of a sphere
Volume of a sphere
Distances of arcs of spheres
Guide students to:
Assist student to establish the formula for finding the volume of a cone. i.e. V =
31 π r 2 h
Guide students to calculate the total surface Area of a pyramid as the sum of thetriangular faces and the base.
Guide students to deduce the formula for the volume of a pyramid
i.e. Volume =31 x base Area x h
Guide students to find the surface areas of spheres of given radii using the formula
A = 4πr²
Guide students to establish the formula for finding the volume of a sphere. i.e.
V =34 πr 3
Guide students to draw a sphere andindicate two points on the same latitude or the same longitudes (great circles).
Guide students to draw a sphere andillustrate two points on the same latitude butdifferent longitudes
Guide students to calculate distancesbetween two towns on the earth surface.
Let students:
use the formula to find volume of a given cone.
calculate the total surface areasof pyramids of given dimensions
calculate the volumes of givenpyramids
calculate surface area of givenradii
calculate the volume of spheresof given radii
solve real life applicationproblems
E. g .time taken for aeroplanes tofly between two towns etc
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 61/66
47
SENIOR HIGH SCHOOL 4
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
UNIT 4.1
LOGICAL REASONING
The student will be able to:
4.1.1 identify and form true or false statements.
4.1.2 form the negation of simple statements.
4.1.3 draw conclusions using the implication sign statements made.
Statements.
.
Negation of statement.
Implication signs⇒ , ⇔
Guide students to identify true or falsestatements.
Guide students to write statements innegation form.E.g. Kofi is not a lazy boy is the negation of Kofi is a lazy boy.
Assist students to use the implication sign todraw conclusions from statements made.
E.g. 41023 =⇒=− x xDiscuss the use of the symbol, ⇔ with
studentsE.g. 41023 =⇒=− x x
and if 10234 =−⇒= x x
so, 41023 =⇔=− x x
Let students:
Identify true or false statements.
negate given statements
draw conclusion from statementsmade using the implication sign
Use the symbol ⇔, iff (if and only
if) to draw conclusions from givenstatements
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 62/66
48
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
4.1 (CONTD)LOGICAL REASONING
The student will be able to:
4.1.4 use Venn diagrams to
determine the validity or otherwise of implications or conclusions.
Use of Venn Diagrams
:
Guide students to draw Venn diagrams to
illustrate given statements E.g. consider thestatement: P : All students are hardworking
S = {students}
H = {hardworking people}
U= {People}
S
Assist students to determine whether givenconclusions are valid or not
Let students:
use Venn diagrams to determinethe validity or otherwise of givenstatements
H
S
U
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 63/66
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 64/66
50
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
4.2 (CONTD)
PERCENTAGES III
The student will be able to:
4.2.4 calculate taxes paid on
goods and services.
4.2.5 calculate and explain thevalue added tax. (VAT)
4.2.6 calculate electricity, water and telephone bills.
Income Tax.
Value Added Tax (VAT).
Household bills.
Guide students to identify the government
agencies responsible for collecting incometaxes.
NB.: Encourage students to appreciate theneed for people to pay taxes.
Assist students to calculate income taxusing a given tax schedule.
Assist students to identify some goods andservices that attract VAT and calculate theVAT on them.
Guide students to identify the varioushousehold bills such as electricity bills, water bills and telephone bills.
Guide students to identify how these billsare calculated.
Note: Emphasize the need for students tobe prudent in the use of these utilities.
Let students:
calculate the income tax for a
given income.
find the VAT on a bill for servicesor sales
calculate the total bill paid by ahousehold at the end of themonth at a given rate
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 65/66
51
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
UNIT 4.3
RIGID MOTION II ANDENLARGEMENT
The student will be able to:
4.3.1 find the image of an object under rotation
4.3.2 carry out an enlargement of a plane shape given a scale factor
4.3.3 identify a scale drawing asan enlargement/reduction
of a plane figure (shape).
4.3.3 establish the relationship between the areas and volumes of plane figures and solids and their images
Rotation
Enlargement
Scale drawing
Areas and Volumes of similar figures.
:
Revise examples of turning in everyday lifesituation to explain rotation
Guide students through construction to findthe images of plane figures under rotation.
Guide students to derive the rules for rotation using graphical method E.g. Anticlockwise about the origin (0,0)through 90o ; (x, y) (-y, x) 180 o ; (x, y) (-x, -y), etc.
Include clockwise rotation about the originand rotation about a point other than theorigin
Guide students to find images of planefigures under enlargement from the origin for given scale factors.
Guide students to use scale drawing toenlarge or reduce plane figures.
Assist students to discover the relationshipbetween the areas and volumes of similar figures and solids.
i.e. Area of image : Area of object = K2
: 1 and Volume of Image : Vol. of solid = K3 : 1 where k is the scale factor
Let students:
identify a rotation among a set of movements
draw a given plane figure on agraph paper and rotate itthrough given angles about theorigin and about a given point
draw the images of plane figuresunder enlargement from theorigin for given scale factors.
use scale drawing to enlarge or reduce plane figures given thescale
calculate areas and volumes of similar plane figures and solidsgiven corresponding dimensions
8/12/2019 Mathematics Syllabus SHS 1-3
http://slidepdf.com/reader/full/mathematics-syllabus-shs-1-3 66/66
UNIT SPECIFIC OBJECTIVES CONTENT TEACHING AND LEARNINGACTIVITIES
EVALUATION
UNIT 4.4
TRIGONOMETRY II
The student will be able to:
4.4.1 draw the graphs of simple trigonometric functions and identify maximum and minimum values
4.4.2 draw the graphs of trigonometric functions and interpret
.
Graphs of trigonometric functions
Trigonometric equations
:
Guide students to prepare tables for giventrigonometric functions for :
xa y sin= and xb y cos= in the range00 3600 ≤≤ x
Guide students to use their tables to drawthe graphs of the functions and find themaximum and minimum values.
Guide students to draw simple graphs of trigonometric functions of the form :
xb xa x f cossin)( += in the range
0° ≤ x ≤ 360°
Guide students to use their graphs to solveequations such as : ,0cossin =+ xb xa
k xb xa =+ cossin , etc.
Let students:
draw graphs of giventrigonometric functions and usethem to solve related problems