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Republic of Zambia

MATHEMATICSHIGH SCHOOL SYLLABUS

GRADES 10 – 12

Prepared by:Curriculum Development Centre

P.O. Box 50092LUSAKA

© Curriculum Development Centre

All rights reserved. No part of this publication may be reproduced, stored in a retrieval, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the Publishers.

TABLE OF CONTENT

Preface ............................................................................................................................................................................................................ ii

Acknowledgement ......................................................................................................................................................................................... iii

Introduction ................................................................................................................................................................................................... iv

General Aims ................................................................................................................................................................................................. v

Terminal Objectives ....................................................................................................................................................................................... vi

Time and period Allocation ........................................................................................................................................................................... vii

Grade 10 ......................................................................................................................................................................................................... 1

Grade 11 .......................................................................................................................................................................................................... 6

Grade 12 .......................................................................................................................................................................................................... 14

Notes ...............................................................................................................................................................................................................

PREFACE

The review of this Syllabus was necessitated by the need to improve the quality of education at High School Level as stipulated in the national policy document “Educating Our Future – 1996”.

Quality education raises the standard of living for all. This leads to sustainable national development. The syllabus also addresses issues of national concern such as Environmental Education, Gender and Equity, Health Education and HIV/AIDS, Family Life Education, Human Rights, Democracy, Reproductive Health, Population Education, Entrepreneurship and Vocation Skills, Life and Values Education.

Another reason for revising this syllabus was to fully localize the High School Examinations which were formerly set by University of Cambridge Local Examinations Syndicate, UK.

It is hoped that this syllabus will provide the users with a sound premise on the basis of which meaningful and effective learning experiences will be developed in order to provide a good foundation for further study of this subject area.

James Mulungushi (Dr.)PERMANENT SECRETARYMINISTRY OF EDUCATIONLUSAKA-ZAMBIA

ACKNOWLEDGEMENTii

The Mathematics Department of the Curriculum Development Centre gratefully acknowledges the contribution of the Mathematic’s working committee and the schools which sent in written suggestions to the draft Senior Secondary Mathematics Syllabus for Zambia. These schools are:

Mwinilunga High Secondary School, Mwinilunga.Zambezi Secondary School, Zambezi.Chikankata Secondary School, Mazabuka.Sefula Secondary School, Mongu.Senanga Secondary School, Senanga.Kantanshi Secondary School, Mufulira.St. Mark’s Secondary School, Mapanza.St. Monica’s Secondary School, Chipata.St. Edmund’s Secondary School, Mazabuka.Roma Girls Secondary School, Lusaka.Solwezi Technical Secondary School, Solwezi.Kitwe Boy’s Secondary School, Kitwe.Mbala Secondary School, Mbala.

The Curriculum Development Centre is also deeply indebted to the Environmental Support Programme operating through the Ministry of Environmental and Natural Resources for funding the review and printing the syllabuses.

INTRODUCTIONiii

This syllabus covers Arithmetics, Algebra, Geometry, Trigonometry, Probability, Statistics. The work to be covered in each of the Grades 10, 11 and 12 levels has been described separately.

The aims and objectives of teaching Mathematics at Senior Secondary School level have been derived from three sources: The Educational Reform Document of 1997, the Structure of Mathematics as an academic discipline and the needs of the society. The syllabus is structured in such a way that the pupil is encouraged to put emphasis on the mathematical concepts, principles and creative thinking processes.

When using this syllabus, it should be realised that Mathematics is a discipline with integrated and hierarchical concepts and skills. It is therefore, recommended that an integrated and spiral approach be used.

GENERAL AIMS

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The general aims of teaching Mathematics at Senior Secondary level are to:

1. provide the pupil; with Mathematics background necessary for terminal and further education.

2. develop logical and substract thinking in the pupil.

3. enable the pupil to develop mathematical language and skills as a means of communication and investigation.

4. develop the ability of the pupil to use Mathematics as a tool in the Environment.

5. provide pupil with Mathematical skills to enable them to perform adequately in other subject areas.

6. enable the pupil to derive satisfaction and confidence from the understanding of mathematical concepts and masterly of mathematical skills.

7. stimulate and encourage creativity and a spirit of enquiry in the pupil.

TERMINAL OBJECTIVES

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At the end of Grade 12 pupils should be able to:

1. demonstrate spatial awareness in two and three dimension.

2. explore mathematical situations.

3. apply mathematical knowledge to problem-solving.

4. estimate, measure and calculate to an appropriate degree of accuracy using suitable methods.

5. recognise patterns and structures in a variety of situations form and justify generalisations.

6. represent, interpret and use data in a variety of situations.

TIME AND PERIOD ALLOCATIONvi

This syllabus is a three-year course in mathematics and will require seven 40 minute periods per week.

GRADE 10vii

TOPIC SPECIFIC OBJECTIVEBOYS AND GIRILS SHOULD BE ABLE TO:

NOTES

1. NUMBER ANDNUMERATION.

1.1 Recognise and use sets of numbers including whole numbers, natural numbers, integers (positive, negative and zero), prime numbers, rational numbers, irrational numbers, real numbers, common factors and common multiples.

2. OPERATIONS ON REAL NUMBERS.

2.1 Use communicative, associative and distributive laws and apply ideas of closure on combined operations of addition, substraction, multiplication and division.

Environmental examples may be used. for example:1. discuss whether planting the seed and

improving the soil are communicative processes.

2. discuss whether reducing poverty and improving the environment ate communicative processes etc.

3. COMMON (VULGAR) ANDDECIMALFRACTIONS ANDPERCENTAGES.

3.1 Convert common fractions to decimal fractions and vice versa.3.2 Convert common fractions to percentages and vice- versa.3.3 Convert decimal fractions to percentages and vice- versa.3.4 Add, substract, multiply and divide common and decimal fractions.

TOPIC SPECIFIC OBJECTIVE NOTES

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BOYS AND GIRILS SHOULD BE ABLE TO:

4. ORDERING. 4.1 Order numbers.4.2 Use equality and inequality signs to show relationship between numbers.

Equality and inequality symbols should include:=, ≠, ˃, ˂, ≥, ≤.

5. SQUARES, SQUAREROOTS.

5.1 Use tables to find squares and square Roots.

6. INDICES. 6.1 Use and Interpret positive, negative, zero and fractional indices.

6.2 Solve simple equations involving indices.

7. COMMONLOGARITHMS.

7.1 Use tables to find logarithms and antilogarithms.7.2 Use logarithms to solve problems.

8. SETS. 8.1 Use appropriate set language and notation.8.2 Carry out operations on sets.8.3 Use Venn diagrams to solve simple logical Problems.

Examples from the environment could be used e.g.:1. set of causes of soil erosion.2. set of Natural calamities.


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9. BASIC PROSESSESOF ALGEBRA.

9.1 Collect and simplify like terms.9.2 Interpret and use brackets.9.3 Add and substract algebraic expressions.

10. FACTORISATION. 10.1 Factorise algebraic expressions. Types of Algebraic expressions should include:ax ± ayax ± bx ± kay ± kbya²x² - b²y²a² ± 2ab + b²ax² ± bx ± c.

11. FORMULAE. 11.1 Construct and use formulae.11.2 Change subject of formulae.

12. EQUATIONS ANDINEQUALITIES.

12.1 Solve linear equations in one variable.12.2 Solve simultaneous equations in two variables.12.3 Solve linear inequations in one variable.

Variety of methods of solving simultaneous equations should be encouraged.Excluding use of matrix method.


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13. ANGLES. 13.1 Calculate angles associated with a point, a straight line, intersecting and parallel lines.

14. GEOMETRICAL CONSTRUCTION.

14.1 Construct perpendicular bisector of a straight line.14.2 Construct angles of 30º, 45º, 60º, and 90º.14.3 Construct angle bisectors.14.4 Construct a perpendicular to a given line14.5 Use mathematical instruments to construct geometrical figures.

15. SCALE DRAWINGAND BEARINGS,

15.1 Draw shapes to scale.15.2 Solve problems involving scale Drawing.15.3 Solve problems on bearings.

Use three figures bearings – measured clockwise from the north.

16. PYTHAGORAS THEOREM.

16.1 Demonstrate and apply Pythagoras Theorem.


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17. SOCIAL ARITHMETIC

17.1 Solve problems involving house hold bills, bank services, postal services, social security schemes and transport.

18. COMMERCIAL ARITHMETIC

18.1 Solve problems involving simple interest.18.2 Solve problems involving compound interest.18.3 Solve problems on discount, profit and loss.18.4 Solve problems involving hire purchase.18.5 Solve problems involving foreign exchange calculations.

GRADE 115


NOTES

1. APPROXIMATIONS AND SCIENTIFIC NOTATION

1.1 Approximate quantities.

1.2 Approximate measures to a given degree of accuracy.

1.3 Write numbers correct to the required number of decimal places.

1.4 Write numbers correct to the required number of significant figures.

1.5 Write numbers in scientific notation (Standard form).

1.6 Calculate estimates of error.1.7 Use approximations to estimate an

Error.

Approximations can include:- length of a string,- sitting capacity of a room,- number of pupils in a school.

Examples of a number in standard form isAx10ⁿ where ‘n’ is a integer and 1≤A˂10. Some of me numbers that are normally

expressed in standard form are:- The diameter of the earth,- The distance to the sun,- The population of the earth.


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2. RELATIONS AND FUNCTIONS.

2.1 Relate members of 2 or more sets according to a given rule.2.2 Determine relationships that are functions.2.3 Use function notation.

Familiarity with terminology of:- Domain,- Range, and- Mapping.

Example of function notation could beF(x) = 2x – 7, f: x a2x - 7

Example of inverse of a function notation could be:f-1 (x) x + 7 and f-1: x → x + 7 2 2

3. GRAPHS OF POLYNOMIAS.

3.1 Draw and interpret graph of Straight lines.

3.2 Draw and interpret graphs of quadratic and cubic functions.

3.3 Calculate the gradient of a curve at a given point.

3.4 Estimate the area under the curve.3.5 Draw graphs using out of real life

Situation.

Attention should be paid to:- Completing tables of values of functions.- the Equation of a line y = mx + crecognise what y, m, x and c stands for.- determining gradient and equation of a line given 2 points.

4. QUADRATIC EQUATIONS.

4.1 Solve quadratic equations algebraically.

4.2 Solve quadratic equations graphically.

The algebraic methods should include:- factorisation- completing the square- use of formular.

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NOTES

5. RATION,PROPORTION AND RATE.

5.1 Solve problems involving ratio.5.2 Solve problems involving direct and inverse

proportion.5.3 Use and demonstrate understanding of common

measures of rate.

5.4 Solve Environmental problems involving ratio, proportion and rate.

Some of the common measures of rate are:- km/hr- price/item- interest/year

some of the environmental problems involving rate could include:- rate of deforestation- rate of population growth- rate of human/animal depletion

6. VARIATION. 6.1 Distinguish between inverse and direct variation

6.2 Express a given variation mathematically using symbols.

6.3 Change a given variation expressed mathematically into an equation.

6.4 Solve problems on direct and inverse variation.

6.5 Draw graphs of direct and inverse variation.6.6 Interpret graphs of direct and inverse variation.

- Number of people in a household and how long a bag of mealie meal can last.

- The price of electricity in relation to the number of people who can afford to pay.

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NOTES

6.7 Solve problems based on other forms of direct and inverse variation of the form y = xn,

where -3 ≤ n ≤ 36.8 Solve problems based on joint variation.6.9 Solve problems on partial variation.

7. DISTANCE-TIMEAND SPEED-TIMEGRAPHS.

7.1 Draw and interpret speed-time and distance-time graphs.

7.2 Calculate the distance covered in a specified time from a speed time graph.

Use the principle of area under a curve to determine distance.

Use the gradient of a line from a speed-time graph to determine acceleration and retardation.

8. SYMMETRY IN TWODIMENSIONS.

8.1 Identify line symmetry in a two dimensional shape.

Symmetry inbuilt in the natural environment can include:- insects- buildings- flowers- people.


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8.2 Identify rotational symmetry in two dimensionalshapes.

8.3 Determine the order of rotational symmetry in two dimensional shapes.

8.4 Identify symmetry inbuilt in the natural environment.

9. CONGRUENCEAND SIMILARITY.

9.1 Identify similarity in figures.9.2 Identify congruency in figures.9.3 Use congruency in solving problems requiring

simple logical deductions.9.4 Find the ratio of sides of similar figures.9.5 Calculate the unknown dies or angles in similar

figures.9.6 Calculate the areas and volumes of similar

figures.9.7 Identify similarity and congruency in the natural

environment.


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10. ANGLEPROPERTIES OF ACIRCLE ANDPOLUGONS.

10.1 Use the following angle properties of a circle:- angle at the centre- angle in a semi-circle- angles in the same segment- angles in opposite segments- angle between tangent and radius of a Circle.

10.2 Use the following angle properties of polygons:- angle properties of triangles and Quadrilaterals.- angle sum of polygons.- finding size of interior and exterior angles of a polygon.- determining sum of interior and exterior angles of a polygon.- solving problems involving angle Properties of a polygon.

Some examples of polygons are Triangle, Quadrilateral Pentagon, Hexagon, Heptagon, Octagon, Nonagon and Decagon.


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11. MENSURATION. 11.1 Calculate the perimeter and area of plane figures.11.2 Calculate the surface area and volumes of three dimensional figures.11.3 Draw nets of cones, cubes, cuboids, pyramids and cylinders.11.4 Use nets of figures to solve problems on surface area.

Two dimensional figures to include rectangle, triangle, parallelogram and trapezium.Three dimensional figures to include cuboid, cylinder, prism, sphere, pyramid and cone.

Include area and circumference of a circle.

12. LOCUS OF POINTS IN TWO AND THREE DIMENSION

12.1 Determine locus of a point in two dimensions.12.2 Use the following loci and method of

intersecting loci. Sets of points in two or three dimensions.

- which are at a given distance from a given point.- which are at a given distance from a given straight line.- which are equidistant from two given Points.

Sets of points in two dimensions which are equidistant from two given intersecting straight lines.

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NOTES

13. TRIGOMETRIC RATIOS.

13.1 Find the three trigonometric ratios of sine, cosine and tangent of acute angle.

13.2 Solve problems involving right-angled triangles using sine, cosine and tangent ratios.

13.3 Apply trigonometric ratios to calculate angles, heights and distances.

13.4 Apply trigonometric ratios to solve problems involving three figure bearing.

Take into account angles of depression, angle of elevation and real life situation.

14. STATISTICS. 14.1 Collect and classify data.

14.2 Present data in form of tables pie charts; bar graph, histogram and line graph.

14.3 Interpret data.14.4 Find mean, mode and median.14.5 Determine most appropriate measure of central

tenancy to given situations.

Data to be used should be from real life situation.

15. SEQUENCES. 15.1 Recognise and continue a sequence.15.2 Identify patterns within and across different

sequences.15.3 Generalise sequences into simple algebraic

statements (including expressions to the nth term).

GRADE 1213


NOTES

1. GRAPHICALREPRESENTATION OF INEQUALITIES.

1.1 Solve simple linear inequations.

1.2 Represent inequations in one variable on a number line.

1.3 Represent inequations in two variable on thegraph.

1.4 Form a linear inequation arising from a given situation.

1.5 Form a system of linear inequations arising from given situations (mathematical model).

1.6 Apply the solution set of a system of linear inequations to solve linear programming problems.

In illustrating inequations on a Cartesian diagram, shade the unwanted region.

2. VECTORS IN TWO DIMENSIONS.

2.1 Represent and interpret vector in differentforms.

2.2 Add and subtract vectors in directed line segment or component form.

TOPIC SPECIFIC OBJECTIVE NOTES 14


2.3 Multiply a vector by a scalar.

2.4 Express a vector in terms of a position vector.2.5 Find the magnitude of a vector.2.6 Use vectors to solve problems involving

properties of a set of points or a set of lines.

Relate the concept of a vector in different contexts i.e. in Physics as a quantity with magnitude and direction, in Biology as a transmission of diseases.

3. MATRICES. 3.1 Present and interpret data in a rectangular array of numbers (matrix).

3.2 State the order of a matrix.3.3 Identify and use equal matrices.3.4 Add and subtract matrices.3.5 Multiply a matrice by a scalar. 3.6 Multiply matrix.3.7 Find the determinant of a square matrix of order

2.3.8 Find the inverse of a square matrix of order 2.3.9 Use matrices to solve simultaneous equations.

Common usage of matrices is league tables.


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4. TRANSFORMATIONS OF THE PLANE.

4.1 Find the image of a shape under a translation.

4.2 Find the column vector representing atranslation.

4.3 Find the image of a shape under areflection.

4.4 Find the equation of the mirror line in a reflection.

4.5 Find the image of a shape under a rotation.4.6 Find the centre, angle and direction of

a rotation.4.7 Find the image of a shape under an

enlargement.4.8 Find the centre and scale factor of an

enlargement.4.9 Find the image of a shape under a shear.4.10 Find the invariant line and shear factor

of a shear.

TOPIC SPECIFIC OBJECTIVE NOTES 16


4.11 Find the image of a shape under a stretch.

4.12 Find the invariant line and scale factorof a stretch.

4.13 Find the image of a shape under a combination of transformations.

4.14 Describe transformations using co-ordinates and matrices.

4.15 State the properties of each transformation.4.16 Identify and describe a transformation fully.

5. EARTH GEOMETRY 5.1 Identify parts of a sphere; radius, small circles and great circles.

5.2 Locate points on the surface of the earth using latitudes and longitudes.

5.3 Calculate the radius of a parallel of latitude given the radius of the earth.

5.4 Calculate distances on parallels of latitude and longitudes.

5.5 Determine a latitude given its circumference.5.6 Find the shortest distance between two places on

the same parallel of latitude.

TOPIC SPECIFIC OBJECTIVE NOTES17


6. TRIGONOMETRY. 6.1 Find sine, cosine and tangent of angles from 0º to 360º.

6.2 Use sine rule to solve problems involving triangles.

6.3 Use cosine rule to solve problems involving triangles.

6.4 Use the sine ratio to find the area of a triangle (½ ab Sin C).

7. STATISTICS. 7.1 Construct and use cummulative frequency curves.

7.2 Find the median, lower and upper quartiles.

7.3 Find the range, the interquartile and the semi-interquartile range and distinguish between the purposes for which they are used.

7.4 Find and interpret the percentile range.

The following are measures of dispersion.

Median, lower and upper quartile, semi Interquartile.

TOPIC SPECIFIC OBJECTIVE NOTES18


8. PROBABILITY. 8.1 Find probabilities of singles events experimentally.

8.2 Find probabilities of single eventstheoretically.

8.3 Find expected frequency of an event.8.4 Find probabilities of mutually exclusive,

independent and dependent events.8.5 Use outcome tables (grids) and tress diagrams to

find probabilities.

Use probabilities in an environment context e.g. If a dinasorous is extinct, what is the probability of spotting it in a game park.

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