Republic of Zambia
MATHEMATICS
HIGH SCHOOL SYLLABUS
GRADES 10 – 12
Prepared by:
Curriculum Development Centre
P.O. Box 50092
LUSAKA
© 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 SECRETARY
MINISTRY OF EDUCATION
LUSAKA-ZAMBIA
ii
ACKNOWLEDGEMENT
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.
iii
INTRODUCTION
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.
iv
GENERAL AIMS
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.
v
TERMINAL OBJECTIVES
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.
vi
TIME AND PERIOD ALLOCATION
This syllabus is a three-year course in mathematics and will require seven 40 minute periods per week.
vii
GRADE 10
TOPIC
SPECIFIC OBJECTIVE
BOYS AND GIRILS SHOULD BE ABLE TO:
1. NUMBER AND
NUMERATION.
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.
3. COMMON
(VULGAR) AND
DECIMAL
FRACTIONS AND
PERCENTAGES.
3.1
NOTES
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.
Convert common fractions to decimal fractions and
vice versa.
3.2 Convert common fractions to percentages and viceversa.
3.3 Convert decimal fractions to percentages and viceversa.
3.4 Add, substract, multiply and divide common and
decimal fractions.
1
TOPIC
SPECIFIC OBJECTIVE
BOYS AND GIRILS SHOULD BE ABLE TO:
NOTES
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, SQUARE
ROOTS.
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. COMMON
LOGARITHMS.
7.1
7.2
8. SETS.
8.1
8.2
8.3
Use tables to find logarithms and
antilogarithms.
Use logarithms to solve problems.
Use appropriate set language and notation.
Carry out operations on sets.
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.
2
TOPIC
SPECIFIC OBJECTIVE
BOYS AND GIRILS SHOULD BE ABLE TO:
9. BASIC PROSESSES
OF ALGEBRA.
9.1
9.2
9.3
10. FACTORISATION.
10.1 Factorise algebraic expressions.
11. FORMULAE.
11.1 Construct and use formulae.
11.2 Change subject of formulae.
12. EQUATIONS AND
INEQUALITIES.
12.1 Solve linear equations in one
variable.
12.2 Solve simultaneous equations in
two variables.
12.3 Solve linear inequations in one
variable.
NOTES
Collect and simplify like terms.
Interpret and use brackets.
Add and substract algebraic expressions.
Types of Algebraic
include:
ax ± ay
ax ± bx ± kay ± kby
a²x² - b²y²
a² ± 2ab + b²
ax² ± bx ± c.
expressions
should
Variety of methods of solving simultaneous
equations should be encouraged.
Excluding use of matrix method.
3
TOPIC
SPECIFIC OBJECTIVE
BOYS AND GIRILS SHOULD BE ABLE TO:
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.
Construct angles of 30º, 45º, 60º, and
90º.
Construct angle bisectors.
Construct a perpendicular to a
given line
Use mathematical instruments to construct
geometrical figures.
14.2
14.3
14.4
14.5
15. SCALE DRAWING
AND BEARINGS,
15.1 Draw shapes to scale.
15.2 Solve problems involving scale
Drawing.
15.3 Solve problems on bearings.
16. PYTHAGORAS
THEOREM.
16.1 Demonstrate and apply Pythagoras
Theorem.
NOTES
Use three figures bearings – measured
clockwise from the north.
4
TOPIC
SPECIFIC OBJECTIVE
BOYS AND GIRILS SHOULD BE ABLE TO:
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.
NOTES
5
GRADE 11
TOPIC
1.
APPROXIMATIONS
AND SCIENTIFIC
NOTATION
SPECIFIC OBJECTIVE
BOYS AND GIRILS SHOULD BE ABLE TO:
1.1
Approximate quantities.
1.2
Approximate measures to a given
degree of accuracy.
Write numbers correct to the required
number of decimal places.
Write numbers correct to the required
number of significant figures.
Write numbers in scientific notation
(Standard form).
1.3
1.4
1.5
1.6
1.7
NOTES

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 is
Ax10ⁿ 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.
Calculate estimates of error.
Use approximations to estimate an
Error.
6
TOPIC
2.
RELATIONS AND
FUNCTIONS.
SPECIFIC OBJECTIVE
BOYS AND GIRILS SHOULD BE ABLE TO:
2.1
2.2
2.3
Relate members of 2 or more sets
according to a given rule.
Determine relationships that are
functions.
Use function notation.
NOTES



3.
GRAPHS OF
POLYNOMIAS.
3.1
3.2
3.3
3.4
3.5
4.1
4.
QUADRATIC
EQUATIONS.
4.2
Draw and interpret graph of
Straight lines.
Draw and interpret graphs of quadratic and
cubic functions.
Calculate the gradient of a curve at a
given point.
Estimate the area under the curve.
Draw graphs using out of real life
Situation.
Solve quadratic equations
algebraically.
Familiarity with terminology of:
- Domain,
- Range, and
- Mapping.
Example of function notation could be
F(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

Attention should be paid to:
- Completing tables of values of
functions.
- the Equation of a line
y = mx + c
recognise what y, m, x and c stands for.
- determining gradient and equation of a
line given 2 points.

The algebraic methods should include:
- factorisation
- completing the square
- use of formular.
Solve quadratic equations
graphically.
7
TOPIC
5.
RATION,
PROPORTION AND
RATE.
SPECIFIC OBJECTIVE
BOYS AND GIRILS SHOULD BE ABLE TO:
5.1
5.2
5.3
6.
VARIATION.
Solve problems involving ratio.

Solve problems involving direct and inverse
proportion.
Use and demonstrate understanding of common
measures of rate.

NOTES
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
5.4
Solve Environmental problems involving ratio,
proportion and rate.
6.1
Distinguish between inverse and direct
- Number of people in a household and how
variation
long a bag of mealie meal can last.
Express a given variation mathematically
using symbols.
Change a given variation expressed mathematically
into an equation.
Solve problems on direct and inverse
- The price of electricity in relation to the
variation.
number of people who can afford to pay.
Draw graphs of direct and inverse variation.
Interpret graphs of direct and inverse variation.
6.2
6.3
6.4
6.5
6.6
8
TOPIC
7.
8.
SPECIFIC OBJECTIVE
BOYS AND GIRILS SHOULD BE ABLE TO:
6.7 Solve problems based on other forms of direct and
inverse variation of the form y = xn,
where -3 ≤ n ≤ 3
6.8 Solve problems based on joint variation.
6.9 Solve problems on partial variation.
DISTANCE-TIME
AND SPEED-TIME
GRAPHS.
7.1
SYMMETRY IN TWO
DIMENSIONS.
8.1
7.2
NOTES
Draw and interpret speed-time and distance-time 
graphs.
Calculate the distance covered in a specified time 
from a speed time graph.
Identify line symmetry in a two dimensional
shape.

Use the principle of area under a curve to
determine distance.
Use the gradient of a line from a speedtime graph to determine acceleration and
retardation.
Symmetry inbuilt in
environment can include:
- insects
- buildings
- flowers
- people.
the
natural
9
TOPIC
SPECIFIC OBJECTIVE
BOYS AND GIRILS SHOULD BE ABLE TO:
8.2
8.3
8.4
9. CONGRUENCE
AND SIMILARITY.
9.1
9.2
9.3
9.4
9.5
9.6
9.7
NOTES
Identify rotational symmetry in two dimensional
shapes.
Determine the order of rotational symmetry in
two dimensional shapes.
Identify symmetry inbuilt in the natural
environment.
Identify similarity in figures.
Identify congruency in figures.
Use congruency in solving problems requiring
simple logical deductions.
Find the ratio of sides of similar figures.
Calculate the unknown dies or angles in similar
figures.
Calculate the areas and volumes of similar
figures.
Identify similarity and congruency in the natural
environment.
10
TOPIC
10.
ANGLE
PROPERTIES OF A
CIRCLE AND
POLUGONS.
SPECIFIC OBJECTIVE
BOYS AND GIRILS SHOULD BE ABLE TO:
10.1
10.2
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.
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.
NOTES
Some examples of polygons are Triangle,
Quadrilateral Pentagon, Hexagon, Heptagon,
Octagon, Nonagon and Decagon.
11
TOPIC
11. MENSURATION.
SPECIFIC OBJECTIVE
BOYS AND GIRILS SHOULD BE ABLE TO:
11.1
11.2
11.3
11.4
12. LOCUS OF POINTS IN
TWO AND THREE
DIMENSION
12.1
12.2


Calculate the perimeter and area of plane
figures.
Calculate the surface area and
volumes of three dimensional
figures.
Draw nets of cones, cubes, cuboids, pyramids
and cylinders.
Use nets of figures to solve problems on surface
area.
NOTES
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.
Determine locus of a point in two
dimensions.
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.
12
TOPIC
13.
TRIGOMETRIC
RATIOS.
SPECIFIC OBJECTIVE
BOYS AND GIRILS SHOULD BE ABLE TO:
13.1
13.2
13.3
13.4
14.
STATISTICS.
15.
SEQUENCES.
Find the three trigonometric ratios of sine, Take into account angles of depression, angle
cosine and tangent of acute angle.
of elevation and real life situation.
Solve problems involving right-angled triangles
using sine, cosine and tangent ratios.
Apply trigonometric ratios to calculate angles,
heights and distances.
Apply trigonometric ratios to solve problems
involving three figure bearing.
14.1
Collect and classify data.
14.2
Present data in form of tables pie charts; bar
graph, histogram and line graph.
Interpret data.
Find mean, mode and median.
Determine most appropriate measure of central
tenancy to given situations.
14.3
14.4
14.5
15.1
15.2
15.3
NOTES
Data to be used should be from real life
situation.
Recognise and continue a sequence.
Identify patterns within and across different
sequences.
Generalise sequences into simple algebraic
statements (including expressions to the nth
term).
13
GRADE 12
TOPIC
1.
SPECIFIC OBJECTIVE
BOYS AND GIRILS SHOULD BE ABLE TO:
GRAPHICAL
REPRESENTATION
OF INEQUALITIES.
1.1
Solve simple linear inequations.
1.2
Represent inequations in one variable on a number
line.
Represent inequations in two variable on the
graph.
Form a linear inequation arising from a given
situation.
Form a system of linear inequations arising from
given situations (mathematical model).
Apply the solution set of a system of linear
inequations to solve linear programming problems.
1.3
1.4
1.5
1.6
2.
VECTORS IN
DIMENSIONS.
TWO
2.1
2.2
NOTES
In illustrating inequations on a Cartesian
diagram, shade the unwanted region.
Represent and interpret vector in different
forms.
Add and subtract vectors in directed line
segment or component form.
14
TOPIC
3.
MATRICES.
SPECIFIC OBJECTIVE
BOYS AND GIRILS SHOULD BE ABLE TO:
NOTES
2.3
Multiply a vector by a scalar.
2.4
2.5
2.6
Express a vector in terms of a position vector.
Find the magnitude of a vector.
Use vectors to solve problems involving
properties of a set of points or a set of lines.
3.1
Present and interpret data in a rectangular array Common usage of matrices is league tables.
of numbers (matrix).
State the order of a matrix.
Identify and use equal matrices.
Add and subtract matrices.
Multiply a matrice by a scalar.
Multiply matrix.
Find the determinant of a square matrix of order
2.
Find the inverse of a square matrix of order 2.
Use matrices to solve simultaneous equations.
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
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.
15
TOPIC
4.
TRANSFORMATIONS
OF THE PLANE.
SPECIFIC OBJECTIVE
BOYS AND GIRILS SHOULD BE ABLE TO:
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
NOTES
Find the image of a shape under a
translation.
Find the column vector representing a
translation.
Find the image of a shape under a
reflection.
Find the equation of the mirror line in a
reflection.
Find the image of a shape under a rotation.
Find the centre, angle and direction of
a rotation.
Find the image of a shape under an
enlargement.
Find the centre and scale factor of an
enlargement.
Find the image of a shape under a shear.
Find the invariant line and shear factor
of a shear.
16
TOPIC
SPECIFIC OBJECTIVE
BOYS AND GIRILS SHOULD BE ABLE TO:
4.11
4.12
4.13
4.14
4.15
4.16
5.
EARTH GEOMETRY
5.1
5.2
5.3
5.4
5.5
5.6
NOTES
Find the image of a shape under a
stretch.
Find the invariant line and scale factor
of a stretch.
Find the image of a shape under a combination of
transformations.
Describe transformations using co-ordinates and
matrices.
State the properties of each transformation.
Identify and describe a transformation fully.
Identify parts of a sphere; radius, small circles
and great circles.
Locate points on the surface of the earth using
latitudes and longitudes.
Calculate the radius of a parallel of latitude given
the radius of the earth.
Calculate distances on parallels of latitude and
longitudes.
Determine a latitude given its circumference.
Find the shortest distance between two places on
the same parallel of latitude.
17
TOPIC
6.
TRIGONOMETRY.
SPECIFIC OBJECTIVE
BOYS AND GIRILS SHOULD BE ABLE TO:
6.1
6.2
6.3
6.4
7.
STATISTICS.
7.1
7.2
7.3
7.4
NOTES
Find sine, cosine and tangent of angles
from 0º to 360º.
Use sine rule to solve problems involving
triangles.
Use cosine rule to solve problems involving
triangles.
Use the sine ratio to find the area of a
triangle (½ ab Sin C).
Construct and use cummulative frequency
The following are measures of dispersion.
curves.
Find the median, lower and upper
Median, lower and upper quartile, semi
quartiles.
Interquartile.
Find the range, the interquartile and the semiinterquartile range and distinguish between the
purposes for which they are used.
Find and interpret the percentile range.
18
TOPIC
8.
PROBABILITY.
SPECIFIC OBJECTIVE
BOYS AND GIRILS SHOULD BE ABLE TO:
8.1
Find probabilities of singles events
experimentally.
8.2
Find probabilities of single events
theoretically.
Find expected frequency of an event.
Find probabilities of mutually exclusive,
independent and dependent events.
Use outcome tables (grids) and tress diagrams to
find probabilities.
8.3
8.4
8.5
NOTES
Use probabilities in an environment context
e.g. If a dinasorous is extinct, what is the
probability of spotting it in a game park.
19