# WAEC Syllabus for Mathematics and Recommended Textbooks

See the **Waec Syllabus for Mathematics**. Note that this syllabus is for both Internal and external candidates..

WEST AFRICAN SENIOR SCHOOL CERTIFICATE EXAMINATION

MATHEMATICS (CORE)/GENERAL MATHEMATICS

PREAMBLE

For all papers which involve mathematical calculations, mathematical and statistical tables published for WAEC should be used in the examination room. However, the use of non-programmable, silent and cordless calculator is allowed. The calculator must not have a paper printout. Where the degree of accuracy is not specified in a question the degree of accuracy expected will be that obtainable from the WAEC mathematical tables. Trigonometrical tables

in the pamphlet have different columns for decimal fractions of a degree, not for minutes and seconds.

No mathematical tables other than the above may be used in the examination. It is strongly recommended that schools/candidates obtain copies of these tables for use throughout the course.

Candidates should bring rulers, protractors, pair of compasses and set squares for all papers.

They will not be allowed to borrow such instruments and any other materials from other candidates in the examination hall. It should be noted that some questions may prohibit the use of tables and /or calculators. The use of slide rules is not allowed.

Graph paper ruled in 2 mm squares, will be provided for any paper in which it is required.

UNITS

Candidates should be familiar with the following units and their symbols.

Length

10000 millimetres (mm) = 100 centimetres (cm) = 1 metre (m)

1000 metres = 1 kilometre (km)

Area

10,000 square metres (m2) = 1 hectare (ha)

Cubic Capacity

1000 cubic centimetres (cm3) = 1 litre (1)

Mass

1000 milligrammes (mg) = 1 gramme (g)

1000 grammes (g) = 1 kilogramme (kg)

WEST AFRICAN SENIOR SCHOOL CERTIFICATE EXAMINATION

MATHEMATICS (CORE)/GENERAL MATHEMATICS

324

CURRENCIES

The Gambia – 100 bututs (b) = 1 dalasi (D)

Ghana – 100 pesewas (p) = 1 Ghana cedi GH(¢)

Liberia – 100 cents (c) = 1 dollar ($)

*Nigeria – 100 kobo (k) = 1 naira (N)

*Sierra Leone – 100 cents (c) = 1 leone (Le)

U. K. – 100 pence (p) = 1 pound (£)

U.S.A. – 100 cents (c) = 1 dollar ($)

French speaking territories : 100 centimes (c) = 1 franc (fr)

Any other units used will be defined.

*General Mathematics/Mathematics (Core).

**AIMS OF THE SYLLABUS**

The syllabus is not intended to be used as a teaching syllabus. Teachers are advised to use

their own National teaching syllabuses. The aims of the syllabus are to test:

(i) computational skills;

(ii) the understanding of mathematical concepts and their applications to everyday living;

(iii) the ability to translate problems into mathematical language and solve them with

related mathematical knowledge;

(iv) the ability to be accurate to a degree relevant to the problems at hand;

(v) precise, logical and abstract thinking.

**EXAMINATION FORMAT**

There will be two papers both of which must be taken.

PAPER 1 – 11/2 hours

PAPER 2 – 21/2 hours

PAPER 1 will contain 50 multiple choice questions testing the whole syllabus excluding those

sections of the syllabus marked with asterisks (*). Candidates are expected to attempt all the

questions. This paper will carry 50 marks.

PAPER 2 will consist of two parts, I and II. This paper will carry 100 marks.

PART I (40 marks) will contain five compulsory questions which are elementary in nature and

will exclude questions on those sections of the syllabus marked with asterisks (*).

PART II (60 marks) will contain ten questions of greater length and difficulty including

questions on those sections of the syllabus marked with asterisks (*). Candidates are expected

to answer any five of the questions. The number of questions from the asterisked sections of

the syllabus would not exceed four.

NOTE : (1) Topics marked with asterisks are to be tested in Part II of Paper 2 only.

(2) Topics marked with double asterisks (**) are peculiar to Ghana.

Questions on such topics should not be attempted by candidates in

Nigeria.

**DETAILED SYLLABUS**

The topics, contents and notes are intended to indicate the scope of the questions which will be

set. The notes are not to be considered as an exhaustive list of illustrations/limitations.

Sections of the syllabus marked with asterisks (*) will be tested only as options in Part II of

Paper 2.

**WASSCE GENERAL MATHEMATICS/MATHEMATICS (CORE) SYLLABUS**

**TOPICS CONTENTS NOTES**

A. NUMBER AND NUMERATION

**(a) Number Bases**

(i) Binary numbers

**(ii) Modular arithmetic

Conversions from base 2 to base 10 and

vice versa. Basic operations excluding

division. Awareness of other number

bases is desirable.

Relate to market days, the clock etc.

Truth sets (solution sets) for various open

sentences, e.g. 3 x 2 = a(mod) 4, 8 + y =

4 (mod) 9.

**(b) Fractions, decimals and approximations**

(i) Basic operations on

fractions and decimals.

(ii) Approximations and

significant figures

Approximations should be realistic e.g. a

road is not measured correct to the

nearest cm. Include error.

**(c) Indices**

(i) Laws of indices.

(ii) Numbers in standard

form.

Include simple examples of negative and

fractions indices.

e.g. 375.3 = 3.753 x 102

0.0035 = 3.5 x 10-3

Use of tables of squares,

square roots and reciprocals.

**(d) Logarithms**

(i) Relationship between

indices and

logarithms e.g.

y = 10k → K = log10 y

(ii) Basic rules of logarithms i.e.

log10 (pq) = log10P + log10q

log10 (p/q) = log10 P – log10q

log10Pn = nlog10P

(iii) Use of tables of logarithms,

Base 10 logarithm and

Antilogarithm tables.

Calculations involving

multiplication, division,

powers and square roots.

**(e) Sequence**

(i) Patterns of sequences.

Determine any term of a

given sequence.

*(ii) Arithmetic Progression (A.P)

Geometric Progression (G.P).

The notation Un = the nth term of

a sequence may be used.

Simple cases only, including word

problems. Excluding sum Sn.

**(f) Sets**

(i) Idea of sets, universal set,

finite and infinite sets, subsets,

empty sets and disjoint sets;

idea of and notation for union,

intersection and complement of

sets.

(ii) Solution of practical problems

involving classification, using

Venn diagrams.

Notations: ℰ,, , , , , P1

(the complement of P).

* Include commutative,

associative and distributive

properties.

The use of Venn diagrams

restricted to at most 3 sets.

**(g) Logical reasoning Simple statements. True and false

statements. Negation of

statements.

Implication, equivalence and valid

arguments.

Use of symbols : ~, , , .

Use of Venn diagrams preferable.

WEST AFRICAN SENIOR SCHOOL CERTIFICATE EXAMINATION

MATHEMATICS (CORE)/GENERAL MATHEMATICS

327

TOPICS CONTENTS NOTES

(h) Positive and Negative

integers. Rational numbers

The four basic operations on

rational numbers

Match rational numbers with

points on the number line.

Notation: Natural numbers (N),

Integers (Z), Rational numbers

(Q)

(i) Surds

Simplification and

Rationalisation of simple surds.

Surds of the form a and a b

b

where a is a rational and b is a

positive integer.

(j) Ratio, Proportion

and Rates

Financial partnerships; rates of

work, costs, taxes, foreign

exchange, density (e.g. for

population) mass, distance,

time and speed.

Include average rates.

(k) Variation

Direct, inverse and partial

variations.

*Joint variations.

Application to simple practical

problems.

(l) Percentages

Simple interest, commission,

discount, depreciation, profit

and loss, compound interest

and hire purchase.

Exclude the use of compound

interest formula.

B. ALGEBRAIC

PROCESSES

(a) Algebraic

Expressions

(i) Expression of

statements in symbols.

(ii) Formulating algebraic

expressions from given

situations.

(iii) Evaluation of algebraic

expressions.

eg. Find an expression for the

cost C cedis of 4 pears at x cedis

each and 3 oranges at y cedis each

C = 4x + 3y

If x = 60 and y = 20.

Find C.

(b) Simple operations on

algebraic xpressions.

(i) Expansion

(ii) Factorisation

e.g. (a+b) (c+d). (a+3) (c+4)

Expressions of the form

(i) ax + ay

(ii) a (b+c) +d (b+c)

(iii) ax2 + bx +c

where a,b,c are integers

(iv) a2 – b2

Application of difference of two

squares e.g.

492 – 472 = (49 + 47) (49 – 47)

= 96 x 2 = 192

(c) Solution of linear

equations

(i) Linear equations in one variable

(ii) Simultaneous linear equations

in two variables.

(d) Change of subject of

a formula/relation

(i) Change of subject of a

formula/relation

(ii) Substitution

e.g. find v in terms of f and u

given that

1 1 1

— = — + —

ƒ u v

(e) Quadratic

equations

(i) Solution of quadratic equations

(ii) Construction of quadratic

equations with given roots.

(iii) Application of solution of

quadratic equations in practical

problems.

Using ab = 0 either a = 0 or b

= 0

* By completing the square and

use of formula.

Simple rational roots only.

e.g. constructing a quadratic

equation.

Whose roots are –3 and 5/2

=> (x = 3) (x – 5/2) = 0.

(f) Graphs of Linear

and quadratic

functions.

(i) Interpretation of graphs,

coordinates of points, table

of values. Drawing

quadratic graphs and

obtaining roots from graphs.

(ii) Graphical solution of a

pair of equations of the

form

y = ax2 + bx + c and

y = mx + k

(iii) Drawing of a tangent to

curves to determine

gradient at a given point.

(iv) The gradient of a line

** (v) Equation of a Line

Finding:

(i) the coordinates of the

maximum and minimum

points on the graph;

(ii) intercepts on the axes.

Identifying axis of

Symmetry. Recognising

sketched graphs.

Use of quadratic graph to

solve a related equation

e.g. graph of y = x2 + 5x + 6

to solve x2 + 5x + 4 = 0

(i) By drawing relevant

triangle to determine the

gradient.

(ii) The gradient, m, of the line

joining the points

(x1, y1) and (x2, y2) is

y2 – y1

m =

x2 – x1

Equation in the form

y = mx + c or y – y1 = m(x-x1)

**(g) Linear inequalities**

(i) Solution of linear

inequalities in one variable

and representation on the

number line.

(ii) Graphical solution of linear

inequalities in two variables

Simple practical problems

**** (h) Relations and functions**

(i) Relations

(ii) Functions

Various types of relations

One – to – one,

many – to – one,

one – to – many,

many – to – many

The idea of a function.

Types of functions.

One – to – one,

many – to – one.

(i) Algebraic fractions

Operations on algebraic

fractions

(i) with monomial

denominators.

(ii) with binomial

denominators.

Simple cases only e.g.

1 1 x + y

— + — = —- (x 0, and y0)

x y xy

Simple cases only e.g.

1 + 1 = 2x – a – b

x –b x – a (x-a) (x – b)

where a and b are constants and

xa or b.

Values for which a fraction is

not defined e.g.

1

x + 3 is not defined for x = -3.

**C. MENSURATION**

(a) Lengths and Perimeters

(i) Use of Pythagoras

theorem, sine and cosine

rules to determine

lengths and distances.

(ii) Lengths of arcs of

circles. Perimeters of

sectors and Segments.

*(iii) Latitudes and Longitudes.

No formal proofs of the theorem

and rules are required.

Distances along latitudes and

longitudes and their

corresponding angles.

(b) Areas

(i) Triangles and special

quadrilaterals – rectangles,

parallelograms and trapezia.

(ii) Circles, sectors and

segments of circles.

(iii) Surface areas of cube, cuboid,

cylinder, right triangular prisms

and cones. *Spheres.

Areas of similar figures.

Include area of triangles is

½ base x height and *1/2 abSin C.

Areas of compound shapes.

Relation between the sector of a

circle and the surface area of a

cone.

**(c) Volumes**

(i) Volumes of cubes, cuboid,

cylinders, cones and right

pyramids. * Spheres.

(ii) Volumes of similar solids

Volumes of compound shapes.

**D. PLANE GEOMETRY**

(a) Angles at a point

(i) Angles at a point add up to

360.

(ii) Adjacent angles on a

straight line are supplementary.

(iii) Vertically opposite angles are

equal.

The results of these standard

theorems stated under contents

must be known but their formal

proofs are not required.

However, proofs based on the

knowledge of these theorems

may be tested.

The degree as a unit of measure.

Acute, obtuse, reflex angles.

(b) Angles and intercepts on parallel lines

(i) Alternate angles are equal.

(ii) Corresponding angles are equal.

(iii) Interior opposite angles are

supplementary.

*(iv) Intercept theorem

Application to proportional

division of a line segment.

(c) Triangles and other

polygons

(i) The sum of the angles of a

triangle is 2 right angles.

(ii) The exterior angle of a

triangle equals the sum of

the two interior opposite

angles.

(iii) Congruent triangles.

(iv) Properties of special

triangles – isosceles,

equilateral, right-angled.

(v) Properties of special

quadrilaterals –

parallelogram, rhombus,

rectangle, square,

trapezium.

(vi) Properties of similar

triangles.

(vii) The sum of the angles of a

polygon.

(viii) Property of exterior angles

of a polygon.

(ix) Parallelograms on the same

base and between the same

parallels are equal in area.

Conditions to be known but

proofs not required. Rotation,

translation, reflection and lines

of symmetry to be used.

Use symmetry where applicable.

Equiangular properties and ratio

of sides and areas.

(d) Circles

(i) Chords

(ii) The angle which an arc of a

circle subtends at the centre

is twice that which it

subtends at any point on the

remaining part of the

circumference.

(iii) Any angle subtended at the

circumference by a diameter

is a right angle.

Angles subtended by chords in a

circle, at the centre of a circle.

Perpendicular bisectors of

chords.

(iv) Angles in the same segment

are equal

(v) Angles in opposite

segments are supplementary.

(vi) Perpendicularity of tangent and

radius.

(vii) If a straight line touches a circle

at only one point and from the

point of contact a chord is drawn,

each angle which this chord

makes with the tangent is equal

to the angle in the alternative

segment.

(e) Construction

(i) Bisectors of angles and line

segments.

(ii) Line parallel or perpendicular

to a given line.

(iii) An angle of 90º, 60º, 45º, 30º

and an angle equal to a given

angle.

(iv) Triangles and quadrilaterals

from sufficient data.

Include combination of these

angles e.g. 75º, 105º, 135º,

etc.

(f) Loci

Knowledge of the loci listed below and

their intersections in 2 dimensions.

(i) Points at a given distance from a

given point.

(ii) Points equidistant from two

given points.

(iii) Points equidistant from two

given straight lines.

(iv) Points at a given distance from

a given straight line.

Consider parallel and

intersecting lines.

E. TRIGONOMETRY

(a) Sine, cosine and

tangent of an angle.

(b) Angles of elevation

and depression.

(c) Bearings

(i) Sine, cosine and tangent

of an acute angle.

(ii) Use of tables.

(iii) Trigonometric ratios of

30º, 45º and 60º.

*(iv) Sine, cosine and

tangent of angles

from 0º to 360º.

*(v) Graphs of sine and

cosine.

Calculating angles of elevation and

depression. Application to heights

and distances.

(i) Bearing of one point from

another.

(ii) Calculation of distances

and angles.

Without use of tables.

Related to the unit circle.

0º ≤ x ≥ 360º

Easy problems only

Easy problems only

Sine and cosine rules may be

used.

**E. STATISTICS AND**

** PROBABILITY**

**(a) Statistics**

(i) Frequency distribution.

(ii) Pie charts, bar charts,

histograms and frequency

polygons.

(iii) Mean, median and mode

for both discrete and

grouped data.

(iv) Cumulative frequency

curve, median; quartiles

and percentiles.

(v) Measures of dispersion:

range, interquartile range,

mean deviation and

standard deviation from the

mean.

Reading and drawing simple

inferences from graphs and

interpretations of data in

histograms.

Exclude unequal class interval.

Use of an assumed mean is

acceptable but nor required. For

grouped data, the mode should

be estimated from the histogram

and the median from the

cumulative frequency curve.

Simple examples only. Note

that mean deviation is the mean

of the absolute deviations.

**(b) Probability**

(i) Experimental and

theoretical probability.

(ii) Addition of probabilities

for mutually exclusive and

independent events.

(iii) Multiplication of

probabilities for

independent events.

Include equally likely events e.g.

probability of throwing a six

with fair die, or a head when

tossing a fair coin.

Simple practical problems only.

Interpretation of ‘and’ and ‘or’

in probability.

****(G) VECTORS AND TRANSPORMATIONS IN A PLANE**

(a) Vectors in a Plane.

(i) Vector as a directed line

segment, magnitude,

equal vectors, sums and

differences of vectors.

(ii) Parallel and equal

vectors.

(iii) Multiplication of a

vector by a scalar.

(iv) Cartesian components of

a vector.

Column notation. Emphasis on

graphical representation.

Notation

0

0 for the zero

vector.

(b) Transformation in the

Cartesian Coordinate

plane.

(i) Reflection

(ii) Rotation

(iii) Translation

The reflection of points and

shapes in the x and y axes and in

the lines x = k and y = k, where

k is a rational number.

Determination of the mirror

lines of points/shapes and their

images.