WAEC Syllabus for Mathematics and Recommended Textbooks

Filed in West African Examinations Council by on April 5, 2016 0 Comments

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

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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.

Candidates should be familiar with the following units and their symbols.
10000 millimetres (mm) = 100 centimetres (cm) = 1 metre (m)
1000 metres = 1 kilometre (km)
10,000 square metres (m2) = 1 hectare (ha)
Cubic Capacity
1000 cubic centimetres (cm3) = 1 litre (1)
1000 milligrammes (mg) = 1 gramme (g)
1000 grammes (g) = 1 kilogramme (kg)




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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).


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.


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


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.



(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

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

(ii) Solution of practical problems
involving classification, using
Venn diagrams.

Notations: ℰ,, , , , , P1
(the complement of P).
* Include commutative,
associative and distributive

The use of Venn diagrams
restricted to at most 3 sets.

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

Implication, equivalence and valid

Use of symbols : ~, , , .

Use of Venn diagrams preferable.



(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

(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
*Joint variations.

Application to simple practical

(l) Percentages

Simple interest, commission,
discount, depreciation, profit
and loss, compound interest
and hire purchase.

Exclude the use of compound
interest formula.


(a) Algebraic

(i) Expression of
statements in symbols.

(ii) Formulating algebraic
expressions from given

(iii) Evaluation of algebraic

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

(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

(ii) Substitution

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

1 1 1
— = — + —
ƒ u v

(e) Quadratic

(i) Solution of quadratic equations

(ii) Construction of quadratic
equations with given roots.

(iii) Application of solution of
quadratic equations in practical

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

Whose roots are –3 and 5/2

=> (x = 3) (x – 5/2) = 0.

(f) Graphs of Linear
and quadratic

(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

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

(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

(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

(i) with monomial

(ii) with binomial

Simple cases only e.g.
1 1 x + y
— + — = —- (x  0, and y0)
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
xa or b.

Values for which a fraction is
not defined e.g.
x + 3 is not defined for x = -3.


(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

(c) Volumes

(i) Volumes of cubes, cuboid,
cylinders, cones and right
pyramids. * Spheres.

(ii) Volumes of similar solids

Volumes of compound shapes.


(a) Angles at a point

(i) Angles at a point add up to

(ii) Adjacent angles on a
straight line are supplementary.

(iii) Vertically opposite angles are

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

*(iv) Intercept theorem

Application to proportional
division of a line segment.

(c) Triangles and other

(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

(iii) Congruent triangles.

(iv) Properties of special
triangles – isosceles,
equilateral, right-angled.

(v) Properties of special
quadrilaterals –
parallelogram, rhombus,
rectangle, square,

(vi) Properties of similar

(vii) The sum of the angles of a

(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

(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

(iv) Angles in the same segment
are equal

(v) Angles in opposite
segments are supplementary.

(vi) Perpendicularity of tangent and

(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

(e) Construction

(i) Bisectors of angles and line

(ii) Line parallel or perpendicular
to a given line.

(iii) An angle of 90º, 60º, 45º, 30º
and an angle equal to a given

(iv) Triangles and quadrilaterals
from sufficient data.

Include combination of these
angles e.g. 75º, 105º, 135º,

(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.


(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

Calculating angles of elevation and
depression. Application to heights
and distances.

(i) Bearing of one point from

(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


(a) Statistics

(i) Frequency distribution.

(ii) Pie charts, bar charts,
histograms and frequency

(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

Reading and drawing simple
inferences from graphs and
interpretations of data in

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.


(a) Vectors in a Plane.

(i) Vector as a directed line
segment, magnitude,
equal vectors, sums and
differences of vectors.

(ii) Parallel and equal

(iii) Multiplication of a
vector by a scalar.

(iv) Cartesian components of
a vector.

Column notation. Emphasis on
graphical representation.





0 for the zero


(b) Transformation in the
Cartesian Coordinate

(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

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