Official WAEC syllabus for Mathematics 2018
WAEC syllabus for Mathematics 2018: This is what I am going to discuss in this article. This page contains the official WAEC mathematics syllabus 2018 and likely questions you should expect.
In my article titled “How to pass WAEC without cheating“, I mentioned the use of WAEC syllabus as one of the ways to blast WAEC. A lot of candidates that wants to pass WAEC started asking me for WAEC mathematics syllabus 2018. After receiving these questions, something struck my mind. I said, “I am going to write an article on WAEC syllabus for mathematics and other subjects”. If you have been searching for:
- WAEC Syllabus for mathematics 2018
- Topics to read for WAEC mathematics
- WAEC Mathematics Syllabus 2018
- Download WAEC syllabus for mathematics pdf
Then this article is for you!
After lots of research and surverys, I have found out something. Most candidate that fail WAEC don’t use the syllabus. some of them start looking for expo while others read out of the syllabus. If you want to have distinctions(As and Bs) in your upcoming WAEC examination, you should use the syllabus while preparing.
To make things easy, I am going to break this down into three parts:
- Aims of WAEC Mathematics syllabus
- WAEC Mathematics examination format
- WAEC Mathematics syllabus – All topics
- Other things you are required to know
AIMS OF THE WAEC MATHEMATICS 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:
(1) computational skills;
(2) the understanding of mathematical concepts and their applications to everyday living;
(3) the ability to translate problems into mathematical language and solve them with
related mathematical knowledge;
(4) the ability to be accurate to a degree relevant to the problems at hand;
(5) precise, logical and abstract thinking.
WAEC MATHEMATICS EXAMINATION FORMAT
There will be two papers, Papers 1 and 2, both of which must be taken.
PAPER 1: will consist of fifty multiple-choice objective questions, drawn from the common areas of the syllabus, to be answered in 1½ hours for 50 marks.
PAPER 2: will consist of thirteen essay questions in two sections – Sections A and B, to be answered in 2½ hours for 100 marks. Candidates will be required to answer ten questions in all.
Section A – Will consist of five compulsory questions, elementary in nature carrying a total of 40 marks. The questions will be drawn from the common areas of the syllabus.
Section B – will consist of eight questions of greater length and difficulty. The questions shall include a maximum of two which shall be drawn from parts of the syllabuses which may not be peculiar to candidates’ home countries. Candidates will be expected to answer five questions for 60marks.
Without wasting your time, I am going to show you the official WAEC syllabus for X right now.
WAEC SYLLABUS FOR MATHEMATICS 2018
WAEC MATHEMATICS SYLLABUS PART 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
Approximations should be realistic e.g. a
road is not measured correct to the
nearest cm. Include error.
(i) Laws of indices.
(ii) Numbers in standard
Include simple examples of negative and
e.g. 375.3 = 3.753 x 102
0.0035 = 3.5 x 10-3
Use of tables of squares,
square roots and reciprocals.
(i) Relationship between
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
powers and square roots.
(i) Patterns of sequences.
Determine any term of a
*(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.
(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
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
Match rational numbers with
points on the number line.
Notation: Natural numbers (N),
Integers (Z), Rational numbers
Rationalisation of simple surds.
Surds of the form a and a b
where a is a rational and b is a
(j) Ratio, Proportion
Financial partnerships; rates of
work, costs, taxes, foreign
exchange, density (e.g. for
population) mass, distance,
time and speed.
Include average rates.
Direct, inverse and partial
Application to simple practical
Simple interest, commission,
discount, depreciation, profit
and loss, compound interest
and hire purchase.
Exclude the use of compound
WAEC MATHEMATICS SYLLABUS PART B – 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.
(b) Simple operations on
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
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
(i) Change of subject of a
e.g. find v in terms of f and u
1 1 1
— = — + —
ƒ u v
(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
* 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
(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
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
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
(ii) Graphical solution of linear
inequalities in two variables
Simple practical problems
** (h) Relations and 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 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.
x + 3 is not defined for x = -3.
WAEC MATHEMATICS SYLLABUS PART 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
(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
(i) Volumes of cubes, cuboid,
cylinders, cones and right
pyramids. * Spheres.
(ii) Volumes of similar solids
Volumes of compound shapes.
WAEC MATHEMATICS SYLLABUS PART D – PLANE GEOMETRY
(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,
(v) Properties of special
(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.
(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
(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
(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,
Knowledge of the loci listed below and
their intersections in 2 dimensions.
(i) Points at a given distance from a
(ii) Points equidistant from two
(iii) Points equidistant from two
given straight lines.
(iv) Points at a given distance from
a given straight line.
Consider parallel and
WAEC MATHEMATICS SYLLABUS PART E – TRIGONOMETRY
(a) Sine, cosine and
tangent of an angle.
(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
(b) Angles of elevation
Calculating angles of elevation and
depression. Application to heights
(i) Bearing of one point from
(ii) Calculation of distances
Without use of tables.
Related to the unit circle.
0º ≤ x ≥ 360º
Easy problems only
Easy problems only
Sine and cosine rules may be
WAEC MATHEMATICS SYLLABUS PART F – STATISTICS AND
(i) Frequency distribution.
(ii) Pie charts, bar charts,
histograms and frequency
(iii) Mean, median and mode
for both discrete and
(iv) Cumulative frequency
curve, median; quartiles
(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.
(i) Experimental and
(ii) Addition of probabilities
for mutually exclusive and
(iii) Multiplication of
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’
WAEC MATHEMATICS SYLLABUS PPART (G) VECTORS AND TRANSPORMATIONS IN A PLANE
(a) Vectors in a Plane.
(i) Vector as a directed line
equal vectors, sums and
differences of vectors.
(ii) Parallel and equal
(iii) Multiplication of a
vector by a scalar.
(iv) Cartesian components of
Column notation. Emphasis on
0 for the zero
(b) Transformation in the
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
Rotation about the origin.
Use of the translation vector.
OTHER THINGS YOU SHOULD KNOW
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:
1000 millimetres (mm) = 100 centimetres (cm) = 1 metre(m).
1000 metres = 1 kilometre (km)
10,000 square metres (m2) = 1 hectare (ha)
1000 cubic centimeters (cm3) = 1 litre (l)
1000milligrammes (mg) = 1 gramme (g)
1000 grammes (g) = 1 kilogramme( kg )
1000 ogrammes (kg) = 1 tonne.
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.
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