GENERAL MATHEMATICS SYLLABUS FOR SSCE STUDENTS

1. AIMS OF THE SYLLABUS

The aims of the syllabus are to test candidates’:

(1) mathematical
competency and computational skills;

(2) understanding
of mathematical concepts and their relationship to the acquisition of
entrepreneurial skills for everyday living in the global world;

(3) ability to
translate problems into mathematical language and solve them using appropriate
methods;

(4) ability to be
accurate to a degree relevant to the problem at hand;

(5) logical,
abstract and precise thinking.

This syllabus is not intended to be used as a teaching syllabus. Teachers are advised to use their own National teaching syllabuses or
curricular for that purpose.

1. EXAMINATION SCHEME

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.

2. 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.

TOPICS CONTENTS NOTES

A. NUMBER AND NUMERATION

( a ) Number bases

( i ) conversion of numbers from one base to another

( ii ) Basic operations on number bases

Conversion from one base to base 10 and vice versa.
Conversion from one base to another base .

Addition, subtraction and multiplication of number bases.

(b) Modular Arithmetic

(i) Concept of
Modulo Arithmetic.

(ii) Addition,
subtraction and multiplication operations in modulo arithmetic.

(iii) Application
to daily life

Interpretation of modulo arithmetic e.g.

6 + 4 = k(mod7),

3 x 5 = b(mod6), m = 2(mod 3), etc.

Relate to market days, clock,shift duty, etc.

( c ) 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.

( d ) Indices

( i ) Laws of indices

e.g. ax x ay = ax + y , ax÷ay = ax – y, (ax)y = axy, etc
where x, y are real numbers and a ≠0. Include simple examples of

( ii ) Numbers in standard form ( scientific notation) negative and fractional indices.

Expression of large and small numbers in standard form e.g.
375300000 = 3.753 x 108

0.00000035 = 3.5 x 10-7

Use of tables of squares, square roots and reciprocals is
accepted.

( e) Logarithms

( i ) Relationship between indices and logarithms e.g. y = 10k implies log10y = k.

( ii ) Basic rules of logarithms e.g. log10(pq) = log10p +
log10q log10(p/q) = log10p – log10q log10pn = nlog10p.

(iii) Use of tables of logarithms and antilogarithms.

Calculations involving multiplication, division, powers and
roots.

( f ) Sequence and Series (i) Patterns of sequences.

(ii) Arithmetic
progression (A.P.) Geometric Progression (G.P.) Determine
any term of a given sequence. The notation Un = the nth termof a sequence may
be used.

Simple cases only, including word problems. (Include sum for
A.P. and exclude sum for G.P).

( g ) Sets (i) Idea
of sets, universal sets, 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: s, <, 𝖴, ∩, { }, Ø, P’( the compliment of P).

• • properties
e.g. commutative, associative and distributive

Use of Venn diagrams restricted to at most 3 sets.

( h ) Logical Reasoning Simple
statements. True and false statements. Negation of

statements, implications. Use
of symbols: ⟹, ➛, use of Venn diagrams.

(i) 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 ).

( j ) Surds (Radicals) Simplification
and rationalization of simple surds. Surds
of the form 𝑎 , a√𝑏 and

√𝑏

a ±√𝑏where a is a rational
number and b is a positive integer.

Basic operations on surds (exclude surd of the form

𝑎 ).

𝑏+𝑐 √𝑑

• ( k )
Matrices and

Determinants ( i )
Identification of order, notation and types of matrices.

( ii ) Addition, subtraction, scalar multiplication and
multiplication of matrices.

( iii ) Determinant of a matrix Not more than 3 x 3 matrices. Idea of columns and rows.

Restrict to 2 x 2 matrices.

Application to solving simultaneous linear equations in two
variables. Restrict to 2 x 2 matrices.

( l ) Ratio, Proportions and Rates Ratio between two similar quantities.

Proportion between two or more similar quantities.

Financial partnerships, rates of work, costs, taxes, foreign
exchange, density (e.g. population), mass, distance, time and speed. Relate to real life situations. Include
average rates, taxes

e.g. VAT, Withholding tax, etc

( m ) Percentages Simple
interest, commission, discount, depreciation, profit and loss, compound
interest, hire purchase and percentage error. Limit
compound interest to a maximum of 3 years.

( n) Financial Arithmetic (
i ) Depreciation/ Amortization. Definition/meaning,
calculation of depreciation on fixed assets, computation of

amortization on capitalized assets.

( ii ) Annuities

(iii ) Capital Market Instruments

Definition/meaning, solve simple problems on annuities.

Shares/stocks, debentures, bonds, simple problems on
interest on bonds and debentures.

( o ) Variation Direct,
inverse, partial and joint variations. Expression
of various types of variation in mathematical symbols e.g. direct (z n ),
inverse (z 1), etc.

𝑛

Application to simple practical problems.

B. ALGEBRAIC PROCESSES

( a ) Algebraic expressions

(i) Formulating algebraic expressions from given situations

( ii ) Evaluation of algebraic expressions

e.g. find an expression for the cost C Naira of 4 pens at x
Naira each and 3 oranges at y naira each.

Solution: C = 4x + 3y

e.g. If x =60 and y = 20, find

C.

C = 4(60) + 3(20) = 300

naira.

( b ) Simple operations on algebraic expressions ( i ) Expansion (ii ) Factorization

• • (iii)
Binary Operations e.g. (a +b)(c + d),
(a + 3)(c - 4), etc.

factorization of expressions of the form ax + ay,

a(b + c) + d(b + c), a2 – b2, ax2 + bx + c where a, b, c are
integers.

Application of difference of two squares e.g. 492 – 472 =
(49 + 47)(49 – 47) = 96 x 2

= 192.

Carry out binary operations on real numbers such as: a*b

= 2a + b – ab, etc.

( c ) Solution of Linear Equations ( i ) Linear equations in one variable Solving/finding the truth set (solution set) for linear

( ii ) Simultaneous linear equations in two variables. equations in one variable.

Solving/finding the truth set of simultaneous equations in
two variables by elimination, substitution and graphical methods. Word problems
involving one or two variables

( d ) Change of Subject of a Formula/Relation ( i ) Change of subject of a
formula/relation

(ii) Substitution. e.g.
if1 = 1 + 1, find v.

ƒ 𝑢 𝑣

Finding the value of a variable e.g. evaluating v given the
values of u and f.

( e ) Quadratic Equations (
i ) Solution of quadratic equations

(ii) Forming
quadratic equation with given roots.

(iii) Application
of solution of quadratic equation in practical problems. Using factorization i.e. ab = 0

⇒ either a = 0 or b = 0.

• By
completing the square and use of formula

Simple rational roots only e.g. forming a quadratic equation

whose roots are -3 and 5 ⇒ (x2 + 3)(x - 5) = 0.2

(f) Graphs of Linear and Quadratic functions.

(i) Interpretation of graphs, coordinate
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 tangents to curves to determine the
gradient at a given point. Finding:

(i) the
coordinates of maximum and minimum points on the graph.

(ii) intercepts on
the axes, identifying axis of symmetry, recognizing sketched graphs.

Use of quadratic graphs to solve related equations e.g.
graph of y = x2 + 5x + 6 to solve x2 + 5x
+ 4 = 0.

Determining the gradient by drawing relevant triangle.

( g ) Linear Inequalities

(i) Solution of linear inequalities in one variable and

representation on the number line.

Truth set is also required. Simple practical problems

(ii) Graphical solution of linear inequalities in two
variables.

(iii) Graphical solution of simultaneous linear
inequalities in two variables.

Maximum and minimum values. Application to real life
situations e.g. minimum cost, maximum profit, linear programming, etc.

( h ) Algebraic Fractions

Operations on algebraic fractions with:

( i ) Monomial denominators

( ii ) Binomial denominators

Simple cases only e.g. 1 + 1

𝑥 𝑦

= 𝑥+𝑦(
xG0, yG 0).

𝑥𝑦

Simple cases only e.g. 1
+

𝑥−𝑎

1 = 2𝑥−𝑎−𝑏 where a andb

𝑥−𝑏 (𝑥−𝑎)(𝑥−𝑏)

are constants and xGa or b. Values for which a fraction is

undefined e.g. 1 is
not

𝑥+3

defined for x = -3.

• •(i)
Functions and Relations Types of
Functions One-to-one, one-to-many,
many-to-one, many-to-many. Functions as a mapping, determination of the rule of
a given mapping/function.

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)
Longitudes and Latitudes.

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
trapeziums

Areas of similar figures. Include area of triangle = ½ base
x height and ½absinC.

Areas of compound shapes.

(ii) Circles, sectors and segments of circles.

(iii) Surface areas
of cubes, cuboids, cylinder, pyramids, righttriangular prisms, cones andspheres. Relationship between the sector of a
circle and the surface area of a cone.

( c ) Volumes (i)
Volumes of cubes, cuboids, cylinders, cones, right pyramids and spheres.

( ii ) Volumes of similar solids

Include volumes of compound shapes.

D. PLANE GEOMETRY

(a) Angles

(i) Angles at a
point add up to 360o.

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

(iii) Vertically
opposite angles are equal.

The degree as a unit of measure.

Consider acute, obtuse, reflex angles, etc.

(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 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, etc

(v) Properties of special

The formal proofs of those underlined may be required.

Conditions to be known but proofs not required e.g. SSS,
SAS, etc.

Use symmetry where applicable.

quadrilaterals
– parallelogram, rhombus, square, rectangle, 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.

Equiangular properties and ratio of sides and areas.

Sum of interior angles = (n - 2)180o or (2n – 4)right
angles, where n is the number of sides

( d ) Circles (i) Chords.

(ii) The angle
which an arc of a circle subtends at the centre of the circle 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.

(iv) Angles in the
same segment are equal.

(v) Angles in
opposite segments are supplementary.

( vi )Perpendicularity of tangent and radius.

(vii )If a tangent is drawn to a circle and from the point
of contact a chord is drawn,

each angle which this chord makes with the tangent is Angles subtended by chords in a circle and
at the centre. Perpendicular bisectors of chords.

the formal proofs of those underlined may be required.

equal to the
angle in the alternate segment.

• ( e )
Construction ( i ) Bisectors of angles and
line segments

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

( iii )Angles e.g. 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.

Application to real life situations.

E. COORDINATE GEOMETRY OF STRAIGHT LINES (i) Concept
of the x-y plane.

(ii) Coordinates
of points on the x-y plane.

Midpoint of two points, distance between two points

i.e. |PQ| =

√(𝑥2 − 𝑥1)2
+ (𝑦2
− 𝑦1)2,
where P(x1,y1) and Q(x2, y2), gradient (slope) of a line

m= 𝑦2− 𝑦1,
equation of a line

𝑥2− 𝑥1

in the form y = mx + c and y – y1 = m(x – x1), where m is
the gradient (slope) and c is a constant.

F. TRIGONOMETRY

(a) Sine, Cosine and Tangent of an angle.

(i) Sine, Cosine
and Tangent of acute angles.

(ii) Use of tables
of trigonometric ratios.

(iii) Trigonometric
ratios of 30o,

Use of right angled triangles

Without the use of tables.

45o and 60o.

(iv) Sine, cosine and tangent of angles from 0o to 360o.

( v )Graphs of sine and cosine.

(vi)Graphs of trigonometric ratios.

Relate to the unit circle. 0o≤ x ≤ 360o.

e.g.y = asinx, y = bcosx

Graphs of simultaneous linear and trigonometric equations.

e.g. y = asin x + bcos x, etc.

( b ) Angles of elevation and depression

(i) Calculating
angles of elevation and depression.

(ii) Application
to heights and distances. Simple
problems only.

• ( c ) Bearings

(i) Bearing of one point from another.

(ii) Calculation
of distances and angles Notation e.g.
035o, N35oE

Simple problems only. Use of diagram is required.Sine and
cosine rules may be used.

G. INTRODUCTORY CALCULUS

(i) Differentiation of algebraic functions.

(ii) Integration
of simple Algebraic functions. Concept/meaning
of differentiation/derived

function, dy , relationship

dx

between gradient of a curve

at a point and the differential coefficient of the equation
of the curve at that point.

Standard derivatives of some basic function e.g. if y = x2,

dy = 2x. If s = 2t3 +
4, ds =

dx dt

v = 6t2, where s = distance, t

= time and v = velocity. Application to real life situation
such as maximum and minimum values, rates of change etc.

Meaning/ concept of integration, evaluation of simple
definite algebraic equations.

H. 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 (Ogive).

(v) Measures of
Dispersion: range, semi inter-quartile/inter- quartile range, variance, mean
deviation and standard deviation.

Construction of frequency distribution tables, concept of
class intervals, class mark and class boundary.

Reading and drawing simple inferences from graphs,
interpretation of data in histograms.

Exclude unequal class interval.

Use of an assumed mean is acceptable but not required. For
grouped data, the mode should be estimated from the histogram while the median,
quartiles and percentiles are estimated from the cumulative frequency curve.

Application of the cumulative frequency curve to every day
life.

Definition of range, variance, standard deviation, inter-
quartile range. Note that mean deviation is the mean of the absolute deviations
from the mean and variance is the square of the standard deviation. Problems on
range, variance, standard deviation etc.

Standard deviation of grouped data

( b ) Probability (i) Experimental and theoretical probability.

(ii) Addition of
probabilities for mutually exclusive and independent events. Include equally likely events

e.g. probability of throwing a six with a fair die or a head
when tossing a fair coin.

With replacement.

without replacement.

(iii)
Multiplication of probabilities for independent events.

Simple practical problems

only. Interpretation of “and” and “or” in probability.

• I. VECTORS
AND TRANSFORMATION

(a) Vectors in a Plane

(b) Transformation
in the Cartesian Plane

Vectors as a directed line segment.

Cartesian
components of a vector e.g. (5 sin 60𝑜).

5𝑐o𝑠60𝑜

Magnitude of
a vector, equal vectors, addition and subtraction of vectors, zero vector,
parallel vectors, multiplication of a vector by scalar.

Knowledge of graphical representation is necessary.

Reflection of
points and shapes in the Cartesian Plane. Restrict
Plane to the x and y

axes and in the lines x = k, y

= x and y = kx, where k is an integer. Determination of
mirror lines (symmetry).

Rotation of
points and shapes in the Cartesian Plane. Rotation
about the origin and a point other than the origin. Determination of the angle
of rotation (restrict angles of rotation to -180o to 180o).

Translation
of points and shapes in the Cartesian Plane. Translation
using a translation vector.

Enlargement Draw the images of plane figures under
enlargement with a given centre for a given scale factor.Use given scales to
enlarge or reduce

plane figures.

3. UNITS

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

( 1 ) Length

1000 millimetres (mm) = 100 centimetres (cm) = 1 metre(m).
1000 metres = 1 kilometre (km)

( 2 ) Area

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

( 3 ) Capacity

1000 cubic centimeters (cm3) = 1 litre (l)

( 4 ) Mass

1000 milligrammes (mg) = 1 gramme (g) 1000 grammes (g) = 1
kilogramme( kg ) 1000 ogrammes (kg) =
1 tonne.

( 5) Currencies

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

Ghana - 100 Ghana pesewas (Gp) = 1 Ghana Cedi (
GH¢) Liberia - 100 cents (c) = 1 Liberian Dollar (LD)

Nigeria - 100 kobo (k) = 1 Naira (N) Sierra Leone - 100
cents (c) = 1 Leone (Le) UK - 100 pence (p) = 1 pound (£)

USA - 100 cents (c) = 1 dollar ($)

French Speaking territories: 100
centimes (c) = 1 Franc (fr) Any other units used will be defined.

4. OTHER
IMPORTANT INFORMATION

( 1) Use of Mathematical and Statistical Tables

Mathematics and Statistical tables, published or approved by
WAEC may be used in the examination room. Where the degree of accuracy is not
specified in a question, the degree of accuracy expected will be that
obtainable from the mathematical tables.

(2) Use of
calculators

The use of non-programmable, silent and cordless calculators
is allowed. The calculators must, however not have the capability to print out
nor to receive or send any information. Phones with or without calculators are
not allowed.

(3) Other
Materials Required for the examination

Candidates should bring rulers, pairs of compasses,
protractors, set squares etc required for papers of the subject. They will not
be allowed to borrow such instruments and any other material from other
candidates in the examination hall.

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

( 4) Disclaimer

In spite of the provisions made in paragraphs 4 (1) and (2) above, it should be noted that some questions may prohibit the use of tables and/or calculators.

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