WAEC Syllabus for Further Mathematics

The West African Examinations Council (WAEC) has released the syllabus for Further Mathematics to guide candidates preparing for the examination. The syllabus contains the topics and areas candidates are expected to study before sitting for the exam.

Going through the WAEC Syllabus for Further Mathematics will help you know exactly what to study and organise your revision properly. It can also help you avoid spending too much time on topics that are not included in the examination.

Below is the complete WAEC Further Mathematics syllabus, including the examination scheme, Pure Mathematics, Statistics and Probability, Vectors and Mechanics, and the required units.

WAEC Further Mathematics Scheme of Examination

The Further Mathematics examination consists of two papers, Papers 1 and 2. Candidates are required to take both papers.

Paper 1

Paper 1 consists of 40 multiple-choice questions covering the entire syllabus. Candidates are required to answer all the questions within 1 hour for a total of 40 marks. The questions are distributed as follows:

Paper 2

Paper 2 consists of Sections A and B. Candidates have 2 hours to answer the questions for a total of 100 marks.

Section A contains eight compulsory elementary questions for 48 marks.

Section B contains seven longer and more difficult questions divided into three parts:

Note: Topics marked with an asterisk (*) are tested in Section B of Paper 2 only. Topics marked with a single asterisk are peculiar to Ghana, while topics marked with two asterisks (**) are peculiar to Nigeria.

Detailed WAEC Further Mathematics Syllabus

Pure Mathematics

Sets

• Idea of a set defined by a property.
• Set notations and their meanings.
• Disjoint sets.
• Universal sets and complement of a set.
• Venn diagrams.
• Use of sets and Venn diagrams to solve problems.
• Commutative and associative laws.
• Distributive properties over union and intersection.

Surds

• Surds of the required forms involving rational numbers and positive integers that are not perfect squares.

Binary Operations

• Closure.
• Commutativity.
• Associativity.
• Distributivity.
• Identity elements.
• Inverses.

Logical Reasoning

• Rules of syntax.
• True and false statements.
• Rules of logic applied to arguments.
• Implications and deductions.
• Truth tables.

Functions

• Domain and co-domain of a function.
• One-to-one mapping.
• Onto mapping.
• Identity and constant mapping.
• Inverse of a function.
• Composite functions.

Polynomial Functions

• Linear functions, equations and inequalities.
• Quadratic functions, equations and inequalities.
• Cubic functions and equations.

Rational Functions

• Rational functions involving polynomial functions.
• Resolution of rational functions into partial fractions.

Indices and Logarithmic Functions

• Indices.
• Logarithms.

Permutation and Combination

• Simple cases of arrangements.
• Simple cases of selection of objects.

Binomial Theorem

• Expansion of (a+b)n(a+b)^n.
• Use of (1+x)n≈1+nx(1+x)^n \approx 1+nx for rational values of nn, where xx is sufficiently small.

Sequences and Series

• Finite and infinite sequences.
• Arithmetic progression (A.P.).
• Geometric progression (G.P.).
• Finite and infinite series.
• Sum of A.P.
• Sum of G.P.
• Recurrence series.*

Matrices and Linear Transformation

• Matrices.
• Determinants.
• Inverse of 2 × 2 matrices.
• Linear transformation.

Trigonometry

• Trigonometric ratios and rules.
• Compound and multiple angles.
• Trigonometric functions and equations.

Coordinate Geometry

• Straight lines.
• Conic sections.

Differentiation

• Idea of a limit.
• Derivative of a function.
• Differentiation of polynomials.
• Differentiation of trigonometric functions.
• Product and quotient rules.
• Differentiation of implicit functions.
• Differentiation of transcendental functions.**
• Second-order derivatives.
• Rates of change and small changes.
• Maxima and minima.

Integration

• Indefinite integral.
• Definite integral.
• Applications of the definite integral.

Statistics and Probability

Statistics

• Tabulation and graphical representation of data.
• Measures of location.
• Probability.
• Measures of dispersion.
• Correlation.

Probability

• Meaning of probability.
• Relative frequency.
• Calculation of probability using simple sample spaces.
• Addition and multiplication of probabilities.
• Probability distributions.

Vectors and Mechanics

Vectors

• Definitions of scalar and vector quantities.
• Representation of vectors.
• Algebra of vectors.
• Commutative, associative and distributive properties.
• Unit vectors.
• Position vectors.
• Resolution and composition of vectors.
• Scalar (dot) product and its application.
• Vector (cross) product and its application.**

Statics

• Definition of a force.
• Representation of forces.
• Composition and resolution of coplanar forces acting at a point.
• Composition and resolution of general coplanar forces on rigid bodies.
• Equilibrium of bodies.
• Determination of resultant.
• Moments of force.
• Friction.

Dynamics

• Concepts of motion.
• Equations of motion.
• Impulse and momentum equations.
• Projectiles.**

Units

Length

• 1,000 millimetres (mm) = 100 centimetres (cm) = 1 metre (m).
• 1,000 metres = 1 kilometre (km).

Area

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

Capacity

• 1,000 cubic centimetres (cm³) = 1 litre (l).

Mass

• 1,000 milligrammes (mg) = 1 gramme (g).
• 1,000 grammes (g) = 1 kilogramme (kg).
• 1,000 kilogrammes (kg) = 1 tonne.

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). 

How to Study for WAEC Further Mathematics

Effective preparation requires a realistic study plan and consistent practice.

• Start by getting the complete WAEC Further Mathematics syllabus and dividing it into smaller sections. Arrange the topics according to your level of understanding, giving more time to difficult areas.
• Study one topic at a time and practise questions immediately after learning the related concepts. This will help you remember the methods and identify areas that need further explanation.
• Past WAEC questions are also very useful. They help you understand the examination format, recognise common question patterns and practise working within the available time. After answering each question, check your solution carefully and correct every mistake.
• If you do not understand a topic, ask your teacher, join a study group or use reliable learning materials. Do not ignore difficult topics because they may appear in the examination.

We hope this WAEC Further Mathematics syllabus helps you prepare for your examination. Make sure you go through all the topics and use the syllabus to guide your revision.

If you have any questions about the WAEC Further Mathematics syllabus or need help with any of the topics, feel free to ask in the comment section below. Also, share this article with your friends and classmates who are preparing for the WAEC examination.