The WAEC exams are coming up soon and students are getting ready to do their best in their subjects. As the exam day gets closer, it’s important to start revising well to get good grades. To help with this, WAEC has released the official syllabus for all subjects, including Further Mathematics. The WAEC Syllabus for Further Mathematics shows all the topics that students need to study and understand to do well in the exam.
Using the WAEC Syllabus for Further Mathematics will help you know exactly what to focus on, so you can study smarter and make sure you’re ready for everything that could come up. Below, we have provided the full WAEC Further Mathematics syllabus for 2025. Make sure to download it and keep it on your device so you can refer to it during your revision.
Scheme of Examination for Further Mathematics WAEC 2025
The WAEC Further Mathematics exam will have two papers: Paper 1 and Paper 2. Both papers must be taken.
Paper 1:
- This paper will have 40 multiple-choice questions covering the whole syllabus.
- You will need to answer all questions in 1 hour, with a total of 40 marks.
- The questions will be divided into the following topics:
- Pure Mathematics: 30 questions
- Statistics and Probability: 4 questions
- Vectors and Mechanics: 6 questions
Paper 2:
- Paper 2 will have two sections: A and B, which you must complete in 2 hours for 100 marks.
- Section A (48 marks) will have 8 compulsory questions that are easier, with the following breakdown:
- Pure Mathematics: 4 questions
- Statistics and Probability: 2 questions
- Vectors and Mechanics: 2 questions
Section B (52 marks) will have 7 longer and more difficult questions, divided into three parts:
- Part I: Pure Mathematics: 3 questions
- Part II: Statistics and Probability: 2 questions
- Part III: Vectors and Mechanics: 2 questions
Important Notes:
- Topics marked with asterisks are only tested in Section B of Paper 2.
- Some topics are specific to certain countries, like Ghana or Nigeria.
WAEC Syllabus For Further Mathematics
| Topic | Subtopics |
|---|---|
| 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 form a\sqrt{a}a and a+b\sqrt{a + b}a+b, where aaa is rational, bbb is a positive integer, and nnn is not a perfect square. | |
| – Binary Operations: Closure, Commutativity, Associativity and Distributivity, Identity elements and inverses. | |
| – Logical Reasoning: Rule of syntax: true or false statements, rule of logic applied to arguments, implications and deductions. The truth table. | |
| – Functions: Domain and co-domain of a function. One-to-one, onto, identity and constant mapping; Inverse of a function. Composite of functions. | |
| – Polynomial Functions: Linear Functions, Equations and Inequality, Quadratic Functions, Equations and Inequalities, Cubic Functions and Equations. Rational Functions: Rational functions of the form Q(x)=g(x)f(x)Q(x) = \frac{g(x)}{f(x)}Q(x)=f(x)g(x) where g(x)g(x)g(x) and f(x)f(x)f(x) are polynomials. Resolution of rational functions into partial fractions. | |
| – Indices and Logarithmic Functions: Indices and Logarithms | |
| – Permutation and Combinations: Simple cases of arrangements, Simple cases of selection of objects. | |
| – Binomial Theorem: Expansion of (a+b)n(a + b)^n(a+b)n. Use of (1+x)n≈1+nx(1 + x)^n \approx 1 + nx(1+x)n≈1+nx for any rational nnn, where xxx is sufficiently small. e.g. (0.998)1/3(0.998)^{1/3}(0.998)1/3 | |
| – Sequences and Series: Finite and Infinite sequences. Linear sequence/Arithmetic Progression (A.P.) and Exponential sequence/Geometric Progression (G.P.). Finite and Infinite series. Linear series (sum of A.P.) and exponential series (sum of G.P.). Recurrence Series. | |
| – Matrices and Linear Transformation: Matrices, Determinants, Inverse of 2×22 \times 22×2 Matrices, Linear Transformation. | |
| – Trigonometry: Trigonometric Ratios and Rules, Compound and Multiple Angles. | |
| Statistics and Probability | – Tabulation and Graphical representation of data. Measures of location Probability. Measures of Dispersion. Correlation. |
| Vectors and Mechanics | – Trigonometric Functions and Equations. Co-ordinate Geometry: Straight Lines, Conic Sections. |
| – Differentiation: The idea of a limit, The derivative of a function, Differentiation of polynomials, Differentiation of Trigonometric Functions, Product and quotient rules. Differentiation of implicit functions such as ax2+by2=cax^2 + by^2 = cax2+by2=c. Differentiation of Transcendental Functions. Second-order derivatives and Rates of change and small changes. Concept of Maxima and Minima. | |
| – Integration: Indefinite Integral, Definite Integral, Applications of the Definite Integral. | |
| Statistics | – Probability: Meaning of probability, Relative frequency. Calculation of Probability using simple sample spaces. Addition and multiplication of probabilities. Probability distributions. |
| 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 | – The concepts of motion, Equations of Motion. The impulse and momentum equations: Projectiles. |
| Measurement Units | – Length: 1000 millimetres (mm) = 100 centimetres (cm) = 1 metre (m). 1000 metres = 1 kilometre (km). |
| – Area: 10,000 square metres (m²) = 1 hectare (ha). | |
| – Capacity: 1000 cubic centimeters (cm³) = 1 litre (l). | |
| – Mass: milligrammes (mg) = 1 gramme (g). 1000 grammes (g) = 1 kilogramme (kg), 1000 kilogrammes (kg) = 1 tonne. |
Important Information
- During the exam, candidates are allowed to use official mathematical and statistical tables that have been published or approved by WAEC. If the accuracy level is not specifically mentioned in a question, candidates are expected to use the degree of accuracy available in the tables.
- Candidates are permitted to use non-programmable calculators that are silent and cordless. The calculators must not have the ability to print or send/receive any information. Phones, whether they have calculators or not, are not allowed in the exam room.
- Candidates must bring their own necessary tools for the exam, such as rulers, compasses, protractors, and set squares. These tools cannot be borrowed from other candidates. For any paper that requires graph work, graph papers with 2mm squares will be provided by WAEC.
- Some questions in the exam may specify that calculators and/or tables cannot be used, despite the general permissions above. Candidates should pay attention to these instructions during the exam.
Did you find this post helpful? Share it with other further maths candidates, and if you need the syllabi for other subjects, you can check our page. Do not hesitate to drop your questions in the comments if you have any.
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