WAEC Syllabus For Further Mathematics 2025
WAEC has published the syllabus for Further Mathematics. The WAEC Syllabus for Further Mathematics outlines the key topics and objectives candidates need to focus on. Following the syllabus ensures you cover all required topics systematically, improving your chances of success. Teachers and tutors can also use it as a guide to structure lessons and support students’ learning.
If you have yet to access the WAEC Syllabus for Further Mathematics, read this post. In this post, we have provided access to the full WAEC Further Mathematics syllabus. You can download it for easy reference. If you read further, you will also find the textbooks recommended by WAEC for your revisions.
WAEC Syllabus For Further Mathematics
| Topic | Content | Notes |
|---|---|---|
| 1. Circular Measure and Radians | – Lengths of Arcs of Circles – Perimeters of Sectors and Segments measured in radians | |
| 2. Trigonometry | – Sine, Cosine, and Tangent of angles – Trigonometric ratios of 30°, 45°, 60° – Heights and distances – Angles of elevation and depression – Bearings, Positive and Negative Angles – Compound and Multiple Angles – Graphical solution of simple trig. equations – Solution of triangles | – Identify without use of tables – Simple cases only – Use in simple identities and trig. ratios – Include a cos x + b sin x = c – Notion of radian and trigonometric ratios of negative angles |
| 3. Indices, Logarithms, and Surds | (a) Indices – Elementary theory of Indices (b) Logarithms – Elementary theory of Logarithm – log_a(xy) = log_ax + log_ay – log_ax^n = n log_ax – Applications | – Meaning of a^0, a^(-n), a^n – Calculations involving multiplication, division, power, nth roots |
| (c) Surds | – Forms like a√b, a + b√n (where a is rational, b is a positive integer, and n is not a perfect square) | – Rationalization of the denominator – Expressions like (a + √b) / (√c – √d) |
| (d) Sequences | – Linear and Exponential Sequences – Finite and Infinite Sequences – Arithmetic Progression (AP): U_n = U_1 + (n – 1)d – Sum of AP: S_n = n(U_1 + U_n)/2 – Geometric Progression (GP): U_n = U_1 * r^(n-1) – Sum of GP | |
| (e) Binomial Theorem | – Use for a positive integral index – Expansion of (a + b)^n | – Proof of Binomial Theorem not required – Use of (1 + x)^n ≈ 1 + nx for small x |
| 4. Algebraic Equations | – Factors and Factorization – Quadratic equations (solution using completing the square and formula) – Symmetric properties of the equation ax² + bx + c = 0 – Solution of simultaneous equations (one linear, one quadratic) | – Condition for real roots: b² – 4ac ≥ 0 – Sum and product of roots – Graphical and analytical methods |
| 5. Polynomials | – Addition, subtraction, multiplication of polynomials – Factor and Remainder Theorems – Zeros of a polynomial function – Graphs of polynomials of degree n ≤ 3 – Division of polynomials (degree ≤ 4) | |
| 6. Rational Functions and Partial Fractions | – Operations on rational functions – Zeros, domain, and range (sketching not required) – Resolution into partial fractions | – Rational functions of form F(x)/Q(x) – G(x) and F(x) are polynomials – G(x) must be factorable into linear and quadratic factors |
| 7. Linear Inequalities | – Graphical and Analytical solutions of simultaneous linear inequalities in two variables – Quadratic inequalities | |
| 8. Logic | – Truth tables using NOT, OR, AND – Implication statements (P ⇒ Q, Q ⇒ P) – Syntax rules (true or false statements, logic applied to arguments, implications, and deductions) | – Validity of compound statements involving implications and connectives – Use of truth table symbols: ~P, P ∨ Q, P ∧ Q, P ⇒ Q |
| 9. Coordinate Geometry | Straight Line: – Distance between two points – Midpoint formula – Gradient of a line – Conditions for parallel and perpendicular lines – Equation of a line (intercept form, gradient form, general form) Conic Sections: – Equation of a circle – Tangents and normals | – Gradient as vertical/horizontal change – Circle equation in center-radius form (x-a)² + (y-b)² = r² – General equation x² + y² + 2gx + 2fy + c = 0 – Parabola equation in rectangular coordinates |
| 10. Differentiation | – Concept of limits – Derivative of a function – Second derivative and rates of change – Maxima and minima | – Relate differentiation to curve gradients – Differentiation from first principles (simple cases) – Polynomial differentiation – Product and quotient rules – Implicit differentiation |
| 11. Integration | – Indefinite and definite integrals – Simple polynomial integration – Applications of definite integrals | – Excludes n = -1 in ∫ x^n dx – Integration by substitution – Plane areas and rates of change |
Recommended WAEC Further Mathematics Textbooks
Here are the texts you can use to do your reading:-
- Ivowi, U. M. O., et al. Further mathematics. Nigerian Educational Research and Development Council (NERDC).
- Moses, T. R. Spectrum new further mathematics (Scholastic series). [Publisher Name].
- Tuttuh, A. M. R., et al.. New further mathematics project (Vols. 1–3). Bounty Press Ltd.
Exam Success Tips
- Organize your study schedule, breaking down topics into manageable chunks.
- Practice with past exam papers to identify patterns and improve time management.
- Discussing topics with others can reinforce learning and clarify doubts.
- Avoid last-minute cramming; regular studying leads to better long-term retention.
- During the exam, ensure you understand what is required before answering.
- Allocate time to each question based on marks and difficulty level.
- Answering familiar questions first builds confidence.
- If you get stuck, take a deep breath and move to the next question.
We wish you the best of luck in your examinations!
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