WAEC Syllabus For Further Mathematics 2025/2026 PDF

Do you want to use the WAEC Syllabus For Further Mathematics 2025/2026 PDF to boost your exam preparation? You’ve found it! Our syllabi provide a comprehensive guide to tackling WAEC questions and cover everything you need to know about your registered subjects.

They are detailed and well-organized, serving as a key communication tool between WAEC and candidates.

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• WAEC Recommended Textbooks for Physics 2025/2026
• WAEC Recommended Textbooks for Mathematics 2025
• WAEC Recommended Textbooks for Government 2025/2026
• WAEC Recommended Textbooks for English 2025/2026

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Aims & Objectives

• Development of further conceptual and manipulative skills in Mathematics
• Understanding of an intermediate course of study which bridges the gap between Elementary Mathematics and Higher Mathematics
• Acquisition of aspects of Mathematics that can meet the needs of potential Mathematicians, Engineers, Scientists and other professionals
• Ability to analyze data and draw valid conclusions
• Logical, abstract and precise reasoning skills

Scheme of Examination

There will be two papers, Papers 1 and 2, both of which must be taken.

PAPER 1:

Section A : will consist of eight compulsory questions that are elementary in type for 48 marks. The questions shall be distributed as follows:

• Pure Mathematics – 4 questions
• Statistics and Probability – 2 questions
• Vectors and Mechanics – 2 questions

Section B:  will consist of seven questions of greater length and difficulty put into three parts: parts I, II and III as follows:

• Part I: Pure Mathematics – 3 questions
• Part II: Statistics and Probability – 2 questions
• Part III: Vectors and Mechanics – 2 questions

KEY:

• Topics that are marked with asterisks shall be tested in Section B of Paper 2 only.
• * Topics peculiar to Ghana only.
• ** Topics peculiar to Nigeria only

WAEC Syllabus For Further Mathematics 2025/2026

Category	Subtopics
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 and their use in solving 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 mappings
	– 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 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
	– 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
	– Trigonometric Functions and Equations
Coordinate 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 (e.g., ax2+by2=cax^2 + by^2 = cax2+by2=c)
	– Differentiation of Transcendental Functions
	– Second-order derivatives, Rates of change, and small changes
	– Concept of 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 and Dispersion
	– Correlation
	– Probability: Meaning, Relative frequency, Calculation using sample spaces, Addition, and multiplication of probabilities
	– Probability distributions
Vectors and Mechanics	– Vectors: Definitions, Representation, Algebra, Unit vectors, Position vectors, Resolution, and Composition
	– Scalar (dot) product and its application
	– Vector (cross) product and its application
	– Statics: Definition, Representation, Composition, and Resolution of forces, Equilibrium, Determination of Resultant, Moments of force, Friction
	– Dynamics: Concepts of motion, Equations of motion, Impulse and momentum equations, Projectiles
Units	– Length: mm, cm, m, km
	– Area: m², ha
	– Capacity: cm³, litre
	– Mass: mg, g, kg, tonne
	– Currencies: Various country-specific units (e.g., bututs, pesewas, cents, etc.)

Above is the Waec Syllabus for Further Mathematics 2025/2026 academic year Note that this syllabus is for both internal and external candidates.

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Instructions

Candidates may use WAEC-approved mathematical and statistical tables in the exam, adhering to the tables’ accuracy if not specified otherwise. Non-programmable, silent, cordless calculators are permitted, but must not have paper printout or communication features.

Phones are prohibited. Candidates must bring their own rulers, compasses, protractors, and set squares, as borrowing is not allowed. Graph papers with 2mm squares will be provided if needed. Note that some questions may restrict the use of tables and/or calculators.