Further Mathematics Waec Syllabus

Below is this years Waec Syllabus for Further Mathematics. Note that this syllabus is for both internal and external candidates.

Aims and 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.


This first paper will consist of forty multiple-choice objective questions covering the entire syllabus.

Candidates will be required to answer all questions in 1 hour for 40 marks. The questions will be drawn from the sections of the syllabus as follows:

  • Pure Mathematics – 30 questions
  • Statistics and probability – 4 questions
  • Vectors and Mechanics – 6 questions


Paper 2 will consist of two sections, Sections A and B, to be answered in 2 hours for 100 marks.

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


  • 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

Detailed Further Mathematics Syllabus

Pure Mathematics

  1. 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.
  2. Surds
    • Surds of the form , a and a+b, where a is rational, b is a positive integer, and n is not a perfect square.
  3. Binary Operations
    • Closure, Commutativity, Associativity and Distributivity, Identity elements and inverses.
  4. Logical Reasoning
    • Rule of syntax: true or false statements, rule of logic applied to arguments, implications and deductions.
    • The truth table
  5. Functions
    • Domain and co-domain of a  function.
    • One-to-one, onto, identity and constant mapping;
    • Inverse of a function.
    • Composite of functions.
  6. Polynomial Functions
    • Linear Functions, Equations and Inequality
    • Quadratic Functions, Equations  and Inequalities
    • Cubic Functions and Equations
  7. Rational Functions
    • Rational functions of the form Q(x) = g(x) 0. where g(x) and f(x) are polynomials. e.g. f:x
    • Resolution of rational functions into partial fractions.
  8. Indices and Logarithmic Functions
    • Indices
    • Logarithms
  9. Permutation And Combinations
    • Simple cases of arrangements
    • Simple cases of selection of objects.
  10. Binomial Theorem
    • Expansion of (a + b)n.  Use of (1+x)n ≈1+nx for any rational n, where x is sufficiently small. e.g (0.998)1/3
  11. Sequences and Series
    • Finite and Infinite sequences.
    • Linear sequence/Arithmetic Progression (A.P.) and Exponential sequence/Geometric Progression (G.P.)
    • (iii) Finite and Infinite series.
    • Linear series (sum of A.P.) and exponential series (sum of G.P.)
    • * Recurrence Series
  12. Matrices and Linear Transformation
    • Matrices
    • Determinants
    • Inverse of 2 x 2 Matrices
    • Linear Transformation
  13. Trigonometry
    • Trigonometric Ratios and Rules
    • Compound and Multiple Angles.
    • Trigonometric Functions and Equations
  14. Co-ordinate Geometry
    • Straight Lines
    • Conic Sections
  15. 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 = c
    • **Differentiation of Transcendental Functions
    • Second-order derivatives and Rates of change and small changes (x)
    • Concept of Maxima and Minima
  16. Integration
    • Indefinite Integral
    • Definite Integral
    • Applications of the Definite Integral

Statistics and Probability

  1. Statistics
    • Tabulation and Graphical representation of data
    • Measures of location Probability
    • Measures of Dispersion
    • Correlation
  2. Probability
    • Meaning of probability.
    • Relative frequency.
    • Calculation of Probability using simple sample spaces.
    • Addition and multiplication of probabilities.
    • Probability distributions.

Vectors and Mechanics

  1. 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.
  2. 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.
  3. Dynamics
    • The concepts of motion
    • Equations of Motion
    • The impulse and momentum equations:
    • **Projectiles.


  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
    • milligrammes (mg) = 1 gramme (g)
    • 1000 grammes (g) = 1 kilogramme( kg )
    • 1000 kilogrammes (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.


  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 a paper printout nor be capable of receiving/sending 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 the subject papers. They will not be allowed to borrow such instruments or any other material from other candidates in the examination hall.

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

  4. Disclaimer

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

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