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.
PAPER 1:
This first paper will consist of forty multiplechoice 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:
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
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
Detailed 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 form , a and a+b, where a is rational, b is a positive integer, and n 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 codomain of a Â function.
 Onetoone, onto, identity and constant mapping;
 Inverse of a function.
 Composite of functions.

 Polynomial Functions
 Linear Functions, Equations and Inequality
 Quadratic Functions, Equations Â and Inequalities
 Cubic Functions and Equations

 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.

 Indices and Logarithmic Functions
 Indices
 Logarithms

 PermutationÂ And Combinations
 Simple cases of arrangements
 Simple cases of selection of objects.

 Binomial Theorem
 Expansion of (a + b)n. Â Use of (1+x)n â‰ˆ1+nx for any rational n, where x is sufficiently small. e.g (0.998)1/3

 SequencesÂ 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

 Matrices and Linear Transformation
 Matrices
 Determinants
 Inverse of 2 x 2 Matrices
 Linear Transformation

 Trigonometry
 Trigonometric Ratios and Rules
 Compound and Multiple Angles.
 Trigonometric Functions and Equations

 CoordinateÂ 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 = c
 **Differentiation of Transcendental Functions
 Secondorder derivatives and Rates of change and small changes (x)
 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 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
 The concepts of motion
 Equations of Motion
 The impulse and momentum equations:
 **Projectiles.
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.

 Currencies
 The Gambia â€“ 100 bututs (b) = 1 Dalasi (D)
 Ghana – 100 Ghana pesewas (Gp) = 1 Ghana Cedi ( GHÂ¢)
 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 (Â£)
 USA – 100 cents (c) = 1 dollar ($)
 French Speaking territories 100 centimes (c) = 1 Franc (fr)
 Any other units used will be defined.
OTHER IMPORTANT INFORMATION

 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.

 Use of calculators
The use of nonprogrammable, 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.

 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.

 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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