Below is this year’s **Waec Syllabus for Further Mathematics**. Note that this syllabus is for both Internal and external candidates… Further maths topics for Wassce.

**AIMS OF THE SYLLABUS**

The aims of the syllabus are to test candidates’

(i) development of further conceptual and manipulative skills in Mathematics;

(ii) understanding of an intermediate course of study which bridges the gap between Elementary Mathematics and Higher Mathematics;

(iii) acquisition of aspects of Mathematics that can meet the needs of potential Mathematicians, Engineers, Scientists and other professionals.

(iv) ability to analyse data and draw valid conclusion

(v) logical, abstract and precise reasoning skills.

**Download Further Mathematics PDF here**

**EXAMINATION SCHEME**

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

PAPER 1: will consist of forty multiple-choice objective questions, covering the entire syllabus. Candidates will be required to answer all questions in 1hours 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 areelementary 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

**Candidates will be required to answer four questions with at least one from each part for 52 marks.**

**DETAILED SYLLABUS**

In addition to the following topics, more challenging questions may be set on topics in the General Mathematics /Mathematics (Core) syllabus.

In the column for CONTENTS, more detailed information on the topics to be tested is given while the limits imposed on the topics are stated under NOTES.

Topics which are marked with asterisks shall be tested in Section B of Paper 2 only.

KEY:

* Topics peculiar to Ghana only.

** Topics peculiar to Nigeria only

Topics Content Notes

## I. Pure Mathematics

### Sets

(i) Idea of a set defined by a property, Set notations and their meanings.

(ii) Disjoint sets, Universal set and complement of set

(iii) Venn diagrams, Use of sets And Venn diagrams to solve problems.

(iv) 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

(i) Rule of syntax: true or false statements, rule of logic applied to arguments, implications and deductions.

(ii) The truth table

### Functions

(i) Domain and co-domain of a function.

(ii) One-to-one, onto, identity and constant mapping;

(iii) Inverse of a function.

(iv) Composite of functions.

### Polynomial Functions

(i) Linear Functions, Equations and Inequality

(ii) Quadratic Functions, Equations and Inequalities

(ii) Cubic Functions and Equations

### Rational Functions

(i) Rational functions of the form Q(x) = ,g(x) 0. where g(x) and f(x) are polynomials. e.g. f:x

(ii) Resolution of rational functions into partial fractions.

### Indices and Logarithmic Functions

(i) Indices

(ii) Logarithms

### Permutation And Combinations

(i) Simple cases of arrangements

(ii) Simple cases of selection of objects.

### 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

### Sequences and Series

(i) Finite and Infinite sequences.

(ii) Linear sequence/Arithmetic Progression (A.P.) and Exponential sequence/Geometric Progression (G.P.)

(iii) Finite and Infinite series.

(iv) Linear series (sum of A.P.) and exponential series (sum of G.P.)

*(v) Recurrence Series

### Matrices and Linear Transformation

(i) Matrices (i) Matrices

(ii) Determinants

(iii) Inverse of 2 x 2 Matrices

(iv) Linear Transformation

### Trigonometry

(i) Trigonometric Ratios and Rules

(ii) Compound and Multiple Angles.

(iii) Trigonometric Functions and Equations

### Co-ordinate Geometry

(i) Straight Lines

(ii) Conic Sections

### Differentiation

(i) The idea of a limit

(ii) The derivative of a function

(iii)Differentiation of polynomials

(iv) Differentiation of trigonometric Functions

(v) Product and quotient rules. Differentiation of implicit functions such as ax2 + by2 = c

**(vi) Differentiation of Transcendental Functions

(vii) Second order derivatives and Rates of change and small changes (x), Concept of Maxima and Minima

### Integration

(i) Indefinite Integral

(ii) Definite Integral

(iii) Applications of the Definite Integral

## II. Statistics and Probability

### Statistics

(i) Tabulation and Graphical representation of data

(ii) Measures of location Probability

(iii) Measures of Dispersion

(iv)Correlation

### Probability

(i) Meaning of probability.

(ii) Relative frequency.

(iii) Calculation of Probability using simple sample spaces.

(iv) Addition and multiplication of probabilities.

(v) Probability distributions.

## Vectors and Mechanics

### Vectors

(i) Definitions of scalar and vector Quantities.

(ii) Representation of Vectors.

(iii) Algebra of Vectors.

(iv) Commutative, Associative and Distributive Properties.

(v) Unit vectors.

(vi) Position Vectors.

(vii) Resolution and Composition of Vectors.

(viii) Scalar (dot) product and its application.

**(ix) Vector (cross) product and its application.

### Statics

(i) Definition of a force.

(ii) Representation of forces.

(iii) Composition and resolution of coplanar forces acting at a point.

(iv) Composition and resolution of general coplanar forces on rigid bodies.

(v) Equilibrium of Bodies.

(vi) Determination of Resultant.

(vii) Moments of forces.

(viii) Friction.

### Dynamics

(i) The concepts of motion

(ii) Equations of Motion

(iii) The impulse and momentum equations:

**(iv) Projectiles.

## UNITS

Candidates should be familiar with the following units and their symbols.

**( 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 )

ogrammes (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.

### OTHER IMPORTANT INFORMATION

**( 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.

**Use of calculators**

The use of non-programmable, silent and cordless calculators is allowed. The calculators must, however not have a paper print out 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 papers of the subject. They will not be allowed to borrow such instruments and any other material from other candidates in the examination hall.

Graph papers ruled in 2mm squares will be provided for any paper in which it is 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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