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.
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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.
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.
* Topics peculiar to Ghana only.
** Topics peculiar to Nigeria only
Topics Content Notes
I. Pure Mathematics
(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 of the form , a and a+b where a is rational, b is a positive integer and n is not a perfect square.
Closure, Commutativity, Associativity and Distributivity, Identity elements and inverses.
(i) Rule of syntax: true or false statements, rule of logic applied to arguments, implications and deductions.
(ii) The truth table
(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.
(i) Linear Functions, Equations and Inequality
(ii) Quadratic Functions, Equations and Inequalities
(ii) Cubic Functions and Equations
(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
Permutation And Combinations
(i) Simple cases of arrangements
(ii) Simple cases of selection of objects.
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
(iii) Inverse of 2 x 2 Matrices
(iv) Linear Transformation
(i) Trigonometric Ratios and Rules
(ii) Compound and Multiple Angles.
(iii) Trigonometric Functions and Equations
(i) Straight Lines
(ii) Conic Sections
(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
(i) Indefinite Integral
(ii) Definite Integral
(iii) Applications of the Definite Integral
II. Statistics and Probability
(i) Tabulation and Graphical representation of data
(ii) Measures of location Probability
(iii) Measures of Dispersion
(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
(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.
(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.
(i) The concepts of motion
(ii) Equations of Motion
(iii) The impulse and momentum equations:
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.