This is the official waec gce 2018 syllabus and hot topics you need to pass waec gce For first series Jan/Feb and Second series beginning around October 2018. 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

(1) Sets

(2) Surds

(3) Binary Operations

(4) Logical Reasoning

(5) Functions

(6) Polynomial Functions

(7) Rational Functions

(8) Indices and Logarithmic Functions

(9) Permutation

And Combinations.

(10) Binomial

Theorem

(11) Sequences

and Series

(12) Matrices and Linear Transformation

(13) Trigonometry

(14) Co-ordinate

Geometry

(15) Differentiation

(16) Integration

II. Statistics and

Probability

(17) Statistics

(18) Probability

III. Vectors and      Mechanics

(19) Vectors

(20) Statics

(21) Dynamics (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.

Properties:

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) ¹ 0.

where g(x) and f(x) are

polynomials. e.g.

f:x ®

(ii) Resolution of rational

functions into partial

fractions.

(i) Indices

(ii) Logarithms

(i) Simple cases of arrangements

(ii) Simple cases of selection of objects.

Expansion of (a + b) .

Use of (1+x) ≈1+nx for any rational n, where x is sufficiently small. e.g (0.998)

(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

(i) Matrices

(ii) Determinants

(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

ax + by = 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

(i) Tabulation and Graphical

representation of data

(ii) Measures of location

(iii) Measures of Dispersion

(iv)Correlation

(i) Meaning of probability.

(ii) Relative frequency.

(iii) Calculation of Probability using       simple sample spaces.

(iv) Addition and multiplication of probabilities.

(v) Probability distributions.

(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.

(viii) Friction.

(i) The concepts of motion

(ii) Equations of Motion

(iii) The impulse and momentum

equations:

**(iv) Projectiles. (x : x is rea Ç, { },Ï, Î, , ,

U (universa set) and

A’ (Comple of set A).

More challenging problems involving u intersectio universal s subset and compleme set.

Three set problems. of De Morg laws to sol related problems

All the four operations surds

Rationalisin the denominat surds such , .

Use of properties t solve relate problems.

Using logic reasoning t determine t validity of compound statements involving implication and connectiviti Include use symbols: P

p q, p Ù q, q

Use of Trut tables to deduce conclusion compound statements Include negation.

The notatio e.g. f : x ®+4;

g : x ® x ; where x Î R .

Graphical representat of a functio Image and range.

Determinati of the inver of a one-to function e.

f: x →sx + inverse rela f : x →x also a func

Notation:(x) =f(g(x)) Restrict to simple algebraic functions o

Recognitio sketching graphs of li functions a equations.

Gradient a intercepts forms of lin equations i

ax + by + c y = mx + c; k. Parallel Perpendicu lines. Linea Inequalities 2x + 5y ≤ + 3y ≥ 3

Graphical representat of linear inequalities two variabl Application Linear Programmi

Recognitio sketching graphs of quadratic functions e

f: x → ax + c, where and c Є R.

Identificati vertex, axis symmetry, maximum minimum, increasing decreasing parts of a parabola. Include val of x for wh

f(x) >0 or f 0.

Solution of simultaneo equations: linear and quadratic. Method of completing squares for solving quadratic equations.

Express f(x ax + bx + the form f( a(x + d) + where k is maximum minimum v Roots of quadratic equations equal roots – 4ac = 0), and unequ roots (b – > 0), imagi roots (b – < 0); sum a product of of a quadra equation e. the roots o equation 3 5x + 2 = 0 and β, for equation w roots are a Solving quadratic inequalities

Recognitio cubic funct e.g. f: x → + bx +cx Drawing gr of cubic functions f given rang Factorizati cubic expression solution of cubic equations. Factorizati a ± b . B operations polynomial remainder factor theo i.e. the remainder f(x) is divid by f(x – a)(a). When f is zero, the – a) is a fa of f(x).

g(x) may b factorised i linear and quadratic factors (De of Numerat less than t of denomin which is le than or eq 4).

The four b operations.

Zeros, dom and range,

sketching required.

Laws of indices.

Application the laws of indices to evaluating products, quotients, powers an root.

Solve equa involving indices.

Laws of Logarithms Application logarithms calculation involving product, quotients, power (log nth roots (l log a ).

Solve equa involving logarithms (including change of base).

Reduction relation su as y = a (a,b are constants) linear form:

log y = b log x+log

Consider ot examples s as

log ab = l + x log b;

log (ab) =(log a + log

= x log ab

*Drawing a interpreting graphs of logarithmic functions e = ax . Estimating values of t constants b from the graph

Knowledge arrangeme and selecti expected. notations: and P fo selection a arrangeme respectivel should be noted and used. e.g. arrangeme students in row, drawi balls from with or wit replaceme

p = n!

(n-r)!

C = n!

r!(n-r)!

Use of the binomial theorem fo positive int index only.

Proof of th theorem no required.

e.g. (i) u ,…, u

(ii) u , u ,

Recognizin pattern of sequence.

(i) U = U (n-1)d, wh

d is the common difference.

(ii) U = U where r is t

common ra

(i) U + U U + … + U

(ii)U + U U + ….

(i) S = (U +U )

(ii) S = [2 (n – 1)d]

(iii) S = Ur ) , r<1

l – r

(iv) S =U (r – r>l.

r – 1

(v) Sum t infinity (S)

r < 1

Generating terms of a recurrence series and finding an explicit for for the sequence e 0.9999 =

+ + + + ….

Concept of matrix – st the order o matrix and indicate th type.

Equal matri – If two matrices ar equal, then their correspond elements a equal. Use equality to missing en of given matrices

Addition an subtraction matrices (u 3 x 3 matri

Multiplicati a matrix by scalar and matrix (up x 3 matrice

Evaluation determinan of 2 x 2 matrices.

**Evaluatio determinan 3 x 3 matri

Application determinan solution of simultaneo linear equations.

e.g. If A = , then

A =

Finding the images of points und given linear transforma

Determinin matrices of given linear transforma Finding the inverse of linear transforma (restrict to 2 matrices)

Finding the compositio linear transforma Recognizin Identity transforma

(i) reflectio the axis

(ii) reflecti the – axis

(iii) reflecti the line x

(iv) for anclockwise rotation thr θ about th origin.

(v) , the ge matrix for reflection i line throug origin maki an angle θ the positivaxis.

*Finding th equation of image of a under a giv linear transforma

Sine, Cosin and Tange general an (0 ≤θ≤360

Identify trigonomet ratios of an 30 , 45 , without us tables.

Use basic trigonomet ratios and reciprocals prove give trigonomet identities.

Evaluate si cosine and tangent of negative angles. Co degrees int radians an vice versa.

Application real life situations s as heights distances, perimeters, solution of triangles, a of elevatio depression, bearing(negative a positive an including u sine and c rules, etc,

Simple cas only.

sin (A B),c B),

tan(A B).

Use of compound angles in simple identities a solution of trigonomet ratios e.g. finding sin cos 150 et finding tan without usi mathemati tables or calculators leaving you answer as surd, etc.

Use of sim trigonomet identities t find trigonomet ratios of compound multiple an (up to 3A).

Relate trigonomet ratios to Cartesian Coordinate points (x, y the circle x y = r .

f:x →sin x,

g: x → a c + b sin x =

Graphs of cosine, tan and functio of the form

asinx + bc Identifying maximum minimum p increasing decreasing portions. Graphical solutions o simple trigonomet equations asin x + bc = k.

Solve trigonomet equations quadratic equations 2sin x – si – 3 =0, for x ≤ 360 .

*Express f( asin x + bc in the form Rcos (x ) o Rsin (x ) fo ≤ ≤ 90 and the result t calculate t minimum a maximum points of a given funct

Mid-point o line segme

Coordinate points whi divides a gi line in a giv ratio.

Distance between t points;

Gradient of line;

Equation of line:

(i) Intercep form;

(ii) Gradien form;

Conditions parallel and

perpendicu lines.

Calculate t acute angl between t intersectin lines e.g. if and m ar gradients o two interse lines, then = . If m m -1, then th lines are perpendicu

*The dista from an external po(x , y ) to given line

ax + by + c using the formula

d = ||.

Loci of vari points whi move unde given conditions

Equation of circle:

(i) Equatio terms of

centre, (a, and          radiu

(x – a) +( b) = r ;

(ii) The ge form:

x +y +2 gx

+c = 0, wh

g, – f ) is th centre and radius, r = .

Tangents a normals to circles

Equations parabola in

rectangular Cartesian coordinate = 4ax, inclu parametric equations ( at)).

Finding the equation of tangent an normal to a parabola at given point

*Sketch gr of given parabola a find the equation of axis of symmetry.

(i) Intuitive treatment limit.

Relate to t gradient of

a curve. e. f (x) = .

(ii) Its mea and its

determinati from first

principles (simple ca only).

e.g. ax + ≤ 3, (n Î I )

e.g. ax –

+ …+k, where m Є is a consta

e.g. sin x, sin x b cos Where a, b constants.

including polynomial the form (a b x ) .

e.g. y = e log 3x,

y = ln x

(i) The equ of a tangen

a curve at point.

(ii) Restrict turning poi to

maxima an minima.

(iii)Include curve sket (up

to cubic functions) linear

kinematics.

(i) Integrati of polynom of

the form a ≠ -1. i.e.

òx dx = + ≠ -1.

(ii) Integrat of sum and

difference polynomial

e.g. ∫(4x +3x -+5) dx

**(iii)Integr of polynom

of the form n = -1.

i.e. ò x ln x

Simple problems o integration substitutio

Integration simple trigonomet functions o form .

(i) Plane and Rate o

Change. In linear

kinematics.

Relate to t area under

curve.

(ii)Volume solid of revolution

(iii) Approximat restricted t

trapezium r

Frequency tables.

Cumulative frequency tables.

Histogram (including unequal

class interv

Cumulative frequency (Ogive) for grouped da

Central tendency: mean, med mode, quar and percen

Mode and modal grou grouped da from a histogram.

Median fro grouped da

Mean for grouped da (use of an assumed required).

Determinati of:

(i) Range, I Quartile an

Semi inter-quartile ran

from an Og

(ii) Mean deviation, variance standard deviation f

grouped an ungrouped

data. Using assumed

mean or tr mean.

Scatter diagrams, of line of b fit to predi one variabl from anoth meaning of correlation; positive, negative a zero correlation

Spearman’ Rank coefficient.

Use data without tie

*Equation line of best by least sq method. (Li of regressi y on x).

Tossing 2 once; drawi from a box or without replaceme

Equally like events, mu exclusive, independe and conditi events.

Include the probability event considered the probabi of a set.

(i) Binomia distribution

P(x=r)= C p , where

Probability success =

Probability failure = q ,

p + q = 1 a is the number trials. Simp problem only.

**(ii) Poiss distribution

P(x) = , wh = np,

n is large a is small.

Representa of vector in form ai + b

Addition an subtraction

multiplicati vectors by vectors, sc and equati

vectors. Triangle, Parallelogr and polygo Laws.

Illustrate through diagram,

Illustrate b solving problems i

elementary plane geo e.g

con-curren medians a

diagonals.

The notatio

i for the un vector 1

0

j for the un vector 0

1

along the x y axes respectivel Calculation unit vector along a i.e. .

Position ve of A relativ O is .

Position ve of the mid of a line segment. R to coordina of mid-poin a line seg

*Position v of a point t divides a li segment internally in ratio (λ : μ

Applying triangle, parallelogra and polygo laws to compositio forces acti a point. e.g find the resultant of forces (12 030 ) and 100 ) acti a point.

*Find the resultant of vectors by scale drawi

Finding an between t vectors.

Using the d product to establish s trigonomet formulae a

(i) Cos (a ±

cos a cos a sin b

(ii) sin (a ±

sin a cos b sin b cosa

(iii) c = a b – 2ab c

(iv) =.

Apply to si problems e

suspension particles by

strings.

Resultant o forces, La theorem

Using the principles moments t solve relate problems.

Distinction between smooth an rough plan

Determinati of the coefficient friction.

The definiti of displaceme

velocity, acceleratio and speed.

Compositio velocities a acceleratio

Rectilinear motion.

Newton’s l of motion.

Application Newton’s L

Motion alo inclined pla (resolving force upon plane into normal and frictional forces).

Motion und gravity (ign air resistan

Application the equatio of motions: u + at,

S = ut + ½

v = u +

Conservati Linear Momentum(exclude coefficient restitution)

Distinguish between momentum impulse.

Objects projected a angle to th horizontal.

1. 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 (m ) = 1 hectare (ha)

( 3 ) Capacity

1000 cubic centimeters (cm ) = 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.

2. 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.