TOPICS

A. NUMBER AND NUMERATION 
( a ) Number bases
(b) Modular Arithmetic
Section A -
Section B -

CONTENTS

( i ) conversion of numbers from one base to another
( ii ) Basic operations on number bases
(i) Concept of Modulo Arithmetic. 
  (ii) Addition, subtraction and multiplication operations in modulo arithmetic. (iii) Application to daily life 
NOTES
Conversion from one base to base 10 and vice versa. Conversion from one base to another base .
Addition, subtraction and multiplication of number bases.
Interpretation of modulo arithmetic e.g.6 + 4 = k(mod7),
3 x 5 = b(mod6), m = 2(mod 3), etc.
Relate to market days, clock,shift duty, etc.
 ( c ) Fractions, Decimals and (i) Basic operations on fractions   Approximations and decimals.    (ii) Approximations and    significant figures.  
( d ) Indices ( i ) Laws of indices
( ii ) Numbers in standard form ( scientific notation)
Approximations should be realistic e.g. a road is not measured correct to the nearest cm.e.g. ax x ay = ax + y , axay = ax – y, (ax)y = axy, etc where x, y are real numbers and a ≠0. Include simple examples of negative and fractional indices.
Expression of large and small numbers in standard form e.g. 375300000 = 3.753 x 108 0.00000035 = 3.5 x 10-7
Use of tables of squares, square roots and reciprocals is accepted.
( e) Logarithms ( i ) Relationship between indices
and logarithms e.g. y =
k10implies log10y = k.Calculations involving
( ii ) Basic rules of logarithms e.g. multiplication, division,
log10(pq) = log10p + log10qpowers and roots.
log10(p/q) = log10p – log10q
log10pn = nlog10p.
(iii) Use of tables of logarithms
and antilogarithms.
( f ) Sequence and Series (i) Patterns of sequences. Determine any term of a
given sequence. The notationUn = the nth termof asequence may be used.
(ii) Arithmetic progression (A.P.) Simple cases only, includingGeometric Progression (G.P.) word problems. (Include sum
for A.P. and exclude sum forG.P).
( g ) Sets (i) Idea of sets, universal sets, Notations: { }, , P’( the
finite and infinite sets, compliment of P).
( h ) Logical Reasoning
(i) Positive and negative integers, rational numbers 
( j ) Surds (Radicals)
( k ) Matrices and Determinants
( l ) Ratio, Proportions and Rates subsets, empty sets and disjoint sets.
Idea of and notation for union, intersection and complement of sets.
(ii) Solution of practical problems involving classification using Venn diagrams.
Simple statements. True and false statements. Negation of statements, implications.
The four basic operations on rational numbers.
Simplification and rationalization of simple surds.
( i ) Identification of order, notation and types of matrices.
( ii ) Addition, subtraction, scalar multiplication and multiplication of matrices.
( iii ) Determinant of a matrix
Ratio between two similar quantities.
Proportion between two or more similar quantities.
Financial partnerships, rates of work, costs, taxes, foreign
properties e.g.
commutative, associative and distributive
Use of Venn diagrams restricted to at most 3 sets.
Use of symbols: use of Venn diagrams.
Match rational numbers with points on the number line. Notation: Natural numbers (N), Integers ( Z ), Rational numbers ( Q ).
Surds of the form , a and a where a is a rational number and b is a positive integer. Basic operations on surds (exclude surd of the form ).
Not more than 3 x 3 matrices. Idea of columns and rows.
Restrict to 2 x 2 matrices.
Application to solving simultaneous linear equations in two variables. Restrict to 2 x 2 matrices.
Relate to real life situations.
Include average rates, taxes e.g. VAT, Withholding tax, etc
exchange, density (e.g.population), mass, distance, timeand speed.
( m ) Percentages Simple interest, commission,
discount, depreciation, profit andloss, compound interest, hirepurchase and percentage error.
*( n) Financial Arithmetic ( i ) Depreciation/ Amortization.
( ii ) Annuities
(iii ) Capital Market Instruments
( o ) Variation Direct, inverse, partial and jointvariations.

B. ALGEBRAIC PROCESSES
( a ) Algebraic expressions (i) Formulating algebraic
expressions from givensituations
( ii ) Evaluation of algebraic expressions
( b ) Simple operations on ( i ) Expansion
algebraic expressions
Limit compound interest to a maximum of 3 years.
Definition/meaning, calculation of depreciation on fixed assets, computation of amortization on capitalized assets.
Definition/meaning, solve simple problems on annuities.
Shares/stocks, debentures, bonds, simple problems on interest on bonds and debentures.

Expression of various types of variation in mathematical symbols e.g. direct (z n ), inverse (z ), etc.
Application to simple practical problems.
e.g. find an expression for the cost C Naira of 4 pens at x Naira each and 3 oranges at y naira each.
Solution: C = 4x + 3y
e.g. If x =60 and y = 20, findC.
C = 4(60) + 3(20) = 300 naira.

e.g. (a +b)(c + d), (a + 3)(c - 4), etc.
(ii ) Factorization
  ¨·§ª (iii) Binary Operations   ( c ) Solution of Linear ( i ) Linear equations in one   Equations variable    ( ii ) Simultaneous linear    equations in two variables.  
( d ) Change of Subject of ( i ) Change of subject of aaFormula/Relation formula/relation
(ii) Substitution.
( e ) Quadratic Equations ( i ) Solution of quadratic equations(ii) Forming quadratic equation with given roots.
(iii) Application of solution of
quadratic equation in
practical problems.
(f) Graphs of Linear and (i) Interpretation of graphs,

factorization of expressions of the form ax + ay,
a(b + c) + d(b + c), a2 – b2, ax2 + bx + c where a, b, c are integers.
Application of difference of two squares e.g. 492 – 472 = (49 + 47)(49 – 47) = 96 x 2 = 192.

Carry out binary operations on real numbers such as: a*b = 2a + b – ab, etc.
Solving/finding the truth set (solution set) for linear equations in one variable.
Solving/finding the truth set of simultaneous equations in two variables by elimination, substitution and graphical methods. Word problems involving one or two variables

e.g. if = + , find v.
Finding the value of a variable e.g. evaluating v given the values of u and f.

Using factorization i.e. ab = 0 either a = 0 or b = 0.
·*§ªBy completing the square and use of formula

Simple rational roots only e.g. forming a quadratic equation whose roots are -3 and (x + 3)(x - ) = 0.
Finding:
Quadratic functions. coordinate of points, table ofvalues, drawing quadratic
graphs and obtaining roots
from graphs.
( ii ) Graphical solution of a pair
of equations of the form:
y = ax2 + bx + c and y = mx + k
*§ª(iii) Drawing tangents to
curves to determine the gradient
at a given point.
( g ) Linear Inequalities (i) Solution of linear inequalities
in one variable andrepresentation on the number
line.
*(ii) Graphical solution of linear
inequalities in two variables.
*(iii) Graphical solution of
simultaneous linearinequalities in two variables.
( h ) Algebraic Fractions Operations on algebraic fractionswith:
( i ) Monomial denominators
( ii ) Binomial denominators
¨·§ª(i) Functions and Relations Types of Functions
(i) the coordinates of maximum and minimum points on the graph. 
(ii) intercepts on the axes, identifying axis of symmetry, recognizing sketched graphs. 

Use of quadratic graphs to solve related equations e.g. graph of y = x2 + 5x + 6 to solve x2 + 5x + 4 = 0. Determining the gradient by drawing relevant triangle.
Truth set is also required. Simple practical problems
Maximum and minimum values. Application to real life situations e.g. minimum cost, maximum profit, linear programming, etc.
Simple cases only e.g. + = ( x0, y 0).
Simple cases only e.g. + = where a andb are constants and xa or b. Values for which a fraction is undefined e.g. is not defined for x = -3. One-to-one, one-to-many, many-to-one, many-to-many. Functions as a mapping, determination of the rule of a
C. MENSURATION
( a ) Lengths and (i) Use of Pythagoras theorem,Perimeters *§ªsine and cosine rules to
determine lengths anddistances.
(ii) Lengths of arcs ofcircles,perimeters of sectorsandsegments.
¨*§ª(iii) Longitudes and Latitudes.
( b ) Areas ( i ) Triangles and special
quadrilaterals – rectangles,parallelograms and
trapeziums
(ii) Circles, sectors and segments
of circles.

(iii) Surface areas of cubes,cuboids, cylinder, pyramids,
righttriangular prisms, cones
andspheres.
( c ) Volumes (i) Volumes of cubes, cuboids,cylinders, cones, right
pyramids and spheres.
( ii ) Volumes of similar solids
D. PLANE GEOMETRY
(a) Angles (i) Angles at a point add up to
360o.
(ii) Adjacent angles on a straightline are supplementary.(iii) Vertically opposite angles areequal.

(b) Angles and intercepts on (i) Alternate angles are equal.
given mapping/function.
No formal proofs of the theorem and rules are required.
Distances along latitudes and Longitudes and their corresponding angles.
Areas of similar figures. Include area of triangle = ½ base x height and ½absinC. Areas of compound shapes. Relationship between the sector of a circle and the surface area of a cone.
Include volumes of compound shapes.
The degree as a unit of measure.
Consider acute, obtuse, reflex angles, etc.
parallel lines. ( ii )Corresponding angles areequal.
( iii )Interior opposite angles aresupplementary
*§ª(iv) Intercept theorem.
(c) Triangles and Polygons. (i) The sum of the angles of a
triangle is 2 right angles.(ii) The exterior angle of a
triangle equals the sum ofthe two interior oppositeangles.
(iii) Congruent triangles.
( iv ) Properties of specialtriangles- Isosceles,equilateral, right-angled, etc
(v) Properties of specialquadrilaterals –
parallelogram, rhombus,
square, rectangle, trapezium.
( vi )Properties of similartriangles.
( vii ) The sum of the angles of apolygon
(viii) Property of exterior anglesof a polygon.
(ix) Parallelograms on the samebase and between the same
parallels are equal in area.
( d ) Circles (i) Chords.
Application to proportional division of a line segment.
*The formal proofs of those underlined may be required.
Conditions to be known but proofs not required e.g. SSS, SAS, etc.
Use symmetry where applicable.
Equiangular properties and ratio of sides and areas.
Sum of interior angles = (n - 2)180o or (2n – 4)right angles, where n is the number of sides
Angles subtended by chords in a circle and at the centre. Perpendicular bisectors of
(ii) The angle which an arc of acircle subtends at the centre
of the circle is twice thatwhich it subtends at anypoint on the remaining partof the circumference.
(iii) Any angle subtended at thecircumference by a diameteris a right angle.
(iv) Angles in the same segmentare equal.(v) Angles in opposite segmentsare supplementary.
( vi )Perpendicularity of tangent
and radius.
(vii )If a tangent is drawn to a
circle and from the point ofcontact a chord is drawn,
each angle which this chordmakes with the tangent is
equal to the angle in thealternate segment.
¨*§ª( e ) Construction ( i ) Bisectors of angles and linesegments
(ii) Line parallel or perpendicular
to a given line.( iii )Angles e.g. 90o, 60o, 45o,
30o, and an angle equal to agiven angle.(iv) Triangles and quadrilateralsfrom sufficient data.
¨*§ª( f ) Loci Knowledge of the loci listed
below and their intersections in 2dimensions.
(i) Points at a given distance froma given point.(ii) Points equidistant from two
chords.
*the formal proofs of those underlined may be required.
Include combination of these angles e.g. 75o, 105o,135o, etc.
E. COORDINATE GEOMETRY OF STRAIGHT LINES 
given points.
( iii)Points equidistant from two given straight lines.
(iv)Points at a given distance from a given straight line.
(i) Concept of the x-y plane. 
(ii) Coordinates of points on the x-y plane. 
Consider parallel and intersecting lines. Application to real life situations.Midpoint of two points, distance between two points i.e. |PQ| = , where P(x1,y1) and Q(x2, y2), gradient (slope) of a line m= , equation of a line in the form y = mx + c and y – y1 = m(x – x1),where m is the gradient (slope) and c is a constant.
F. TRIGONOMETRY 
(a) Sine, Cosine and Tangent of an angle. 
( b ) Angles of elevation and depression
¨*§ª( c ) Bearings
(i) Sine, Cosine and Tangent of acute angles. 
(ii) Use of tables of trigonometric ratios. 
(iii) Trigonometric ratios of 30o, 45o and 60o. 
(iv) Sine, cosine and tangent of angles from 0o to 360o. 
( v )Graphs of sine and cosine.
(vi)Graphs of trigonometric ratios.
(i) Calculating angles of elevation and depression. 
(ii) Application to heights and distances. 
(i) Bearing of one point from another. 
Use of right angled triangles
Without the use of tables.
Relate to the unit circle. 0o x 360o.
e.g.y = asinx, y = bcosx
Graphs of simultaneous linear and trigonometric equations. e.g. y = asin x + bcos x, etc.
Simple problems only.
Notation e.g. 035o, N35oE
*G. INTRODUCTORY
CALCULUS
(ii) Calculation of distances and angles
(i) Differentiation of algebraic functions. 
Simple problems only. Use of diagram is required.*§ªSine and cosine rules may be used.Concept/meaning of differentiation/derived function, , relationship between gradient of a curve at a point and the differential coefficient of the equation of the curve at that point. Standard derivatives of some basic function e.g. if y = x2, = 2x. If s = 2t3 + 4, = v = 6t2, where s = distance, t = time and v = velocity. Application to real life situation such as maximum and minimum values, rates of change etc.
H. STATISTICS AND PROBABILITY.( A ) Statistics
(ii) Integration of simple Algebraic functions.
(i) Frequency distribution
( ii ) Pie charts, bar charts, histograms and frequency polygons
(iii) Mean, median and mode for both discrete and grouped data.
Meaning/ concept of integration, evaluation of simple definite algebraic equations.
Construction of frequency distribution tables, concept of class intervals, class mark and class boundary.
Reading and drawing simple inferences from graphs, interpretation of data in histograms.
Exclude unequal class interval.
Use of an assumed mean is acceptable but not required. For grouped data, the mode should be estimated from the histogram while the median,
(iv) Cumulative frequency curve (Ogive). 
(v) Measures of Dispersion: range, semi inter-quartile/inter-quartile range, variance, mean deviation and standard deviation. quartiles and percentiles are estimated from the cumulative frequency curve.Application of the cumulative frequency curve to every day life.Definition of range, variance, standard deviation, inter-quartile range. Note that mean deviation is the mean of the absolute deviations from the mean and variance is the square of the standard deviation. Problems on range, variance, standard deviation etc.
*§ªStandard deviation of grouped data
( b ) Probability (i) Experimental and theoreticalprobability.
(ii) Addition of probabilities formutually exclusive andindependent events.
(iii) Multiplication of probabilitiesfor independent events.

¨§ªI. VECTORS AND
TRANSFORMATION
(a) Vectors in a Plane Vectors as a directed line
segment.
Cartesian components of a vector
Magnitude of a vector, equal
vectors, addition and subtraction

Include equally likely events e.g. probability of throwing a six with a fair die or a head when tossing a fair coin.
With replacement. *§ªwithout replacement.
Simple practical problems only. Interpretation of “and” and “or” in probability.
(5, 060o)
e.g. .
Knowledge of graphical representation is necessary.
of vectors, zero vector, parallelvectors, multiplication of avector by scalar.
(b) Transformation in the Reflection of points and shapes inCartesian Plane the Cartesian Plane.
Restrict Plane to the x and y axes and in the lines x = k, y = x and y = kx, where k is an integer. Determination of mirror lines (symmetry).
Rotation of points and shapes in the Cartesian Plane.Translation of points and shapes in the Cartesian Plane.Enlargement
3. UNITS
Rotation about the origin and a point other than the origin. Determination of the angle of rotation (restrict angles of rotation to -180o to 180o).
Translation using a translation vector.Draw the images of plane figures under enlargement with a given centre for a given scale factor.Use given scales to enlarge or reduce plane figures.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
1000 milligrammes (mg) = 1 gramme (g)
1000 grammes (g) = 1 kilogramme( kg )
1000 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.
4. 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 the capability to print out nor to receive or send 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.