# Waec Mathematics 2021 Syllabus And Topics

It is no longer news that Waec 2021 registration has begun and the May/June examination is very close. So many Waec candidates have been asking questions about the 2021 Waec syllabus and topics to read so as to pass Waec 2021 without much stress.

The relevance of Jamb syllabus and expo on the topics to focus on cannot be overemphasized. There are four weapons you need you need to pass the WAEC 2021 examination. They are:

- WAEC Syllabus
- WAEC past questions and answers
- Hot topics to read to pass Waec 2021
- The recommended Waec textbooks and
- Your complete preparation.

In this article, I will bread down the Waec mathematics syllabus for you.

See Also: How to pass Waec without expo

For all papers which involve mathematical calculations, mathematical and statistical tables published for WAEC should be used in the examination room. However, the use of non-programmable, silent and cordless calculator is allowed.

The calculator must not have a paper printout. Where the degree of accuracy is not specified in a question the degree of accuracy expected will be that obtainable from the WAEC mathematical tables.

Trigonometrical tables

in the pamphlet have different columns for decimal fractions of a degree, not for minutes and seconds.

No mathematical tables other than the above may be used in the examination. It is strongly recommended that schools/candidates obtain copies of these tables for use throughout the course.

Candidates should bring rulers, protractors, pair of compasses and set squares for all papers.

They will not be allowed to borrow such instruments and any other materials from other candidates in the examination hall. It should be noted that some questions may prohibit the use of tables and /or calculators. The use of slide rules is not allowed.

**Aims of Waec Mathematics Syllabus**

The syllabus is not intended to be used as a teaching syllabus. Teachers are advised to use

their own National teaching syllabuses. The aims of the syllabus are to test:

(i) computational skills;

(ii) the understanding of mathematical concepts and their applications to everyday living;

(iii) the ability to translate problems into mathematical language and solve them with

related mathematical knowledge;

(iv) the ability to be accurate to a degree relevant to the problems at hand;

(v) precise, logical and abstract thinking.

**WAEC EXAMINATION FORMAT**

There will be two papers both of which must be taken.

PAPER 1 – 11/2 hours

PAPER 2 – 21/2 hours

**Wassce General Mathematics Syllabus**

**TOPICS CONTENTS NOTES**

A. NUMBER AND NUMERATION

**(a) Number Bases**

(i) Binary numbers

**(ii) Modular arithmetic

Conversions from base 2 to base 10 and vice versa. Basic operations excluding division. Awareness of other number bases is desirable.

Relate to market days, the clock etc.

Truth sets (solution sets) for various open

sentences, e.g. 3 x 2 = a(mod) 4, 8 + y =

4 (mod) 9.

**(b) Fractions, decimals and approximations**

(i) Basic operations on

fractions and decimals.

(ii) Approximations and

significant figures

Approximations should be realistic e.g. a road is not measured correct to the nearest cm. Include error.

**(c) Indices**

(i) Laws of indices.

(ii) Numbers in standard

form.

Include simple examples of negative and

fractions indices.

e.g. 375.3 = 3.753 x 102

0.0035 = 3.5 x 10-3

Use of tables of squares,

square roots and reciprocals.

**(d) Logarithms**

(i) Relationship between indices and logarithms e.g.

y = 10k †’ K = log10 y

(ii) Basic rules of logarithms i.e.

log10 (pq) = log10P + log10q

log10 (p/q) = log10 P – log10q

log10Pn = nlog10P

(iii) Use of tables of logarithms, Base 10 logarithm and Antilogarithm tables. Calculations involving multiplication, division, powers and square roots.

**(e) Sequence**

(i) Patterns of sequences.

Determine any term of a

given sequence.

*(ii) Arithmetic Progression (A.P)

Geometric Progression (G.P).

The notation Un = the nth term of

a sequence may be used.

Simple cases only, including word

problems. Excluding sum Sn.

**(f) Sets**

(i) Idea of sets, universal set, finite and infinite sets, 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.

The use of Venn diagrams restricted to at most 3 sets.

**(g) Logical reasoning Simple statements. True and false statements. The negation of statements.

Implication, equivalence and valid

arguments.

Use of Venn diagrams preferable.

(h) Positive and Negative

integers. Rational numbers

The four basic operations on rational numbers

Match rational numbers with points on the number line.

Notation: Natural numbers (N),

Integers (Z), Rational numbers

(Q)

(i) Surds

Simplification and Rationalisation of simple surds.

(j) Ratio, Proportion

and Rates

Financial partnerships; rates of work, costs, taxes, foreign exchange, density (e.g. for population) mass, distance, time and speed. Include average rates.

(k) Variation

Direct, inverse and partial variations.

*Joint variations.

Application to simple practical problems.

(l) Percentages

Simple interest, commission, discount, depreciation, profit and loss, compound interest and hire purchase.

Exclude the use of compound

interest formula.

B. ALGEBRAIC

PROCESSES

(a) Algebraic

Expressions

(i) Expression of

statements in symbols.

(ii) Formulating algebraic

expressions from given

situations.

(iii) Evaluation of algebraic

expressions.

eg. Find an expression for the

cost C cedis of 4 pears at x cedis

each and 3 oranges at y cedis each

C = 4x + 3y

If x = 60 and y = 20.

Find C.

(b) Simple operations on

algebraic xpressions.

(i) Expansion

(ii) Factorisation

e.g. (a+b) (c+d). (a+3) (c+4)

Expressions of the form

(i) ax + ay

(ii) a (b+c) +d (b+c)

(iii) ax2 + bx +c

where a,b,c are integers

(iv) a2 – b2

Application of difference of two

squares e.g.

492 – 472 = (49 + 47) (49 – 47)

= 96 x 2 = 192

(c) Solution of linear

equations

(i) Linear equations in one variable

(ii) Simultaneous linear equations

in two variables.

(d) Change of subject of

a formula/relation

(i) Change of subject of a

formula/relation

(ii) Substitution

(e) Quadratic equations

(i) Solution of quadratic equations

(ii) Construction of quadratic

equations with given roots.

(iii) Application of solution of quadratic equations in practical problems.

(f) Graphs of Linear and quadratic functions.

(i) Interpretation of graphs, coordinates of points, table of values. 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

(iii) Drawing of a tangent to

curves to determine

gradient at a given point.

(iv) The gradient of a line

** (v) Equation of a Line

Finding:

(i) the coordinates of the maximum and minimum points on the graph;

(ii) intercepts on the axes. Identifying axis of Symmetry. Recognising sketched graphs.

Use of quadratic graph to solve a related equation

e.g. graph of y = x2 + 5x + 6 to solve x2 + 5x + 4 = 0

(i) By drawing relevant triangle to determine the gradient.

(ii) The gradient, m, of the line

joining the points

**(g) Linear inequalities**

(i) Solution of linear

inequalities in one variable

and representation on the

number line.

(ii) Graphical solution of linear

inequalities in two variables

Simple practical problems

**(h) Relations and functions**

(i) Relations

(ii) Functions

Various types of relations

One – to – one,

many – to – one,

one – to – many,

many – to – many

The idea of a function.

Types of functions.

One – to – one,

many – to – one.

(i) Algebraic fractions

Operations on algebraic

fractions

(i) with monomial

denominators.

(ii) with binomial

denominators.

**C. MENSURATION**

(a) Lengths and Perimeters

(i) Use of Pythagoras

theorem, sine and cosine

rules to determine

lengths and distances.

(ii) Lengths of arcs of

circles. Perimeters of

sectors and Segments.

*(iii) Latitudes and Longitudes.

No formal proofs of the theorem

and rules are required.

Distances along latitudes and

longitudes and their

corresponding angles.

(b) Areas

(i) Triangles and special

quadrilaterals – rectangles,

parallelograms and trapezia.

(ii) Circles, sectors and

segments of circles.

(iii) Surface areas of cube, cuboid,

cylinder, right triangular prisms

and cones. *Spheres.

Areas of similar figures.

Include area of triangles is

½ base x height and *1/2 abSin C.

Areas of compound shapes.

Relation between the sector of a

circle and the surface area of a

cone.

**(c) Volumes**

(i) Volumes of cubes, cuboid,

cylinders, cones and right

pyramids. * Spheres.

(ii) Volumes of similar solids

Volumes of compound shapes.

**D. PLANE GEOMETRY**

(a) Angles at a point

(i) Angles at a point add up to

360ï‚°.

(ii) Adjacent angles on a

straight line are supplementary.

(iii) Vertically opposite angles are

equal.

The results of these standard theorems stated under contents must be known but their formal proofs are not required. However, proofs based on the knowledge of these theorems may be tested.

The degree as a unit of measure.

Acute, obtuse, reflex angles.

(b) Angles and intercepts on parallel lines

(i) Alternate angles are equal.

(ii) Corresponding angles are equal.

(iii) Interior opposite angles are

supplementary.

*(iv) Intercept theorem

Application to proportional division of a line segment.

(c) Triangles and other polygons

(i) The sum of the angles of a triangle is 2 right angles.

(ii) The exterior angle of a triangle equals the sum of the two interior opposite angles.

(iii) Congruent triangles.

(iv) Properties of special triangles – isosceles, equilateral, right-angled.

(v) Properties of special quadrilaterals – parallelogram, rhombus, rectangle, square, trapezium.

(vi) Properties of similar triangles.

(vii) The sum of the angles of a polygon.

(viii) Property of exterior angles of a polygon.

(ix) Parallelograms on the same base and between the same parallels are equal in area.

Conditions to be known but proofs not required. Rotation, translation, reflection and lines of symmetry to be used. Use symmetry where applicable. Equiangular properties and ratio of sides and areas.

(d) Circles

(i) Chords

(ii) The angle which an arc of a circle subtends at the centre is twice that which it subtends at any point on the remaining part of the circumference.

(iii) Any angle subtended at the circumference by a diameter is a right angle.

Angles subtended by chords in a circle, at the centre of a circle. Perpendicular bisectors of chords.

(iv) Angles in the same segment are equal

(v) Angles in opposite segments are supplementary.

(vi) Perpendicularity of tangent and radius.

(vii) If a straight line touches a circle at only one point and from the point of contact a chord is drawn,

each angle which this chord makes with the tangent is equal to the angle in the alternative segment.

(e) Construction

(i) Bisectors of angles and line

segments.

(ii) Line parallel or perpendicular

to a given line.

(iii) An angle of 90º, 60º, 45º, 30º

and an angle equal to a given

angle.

(iv) Triangles and quadrilaterals

from sufficient data.

Include combination of these

angles e.g. 75º, 105º, 135º,

etc.

(f) Loci

Knowledge of the loci listed below and

their intersections in 2 dimensions.

(i) Points at a given distance from a

given point.

(ii) Points equidistant from two

given points.

(iii) Points equidistant from two

given straight lines.

(iv) Points at a given distance from

a given straight line.

Consider parallel and

intersecting lines.

E. TRIGONOMETRY

(a) Sine, cosine and

tangent of an angle.

(b) Angles of elevation

and depression.

(c) Bearings

(i) Sine, cosine and tangent

of an acute angle.

(ii) Use of tables.

(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.

Calculating angles of elevation and depression. Application to heights and distances.

(i) Bearing of one point from another.

(ii) Calculation of distances and angles.

**E. STATISTICS AND ****PROBABILITY**

**(a) Statistics**

(i) Frequency distribution.

(ii) Pie charts, bar charts, histograms and frequency polygons.

(iii) Mean, median and mode for both discrete and grouped data.

(iv) Cumulative frequency curve, median; quartiles and percentiles.

(v) Measures of dispersion: range, interquartile range, mean deviation and standard deviation from the mean.

Reading and drawing simple inferences from graphs and interpretations of data in histograms.

Exclude unequal class interval. Use of an assumed mean is acceptable but nor required. For grouped data, the mode should be estimated from the histogram and the median from the cumulative frequency curve.

Simple examples only. Note that mean deviation is the mean of the absolute deviations.

**(b) Probability**

(i) Experimental and theoretical probability.

(ii) Addition of probabilities for mutually exclusive and independent events.

(iii) Multiplication of probabilities for independent events.

Include equally likely events e.g. probability of throwing a six with fair die, or a head when tossing a fair coin.

Simple practical problems only. Interpretation of ”˜and’ and ”˜or’ in probability.

****(G) VECTORS AND TRANSFORMATIONS IN A PLANE**

(a) Vectors in a Plane.

(i) Vector as a directed line segment, magnitude, equal vectors, sums and differences of vectors.

(ii) Parallel and equal

vectors.

(iii) Multiplication of a

vector by a scalar.

(iv) Cartesian components of

a vector.

Column notation. Emphasis on graphical representation.

(b) Transformation in the Cartesian Coordinate plane.

(i) Reflection

(ii) Rotation

(iii) Translation

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