## WAEC 2021 Mathematics Syllabus. Comprehensive Waec Syllabus of Mathematics 2021/2022

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The Waec Syllabus for Math 2021 is now available. Candidates preparing for Waec 2020 are encouraged to download the Waec Syllabus for 2021 to be prepared for the forthcoming Waec Examination.

Candidates will find the Waec Syllabus for Mathematics 2021 to help them pinpoint their reading and study towards better topics or courses for the 2020 Waec exam.

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**What is WAEC Syllabus for Mathematics 2021 all about? WAEc Syllabus for Mathematics 2021**

This simply means a summary on topics Waec converted during an academic subject that is expected to be asked during Examination day on the upcoming WAEC examination.

Students face many challenges, including the inability to find the right materials or tools to study. However, there are ways to read your syllabus. The mathematics 2021 Waec syllabus is more than just a list of topics that you need to study.

Meanwhile, I want to let you know that the importance of the Waec syllabus for mathematics 2021 cannot be overemphasized. Candidates who take responsibility for their exams are the ones who get good grades and scores. Let’s get started with the Waec Syllabus For Mathematics 2021

## A. NUMBER AND NUMERATION

### ( a) Bases

(i) Conversion of numbers from one base into another

( iii) Basic operations on a variety of bases

### Modular Arithmetic

(i) Concept of Modulo Arithmetic.

(iii) Multiplication, addition, and subtraction in modulo algebra.

(iii). Application to everyday life

### ( c) Fractions and Decimals.

(i) Basic operations for fractions and decimals

(iii) Approximations of significant figures.

### ( d ) Indices

( i) Laws of Indicators

( iii) Numbers in scientific notation (standard form)

### (e) Logarithms

( i) Relationship between logarithms and indices y = 10k implies log10y = k.

( iii) Logarithm basics e.g.

log10(pq), = log10p + Log10q

log10(p/q), = log10p + log10q

log10pn = Nlog10p.

(iii). Use of tables for logarithms or antilogarithms.

Multiplication, division, powers, and roots are all possible calculations.

### (f) Sequences and Series

(i) Patterns and sequences.

(iii) – Arithmetic progression, A.P.

Geometric Progression (G.P.

Any term in a sequence can be determined. You can use the notation Un to identify the nth term in a sequence.

Only simple cases, no word problems. (Include sum to A.P. (Include sum for A.P.

### ( g) Sets

(i) The idea of sets, universal sets. Finite and infinite sets. Subsets.

The idea and notation for the union, intersection, and complement of sets.

(iii) Solutions to practical problems that involve classification using Venn diagrams.

Notations:

### Logical Reasoning

Simple statements. False and true statements. Negation of statements and implications

Use symbols: Venn diagrams are used.

### (i) Positive integers and negative integers, rational number

These are the four fundamental operations that can be used to calculate rational numbers.

Match rational numbers and points on the number line.

Notation: Rational numbers (Q), Natural numbers (N), Integers [ Z ], Integers [ N ].

### (j) Surds

Simplicity and rationalization simple surds.

Surds of form a and a, where a is an integer and b a number.

Basic operations on surds

### ** (k) Determinants and Matrices

( i) Identification of order and notation for matrices.

( ii) Subtraction, addition, scalar multiplication, and multiplication of matrixes.

( iii) Determinant of the matrix

### (l) Ratios, Proportions and Rates

The ratio of the two quantities is similar.

The ratio between two or more quantities that are similar.

Rates of work, costs, taxes, and foreign exchange. Population, mass, distance, speed, and time

### ( m) Percentages

Simple interest, commissions, discount, depreciation profit, loss, compound interest, and percentage error.

### *(n) Financial Arithmetic

( i ) Depreciation/ Amortization.

( ii ) Annuities

Capital Market Instruments (iii)

### (o) Variation

There are direct, indirect, partial, joint, and inverse variations.

Simple practical problems can be applied.

## B. ALGEBRAIC PROCESSES

### (a) Algebraic expressions

(i) Forming algebraic expressions based on given situations

( iii) Evaluation of algebraic equations

### ( b) Simple operations on algebraic equations

( i ) Expansion

(ii ) Factorization

### (c) Solving Linear Equations

( i) Linear equations for one variable

( ii) Simultaneous linear equations with two variables.

### (d) Modification of the Subject of a Formula/Relation

(i) Subject change in a formula/relation

(iii) Substitution

### (e) Quadratic Equations

(i ) Quadratic equations solved

(iii) Forming quadratic equations with given roots.

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

### (f) Graphs with Linear and Quadratic Functions

(i) Interpretation and table of values.

( ii) Graphical solution to a pair equations of form: y=ax2+ bx+ c and = mx+ k

(iii). Drawing tangents to curves in order to determine the gradient at a particular point.

### (g) Linear Inequalities

(i) Solving linear inequalities for one variable and their representation on the number line.

*(iii) Graphical solution to linear inequalities for two variables.

*(iii). The graphical solution to simultaneous linear inequalities for two variables.

### (h) Algebraic Fractions

Operation on algebraic fractions using:

( i ) Monomial denominators

( ii ) Binomial denominators

For simple cases, e.g. + = ( x0, y 0).

### (i) Functions & Relations

Different types of functions

One-to-one, one-to-many, many-to-one, many-to-many.

Functions as a mapping, determination the rule of a particular mapping/function.

## C. MENSURATION

### (a) Lengths & Perimeters

(i) Use Pythagoras’ theorem, *SSasine, and cosine rules for determining lengths and distances.

(iii) Lengths and perimeters of segments, sectors, and segments.

(iii). Longitudes and Latitudes.

### (b) Areas

( i) Triangles and special quadrilaterals: rectangles, parallelograms, and trapeziums

(iii) Segments, sectors, or circles.

(iii). Surface areas of cubes and cuboids, cylinders or pyramids, right triangular prisms as well as cones and spheres.

Areas with similar figures Add the triangle area = 1/2 base height and 1/2 absin C.

Compound shapes in certain areas.

Relationship between the circle’s sector and the cone’s surface area

### (c) Volumes

(i) Volumes in cubes, cuboids, and cylinders.

( iii) Volumes of similar solids

Add volumes to compound shapes.

## D. PLANE GEOMETAIRE

### (a) Angles

(i) The angles at a point can add up to 360 degrees.

(iii) An adjacent angle on a straight line is supplementary.

(iii). Vertically opposite angles are equal.

### (b) Angles or intercepts on parallellines

(i) Alternate angles equal.

( ii) Corresponding angles are equal.

( iii)Interior opposite angles can be supplementary

**a(iv). Intercept theorem.

### (c) Triangles and Polygons

(i) The summation of all angles in a triangle is two right angles.

(iii) The sum of two interior opposite angles is the exterior angle of a triangle.

(iii). Congruent triangles.

( iv) Properties of special triangles – Isosceles and equilaterals, right-angled, etc

(v) Special quadrilateral properties – parallelograms, rhombuses, squares, rectangles, trapezium.

( vi)Properties of triangles are similar.

(vii) The summation of all angles in a polygon

(viii) Exterior angles property of a polygon

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

### ( d) Circles

(i) Chords.

(ii) An arc of a circle at the center is twice as wide as the angle it subtends at any other point along the circumference.

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

(iv) Angles within the same segment are equal.

(v) Angles in opposing segments are supplementary.

( vi) Perpendicularity between tangent, radius.

(vii) If a tangent draws to a circle, and a chord is drawn from the point where contact is made, every angle this chord makes with a tangent equals the angle in an alternate segment.

Angles are subtended by chords at the center and in a circle. Perpendicular bisectors for chords.

### (e) Construction

( i) Bisectors for angles and line segments

(iii) Parallel or perpendicular line to a particular line.

( iii )Angles e.g. 90o, 60o and 45o angles, respectively.

(iv) Quadrilaterals and triangles can be calculated from sufficient data.

### (f) Loci

The following loci and their intersections are available in 2 dimensions.

(i) Distances between points.

(iii) Points that are equal to or less than two points.

( iii ) Points that are equal to two straight lines.

(iv) Points at a certain distance from a straight line.

### E. COORDINATE GEOMMETRY OF STRAIGHT LINS

(i) Concept of the x-y plane

(iii) Coordinates for points on the x and y planes

### F. TRIGONOMETRY

(a) Sine and Cosine.

(i) Sine and Cosine of acute angles.

(iii) Use tables for trigonometric ratios.

(iii). Trigonometric ratios 30o, 45o and 60o.

(iv) sine and cosine as well as the tangent of angles between 0o and 360o.

( v) Graphs of sine or cosine.

(vi) Graphs of trigonometric proportions.

### (b) Angles between elevation and depression

(i) Calculating the angle of elevation and depression.

(iii) Applicable to heights or distances.

### Bearings

(i) Bearing one point from the other.

(iii) Calculation distances and angles

## G. INTRODUCTORY CALCULUUS

(i) Differentiation algebraic functions

(iii) Integration of simple Algebraic functions.

Concept/meaning of differentiation/derived function, the relationship between the gradient of a curve at a point, and the differential coefficient of the equation of the curve at that point. The standard derivatives of a basic function, e.g. if y = x2, = 2x. If s= 2t3+ 4, = v= 6t2, where distance, time, and velocity are all equal to s. Real-life applications such as maximum and minimal values, change rates, etc.

Integration, Evaluation of simple definite algebraic equations.

## H. STATISTICS & PROBABILITY

### (a) Statistics

(i) Frequency distribution

( ii) Bar charts, histograms, and pie charts

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

(iv) Cumulative frequency (Ogive).

(v) Measures of Dispersion: range, semi inter-quartile/interquartile range, variance, mean deviation, and standard deviation.

### (b) Probability

(i) Experimental or theoretical probability.

(iii) Addition probabilities for events that are mutually exclusive or independent.

(iii). Multiplication of probabilities in independent events

## I. VECTORS & TRANSFORMATION

### Vectors in a Plane

Vectors as a directed line segment.

Cartesian components in a vector

The magnitude of a Vector, equal vectors and addition, and subtraction, zero vector, parallel vectors, multiplication by a Scalar.

### Transformation in the Cartesian Plane

Reflection in the Cartesian Plane of shapes and points

Rotation of shapes and points in the Cartesian Plane

The Cartesian Plane allows for the translation of points and forms.

#### Summary of the Waec Syllabus For Mathematics 2021

The Waec Syllabus of Mathematics 2021 is an essential guideline for candidates who want to succeed after studying.

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