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All Systems Operational

Maths syllabus for WAEC WASSCE | Learn | Learn by Rightal

WAEC WASSCE course

Maths

WAEC WASSCE

445 topics sit in this course for WAEC WASSCE.

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Topics with a public outline

Differentiation of Algebraic Functions
Concept/meaning of differentiation/derived function, dy/dx, 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, dy/dx = 2x. If s = 2t³ + 4, ds/dt = 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.
Number Bases - Conversion
Conversion from one base to base 10 and vice versa. Conversion from one base to another base.
Length Conversions
1000 millimetres (mm) = 100 centimetres (cm) = 1 metre(m). 1000 metres = 1 kilometre (km)
Algebraic Expressions - Formulating
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.
Integration of Simple Algebraic Functions
Meaning/ concept of integration, evaluation of simple definite algebraic equations.

Vectors in a Plane - Properties and Operations

Magnitude of a vector, equal vectors, addition and subtraction of vectors, zero vector, parallel vectors, multiplication of a vector by scalar. Knowledge of graphical representation is necessary.

Modular Arithmetic - Concept

Interpretation of modulo arithmetic e.g. 6 + 4 = k(mod7), 3 x 5 = b(mod6), m = 2(mod 3), etc.

Transformation - Reflection

Reflection of points and shapes in 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).

Mass Conversions

1000 milligrammes (mg) = 1 gramme (g). 1000 grammes (g) = 1 kilogramme( kg ). 1000 kilogrammes (kg) = 1 tonne.

Areas - Triangles and Quadrilaterals

Areas of similar figures. Include area of triangle = ½ base x height and ½absinC. Areas of compound shapes.

Algebraic Expressions - Factorization

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.

Transformation - Rotation

Rotation of points and shapes in the Cartesian Plane. Rotation about the origin and a point other than the origin. Determination of the angle of rotation (restrict angles of rotation to -180° to 180°).

Transformation - Translation

Translation of points and shapes in the Cartesian Plane. Translation using a translation vector.

Areas - Surface Areas of 3D Shapes

Surface areas of cubes, cuboids, cylinder, pyramids, righttriangular prisms, cones andspheres.

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.

Linear Equations - One Variable

Solving/finding the truth set (solution set) for linear equations in one variable.

Transformation - Enlargement

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.

Linear Equations - Simultaneous in Two Variables

Solving/finding the truth set of simultaneous equations in two variables by elimination, substitution and graphical methods. Word problems involving one or two variables.

Approximations and Significant Figures

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

Indices - Laws of Indices

e.g. aˣ aʸ = aˣ⁺ʸ, aˣ÷aʸ = aˣ⁻ʸ, (aˣ)ʸ = aˣʸ, etc where x, y are real numbers and a ≠0. Include simple examples of negative and fractional indices.

Numbers in Standard Form (Scientific Notation)

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.

Quadratic Equations - Solution

Using factorization i.e. ab = 0 ⇒ either a = 0 or b = 0. By completing the square and use of formula.

Quadratic Equations - Forming with Given Roots

Simple rational roots only e.g. forming a quadratic equation whose roots are -3 and 5/2 ⇒ (x + 3)(x - 5/2) = 0.

Logarithms - Basic Rules

e.g. log₁₀(pq) = log₁₀p + log₁₀q, log₁₀(p/q) = log₁₀p – log₁₀q, log₁₀pⁿ = nlog₁₀p. Calculations involving multiplication, division, powers and roots.

Sequence and Series - Patterns

Determine any term of a given sequence. The notation Uⁿ = the nth term of a sequence may be used.

Graphs of Linear and Quadratic Functions - Interpretation and Drawing

Finding: (i) the coordinates of maximum and minimum points on the graph. (ii) intercepts on the axes, identifying axis of symmetry, recognizing sketched graphs.

Triangles and Polygons - Sum of Angles in a Polygon

Sum of interior angles = (n - 2)180° or (2n – 4)right angles, where n is the number of sides.

Graphs - Graphical Solution of Equations

Graphical solution of a pair of equations of the form: y = ax² + bx + c and y = mx + k. Use of quadratic graphs to solve related equations e.g. graph of y = x² + 5x + 6 to solve x² + 5x + 4 = 0.

Arithmetic Progression (A.P.) and Geometric Progression (G.P.)

Simple cases only, including word problems. (Include sum for A.P. and exclude sum for G.P).

Sets - Concepts and Notations

Idea of sets, universal sets, finite and infinite sets, subsets, empty sets and disjoint sets. Idea of and notation for union, intersection and complement of sets. Notations: ∈, ⊂, ∪, ∩, { }, Ø, P'( the compliment of P). Properties e.g. commutative, associative and distributive.

Circles - Chords

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

Logical Reasoning - Simple Statements

Simple statements. True and false statements. Negation of statements, implications. Use of symbols: ⇒, ⇔, use of Venn diagrams.

Linear Inequalities - Graphical Solution in Two Variables

Maximum and minimum values. Application to real life situations e.g. minimum cost, maximum profit, linear programming, etc.

Rational Numbers - Operations

The four basic operations on rational numbers. Match rational numbers with points on the number line.

Surds (Radicals) - Simplification and Rationalization

Notation: Natural numbers (N), Integers (Z), Rational numbers (Q). Surds of the form a/√b and a ±√bwhere a is a rational number and b is a positive integer. Basic operations on surds (exclude surd of the form a / (b+c√d)).

Algebraic Fractions with Binomial Denominators

Simple cases only e.g. 1/(x-a) + 1/(x-b) = (2x-a-b)/((x-a)(x-b)) where a and b are constants and x≠a or b. Values for which a fraction is undefined e.g. 1/(x+3) is not defined for x = -3.

Functions and Relations - Types

One-to-one, one-to-many, many-to-one, many-to-many. Functions as a mapping, determination of the rule of a given mapping/function.

Matrices and Determinants - Determinant of a Matrix

Application to solving simultaneous linear equations in two variables. Restrict to 2 x 2 matrices.

Ratio, Proportions and Rates - Concepts

Ratio between two similar quantities. Proportion between two or more similar quantities. Relate to real life situations.

Ratio, Proportions and Rates - Financial Applications

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

Percentages

Simple interest, commission, discount, depreciation, profit and loss, compound interest, hire purchase and percentage error. Limit compound interest to a maximum of 3 years.

Financial Arithmetic - Depreciation/Amortization

Definition/meaning, calculation of depreciation on fixed assets, computation of amortization on capitalized assets.

Construction - Angles

Angles e.g. 90°, 60°, 45°, 30°, and an angle equal to a given angle. Include combination of these angles e.g. 75°, 105°,135°, etc.

Financial Arithmetic - Capital Market Instruments

Shares/stocks, debentures, bonds, simple problems on interest on bonds and debentures.

Variation

Direct, inverse, partial and joint variations. Expression of various types of variation in mathematical symbols e.g. direct (z ∝ n), inverse (z ∝ 1/n), etc. Application to simple practical problems.