Math

WASSCE Math Prep Course

Our Math Prep Course cover every topic. Passing the Math Exam is one of the major steps you will take toward gaining admission to a top university.

 

With our QBank (Question Bank) and problem-solving strategies, we aim to help you gain confidence in your Math skills. Remember, practice makes perfect, we’re here to help you succeed in your WASSCE journey and beyond!

Course Descriptions

Core Mathematics

1. Sets & Operation on Sets

Introduction to Sets:

  • Definition of a set, elements (members) of a set
  • Set notation (curly braces {}, use of capital letters for sets)
  • Describing sets: Roster method (listing elements) and Set-builder notation (rule method)

Types of Sets

Operations on Sets:

  • Union of sets (∪)
  • Intersection of sets (∩)
  • Complement of a set (A' or Aᶜ)
  • Difference of sets (A - B)
  • Disjoint sets

Venn Diagrams

  • Using Venn diagrams to represent sets and operations (2-set and 3- set problems)
  • Solving practical problems using Venn diagrams

Cardinality of Sets

  • Number of elements in a set n(A)
  • Problems involving n(A∪B) and n(A∪B∪C)

2. Algebraic Expressions

Basic Concepts:

  • Variables, constants, terms, coefficients
  • Like and unlike terms

Operations on Algebraic Expressions:

  • Addition and subtraction of algebraic expressions (collecting like terms)
  • Multiplication of algebraic expressions (monomial by polynomial, binomial by binomial, etc.)
  • Division of algebraic expressions (polynomial by monomial)

Expansion and Factorisation:

Expanding brackets (including binomial expansion like (a+b)²) * Factorisation:

  • Common factors
  • Difference of two squares (a² - b²) * Quadratic trinomials (ax² + bx + c)
  • Grouping

Algebraic Fractions

  • Simplifying algebraic fractions
  • Addition, subtraction, multiplication, and division of algebraic fractions

Indices and Surds (as part of algebraic manipulation):

  • Basic laws of indices applied to algebraic terms
  • Simplification and rationalisation of surds

3. Formulas, Linear Equations & Inequalities

Formulas:

  • Substitution of values into formulas
  • Changing the subject of a formula

Linear Equations:

  • Solving linear equations in one variable (including those with brackets and fractions)
  • Word problems leading to linear equations
  • Simultaneous linear equations in two variables:
  • Elimination method
  • Substitution method
  • Graphical method

Linear Inequalities

  • Solving linear inequalities in one variable

Representing solutions on a number line

  • Solving simultaneous linear inequalities in one variable
  • (Introduction to graphical representation of linear inequalities in two variables)

4. Bearings & Vectors in a Plane

Bearings:

  • Understanding and measuring bearings (three-figure bearings, e.g., 045°, 120°)
  • Finding the bearing of one point from another
  • Back bearings
  • Solving problems involving distances and bearings (often using trigonometry)

Vectors:

  • Definition of a vector (magnitude and direction)
  • Representation of vectors (e.g., AB, a, column vectors)
  • Position vectors
  • Equal vectors, negative vectors
  • Addition and subtraction of vectors (triangle law, parallelogram law)
  • Scalar multiplication of a vector
  • Magnitude (or modulus) of a vector
  • Using vectors to solve simple geometric problems (e.g., showing collinearity, properties of shapes)

5. Statistics & Probability

Statistics:

Data Collection and Presentation:

  • Types of data (discrete, continuous)
  • Frequency tables (for ungrouped and grouped data)
  • Graphical representation: Pictograms, bar charts, pie charts, histograms (for grouped data), frequency polygons
  • Cumulative frequency tables and curves (ogives)

Statistics:

Measures of Central Tendency:

  • Mean, median, and mode for ungrouped data
  • Mean, median (estimation from ogive), and modal class for grouped data

Statistics:

Measures of Dispersion (Spread):

  • Range
  • Interquartile range (IQR) and semi-interquartile range (quartile deviation) – often estimated from ogive
  • (Introduction to Variance and Standard Deviation for ungrouped data)

Probability:

  • Basic concepts: Experiment, sample space, event, outcome
  • Theoretical probability: P(Event) = (Number of favourable outcomes) / (Total possible outcomes)
  • Experimental probability (relative frequency)
  • Range of probability (0 ≤ P(Event) ≤ 1)
  • Mutually exclusive events: P(A or B) = P(A) + P(B)
  • Independent events: P(A and B) = P(A) × P(B)
  • Using possibility diagrams and tree diagrams to solve probability problems

6. Indices & Logarithms

Indices (Exponents):

Laws of indices:

  • aᵐ × aⁿ = aᵐ⁺ⁿ
  • aᵐ ÷ aⁿ = aᵐ⁻ⁿ
  • (aᵐ)ⁿ = aᵐⁿ
  • a⁰ = 1
  • a⁻ⁿ = 1/aⁿ
  • a¹/ⁿ = ⁿ√a
  • aᵐ/ⁿ = (ⁿ√a)ᵐ or ⁿ√(aᵐ)

Solving equations involving indices

Logarithms:

Definition of logarithm: y = aˣ ⇔ x = logₐy

Laws of logarithms:

  • logₐ(xy) = logₐx + logₐy
  • logₐ(x/y) = logₐx - logₐy
  • logₐ(xⁿ) = n logₐx

Logarithms to base 10 (common logarithms) and base e (natural logarithms - introduction)

Change of base of logarithms

Solving equations involving logarithms

7. Quadratic Functions & Equations

Quadratic Expressions:

  • Expansion: (ax+b)(cx+d)
  • Factorisation of quadratic expressions: ax² + bx + c

Quadratic Equations:

Solving quadratic equations by:

  • Factorisation
  • Completing the square
  • Using the quadratic formula: x = [-b ± √(b²-4ac)] / 2a

The discriminant (Δ = b²-4ac) and the nature of roots (real distinct, real equal, no real roots)

Forming quadratic equations given their roots (sum and product of roots)

Word problems leading to quadratic equations

Graphs of Quadratic Functions:

  • Plotting graphs of y = ax² + bx + c
  • Identifying features: Shape (parabola), axis of symmetry, vertex (minimum/maximum point), x-intercepts (roots), y-intercept
  • Solving quadratic equations graphically
  • (Solving simultaneous linear and quadratic equations)

8. Mensuration

Perimeter and Area of Plane Shapes:

  • Triangles (including Heron's formula if covered)
  • Quadrilaterals: Square, rectangle, parallelogram, rhombus, trapezium, kite
  • Circles: Circumference, arc length, area of a circle, area of a sector, area of a segment
  • Area of composite plane shapes

Surface Area and Volume of Solid Shapes:

  • Cube and Cuboid
  • Cylinder (curved surface area, total surface area, volume)
  • Cone (curved surface area, total surface area, volume)
  • Sphere (surface area, volume)
  • Pyramid (right pyramids with rectangular or triangular base)
  • Prism (right prisms with triangular or rectangular base)
  • Volume and surface area of frustums (of cones and pyramids - if covered)
  • Volume and surface area of composite solid shapes

9. Trigonometry

Right-Angled Triangles:

  • Trigonometric ratios: Sine (sin), Cosine (cos), Tangent (tan) - SOH CAH TOA
  • Solving right-angled triangles (finding unknown sides and angles)
  • Angles of elevation and depression

Trigonometry of General Angles:

  • Trigonometric ratios for angles beyond 90° (0° to 360°) using the unit circle or CAST diagram
  • Sine Rule: a/sinA = b/sinB = c/sinC
  • Cosine Rule: a² = b² + c² - 2bc cosA (and its rearrangements)
  • Area of a triangle: ½ab sinC

Graphs of Trigonometric Functions:

  • Graphs of y = sin x, y = cos x, y = tan x (periodicity, amplitude for sin/cos)

Simple Trigonometric Identities and Equations:

  • Basic identities: sin²θ + cos²θ = 1, tanθ = sinθ/cosθ
  • Solving simple trigonometric equations (e.g., sin x = 0.5 for 0° ≤ x ≤ 360°)

10. Sequences & Series

Introduction to Sequences:

  • Definition of a sequence, terms of a sequence
  • Finding the nth term (rule) for simple sequences

Arithmetic Progression (AP) / Linear Sequence:

  • Definition, common difference (d)
  • The nth term: Tₙ = a + (n-1)d
  • Sum of the first n terms: Sₙ = n/2 [2a + (n-1)d] or Sₙ = n/2 [a + l] (where l is the last term)

Geometric Progression (GP) / Exponential Sequence:

  • Definition, common ratio (r)
  • The nth term: Tₙ = arⁿ⁻¹
  • Sum of the first n terms: Sₙ = a(rⁿ-1)/(r-1) or Sn = a(1-rⁿ)/(1-r) (for r ≠ 1)
  • Sum to infinity of a GP (for |r| < 1): S∞ = a/(1-r)

Sets & Functions

  • Review of sets, subsets, and Venn diagrams
  • Functions and mappings
  • Domain, range, composite and inverse functions

Surds & Indices

  • Simplification of surds
  • Laws of indices
  • Rationalization of denominators

Polynomials & Factorization

  • Polynomial expressions and long division
  • Factor and remainder theorems
  • Solving polynomial equations

Quadratic and Simultaneous Equations

  • Solving quadratic equations by formula, completing square, and factorization
  • Simultaneous linear and quadratic equations

Trigonometry Basics

  • Trigonometric ratios
  • Trigonometric identities and equations
  • Graphs of sine, cosine, and tangent

Plane Geometry

  • Circle theorems
  • Properties of triangles and quadrilaterals
  • Congruency and similarity

Coordinate Geometry

  • Distance between two points
  • Midpoint and gradient
  • Equation of a line

Linear and Quadratic Inequalities

  • Inequalities in one variable
  • Linear inequalities in two variables
  • Graphical solution of inequalities

Differentiation

  • Limits and continuity
  • Derivatives from first principles
  • Rules of differentiation

Applications of Differentiation

  • Tangents and normals
  • Maxima and minima
  • Rate of change

Vectors

  • Vector notation and operations
  • Position vectors
  • Vector equations of lines

Mechanics (Intro)

  • Scalars and vectors in motion
  • Displacement, velocity, and acceleration

Linear Transformation

  • Matrix representation of transformations
  • Reflection, rotation, translation, enlargement
  • Inverse of transformation

Matrices

  • Matrix addition, subtraction, and multiplication
  • Determinants and inverse of 2x2 matrices
  • Solving equations using matrices

Permutation & Combination

  • Factorials
  • nPr and nCr formulas
  • Application to real-life problems

Probability

  • Sample space and events
  • Probability rules
  • Tree diagrams and Venn diagrams

Statistics

  • Data presentation (bar chart, histogram, pie chart)
  • Measures of central tendency: mean, median, mode
  • Measures of dispersion: range, variance, standard deviation

Integration

  • Indefinite and definite integrals
  • Integration of polynomials
  • Area under curves

Elective Mathematics

Gold Package

This is our one-year Elective Mathematics program.

Silver Package

This is our six-month Elective Mathematics program

Bronze Package

This is our three-month Elective Mathematics program.

Core Mathematics

Gold Package

This is our one-year Core Mathematics program.

Silver Package

This is our six-month Core Mathematics program

Bronze Package

This is our three-month Core Mathematics program

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