Week 1 Day 1: Rational Indices and General Laws of Indices

Week 1 Day 2: Surds — Simplification, Rationalisation and Operations

Week 1 Day 3: Direct, Inverse and Joint Variation

Week 1 Day 4: Partial and Total Variation — Modelling Life Situations

Week 1 Day 5: Week 1 Quiz — Indices & Proportionality

Week 2 Day 1: Polynomial Operations — Addition, Subtraction, Multiplication, Division

Week 2 Day 2: Factor and Remainder Theorems

Week 2 Day 3: Quadratic Operations and Factorisation Techniques

Week 2 Day 4: Solving Cubic and Higher Order Polynomial Equations

Week 2 Day 5: Week 2 Quiz — Polynomials

Week 3 Day 1: Algebraic Identities — Definition and Unknown Coefficients

Week 3 Day 2: Linear and Simultaneous Equations

Week 3 Day 3: Quadratic Equations — Discriminant and Nature of Roots

Week 3 Day 4: Linear and Quadratic Inequalities — Sign Diagrams

Week 3 Day 5: Week 3 Quiz — Identities & Inequalities

Week 4 Day 1: Introduction to Partial Fractions — Distinct Linear Factors

Week 4 Day 2: Repeated Linear Factors and Irreducible Quadratic Factors

Week 4 Day 3: Improper Fractions and Long Division

Week 4 Day 4: Applications of Partial Fractions in Series and Integration

Week 4 Day 5: Week 4 Quiz — Partial Fractions

End of Month 1 Test — Comprehensive Quiz (Weeks 1–4)

Week 5 Day 1: Relations — Definition, Description, Domain and Range

Week 5 Day 2: Functions — Domain, Co-domain and Range

Week 5 Day 3: Types of Functions — Injective, Surjective, Bijective

Week 5 Day 4: Rational and Modulus Functions — Graphs and Properties

Week 5 Day 5: Week 5 Quiz — Relations & Functions

Week 6 Day 1: Composite Functions and Their Domains

Week 6 Day 2: Inverse Functions — Finding and Graphing

Week 6 Day 3: Logarithmic Functions — Definition and Laws

Week 6 Day 4: Exponential Functions — Graphs, Equations and Applications

Week 6 Day 5: Week 6 Quiz — Composite, Inverse, Logs & Exponentials

Week 7 Day 1: Types of Matrices — Null, Identity, Singular, Non-Singular

Week 7 Day 2: Basic Matrix Operations — Addition, Subtraction, Multiplication

Week 7 Day 3: Determinant of a Square Matrix (up to 3×3)

Week 7 Day 4: Inverse of a 3×3 Matrix and Non-Singular Matrices

Week 7 Day 5: Week 7 Quiz — Matrix Operations

Week 8 Day 1: Solving Simultaneous Equations Using Matrices (AX = B)

Week 8 Day 2: Matrix Transformations — Enlargement, Rotation, Reflection

Week 8 Day 3: Stretch, Shear and Composite Transformations

Week 8 Day 4: Determinant as Area Scale Factor and Inverse Transformations

Week 8 Day 5: Week 8 Quiz — Matrix Applications

End of Month 2 Test — Comprehensive Quiz (Weeks 5–8)

Week 9 Day 1: Definition of a Sequence and Sequence Notation

Week 9 Day 2: Recurrence Relations and Successive Terms

Week 9 Day 3: Behaviour of Sequences — Periodic, Oscillating, Converging, Diverging

Week 9 Day 4: Limits of Sequences and Convergence Tests

Week 9 Day 5: Week 9 Quiz — Sequences

Week 10 Day 1: Arithmetic Progressions — nth Term and Sum

Week 10 Day 2: Geometric Progressions — nth Term and Sum

Week 10 Day 3: Sum to Infinity of a Converging Geometric Series

Week 10 Day 4: Applications of Series in Life — Finance, Growth and Decay

Week 10 Day 5: Week 10 Quiz — Series

Week 11 Day 1: Sigma Notation — Use and Manipulation

Week 11 Day 2: Binomial Theorem — Expansion of (a + b)^n

Week 11 Day 3: Binomial Coefficients and Pascal’s Triangle

Week 11 Day 4: Finding a Particular Term or Coefficient in a Binomial Expansion

Week 11 Day 5: Week 11 Quiz — Sigma & Binomial

Week 12 Day 1: Mathematical Induction — Proof by Induction

Week 12 Day 2: Conjecture and Proof — Divisibility and Series Identities

Week 12 Day 3: Binary Operations — Closure, Commutativity, Associativity

Week 12 Day 4: Groups — Identity, Inverse and Basic Properties

Week 12 Day 5: Week 12 Quiz — Induction & Groups

End of Month 3 Test — Comprehensive Quiz (Weeks 9–12)

Week 13 Day 1: Equations of Parallel and Perpendicular Lines

Week 13 Day 2: Distance Between Two Points and Point-to-Line Distance

Week 13 Day 3: Equation of a Circle — Standard and General Form

Week 13 Day 4: Tangents and Normals to Circles

Week 13 Day 5: Week 13 Quiz — Coordinate Geometry

Week 14 Day 1: Parametric Equations — Definition and Conversion

Week 14 Day 2: Sketching Curves Defined Parametrically

Week 14 Day 3: Curve Sketching — y = f(x), y = 1/f(x), y = f(|x|)

Week 14 Day 4: Reducing Equations to Appropriate Linear Form

Week 14 Day 5: Week 14 Quiz — Parametric & Curve Sketching

Week 15 Day 1: Vector Notation and Vector Operations

Week 15 Day 2: Types of Vectors — Position, Free, Displacement, Unit

Week 15 Day 3: Addition, Subtraction and Scalar Multiplication of Vectors

Week 15 Day 4: Scalar (Dot) Product and Vector Applications in Geometry

Week 15 Day 5: Week 15 Quiz — Vectors

Week 16 Day 1: Radians and Degrees — Conversion and Use

Week 16 Day 2: Arc Length and Area of a Sector

Week 16 Day 3: Area of Segments and Mixed Problems

Week 16 Day 4: Small Angle Approximations and Applications

Week 16 Day 5: Week 16 Quiz — Trigonometry Basics

End of Month 4 Test — Comprehensive Quiz (Weeks 13–16)

Week 17 Day 1: Trigonometric Functions — Graphs and Properties

Week 17 Day 2: Trigonometric Identities — Proving and Using

Week 17 Day 3: Compound Angle and Double Angle Formulae

Week 17 Day 4: Solving Trigonometric Equations — General Solutions

Week 17 Day 5: Week 17 Quiz — Trigonometric Functions & Identities

Week 18 Day 1: Differentiation from First Principles

Week 18 Day 2: Derivative Notation and Rules — Power, Sum, Constant

Week 18 Day 3: Derivatives of Polynomials, Rational, Exponential and Logarithmic Functions

Week 18 Day 4: Derivatives of Trigonometric Functions — sin, cos, tan

Week 18 Day 5: Week 18 Quiz — Differentiation Rules

Week 19 Day 1: Product Rule — Differentiation of uv and Applications

Week 19 Day 2: Quotient Rule — Differentiation of u/v and Applications

Week 19 Day 3: Chain Rule — Composite Functions

Week 19 Day 4: Implicit and Parametric Differentiation

Week 19 Day 5: Week 19 Quiz — Advanced Differentiation

Week 20 Day 1: Gradients, Tangents and Normals

Week 20 Day 2: Stationary Points — Maximum, Minimum, Point of Inflection

Week 20 Day 3: Second Derivative Test and Optimisation Problems

Week 20 Day 4: Rates of Change and Modelling Real-Life Situations

Week 20 Day 5: Week 20 Quiz — Differentiation Applications

End of Month 5 Test — Comprehensive Quiz (Weeks 17–20)

Week 21 Day 1: Integration as the Reverse of Differentiation

Week 21 Day 2: Indefinite Integrals of Polynomial, Rational, Exponential and Trigonometric Functions

Week 21 Day 3: Standard Integrals — Exponential, Sine and Cosine

Week 21 Day 4: The Constant of Integration and Initial Conditions

Week 21 Day 5: Week 21 Quiz — Indefinite Integrals

Week 22 Day 1: Definite Integrals — Fundamental Theorem of Calculus

Week 22 Day 2: Area Under a Curve Between Two Limits

Week 22 Day 3: Area Between Two Curves

Week 22 Day 4: Improper Integrals and Convergence

Week 22 Day 5: Week 22 Quiz — Definite Integrals

Week 23 Day 1: Integration by Recognition

Week 23 Day 2: Integration by Substitution

Week 23 Day 3: Integration by Parts — Formula and Examples

Week 23 Day 4: Integration Using Partial Fractions

Week 23 Day 5: Week 23 Quiz — Advanced Integration

Week 24 Day 1: Volumes of Revolution about the x-axis

Week 24 Day 2: Volumes of Revolution about the y-axis

Week 24 Day 3: Modelling Life Phenomena with Integration

Week 24 Day 4: Solving Differential Equations by Separation of Variables

Week 24 Day 5: Week 24 Quiz — Integration Applications

End of Month 6 Test — Comprehensive Quiz (Weeks 21–24)

Week 26 Day 1: Introduction to Complex Numbers — Real and Imaginary Parts

Week 26 Day 2: Arithmetic Operations — Addition, Subtraction, Multiplication, Division

Week 26 Day 3: Complex Conjugate and Modulus

Week 26 Day 4: Solving Polynomial Equations with Non-Real Roots

Week 26 Day 5: Week 26 Quiz — Complex Numbers

Week 27 Day 1: Argand Diagrams — Representing Complex Numbers

Week 27 Day 2: Polar Form — Modulus and Argument

Week 27 Day 3: Multiplication and Division in Polar Form

Week 27 Day 4: De Moivre’s Theorem and Applications

Week 27 Day 5: Week 27 Quiz — Polar Form & Argand Diagrams

Week 28 Day 1: Paper 1 Review — Algebra, Geometry and Vectors

Week 28 Day 2: Paper 1 Review — Series, Trigonometry and Calculus

Week 28 Day 3: Paper 2 Review — Matrices, Numerical Methods and Complex Numbers

Week 28 Day 4: Exam Technique — Proof Writing, Time Management and Final Tips

Week 28 Day 5: Week 28 Quiz — Full Syllabus Review

Final Exam — Comprehensive Test (Full Syllabus)