Number and Algebra

Numbers, expressions, equations, functions, sequences and other core algebra.

Chapter 1
Introduction to Mathematics
What is Mathematics? · Branches of Mathematics · Mathematics in Daily Life and Careers · Contributions of Muslim Mathematicians
4 topicsInteractive lesson
Class 9Class 10Class 11Class 12O LevelA Level
Chapter 2
Real Numbers
Natural Numbers, Integers, Rational and Irrational Numbers · The Real Number Line · Properties of Real Numbers · Surds and Rationalising the Denominator …
7 topicsInteractive lesson
Class 9O Level
Chapter 3
Complex Numbers
The Imaginary Unit i · Complex Numbers and Equality · Operations on Complex Numbers · Conjugate and Modulus …
7 topics
Class 9Class 11A Level
Chapter 4
Logarithms and Exponentials
What is a Logarithm? · Common and Natural Logarithms · Laws of Logarithms · Using Logarithms in Calculations …
6 topics
Class 9A Level
Chapter 5
Algebraic Expressions and Formulas
Algebraic Expressions · Evaluating Expressions · Algebraic Identities and Formulas · Rational Expressions and Simplification …
5 topics
Class 9O Level
Chapter 6
Factorisation and Algebraic Manipulation
Common Factors and Grouping · Difference of Two Squares · Perfect Squares and Trinomials · Remainder Theorem and Factor Theorem …
7 topics
Class 9O LevelA Level
Chapter 7
Linear Equations and Inequalities
Solving Linear Equations · Equations with Absolute Value · Linear Inequalities · Simultaneous Linear Equations …
5 topics
Class 9O Level
Chapter 8
Linear Graphs and their Applications
The Cartesian Plane · Drawing Linear Graphs · Gradient and Intercept · Conversion Graphs …
6 topics
Class 9O Level
Chapter 9
Quadratic Equations
Standard Form of a Quadratic · Solving by Factorisation · Completing the Square · Quadratic Formula …
10 topics
Class 9Class 10O LevelA Level
Chapter 10
Partial Fractions
Proper and Improper Fractions · Linear Factors · Repeated Linear Factors · Quadratic Factors
4 topics
Class 10A Level
Chapter 11
Sets and Functions
Sets and Set Notation · Operations on Sets · Venn Diagrams · Ordered Pairs and Cartesian Product …
7 topics
Class 10O Level
Chapter 12
Functions and Graphs
Function Notation · Composite Functions · Inverse Functions · Graphs of Polynomial, Rational and Modulus Functions …
6 topics
Class 11O LevelA Level
Chapter 13
Ratio, Proportion and Variation
Ratio · Proportion · Direct Variation · Inverse Variation …
7 topics
Class 10O Level
Chapter 14
Matrices and Determinants
Types of Matrices · Addition, Subtraction and Scalar Multiplication · Matrix Multiplication · Determinant of a Matrix …
8 topics
Class 10Class 11
Chapter 15
Sequences and Series
Sequences and the nth Term · Arithmetic Progression · Sum of an Arithmetic Series · Geometric Progression …
9 topics
Class 11O LevelA Level
Chapter 16
Mathematical Induction and Binomial Theorem
Principle of Mathematical Induction · Binomial Theorem for Positive Integers · General Term of a Binomial Expansion · Binomial Series for Any Index
4 topics
Class 11A Level
Chapter 17
Linear Programming
Linear Inequalities in Two Variables · Feasible Region · Objective Function · Finding the Optimal Solution
4 topics
Class 11

Geometry and Trigonometry

Triangles, circles, constructions, shapes and solids, and trigonometry.

Coordinate Geometry and Vectors

Lines, circles and conic sections on the coordinate plane, and vectors.

Calculus and Numerical Methods

Limits, differentiation, integration, differential equations and numerical methods.

Statistics and Probability

Collecting and summarising data, counting, probability and probability distributions.

Mechanics (A Level Mathematics)

The mechanics paper of Cambridge A Level Mathematics: forces, motion, energy and momentum.

Number and Algebra

Introduction to Mathematics

Real Numbers

Complex Numbers

Logarithms and Exponentials

Algebraic Expressions and Formulas

Factorisation and Algebraic Manipulation

Linear Equations and Inequalities

Linear Graphs and their Applications

Quadratic Equations

Partial Fractions

Sets and Functions

Functions and Graphs

Ratio, Proportion and Variation

Matrices and Determinants

Sequences and Series

Mathematical Induction and Binomial Theorem

Linear Programming

Geometry and Trigonometry

Triangles and Congruence

Practical Geometry

Pythagoras' Theorem

Circle Geometry

Similarity, Symmetry and Transformations

Mensuration

Trigonometry

Trigonometric Identities and Equations

Coordinate Geometry and Vectors

Coordinate Geometry: the Straight Line

The Circle

Conic Sections

Vectors

Calculus and Numerical Methods

Functions and Limits

Differentiation

Applications of Differentiation

Differentiation of Vector Functions

Integration

Differential Equations

Partial Differentiation

Numerical Methods

Introduction to MAPLE

Statistics and Probability

Basic Statistics

Permutations and Combinations

Probability

Probability Distributions

Mechanics (A Level Mathematics)

Forces and Equilibrium

Kinematics in a Straight Line

Newton's Laws of Motion

Energy, Work and Power

Momentum