1. Proof

1.1 Proof

1.1.1 Language of Proof

1.1.2 Proof by Deduction

1.1.3 Proof by Exhaustion

1.1.4 Disproof by Counter Example

2. Algebra & Functions

2.1 Laws of Indices & Surds

2.1.1 Laws of Indices

2.1.2 Manipulating Surds

2.1.3 Surds - Rationalising the Denominator

2.2 Quadratics

2.2.1 Quadratic Graphs

2.2.2 Discriminants

2.2.3 Completing the square

2.2.4 Solving Quadratic Equations

2.2.5 Further Solving Quadratic Equations (Hidden Quadratics)

2.3 Simultaneous Equations

2.3.1 Linear Simultaneous Equations - Elimination

2.3.2 Linear Simultaneous Equations - Substitution

2.3.3 Quadratic Simultaneous Equations

2.4 Inequalities

2.4.1 Linear Inequalities

2.4.2 Quadratic Inequalities

2.4.3 Inequalities on Graphs

2.5 Polynomials

2.5.1 Expanding Brackets

2.5.2 Polynomial Division

2.5.3 Factor Theorem

2.5.4 Factorisation

2.6 Graphs of Functions

2.6.1 Sketching Polynomials

2.6.2 Reciprocal Graphs - Sketching

2.6.3 Solving Equations Graphically

2.6.4 Proportional Relationships

2.7 Transformations of Functions

2.7.1 Translations

2.7.2 Stretches

2.7.3 Reflections

2.8 Modelling with Functions

2.8.1 Modelling with Functions

3. Coordinate Geometry

3.1 Equation of a Straight Line

3.1.1 Basic Coordinate Geometry

3.1.2 Parallel & Perpendicular Gradients

3.1.3 Equation of a Straight Line

3.1.4 Modelling with Straight Lines

3.2 Circles

3.2.1 Equation of a Circle

3.2.2 Finding the Centre & Radius

3.2.3 Bisection of Chords

3.2.4 Angle in a Semicircle

3.2.5 Radius & Tangent

4. Sequences and Series

4.1 Binomial Expansion

4.1.1 Binomial Expansion

5. Trigonometry

5.1 Basic Trigonometry

5.1.1 Trigonometry - Definitions

5.1.2 Right-Angled Triangles

5.1.3 Non-Right-Angled Triangles

5.2 Trigonometric Functions

5.2.1 Graphs of Trigonometric Functions

5.2.2 Transformations of Trigonometric Functions

5.3 Trigonometric Equations

5.3.1 Trigonometry - Simple Identities

5.3.2 Linear Trigonometric Equations

5.3.3 Quadratic Trigonometric Equations

5.3.4 Strategy for Trigonometric Equations

6. Exponentials & Logarithms

6.1 Exponential & Logarithms

6.1.1 Exponential Functions

6.1.2 Logarithmic Functions

6.1.3 "e"

6.1.4 Derivatives of Exponential Functions

6.2 Laws of Logarithms

6.2.1 Laws of Logarithms

6.2.2 Exponential Equations

6.3 Modelling with Exponentials & Logarithms

6.3.1 Exponential Growth & Decay

6.3.2 Using Exps & Logs in Modelling

6.3.3 Using Log Graphs in Modelling

7. Differentiation

7.1 Differentiation

7.1.1 Definition of Gradient

7.1.2 First Principles Differentiation

7.1.3 Differentiating Powers of x

7.2 Applications of Differentiation

7.2.1 Gradients, Tangents & Normals

7.2.2 Increasing & Decreasing Functions

7.2.3 Second Order Derivatives

7.2.4 Stationary Points & Turning Points

7.2.5 Sketching Gradient Functions

7.2.6 Modelling with Differentiation inc. Optimisation

8. Integration

8.1 Integration

8.1.1 Fundamental Theorem of Calculus

8.1.2 Integrating Powers of x

8.1.3 Definite Integration

8.1.4 Area Under a Curve

8.1.5 Area between a curve and a line

9. Vectors

9.1 Vectors in 2 Dimensions

9.1.1 Basic Vectors

9.1.2 Magnitude & Direction

9.1.3 Vector Addition

9.1.4 Position Vectors

9.1.5 Problem Solving using Vectors