1. Algebra & Functions

1.1 Quadratics

1.1.1 Expanding Brackets

1.1.2 Quadratic Graphs

1.1.3 Discriminants

1.1.4 Completing the square

1.1.5 Solving Quadratic Equations

1.1.6 Further Solving Quadratic Equations (Hidden Quadratics)

1.2 Inequalities & Simultaneous Equations

1.2.1 Linear Simultaneous Equations - Elimination

1.2.2 Linear Simultaneous Equations - Substitution

1.2.3 Quadratic Simultaneous Equations

1.2.4 Linear Inequalities

1.2.5 Quadratic Inequalities

1.2.6 Inequalities on Graphs

1.3 Functions

1.3.1 Language of Functions

1.3.2 Composite Functions

1.3.3 Inverse Functions

1.4 Graphs of Functions

1.4.1 Sketching Polynomials

1.4.2 Reciprocal Graphs - Sketching

1.4.3 Solving Equations Graphically

1.4.4 Proportional Relationships

1.5 Transformations of Functions

1.5.1 Translations

1.5.2 Stretches

1.5.3 Reflections

1.6 Combinations of Transformations

1.6.1 Combinations of Transformations

1.7 Modelling with Functions

1.7.1 Modelling with Functions

2. Coordinate Geometry

2.1 Equation of a Straight Line

2.1.1 Basic Coordinate Geometry

2.1.2 Parallel & Perpendicular Gradients

2.1.3 Equation of a Straight Line

2.1.4 Modelling with Straight Lines

2.2 Circles

2.2.1 Equation of a Circle

2.2.2 Finding the Centre & Radius

2.2.3 Bisection of Chords

2.2.4 Angle in a Semicircle

2.2.5 Radius & Tangent

3. Trigonometry

3.1 Basic Trigonometry

3.1.1 Trigonometry - Definitions

3.1.2 Right-Angled Triangles

3.1.3 Non-Right-Angled Triangles

3.2 Trigonometric Functions

3.2.1 Graphs of Trigonometric Functions

3.2.2 Transformations of Trigonometric Functions

3.3 Circular Measure (Radians)

3.3.1 Radian Measure

3.3.2 Trigonometry Exact Values

3.4 Trigonometric Equations

3.4.1 Trigonometry - Simple Identities

3.4.2 Linear Trigonometric Equations

3.4.3 Quadratic Trigonometric Equations

3.4.4 Strategy for Trigonometric Equations

3.5 Modelling with Trigonometric Functions

3.5.1 Modelling with Trigonometric Functions

4. Sequences & Series

4.1 Binomial Expansion

4.1.1 Binomial Expansion

4.2 Arithmetic Progressions

4.2.1 Arithmetic Sequences

4.2.2 Arithmetic Series

4.3 Geometric Progressions

4.3.1 Geometric Sequences

4.3.2 Geometric Series

4.4 Further Sequences & Series

4.4.1 Language of Sequences & Series

4.4.2 Sigma Notation

4.4.3 Recurrence Relations

4.4.4 Modelling with Sequences & Series

5. Differentiation

5.1 Differentiation

5.1.1 Definition of Gradient

5.1.2 Definition of Derivatives

5.1.3 Differentiating Powers of x

5.1.4 Chain Rule

5.2 Applications of Differentiation

5.2.1 Gradients, Tangents & Normals

5.2.2 Increasing & Decreasing Functions

5.2.3 Second Order Derivatives

5.2.4 Stationary Points & Turning Points

5.2.5 Sketching Gradient Functions

5.2.6 Modelling with Differentiation inc. Optimisation

5.2.7 Connected Rates of Change

6. Integration

6.1 Integration

6.1.1 Fundamental Theorem of Calculus

6.1.2 Integrating Powers of x

6.1.3 Definite Integration

6.1.4 Reverse Chain Rule

6.1.5 Improper Integrals

6.2 Further Integration

6.2.1 Area Under a Curve

6.2.2 Area between a curve and a line

6.2.3 Area between 2 curves

6.2.4 Volumes of Revolution

6.2.5 Adding and Subtracting Volumes

6.2.6 Modelling with Volumes of Revolution