Proof

Proof

Language of Proof

Proof by Deduction

Proof by Exhaustion

Disproof by Counter Example

Algebra & Functions

Laws of Indices & Surds

Laws of Indices

Manipulating Surds

Rationalising the Denominator with Surds

Quadratics

Quadratic Graphs

Discriminants

Completing the square

Solving Quadratic Equations

Solving Hidden Quadratics using Substitutions

Simultaneous Equations

Linear Simultaneous Equations using Elimination

Linear Simultaneous Equations using Substitution

Quadratic Simultaneous Equations

Inequalities

Linear Inequalities

Quadratic Inequalities

Inequalities on Graphs

Polynomials

Expanding Brackets

Polynomial Division

Factor Theorem

Factorisation

Graphs of Functions

Sketching Polynomials

Sketching Reciprocal Graphs

Solving Equations Graphically

Proportional Relationships

Transformations of Functions

Translations

Stretches

Reflections

Modelling with Functions

Modelling with Functions

Coordinate Geometry

Equation of a Straight Line

Basic Coordinate Geometry

Equation of a Straight Line

Parallel & Perpendicular Gradients

Modelling with Straight Lines

Circles

Equation of a Circle

Finding the Centre & Radius

Bisection of Chords

Angle in a Semicircle

Radius & Tangent

Sequences & Series

Binomial Expansion

Binomial Expansion

Trigonometry

Basic Trigonometry

Definitions of Trigonometric Functions

Right-Angled Triangles

Non-Right-Angled Triangles

Trigonometric Functions

Graphs of Trigonometric Functions

Transformations of Trigonometric Functions

Simple Trigonometric Identities

Trigonometric Equations

Linear Trigonometric Equations

Quadratic Trigonometric Equations

Strategy for Trigonometric Equations

Exponentials & Logarithms

Exponential & Logarithms

Exponential Functions

Logarithmic Functions

"e"

Derivatives of Exponential Functions

Laws of Logarithms

Laws of Logarithms

Exponential Equations

Modelling with Exponentials & Logarithms

Exponential Growth & Decay

Using Exponentials & Logarithms in Modelling

Logarithmic Graphs

Differentiation

Differentiation

Definition of Gradient

Differentiation from First Principles

Differentiating Powers of x

Applications of Differentiation

Gradients, Tangents & Normals

Increasing & Decreasing Functions

Second Order Derivatives

Stationary Points & Turning Points

Sketching Gradient Functions

Modelling with Differentiation (Optimisation)

Integration

Integration

Fundamental Theorem of Calculus

Integrating Powers of x

Definite Integration

Area Under a Curve

Area Between a Curve & a Line

Vectors

Vectors in 2D

Basic Vectors

Magnitude & Direction

Vector Addition

Position Vectors

Problem Solving using Vectors

Exam boards

• Edexcel AS Maths: Statistics
• Edexcel AS Maths: Mechanics
• OCR AS Maths A: Pure
• OCR AS Maths A: Statistics
• OCR AS Maths A: Mechanics

Study tools

• Edexcel AS Maths · Exam Questions
• Edexcel AS Maths · Past Papers

Related links

• AS Maths · Revision Notes
• AS Maths · Exam Questions
• AS Maths · Past Papers