Outlined below are the pure maths / core topics covered for AQA Mathematics A-Level

It is advisable to check the official AQA Mathematics A-Level specification for any changes.

## Contents for Pure Maths AQA

## Prior Knowledge

## Algebra Basics

- Expanding a single bracket
- Expanding two or more brackets
- Squaring a bracket
- Terms in expressions and equations
- Identity or equation - what is the difference?
- Linear Equations with a positive x term
- Linear equations with a negative x-term
- Linear equations with two x-terms
- Linear equations with brackets
- Fractional linear equations
- f(x) notation
- Polynomials

## Polynomials

## Pythagoras’ Theorem

## Trigonometry Introduction

## Algebra and Functions : 1

## Indices

- Introduction to indices (exponents)
- Multiplication rules for indices
- Division rule for indices
- Negative indices
- Fractions raised to a negative index
- Rational (fractional) indices
- Simplifying terms with negative powers
- Expressing terms in the form ax
^{n} - Equations in which the power has to be found
- Summary of indices
- Exam Questions - Indices

## Surds

## Functions

## Factorising

## Completing the Square

## Quadratic Equations

## Quadratic Equations – Roots and Discriminant

## Quadratic Graphs

## Simultaneous Equations

## Inequalities

## Algebraic Long Division

## Rational Expressions – Simplifying

- Simplifying algebraic fractions
- Exam Questions - Simplifying a rational expression
- Addition and subtraction of algebraic fractions
- Exam Questions - Addition & subtraction
- Multiplication of algebraic fractions
- Further simplifying of 'stacked fractions'
- Division of algebraic fractions
- Exam Questions - Algebraic long division

## Coordinate Geometry

## Gradient of Straight Lines

## Straight Lines

## Intersection of Graphs

## Exam Questions – Straight Lines

## Circles

## Parametric Equations

## Algebra and Functions : 2

## Sketching Cubic and Reciprocal Curves

## Modulus Functions, Equations and Inequalities

## Working with Functions

## Graph Transformations

## Partial Fractions

## Sequences and Series

## Binomial Expansion

- Binomial expansion
- Exam Questions - Binomial expansion for positive integer powers
- Exam Questions - Binomial expansion, comparing coefficients
- Exam Questions - Binomial expansion, estimating a value
- Exam Questions - Binomial expansion, other
- Exam Questions - Binomial expansion for rational and negative powers
- Exam Questions - Partial fractions with the binomial expansion

## Working with Sequences and Series

## Arithmetic Sequence and Series

## Geometric Sequence and Series

## Trigonometry

## Trigonometric Ratios

## Trigonometric Graphs and Transformations

## Applications of Trigonometry

## Trigonometric Equations

## Trigonometric Identities

## Sec θ, Cosec θ and Cot θ

## Inverse trigonometric functions

## Identities & Equations – Pythagorean Type

## Small-angle Approximations

## Identities – Addition type

## Identities & Equations – Double angle type

## Identities – Half angle type

## Identities – Triple angle type

## Identities & Equations – Harmonic Formulae

## Exam Questions – Mixed trigonometry

## Logarithmic and Exponential Functions

## Exponential Functions and Logarithms

## The Exponential Function e^{x} and Natural Log Functions

## Modelling Curves of the form y=kx^{n} and y=ka^{x}

## Differentiation

## Differentiation – Introduction

## Tangents and Normals

## Stationary Points

## Increasing and Decreasing functions

## Standard Differentials

## The Chain Rule

## The Product and Quotient Rules

## More Standard Differentials

## The Reciprocal Function of dy/dx

## Exam Questions – Differentiation

## Exponential Functions

## Parametric Functions

## Connected Rates of Change

## Integration

## Integration – Introduction

## Equations of Curves

## Definite Integration

## Integration – Common Functions

- Integration:(ax+b)
^{n}types - Exam Questions - Integration:(ax+b)
^{n}types - Integrating exponential functions e
^{x}, e^{ax}and e^{(ax+b)} - Exam Questions - Integrating exponential functions e
^{x}, e^{ax}and e^{(ax+b)} - Integrating reciprocal functions 1/x and 1/(ax+b)
- Exam Questions - Integrating reciprocal functions 1/x and 1/(ax+b)
- Integrals of the form : f '(x)/f(x)
- Integrals of the form : f'(x)e
^{f(x)}

## Integrals of Trigonometric Functions

## Integrals involving Partial fractions

## Integration by Substitution

## Integrals of the form f[g(x)]g'(x) by inspection

## Integration by Parts

## General Methods – Integration

## Applications of Integration – Area bound by a curve

## Differential equations – Separating the variables

## Differential equations – Forming differential equations

## Numerical Methods

## Solution of Equations by Numerical methods

## Numerical Integration

## Vectors

## Vectors

- What is a vector and a scalar quantity?
- Vector notation 2d
- Vector notation
- Position vectors 2d
- Position vectors
- Equal and negative vectors
- Multiplying a vector by a scalar 2d
- Multiplying a vector by a scalar
- Addition and subtraction of vectors 2d
- Addition and subtraction of vectors
- Magnitude of a 2 dimensional vector
- Magnitude of a 3 dimensional vector
- Unit vectors
- Exam Questions - Vectors

- circles
- chain rule
- change of sign
- completing the square
- connected rates of change
- coordinate geometry
- cosine rule
- cubic graph

- sector
- segment
- sequences and series
- sigma notation
- simultaneous equations
- sine rule
- stationary points
- straight lines
- surds

- tangents to curves
- transformations:
- graphs
- trapezium rule
- trigonometric:
- equations
- graphs
- ratios 30°, 60°, 45°
- trigonometry
- cosine rule
- cosec, sec and cot θ
- inverse functions
- sine rule
- small angles
- trigonometry – identities:
- addition formulae
- double angle formulae
- half angle formulae
- harmonic formulae
- Pythagorean
- triple angle formulae