# AQA Pure Maths AS Tutorials

Outlined below are the topics covered for AQA Pure maths AS course

It is advisable to check the official AQA Pure maths AS specification in case of changes: specification

## Contents for Pure Maths AS 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

## Coordinate Geometry

## Gradient of Straight Lines

## Straight Lines

## Intersection of Graphs

## Exam Questions – Straight Lines

## Circles

## Algebra and Functions : 2

## Sketching Cubic and Reciprocal Curves

## Graph Transformations

## Sequences and Series

## Binomial Expansion

## Trigonometry

## Trigonometric Ratios

## Trigonometric Graphs and Transformations

## Applications of Trigonometry

## Trigonometric Equations

## Trigonometric Identities

## Logarithmic and Exponential Functions

## Exponential Functions and Logarithms

- Exponential functions: what they are and their graphs
- What do we mean by a log?
- Rules of logs
- Logarithms - Change of Base
- Simplifying and expanding
- Converting between Logarithmic and Power (Exponential) equations
- Modelling exponential growth and decay
- Modelling exponential equations | Exam Questions
- Exponential and log equations
- Simultaneous equations
- Solving inequalities
- Exam Questions - 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

## Integration

## Integration – Introduction

## Equations of Curves

## Definite Integration

## Vectors

## Vectors

- quadrant rule
- quadratics:
- discriminant
- equations
- graphs

- tangents to curves
- transformations:
- graphs
- trigonometric:
- equations
- graphs
- identities
- ratios 30°, 60°, 45°
- trigonometry
- cosine rule
- sine rule