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 axn
- 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 ex and Natural Log Functions
Modelling Curves of the form y=kxn and y=kax
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