# AS/A Level Course ContentAS/A Level Mathematics | AS/A Level Further Mathematics

A summary of the various modules taken at AS/A Level is shown below. For more detailed information, please see the latest specification, available from the AQA Mathematics A-Level website.

Visit the Revision Materials page for past examination question papers and other resources.

For further revision notes, video tutorials and online exercises, visit the mathcentre website.

## AS/A Level Mathematics

### Year 12 (AS Level)

In the first year of the A Level course, students study the following modules:

- Pure Core 1
- This module revises and extends many of the topics covered at GCSE before moving onto some simple calculus. No calculators are allowed in the examination for this module. Topics included are:
- Algebra
- Coordinate Geometry
- Differentiation
- Integration

- Pure Core 2
- This module extends the topics in Pure Core 1 and introduces some new ideas. Topics included are:
- Algebra and Functions
- Sequences and Series
- Trigonometry
- Exponentials and logarithms
- Differentiation
- Integration

- Decision 1
- This module covers an area of mathematics known as 'Discrete Mathematics' that is not tackled at GCSE level. Topics included are:
- Simple Ideas of Algorithms
- Graphs and Networks
- Spanning Tree Problems
- Matchings
- Shortest Paths in Networks
- Route Inspection Problem
- Travelling Salesperson Problem
- Linear Programming
- Mathematical Modelling

### Year 13 (A Level)

In the second year of the A Level course, students study the following modules:

- Pure Core 3
- Topics included are:
- Algebra and Functions
- Trigonometry
- Exponentials and Logarithms
- Differentiation
- Integration
- Numerical Methods

- Pure Core 4
- Topics included are:
- Algebra and Functions
- Coordinate Geometry in the (x, y) plane
- Sequences and Series
- Trigonometry
- Exponentials and Logarithms
- Differentiation and Integration
- Vectors

- Statistics 1
- This module starts with revision of the key statistical ideas covered at GCSE and extends to the ideas of probability distributions:
- Numerical Measures
- Probability
- Binomial Distribution
- Normal Distribution
- Estimation
- Correlation and Regression

## AS/A Level Further Mathematics

### Year 12 (AS Level)

In the first year of the A Level course, students study the following modules:

- Further Pure 1
- This module tackles a variety of mathematical topics which would not normally be covered in a standard A-Level:
- Algebra and Graphs
- Complex Numbers
- Roots and Coefficients of a quadratic equation
- Series
- Calculus
- Numerical Methods
- Trigonometry
- Matrices and Transformations

- Mechanics 1
- An introduction to the ideas of mathematical modelling of physical situations:
- Mathematical Modelling
- Kinematics in One and Two Dimensions
- Statics and Forces
- Momentum
- Newton's Laws of Motion
- Connected Particles
- Projectiles

- Decision 2
- Topics included are:
- Critical Path Analysis
- Allocation
- Dynamic Programming
- Network Flows
- Linear Programming
- Game Theory for Zero Sum Games
- Mathematical Modelling

### Year 13 (A Level)

In the second year of the A Level course, students study two Further Pure modules with a choice of either Statistics 2 or Mechanics 2 depending on the needs of the group:

- Further Pure 2
- Topics included are:
- Roots of Polynomials
- Complex Numbers
- De Moivre's Theorem
- Proof by Induction
- Finite Series
- The Calculus of Inverse Trigonometrical Functions
- Hyperbolic Functions
- Arc Length and Area of surface of revolution about the x-axis

- Further Pure 3
- Topics included are:
- Series and Limits
- Polar Coordinates
- First and Second Order Differential Equations

- Statistics 2
- This module extends the ideas covered in Statistics 1:
- Discrete Random Variables
- Poisson Distribution
- Continuous Random Variables
- Estimation
- Hypothesis Testing
- Chi-Square Contingency Table Tests

- Mechanics 2
- This module extends the ideas covered in Mechanics 1:
- Mathematical Modelling
- Moments and Centres of Mass
- Kinematics
- Newton's Laws of Motion
- Application of Differential Equations
- Uniform Circular Motion
- Work and Energy
- Vertical Circular Motion

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