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Pure Mathematics

The Pure Mathematics elements of both the AS and the A-Level in Mathematics consist of the following topic areas:
Proof, Algebra & Functions, Coordinate Geometry, Sequences & Series, Trigonometry, Exponentials & Logarithms, Differentiation, Integration, Vectors

  • Proof
  • Algebra & Functions
  • Coordinate Geometry
  • Sequences & Series
  • Trigonometry
  • Exponentials & Logarithms
  • Differentiation
  • Integration
  • Vectors
  • Numerical Methods


AS Level Maths

Proof in AS-Level Maths:

 


A Level Maths

Proof in A-Level Maths:

In addition to the above:

  • proof by contradiction


AS Level Maths

Algebra & Functions in AS-Level Maths:

 


A Level Maths

Algebra & Functions in A-Level Maths:

In addition to the above:

  • simplifying rational expressions
  • the modulus of a linear function
  • composite and inverse functions
  • more transformations
  • partial fractions
  • modelling


AS Level Maths

Coordinate Geometry in AS-Level Maths:

 


A Level Maths

Coordinate Geometry in A-Level Maths:

In addition to the above:

  • parametric equations


AS Level Maths

Sequences & Series in AS-Level Maths:

 


A Level Maths

Sequences & Series in A-Level Maths:

In addition to the above:

  • more binomial expansion, nth term
  • increasing, decreasing and periodic sequences
  • sigma notation
  • arithmetic sequences & series
  • geometric sequences & series
  • sequences in modelling

AS Level Maths

Trigonometry in AS-Level Maths:

 


A Level Maths

Trigonometry in A-Level Maths:

In addition to the above:

  • arc length and area of a sector
  • small angle approximations
  • exact values of sin, cos and tan
  • reciprocal and inverse trigonometric functions
  • more trigonometric identities
  • double angle and compound angle formulae
  • trigonometric proof
  • problems in context

AS Level Maths

Exponential & Logarithmic Functions in AS-Level Maths:

 


A Level Maths

Exponential & Logarithmic Functions in A-Level Maths:

  • No additional content

AS Level Maths

Differentiation in AS-Level Maths:

 


A Level Maths

Differentiation in A-Level Maths:

In addition to the above:

  • differentiate trigonometric functions from first principles, convex/concave functions
  • differentiate trigonometric and exponential functions
  • product rule, quotient rule and chain rule
  • implicit and parametric differentiation
  • construct simple differential equations

AS Level Maths

Integration in AS-Level Maths:

 


A Level Maths

Integration in A-Level Maths:

In addition to the above:

  • integrate linear combinations, exponential and trigonometric functions
  • finding areas
  • understand that integration is the limit of a sum
  • integration by substitution and integration by parts
  • integrate using partial fractions
  • separation of variables
  • interpret the solution of a first order differential equation

AS Level Maths

Vectors in AS-Level Maths:

 


A Level Maths

Vectors in A-Level Maths:

In addition to the above:

  • Three-dimensional vectors


AS Level Maths

Numerical Methods in AS-Level Maths:

 

  • Not covered in AS-Level Maths

A Level Maths

Numerical Methods in A-Level Maths:

 

  • Approximate location of roots
  • Iterative methods
  • Newton-Raphson method
  • Numerical integration
  • Problems in context