Pure Maths can be thought of as the heart of mathematics. It consists of the core aspects of maths before any application to the real world. There are many extensive topics in Pure Maths but before any student can explore these, they must learn the basics at A-Level. The Pure Maths 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


pure maths

Proof in AS-Level Pure Maths:

In AS-Level pure maths, students will be expected to be familiar with the following areas of proof:


pure maths

Proof in A-Level Pure Maths:

In addition to the above:

  • Proof by contradiction.

pure maths

Algebra & Functions in AS-Level Pure Maths:

In AS-Level Maths, students will be expected to be familiar with the following area of Algebra & Functions:


pure maths

Algebra & Functions in A-Level Pure Maths:

In addition to the above:

  • Simplifying rational expressions.
  • The modulus of a linear function.
  • Composite and inverse functions.
  • More transformations.
  • Partial fractions.
  • Modelling.

pure maths

Coordinate Geometry in AS-Level Maths:

In AS-Level Maths, students will be expected to be familiar with the following area of Coordinate Geometry:


pure maths

Coordinate Geometry in A-Level Pure Maths:

In addition to the above:

  • Parametric equations.

pure maths

Sequences & Series in AS-Level Pure Maths:

At AS-Level Maths, students will be expected to be familiar with the following areas of Sequences & Series:


pure 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.

pure maths

Trigonometry in AS-Level Maths:

In AS-Level Maths, students will be expected to be familiar with the following area of Trigonometry:


pure 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

pure maths

Exponential & Logarithmic Functions in AS-Level Maths:

In AS-Level Maths, students will be expected to be familiar with the following area of Exponentials & Logarithms:


pure maths

Exponential & Logarithmic Functions in A-Level Maths:

  • No additional content

pure maths

Differentiation in AS-Level Maths:

In AS-Level Maths, students will be expected to be familiar with the following area of Differentiation:


pure 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

pure maths

Integration in AS-Level Pure Maths:

In AS-Level Maths, students will be expected to be familiar with the following area of Integration:


pure maths

Integration in A-Level Pure 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.

pure maths

Vectors in AS-Level Maths:

In AS-Level Maths, students will be expected to be familiar with the following area of Vectors:


pure maths

Vectors in A-Level Pure Maths:

In addition to the above:

  • Three-dimensional vectors

pure maths

Numerical Methods in AS-Level Maths:

In AS-Level Maths, students will be expected to be familiar with the following area of Numerical Methods:

  • Not covered in AS-Level Pure Maths

pure maths

Numerical Methods in A-Level Maths:

 

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

 

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The Edexcel Specification gives a long list of expected criteria. In general, there is a larger emphasis on the deeper understanding of pure maths and its applications. This means that students will be required to use a high level of reasoning. This means that they must be able to justify with logic and recognise incorrect reasoning. Skills include being able to generalise mathematically and constructing mathematical proof. Students must be able to select a strategy for challenging problems and use diagrams to explore mathematical scenarios where appropriate. Effective communication of interpretation of solution will be required.