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

• ##### Num. Methods ### Proof in AS-Level Pure Maths:

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

Take the StudyWell Proof TEST. ### Proof in A-Level 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: ### Algebra & Functions in A-Level Pure Maths:

• Simplifying rational expressions.
• The modulus of a linear function.
• Composite and inverse functions.
• More transformations.
• Partial fractions.
• Modelling. ### Coordinate Geometry in AS-Level Maths:

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

• Parametric equations. ### 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: ### Sequences & Series in A-Level Maths:

• More binomial expansion, nth term.
• Increasing, decreasing and periodic sequences.
• Sigma notation.
• Arithmetic sequences & series.
• Geometric sequences & series.
• Sequences in modelling. ### Trigonometry in AS-Level Maths:

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

• 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 ### 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: ### Exponential & Logarithmic Functions in A-Level Maths: ### Differentiation in AS-Level Maths:

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

• 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 ### Integration in AS-Level Pure Maths:

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

• 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. ### Vectors in AS-Level Maths:

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

• Three-dimensional vectors ### 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 ### Numerical Methods in A-Level Maths:

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