## 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

### Algebra & Functions in A-Level Maths:

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

### Coordinate Geometry in A-Level Maths:

• parametric equations

### 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 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

### 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 A-Level 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 A-Level Maths:

• Three-dimensional vectors

### Numerical Methods in AS-Level Maths:

• Not covered in AS-Level Maths

### Numerical Methods in A-Level Maths:

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