Further Mathematics

Exam Board



About the subject

Further maths isn't just about "doing harder maths", it's about experiencing a huge wealth of mathematics beyond what is covered in the A-Level course and getting to discover some truly fascinating and beautiful aspects of mathematics. You will use a significant number of the same skills as you will learn in A-Level maths, but learn how to apply them to knew knowledge, gaining a much broader appreciation of the subject and the strong links between seemingly disparate topics. You'll also get to learn about a completely new area of maths known as Decision Mathematics, which is heavily related algorithms and computer science.

If you really love maths, and you want to study maths, engineering or physics (in particular) at university, then you really need to give serious consideration to taking this extra A-Level.

Entry Requirements

Grade 8 in GCSE Mathematics (you must also take A-Level Mathematics)

Year 12 Topics

Pure Mathematics
1 Complex Numbers
2 Argand Diagrams
3 Series
4 Roots of Polynomials
5 Volumes of Revolution
6 Matrices
7 Linear Transformations
8 Proof by Induction
9 Vectors

Applied Mathematics
D1 Algorithms
D2 Graphs and Networks
D3 Algorithms on graphs
D4 Route Inspection
D5 Linear Programming
D6 Critical Path Analysis
M1 Momentum and Impulse
M2 Work, Energy and Power
M3 Elastic Collisions in One Dimension

Year 13 Topics

Pure Mathematics
1 Complex Numbers
2 Series
3 Methods in Calculus
4 Volumes of Revolution
5 Polar Coordinates
6 Hyperbolic Functions
7 Methods in Differential Equations
8 Modelling with Differential Equations

Applied Mathematics
D1 Graphs and Networks
D2 Route Inspection
D3 The Travelling Salesman Problem
D4 The Simplex Algorithm
D5 Critical Paths Analysis
M1 Momentum and Impulse
M2 Elastic Strings and Springs
M3 Elastic Collisions in Two Dimensions


You will have 4 exam papers at the end of Year 13.
- Paper 1 and 2 are Core Pure Mathematics (and makes up 2/3 of the marks). Each paper is 1 hr 30 mins.
- Paper 3a is Mechanics (worth 1/6 of the marks). This paper is 1 hr 30 mins.
- Paper 3b is Decision (worth 1/6 of the marks). This paper is 1 hr 30 mins.

There is no specific content for Paper 1 and 2, but they will exam only the Core Pure element of the course.
Paper 3a and 3b will contain only Mechanics and Decision content, respectively.

Online Resources