A Level Further Mathematics

## What is it about at sixth form level?

The mathematical family does not grow without labour pains. According to the Greek philosopher Iamblichus, the discovery of irrational numbers by Hippasus so shocked the followers of Pythagoras, who believed that all numbers could be expressed as fractions, that he was drowned at sea. It took a long time before zero was mathematically acceptable and negative numbers were not dismissed as imaginary. But what of their square roots? The laws of mathematics seemingly dictate that a negative squared is a positive. Yet they too are now embraced, even though they have inherited the label *imaginary numbers*. The level of abstraction here is indicative of the progression towards degree level mathematics that you will find in the Further Mathematics A level, which will build on the knowledge of the single A level to introduce new and fascinating areas of the subject such as algorithms and hyperbolic trigonometry. It can be taken at AS level only or as a full A level.

Lower sixth

For the AS, students study three modules. Further Pure Maths 1 (FP1) introduces complex numbers, matrices, further coordinate geometry, numerical methods and mathematical proof. Decision Maths 1 (D1) covers algorithms and networks. Statistics 2 (S2), extends the knowledge of S1 to cover discrete and continuous distributions, distributional approximations and hypothesis testing.

Upper sixth

Those who are studying the subject to A2 must take three additional modules. Further Pure Maths 2 builds on material in C4 and FP1 to include first and second order differential equations, further complex numbers and polar functions. Further Pure Maths 3 also builds on the material in C4 and FP1 and explores calculus, vectors, matrices and coordinate systems in considerable depth. Mechanics 2 (M2) builds on principles met in M1 and examines projectile motion, variable acceleration, work, energy and power, centre of mass, collisions and general equilibrium.

## Why study it and what skills does it develop?

The AS Further Mathematics units introduce new ideas that are designed to broaden the range of techniques learnt in AS Mathematics. A2 Further Mathematics is generally suited to those who are considering Higher Education courses in Mathematics, Engineering, Physics, and other highly numerate disciplines or simply for those who enjoy mathematics!

Further Mathematics is a second A level in mathematics and regarded as a subject in its own right. It is useful, though not essential, for any degree course with substantial mathematical content.

## What prior knowledge and skills are required?

AS Further Mathematics requires only C1 and C2 can therefore be taken alongside the A2 in Mathematics in the second year. To pursue Further Mathematics at A2 requires students to complete the single subject A level in their first year. This is an academically demanding programme designed for the strongest mathematicians. Students should therefore expect to obtain a grade A in modules C3 and C4 in their first year before considering Further Mathematics at A2 Level.

## How is the course assessed?

AS level

The course is assessed entirely by written examinations. For the AS, you will have three exams on papers FP1, D1 and S2. Each paper is worth a third of the AS and lasts 1 hour 30 minutes.

A2 level

For the A2, you will likewise have three papers on FP2, FP3 and M2. Each paper is worth a third of the A2 and lasts 1 hour 30 minutes. The A level is therefore constituted by and graded by performance on all six papers.

## Reading

**Edexcel AS and A Level Modular Mathematics: Further Pure Mathematics 1**

*By K. Pledger*

Published by Heinemann, ISBN 978-0435519216

**Edexcel AS and A Level Modular Mathematics: Further Pure Mathematics 2***By K. Pledger*

Published by Heinemann, ISBN 978-0435519216

**Edexcel AS and A Level Modular Mathematics: Further Pure Mathematics 3***By K. Pledger*

Published by Heinemann, ISBN 978-0435519223

**Edexcel AS and A Level Modular Mathematics: Decision Mathematics 1***By S. Jameson*

Published by Heinemann, ISBN 978-1846908934

**Edexcel AS and A Level Modular Mathematics: Statistics 2***By K. Pledger*

Published by Heinemann, ISBN 978-0435519131

**Edexcel AS and A Level Modular Mathematics: Mechanics 2***By K. Pledger*

Published by Heinemann, ISBN 978-0435519179

## Exam Board and Specification Codes

AS: Pearson-Edexcel 8371, A2: Pearson-Edexcel 9371 (legacy)

**Mike Danzelman**

Head of Department