# 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.

Upper sixth

This one year course builds on the skills and knowledge developed in the single subject A level which is taken in the lower sixth. Students take two compulsory units of Further Pure Mathematics and two modules of Applied Mathematics. Many of the ideas met in these pure modules build on the previous year’s work while others are entirely new. Topics include complex numbers, matrices, polar coordinates, hyperbolic functions and differential equations. Statistics investigates the ideas of correlation, regression and hypothesis tests in more depth and introduces students to new distributions including the Poisson process. Mechanics extends the basic ideas met at A level to include momentum and impulse, collisions, centre of mass, work and energy and elastic strings and springs.

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

Further Mathematics is a second A level in mathematics and regarded as a subject in its own right. The aim is to build on skills developed in A level mathematics and increase depth and breadth of subject knowledge. Further Maths an academically rigorous and demanding subject and is suited to those who are considering Higher Education courses in Mathematics, Engineering, Physics, and other highly numerate disciplines or simply for those who really enjoy mathematics!

## What prior knowledge and skills are required?

Further Mathematics is a one year self-contained course and is available only as a full A level. Students embarking on the two year programme should have a Grade 9 at GCSE or IGCSE and preferably either OCR Additional Mathematics, Edexcel Further Pure IGCSE Mathematics or an equivalent qualification. In addition, students must attain at least a grade A in single mathematics before considering an A level in Further Mathematics.

## How is the course assessed?

The course is assessed entirely by four written examinations at the end of the upper sixth: two Further pure mathematics papers and two applied papers. All papers are equally weighted and are 1 hour 30 minutes each in duration.

## Reading

**Edexcel AS and A Level Further Mathematics: Further Pure Mathematics Book 1/AS Textbook + e-book**

Published by Pearson, ISBN 978-1292183336

**Edexcel A Level Further Mathematics: Further Pure Mathematics Book 2 Textbook + e-book**

Published by Pearson, ISBN 978-1292183343

**Edexcel AS and A Level Further Mathematics: Further Statistics 1 Textbook + e-book**

Published by Pearson, ISBN 978-1292183374

**Edexcel AS and A Level Further Mathematics: Further Mechanics 1 Textbook + e-book**

Published by Pearson, ISBN 978-1292183312

## Exam Board and Specification Codes

A level: Pearson-Edexcel 9FM0

**Mike Danzelman**

Head of Department