# 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.

Lower and upper sixth

This course builds on the skills and knowledge developed in single subject A level Maths. Students take exam units in Further Pure Maths and Applied Maths. Many of the ideas met in these pure modules build on those encountered in A level Maths, while others are entirely new. Topics include complex numbers, matrices, polar coordinates, hyperbolic functions and differential equations. Statistics investigates the idea of hypothesis tests in more depth and introduces the students to additional distribution functions, including the Poisson distribution and the notion of the quality of tests. Theoretical aspects of statistics are studied through discrete random variables and probability generating functions. Mechanics extends the basic ideas met at A level to include momentum and impulse, energy and power, elastic strings and springs and collisions in one and two dimensions.

## 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 self-contained course. Students should be realistically aiming at least at a grade A in single subject A level Mathematics in considering an A level in Further Mathematics.

## How is the course assessed?

The course is assessed entirely by written examinations at the end of the upper sixth year: two papers on Further Pure Maths and one paper each on Statistics and Mechanics. Each of the four papers is 90 minutes long and they all carry the same weight in the final grade.

To be confirmed at start of course

Edexcel AS and A level Further Mathematics Further Pure Mathematics Book 1/AS Textbook + e-book

Edexcel A level Further Mathematics Further Pure Mathematics Book 2 Textbook + e-book

Edexcel AS and A level Further Mathematics Further Statistics 1 Textbook + e-book