Further Mathematics

A Level
2 years
Curriculum Manager: 
Dr David Lynch

What is Further Mathematics?

To set the World Record, a team set off early one morning at the end of the Piccadilly line at Heathrow.  They must visit all the tube stations in London in less than 16 hours to claim their prize.  What route should they take?

We created negative numbers, fractions and surds to solve equations such as x + 3 = 0, 3x – 2 = 0 and x2 – 3 = 0, but what if you want to solve x2 + 4 = 0?

The Canadian lynx feeds almost exclusively on the snowshoed hare.  As the lynx eat hares, the hare population goes down; but then the lynx run out of food, so their population decreases, which means less hares get eaten, etc.  Can you model how the population of one affects the population of the other?

You probably know that the volume of a sphere is .  But can you prove it? 

And how are computer animation films made?

Further Maths will allow you to answer these and many other questions!

What Mathematics will I do?

If you are a good Mathematician who is likely to get a grade 7 (or preferably grade 8 or 9) at GCSE, plus a range of other good grades, you should consider taking A-level Mathematics and Further Maths.

At time of going to press, the exam boards have not published the final specifications so we do not know the exact make-up of the course.  However, the Further Maths course will consist of a mixture of Pure Maths, Mechanics, Statistics and Decision Maths, with probably a number of options.  The options that are taught will likely depend on the preferences of all the students. 

We encourage all Further Mathematicians to do the Senior Maths Challenge each year.  Our students do very well, gaining many more gold, silver and bronze awards than the national average.  There is an opportunity for gifted students to extend their mathematics even further by studying additional options, to prepare for MAT and STEP (the Oxford and Cambridge Maths entrance exams) in their second year or to do an Extended Project on a mathematical topic, such as the mysteries of e.  Our very best students participate in the Senior Team Maths Challenge.  We hope to continue our regular success in this competition, by winning the regional and national finals again.

What do the different types of Maths involve?

In Further Pure you will learn how to solve x2 + 4 = 0, using imaginary numbers, which are square roots of negative numbers. Imaginary numbers are used in numerous practical applications, such as electronics, weather prediction, etc.  You will also learn about matrices which are used to represent transformations of sets of co-ordinates, such as those representing the position of the arms, legs, head and body of a cartoon character – needed when making computer animation.  You will also discover the Maths behind why satellite dishes are parabolic, prove the formulae for the volume of a sphere and cone, and use differential equations to model the populations of predators and their prey.

Mechanics will give you the skills to understand the Maths behind circular motion and why motorway corners are banked.   You will use Newton’s Laws of Motion and to find the acceleration of a car driving up a hill for a given power output of the engine and also differential equations to model the motion of a mass on the end of spring.

Decision Maths will give you the skills to determine the shortest path around all the London underground stations.  You will be able to see how computers can sort the results of all Maths exams taken by students at the college, to get a rank of students’ achievement.  You will also understand the methods used to schedule complex projects, such as building the Olympic Stadium, in order to complete it in the least time.  And you will learn how businesses decide what quantity of two different products to produce in order to maximise their profit.


Mathematics is highly valued in a very wide range of careers and professions as it provides good evidence of the ability to think clearly and logically.  It is accepted almost everywhere as a good entry qualification for practically every subject at degree level.  It is usually a requirement for anyone interested in Physics, Engineering, Statistics, Computing, Economics and other scientific and business related careers.

By also studying Further Maths, the extra depth and breadth of modules you study will give better preparation for degrees in Mathematics, Engineering or Physics.  Studying Further Mathematics is seen as an indication of high academic aptitude which is often essential when making applications to certain courses and universities.  It is also considered to be a facilitating subject by the Russell Group of universities.

Entry requirements

For A-level Further Maths you must have at least a Grade 7 (preferably Grade 8 or 9) in GCSE Maths (at the higher tier).  You must also do A-level Maths.

Course costs

Students will be expected to provide their own stationery and textbooks.  All students must also have a scientific calculator with natural display that can calculate Binomial & Normal probabilities and work with matrices.  The best option will be the Casio FX-991EX (around £20), but it isn’t available in the UK yet.  Some students also buy a graphics calculator, such as the Casio FX-9750GII (around £60).  In addition, all students must purchase both the A-level Maths and A-level Further Maths Student Course Materials via the college’s Online Store.  They will be about £5 each and will include interactive ICT resources, Senior Maths Challenge entry and exercise books to write your notes in.

If the costs of equipment, materials and trips may cause you financial hardship, you may wish to read through details of our financial support scheme on our website.

Course code