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 Mathematics. Students take exam units in Further Pure Mathematics and Applied Mathematics. Many of the ideas met in these pure modules build on those encountered in A level Mathematics, 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 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: these cover Further Pure and Applied Mathematics.


Details to be confirmed in light of the on-going OFQAL accreditation process (at the time of going to press).

Edexcel AS and A level Further Mathematics Further Pure Mathematics Book 1/AS Textbook + e-book
Published by Pearson, ISBN 9781292183336

Edexcel A level Further Mathematics Further Pure Mathematics Book 2 Textbook + e-book
Published by Pearson, ISBN 9781292183343

Edexcel AS and A level Further Mathematics Further Statistics 1 Textbook + e-book
Published by Pearson, ISBN 9781292183374

Edexcel AS and A level Further Mathematics Further Mechanics 1 Textbook + e-book
Published by Pearson, ISBN 9781292183312


Exam Board and Specification Codes

A level: Pearson Edexcel 9FM0


Grades achieved at MPW

Progressed to
Warwick University (Chemistry)

“I have definitely made the right decision to come to MPW - my grades have gone from averaging Es to straight As. Teaching at MPW is much more personal and I felt like talking to teachers. They are very good and give you lots of support if you do not understand something. My Personal Tutor took me through the UCAS process step by step. We went through my Personal Statement many times to make sure it was completely perfect. I am very excited about my firm choice.”


Grades achieved at MPW

Progressed to
Nottingham University (Philosophy)

As a dyslexic student who initially got CCEE for my AS, I was convinced that I could not achieve any higher. My time at MPW proved me wrong. Initially I was reluctant to move from my local school in York to a college so far away from home, my parents, and friends. At the end of my first year I was overjoyed to find that many hours of hard work and renewed revision techniques had resulted in me achieving three A's in my subjects. I wanted to continue at A2 as I knew it would greatly improve my university prospects and encourage me to work even harder. After two fantastic years at MPW I can emphatically say that going to MPW was the best decision I ever made. 


Grades achieved at MPW

Progressed to
University of York (Law) 

“Having a Personal Tutor to discuss ANYTHING with, from my UCAS application to organising my life in general, really did make life at the college more streamlined and in general less stressful.”


Grades achieved at MPW

Progressed to
University College London (Economics) 

“Honestly, I could not imagine when I joined MPW that, due to language and adaptation barriers, I would achieve top grades in my first A-level exam sittings. This view changed completely after only a few weeks in the college’s supportive and motivational environment; with teachers who aimed at finding a personal touch with each student and with my Personal Tutor who made my adjustment to the UK education system not only an easy step in my life but, more importantly, an enjoyable one.”


Grades achieved at MPW

Progressed to
University College London (Mathematics and Statistics)

“International students have many aspects to think about, such as accommodation and guardians, but MPW surprised me by having a highly organised and supportive administration. Also, because most MPW Cambridge students are local, as an ‘international’ student, I found this very useful in both improving my English and in giving me a taste of a genuinely ‘English’ college.”


Grades achieved at MPW

Progressed to
King's College London (International Relations)

 “The teachers really helped me overcome any difficulties I came across; they always seemed willing to offer support be it inside or outside of the classroom. I could safely say my teachers inspired me to work hard and aim for the best, sometimes simply by being passionate about what they do.”