Further Mathematics

What’s it about?

Why study Further Mathematics?

Entry requirements

What you learn

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Why study A Level Further Mathematics?

There are many good reasons to take Further Mathematics, but five good reasons would be:

  1. Enjoyable, rewarding, stimulating and empowering experience.
  2. Provides challenge; the chance to explore more sophisticated mathematical concepts.
  3. Boosts your marks in A Level Mathematics.
  4. Easier transition from sixth form to university courses
  5. Distinguish yourself as an able mathematician in applications

Further Mathematics is a challenging qualification, which both extends and deepens your knowledge and understanding beyond the A Level Mathematics course. If you wish to study A Level Further Mathematics then you must also be studying A Level Mathematics.  Students who study Further Mathematics often say it is their favourite subject.  As well as new learning new areas of pure mathematics you will study further applications of mathematics in mechanics, statistics and decision mathematics.  Studying Further Mathematics consolidates and reinforces your standard A Level Mathematics work, helping you to achieve your best possible grades.  If you are planning to take a degree such as Engineering, Sciences, Computing, Finance/Economics, etc., or perhaps Mathematics itself, you will benefit enormously from taking Further Mathematics, at least to AS level. Further Mathematics introduces new topics such as matrices and complex numbers that are vital in many STEM degrees. Students who have studied Further Mathematics find the transition to such degrees far more straightforward.

Further Mathematics qualifications are highly regarded and are warmly welcomed by universities. Students who take Further Mathematics are really demonstrating a strong commitment to their studies, as well as learning mathematics that is very useful for any mathematically rich degree. Some prestigious university courses require you to have a Further Mathematics qualification and others may adjust their grade requirements more favourably to students with Further Mathematics.  Whilst the number of young people studying A Level Mathematics and Further Mathematics is increasing there is still a huge demand from science, engineering and manufacturing employers.

The Course Structure

Further Mathematics can either be taken as an A Level course (as one of 3, or one of 4, A Level courses) or as an AS Level course as a 4th option subject. The same route is followed by all Further Mathematics students in Year 12, leading to external AS Level exams in May. Each student may then opt to continue with Further Mathematics in Year 13 to complete the A Level course.

AS Level and A Level Further Mathematics is a course of study that supports the development of mathematically informed individuals.  It will encourage you to think and act mathematically, using mathematical skills and forms of communication to analyse situations within mathematics and elsewhere. The course provides a balance between breadth and depth of mathematical knowledge. The pure core provides the foundations for further mathematical study, onto which you will add two options; Discrete Mathematics and Mechanics. These options provide flexibility to prepare you for further study and employment in a wide range of highly mathematical disciplines that require knowledge and understanding of sophisticated mathematical ideas and techniques.

AS Level and A Level Further Mathematics is designed for students who wish to study beyond A Level Mathematics, and provides a solid foundation for progression into further study particularly in mathematics, engineering, computer science, the sciences and economics. Further Mathematics is both broader and deeper than A Level Mathematics, building upon GCSE (9–1) Mathematics and A Level Mathematics. As well as building on the algebra and calculus introduced in A Level Mathematics, Further Mathematics pure core content introduces complex numbers and matrices; fundamental mathematical ideas with wide applications in mathematics, engineering, physical sciences and computing. The non-core content includes different options that will enable you to specialise in areas of mathematics that are particularly relevant to your interests and future aspirations, and gives you the opportunity to extend your knowledge in applied mathematics and logical reasoning.

Internal Assessment

Students will complete a cross-topic test approximately every half term. Students will also sit formal mock examinations in Year 12 and Year 13.

External Assessment

There is no coursework assessment.

Year 12 (AS Level):

  • Paper 1 (Pure Core): 60 marks, 75 mins written paper, 1/3 of AS Level qualification
  • Paper 2 (Mechanics): 60 marks, 75 mins written paper, 1/3 of AS Level qualification
  • Paper 3 (Discrete Maths): 60 marks, 75 mins written paper, 1/3 of AS Level qualification.

Year 13 (A Level):

  • Paper 1 (Pure Core 1): 75 marks, 90 mins written paper, ¼ of A Level qualification
  • Paper 2 (Pure Core 2): 75 marks, 90 mins written paper, ¼ of A Level qualification
  • Paper 3 (Mechanics): 75 marks, 90 mins written paper, ¼ of A Level qualification
  • Paper 4 (Discrete Maths): 75 marks, 90 mins written paper, ¼ of A Level qualification.


Where does A Level Further Mathematics lead?

For progression to many courses at university it is important to have strong mathematics skills. For most science, technology, engineering and mathematics (STEM) degree courses A Level Mathematics is a requirement and AS or A Level Further Mathematics is often a preferred subject.  Anyone applying to study a degree in a STEM subject should consider taking Further Mathematics to at least AS Level as the additional content helps ensure a successful progression to university. AS Level Further Mathematics is accessible to most A Level Mathematics students. Having A Level Further Mathematics on your university application is a way to make it stand out.

Potential Careers

  • Accounting
  • Astrophysics
  • Business
  • Civil service
  • Computer programming
  • Construction
  • Consultancy
  • Design
  • Engineering
  • Finance
  • Forensic pathology
  • Games development
  • Information Technology
  • Medicine
  • Scientific research
  • Teaching

Specific job roles include actuary, business analyst, software engineer, technology analyst, information engineer and speech technology researcher.

Here’s some more information about the many fascinating courses and careers that studying Maths can lead to.

 Why Study Further Mathematics?

 Entry Requirements

Subject Qualification (Level 3) Required GCSE Grades
(in addition to Sixth Form entry requirements)
Additional Information
Mathematics (Further) AS/A Level 7+ Mathematics Must also be taking A Level Mathematics. Can be taken as an A Level course (as one of 3, or one of 4, A Level courses) or as an AS Level course as a 4th option subject.

What You Learn

Our Learning Journeys have been created to give you a flavour for the types of topics students study in each year at our school. They show what will be covered throughout the year and during each half-term, but please note there is some flexibility to what is taught when. We hope you find them helpful.