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Mathematics (Further Mathematics)

A level

If you are a strong mathematician, who enjoys complex problem solving and exploring new Mathematics ideas, you should consider Further Mathematics.  

Further Mathematics can only be taken in addition to the Mathematics A level course and so you will achieve two A levels.  

The maths syllabus is taught using a theme-based approach, where students engage with problem solving from the start. In lessons you will learn a lot of new mathematics as well as effective study skills and how to work in groups.

Course content

Year 1

You will study the following compulsory topics from Further Pure Maths: complex numbers, matrices, proof by induction, sums of standard series and vectors.

Over the two years, you will also be studying topics from two applied options, Statistics and Mechanics. The statistics and mechanics will develop the ideas introduced in the mathematics course and also bring in some additional topics.

In statistics, new topics include discrete random variables, bivariate data and chi-squared tests. In mechanics, new topics include dimensional analysis, work, energy and power, momentum and impulse and centre of mass.

Year 2

In the second year of the course there is a greater focus on the compulsory Further Pure Maths. We cover year 1 topics in greater depth and also consider the following topics: Maclaurin series, further vectors, calculus (including the use of polar coordinates), hyperbolic functions and differential equations. We will also continue our study of the applied options, Statistics and Mechanics.

Assessment is by examination at the end of Year 2.

Is it for me?

You will enjoy and benefit from Further Mathematics if you:

  • have already taken additional Maths qualifications before coming to Long Road (for example, Statistics GCSE, Additional Mathematics GCSE or indeed AS Mathematics Modules).
  • if you are hoping to study Maths, Physics or Engineering at a selective university.
  • have strong algebra skills, and enjoy abstract methods and concepts.

Special features

Cambridge benefits from having a Further Mathematics Centre based at the Centre for Mathematical Sciences and they often provide revision sessions for Further Mathematics modules. Students also benefit from the STIMULUS project.

Students are entered for the Senior Maths Challenge*. In addition we enter a team for the Senior Team Challenge made up of students from years 12 and 13. There are also opportunities to attend lectures and other activities arranged by the Further Mathematics Network in Cambridge.


*For details, visit

Entry requirements

At least 7 Grade 4s at GCSE in appropriate subjects including English. You need to have a Grade 7 (but Grade 8/9 preferred ) in Maths.

Examination board: OCR


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