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Further Mathematics


As mathematics is such a vast subject, it is impossible to cover it all in one course. Further mathematics extends the breadth and depth of study; some of the concepts met in A-Level mathematics are extended, whilst some topics not met on the standard A-Level course are introduced.

The course is aimed at very able mathematicians who enjoy the subject and are keen to go beyond A Level mathematics. Many students taking this course go on to study mathematics or a mathematics-related degree at university such as engineering. For many university courses, completion of further mathematics can lead to a lower offer for entry.

Summary of course content

Half of the course contact is further pure mathematics and includes the following topics.

Topics covered

• Proof
• Complex numbers
• Matrices
• Further algebra and functions
• Further calculus
• Further vectors

The remaining half is divided between two optional components, which are further mechanics and decision mathematics. The former extends the mechanics contact from the standard A Level, whilst the latter introduces concepts related to algorithms and processes of use in computing.

Yr12 Curriculum Overview

Yr13 Curriculum Overview


This is a linear course, with four examinations completed at the end of Year 13. Each is one and a half hours long and calculators are allowed throughout. The first two papers examine the pure content whilst the third and fourth papers cover the optional components. Internal assessments will of course be completed regularly throughout the course. There is no coursework element.

How the course differs from GCSE

The new specifications have been designed to build on the new GCSE specification and build rapidly from the higher grade skills covered at that level. Potential further mathematic students should be confident GCSE students, particularly in the areas of proof, algebra and trigonometry.

Skills acquired

• To enable students to acquire extensive knowledge and skills with confidence, satisfaction and enjoyment.
• To give students experience of mathematical activities and develop resourcefulness in solving advanced problems
• To enable students to apply further mathematics and recognise its significance to other disciplines
• To develop students’ understanding of mathematical reasoning.

Where the course leads

This course is good for those students considering applying for a competitive degree course such as engineering, physics, mathematics and/or considering Oxbridge entry. Further mathematics is a very impressive qualification to have on your CV for university applications.

Special entry requirements

To study further mathematics you must also study A Level mathematics. This course is intended for students who have achieved at least a grade 7 in mathematics at GCSE and ideally a grade 8 or 9. Consequently, students will be expected to have studied the higher GCSE course and have a high degree of mathematical ability. Students will have to be highly motivated and able to work hard to reach deadlines. This is a course for students who enjoy mathematics and rise to a challenge!