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Upton Hall School

Further Mathematics

Course Overview

Students of A Level Further Mathematics have the opportunity to tackle Mathematics beyond the scope of the single A Level. In the Pure topics, very abstract concepts are studied, including  complex numbers and proof by induction. During Year 13, the topics include methods for solving  demanding differential equations.

The Applied content for this course will consist of Mechanics topics beyond those studied at the single A Level.

Studying this course gives an excellent grounding for girls wishing to pursue Mathematics or related courses to University.

Entry Requirements

To take Further Mathematics, you must also be taking Mathematics. 

You need to have achieved an grade 8 in Mathematics at GCSE. 

You should enjoy a challenge.

A Level Topics and Assessment

There will be four exams taken at the end of the course. The first two exams are on Advanced Core Mathematics. Any part of the syllabus for these two exams could appear on either paper. The third exam is Further Pure Mathematics 1, and the fourth exam is Further Mechanics 1.

Topics in the Advanced Core Papers include: mathematical induction; manipulation of complex numbers; complex roots of equations; the uses of matrices and their inverses in transformations; Maclaurin Series; differentiation of inverse trigonometric functions.

Topics in the Further Pure 1 Paper include:  the t-formulae and their applications; derivation and use of Taylor Series; Leibnitz’s Theorem; the Weierstrass substitution.

Topics in Further Mechanics 1 include: momentum and impulse; conservation of energy; elastic collisions in two dimensions


Edexcel Exam 

Further Pure 1 

Further Pure 2

Further Pure 3

Further Mechanics


1 hour 30 minutes 

1 hour 30 minutes 

1 hour 30 minutes 

1 hour 30 minutes 


25% of A Level

25% of A Level

25% of A Level

25% of A Level

Beyond the Classroom and Future Prospects

Students of A Level Further Mathematics are given opportunities to extend themselves beyond the limits of the syllabus. In particular, lunchtime enrichment sessions are in place to challenge very able students, and to prepare those who are looking to apply to Oxford or Cambridge.  A Level Further Mathematics is a very challenging course. For this reason, it is highly valued by universities and by employers.

Many of our Further Mathematicians go on to study Mathematics, Engineering or Physics at university.


Student Experience

Studying Further Maths was a challenging but rewarding experience. It introduced me to some of the more complex topics within Maths, and gave me a greater appreciation of the subject.

Laura, who completed A Level Further Maths in 2017.