Further Mathematics A Level 3

For students applying from other schools please see the information below.

For existing students at OPGS - you will be applying internally and will receive separate instructions

Applications Open - 11th December 2025

Applications Close - 30th January 2026

Entry Requirements:-

Students achieving a minimum of at least six GCSEs (9 – 5) of which at least four are at a grade 6 (or equivalent).

In addition, students must meet subject entry requirements, which in most cases require a minimum of Grade 6 in the subject to be studied, or related subjects. Some subjects will require a grade 7 or higher. Please see school website (https://www.opgs.org) for entry requirements needed for individual A level subjects.

Students must also achieve a minimum of a grade 5 in English Language and Mathematics.

Typically, we would expect students following essay-based subjects to gain at least a grade 6 in English Language and students following scientific courses to gain at least a grade 7 in Mathematics.

The school shall determine which grades at 6 are required when A level subjects requested have not been taken at GCSE Level.

Priority will be given to existing pupils transferring from Year 11 who meet the entrance criteria

How to Apply

Students should select three or four A level subjects and include a 4th/5th as a reserve subjects. Please list your subjects in priority order and indicate which is your reserve choice.

Subject Choice

In choosing your subjects for A level you need to find out about the syllabus, examination requirements, coursework and the approach to study. Choose subjects that interest you and think carefully about the range and combination of subjects you would like to study. You may also wish to consider requirements for Higher Education or career paths.

Students should also note that the school cannot guarantee courses will run if there are not enough applicants. It is also possible that, in some subjects, numbers will have to be limited.

It provides a very good foundation for the study of Mathematics at a higher level, which is essential for further study in some Mathematical and Physical sciences, and desirable for many others including Physics, Engineering, Economics, Accountancy and Finance and Computer Science, Medicine and Veterinary Medicine, Philosophy, Architecture, Biology, Chemistry and Geology as well as Mathematics itself. Many top universities desire Further Maths at A-Level as a pre-requisite for studying maths based courses.

You cannot study Further Maths A level without studying Maths A level too.

Paper 1: Core Pure Mathematics 1

Complex Numbers

Series

Roots of polynomials

Volumes of revolution

Matrix Algebra

Further vectors

Proof by induction

Paper 2: Core Pure Mathematics 2

Further Complex Numbers

Further series

Further calculus

Polar coordinates

Hyperbolic functions

Differential equations

Paper 3: Further Pure Mathematics 1

Vectors

Conic sections

Inequalities

Taylor Series

Methods in calculus

Numerical methods

Reducible differential equations

Paper 4: Further Mechanics 1

Momentum and impulse

Energy and Power

Elastic, springs and strings

Elastic collisions in one dimension

Elastic collisions in two dimensions

Students are assessed in school using a variety of end of topic tests, end of unit tests and homework assignments. These are monitored closely and are linked to reporting, rewards and interventions

Six 9-5 GCSE grades with at least four at grade 6

A minimum of a grade 5 in English Language

Grade 8 in GCSE Maths

Typically, we would expect students following essay-based subjects to gain at least a grade 6 in English Language and students following scientific courses to gain at least a grade 7 in Mathematics.

You could take this course with other advanced level courses to prepare for higher education in areas of Mathematics, related areas such as Engineering, Economics, Physics or more general higher education courses. With further training, you could go into a job related to Mathematics such as an Accountant, Engineer, Financial Adviser or Teacher. The course also helps you develop the skills, understanding and knowledge that many employers across lots of industries are looking for, especially in the economic and financial sectors.