A Level Further Mathematics

A Level Further Mathematics, which must be studied alongside A Level Mathematics, is a demanding, enlightening and hugely rewarding course.  This qualification shows a confirmed dedication to the subject of Mathematics and success here demonstrates a high level of analytical skills.  You will be introduced to a variety of new concepts which will take your knowledge far beyond the essential skills that will have mastered for a grade 7, 8 or 9 in GCSE Mathematics. You will ponder the practicalities of complex numbers, delight in your deliberations with Discrete Mathematics and be overcome by the variety of vector applications you encounter.

As in A Level Mathematics, you will be taught by two teachers, each offering their own unique blend of experience, support, practical knowledge and skills.  In the classroom, you will be introduced to the necessary skills and techniques needed to succeed in Further Mathematics.  In your own study time you will be set regular tasks to complete, including written assignments, research tasks, and frequent exam paper practice.


Year 12 – AQA A Level Further Mathematics (7367) – Reformed

You will study a two year course which covers Pure Mathematics and Applied Mathematics, studying them both as specific skills to be mastered and as topics that can be linked through functional questions and problem solving tasks.

Pure Mathematics (⅔ of the final course)

The Pure Mathematics section of the course continues from the algebra and trigonometry within the Higher GCSE course, and also build on the concepts that you will encounter in A Level Mathematics.  Topics covered will include:


Complex Numbers


Further Algebra and functions

Further Calculus

Further Vectors

Polar Coordinates

Hyperbolic Functions

Differential Equations


Numerical methods


Mechanics (1/6 of the final course)

This applied Mathematics unit will develop many of the concepts already encountered in GCSE Physics.  Topics covered will include:


Dimensional Analysis

Momentum and Collisions

Work, Energy and Power

Circular Motion

Centres of mass and moments


Discrete Mathematics (1/6 of the final course)

This applied Mathematics unit will introduce many new concepts that can be applied to real life situations by following algorithms and applying methodologies to problem solving questions.

Topics covered will include:

Graphs (Topology)

Networks and Route Inspection

Network Flows

Linear programming

Critical Path Analysis

Game Theory

Binary Operations and Group Theory



It is a requirement of the reformed A level course that students are expected to use the new style calculators, such as the Casio Class-Wiz FX-991EX (pictured).  Students will need to be in possession of this for the start of Year 12.  They are available from the usual stockists or may be purchased from Mrs Prince.


Examination board

AQA Mathematics (7367)

For full details of the course specification please follow the link below.




Three written papers; each of two hours, all taken in the summer term of Year 13.


Year 13 – AQA A Level Mathematics (6360) – Unreformed

You will study these three, equally weighted, modules over the year, based on core and applied mathematical skills.

Further Pure Mathematics 2

This unit will cover finding roots of polynomials, polar coordinates, Argand diagrams, De Moivre’s theorem, proof by induction, summation of finite series, the calculus of inverse trigonometric functions, hyperbolic functions and surface areas of solids of revolution.

Further Pure Mathematics 4

This unit will cover vectors in three dimensional geometry, matrix algebra and matrix transformations in two directions, eigenvalues and eigenvectors, solution of linear equations, the application of second and third order determinants and the linear independence of vectors.

Mechanics 2

This applied Mathematics unit will develop the concepts already encountered in Mechanics 1 and will include moments, centres of mass, kinematics in two and three dimensions, position, velocity and acceleration vectors, variable acceleration, uniform circular motion in a horizontal or vertical plane, angular speed, work done by a force, kinetic and potential energy, Hooke’s law and elastic potential energy.


Examination board

AQA Further Mathematics (6360)

For full details of the course specification please follow the link below.




A2: Three written papers; each of ninety minutes, all taken in the summer term



To study A level Further Mathematics students are required to have achieved a grade 7 or above at GCSE.

Students applying to study Further Mathematics must also apply to study Mathematics


Future Opportunities

Further Mathematics A level is highly regarded by universities and employers.  For those considering Mathematics, Engineering, Sciences, Computing, Finance or Economics at university Further Mathematics, at least to AS level, is desirable at many institutions.

If you require any further information, please do not hesitate to email Mrs Bauwens, the head of key stage 5 Mathematics, on bauwensa@crispins.co.uk.