AS and A Level Further Mathematics





Course code:

Further Maths AS Level: 8372  Further Maths A2 Level: 9372


2 years (full A level) or 1 year (AS level)

Aims of the course:

  • To develop students’ understanding of mathematics and mathematical processes in a way that promotes confidence and fosters enjoyment
  • To develop abilities to reason logically and recognise incorrect reasoning, to generalise and to construct mathematical proofs
  • To extend their range of mathematical skills and techniques and use them in more difficult, unstructured problems
  • To develop an understanding of coherence and progression in mathematics and of how different areas of mathematics can be connected
  • To recognise how a situation may be represented mathematically and understand the relationship between ‘real-world’ problems and standard and other mathematical models and how these can be refined and improved
  • To use mathematics as an effective means of communication
  • To read and comprehend mathematical arguments and articles concerning applications of mathematics
  • To acquire the skills needed to use technology such as calculators and computers effectively, recognise when such use may be inappropriate and be aware of limitations
  • To develop an awareness of the relevance of mathematics to other fields of study, to the world of work and to society in general
  • To take increasing responsibility for their own learning and the evaluation of their own mathematical development.

Topics covered:

AS level Further Mathematics

FP1:  Series; complex numbers; numerical solution of equations; coordinate systems, matrix algebra, proof.

FP2: Inequalities; series, fi rst order differential equations; second order differential equations; further complex numbers, Maclaurin and Taylor series.

M3:  Further kinematics; elastic strings and springs; further dynamics; motion in a circle; statics of rigid bodies.

A2 level Further Mathematics

FP3: Further matrix algebra; vectors, hyperbolic functions; differentiation; integration, further coordinate systems.

M4: Relative motion; elastic collisions in two dimensions; further motion of particles in one dimension; stability.

M5:  Applications of vectors in mechanics; variable mass; moments of inertia of a rigid body; rotation of a rigid body about a fixed smooth axis.


By examination. 
FP1 module taken in January.
FP2 & M3 modules taken in May/June.

By examination. 
M4 module taken in January.
FP3 & M5 modules taken in May/June.

Assessment details:

All units equally weighted at 16 2/3% of the complete A level

Each examination paper lasts 1 hour and 30 minutes


Calculators may be used in all units

Leads to:

An A-level mathematics course provides not only an 'in depth' study of mathematics but also aims to develop those skills essential for a successful university career in mathematics, physics, actuarial science, statistics, engineering, operations research, computer science, business and industrial management, economics, finance, chemistry, geology, life sciences, behavioural sciences and cryptography.  Mathematicians are highly employable due to their strong analytical and reasoning skills.

Both universities and employers hold an A level qualification in Further Mathematics in high regard. With the appropriate combination of other AS and A levels, A level Further Mathematics can lead to a wide variety of options when choosing higher education courses. Typical examples include Medicine, Engineering, Law, Business, Social and Political sciences, Natural sciences, and of course Mathematics itself. Similarly the employment opportunities are equally diverse.

Further Mathematics is strongly recommended for those students who wish to apply to those universities listed in the “top ten” for such subjects as Engineering, Economics, Mathematics or Physics.