A Level Further Mathematics


Studying Further Mathematics at A Level will require that you also study the Mathematics course. You will be introduced to sophisticated, challenging branches of mathematics that lead on to university courses in the subject, and which will not be covered in the Mathematics course alone, such as numerical methods, complex numbers, matrix and vector algebra and algorithms.

Entry requirements

GCSE Maths at grade 8. Students with a grade 7 will be assessed for their suitability to take this course on an individual basis. Students applying to study Further Mathematics must also apply to study Mathematics.

Year 12

In Year 12 students study Further Pure 1, Decision 1 and Decision 2. Further Pure 1 covers Complex Numbers, Matrices, Calculus, Series, Numerical Methods, Rational Functions and Parabolas, Ellipses and Hyperbola. Decision Maths 1 and 2 cover Algorithms, Graphs and Networks, Shortest Path Problems, Route Inspection, Linear Programming, The Travelling Salesman Problem, Network Flows, Dynamic Programming, The Simplex Algorithm and Game Theory.

Year 13

In Year 13 students study Further Pure 2, Further Pure 4 and Mechanics 2. Further Pure 2 and 4 cover Complex Numbers, Polynomial Equations, De Moivre’s Theorem, Hyperbolic Functions, Surfaces of Revolution, Matrix Algebra and Vectors. Mechanics 2 covers Moments of a Force, Centre of Mass, Variable Acceleration, Circular Motion, Work and Power, Hooke’s Law and Differential Equations.

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:

  • Proof
  • Complex Numbers
  • Matrices
  • Further Algebra and functions
  • Further Calculus
  • Further Vectors
  • Polar Coordinates
  • Hyperbolic Functions
  • Differential Equations
  • Trigonometry
  • Numerical methods

Mechanics ( 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 ( 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.

Examination board

AQA Further 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.

Paper 1 – Pure 1

Paper 2 – Pure 2

Paper 3 – Mechanics and Discrete

Future Opportunities

Further Mathematics A Level is highly respected by universities and employers. For those considering Mathematics at university then Further Mathematics is desirable at many institutions. Recent destinations for leavers reading Mathematics have included Trinity College, Cambridge.

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