Further Mathematics

A Level

The Further Mathematics course is for those with a real passion for the subject. The course leads to two A Levels, one in Mathematics and one in Further Mathematics. Students are taught in separate sets from those taking the single A Level and Further Mathematics takes up two timetable option blocks.

Students cover the A Level Course during the first year and then progress to the more challenging Further Mathematics modules during the second year. We offer specialist support for students who require STEP qualifications as part of their university application.

Coursework/Examination Requirement

100% written examination.

The College expects students to have

Grade 8 GCSE Mathematics. A Casio Classwiz or Graphics calculator is recommended.


Although A Level Mathematics is an excellent entry qualification to many degree courses, those who wish to study Mathematics, Science and Engineering at elite universities will find Further Mathematics a real advantage, with clear future career benefits in these areas.

Course Content

Paper 1 and 2

Assesses the following content Proof - using mathematical induction; including sums of series and divisibility

Complex numbers: carry out calculations involving complex numbers and show them on an argand diagram

Matrices: add, subtract and multiply matrices, multiply by a scalar

Further algebra and functions: understand and use the relationship between roots and coefficients of polynomial equations, use the method of differences for summation of series

Further calculus: evaluate improper integrals, derive formulae for and calculate volumes of revolution

Further Vectors: use the Vector and Cartesian forms of an equation of a straight line in 3D

Polar coordinates: use polar coordinates and be able to convert between Polar and Cartesian coordinates; Hyperbolic functions:

Understand the definitions of Hyperbolic functions

Differential equations: Numerical methods.

Paper 3

Will assess the applied topics of the course:

Mechanics topics: Dimensional analysis: finding dimensions of quantities, prediction of formulae; Momentum and Collisions: coefficient of Restitution and Newton’s experimental law; Work, energy and power: Work done by a force acting in the direction of motion or directly opposing the motion; Circular motion: motion of a particle moving in a circle with constant speed; Centres of mass and moments: Centre of mass of a lamina by integration.

Discrete Maths topics: Graphs: use the language of graphs, including vertex, edge, trail, cycle, connected, degree, subgraph, subdivision, multiple edge and loop; Networks: use the language of networks including: node, arc and weight; Network flows: interpret flow problems represented by a network of directed arcs; Linear programming: formulate constrained optimization​ problems; Critical path analysis: Game theory for zero-sum games: Binary operations and group theory.

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