Further Mathematics

Subject Intent: Why Further Mathematics?

Students who want to continue with Mathematics or Computer Science at degree level will benefit from studying Further Mathematics as it is a requirement for some higher education providers. Students will see the links between different areas of mathematics and apply their mathematical skills across all areas. Students will learn how to reason logically and recognise incorrect reasoning. Students are taught to read and comprehend mathematical arguments, including justifications of methods and formulae, and students will gain confidence to communicate their understanding. Students will use their mathematical skills and techniques to solve challenging problems, which require them to decide on the solution strategy. All of these skills are highly desirable in the work place and in further education.

What will I study?

If studied, Further Maths must be a fourth subject and you must also be taking A-Level Maths. The course will include: 
  • Proof.
  • Complex numbers.
  • Matrices.
  • Further algebra and functions.
  • Further calculus.
  • Further vectors.
  • Polar coordinates.
  • Hyperbolic functions.
  • Differential equations.
  • Further numerical methods
  • Further mechanics (including energy, circular motion, momentum, and centres of mass).
  • Further statistics (including random variables, further hypothesis testing, and confidence intervals).

Further Mathematics

Please note: Subject videos have been filmed from colleges across our Trust.

What are lessons like in this subject?

Just as in Mathematics, further Mathematics lessons always begin with retrieval practice – a quiz, skills check, or past exam question. Then new concepts are introduced using teacher examples, enhanced with interactive graphing software and other exploratory activities. The emphasis is on building a strong conceptual understanding in order to develop problem-solving ability.

Time in lessons is devoted to doing as much mathematics as possible – individually, working in small groups, or in whole-class discussion, with students being invited to contribute their solution strategies or lead examples on the board. The use of a graphical calculator is essential for further mathematics and so this is explicitly taught in lessons. Further mathematicians often lead our entries to the UKMT individual and team challenges, and support is provided for those wishing to apply to top-tier universities through mock interviews and assistance with preparing for the STEP, MAT, and TMUA papers.

What our


Further Mathematics introduces new intricate methods and deeper ways of thinking about how to apply previously known techniques to solve many problems, even as non-mathematical as they may first seem. The course is challenging but rewarding, encourages discussion, and allows for a lot of creative thinking and problem solving while presenting a large variety of new question types. The course content is exciting as it explores entirely new areas of Mathematics, and allows for a lot of experimenting with the new Mathematics learnt.

Oliver Britton, Castleford Academy

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