A Level Further Mathematics Revision Guide

About this guide

The content covers the four main strands of the subject: Further Pure Mathematics, Further Mechanics and Further Probability & Statistics, presented concisely with plenty of worked examples and detailed model solutions.

This handbook helps students consolidate formulae, solution techniques and the trickiest question types, ready for the exam as well as a firm foundation for university study in engineering and the sciences.

What is inside

• Further Pure Mathematics 1: matrices, polar curves, mathematical induction, series and complex numbers
• Further Pure Mathematics 2: hyperbolic functions, advanced differentiation and integration, differential equations
• First- and second-order differential equations and their applications
• Complex numbers: polar form, De Moivre's theorem and applications
• Further Mechanics: motion, momentum, collisions, circular motion and simple harmonic motion
• Further Probability & Statistics: continuous distributions, hypothesis testing, chi-squared tests and moment generating functions
• Vectors in space, linear transformations and determinants
• A summary of key formulae and quick techniques for the most common question types

Who this guide is for

• High-achieving maths students taking Cambridge AS & A Level Further Mathematics (9231)
• Students studying Mathematics and Further Mathematics in parallel
• Candidates aiming for engineering, computer science, physics or quantitative finance
• Students who need to practise advanced question types and demanding solution techniques
• Teachers who need a reference resource for advanced or specialist classes

How to use this guide

• Make sure you have a solid grasp of Mathematics (9709) before starting, as the content builds directly on it
• Study strand by strand (Pure, Mechanics, Statistics) and master the formulae before tackling past papers
• Re-solve the worked examples yourself before checking the solutions to sharpen your thinking
• Keep your own formula notebook for complex numbers, matrices and differential equations
• Practise past papers under timed conditions to build speed and accuracy in calculation
• Note the steps where presentation errors commonly occur to avoid losing method marks

Questions about this guide