This page gathers all the Further Maths: lessons, worksheets, quizzes and tests on 11 topics for pupils aged 16-18 (Post-16 (A level)). They also help you prepare for the A level Further Mathematics.
Everything for Further Maths maths is split by type, so you can go straight to what you need: lessons, worksheets, multiple choice questions, quizzes, tests or starters. Each card opens the full list of topics.
- Lessons
Notes and worked examples - Worksheets
Printable PDF with answers - Multiple choice
Ten questions per topic - Quizzes
Quick checks with instant results - Tests
Marked out of 20 - Starters
Mental maths warm-ups
About Further Maths
In Further Maths, the topics are grouped into 1 strands: Pure Mathematics (11). First, choose a topic in the list, then open its page. Every topic has a lesson, a worksheet with a separate answer page, multiple choice questions, a quiz, a test and starters. Also, most pages have a PDF, so you can print them for homework or revision.
Finally, when a topic feels easy, move on to the next one, because each topic builds on the one before. Because every topic page links to the others, you can switch from learning to practising in one click. Meanwhile, the sidebar shows the other year groups, so you can go back or move ahead. In addition, the answers always sit on their own page; therefore you can try first and check later.
Topics in Further Maths
- Proof by induction – Prove summation, divisibility and matrix statements by induction.
- Complex numbers – Calculate with complex numbers and use Argand diagrams and loci.
- De Moivre's theorem and roots of unity – Use de Moivre's theorem, Euler's form and roots of unity.
- Matrices and linear transformations – Use matrix algebra, determinants and linear transformations.
- Inverse matrices and systems of equations – Find inverses and solve three simultaneous equations.
- Roots of polynomials, series and Maclaurin – Relate roots and coefficients, use summation formulae and the method of differences and find Maclaurin series.
- Further calculus – Evaluate improper integrals and volumes of revolution.
- Further vectors – Use scalar products and equations of lines and planes.
- Polar coordinates – Sketch polar curves and find enclosed areas.
- Hyperbolic functions – Use sinh, cosh, tanh, their inverses, identities and calculus.
- Differential equations – Solve first and second order differential equations and model with them.