Track further pure, mechanics and probability & statistics beyond single Mathematics (9709). Route options may vary by centre — use this list with your syllabus document.
| Topic | Sub-Topic | Confidence (1–5) | Last Reviewed | Next Review |
|---|---|---|---|---|
| Further Pure Mathematics 1 | Roots of polynomial equations | |||
| Further Pure Mathematics 1 | Rational functions and partial fractions | |||
| Further Pure Mathematics 1 | Polar coordinates and curves | |||
| Further Pure Mathematics 1 | Proof by induction | |||
| Further Pure Mathematics 1 | Summation of series | |||
| Further Pure Mathematics 1 | Complex numbers: modulus, argument, loci | |||
| Further Pure Mathematics 1 | De Moivre’s theorem and roots of unity | |||
| Further Pure Mathematics 2 | Matrices: transformations, inverse, eigenvalues and eigenvectors | |||
| Further Pure Mathematics 2 | Hyperbolic functions and identities | |||
| Further Pure Mathematics 2 | Differentiation and integration techniques | |||
| Further Pure Mathematics 2 | First- and second-order differential equations | |||
| Further Pure Mathematics 2 | Maclaurin and Taylor series | |||
| Further Pure Mathematics 2 | Further work on vectors and geometry | |||
| Further Mechanics | Motion in two dimensions: projectiles | |||
| Further Mechanics | Equilibrium of rigid bodies | |||
| Further Mechanics | Circular motion | |||
| Further Mechanics | Hooke’s law and elastic strings/springs | |||
| Further Mechanics | Work, energy and power in dynamics | |||
| Further Mechanics | Momentum and impulse in two dimensions | |||
| Further Probability & Statistics | Continuous random variables | |||
| Further Probability & Statistics | Linear combinations of random variables | |||
| Further Probability & Statistics | Inference using normal and t-distributions | |||
| Further Probability & Statistics | Chi-squared tests and goodness of fit | |||
| Further Probability & Statistics | Non-parametric tests (where in syllabus) | |||
| Further Probability & Statistics | Bivariate data: correlation and regression |
Use with our Past Paper Finder for Further Mathematics past papers.
Quick answers about this free revision checklist, how to use it for exam prep, and how it relates to the official syllabus.
This revision checklist mirrors the official Cambridge A Level Further Mathematics 9231 syllabus for the 2026 examination series. Every topic and sub-topic on the page is taken from the published syllabus document, so working through the list in order gives you full coverage of what your exam can assess. It is aligned to the A Level tier expectations. For the authoritative version, always cross-check with the latest syllabus PDF on your exam board's website before your final revision push.
The number of top-level topic groups varies by subject, but you can see the exact count on this page — each major heading in the checklist corresponds to one syllabus topic group, and each row below it is a syllabus-level sub-topic. Use the confidence column (1–5) to flag which sub-topics need more work, and re-score yourself weekly to track real progress instead of guessing.
12–16 weeks of focused revision, working through one topic group per week with weekly past-paper practice, is a realistic target for most A Level students. Use this checklist to plan your weeks: filter by topics you have rated 1–3 and spend your first revision block there. Subjects with heavy practical or extended-writing components (e.g. sciences, English) need more past-paper time in the final block than the topic-by-topic phase.
Revise in roughly the order the syllabus lists the topics — exam boards build later topics on earlier ones, so taking them in syllabus order avoids gaps. Once you have rated every topic, switch to weakest-first: filter the checklist by confidence ≤ 2 and prioritise those topics in your next study block. This is more effective than re-revising topics you already score 4–5 on.
You can find past papers and mark schemes via Tutopiya's Past Paper Finder and on your exam board's official site. Once you have rated each sub-topic on this checklist, attempt past-paper questions on your weakest topics first — practising under timed conditions is the single best predictor of exam performance, more so than re-reading notes.
Use the Download CSV or Print PDF button at the bottom of the checklist. CSV opens in Excel, Numbers or Google Sheets so you can sort by confidence and re-arrange revision order. The PDF is print-ready for offline use. A free Tutopiya account is required for download — this also unlocks the matching topic resources, notes and worked examples on the Learning Portal.
Yes, the checklist itself is free — you can view, score and re-score every topic on this page without an account. The CSV / PDF downloads and access to matching Tutopiya Learning Portal resources require a free account. There is no payment required at any point; teachers and parents can also use this checklist freely with their students.
Yes. The topics and sub-topics on this page are drawn from the current 2026 Cambridge A Level Further Mathematics 9231 specification published by Cambridge. Exam boards occasionally tweak weighting or assessment structure mid-cycle, so do a quick sanity-check against the official syllabus PDF when you start your revision and again 4 weeks before the exam.