Cambridge International · International A Level · 9231
Further Mathematics — Keywords & Key Terms — Definitions Glossary (2026)
Cambridge International A Level Further Mathematics (9231)
Topic-by-topic keywords, key terms and definitions for precise exam language—separate from our revision checklists (topic coverage) and formula sheets (equations).
Keywords & Key Terms — definitions
Examiner-style keywords and definitions organised by syllabus topic. Terms are tagged Essential (start here), Core (typical exam standard), and Advanced for harder distinctions — tick each row when you can recall it. Your progress is saved in this browser for this list.
Cambridge International International A Level Further Mathematics (9231)
Cambridge International International A Level Further Mathematics (9231)
Cambridge International A Level Further Mathematics (9231)
Cambridge 9231 (2026) extends 9709 with further pure (matrices, complex numbers, hyperbolics, induction), further mechanics (circular motion, SHM, elastic strings), further statistics (chi-squared, Poisson, t-tests), and numerical methods.
Mark schemes: Cambridge A Level Further Mathematics awards method marks for rigorous working, correctly stated theorems (De Moivre, induction structure), and exact answers in required form; skipped steps or decimal approximations where exact form is required lose accuracy marks.
Active recall: 0 / 21 terms ticked
| Recalled | Topic | Level | Keyword | Definition |
|---|---|---|---|---|
| Further pure | Core | Matrix multiplication | Row-by-column product — non-commutative in general. | |
| Further pure | Core | Determinant & inverse matrix | det(A) ≠ 0 ⇒ A⁻¹ = adj(A)/det(A) for invertibility. | |
| Further pure | Core | Eigenvalue & eigenvector | Av = λv — λ is the eigenvalue, v the corresponding eigenvector. | |
| Further pure | Core | Complex number & Argand diagram | z = x + iy plotted on the complex plane. | |
| Further pure | Core | Modulus-argument & polar form | z = r(cos θ + i sin θ) where r = |z|, θ = arg(z). | |
| Further pure | Core | De Moivre's theorem | (cos θ + i sin θ)ⁿ = cos(nθ) + i sin(nθ). | |
| Further pure | Core | Hyperbolic functions | sinh x = (eˣ − e⁻ˣ)/2; cosh x = (eˣ + e⁻ˣ)/2; tanh x = sinh x / cosh x. | |
| Further pure | Advanced | Proof by induction | Base case, inductive hypothesis, inductive step — conclusion for all n. | |
| Further pure | Advanced | Method of differences | Telescoping sums where consecutive terms cancel. | |
| Further mechanics | Core | Circular motion | Centripetal acceleration v²/r = ω²r directed toward the centre. | |
| Further mechanics | Core | Work-energy in 2D | Work done equals change in kinetic energy along the path. | |
| Further mechanics | Core | Hooke's law (elastic strings) | Tension T = λx/l where λ is modulus of elasticity, l natural length. | |
| Further mechanics | Advanced | Simple harmonic motion (SHM) | ẍ = −ω²x with solution x = A sin(ωt + φ). | |
| Further statistics | Core | Chi-squared test | Compares observed vs expected frequencies — tests goodness-of-fit and independence. | |
| Further statistics | Core | Poisson distribution | P(X = x) = e⁻ᵃaˣ/x! — models rare independent events with mean a. | |
| Further statistics | Core | Geometric distribution | P(X = x) = (1−p)ˣ⁻¹p — number of trials until first success. | |
| Further statistics | Core | t-test | Tests difference of means with small samples or unknown σ. | |
| Further statistics | Advanced | Continuous distributions & PDF | Probability density function f(x) where ∫f(x)dx = 1 over the range. | |
| Numerical methods | Core | Newton-Raphson | xₙ₊₁ = xₙ − f(xₙ)/f'(xₙ) — iterative root-finding via tangents. | |
| Numerical methods | Core | Fixed-point iteration | Rearrange f(x) = 0 as x = g(x); converges if |g'(x)| < 1 near root. | |
| Numerical methods | Advanced | Simpson's rule | ∫ ≈ (h/3)[y₀ + yₙ + 4(odd y) + 2(even y)] for numerical integration. |
Pair this with our revision checklists, formula sheets hub and past paper finder.
Further Mathematics (9231) — Keywords & Key Terms FAQ
- What is on this Cambridge International A Level Further Mathematics keywords and key terms list?
- It is a topic-organised glossary of important further mathematics terms with short, exam-style definitions aligned to Cambridge International A Level Further Mathematics (9231) (9231). It is designed for “define”, “state”, “outline” and “explain” questions where precise vocabulary earns marks.
- How should I use this Further Mathematics glossary alongside past papers?
- Tick terms when you can recall them without reading the answer, then check your wording against mark schemes. Pair vocabulary practice with past papers for A Level Further Mathematics (9231) so you apply terms in context.
- Is this the same as a revision checklist or a formula sheet?
- No. Revision checklists help you track which syllabus topics you have covered and your confidence—separate pages on Tutopiya. Formula sheets summarise equations and quantitative relationships. This page is only a definitions and key-terms glossary for Further Mathematics.
- Can I download this Further Mathematics keywords and key terms list for free?
- Yes. After a quick free sign-up you can download a UTF-8 CSV (opens in Excel or Google Sheets) or open a print-friendly page and save as PDF. Browsing the list on the page is free.
- Is this Further Mathematics list aligned to the 9231 specification?
- Topic groupings and wording follow Cambridge International A Level Further Mathematics (9231) for Cambridge International A Level. Always confirm final learning objectives and any regional options in your official specification and recent examiner reports for your exam session.
- Why focus on definitions instead of full notes?
- Mark schemes reward correct technical terms and clear links between ideas. A compact glossary lets you drill the exact language examiners expect for Further Mathematics at A Level, separate from longer notes or topic trackers.