Cambridge International · International A Level · 9709
Mathematics — Keywords & Key Terms — Definitions Glossary (2026)
Cambridge International A Level Mathematics (9709)
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 Mathematics (9709)
Cambridge International International A Level Mathematics (9709)
Cambridge International A Level Mathematics (9709)
Aligned to Cambridge 9709 (2026): Pure Mathematics 1/2/3, Mechanics, and Probability & Statistics — paper combination depends on AS vs A Level route (e.g. P1+P4+M1 or P1+P3+P4+M1+S1). Complex numbers, further calculus and DE appear in the appropriate Pure papers for your combination.
Mark schemes: Cambridge uses M (method), A (accuracy), B (independent) and sometimes R (rounding) marks. Show explicit substitution where a formula is quoted. Answers in exact surd/fraction/π form unless otherwise stated. ‘Hence’ requires the previous result to be used. Small slips may forfeit A but retain M where the method is sound.
Active recall: 0 / 48 terms ticked
| Recalled | Topic | Level | Keyword | Definition |
|---|---|---|---|---|
| Pure: algebra, functions & graphs | Essential | Function | Rule mapping each element of domain to at most one image in codomain. | |
| Pure: algebra, functions & graphs | Core | Domain & range | Set of allowed inputs; set of possible outputs. | |
| Pure: algebra, functions & graphs | Core | Composite function | f(g(x)) — order matters. | |
| Pure: algebra, functions & graphs | Core | Inverse function | f⁻¹ undoes f; graph reflection in y = x for one-to-one f. | |
| Pure: algebra, functions & graphs | Core | Modulus function | |x| — piecewise linear; solve |f(x)| = g(x) by cases or squaring where valid. | |
| Pure: algebra, functions & graphs | Core | Partial fractions | Decompose rational into simpler terms for integration/summation. | |
| Pure: algebra, functions & graphs | Core | Binomial series | (1 + x)ⁿ for rational n — state validity |x| < 1 when required. | |
| Pure: algebra, functions & graphs | Advanced | Rational function | Asymptotes vertical (denominator zero) and oblique/long division for behaviour. | |
| Pure: trigonometry & coordinates | Core | R cos(θ ± α) form | Combine a cos θ + b sin θ into single sinusoid. | |
| Pure: trigonometry & coordinates | Core | Small-angle approximations | sin θ ≈ θ, cos θ ≈ 1 − θ²/2, tan θ ≈ θ for θ in radians small. | |
| Pure: trigonometry & coordinates | Core | Parametric equations | x = f(t), y = g(t) — eliminate t or differentiate dy/dx = (dy/dt)/(dx/dt). | |
| Pure: trigonometry & coordinates | Core | Polar coordinates | If in syllabus — (r, θ) and area integrals context. | |
| Pure: differentiation & integration | Core | Chain rule | dy/dx = dy/du · du/dx. | |
| Pure: differentiation & integration | Core | Product rule | d(uv)/dx = u’v + uv’. | |
| Pure: differentiation & integration | Core | Quotient rule | d(u/v)/dx = (u’v − uv’)/v². | |
| Pure: differentiation & integration | Core | Implicit differentiation | Differentiate y as function of x term-by-term. | |
| Pure: differentiation & integration | Core | Integration by substitution | Reverse chain rule. | |
| Pure: differentiation & integration | Advanced | Integration by parts | ∫u dv = uv − ∫v du — choose u to simplify. | |
| Pure: differentiation & integration | Core | Partial fractions integration | Linear/quadratic denominators. | |
| Pure: differentiation & integration | Core | Trapezium rule | Numerical area — error related to curvature. | |
| Pure: differentiation & integration | Core | Differential equation | Relates function and derivatives — separate variables or integrating factor. | |
| Pure: series, proof & numerical methods | Core | Arithmetic series | nth term and sum formulas. | |
| Pure: series, proof & numerical methods | Core | Geometric series | Sum to n terms; sum to infinity if |r| < 1. | |
| Pure: series, proof & numerical methods | Core | Maclaurin series | f(x) = f(0) + f’(0)x + … — coefficients from derivatives at 0. | |
| Pure: series, proof & numerical methods | Core | Proof by induction | Base case; assume true for n = k; prove for k + 1. | |
| Pure: series, proof & numerical methods | Core | Proof by contradiction | Assume conclusion false; deduce impossible statement. | |
| Pure: series, proof & numerical methods | Advanced | Newton–Raphson | xₙ₊₁ = xₙ − f(xₙ)/f’(xₙ) — root finding. | |
| Pure: vectors | Core | Position vector | Vector from origin to point. | |
| Pure: vectors | Core | Scalar product | a·b = |a||b| cos θ — perpendicular when zero. | |
| Pure: vectors | Core | Vector equation of line | r = a + λb. | |
| Pure: vectors | Core | Equation of plane | n·r = d or scalar triple product for coplanarity. | |
| Pure: vectors | Advanced | Shortest distance | Between skew lines or point to plane — vector methods. | |
| Mechanics | Core | Equilibrium | Resultant force zero; resultant moment zero about any point. | |
| Mechanics | Core | Friction | F ≤ μR; limiting friction when sliding impends. | |
| Mechanics | Core | Centre of mass | Point where weight acts for uniform fields. | |
| Mechanics | Core | Work–energy | Change in KE = total work done by forces. | |
| Mechanics | Core | Circular motion | v = rω; centripetal acceleration rω² or v²/r. | |
| Mechanics | Core | Hooke’s law | T = kx for elastic string/spring within limit. | |
| Mechanics | Advanced | Oblique impact | Coefficient of restitution along line of centres. | |
| Probability & statistics | Core | Discrete random variable | Probability function p(x) sums to 1. | |
| Probability & statistics | Core | Expectation E(X) | Σ x p(x). | |
| Probability & statistics | Core | Variance Var(X) | E(X²) − [E(X)]². | |
| Probability & statistics | Core | Binomial B(n,p) | Independent trials, fixed p. | |
| Probability & statistics | Core | Normal distribution | Standardisation Z = (X − μ)/σ. | |
| Probability & statistics | Core | Linear combination | E(aX + b) = aE(X) + b; Var(aX + b) = a²Var(X). | |
| Probability & statistics | Advanced | Hypothesis test | H₀ vs H₁; critical region or p-value; significance level α. | |
| Probability & statistics | Core | Type I / Type II error | Reject true H₀; fail to reject false H₀. | |
| Probability & statistics | Core | Sampling distribution of mean | Central limit idea for large n. |
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Mathematics (9709) — Keywords & Key Terms FAQ
- What is on this Cambridge International International A Level Mathematics keywords and key terms list?
- It is a topic-organised glossary of important mathematics terms with short, exam-style definitions aligned to Cambridge International A Level Mathematics (9709) (9709). It is designed for “define”, “state”, “outline” and “explain” questions where precise vocabulary earns marks.
- How should I use this 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 International A Level Mathematics (9709) 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 Mathematics. Use formula sheets for equations; use this list for precise terms and definitions.
- Can I download this 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 Mathematics list aligned to the 9709 specification?
- Topic groupings and wording follow Cambridge International A Level Mathematics (9709) for Cambridge International 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 Mathematics at International A Level, separate from longer notes or topic trackers.