AQA · International A Level · AA HL/SL
Mathematics AA — Keywords & Key Terms — Definitions Glossary (2026)
IB Diploma Programme Mathematics: Analysis and Approaches (HL/SL)
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.
IB Diploma Programme Mathematics AA (AA HL/SL)
IB Diploma Programme Mathematics AA (AA HL/SL)
IB Diploma Programme Mathematics: Analysis and Approaches (HL/SL)
Topics follow the IB DP Mathematics AA syllabus (first assessment 2021, valid to 2025+). HL content includes proof, complex numbers, further calculus and additional statistics.
Mark schemes: IB Maths mark schemes award M marks (method), A marks (accuracy) and R marks (reasoning/justification). Working must be shown for M marks. For 'show that' questions, every step must be justified.
Active recall: 0 / 38 terms ticked
| Recalled | Topic | Level | Keyword | Definition |
|---|---|---|---|---|
| Algebra | Core | Arithmetic sequence | Sequence with a constant difference d between consecutive terms: uₙ = u₁ + (n–1)d. | |
| Algebra | Core | Geometric sequence | Sequence with a constant ratio r between consecutive terms: uₙ = u₁ × rⁿ⁻¹. | |
| Algebra | Core | Sigma notation | Σ notation representing the sum of a series. | |
| Algebra | Core | Binomial theorem | Expansion of (a + b)ⁿ using binomial coefficients ⁿCᵣ. | |
| Algebra | Core | Logarithm | Inverse of exponentiation: logₐ(x) = y ↔ aʸ = x. | |
| Algebra | Core | Natural logarithm (ln) | Logarithm with base e (Euler's number ≈ 2.718). | |
| Algebra | Advanced | Proof by induction | Mathematical proof technique: prove base case, assume true for n = k, prove true for n = k+1. | |
| Algebra | Advanced | Proof by contradiction | Assume the opposite is true and derive a contradiction. | |
| Algebra | Advanced | Complex number | Number of the form z = a + bi where i = √(–1). | |
| Algebra | Advanced | Modulus-argument form | z = r(cos θ + i sin θ) = re^(iθ); r = modulus, θ = argument. | |
| Functions | Essential | Function | Rule that maps each element of the domain to exactly one element of the range. | |
| Functions | Core | Domain | Set of all valid input values of a function. | |
| Functions | Core | Range | Set of all output values of a function. | |
| Functions | Core | Inverse function (f⁻¹) | Function that reverses f; f⁻¹(f(x)) = x. Exists only if f is one-to-one. | |
| Functions | Core | Composite function | (g ∘ f)(x) = g(f(x)); output of f becomes input of g. | |
| Functions | Core | Even function | Symmetric about the y-axis: f(–x) = f(x). | |
| Functions | Core | Odd function | Rotationally symmetric about the origin: f(–x) = –f(x). | |
| Functions | Core | Asymptote | Line that a curve approaches but never reaches. | |
| Functions | Core | Transformation | Translation, reflection, stretch or combination applied to a graph. | |
| Calculus | Core | Derivative (f'(x)) | Rate of change of a function with respect to its variable; gradient of tangent. | |
| Calculus | Core | Integral | Reverse of differentiation; represents area under a curve. | |
| Calculus | Core | Chain rule | d/dx[f(g(x))] = f'(g(x)) · g'(x). Used for composite functions. | |
| Calculus | Core | Product rule | d/dx[uv] = u'v + uv'. Used when differentiating a product of two functions. | |
| Calculus | Core | Quotient rule | d/dx[u/v] = (u'v – uv') / v². Used when differentiating a quotient. | |
| Calculus | Core | Definite integral | ∫ₐᵇ f(x) dx; represents the signed area between the curve and the x-axis from a to b. | |
| Calculus | Core | Fundamental theorem of calculus | Links differentiation and integration: d/dx[∫ₐˣ f(t) dt] = f(x). | |
| Calculus | Advanced | L'Hôpital's rule | For indeterminate forms 0/0 or ∞/∞: lim[f(x)/g(x)] = lim[f'(x)/g'(x)]. | |
| Calculus | Advanced | Differential equation | Equation relating a function and its derivatives; solved by separation of variables or integrating factor. | |
| Statistics and Probability | Core | Probability | Measure of likelihood that an event occurs: P(A) = n(A)/n(U) for equally likely outcomes. | |
| Statistics and Probability | Core | Mutually exclusive events | Events that cannot occur simultaneously: P(A ∪ B) = P(A) + P(B). | |
| Statistics and Probability | Core | Independent events | Events where one does not affect the other: P(A ∩ B) = P(A) × P(B). | |
| Statistics and Probability | Core | Conditional probability | P(A|B) = P(A ∩ B) / P(B); probability of A given B has occurred. | |
| Statistics and Probability | Core | Normal distribution | Symmetric bell-shaped distribution characterised by mean μ and standard deviation σ. | |
| Statistics and Probability | Core | Standard normal distribution | Normal distribution with μ = 0 and σ = 1; Z-scores used to compare distributions. | |
| Statistics and Probability | Core | Binomial distribution | Discrete distribution for n independent trials each with probability p of success. | |
| Statistics and Probability | Advanced | Unbiased estimator | Statistic whose expected value equals the population parameter it estimates. | |
| Statistics and Probability | Advanced | Hypothesis test | Statistical procedure to decide whether sample evidence supports or contradicts a claim about a population. | |
| Statistics and Probability | Advanced | p-value | Probability of obtaining results at least as extreme as observed, assuming the null hypothesis is true. |
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Mathematics AA (AA HL/SL) — Keywords & Key Terms FAQ
- What is on this AQA International A Level Mathematics AA keywords and key terms list?
- It is a topic-organised glossary of important mathematics aa terms with short, exam-style definitions aligned to IB Diploma Programme Mathematics: Analysis and Approaches (HL/SL) (AA HL/SL). It is designed for “define”, “state”, “outline” and “explain” questions where precise vocabulary earns marks.
- How should I use this Mathematics AA 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 AA (AA HL/SL) 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 AA.
- Can I download this Mathematics AA 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 AA list aligned to the AA HL/SL specification?
- Topic groupings and wording follow IB Diploma Programme Mathematics: Analysis and Approaches (HL/SL) for AQA 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 AA at International A Level, separate from longer notes or topic trackers.