IB Math RevisionIB Math AI HL past papers
IB Mathematics: applications and interpretation, Higher Level. The IB sells its past papers and markschemes, so the only free official papers are the specimen papers. Here they are, with where to buy past papers, the paper format, and our own practice papers you can sit on screen with a timer.
Papers are © the International Baccalaureate Organization; we link to the official copies. Details
The IB does not publish past papers for free. Its specimen papers are free on ibo.org; past papers and markschemes are sold through the official IB store (Follett).
Official IB papers
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Applications and interpretation: specimen papers (SL and HL, Papers 1-3) Maths AI Specimen
IB past papers and markschemes (May and November sessions)
The specimen document covers SL and HL: HL students use the HL Papers 1, 2 and 3.
Sit it under exam conditions: open the paper, press Start timer, press Finish when time is up, then mark it against the mark scheme. Timing is free, no sign-in; a free account saves your time and lets you enter your mark to track your progress.
Our AI HL practice and prediction papers
Written by us (not IB papers), free to use on this site.
HL AI Practice Paper 1 (interactive) Written by us
HL AI Practice Paper 2 (interactive) Written by us
HL AI Paper 3 practice Written by us
Prediction Papers Written by us
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The IB Math AI HL exam papers
| Paper | Format | Time | Marks | Weight |
|---|---|---|---|---|
| Paper 1 | Technology allowed (GDC); short-response questions | 2 h | 110 | 30% |
| Paper 2 | Technology allowed (GDC); extended-response questions | 2 h | 110 | 30% |
| Paper 3 | Technology allowed (GDC); two compulsory extended-response problem-solving questions | 1 h 15 min | Not confirmed | 20% |
The internal assessment (the mathematical exploration) is the remaining 20%. First assessment 2021 syllabus.
Practise these topics
Every paper can test all five syllabus topics. Each link opens a page to learn the sub-topic and practise it.
Number and Algebra
- Matrices — multiplication, inverse, and determinant
- Systems of linear equations and Gaussian elimination
- Complex numbers and Argand diagrams
- Sequences, series, and the sum to infinity
- Exponential models for real-world decay
Functions
Geometry and Trigonometry
- Voronoi diagrams — construction and applications
- 3D vectors — dot product and cross product
- Vector equations of lines in 2D and 3D
- Sinusoidal modelling with seasonal data
- Graph theory — adjacency matrices, spanning trees and route problems
Statistics and Probability
- Chi-squared test and confidence intervals
- Linear regression and residual analysis
- Normal and Poisson distributions
- Hypothesis testing — t-test and chi-squared
- Markov chains and transition matrices
Calculus
- Differentiation — chain, product and quotient rules, related rates
- Integration — standard integrals and substitution by inspection
- Differential equations — first-order separable and Euler's method
- Slope fields and qualitative DE analysis
- Optimisation in context
AI HL exam-style questions by topic → · Skill Builders → · Revision notes → · Mock exam guide → · Course →
Where AI HL marks are lost
From the IB subject reports we summarise on AI HL Examiner Insights, in our own words:
- Accuracy: premature rounding, 2 s.f. answers and ignored instructions. Use the full GDC value in every later step, round once at the end to 3 s.f. (or as instructed), and write the unrounded value first. Round, don't truncate. Give a sensible level of accuracy for the context.
- Hypothesis tests: hypotheses in words, the wrong test, and conclusions that don't follow. Write H₀ and H₁ with symbols for population parameters (μ, ρ, p). Choose the test from the design (paired data → paired t; σ unknown → t). State the p-value, compare it with the stated significance level, then conclude in context. For goodness of fit: df = cells − 1 − parameters estimated.
- HL algebra: product rule, brackets, logs and exact solutions. Practise the core manipulations without the GDC: product and chain rules, brackets, log laws, exponentiating both sides, exact quadratic solutions. Then use the GDC to check.
- IB notation: AB as a length, vectors in columns, f⁻¹ vs f′, the variables asked for. AB (no arrow) is a length; AB with an arrow is a vector, written as a column. Displacement AB = b − a. f⁻¹ is the inverse, f′ the derivative. Answer in the question's variables.
Formula booklet
Mathematics: applications and interpretation HL formula booklet · International Baccalaureate · First assessment 2021 (current edition)
The HL booklet includes the SL formulas as well as the HL ones. The IB gives it to schools (Programme Resource Centre) rather than posting it publicly, and a clean copy is provided in every HL exam. Ask your teacher for the current version; the link goes to the IB's DP Mathematics page.
Questions students ask
Are IB Math AI HL past papers free?
Not officially. The IB sells past papers and markschemes through its official store (opens in a new tab); your school may also have them. The only free official papers are the specimen papers on ibo.org, linked above. Copies on other websites are not licensed by the IB.
How many papers are there in IB Math AI HL?
3 exam papers: Paper 1 (2 h, 110 marks, 30% of the grade; technology allowed (GDC); short-response questions); Paper 2 (2 h, 110 marks, 30% of the grade; technology allowed (GDC); extended-response questions); Paper 3 (1 h 15 min, 20% of the grade; technology allowed (GDC); two compulsory extended-response problem-solving questions). The internal assessment (exploration) is the other 20%.
Where are the IB Math AI HL grade boundaries?
The IB publishes grade boundaries to schools after each session (in the subject reports on its Programme Resource Centre), not as a public web page. Ask your teacher for the latest ones: we don't quote numbers we can't verify.
Which formula booklet do I get in the exam?
The applications and interpretation HL formula booklet. SL and HL have separate booklets, and the HL booklet includes the SL formulas as well as the HL ones. A clean copy is provided in every exam.
Other courses: IB Math AA SL past papers · IB Math AA HL past papers · IB Math AI SL past papers · All IB past papers · IB Math grade boundaries