Past-paper analysis
IB Maths AI HL past paper analysis
We tagged 436 questions worth 4,675 marks from 17 exam sittings between 2021 and 2025. This page shows what each topic is worth, which paper it sits on, and how that has moved over five years.
- 436 questions
- 4,675 marks
- 17 sittings
- 2021–2025
Written by Ejaz Ahmad. Published 18 October 2026. See how we analyse papers.
Marks by topic
Probability Distributions (9%), Hypothesis Testing (7.5%) and Trigonometry (6.3%) lead the table. The top five topics together carry 34.6% of all marks, and even the smallest of the 22 topics, Univariate Statistics, holds 1.9%.
Share of marks by topic
| Topic | % of all marks |
|---|---|
| Probability Distributions | 9% |
| Hypothesis Testing | 7.5% |
| Trigonometry | 6.3% |
| Differentiation | 6.1% |
| Graph Theory | 5.7% |
| Differential Equations | 5.7% |
| Eigenvalues / Markov | 5.4% |
| Vectors | 5.3% |
| Integration | 5.1% |
| Functions | 4.6% |
| Modelling / Regression | 4% |
| Sequences & Series | 3.8% |
| Coupled DEs | 3.8% |
| Kinematics | 3.4% |
| Loans & Annuities | 2.9% |
| Voronoi | 2.8% |
| Bivariate Statistics | 2.6% |
| Exp & Logarithms | 2.5% |
| Complex Numbers | 2.4% |
| Trig Graphs | 2.3% |
| Probability | 2.1% |
| Univariate Statistics | 1.9% |
Share of all 4,675 marks. Marks from multi-topic questions are split equally between their tags.
Paper 1 vs Paper 2, and Paper 3
Eigen / Markov leans towards Paper 2 (7.7% of its marks against 2.7% in Paper 1), while Functions leans towards Paper 1 (8.6% against 2.8% in Paper 2).
Share of each paper's marks, by topic
| Topic | Paper 1 | Paper 2 |
|---|---|---|
| Prob. Distributions | 9% | 9.9% |
| Hypothesis Testing | 5% | 5.6% |
| Trigonometry | 6.5% | 7% |
| Differentiation | 6.2% | 7.6% |
| Graph Theory | 2.9% | 7.2% |
| Diff. Equations | 4.5% | 4.3% |
| Eigen / Markov | 2.7% | 7.7% |
| Vectors | 6.1% | 4.9% |
| Integration | 5.8% | 6.3% |
| Functions | 8.6% | 2.8% |
| Modelling | 4.7% | 1.6% |
| Complex Numbers | 4.1% | 1.1% |
Each column is a share of that paper's own marks.
Paper 3 at a glance
Paper 3 (HL only) is a long investigation paper, so it is counted separately from Papers 1 and 2.
Paper 3: share of marks by topic
| Topic | % of Paper 3 marks |
|---|---|
| Hypothesis Testing | 15.9% |
| Differential Equations | 10.7% |
| Graph Theory | 8.3% |
| Modelling / Regression | 7.5% |
| Bivariate Statistics | 7.3% |
| Probability Distributions | 7.2% |
| Coupled DEs | 6.5% |
| Eigenvalues / Markov | 6% |
| Other | 30.6% |
2021–2025 Paper 3 papers.
Paper 3: recurring topics and techniques
| Topic or technique | Marks contributed to Paper 3 |
|---|---|
| Hypothesis Testing | 149 |
| Differential Equations | 100 |
| Graph Theory | 77.5 |
| Modelling / Regression | 70.5 |
| Bivariate Statistics | 68 |
| Prob. Distributions | 67 |
| Coupled DEs | 60.5 |
| Eigenvalues / Markov | 56.5 |
| Vectors | 42.5 |
| Sequences | 42 |
Paper 3 is the HL extended-investigation paper.
Average marks per question
Coupled DEs averages 15.4 marks a question and Hypothesis Testing 14.2, so they usually arrive as long, multi-step questions. Sequences averages 8.3, which points to shorter questions.
Average marks per question, by topic
| Topic | Average marks |
|---|---|
| Coupled DEs | 15.4 |
| Hypothesis Testing | 14.2 |
| Eigenvalues / Markov | 13.9 |
| Graph Theory | 13.1 |
| Kinematics | 13 |
| Diff. Equations | 12.3 |
| Trig Graphs | 12 |
| Voronoi | 11.7 |
| Probability | 11.5 |
| Bivariate Statistics | 11.4 |
| Vectors | 10.9 |
| Affine Transf. | 10.3 |
| Integration | 10.1 |
| Modelling / Reg | 9.6 |
| Prob. Distributions | 9.5 |
| Trigonometry | 9.3 |
| Sequences | 8.3 |
Higher means the topic tends to appear as a longer question.
How topics changed by year
Integration rose from 2 questions in 2021 to 8 questions in 2025; Probability Distributions fell from 8 questions to 5 questions. Each cell is the questions tagged with the topic that year.
Topics by year
| Topic | 2021 | 2022 | 2023 | 2024 | 2025 |
|---|---|---|---|---|---|
| Probability Distributions | 8 | 7 | 7 | 8 | 5 |
| Hypothesis Testing | 6 | 7 | 6 | 4 | 8 |
| Differentiation | 4 | 4 | 7 | 5 | 8 |
| Integration | 2 | 6 | 4 | 5 | 8 |
| Differential Equations | 5 | 4 | 4 | 3 | 7 |
| Graph Theory | 4 | 4 | 4 | 2 | 5 |
Darker cells are larger values. Only the main movers are shown.
What this means for your revision
- Start with the top five topics (Probability Distributions, Hypothesis Testing, Trigonometry, Differentiation and Graph Theory). Together they carry 34.6% of marks.
- Practise by paper. Eigen / Markov is mostly a Paper 2 skill and Functions a Paper 1 skill, so train each in the format it is asked.
- Watch the direction of travel: Integration has grown since 2021.
- Rehearse full solutions for topics that arrive as long questions, such as Coupled DEs.
- Do not drop the small topics. The smallest, Univariate Statistics, still holds 1.9% of marks.
Past frequency shows where marks have gone so far. It does not promise what a future paper will contain.
Guidebook
IB Maths AI HL guidebook
Full course coverage by Photon, with exam-style practice that follows these weightings.
Guidebook
HL Paper 3 (AA and AI) guidebook
Full course coverage by Photon, with exam-style practice that follows these weightings.
Free cheatsheets
Revise the top topics
Start with Probability Distributions: every IB Maths AI HL topic has a free cheatsheet with the formulas, methods and common traps.
Course page
IB Maths AI HL resources
Cheatsheets, guidebook details and revision resources for this course.
Method
We counted every IB Maths AI HL paper from the 17 May and November sittings between 2021 and 2025 (51 papers). Each question is read and tagged by topic. When a question carries more than one tag, its marks are split equally between them, so nothing is counted twice and the shares add up to 100%.
Tagging involves judgement, and these are counts of past marks, not a forecast. Read the full method.