IB Math AI HL · 2021 to 2025
Unit 5: Calculus
380 past paper questions from 48 papers across 11 exam sessions. See what repeats, then practise the same skills with AI marking.
Starter set across the most-tested skills, with AI marking and model answers.
HL archive · 2021 to 2026
Unit 5: Calculus
Latest exam session: May 2026
- questions
- 380
- questions
- papers
- 48
- papers
- exam sessions
- 11
- exam sessions
- micro-topics
- 20
Topics in Unit 5: Calculus
In syllabus order. The ring is the share of the marks each one carries.
5.2
Increasing and decreasing functions
0% of marks4 of the 1278 marks across the 54 Math AI HL papers analysed (0%) were on this topic. A past-paper pattern, not a guarantee for your next paper. · 2 questions
5.4
Tangents and normals
1% of marks12 of the 1278 marks across the 54 Math AI HL papers analysed (1%) were on this topic. A past-paper pattern, not a guarantee for your next paper. · 5 questions
5.5
Introduction to integration
2% of marks28 of the 1278 marks across the 54 Math AI HL papers analysed (2%) were on this topic. A past-paper pattern, not a guarantee for your next paper. · 10 questions
5.6
Stationary points, local maximum and minimum
1% of marks16 of the 1278 marks across the 54 Math AI HL papers analysed (1%) were on this topic. A past-paper pattern, not a guarantee for your next paper. · 4 questions
5.7
Optimization
19% of marks248 of the 1278 marks across the 54 Math AI HL papers analysed (19%) were on this topic. A past-paper pattern, not a guarantee for your next paper. · 76 questions
5.8
Trapezoid rule
2% of marks30 of the 1278 marks across the 54 Math AI HL papers analysed (2%) were on this topic. A past-paper pattern, not a guarantee for your next paper. · 12 questions
5.9
Differentiation rules (HL only)
7% of marks87 of the 1278 marks across the 54 Math AI HL papers analysed (7%) were on this topic. A past-paper pattern, not a guarantee for your next paper. · 31 questions
5.10
Second derivatives (HL only)
1% of marks7 of the 1278 marks across the 54 Math AI HL papers analysed (1%) were on this topic. A past-paper pattern, not a guarantee for your next paper. · 3 questions
5.11
Integration techniques (HL only)
2% of marks31 of the 1278 marks across the 54 Math AI HL papers analysed (2%) were on this topic. A past-paper pattern, not a guarantee for your next paper. · 9 questions
5.12
Areas & volumes of revolution (HL only)
13% of marks160 of the 1278 marks across the 54 Math AI HL papers analysed (13%) were on this topic. A past-paper pattern, not a guarantee for your next paper. · 43 questions
5.13
Kinematics (HL only)
5% of marks64 of the 1278 marks across the 54 Math AI HL papers analysed (5%) were on this topic. A past-paper pattern, not a guarantee for your next paper. · 22 questions
5.14
Differential equations (HL only)
18% of marks224 of the 1278 marks across the 54 Math AI HL papers analysed (18%) were on this topic. A past-paper pattern, not a guarantee for your next paper. · 58 questions
5.15
Slope fields (HL only)
2% of marks26 of the 1278 marks across the 54 Math AI HL papers analysed (2%) were on this topic. A past-paper pattern, not a guarantee for your next paper. · 13 questions
5.16
Euler's method (1st order) (HL only)
3% of marks32 of the 1278 marks across the 54 Math AI HL papers analysed (3%) were on this topic. A past-paper pattern, not a guarantee for your next paper. · 10 questions
5.17
Phase portraits (HL only)
20% of marks258 of the 1278 marks across the 54 Math AI HL papers analysed (20%) were on this topic. A past-paper pattern, not a guarantee for your next paper. · 72 questions
5.18
Euler's method (2nd order) (HL only)
4% of marks51 of the 1278 marks across the 54 Math AI HL papers analysed (4%) were on this topic. A past-paper pattern, not a guarantee for your next paper. · 10 questions
Exam pattern
How often each micro-topic has been examined, year by year. Each label is explained under the grid.
Does it repeat?
Top 4 of 20 micro-topics for the next sitting. Numbers are questions per year.
fewermore
| Micro-topic | 2021 | 2022 | 2023 | 2024 | 2025 | 2026 |
|---|---|---|---|---|---|---|
| 11Differential equations (separation of variables), 2021: 11 questions | 15Differential equations (separation of variables), 2022: 15 questions | 8Differential equations (separation of variables), 2023: 8 questions | 12Differential equations (separation of variables), 2024: 12 questions | 7Differential equations (separation of variables), 2025: 7 questions | 5Differential equations (separation of variables), 2026: 5 questions | |
5.12.2Volumes of revolution | 6Volumes of revolution, 2021: 6 questions | 5Volumes of revolution, 2022: 5 questions | 10Volumes of revolution, 2023: 10 questions | 8Volumes of revolution, 2024: 8 questions | 6Volumes of revolution, 2025: 6 questions | 1Volumes of revolution, 2026: 1 question |
| 27Phase portraits of coupled systems, 2021: 27 questions | 8Phase portraits of coupled systems, 2022: 8 questions | 16Phase portraits of coupled systems, 2023: 16 questions | 18Phase portraits of coupled systems, 2024: 18 questions | 2Phase portraits of coupled systems, 2025: 2 questions | 1Phase portraits of coupled systems, 2026: 1 question | |
| 12Optimisation in Context, 2021: 12 questions | 9Optimisation in Context, 2022: 9 questions | 26Optimisation in Context, 2023: 26 questions | 14Optimisation in Context, 2024: 14 questions | 15Optimisation in Context, 2025: 15 questions | ·Optimisation in Context, 2026: 0 questions |
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Questions on Unit 5: Calculus, by exam session
Which papers asked about Unit 5: Calculus, and which question numbers. Open a paper to see them highlighted.
May 2026
8 questions across 3 papers
May 2025
19 questions across 6 papers
November 2024
6 questions across 3 papers
May 2024
14 questions across 5 papers
November 2023
6 questions across 3 papers
May 2023
17 questions across 9 papers
November 2022
6 questions across 3 papers
May 2022
11 questions across 5 papers
November 2021
8 questions across 3 papers
May 2021
11 questions across 5 papers
Specimen 2021
6 questions across 3 papers
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Frequently asked questions
Short answers about this page.
Which Math AI HL exam sessions are covered for Unit 5: Calculus?
11 exam sessions from 2021 to 2026, the latest May 2026. Every Paper 1, 2 and 3 in every timezone is read and classified in full, which gives 48 papers in this archive.
Which Unit 5: Calculus topic comes up most?
Differential equations (separation of variables) (5.14.1): in 26% of papers, last seen May 26 P3 TZB. Usually "find / solve", worth about 16 marks in a paper that includes it.
Can I see the original question and mark scheme?
No. The wording belongs to the IB. You get the citation, the marks, the command term and the skill tested, plus our own matched practice questions with worked answers and AI marking.
What do "banker", "due" and "rising" mean?
Banker: examined in at least one sitting in four and still appearing. Due: regular before, but absent for the last two exam sessions. Rising: clearly more common in the last two years. Our classification of real papers, not an IB statistic.
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