Maths IA guide
AA vs AI, SL vs HL: how the Maths IA differs
The exploration is the same task in all four IB Maths courses: 20 marks, 20% of your final grade, five criteria. Four of those criteria are identical everywhere. What changes is the mathematics you are expected to use: it has to be at the level of your own course, and at HL Criterion E asks for more. Here is exactly what differs, and what doesn't.
What is the same in every course
- The task: a 12–20 page exploration of a question you choose.
- The weighting: 20% of the final grade at SL and HL, in AA and AI.
- Criteria A (Presentation, 4), B (Mathematical communication, 4), C (Personal engagement, 3) and D (Reflection, 3): the same descriptors in all four courses.
- Marking and moderation: your teacher marks it, and the IB moderates a sample from your school.
- The academic integrity rules, including the single teacher-feedback draft.
What is different
Criterion E at SL
Rewards mathematics that is relevant to the aim, correct, and commensurate with the level of the course, with thorough knowledge and understanding shown. Using SL techniques well, and explaining them, is exactly what is asked.
Criterion E at HL
Has the same six marks but asks for more at the top: the mathematics must be commensurate with the HL course, and the top bands expect it to be sophisticated and rigorous — sophistication in the choice and use of mathematics, rigour in the precision of the reasoning. An HL exploration that only uses SL techniques will find the top of E hard to reach.
AA vs AI
No difference in the criteria. The difference is what “the level of the course” means: AA explorations tend to lean on calculus, functions, proof and probability theory; AI explorations on modelling with technology, statistical inference, networks and Voronoi diagrams. Mathematics from outside your course is allowed if you understand and explain it.
Descriptor summaries are ours; the official descriptors are in the IB Mathematics guides your teacher has. Full detail: Criterion E guide.
Typical IA mathematics by course
| Course | Mathematics that often works well in an IA |
|---|---|
| AA SL | Differentiation and integration (optimisation, areas, kinematics), exponential and logarithmic models, trigonometric functions, sequences and series, binomial and normal distributions, regression and correlation. |
| AA HL | Everything in AA SL, plus: differential equations by separation of variables, Maclaurin series, complex numbers, proof by induction and contradiction, integration by parts and substitution, volumes of revolution, Bayes' theorem, continuous random variables. |
| AI SL | Modelling with linear, exponential, power and sinusoidal functions using technology, regression and Spearman's rank, chi-squared and t-tests, Voronoi diagrams, financial mathematics, basic differentiation and the trapezoidal rule. |
| AI HL | Everything in AI SL, plus: differential equations with slope fields and Euler's method, coupled systems, Markov chains and matrices, graph theory and network algorithms, Poisson distributions, confidence intervals, further hypothesis tests, linearising models with logarithms. |
Ideas that fit each course: AA SL IA ideas · AA HL IA ideas · AI SL IA ideas · AI HL IA ideas.
Changes from 2027
For students who start the Diploma Programme in August 2027 (first exams in May 2029), the IB's revised courses keep the exploration but use new criteria that are the same at SL and HL. If your exams are in 2026, 2027 or 2028, follow the current criteria described here.
Frequently asked questions
Are the IA criteria different for AA and AI?
No. Both courses use the same five criteria. The only difference is that Criterion E judges your mathematics against the level of your own course.
What is the difference between an SL and an HL Maths IA?
Only Criterion E. At HL, the top bands expect mathematics commensurate with the HL course that is sophisticated and rigorous; at SL, relevant, correct mathematics at the SL level with good understanding reaches the top.
Can an AA student use AI-course maths (or vice versa)?
Yes, if it helps answer your aim and you understand and explain it. Say when a technique is new to you. What matters for Criterion E is the level and quality of the mathematics overall.
Can an HL student write an IA using only SL maths?
They can, but it is risky: the top bands of HL Criterion E expect sophisticated, rigorous mathematics at the HL level. Plan at least one genuinely HL technique that the question needs.
Not sure your maths is at the right level?
An examiner can tell you whether your exploration's mathematics is commensurate with your course, criterion by criterion. €100. Feedback in general terms, like a teacher's draft comments — never edits, and no promised mark.