The IB Maths IA: how it is marked and how to choose a topic
The exploration is 20% of the final IB Maths grade, and the only part a student can work on, and revise, before exam day. This guide explains the five criteria, what changes between SL and HL, how to turn an interest into a question that can score well, and what changes for students who start the DP in August 2027.
IB subject guides, subject briefs and announcements checked October 2026 · Alex Koo
20%of the final grade at SL and HLAA and AI alike
12–20pages, double-spacedgraphs and tables included
1draft the teacher can comment onthe next version is final
17 · 18IA mark for a grade 7 (HL · SL)out of 20, every session 2022–2025
Why it matters
What one IA mark is worth
Each IA mark is 1% of the final grade. In the exams, the same 1% takes between 2 and almost 4 marks, so IA marks are a large part of the grade that is earned before exam day.
Exam marks worth the same as one IA mark (AA and AI, exams up to November 2028)
SL · Paper 1 or 280 marks = 40%
2.0
HL · Paper 355 marks = 20%
2.8
HL · Paper 1 or 2110 marks = 30%
3.7
01234
From May 2029 the papers get shorter (SL 75 marks; HL 100 and 50), so one IA mark becomes about 1.9 SL marks and 2.5–3.3 HL marks.
Example
Raising the IA from 14 to 17 adds 3% to the final total: about 11 more marks on HL Paper 1, or 6 more on SL Paper 1.
Calculation: paper marks ÷ paper weighting (%). For example, HL Paper 1 has 110 marks for 30% of the grade, so 1% = 110 ÷ 30 ≈ 3.7 marks. Weightings from the IB subject briefs; IA boundaries from IB subject reports, 2022–2025.
The teacher marks the exploration against five criteria, and the IB moderates a sample from each school. Criteria A to D are identical at SL and HL; only E, Use of mathematics, is judged against the level of the course.
A 4
B 4
C 3
D 3
E 6
Marks by criterion (the 6-mark criterion highlighted)
A
Presentation
4 marks
Some coherence or organisation → coherent and well organised → also concise
What it rewards
Can a classmate taking the same course follow the whole exploration without asking you anything? Every section should serve the aim.
Where marks go
Long historical background, repeated calculations in the body, graphs with no explanation, an aim that drifts.
For the top band
State a clear aim early, let each section build on the last, move repetitive working to an appendix, and end by answering the aim.
B
Mathematical communication
4 marks
Partly appropriate → relevant and appropriate → consistent throughout
What it rewards
Correct notation and terminology, defined variables, and a sensible choice of formulas, graphs, tables and diagrams.
Define each variable when it first appears, keep the same notation throughout, label every graph and table, and state the accuracy you work to.
C
Personal engagement
3 marks
Some → significant → outstanding
What it rewards
Evidence that the exploration is your own: your question, data, decisions, predictions and ways of looking at the problem.
Where marks go
Textbook-style explanations of well-known mathematics, or a paragraph on why you like the topic with nothing personal in the mathematics itself.
For the top band
Make decisions only you could make, such as collecting your own data, choosing and testing assumptions or trying a variation, and show them throughout.
D
Reflection
3 marks
Limited → meaningful → substantial and critical
What it rewards
Questioning results as you go: are they reasonable, what do they depend on, where does the method stop working, and what should you do next because of them?
Where marks go
Reflection only in the conclusion, or a list of limitations added at the end that changes nothing.
For the top band
Reflect throughout and let it change the direction of the work, for example by refining a model after checking it against data.
E
Use of mathematics
6 marks
Judged against the course: SL and HL have different descriptors (see below)
What it rewards
Mathematics that is relevant to the aim, at the level of your course, correct, and clearly understood.
Where marks go
Mathematics below the course (only percentages or basic trigonometry), or advanced mathematics copied from a source that you cannot explain.
For the top band
Use course-level mathematics correctly and explain why each step works. At HL, the top marks also need sophistication, rigour and precision.
These summaries paraphrase the IB descriptors. The exact wording is in the subject guide your teacher uses.
Source: IB, Mathematics: analysis and approaches guide and Mathematics: applications and interpretation guide (first assessment 2021), internal assessment criteria.
SL and HL
Criterion E: the same 6 marks, a higher bar at HL
Both levels ask for relevant mathematics at the level of the course. The difference is what each mark demands: at HL the mathematics must be correct from level 3, and the top two levels add sophistication and rigour.
Level
SL
HL
3
Course-level mathematics; limited understanding
Course-level mathematics, correct; some understanding
4
Partly correct; some understanding
Correct; good understanding
5
Mostly correct; good understanding
Correct, with sophistication or rigour; thorough understanding
6
Correct; thorough understanding
Precise, with sophistication and rigour; thorough understanding
What the terms mean
Commensurate with the level of the course
The main mathematics should come from your course. Mathematics below it (IGCSE level only) keeps E at the lowest levels, however well it is done.
Sophistication
Challenging concepts, looking at the problem from more than one angle, or linking different areas of mathematics.
Rigour
Clear logic and language in every argument and calculation.
Precision
No errors, and an appropriate level of accuracy throughout.
The same piece of work can score lower under the HL descriptors than under SL, so HL students should check early that the topic leaves room for HL-level mathematics.
Summary of the IB criterion E descriptors and clarifications for SL and HL (first assessment 2021).
Choosing a topic
Four checks before you commit to a topic
It is a question, not a theme
“The maths of rain” is a theme. “Given my height, what is the smallest umbrella that keeps the bottom of my trousers dry while I walk?” is a question you can answer, and every section can serve it.
The main mathematics is in your course
Course-level mathematics that you can explain scores better than advanced mathematics copied from a paper. At HL, check that the question leaves room for HL-level work, not only SL techniques.
There are decisions only you can make
Your own data, the assumptions you choose and test, the model you pick and why, a variation you try. This is where criteria C and D come from.
It fits in 12 to 20 pages
Too broad and the exploration loses focus; too narrow and there is too little mathematics. If the aim needs a paragraph to explain, narrow it.
From interest to question
Questions my students have explored
Each started from something the student did, used or wondered about, and became a question that could be answered. They show the scope that works; a good IA starts from your own question, not a copy of these.
Started from
Question
Mathematics
Walking in the rain
Given my height, what is the smallest umbrella that keeps the bottom of my trousers dry while I walk?
Trigonometry, relative velocity, optimisation · AA SL/HL
Skydiving
If I go skydiving, how long does it take me to reach terminal velocity?
Differential equation with air resistance, integration · AA HL
Badminton
Badminton is the fastest racket sport, so why does a shuttlecock lose speed so much more than the balls in other racket sports?
Air-resistance models, differential equations, comparing parameters · AA HL
A method from class
Solving a second-order differential equation with Euler’s method
Euler’s method on a coupled first-order system · AA HL
A coffee cup
Redesigning a Starbucks cup to hold the same volume with less material
Volume and surface area, optimisation with calculus · AA SL/HL
Football
With air resistance proportional to the square of speed, can a goalkeeper score in the opposite goal from their own end?
Projectile motion with quadratic drag, Euler’s method · AA HL
Many of these are modelling questions: the marks come from the mathematics and the student’s own decisions, not from the physics. AA and AI use the same criteria; what changes is the course that criterion E is judged against.
How it runs
From topic to moderation
Step 1
Topic and question
Agree the topic and the research question with the teacher before writing.
Step 2
First draft
Research, calculations and a complete draft, all written by the student.
Step 3
Feedback on one draft
The teacher comments on one draft but does not edit or correct it. The next version handed in is the final one.
Step 4
Marking and moderation
The teacher marks the final version. The IB re-marks a sample from the school and can move the whole school’s marks up or down.
The student’s own work
The exploration is individual work. Discussing ideas with the teacher is expected, but the writing, the calculations and the decisions must be the student’s. Every idea, formula, image or data set from elsewhere is cited where it is used.
AI tools
The IB has not banned AI tools, but it does not count anything an AI produced, even in part, as the student’s own work. Such content must be credited in the text and in the bibliography.
Time and deadlines
The IB allocates 30 hours of each course to investigation, modelling and the exploration. Internal deadlines are set by each school, so check the school calendar early.
Sources: IB subject guides (internal assessment); IB, “Statement from the IB about ChatGPT and artificial intelligence in assessment and education” (ibo.org); IB mathematics course fact sheet (2023).
From August 2027
Four new criteria for students starting in August 2027
The IB is updating both maths courses. The exploration stays mostly the same, with 20 marks, a 20% weighting and 30 hours, but the five criteria become four. They are identical at SL and HL and follow the steps of mathematical inquiry.
Exams up to November 2028Current five criteria
Students now in Grades 11 and 12 at August-start schools.
First teaching August 2027 · first exams May 2029New four criteria
Students now in Grade 10.
Now · exams to November 2028
A 4
B 4
C 3
D 3
E 6
A
Presentation
4
B
Mathematical communication
4
C
Personal engagement
3
D
Reflection
3
E
Use of mathematicsDifferent descriptors for SL and HL
6
New · first exams May 2029
A 4
B 6
C 4
D 6
A
Problem specificationProblem in context · desired outcomes
4
B
AbstractionAssumptions · techniques and tools · mathematical form
6
C
ComputationCalculations · mathematical communication
This guide summarises published IB documents and is not affiliated with or endorsed by the International Baccalaureate Organization. The teacher and the current subject guide are the final word on a school’s IA requirements, and the exploration must be the student’s own work.
