Mathematics Internal Assessment: How Your 20 Marks Are Really Awarded
The mathematics internal assessment — the IB calls it the exploration — is a piece of mathematical writing of about 12 to 20 pages that you choose and write yourself. It is worth 20% of your final Maths grade in both Analysis and Approaches and Applications and Interpretation, at SL and HL. Your teacher marks it out of 20 against five criteria, and the IB then moderates those marks. The five criteria are A Presentation (4), B Mathematical communication (4), C Personal engagement (3), D Reflection (3) and E Use of mathematics (6).
Now the part that made us write this page.
Before writing it we read the eight pages that currently rank highest for this topic. Five of them do not tell you the marking criteria at all. The three that do are all wrong — one is still printing the rubric that was replaced in 2021, one has invented a version that has never existed, and one has the right marks attached to the wrong letters.
So thousands of students are writing their exploration for a mark scheme their moderator is not using. That is where this page starts.
This is not another list of topic ideas. We already have one of those, with thirty of them, over on IB Maths IA topic ideas. This page is the other half: what the twenty marks are, who awards them, what a moderator does with your teacher’s marking afterwards, and how to check your own draft before anybody else sees it.
What the Maths IA actually is
Every IB Diploma Maths student writes one. It goes by three names and they all mean the same thing: the internal assessment, the IA, and the exploration, which is what the IB’s own documents call it. If your teacher says exploration and a website says IA, nothing has changed.
- Length: about 12 to 20 pages with double line spacing. That is guidance, not a rule, and there is no word limit. Diagrams and graphs count towards it. A bibliography does not.
- Worth: 20% of your final Maths grade. The written papers are the other 80%.
- Marked out of: 20, across five criteria.
- Marked by: your own teacher first. The IB moderates afterwards, which is covered further down and is the part most students have never had explained.
- Same for everyone: AA and AI, SL and HL all use the same five criteria and the same 20 marks. What changes between courses is the level of mathematics criterion E expects, and there is a table for that below.
It is called an exploration for a reason. The IB is not asking for an essay about mathematics. It is asking you to do some mathematics on a question you chose, and to write down your thinking as you go.
Most students have never seen one before they have to write one, so here is the shape of a typical exploration before we go anywhere near the marks.
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Two things in that picture surprise people. The mathematics is not a section in the middle of an essay — it is most of the exploration. And reflection is not a chapter at the end. It is the stripe down the side, appearing wherever you made a decision or got a result you had to think about.
The exploration is not a report on something you read. It is a record of something you worked out.
Before you read any other guide: the rubric changed in 2021
The Maths courses were rewritten for first examinations in 2021. The IA criteria changed with them. Two criteria swapped names, and personal engagement dropped from 4 marks to 3 while mathematical communication rose from 3 to 4.
A lot of pages written before 2021 are still online, still ranking, and still showing the old numbers. Here are the two side by side.
| Old rubric, before 2021 | Current rubric | What changed |
|---|---|---|
| Communication — 4 | A Presentation — 4 | Renamed |
| Mathematical presentation — 3 | B Mathematical communication — 4 | Up one mark |
| Personal engagement — 4 | C Personal engagement — 3 | Down one mark |
| Reflection — 3 | D Reflection — 3 | Same |
| Use of mathematics — 6 | E Use of mathematics — 6 | Same |
Look at what it says personal engagement is worth. If it says 4 marks, the page is out of date and everything else on it was written for a mark scheme that no longer exists. If it calls criterion A “Communication” rather than “Presentation”, same answer.
It matters more than it sounds. A student who believes personal engagement is worth 4 and mathematical communication only 3 will spend their time on the wrong things — and the two things they get wrong are worth two marks out of twenty between them.
One more thing while you are checking sources. Your teacher has the real document. The IB publishes the criteria in the Mathematics subject guide, with the full wording of every mark band, and your school has a copy. Ask for the IA pages. No blog, including this one, outranks that.
Where the 20 marks actually sit
Students treat the five criteria as if they weigh the same. They do not. One of them is worth almost a third of the paper on its own.
Scroll sideways to see the whole chart
Read that chart as a timetable. Criterion E, the mathematics itself, is worth 6 of the 20. Criteria A and B together, which are about how clearly you lay the work out, are worth 8. So more than two thirds of the paper is the maths and the way you present it.
Personal engagement and reflection together are worth 6. They matter, and they are the easiest marks on the page to pick up, because they cost you writing rather than mathematics. But a student who spends three weeks making their topic feel personal and two days on the mathematics has it backwards.
The five criteria, one by one
Each one below is laid out the same way: what it is for, what a moderator is looking at, and the same idea written weakly and then written well. The weak versions are not made up to be silly. They are the sentences that turn up again and again.
Presentation
Is the exploration organised, coherent and concise? Can a reader follow it from start to finish without going back?
What a moderator is looking at
- Whether there is a clear aim stated near the beginning, and whether everything afterwards serves it.
- Whether the sections run in an order that makes sense, rather than in the order you happened to do the work.
- Whether it is concise. Conciseness is written into this criterion. Padding costs marks here, which is why a 30-page exploration often scores lower than a 15-page one.
- Whether the reader has to hold things in their head. If a symbol appears on page 3 and is explained on page 9, that is a presentation problem.
The same idea, written two ways
Loses marks
In this exploration I will look at various aspects of basketball and apply different mathematical techniques to see what I can find.
Earns marks
The aim of this exploration is to find the launch angle that maximises the margin for error on a free throw, and to test whether that angle matches the one I actually use.
The second one tells the moderator what the next twelve pages are for. The first one tells them nothing, and every page after it has to work harder.
Mathematical communication
Are you using proper mathematical notation, symbols and terminology, and using them consistently? This is the criterion that went up a mark in 2021, and it is the one students most often underrate.
What a moderator is looking at
- Real notation, not calculator notation. Writing x^2, sqrt(5) or 1.5E6 is typing, not mathematics. It should be x2, √5 and 1.5 × 106.
- Every variable defined, once, in words, with its units. “Let h be the height” is half a definition. “Let h be the height of the ball above the ground, in metres” is a whole one.
- Graphs with labelled axes, units and a caption. A screenshot straight out of Desmos with no axis labels is a thrown-away mark.
- Consistency. If t is seconds on page 4, t is not minutes on page 9. If you switch between degrees and radians, say so.
- More than one form where it helps — an equation, a graph and a table of the same relationship shows control of the material.
The same working, written two ways
Loses marks
I put y=-4.9x^2+20x+1.5 into my calculator and it gave me 21.9 for the max.
Earns marks
Let h(t) = −4.9t2 + 20t + 1.5, where h is the height in metres and t is the time in seconds after release. Setting h′(t) = 0 gives t = 2.04 s and a maximum height of 21.9 m.
Personal engagement
Is there evidence that you thought about this yourself, rather than following a method you found? Note the number: 3 marks, not 4. Any page telling you 4 is out of date.
What a moderator is looking at
- Evidence in the choices you made, not in a sentence announcing enthusiasm. “I have always loved football” earns nothing. Collecting your own data from forty of your own penalty kicks earns something.
- Using your own data where it is possible. Primary data you gathered beats a dataset you downloaded, every time, for this criterion.
- Adapting a method rather than running it. “The standard model assumes no air resistance, so I added a drag term and compared the two” is engagement. Following a worked example is not.
- Asking a question your textbook does not ask.
The same opening, written two ways
Loses marks
I have always been passionate about music, so I decided to explore the mathematics of sound waves, which I find fascinating.
Earns marks
I recorded my own guitar’s open A string and found it was 3 Hz sharp of 110 Hz. That made me ask how far out of tune a string has to be before I can hear it, which is the question this exploration answers.
The second one has not used the word passionate once, and shows more engagement than the first does in a paragraph. If you are still choosing your subject, our list of 30 Maths IA topic ideas is built around questions you can make personal in exactly this way.
Reflection
Do you stop and think about what your own results mean, what they do not mean, and what you would do differently? This is the criterion with the clearest ladder, and it has a section of its own below, because it is where most students leave marks on the table.
The single most important thing: reflection has to be spread through the exploration, not saved for the conclusion. A paragraph of thinking at the moment you noticed something is worth more than three paragraphs of it on the last page.
Use of mathematics
The biggest block of marks on the page. Is the mathematics relevant to your aim, correct, and at the level of your course? And do you show that you actually understand it?
What a moderator is looking at
- Relevance. Mathematics bolted on to look impressive, that does not move the aim forward, does not help here and hurts criterion A.
- Correctness. Not perfection, but errors that change your conclusion are expensive.
- Level. This is the one that caps explorations. More below.
- Understanding. Showing the steps, explaining why you chose a method, and knowing what your answer means. A result produced by a calculator with no commentary shows nothing.
- Processes, not just answers. Modelling, proving, optimising, finding and testing a pattern, deriving a result. Reproducing textbook algebra is not a mathematical process you chose.
Reflection: the three-rung ladder
Criterion D is only worth 3 marks, and almost every student scores 1 of them. The reason is that reflection sounds like something you feel, so students write feelings. It is not. It is what you do with a result once you have it.
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Here is the same moment in the same exploration, written at each of the three rungs. The student has fitted an exponential model to a cooling cup of coffee and the fit has gone off near the end.
Describing what happened
This is a description with a feeling attached. It could be written about any exploration, which is exactly the problem.
Explaining why it happened
Now the student has connected a feature of their data to a specific assumption in their mathematics. This is real reflection.
Judging what it is now worth
This student has judged the limits of their own work, named a specific alternative, weighed its cost, made a decision and said why. That is the top rung, and it took them four sentences.
Reflection is not “what I felt”. It is “what this result is now worth, and why”.
Three places where reflection fits naturally, and where students usually skip it: when you choose a method over another one, when a result surprises you, and when your data refuses to do what you expected. Data that does not support your hypothesis is not a failed exploration. It is the best reflection opportunity you will get, and moderators notice when a student rides it honestly instead of quietly dropping the awkward points.
Criterion E: what “the level of your course” means
This is the sentence that quietly caps more explorations than any other. Criterion E asks for mathematics commensurate with the level of the course — in plain words, maths that belongs to the course you are actually sitting.
It cuts both ways. A Maths AA HL exploration built entirely on mean, median and a bar chart will be capped under criterion E even if every number in it is correct. And an AI SL exploration that reaches for undergraduate topology is not rewarded for ambition if the student cannot show they understand it.
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What the middle box means in practice depends on which course you are sitting.
| Course | What criterion E expects | What typically falls short |
|---|---|---|
| AA SL | Calculus, functions or trigonometry from the SL course, applied properly to a question the textbook does not answer. | Descriptive statistics on a downloaded dataset, with no modelling or argument. |
| AA HL | HL-level rigour. Proof, deeper calculus, complex numbers, vectors, series — with the argument written out, not asserted. | SL content done neatly. Correct, but not at the level of the course. |
| AI SL | Modelling with real data: choosing a model, justifying the choice, testing how well it fits, and reading the answer back into the real situation. | A single line of best fit with an R² value and no discussion of whether a line was the right shape. |
| AI HL | More demanding applied work — non-linear regression, hypothesis testing with the assumptions checked, matrices, graph theory, differential equations used to model something. | AI SL work with more pages. Volume is not level. |
If you are not sure which side of the line your idea sits on, the quickest check is to open your own course’s syllabus and find the topics your exploration will actually use. Ours are laid out by course on the IB Maths page, with the AA and AI content split out at SL and HL. If the topics you land on are all from the first term of DP1, the exploration probably needs more.
Moderation: why a 17 from your teacher can come back as a 14
Almost nobody explains this to students, and then in July somebody opens their results and cannot work out what happened. Here is the whole process.
- Your teacher marks every exploration in your school out of 20, using the five criteria.
- The school sends a sample to the IB. The IB decides which students are in it. You do not, and neither does your teacher.
- An IB moderator marks the sample again from scratch, against the same criteria, without seeing your teacher’s marks first.
- The moderator compares. The question is not whether your teacher was kind to you. It is whether the school as a whole is marking at the same standard as every other IB school in the world.
- If the school is off that standard, an adjustment is applied — and it lands on every student in the school, including the ones whose work was never sent to anybody.
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Moderation corrects the school, not the student. That is why your mark can move even though nobody at the IB ever read your exploration.
Three things follow from this, and they are worth knowing before you spend a weekend arguing with your teacher about a mark.
- It can go up. Moderation is not a punishment. A school that marks harshly gets corrected upwards, and students there gain marks. The direction depends entirely on where the school sits against the standard.
- Talking your teacher up does not work. If your teacher gives you a generous 18 and the school is marking generously overall, the adjustment takes it back off. The only thing that survives moderation is the work.
- You will never see the breakdown. Your final mark does not arrive with a criterion-by-criterion explanation. If you want to know where your marks actually went, you have to find that out before you submit, not after.
That last point is the whole reason our coursework assessor exists. It marks an exploration against the five criteria and tells you which band each one sits in, before your school deadline, while you can still do something about it. It covers Maths AA and AI explorations, and the feedback is generated by our assessor rather than by an IB examiner, so treat it as a very well-informed second opinion rather than an official mark. If you would rather a real examiner read it, that is a separate option on the same page.
And if you are wondering how the 20 turns into your final grade: your IA mark is combined with your paper marks, then grade boundaries are applied to the total. We walk through that arithmetic in how the IB score is calculated. The short version is that two or three marks on the IA move your Maths grade more often than students expect, because so many people finish close to a boundary.
The one-draft rule, and the timeline it forces on you
Your teacher is allowed to give you feedback on one draft. One. After that, the help they can give you is limited, because the exploration has to remain your own work.
They are also not allowed to correct it line by line. You will get comments like “criterion D is thin in section 3”, not a corrected version you can type up. That is the rule working as intended: if a teacher edited your exploration, the mark would be partly theirs.
Students hand in a half-finished draft to “see if they are on the right track” — and spend their single piece of feedback on an introduction. Then the finished version, the one with all the mathematics in it, gets read by nobody until it is marked for real.
Hand in a complete draft. Rough, ugly, unformatted, with the conclusion half-written — but complete, with every section present. That is the version worth spending your one go on.
Schools run slightly different internal deadlines, so check yours, but the shape is almost always this.
Scroll sideways to see the whole timeline
The summer between DP1 and DP2 is the part students waste. You will never again have a block of time with no lessons, no mocks and no other deadlines. Collecting your data then costs you a few afternoons. Collecting it in February costs you a mock exam.
Exemplars, honesty, and where the line actually is
Most of the pages competing for this search are databases of other students’ explorations. They are useful, and they are also where people get into trouble. Here is the honest version.
What exemplars are good for
- Seeing what 15 pages of mathematical writing actually looks like, which is hard to imagine from a description.
- Seeing how someone moved from a question to a method.
- Calibrating depth — whether your idea has enough mathematics in it to fill an exploration.
What they are not good for is anything after you start writing. Read them before you choose your topic, then close them. A structure you half-remember is yours. A structure you have open in another tab is not.
There is also a better source almost nobody mentions. The IB publishes its own marked exemplars, with the examiner’s comments explaining where each mark went. They sit in the teacher support material, which your school has. Ask your Maths teacher for them. One authenticated exemplar with examiner commentary teaches you more than forty anonymous uploads with an unexplained number next to them.
1. You sign for it. Work submitted to the IB carries a declaration that it is your own. That is not a formality.
2. It can be checked. Submitted coursework can be run through similarity checking. Explorations built around a popular topic get compared against a lot of other explorations on that topic.
3. AI has to be acknowledged. If you use an AI tool, the IB treats it like any other source — it has to be credited, in the exploration, the same way you would credit a book. Using one without saying so is the same category of problem as copying from a website without saying so.
The practical test we give our own students is simple. If a sentence in your exploration could appear word for word in somebody else’s, it is not earning you criterion C. Personal engagement and academic honesty are not two separate problems. Work that is genuinely yours solves both at once.
Mark your own draft: 20 questions
Print this, or tick it on screen. Each line is something a moderator checks. Go through it with your draft open beside you and be unkind to yourself — it is cheaper now than in July.
Nothing you tick is saved or sent anywhere. Close the page and the ticks are gone.
If more than three of those are unticked, you have found your redraft. Work the unticked ones in criterion order — E first, because it is worth the most.
Seven ways marks quietly disappear
None of these are about being bad at Maths. Every one of them happens to students who understand their topic perfectly well.
- A topic with nothing to do. “The mathematics of the Golden Ratio in architecture” sounds lovely and gives you nothing to calculate. If you cannot say what you will work out, it is a title, not an aim.
- Mathematics below your course level. Covered above, and it is the single most common cap on criterion E. Correct work can still be the wrong level.
- Reflection saved for the last page. Three paragraphs at the end, written the night before, read exactly like three paragraphs written at the end the night before.
- Calculator output pasted in raw. Unlabelled Desmos screenshots and tables of numbers with no units are free marks handed back under criterion B.
- Length instead of depth. Conciseness is part of criterion A. Twenty-eight pages that could be sixteen loses marks twice — once for the padding, once because the good parts are buried.
- Quietly dropping the data that did not fit. Moderators have seen it. Keeping it and explaining it scores under criterion D; deleting it scores nothing and risks worse.
- Spending the one draft on half a draft. Covered above, and it costs more than any single criterion.
If you want the same treatment for the exams rather than the IA, our strategies for scoring a 7 in Maths AA HL covers where marks go in the papers, and internal assessments across the IB covers the rules that apply to every subject’s IA, not only Maths.
The whole thing on one card
Photograph this and keep it next to your draft.
Maths IA — quick reference
- 20% of your Maths grade. About 12 to 20 pages, double spaced. Same five criteria for AA and AI, SL and HL.
- If a website says personal engagement is worth 4, it is using the rubric that was replaced in 2021. Close it.
- E is worth twice C. Spend your time accordingly.
- Aim in the first page, in one specific sentence.
- No calculator notation. Define every variable with its units. Label every graph.
- Reflection goes in the middle, not only at the end, and says what the result is worth.
- Maths at your course level, not the one below.
- Your teacher reads one draft. Make it a complete one.
- Moderation adjusts the whole school, so the only thing that survives it is the work.
Frequently asked questions
What is the mathematics internal assessment?
How much is the Maths IA worth?
What are the five Maths IA criteria and their marks?
How long should the Maths IA be?
Can my teacher read more than one draft?
Why did my IA mark change after my teacher marked it?
Is the Maths IA the same for AA and AI?
What counts as personal engagement?
Can I use a topic someone else has already done?
Can I use AI for my Maths IA?
What is a good Maths IA score?
Does my data have to support my hypothesis?
What happens if I do not submit my Maths IA?
Where can I see a Maths IA that was actually marked?
Is the exploration the same thing as the IA?
How do I choose a Maths IA topic?
One last thing
The students who do well on this are not the ones who are best at Maths. They are the ones who worked out early what the twenty marks were actually for, and then wrote towards them. That is a smaller advantage than it sounds and it is available to anybody who reads the criteria properly.
So do that this week, before you write another page: open your draft next to the checklist above and be honest about which boxes you can tick.
Want to know your mark before the IB decides it?
Our tutors are practising IB examiners, moderators and subject authors, so we read explorations from the marking side. Bring us your draft and we will show you, criterion by criterion, where the marks are and where they are leaking.
Book a free 30-minute meetingOr get it marked against the five criteria first with our coursework assessor, and see which band each criterion lands in.