Maths IA criteria explained: what moves you up each band in A to E

The IB Maths IA (the mathematical exploration) is marked on five criteria: A Presentation (4 marks), B Mathematical communication (4), C Personal engagement (3), D Reflection (3) and E Use of mathematics (6). That is 20 marks, worth 20% of your final grade in both AA and AI, at SL and at HL. The same criteria apply to everyone; the only difference is that HL is held to a higher standard on criterion E.

Below, for each criterion: what moves you from one band to the next, with weak and strong sentences side by side. This applies to the current course, examined until November 2028. For a complete exploration annotated against these criteria, see the Maths IA example.

The guidance is roughly 12–20 double-spaced pages, graphs and tables included, bibliography excluded, so there is no room for padding under any criterion.

Criterion A: what makes a Maths IA well presented?

Presentation is about the reader's experience, not fonts. Think of it as three steps up:

• Bottom of the scale: the reader cannot tell what you set out to do, or the exploration stops without a conclusion.
• Middle: there is an introduction with an aim, a body and a conclusion, but parts wander: background that is never used, calculations repeated six times, a conclusion that answers a different question.
• Top: every section follows from the one before, a classmate could read it once without getting lost, and nothing could be cut without losing something.

What gets you there:

• State the aim in one sentence on the first page, and answer that exact aim in the conclusion.
• Cut history and background you do not use later. A paragraph on who invented the logistic model earns nothing.
• Show a repeated calculation once in full, then put the rest in a table.
• Move raw data to an appendix and keep a summary in the body.
• Use short signposting sentences between sections: "The linear model underestimates both ends, so the next section tests a quadratic."

Criterion B: what counts as good mathematical communication?

Criterion B rewards writing maths the way mathematicians write it: correct notation, consistent symbols, defined variables and well-chosen representations (equations, graphs, tables, diagrams) where each one helps. One undefined variable or one calculator-style expression is a small slip; a pattern of them caps your mark.

For every graph: a title or caption, both axes labelled with quantities and units, a sensible scale, and a sentence in the text that refers to it ("Figure 3 shows…"). A graph nobody mentions is decoration.

Criterion C: how do you show personal engagement properly?

Personal engagement is not a paragraph about why you love the topic. It is evidence, throughout the exploration, that you were thinking: asking your own questions, making decisions, testing ideas, creating examples, explaining things in your own way.

• Low: an anecdote at the start, then routine textbook work that anyone could have done.
• Middle: some of your own choices are visible, for example in how you collected data, but most of the maths follows a standard path.
• Top: your curiosity drives the whole thing. You make decisions, explain why, notice something surprising and follow it up.

The strong versions do not announce engagement; they show it through decisions. If your topic is not personal, you can still score here by testing your own cases, building your own examples and questioning the standard approach.

Criterion D: what does real reflection look like?

Reflection is critical thinking about what you found and how you found it. The step up from the middle to the top is the step from describing results to questioning them: are they reliable, what do they mean, what did your method assume, what would change if you did it differently? It should appear wherever you get a result, not only in the last paragraph.

Good reflection is specific: it names a number, a section of the data or an assumption. If a sentence could be pasted into anyone else's exploration, it is not reflection.

Criterion E: what does use of mathematics mean at SL and HL?

Criterion E carries 6 of the 20 marks. It asks three things: is the maths relevant to your aim, is it correct, and do you clearly understand it? The bar is set by your course and level.

Commensurate with your level

Your exploration should use maths that is genuinely at the level of your course. An HL student who only fits a straight line on a calculator has used SL-level maths, however neat the write-up. An SL student does not need HL content to reach the top band, but needs more than routine calculator work.

Rigour and sophistication

These are what separate the top band, especially at HL. Rigour means every step is justified: conditions checked, domains stated, a stationary point confirmed as a maximum rather than assumed, a general result proved rather than shown for three cases. Sophistication means choosing or adapting methods with insight, rather than applying the first formula you find: comparing models, generalising a result, seeing the problem from a second angle.

The same topic at SL and HL

Take a cooling cup of tea. An SL exploration might linearise the data by plotting ln(T − T_room) against t, find the cooling constant, interpret it, and compare the fit with an alternative model using residuals. An HL exploration might derive the model from the differential equation dT/dt = −k(T − T_room) by separating variables, estimate k from the data, and test how sensitive the predictions are to the room temperature. These are illustrations, not rules: what matters is that the maths fits your aim and your level.

Maths IA criteria checklist before you submit

• The aim is one sentence on page one, and the conclusion answers that aim.
• Every paragraph of background is used later.
• Every variable is defined with units the first time it appears.
• No calculator notation anywhere: no ^, *, E, sqrt or R2.
• Every graph has a caption, labelled axes with units, and is referred to in the text.
• Rounding is consistent, and ≈ is used where you have rounded.
• At least three decisions in the exploration say why you made them.
• Every result is followed by a comment on what it means and how far to trust it.
• Limitations name specific data, assumptions or sections, not "more data".
• The maths includes work at the level of your course, done and explained by you, not only calculator output.
• Stationary points, domains and conditions are justified, not assumed.
• It is roughly 12–20 pages, with raw data in an appendix.
• Sources, software and any AI use are acknowledged as your school requires.

Still choosing a topic? The Maths IA topics list has 36 ideas with aims and a feasibility note for each.

What changes in the Maths IA criteria from 2029?

If you are examined in 2026, 2027 or 2028, nothing below applies to you. A new Maths curriculum is taught from August 2027, with first exams in May 2029. Its exploration is still 20 marks and 20% at SL and HL, but the criteria are replaced by four that follow a problem-solving cycle:

The new criteria are the same at SL and HL. Personal engagement and reflection are no longer separate criteria, though specifying your own problem and interpreting your results critically clearly carry over. If you are in that cohort, your teacher will have the new guide and its descriptors; work from those.