Final checks before submission

A complete checklist for the finished exploration, organised by criterion, plus the quick fixes that most often raise the mark in the last days before submission.

IB Mathematics: Analysis and Approaches
Internal assessment
SL and HL

10 min readLast reviewed 14 Oct 2026

The final version of the exploration cannot be changed once it is submitted, and the teacher can give feedback on only one draft. The last check is therefore the student's own. A careful read against each criterion, with the checklists here, usually finds several small problems that are quick to fix and together are worth several marks.

The checks work best in separate passes, each looking for one thing: first the structure, then the notation, then the mathematics, and so on. Reading the whole exploration once and hoping to spot everything rarely works, because attention goes to the content and the details slip past.

Criterion A: Presentation

Criterion A rewards an exploration that is coherent, well organised and concise. The questions to ask are whether a reader can follow it, whether each part is in the right place and whether anything could be removed.

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The aim is stated clearly in the introduction, as one precise sentence.
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The introduction explains the motivation briefly and leads straight to the mathematics.
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Each section has a clear purpose linked to the aim, and its first sentence says what it does.
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Each section leads naturally to the next; there are no sudden jumps in topic.
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The conclusion answers the aim directly, using the results.
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Every graph, table and diagram is placed in the text where it is discussed.
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Repeated calculations are shown once in full and then summarised; the rest are in an appendix or removed.
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There is no background material, history or definition that the exploration never uses.
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The length is about 12 to 20 pages with double line spacing, excluding the bibliography and appendices.
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Pages are numbered, and any contents list matches the headings.

Criterion B: Mathematical communication

Criterion B rewards notation, terminology and representations that are appropriate and consistent throughout. These checks are mechanical and quick, and they are among the easiest marks to secure.

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All mathematics is typed with an equation editor; there is no calculator or programming notation such as "x^2", "*", "sqrt" or "E-3".
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Every variable and constant is defined in words when it first appears, with units.
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Each symbol keeps the same meaning throughout.
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Domains of functions and restrictions on variables are stated where they matter.
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Every graph has a number, a caption, labelled axes with units and a sensible scale.
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Every table has a number, a title and column headings with units.
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Every graph and table is referred to and discussed in the text.
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Rounded values state their accuracy, and unrounded values are used in later calculations.
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The degree of accuracy suits the context and the precision of the data.
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"=" is used only between equal quantities, and " $\approx$ " for rounded values.
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Mathematical terms are used correctly (for example, "function", "gradient", "residual", "probability").

A student's graph caption reads "Graph 2". The graph shows measured heights of a ball and a fitted quadratic. Suggest an improved caption and an accompanying sentence in the text.

Show the solution

The caption gives no information about what the graph shows or what to see in it.

An improved caption: "Figure 2: Measured height $h$ (m) of the ball against time $t$ (s), with the fitted model $h (t) = - 4.87 t^{2} + 6.12 t + 1.58$ ."

An accompanying sentence in the text: "Figure 2 shows that the model passes close to all the measured points during the rise, but lies slightly below the last three points, which suggests that the ball slowed less than the model predicts near the end of its flight."

The caption now identifies the variables, units and model, and the text says what the graph shows and leads into reflection.

Criterion C: Personal engagement

Criterion C rewards evidence of the student's own thinking throughout the work. The final check looks for that evidence in the mathematics, not only in the introduction.

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The reason for choosing the topic leads to a genuine mathematical question.
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The exploration includes something original: my own data, my own variation of a problem, my own conjecture or my own way of presenting an idea.
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Decisions are explained where they are made ("A logistic model was chosen next because…").
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Questions that arose during the work are stated and followed up.
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Where a source's method is used, my own contribution beyond it is clear.
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The writing is in my own voice, and I can explain every sentence and every calculation if asked.

Criterion D: Reflection

Criterion D rewards reflection that is critical and appears throughout. The final check makes sure every important result is followed by a comment on what it means and how far it can be trusted.

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Every significant result is followed by an interpretation in context.
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Results are checked for reasonableness (for example, against a graph, a known value or a common-sense estimate).
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The assumptions behind each model or method are stated, and their effect on the results is discussed.
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Limitations are specific: they say what the limitation is, how it affects the result and roughly by how much.
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The chosen approach is compared with at least one alternative, with its strengths and weaknesses.
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The conclusion evaluates how reliable the answer to the aim is.
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Extensions are specific and follow from what was found, not generic ("collect more data").

A student's limitations paragraph reads: "My data might have errors and the model is not perfect. In the future I could collect more data." Rewrite it as specific, critical reflection, for an exploration modelling the cooling of a cup of tea with $T = T_{r} + A e^{- k t}$ , where $T_{r}$ is room temperature.

Show the solution

"The thermometer reads to $\pm 0.5 ° C$ , which is small compared with the temperature change over the first 20 minutes but becomes comparable with it after about 60 minutes, when the tea is within a few degrees of room temperature. The estimate of $k$ therefore depends mostly on the early readings. The model also assumes that room temperature stayed constant at $T_{r} = 21 ° C$ ; the room warmed by about $1 ° C$ during the experiment, which would make the tea appear to cool more slowly towards the end. Repeating the experiment with a lid on the cup would test whether evaporation, which the model ignores, changes the value of $k$ ."

Each limitation is now specific, its effect on the result is explained, and the extension is a concrete test that follows from the findings.

Criterion E: Use of mathematics

Criterion E is worth the most marks, and errors here are the most costly. The final check is a careful re-working of the mathematics, not just a re-reading.

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The mathematics is relevant: every method helps to answer the aim.
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The mathematics is at the level of the course (SL or HL), not only prior knowledge.
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Every calculation has been checked, ideally by a different method (substituting back, a graph, a GDC).
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Algebra has been re-worked line by line, and no step has been skipped where a reader would need it.
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Each method is introduced with a reason, and its conditions (such as independence, or a function's domain) are stated.
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Formulas taken from sources are explained or derived, not only quoted.
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Technology output is interpreted, and what the technology calculates is understood.
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One example of each repeated calculation is shown in full.
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Final answers have units and an appropriate accuracy.
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Graphs of models are consistent with the calculations (the maximum on the graph is where the calculus says it is).

Extra checks at HL

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The mathematics as a whole is at HL level, not only SL techniques.
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General claims are proved or justified, not just checked on examples.
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Logic is clear: each step follows from the previous one, and conditions are stated.
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The work shows sophistication: a challenging idea, an unusual application, or more than one perspective on the problem.
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The mathematics is precise: there are no errors at all, and every value has a suitable accuracy.

Sources and academic integrity

These checks protect the whole exploration. Unacknowledged material can lead to the work receiving no mark at all.

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Every data set, formula, method, image and paraphrased idea from a source has an in-text citation where it is used.
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The bibliography lists every cited source in one consistent style, with access dates for websites.
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The source of each data set appears in the caption of the table or graph that shows it.
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Any use of a generative AI tool is acknowledged in the text and the bibliography.
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No part of the exploration was written by someone else, and no draft was shared with another student.
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Data were collected with consent and anonymity where people were involved, and no data have been invented or altered.

Format and submission

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The front page shows only what the school asks for (usually the title and candidate code, not the student's name, so that moderation is anonymous).
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The file is in the format the school asks for, with figures and equations displayed correctly after conversion (check the PDF).
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Appendices are labelled and referred to in the text, and the main text makes sense without them.
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The spelling and grammar have been checked.
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The declaration of authenticity is ready to be signed.

The most common last-minute fixes

Most explorations can gain marks in the last few days without new mathematics. The table lists the fixes that make the most difference for the least time.

Problem found	Quick fix	Criterion
Calculator notation in the text	Retype each expression with the equation editor	B
Variables not defined	Add a "where…" sentence after each formula	B
Graphs with no caption or labels	Number, caption and label every graph, with units	B
Graph or table not mentioned in the text	Add a sentence saying what it shows	A, B
Pages of repeated calculations	Keep one in full; summarise the rest in a table; move detail to an appendix	A
Long historical introduction	Cut it to two or three sentences that lead to the aim	A
Conclusion lists the steps taken	Rewrite it to answer the aim with numbers	A, D
Reflection only at the end	Add a short comment after each main result	D
Generic limitations	Say how each limitation affects the result, and by how much	D
Claims supported only by examples	Prove the claim, or describe it as a conjecture	E
Data or formulas with no source	Add in-text citations and bibliography entries	Integrity
Inconsistent rounding	Choose an accuracy for each type of value and apply it everywhere	B, E

What not to change at the last minute

The last few days are not the time for large changes. Replacing the model, adding a new section of difficult mathematics, or changing the aim usually introduces errors and breaks the coherence of the work. If a serious problem is found late, it is better to acknowledge it honestly in the reflection (and explain how it could be fixed) than to rewrite half the exploration in a hurry.

A final read as a moderator

The last check is to read the exploration from start to finish as a moderator would: someone who knows the course well, has not seen the work before and has the five criteria in front of them. For each criterion, decide honestly which level description fits best and find the evidence in the text. If the evidence is hard to find, a moderator will not find it either, and that part of the work needs one more change.

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