Your IB Math IA: What the Examiner Is Actually Looking For

The Internal Assessment is worth 20% of your final IB Mathematics grade. That is a significant contribution — enough to move a 5 to a 6, or a 6 to a 7, with a strong exploration.

And yet most students approach the IA in a way that leaves marks on the table. Not because the mathematics is wrong, but because they don't understand what the five assessment criteria are actually measuring.

Here is a clear breakdown of what examiners are looking for — and the most common ways students fall short in each area.

The five criteria — and what they really mean

The IB Mathematics IA is assessed across five criteria: Presentation, Mathematical Communication, Personal Engagement, Reflection, and Use of Mathematics. Together they total 20 marks.

Criterion A: Presentation

Presentation is not about formatting or fonts. It is about whether your exploration has a clear structure — a beginning that sets up the problem, a middle that develops the mathematics, and an end that brings it together.

The most common failure here is an exploration that reads like a collection of calculations rather than an investigation. A student might do perfectly valid mathematics but jump between ideas without explaining the connection between them.

Ask yourself: if a fellow IB student read your exploration without knowing the topic, would they understand what you were trying to find out, why each section follows from the last, and what you concluded?

Criterion B: Mathematical Communication

Mathematical Communication requires consistent, correct use of notation throughout. This means defining variables before using them, labelling graphs clearly, writing equations in the correct form, and using the correct notation for functions, limits, derivatives, and so on.

Students who lose marks here often do so because they are inconsistent — they use correct notation in one section and informal notation in another, or they define a variable once and then redefine it implicitly later.

A simple rule: every variable must be defined when it first appears, and that definition must remain consistent throughout the exploration.

Criterion C: Personal Engagement

This is the criterion that most students struggle to understand. Personal engagement does not mean writing "I find this interesting because..." at the start of each section.

It means making choices in your investigation that reflect your own thinking. Why did you choose this particular model rather than another? Why did you extend the problem in this direction? What did you notice that prompted you to investigate further?

Generic explorations — the ones that follow a template or could have been written by any student — score 0 or 1 on this criterion. The explorations that score 3 are the ones where an examiner can see that a real student made real decisions about how to develop the investigation.

Criterion D: Reflection

Reflection is the most misunderstood criterion. Students think it means summarising what they found. It does not. It means thinking critically about the mathematics.

Strong reflection discusses the limitations of the approach — what assumptions were made, what the model cannot capture, what a different method would reveal. It asks what happens if the parameters change. It considers whether the conclusion is robust.

A conclusion that says "I found that the optimal angle is 45 degrees" scores at most 1 mark. A reflection that says "This result assumes a flat surface; on a curved surface the optimal angle would depend on the radius of curvature, which I investigated by..." scores 3.

Criterion E: Use of Mathematics

This criterion carries the most marks and the most weight in distinguishing HL from SL explorations. There are three levels:

• Adequate (1–2 marks): mathematics is correct and relevant but limited in scope — mostly applying standard techniques from the syllabus.
• Thorough (3–4 marks): a wider range of techniques, applied correctly and purposefully.
• Sophisticated (5–6 marks): mathematics that goes beyond routine application — drawing connections between different areas, using techniques in creative or unexpected ways, or extending beyond the standard curriculum.

For HL students, sophisticated mathematics is expected. For SL students, thorough is a realistic aim. In both cases, accuracy matters — a single unexplained error that propagates through the exploration will cost marks.

The mistakes that cost the most marks

After moderating many IB Mathematics IA explorations, these are the patterns I see most often:

• Borrowing a topic without making it your own. An exploration on "the mathematics of the Golden Ratio" that follows the standard treatment will score poorly on Personal Engagement regardless of how well it is written.
• Summary conclusions instead of critical reflection. Restating what you found is not reflection. Reflection asks: why does this result hold, when would it break down, and what does it imply?
• Mathematics that is technically correct but not connected to the exploration. Using an integral in the middle of an exploration without explaining what it represents or why it's relevant will not score marks on Use of Mathematics.
• Undefined notation. Every symbol must be defined. Examiners do not fill in the blanks.

What a strong exploration looks like

The strongest explorations I have seen share a common structure: they start with a specific, genuine question — not a topic, but a question — and every section of the exploration is clearly in service of answering that question.

The mathematics develops from simple to complex. Each step builds on the last. When a result is surprising or ambiguous, the student notices and investigates further. The conclusion honestly addresses what the exploration achieved and what it could not.

A word count of 12–20 pages is appropriate for most explorations. More is rarely better — examiners read hundreds of IAs, and a concise exploration that makes every section count will always score better than a padded one.

If you are working on your IA and want to check specific mathematics — whether a method is correct, how to write a result properly, or what a particular criterion is looking for — HAN can help. Try it free at askhanyong.com.