The IB Maths IA is not just a long homework write-up. It is an individual mathematical exploration, and the official IB subject briefs say it counts for 20% of the final grade in both SL and HL Mathematics: Analysis and Approaches and Applications and Interpretation.

That matters because many students treat the IA as if the goal is to choose an impressive topic, do a lot of calculations, and add a personal paragraph at the end. The official criteria point in a different direction. The exploration is marked on presentation, mathematical communication, personal engagement, reflection, and use of mathematics. The IB also explains more generally that Diploma Programme assessment includes internal assessment, including mathematical investigations, alongside external exams on its assessment and exams page.

Here are the most common mistakes to avoid.

1. Choosing a topic before choosing a question

A weak IA often starts with a broad topic: basketball, music, architecture, traffic, finance, or football. Those can all work, but only if they become a focused mathematical question.

For example, "the maths of basketball" is not an IA question. "How accurately can a quadratic model predict the angle needed for a successful free throw from different release heights?" is much stronger because it gives the exploration a clear aim, a method, and a way to evaluate the result.

Before writing, test your topic with this question: can I state exactly what I am trying to find, model, compare, prove, or optimize? If not, the IA will probably drift.

2. Writing a textbook chapter instead of an exploration

One of the clearest warnings in the IB criteria is that textbook-style work and reproduction of readily available mathematics are unlikely to reach the higher levels for personal engagement. This is a major issue in popular IA topics such as the golden ratio, the SIR model, projectile motion, correlation in sports, or modelling population growth.

The problem is not that these topics are banned. The problem is copying a standard explanation and changing the data. A strong IA needs your decisions to shape the work: why this model, why this data set, why this method, why this assumption, why this comparison?

If your IA could have been written by any student with the same topic, it is not yet personal enough.

3. Confusing personal engagement with autobiography

Personal engagement does not mean adding a paragraph that says, "I chose this topic because I like football." That may explain interest, but it does not show mathematical ownership.

Better evidence of personal engagement includes making a prediction and testing it, comparing two possible models, explaining why one assumption is more realistic than another, adapting a method, collecting your own data, or noticing a limitation and changing direction.

The key phrase is this: your engagement should drive the mathematics forward. If the personal section can be deleted without changing the exploration, it is probably not doing much for the criterion.

4. Using mathematics that is too simple, too difficult, or irrelevant

Many students think harder mathematics automatically means a higher IA mark. It does not. The IB criterion for use of mathematics rewards relevant mathematics that supports the aim of the exploration. Overcomplicated mathematics is not helpful if simpler mathematics would answer the question better.

The opposite problem is also common: using mathematics below the level of the course. A few averages, percentages, or simple substitutions will usually not be enough for a strong IA unless they are part of a deeper argument.

Aim for mathematics that is appropriate, explained, and necessary. A focused exploration using a few techniques well is usually stronger than a crowded IA full of methods the student cannot properly justify.

5. Letting technology do the thinking

Technology is encouraged in DP mathematics. The IB mathematics curriculum page also notes that all DP mathematics courses require students to appreciate the use of technology and become proficient with graphic display calculators. But technology does not replace explanation.

A common weak pattern is: paste data into Desmos, GeoGebra, Excel, or a GDC; produce a regression equation; screenshot the graph; state that the model fits. That is not enough.

You need to explain what the technology is doing mathematically. Why is a linear, quadratic, exponential, logistic, normal, binomial, or trigonometric model reasonable? What do the parameters mean in context? How good is the fit? Where does it fail? What would happen if the assumptions changed?

The tool can produce results, but you must demonstrate understanding.

6. Poor mathematical communication

Students lose marks when the mathematics is hard to follow even if the calculations are mostly correct. Common communication problems include undefined variables, inconsistent notation, unlabelled graphs, screenshots with no explanation, tables dumped into the main text, and calculator syntax used as if it were formal mathematical notation.

The reader should know what every symbol means, where every equation comes from, and how each graph supports the argument. If you use a diagram, table, or graph, introduce it before the reader sees it and interpret it afterwards.

Good communication is not decoration. It is part of the mathematics.

7. Saving reflection for the conclusion

Reflection is one of the most misunderstood IA criteria. Many students write a conclusion that says the model was "quite accurate" and that more data would improve it. That is usually limited reflection.

Stronger reflection appears throughout the IA. It happens when you pause after a result and ask what it means, whether it makes sense, whether it answers the aim, whether another method would be better, or whether a limitation changes the value of the conclusion.

For example, do not just say, "The correlation coefficient is 0.82." Explain whether that is strong enough for your purpose, whether correlation is the right measure, whether outliers affect it, and what it cannot prove.

8. Treating the page limit as a target

The official guide describes the final report as approximately 12 to 20 pages with double line spacing. That does not mean 20 pages is better than 12. The presentation criterion rewards work that is coherent, well organized, and concise.

Long IAs often lose focus because they include repeated calculations, oversized screenshots, unnecessary background theory, or tables that belong in an appendix. Concision is not about making the IA short; it is about making every section earn its place.

If a paragraph does not help answer the research question, explain a method, interpret a result, or evaluate the exploration, cut it or move it.

9. Not justifying assumptions

Every IA makes assumptions. A projectile model may ignore air resistance. A regression model may assume the relationship continues beyond the observed data. A probability model may assume independence. A statistics IA may assume the sample is representative.

The mistake is not making assumptions. The mistake is hiding them.

State your assumptions clearly, explain why they are reasonable, and discuss how they affect the conclusion. This is an easy way to improve both reflection and mathematical understanding.

10. Weak or careless sourcing

The IA should include a proper bibliography, and sources should be referenced. This applies to data, diagrams, formulas taken from a source, code, images, and direct quotations. If you collect your own data, explain how. If you use public data, link to the original source, not just a repost.

Students sometimes cite a website for background information but forget to cite the actual data set. That is a serious weakness because the data is often the foundation of the mathematics.

Use primary sources where possible: official statistics agencies, original sports databases, scientific papers, company reports, or the original platform that generated the data.

A quick IA checklist

Before submitting, ask:

Is my research question specific enough to guide the whole exploration?
Does every section help answer that question?
Have I defined all variables and labelled all graphs?
Have I explained why each mathematical method is appropriate?
Have I shown understanding rather than only giving answers?
Have I reflected throughout, not only at the end?
Is my personal engagement visible in the mathematics itself?
Are my sources cited properly, especially data sources?
Is the IA concise, or have I included filler to make it look longer?

Final thought

The best IB Maths IAs are not necessarily the ones with the most advanced topic. They are the ones where the student asks a clear question, uses relevant mathematics carefully, communicates it cleanly, and reflects honestly on what the results do and do not show.

If you want a simple rule: do fewer things, but do them with more explanation, ownership, and evaluation. That is much closer to what the IA criteria actually reward.

Common IB Maths IA Mistakes