IB Math IA: how to choose a topic that can score well
Krsna Academy · · 6 min read
A good IB Math IA topic is a narrow question you actually want answered, that needs mathematics from your own course to answer it. Choose the question first and the mathematics second, and test the idea against the five criteria before you write a word. Most low marks trace back to a topic that was too broad, too easy, or copied from a list.
What the IA is and how it is marked
The Internal Assessment in both Analysis and Approaches (AA) and Applications and Interpretation (AI) is a written mathematical exploration. It counts for 20% of your final grade at both HL and SL. Your teacher marks it out of 20 and the IB moderates a sample from each school.
| Criterion | Marks | What it rewards |
|---|---|---|
| A: Presentation | 4 | A clear aim, a logical structure, and no padding |
| B: Mathematical communication | 4 | Correct notation, defined terms, and labelled graphs and tables |
| C: Personal engagement | 3 | Evidence that the thinking and the choices are yours |
| D: Reflection | 3 | Honest evaluation of your results, limits, and next steps |
| E: Use of mathematics | 6 | Relevant mathematics at the level of your course, used correctly |
The criteria and mark totals are the same at SL and HL. The difference is in Criterion E: at HL the mathematics is also expected to show sophistication and rigour. The guide recommends 12 to 20 pages. Ask your teacher for the criteria from the current subject guide and keep them beside you while you plan.
Start with a question, not a topic
"The mathematics of music" is a topic. "How well does a sum of sine functions model the note my guitar produces?" is a question. A question tells you what data you need, which mathematics to use, and when you are finished. A topic does none of that.
Good questions usually come from something you already do or notice: a sport, an instrument, a part-time job, a commute, a game, a design you like. That is not a rule, and a purely mathematical question can score just as well. What matters is that you can explain why you chose it and what you expected to find.
Five questions to test any idea
- Can I state the aim in one sentence? If not, the idea is still too broad.
- Which mathematics from my course does it need? Name the specific topics. If the honest answer is only arithmetic and a line of best fit, Criterion E will be capped.
- Do I understand that mathematics well enough to explain every step? Mathematics you cannot explain earns less than simpler mathematics you can.
- Can I get the data or build the model myself, this month? If the data does not exist or the measurement needs equipment you do not have, change the idea now.
- Is there something to reflect on? A good exploration has results that can be checked, compared, or questioned.
An idea that passes all five is workable. An idea that fails the second or third question is the one to drop, however interesting it sounds.
AA and AI: where good topics tend to come from
- AA students often do well with modelling using functions and calculus: optimizing a shape or a cost, finding a volume of revolution for a real object, or modelling motion or growth with differential equations at HL.
- AI students often do well with statistics and modelling from real data: testing a hypothesis with data they collected, comparing regression models, or using probability to analyze a game or a decision.
- Either course can use the other's strengths. What matters is that the mathematics is in your syllabus or a small step beyond it.
If you are still deciding between the two courses, read IB Math AA vs AI: how to choose.
Topic mistakes that cap the mark
- Too broad. "The golden ratio" or "fractals" turns into a summary of other people's work. Narrow it to one thing you can calculate or test.
- Too easy. Mathematics from earlier grades, however neatly presented, cannot reach the top of Criterion E.
- Too hard. University-level mathematics copied from a source, without understanding, loses marks for use of mathematics and for personal engagement.
- A textbook problem in disguise. If the full solution is one search away, there is little room to show your own thinking.
- No room for reflection. If the exploration only arrives at a known formula, there is nothing to evaluate.
Popular topics are not banned, but they need your own angle: your own data, your own extension, or a comparison nobody handed you.
From topic to plan
- Write the aim and a half-page outline: question, data or model, mathematics, and what a result would look like.
- Show it to your teacher early. Your teacher knows your school's deadlines and what feedback they are allowed to give.
- Do a small trial of the hardest piece of mathematics before you commit. One page of working tells you whether the idea holds.
- Record your decisions as you go: why you chose a model, what went wrong, what you changed. That record becomes your reflection and your personal engagement.
- Cite every source, including software and data. The exploration must be your own work.
Where a tutor can help
A tutor can help you test a topic against the criteria, strengthen the mathematics behind it, and explain how each criterion is applied. A tutor should not choose the topic, write, or edit the exploration for you. Our IB tutoring works within IB academic integrity rules, and if you would like to talk an idea through, you can book a free consultation.