Choosing an IA topic that doesn't run out after two pages
The exploration is worth a fifth of the final grade, and most of that is decided before a word is written — by the topic.
Every IB Mathematics student writes a mathematical exploration — an independent piece of mathematical writing, around twelve to twenty pages, carrying a fixed share of the final grade regardless of course or level.
It is the only part of the course where a student is not answering a question someone else set. Nothing at IGCSE prepares them for that, and the difficulty is rarely the mathematics. It is deciding what to do.
Topic choice decides most of it
By the time a student is writing, the ceiling is largely set. A well-chosen topic makes the criteria easy to satisfy, because the mathematics has somewhere to go and the student has something to say about it. A poorly chosen one cannot be rescued by effort.
This is why the weeks spent choosing are not wasted time, and why a student who says "I'll pick something and start" usually loses more time than they save.
The three ways explorations fail
Too broad. "The mathematics of music", "Fibonacci in nature", "game theory". These produce description — a tour of things other people have proved, with the student narrating. There is nothing for them to actually do, so the work reads as a report rather than an exploration.
Too narrow. A single calculation, correctly performed, and then nothing. The student finds themselves at page four with the question answered, padding the rest. This is the most common way an exploration goes wrong, because narrow topics look safe.
Too ambitious. A genuinely interesting question requiring mathematics two years beyond the course. The student either abandons it late, having lost a term, or produces something they cannot explain — which the criteria detect, because they reward understanding rather than sophistication.
The test worth applying before committing
One question separates workable topics from unworkable ones:
What, specifically, will I calculate — and then what will I do with the result?
If a student can answer both halves in concrete terms, the topic has a spine. If the answer is vague — "I'll look at how it works", "I'll show the pattern" — the topic is not ready, however interesting it sounds.
The second half matters more than the first. Plenty of topics support one calculation. What makes an exploration is having a next step: comparing two models, testing whether a result holds when an assumption changes, extending a case, checking a prediction against data.
Start from something they actually do
The criteria reward genuine personal engagement, and moderators are good at telling the difference between real interest and a topic chosen because it appeared on a list.
The most reliable source is something the student already does — a sport, an instrument, a game, a job, a journey they make every week, something they have wondered about. Not because personal topics score better by right, but because a student who cares about the question asks better follow-up questions, and follow-up questions are what the exploration is made of.
A caution about topic lists found online: they are the same lists every other candidate is reading. A topic is not disqualified for appearing on one, but a student choosing from a list is starting where thousands have started, and usually without the personal angle that would make it theirs.
Match the mathematics to the level
The mathematics should sit at or a little above the level of the course. Not below, and not far above.
A Standard Level student who explores Higher Level content badly scores worse than one who uses Standard Level content well and understands every line of it. Reaching beyond the course is only worth it when the student can genuinely follow what they are doing.
Equally, an exploration built entirely from material a student mastered two years ago has nowhere to demonstrate anything.
Where a tutor helps, and where they must not
I help with choosing a workable topic, checking that the mathematics is appropriate for the level, and understanding what the assessment criteria actually reward. I read drafts and I am specific about what would raise them.
I do not write, rewrite or edit the exploration. That is a condition of IB academic integrity and of working with me. The writing, the analysis and the conclusions have to be the student's own — and examiners are experienced at spotting work that is not.
This matters practically as well as ethically. An exploration a student cannot explain is a liability, and academic integrity findings in the IB are serious in a way that a poor grade is not.
Timing
Schools set their own deadlines, usually with a topic proposal well before the draft. The useful move is to be choosing early and deliberately rather than answering a deadline — a student who has spent a fortnight testing two or three candidate questions is in a far better position than one who picks something the night before the proposal is due.
If your child is earlier in the course, the groundwork is simply the mathematics itself: see what changes in the step up from IGCSE, and how the AA and AI routes differ, since the exploration looks quite different in each.