We went back through our own IMC-style practice material — one deck built for every Intermediate Maths Challenge sitting from 2015 to 2026, plus a general toolkit deck, 13 decks in total — and counted which specific topics show up again and again. This isn't a guess or a general impression of "what's usually on the paper" — it's a straightforward count of how many of the 13 decks contain a card on each idea. What follows is genuinely data-driven, and it points fairly clearly at where revision time is best spent. For what each of these facts actually says, see our companion list of IMC facts to know.

The whole-subject picture first

Before individual topics, the broadest signal is which strands of maths recur most:

Strand Appears in
Geometry & measures 13 of 13 decks
Number 13 of 13 decks
Algebra 12 of 13 decks
Probability 7 of 13 decks
Statistics 6 of 13 decks
Ratio & proportion 6 of 13 decks

Geometry and number are, without exception, present every single year. Algebra is very close behind. Probability, statistics and ratio & proportion recur roughly half the time — real, but clearly the second tier. If a family only has an hour a week and has to choose where it goes, this table alone is a reasonable answer.

The specific topics that recur most

Within those strands, some individual ideas turn up far more than others. Here are the ones that have shown up in at least three of the 13 decks, ranked by how often — with the number telling you, quite literally, "this exact idea has featured in N of the last 13 IMC-style decks we've built."

A prime number has exactly two factors — 10 of 13 decks. By a clear margin, the single most recurring specific fact on the whole list. It's also the fact behind why 1 is not prime, which is the part that actually catches people out.

The units digit of a power runs in a short repeating cycle — 7 of 13 decks. Questions built around "what is the last digit of 3¹⁰⁰" (or similar) are a near-permanent fixture, because they let a paper test genuine reasoning without a calculator.

The interior angles of any polygon sum to 180(n − 2) degrees — 7 of 13 decks. The single most-used geometry formula on the paper, applied to everything from hexagons to irregular shapes.

The 5-12-13 Pythagorean triple — 6 of 13 decks. Recognising it instantly, rather than working through Pythagoras' theorem from scratch, is one of the highest-value single facts a candidate can carry into the exam.

The laws of indices, used to compare or match powers with different bases — 6 of 13 decks. Especially rewriting everything in the same base before comparing — a recurring rescue move on questions that otherwise look intimidating.

Multiplying (not adding) the number of independent choices — 5 of 13 decks. The counting-rule question, in one form or another, is close to an annual fixture.

The range as largest minus smallest value — 4 of 13 decks. A simple fact, but one that keeps being tested precisely because it's easy to blur with the mean.

Finding the total area of two overlapping shapes by subtracting the overlap — 4 of 13 decks. The "sum minus overlap" idea, and its sibling about perimeter falling by 2k at each join, both belong to this recurring family of compound-shape questions.

A further group of topics each appear in exactly 3 of the 13 decks — genuinely recurring, if a level below the ones above: angle-chasing across a diagram, the k² area-scaling rule for similar shapes, counting factors from a prime factorisation, two-digit square numbers, simultaneous equations solved by combination rather than substitution, the properties of a rhombus's diagonals, powers of ten in standard form, recurring decimals written as ninths, and the coordinate rules for reflecting a shape. One of these, arcs and sectors, sits on the GCSE horizon rather than squarely inside KS3 — worth knowing it's there, even if it's the lightest-touch item on this list.

What this actually means for revision

Three things follow reasonably directly from the counts above.

Geometry and number earn first claim on revision time. They're the only two strands present in literally every deck we've built, which means they're present in effectively every year's paper in some form.

A short list of specific facts is worth over-learning. The prime-factors rule, units-digit cycles, the polygon angle formula and the 5-12-13 triple aren't just "useful" — at 6 to 10 decks out of 13, they're closer to structural features of the paper than to occasional extras.

Probability and statistics are real but secondary. They recur in roughly half of our decks — enough to be worth a look, not enough to justify equal time against geometry, number and algebra if the week is tight.

None of this is a claim that the same questions repeat — UKMT writes a fresh paper every year, and no single question here has ever knowingly been reused. What repeats is the underlying idea a question is built to test, and that's exactly the kind of pattern that only shows up once you've looked across many years at once, rather than at any single paper on its own.

Where this comes from

The count above is drawn from our own IMC-style practice decks — one for every sitting from 2015 to 2026, plus a general toolkit deck — built and maintained by our maths tutor, Professor Pi. If you'd like to see the mistakes that attach to these specific recurring facts, our misconceptions piece is the natural next read, and our facts list explains each idea properly rather than just counting it. For how to actually get a short list like this to stick over months rather than days, see spaced repetition and the IMC.

FAQ

How was this list of recurring topics worked out?

We counted, across our own IMC-style practice decks for every sitting from 2015 to 2026 (13 decks in total, one per year plus a toolkit deck), how many separate decks contain a card on each specific topic. A topic that appears in most decks is one that keeps recurring in IMC-style questions.

Does a high count mean that exact question comes up every year?

No — it means the underlying idea does. The 2019 question that uses the 5-12-13 triangle and the 2023 question that uses it look nothing alike on the surface, but they both reward the same recognition. The count is about the idea recurring, not the question being repeated.

Which subject area matters most for the IMC — number, algebra or geometry?

Geometry & measures and number both appear in all 13 of our decks — every single sitting we've built practice for touches both. Algebra is close behind, in 12 of 13. Probability and statistics appear less often, in about half.

Duke Harewood built aitutors.me's KS3 maths tutor (Professor Pi) for his Year 8 daughter. Updated 26 August 2026.