Measured on 180 real questions
What actually comes up in TMUA Paper 2
TMUA Paper 2 tests mathematical reasoning, so we tagged all 180 questions by the reasoning move each one demands rather than by syllabus topic.
"Which of these statements is true" and direct argument are 40.5% of Paper 2 between them. Formal proof structure is 8.9%.
Paper 2 is the half of the TMUA that candidates find hardest to revise, because a topic list does not describe it. The mathematical content is largely the same as Paper 1; what changes is the move being tested. So we tagged all 180 questions by reasoning mechanic instead.
The same caveat applies as to Paper 1: these are the 2016 to 2023 Cambridge-era sittings plus the early specimen. The TMUA moved to a different awarding body for 2024 and those papers are not in our corpus.
Topic frequency
Every TMUA Paper 2 topic, by how often it actually appeared.
180 questions, 8 topics. Each question carries exactly one topic tag, so these shares add to 100% and can be read as shares of a paper. The 95% confidence interval is the range the true share plausibly sits in given this sample size.
| # | Topic | Questions | Share | 95% CI |
|---|---|---|---|---|
| 1 | Pure-mathematics reasoning | 42 / 180 | 23.3% | 17.8-30.0% |
| 2 | Which statement is true | 38 / 180 | 21.1% | 15.8-27.6% |
| 3 | Direct argument | 35 / 180 | 19.4% | 14.3-25.8% |
| 4 | Necessary and sufficient conditions | 24 / 180 | 13.3% | 9.1-19.1% |
| 5 | Proof structure | 16 / 180 | 8.9% | 5.5-14.0% |
| 6 | Counterexample | 13 / 180 | 7.2% | 4.3-12.0% |
| 7 | Quantifiers | 8 / 180 | 4.4% | 2.3-8.5% |
| 8 | Implication (if-then) | 4 / 180 | 2.2% | 0.9-5.6% |
Evidence base: TMUA 2016-2023 sittings plus the early specimen (Cambridge-era papers).
Where the data disagrees with the revision guides
Logic notation is worth more than proof drills
Preparation for Paper 2 tends to concentrate on writing proofs. In the tagged papers, explicit proof structure was the mechanic in 16 of 180 questions. Necessary and sufficient conditions, quantifiers and implication - the notation-and-logic cluster that gets a fraction of the attention - accounted for 36 between them, more than twice as many.
What this means for your revision
Four things the numbers say about TMUA Paper 2.
- 01
Pure-mathematics reasoning (23.3%) is the largest single mechanic, followed closely by "which statement is true" (21.1%) and direct argument (19.4%).
- 02
Necessary and sufficient conditions (13.3%) is the highest-yield piece of formal logic in the paper. It is also the one most often skipped, because it is not on any A-level syllabus.
- 03
Proof structure (8.9%) and counterexample (7.2%) are smaller than their reputation suggests, but they are where the hardest questions cluster.
- 04
Practise recognising the mechanic before attempting the mathematics. On this evidence, four mechanics cover 77.1% of the paper.
Free resource
The recall sheet these numbers came from.
Neither the ESAT nor the TMUA gives you a formulae booklet or a calculator, so everything on the specification is a memorisation liability. Our recall sheet lists every formula, rule and technique for all seven modules, each one tied to the spec clause that requires it, with the measured frequency beside it. It is free.
Get the free TMUA recall sheetMethod and coverage
How this was measured, and what it does not cover.
The corpus is 1,250 real past-paper questions across all seven modules, of which 180 are TMUA Paper 2 - and every percentage on this page is out of that 180, not out of the full corpus.
Not one question we wrote ourselves is counted. Our own question bank is excluded on purpose: treating questions we authored as evidence of what Cambridge asks would be circular.
What the corpus holds
| Paper | Years | Published | Held |
|---|---|---|---|
| ENGAA | 2016-2023 | 362 | 315 |
| NSAA | 2016-2023 | 680 | 575 |
| TMUA | 2016-2023 + early specimen | - | 360 |
What it does not hold
A frequency table is a claim about a denominator, so a gap in the denominator biases every percentage above. These are the gaps, audited 2026-08-17. The first two matter to a candidate; the rest are recorded for completeness.
TMUA 2024 onwards
TMUA figures cover the 2016-2023 sittings and the early specimen. The 2024 and later sittings are not held.
This is the one gap that touches a LIVE test. TMUA percentages describe the Cambridge-era papers, which are the closest available evidence but are not the most recent sittings a current candidate will have seen.
ESAT, all years
No live ESAT paper has ever been released. Only the 2024 specimen and sample exist, and the sample has no answer key.
This is the whole reason ENGAA and NSAA stand in as the evidence base: they are ESAT's direct predecessors, filtered to the current ESAT specification.
NSAA 2016-2019 · 72 questions
NSAA Section 1 had a fifth part (E, Advanced Maths and Physics) in 2016-2019 which this corpus does not carry.
NSAA papers contain 680 questions. 608 are held here, and 575 of those fall inside the current ESAT specification - 575 is the number every ESAT percentage on this page is drawn from. Because Part E is out of ESAT scope, excluding it makes the ESAT-relevant percentages MORE accurate, not less: it would otherwise dilute every count with material ESAT never tests.
ENGAA and NSAA, all years
Only Section 1 papers are held. Neither test's Section 2 is in the corpus.
No effect on ESAT-relevant frequency: the format being measured does not exist in ESAT.