Measured on 180 real questions
What actually comes up in TMUA Paper 1
Topic frequency for TMUA Paper 1, Applications of Mathematical Knowledge, measured on 180 real past-paper questions.
Algebra (23.3%), calculus (22.2%) and trigonometry (15.6%) carry 61.1% of Paper 1 between them.
TMUA Paper 1 tests applications of mathematical knowledge, and its distribution is more concentrated than the specification suggests. Three topics carry nearly two thirds of the paper.
We tagged all 180 questions from the 2016 to 2023 sittings plus the early specimen. One caveat travels with every TMUA figure on this site and belongs up front: the TMUA moved to a different awarding body for 2024, and those sittings are not in our corpus. These numbers describe the Cambridge-era papers, which are the closest available evidence, not the most recent papers a current candidate may have seen.
Topic frequency
Every TMUA Paper 1 topic, by how often it actually appeared.
180 questions, 9 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 | Algebra | 42 / 180 | 23.3% | 17.8-30.0% |
| 2 | Calculus | 40 / 180 | 22.2% | 16.8-28.8% |
| 3 | Trigonometry | 28 / 180 | 15.6% | 11.0-21.6% |
| 4 | Exponentials and logarithms | 22 / 180 | 12.2% | 8.2-17.8% |
| 5 | Sequences and series | 16 / 180 | 8.9% | 5.5-14.0% |
| 6 | Coordinate geometry | 15 / 180 | 8.3% | 5.1-13.3% |
| 7 | Number | 9 / 180 | 5.0% | 2.7-9.2% |
| 8 | Geometry | 5 / 180 | 2.8% | 1.2-6.3% |
| 9 | Probability | 3 / 180 | 1.7% | 0.6-4.8% |
Evidence base: TMUA 2016-2023 sittings plus the early specimen (Cambridge-era papers).
What this means for your revision
Four things the numbers say about TMUA Paper 1.
- 01
Algebra (23.3%) and calculus (22.2%) are effectively joint first. Neither can be a weak spot.
- 02
Trigonometry (15.6%) and exponentials and logarithms (12.2%) form the second tier; together the top four are 73.3%.
- 03
Geometry (2.8%) and probability (1.7%) are genuinely rare - 8 questions between them across 180.
- 04
Paper 1 rewards speed on standard techniques. The frequency table is a ranking of which techniques to make automatic first.
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 1 - 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.