Measured on 257 real questions
What actually comes up in ESAT Mathematics 1
Topic frequency for ESAT Maths 1, measured on 257 real past-paper questions from the test’s predecessor papers.
Geometry and mensuration is the largest single topic at 24.9%, and the five commonest topics carry 71.6% of the paper.
ESAT Mathematics 1 is the module every candidate sits, and the one most often revised by working through a textbook front to back. That approach spreads effort evenly across a specification whose questions are not evenly spread at all.
We tagged 257 questions from ENGAA and NSAA Section 1 (2016 to 2023) that fall inside the current ESAT specification. Each question carries exactly one topic tag, so the percentages below add to 100% and can be read as shares of a paper.
Topic frequency
Every ESAT Mathematics 1 topic, by how often it actually appeared.
257 questions, 13 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 | Geometry and mensuration | 64 / 257 | 24.9% | 20.0-30.5% |
| 2 | Algebraic manipulation | 40 / 257 | 15.6% | 11.6-20.5% |
| 3 | Number, ratio and percentages | 37 / 257 | 14.4% | 10.6-19.2% |
| 4 | Coordinate geometry | 23 / 257 | 8.9% | 6.0-13.1% |
| 5 | Quadratics and polynomials | 20 / 257 | 7.8% | 5.1-11.7% |
| 6 | Probability | 19 / 257 | 7.4% | 4.8-11.3% |
| 7 | Trigonometry | 17 / 257 | 6.6% | 4.2-10.3% |
| 8 | Equations and inequalities | 14 / 257 | 5.4% | 3.3-8.9% |
| 9 | Statistics and data | 8 / 257 | 3.1% | 1.6-6.0% |
| 10 | Sequences and series | 7 / 257 | 2.7% | 1.3-5.5% |
| 11 | Logarithms and exponentials | 6 / 257 | 2.3% | 1.1-5.0% |
| 12 | Graphs and functions | 1 / 257 | 0.4% | 0.1-2.2% |
| 13 | Thermal physics | 1 / 257 | 0.4% | 0.1-2.2% |
Evidence base: ENGAA and NSAA Section 1, 2016-2023, filtered to the current ESAT specification.
What this means for your revision
Four things the numbers say about ESAT Mathematics 1.
- 01
Geometry and mensuration alone is 24.9% of the module - roughly one question in four.
- 02
Add algebraic manipulation (15.6%) and number, ratio and percentages (14.4%) and you have covered 54.9% of the paper with three topics.
- 03
The tail is long and thin: 13 topics appear, but the bottom five together account for under 9%. Do not spend a revision block on graphs and functions (0.4%) before circuits of the top three are automatic.
- 04
Speed matters more than range here. With no calculator, the top three topics are exactly the ones where a slow method costs you a question you could have answered.
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 ESAT 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 257 are ESAT Mathematics 1 - and every percentage on this page is out of that 257, 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.