Measured on 73 real questions
What actually comes up in ESAT Mathematics 2
Topic frequency for the optional Mathematics 2 module, measured on 73 real past-paper questions - a small sample, and the page says so throughout.
Calculus is the spine of Mathematics 2: differentiation (17.8%) and integration (12.3%) together are about 30% of the module.
Mathematics 2 is the module candidates most often add late, and the one where the least public guidance exists. It is also the module where our evidence base is thinnest: 73 questions, all from ENGAA, because NSAA had no equivalent paper inside the current ESAT specification.
That matters for how you read the table. At n=73 the confidence intervals are wide - the top topic’s true share could plausibly sit anywhere between 10.7% and 28.1%. The ranking is informative; the exact percentages should not be treated as precise.
Topic frequency
Every ESAT Mathematics 2 topic, by how often it actually appeared.
73 questions, 12 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 | Differentiation | 13 / 73 | 17.8% | 10.7-28.1% |
| 2 | Sequences and series | 12 / 73 | 16.4% | 9.7-26.6% |
| 3 | Integration | 9 / 73 | 12.3% | 6.6-21.8% |
| 4 | Logarithms and exponentials | 8 / 73 | 11.0% | 5.7-20.2% |
| 5 | Quadratics and polynomials | 7 / 73 | 9.6% | 4.7-18.5% |
| 6 | Coordinate geometry | 6 / 73 | 8.2% | 3.8-16.8% |
| 7 | Trigonometry | 6 / 73 | 8.2% | 3.8-16.8% |
| 8 | Advanced algebra | 3 / 73 | 4.1% | 1.4-11.4% |
| 9 | Equations and inequalities | 3 / 73 | 4.1% | 1.4-11.4% |
| 10 | Geometry and mensuration | 3 / 73 | 4.1% | 1.4-11.4% |
| 11 | Graphs and functions | 2 / 73 | 2.7% | 0.8-9.5% |
| 12 | Algebraic manipulation | 1 / 73 | 1.4% | 0.2-7.4% |
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 2.
- 01
Differentiation (17.8%) and integration (12.3%) are the two pillars. If calculus is not fluent, Mathematics 2 is not worth sitting.
- 02
Sequences and series is the surprise at 16.4%, second only to differentiation and ahead of integration.
- 03
Logarithms and exponentials (11.0%) round out a top four that covers 57.5% of the module.
- 04
Read the confidence intervals before planning around any single figure. With 73 questions, a difference of two or three percentage points between adjacent topics is not a real difference.
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 73 are ESAT Mathematics 2 - and every percentage on this page is out of that 73, 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.