ESAT Maths 2 preparation: topics, timing and question sources
Mathematics 2 has the ESAT's hardest questions and its tightest clock: half of all candidates run out of time on at least one question. Here is how to protect the marks you can win.
Try Maths 2 before you plan the rest
Answer 2 original Maths 2 questions and read the worked solutions. Start free, without an account.
Why Mathematics 2 needs its own plan
It covers algebra and functions, sequences and series, coordinate geometry, trigonometry, exponentials and logarithms, differentiation, integration and graphs, set in problems you have not seen before. The median is 4.5 and the top 10% start at 6.8.
Plan your Maths 2 weeks, in three taps
The Mathematics 2 topic map
How 48 Mathematics 2 questions in ENGAA 2019 to 2023 Part B were spread. These are older papers, so treat the spread as a guide to practice, not a forecast of the 2026 test.
| Spec area | Classified questions | Share of the sample |
|---|---|---|
| Sequences and series | 8 | about 17% |
| Coordinate geometry | 8 | about 17% |
| Advanced algebra | 8 | about 17% |
| Differentiation | 6 | about 13% |
| Integration | 5 | about 11% |
| Logarithms and exponentials | 5 | about 11% |
| Trigonometry | 5 | about 11% |
| Graph transformations and curve sketching as the subject | about 3 | about 6% |
Every heading can appear. With one week, start with the topics where your own recent errors are, and keep all eight in rotation.
The topics that recur across the corpus
Logarithms, trigonometry and differentiation came up in every paper, so drill them little and often.
| Topic | First move to practise |
|---|---|
| Sequences and series | Classify the recurrence first. Do not expand a binomial expression until the question needs it. |
| Coordinate geometry | Write the given coordinate condition before drawing conclusions from the diagram. |
| Advanced algebra | Factor or compare structure before expanding a polynomial or rational expression. |
| Differentiation | Translate the question into the derivative condition it asks for. |
| Integration | Decide whether the question wants an antiderivative or an area. |
| Logarithms and exponentials | Turn the log statement into a power question and check the allowed argument. |
| Trigonometry | Fix the angle range before solving an identity or equation. |
What TMUA Paper 1 can transfer
UAT-UK's Mathematics notes cover both TMUA Paper 1 and ESAT Mathematics 2, so they are good extra practice for algebra and calculus. Finish with ESAT blocks on the ESAT clock.
The Mathematics 2 question route
Give every question an opening move. A full school-method solution is often too slow for the first pass.
- Write what the question asks for. It may want a term, a root, a coordinate, an area or a maximum.
- Keep the structure visible. Factor before expanding, use the given relation before substituting, and preserve exact surds until the options make the comparison clear.
- Use the options as a check. Exact near-neighbour answers can expose a dropped factor or a missed sign, but an option is not a proof.
- Set an abandon point. If the first route has not appeared, mark the item, take the accessible marks elsewhere, and return with a full clock check.
ENGAA 2023 has log equations and maximum-value problems with close exact-form options. Learn the move from wording to structure, not the question. Every ENGAA and NSAA paper and the official ESAT practice tests are on our ESAT past papers page, sorted by module.
You average 88.9 seconds a question. Spend longer when the route is clear, and park anything that would eat the time for four easier ones.
The hard-question endgame
Wrong answers cost nothing. In the final sweep, return to flagged questions, cross out impossible options and answer everything. A blank can never score.
A Mathematics 2 review log
After each set, tag every error with its cause.
| Tag | What happened | Next practice |
|---|---|---|
| Content | You could not name the method or condition. | Revisit that specification point, then do a short set on the same method. |
| Recognition | You knew the topic but did not see the first move. | Mix the topic with nearby topics and write the first line only. |
| Algebra or arithmetic | The route was sound but a sign, factor or exact form failed. | Use a calculator-free exact-manipulation drill. |
| Interpretation | You solved a related problem rather than the one asked. | Rewrite the requested quantity before working. |
| Pacing | The item was left unseen or received five seconds or less. | Repeat a timed block and practise the abandon point. |
Log it like this: ENGAA 2022 Part B, 21/27, 24 reached, 39 minutes, two recognition errors. To turn that mark into a scaled score, use the converter.