ESAT preparation guide

ESAT Mathematics 2, module by module

Q: What does ESAT Mathematics 2 actually cover?

The specification lists eight topics: algebra and functions, sequences and series, coordinate geometry in the (x, y)-plane, trigonometry, exponentials and logarithms, differentiation, integration, and graphs of functions. It also states that all modules assume knowledge of the content of Mathematics 1, and it maps Mathematics 2 to the M and MM topic sets together. The real scope is therefore those eight headings plus the seven Mathematics 1 headings: units, number, ratio and proportion, algebra, geometry, statistics and probability. Only headings are published, not sub-topics.

Q: Do I need to take Mathematics 2?

It depends on the course. Cambridge Engineering (H100), Oxford's Engineering Science and physics routes, and Imperial's Aeronautics, Civil and Environmental, Electrical and Electronic, Mechanical and Physics all specify Mathematics 1, Mathematics 2 and Physics. Imperial Chemical Engineering specifies Mathematics 1, Mathematics 2 and Chemistry. Imperial's MEng Design Engineering takes Mathematics 1 and Mathematics 2 only. Cambridge Natural Sciences, Veterinary Medicine and Chemical Engineering and Biotechnology, Oxford Biomedical Sciences and UCL Electronic and Electrical Engineering are all Mathematics 1 plus any two, with Mathematics 2 a valid pick. Check the Course List row for the exact UCAS code you are applying under.

Q: Can I take Mathematics 2 without Further Maths?

The specification is a content list: it sets out what can be examined, not which qualifications you must have taken, so check your course's own entry requirements and the UAT-UK registration pages for eligibility. What can be observed is that the eight published headings contain none of the topics that usually mark out Further Maths, such as matrices, complex numbers, hyperbolic functions, differential equations or polar coordinates, and that they overlap closely with the pure content of A level Maths. What needs extra work is not new content but fluency by hand without a calculator, refreshing the seven Mathematics 1 topics, multiple-choice technique and speed.

Q: Do Mathematics 1 and Mathematics 2 overlap, and is taking both a waste?

They overlap, by design. The specification states that all modules assume knowledge of Mathematics 1, and maps Mathematics 2 to M plus MM. The two modules therefore share the seven M topics as a foundation. That is leverage rather than waste: solid Mathematics 1 pays into both modules, and a substantial share of your 54 questions rests on the same fundamentals. For a course such as Imperial Design Engineering, where those two modules are the entire test, the leverage is at its maximum.

Q: Can I use a calculator in Mathematics 2?

No. UAT-UK states that no calculator and no dictionary may be used, in either the ESAT or the TMUA. The test is computer based, and the centre provides erasable rough working materials and a pen, which you can ask to have replaced at any point during the test by raising your hand. In practical terms this means common denominators, surd simplification, exact trigonometric values for standard angles, log manipulation and squares and cubes all need to be automatic.

Q: What is a good Mathematics 2 score?

Officially there is no answer, and we are not going to invent one. UAT-UK states that there is no pass or fail score for the ESAT and publishes no grade boundaries; scores are used alongside the rest of your application. What is certain is the mechanism: each module is reported separately on a scale from 1 (low) to 9 (high) to one decimal place, there is no combined total, each module is equated and scaled separately, and appeals against scores are not accepted. The only published score data comes from Imperial, which reports mean raw marks out of 27 among 2025-entry offer-holders and states itself that this is historic data and not indicative of requirements for current or future cycles. Specific thresholds circulating online have no official source, so ask which official page they come from.

Q: Can I change my modules after booking?

Not directly. UAT-UK states that module choices cannot be changed without cancelling and rebooking. More importantly, if you are applying to two or more courses that require the ESAT and one of them offers a free choice of modules, your selection must be dictated by the courses that list compulsory modules, and failing to register for those compulsory modules may invalidate your application to that course. Reconcile every UCAS choice against the official Course List before you complete the booking.

The ESAT has five modules. Everybody sits Mathematics 1, and most candidates add two more. Of those four optional modules, Mathematics 2 is the only one with differentiation and integration on its published syllabus, and it is the one that Cambridge Engineering, Oxford's engineering and physics routes and most of Imperial's engineering departments name explicitly. The specification lists eight topics for it: algebra and functions, sequences and series, coordinate geometry, trigonometry, exponentials and logarithms, differentiation, integration and graphs of functions. What actually sets your revision scope, though, is a different sentence in the specification: every module assumes knowledge of the content of Mathematics 1. The examinable surface of Mathematics 2 is therefore the M topic set and the MM topic set stacked together. You get 27 multiple-choice questions in 40 minutes, no calculator, and no way to carry spare time into the next module. This page covers four things: the eight headings, the courses that require them, how the module lines up with A level maths, and how to pace it on the day.

10 sections3,167 words16 min read10 official sources

Practise 72 ESAT papers (2 free)Full ESAT guide

Papers: 72
Questions: 2790
Free to try: 2

Mathematics 2 at a Glance

Examinable scope: The eight MM topics plus all seven Mathematics 1 topics
Format: 27 multiple-choice questions in 40 minutes, no calculator, about 89 seconds each
Who must take it: Cambridge Engineering (H100), Oxford engineering and physics routes, most Imperial engineering departments
Scoring: 1 to 9 per module to one decimal place; no negative marking, no pass mark, no boundaries
Attempts: One sitting per admissions cycle; 2027-entry windows fall in October 2026 and January 2027

Figures from the UAT-UK content specification (for assessment in October 2026 and January 2027), the 2027-entry Course List and UAT-UK's official test pages.

In short

Mathematics 2 examines its own eight topics plus all seven Mathematics 1 topics, because the specification states every module assumes Mathematics 1.
Cambridge Engineering (H100), Oxford's Engineering Science and physics routes and Imperial's Aeronautics, Civil, EEE, Mechanical, Physics and Chemical Engineering all specify Mathematics 2.
Imperial's MEng Design Engineering takes only two modules, Mathematics 1 and Mathematics 2, so Mathematics 2 is half of everything you sit.
The eight headings overlap heavily with A level pure maths; the new variables are no calculator, roughly 89 seconds per question, and dusting off the Mathematics 1 topics.
Each module is reported separately on a 1 to 9 scale to one decimal place; there is no pass mark and UAT-UK publishes no grade boundaries.

Part 1 of 3

Sections 01 to 04

Start here: Mathematics 2 tests two topic sets, not one

Appendix 1 of the official specification gives Mathematics 2 eight topic headings, numbered MM1 to MM8. The sentence that matters more sits in the main body: questions draw upon the topics listed for each module in Appendix 1, and all modules assume knowledge of the content of Mathematics 1. The table on page 3 spells it out, module by module, as two topic sets each:

Biology

B + M

Chemistry

C + M

Physics

P + M

Mathematics 2

M + MM

The eight MM headings stacked on the seven M headings

The examinable surface of your 40 minutes of Mathematics 2 is therefore the eight MM headings together with all seven Mathematics 1 headings: Units, Number, Ratio and proportion, Algebra, Geometry, Statistics and Probability. That is not an inference, it is the stated design. Candidates who revise Mathematics 2 as "the calculus module" routinely drop marks on ratio, unit conversion and probability, which look too elementary to bother with, on questions they had ninety seconds for.

There is a second consequence. If your course requires Mathematics 1 and Mathematics 2, the M content faces you twice across 54 questions, and a substantial share of them stands on the same foundation. Time spent making Mathematics 1 automatic pays off in both modules; time spent only on MM pays off in one.

The eight headings, and what the specification stops short of saying

The specification publishes topic headings only. The map below lays MM1 to MM8 out by how they relate to one another, because these are not eight parallel blocks. The headings are verbatim; the grouping is our teaching reading.

The eight Mathematics 2 topics

MM1 to MM8, official headings

The skeletonHow functions are built and what they look like drawn

MM1 Algebra and functions
MM8 Graphs of functions

Three languagesCoordinates, angle and periodicity, growth and decay

MM3 Coordinate geometry in the (x, y)-plane
MM4 Trigonometry
MM5 Exponentials and logarithms

Two operatorsActing on everything above

MM6 Differentiation
MM7 Integration

Standing apartSummation and convergence at its centre

MM2 Sequences and series

Tap a branch to unfold

On difficulty, the specification offers one line: the test is designed to be challenging in order to differentiate effectively between able applicants, including those who might have achieved the highest possible grades in school examinations. The revision consequence, in our experience of teaching it, is that drilling one heading at a time will not get you there. Marks tend to go missing where two or three headings are bolted together, for instance differentiating a composite built from an exponential or a trigonometric function and then reading a property off the resulting graph. Topic-by-topic practice sharpens the tools; mixed practice teaches you to reach for the right one.

The specification does not publish sub-topics under these headings, so anything advertised as an "official detailed checklist" is not official. The grouping above and the advice about mixed practice are our teaching judgement, not official statements.

The courses that specify Mathematics 2

The official Course List for 2027 entry sets out module requirements course by course. Wherever the maths and physics density is high, Mathematics 2 is named:

	Course (code)	Modules required
Cambridge	BA/MEng Engineering (H100)	Mathematics 1 + Mathematics 2 + Physics
Oxford	Engineering Science (H100)	Mathematics 1 + Mathematics 2 + Physics
Oxford	Physics (F303), Physics and Philosophy (VF53)	Mathematics 1 + Mathematics 2 + Physics
Oxford	Biomedical, Chemical, Civil, Electrical, Information and Mechanical Engineering	Mathematics 1 + Mathematics 2 + Physics
Imperial	Aeronautics, Civil and Environmental, Electrical and Electronic, Mechanical, Physics	Mathematics 1 + Mathematics 2 + Physics
Imperial	Chemical Engineering	Mathematics 1 + Mathematics 2 + Chemistry
Imperial	MEng Design Engineering (28G3)	Mathematics 1 + Mathematics 2, two modules only

Several Oxford engineering routes also have with Foundation Year variants, listed on their own rows in the Course List. Check against the exact UCAS code you are applying under rather than going by course name.

One rule catches people out every cycle. UAT-UK states that if you apply to two or more courses requiring the ESAT and one of them offers a free choice of modules, your selection must be dictated by the courses with compulsory modules listed, and failing to register for the compulsory modules may invalidate your application to that course. A common example: Imperial Mechanical Engineering (Mathematics 2 and Physics specified) alongside Cambridge Natural Sciences (any two) fixes your combination at Mathematics 2 and Physics. The freedom Natural Sciences appears to offer is not freedom you actually have.

One thing to get straight about who uses this test at all. UAT-UK states that Imperial, Cambridge, Oxford and UCL use the ESAT. Imperial's own ESAT page additionally lists Durham, LSE and Warwick under "ESAT for other universities", but in the official 2027 Course List those three carry TMUA requirements and no ESAT courses at all. UAT-UK separately says seven UK universities use one or more of its tests, which is exactly the number on Imperial's list, so that section reads like the membership list rather than the ESAT list. For module requirements, the Course List table is the document to trust.

Imperial Design Engineering: the two-module exception

In the official Course List, the row for Imperial's MEng Design Engineering (28G3) is flagged Two Modules Only, and the two are Mathematics 1 and Mathematics 2. It is the one row on the table that deserves its own section, and three things follow:

80 minutes

Total test time, against the 120 most candidates sit, with no break between modules

Half

Mathematics 2's share of everything the university sees; no physics or chemistry score dilutes it

7 topics

The shared M foundation: the whole sitting is two samples from one base, the highest overlap of any combination

For Design Engineering applicants that is both bad news and good news. The bad news is that if your maths wobbles, nothing else on the paper can carry you. The good news is that your preparation path is unusually clean: everything goes into maths, and you never have to ration revision time across three subjects.

In practice, treat Mathematics 1 and Mathematics 2 as one course rather than two: get the seven M topics to the point where they require no thought, layer the eight MM topics on top, then rehearse in 40-minute blocks. The classic failure mode among candidates who revise them separately is that ratio and geometry feel solid inside a Mathematics 1 practice set, but become unrecognisable the moment they turn up wearing Mathematics 2 clothing inside a question about functions or graphs.

Part 2 of 3

Sections 05 to 08

Where the choice is yours: when to pick Mathematics 2 anyway

A handful of courses do not specify modules and hand the choice back to you. The Course List wording is Mathematics 1 plus any two chosen from Biology, Chemistry, Physics and Mathematics 2: Cambridge Natural Sciences (BCF0) Cambridge Chemical Engineering and Biotechnology (H810) Cambridge Veterinary Medicine (D100) Oxford Biomedical Sciences (BC98) UCL Electronic and Electrical Engineering (H600/H601), which requires the ESAT from September 2027 entry, or September 2028 deferred entry Mathematics 2 is a legitimate option in every one of these. A surprising number of applicants assume Natural Sciences forces a choice between the three sciences; it does not. Three questions decide it.

01Question 1

Is your maths clearly stronger than your second science?

If your A level maths clearly outruns your second science, Mathematics 2 is usually the better bet than grinding through a subject you half know: it shares its foundation with compulsory Mathematics 1, so its marginal preparation cost is the lowest on the menu.

02Question 2

Which direction are you heading in?

A physical or materials route through Natural Sciences means you should be sharpening physics anyway, and Mathematics 2 pairs with it naturally; a biochemical route makes Chemistry and Biology the closer fit.

03Question 3

Does anything on your list specify modules?

The moment another course on your UCAS form specifies modules, this free choice evaporates and the specified combination wins.

UCL Electronic and Electrical Engineering is worth flagging in particular. The choice is formally open, and Mathematics 2 with Physics is the combination that maps most closely onto what the degree then asks of you, but that is a judgement about fit rather than something UCL states as a requirement.

From an A level standpoint: you know the content, that is not the problem

Put the eight headings next to the pure maths content of A level Maths and the overlap is close to line by line; the sequence reads like a contents page from AS and A2 pure. Equally telling is what the official list does not contain: no matrices, no complex numbers, no hyperbolic functions, no differential equations, no polar coordinates. None of the headings that usually mark out Further Maths appear among the eight. For a student partway through A level Maths, then, Mathematics 2 asks for very little genuinely new content. Four other things are what actually need work.

No calculator

Being slow, not being unable

Common denominators, surds, exact trig values, log rules, squares and cubes; two calculator years erode them fast

The seven M1 topics

Dusting off GCSE-era material

Units, number, ratio, algebra, geometry, statistics and probability: long unused, and assumed

Multiple-choice technique

Working backwards, estimating, special values

None of it is trained by A level long-answer practice

Speed

About 89 seconds per question

Pacing gets its own section below

One small thing the specification states outright and almost everybody skips: under Units, candidates are expected to be familiar with the SI prefixes from nano- to giga-, and with units written using negative indices, for example m s⁻¹ for velocity. Mathematics 2 assumes that too.

For candidates coming out of the Chinese secondary system the gap sits elsewhere. Derivatives and definite integrals are on the national curriculum, but British notation, radians as the default, the conventions around log and ln, and the way graph transformations are described all need a dedicated round of adjustment. Chinese maths education also tends to train inequalities and analytic geometry harder than the British system does, which is an advantage you can spend less time on.

27 questions, 40 minutes, calculus included: how to pace it

The arithmetic is blunt: 27 questions in 40 minutes is about 89 seconds each. Read that alongside two official rules. Each module is separately timed, and if you finish one early the time is not carried over to the next, so there is nothing to be gained by banking minutes in Mathematics 2. And there are no breaks between modules, so you go from the last question of one straight into the first question of the next.

Ninety seconds with calculus in the mix sounds brutal, and is less so than it reads, because the no-calculator rule protects you: whoever wrote the question had to make the numbers workable by hand. That gives you a genuinely useful diagnostic. As soon as your intermediate values turn ugly, the problem is almost never that the question is hard, it is that you have taken the long road. Stop, reread the stem, and look for the shortcut, usually symmetry, structure, a graphical feature, or differentiating and substituting immediately.

01About 20 min

First pass: sweep all 27

Answer anything you can see a route into, mark and skip anything that needs sustained algebra, and never sink into a single question.

02About 15 min

Second pass: the marked questions

Easiest first, by your own marking instinct.

03Final 5 min

Close: fill and recheck

Fill in every remaining blank, then recheck the handful you rushed on the first pass.

There is no negative marking: your score is based on the number of correct answers, so every question is worth attempting. An unanswered question scores identically to a wrong one, and a blank is worth exactly nothing, which makes clearing your blanks in the final thirty seconds the highest-return action available to you all day.

Scoring: 1 to 9 per module, and no boundary to aim at

Marking

One mark per correct answer, no deductions

Reported scale

1 (low) to 9 (high) per module, to one decimal place

Overall total

None; each module you sit gets its own score

Equating and scaling

Done separately per module

Unlike the TMUA, whose two papers are scaled together into one score

For Mathematics 2 that means one thing above all: the number stands on its own. A strong Physics score does nothing arithmetically for the Mathematics 2 line, and a course specifying three modules puts three parallel figures in front of the admissions tutor, not an average. Preparation effort should follow your weakest required module rather than your favourite one.

UAT-UK states that there is no pass or fail score for the ESAT and publishes no grade boundaries; scores are used alongside the rest of your application. The figures circulating online for what counts as "safe" or "competitive" have no official source behind them. If someone hands you a number and calls it a threshold, ask which page of which official document it came from.

The one institution that has published any score data is Imperial. The 2025-entry mean marks among offer-holders are below; read the three caveats underneath before you lean on the numbers.

	Mean mark, 2025-entry offer-holders (out of 27)
Aeronautics	17.5
Physics	17.5
Electrical and Electronic Engineering	16.6
Mechanical	15.8
Chemical Engineering	14.2
Civil and Environmental	12.6
Design Engineering	8.9

The Overseas column is higher in every department, 19.8 for EEE and 19.4 for Physics among them. A historic reference point, not a boundary.

What kind of number is a 17.5?

The dashboard reports a raw mark labelled "Mean test score (maximum is 27)", not the 1 to 9 scaled score, and the page does not say whether that is one module or an average across the modules a candidate sat.

Which columns can be trusted?

Only the offer-holder column is solid. For the not-shortlisted column, the page does not say whether it includes applicants who registered but never sat the test.

Can these be used as cut-offs?

No. Imperial states plainly that this is historic data and should not be taken as indicative of requirements or outcomes for current or future cycles: a high score does not guarantee an offer, a low one does not rule you out, and there are no grade boundaries or pass marks for the ESAT or TMUA.

Three practical points go with this. Results arrive approximately four weeks after your sitting; for 2027 entry the confirmed dates are 16 November 2026 for the October window and 8 February 2027 for January. Results are matched course by course against your UCAS application and sent automatically to institutions whose courses require the test, and candidates cannot choose which institutions see them. And UAT-UK does not accept appeals against test scores.

III

Part 3 of 3

Sections 09 to 10

A preparation path, and three lines not to cross

01Step 1

Drill the seven M1 topics until they need no thought

They underpin Mathematics 2 and your other module alike.

02Step 2

Rebuild tools heading by heading through MM

The focus is fluency by hand without a calculator, not new content.

03Step 3

Mixed practice

Questions welding two or three headings together should become normal rather than surprising.

04Step 4

Full 40-minute timed modules

Rehearse until the three-pass structure is automatic.

05Step 5

Review errors under three headings

Did not know it, knew it and miscalculated, ran out of time: the remedies differ completely, and reviewing them as one pile wastes the review.

On archive papers: UAT-UK's preparation materials page provides historic ENGAA and NSAA papers and flags the questions that fall outside the current specification. Using them is sensible, provided you respect those flags rather than burning hours on material that is no longer examinable. One version check before you start: the current specification is for assessment in October 2026 and January 2027, so make sure the syllabus in front of you matches the sitting you are booked for.

Three lines not to cross: Module choices cannot be changed without cancelling and rebooking, so reconcile every course on your UCAS list before you complete your registration. Sharing or discussing test content is prohibited. It was reports in October 2024 of candidates attempting to obtain and sell test content that led to the tightened test days in China, Hong Kong and Macau, a cost borne by everyone sitting in those regions since. UAT-UK states that it is not connected to, and does not endorse or promote, commercial preparation services, and that all necessary preparatory materials are available free of charge. FrontierVUE has no affiliation with or authorisation from UAT-UK, Pearson or any university; we build practice and explanation around the official documents, which remain your first source.

Sittings: one attempt per admissions cycle

Two windows exist for 2027 entry: 12 to 16 October 2026, and 4 to 8 January 2027. Candidates in mainland China, Hong Kong and Macau have fixed days rather than a free choice within the window: the ESAT runs on 12 or 13 October and on 6 January, so book on the day registration opens. The timeline below lines up every booking, access-arrangement and bursary deadline.

2026 – 2027Timeline

Jun 26

Jul 26

Aug 26

Sep 26

Oct 26

Nov 26

Dec 26

Jan 27

Accounts, access arrangements and bursaries open

1 Jun 2026

Open from 1 June 2026 at 15.00 UK time.

October sitting: booking window

20 Jul to 28 Sep

Opens 20 July 2026 at 15.00 and closes 28 September 2026 at 18.00, UK time.

October sitting: access arrangements deadline

14 Sep 2026

Closes 14 September 2026 at 18.00 UK time, earlier than booking itself; do not leave it late.

October sitting: bursary deadline

21 Sep 2026

Closes 21 September 2026 at 18.00 UK time.

October test window

12 to 16 Oct

In mainland China, Hong Kong and Macau the ESAT runs only on Monday 12 or Tuesday 13 October.

January sitting: booking window

26 Oct to 21 Dec

Opens 26 October 2026 at 15.00 and closes 21 December 2026 at 18.00, UK time.

January sitting: access arrangements deadline

7 Dec 2026

Closes 7 December 2026 at 18.00 UK time.

January sitting: bursary deadline

14 Dec 2026

Closes 14 December 2026 at 18.00 UK time.

January test window

4 to 8 Jan

In mainland China, Hong Kong and Macau the ESAT runs only on Wednesday 6 January.

Hard deadline Event WindowAll openings are at 15.00 and all deadlines at 18.00, UK time.

You are permitted to sit each UAT-UK test only once per admissions cycle, and the cycle includes both windows above. Attempting to register or sit a second time within the cycle, including by booking under a second UAT-UK account, is treated as misconduct. Mathematics 2 is a single attempt, with no resit option.

One rule constrains the choice of window. Applicants to Cambridge or Oxford whose course requires the test will normally be required to sit in October, the exceptions being mature applicants to a Cambridge mature college with a January admissions deadline, and applicants to Oxford's Astrophoria Foundation Year. Applicants to other institutions may decide when to sit, and UAT-UK states there is no advantage to either session. Imperial adds that you take the ESAT once per cycle, in October or January as you prefer, and that only your first score is considered.

Fee: UK and Ireland

£78

Set by test-centre location, not nationality or home address

Fee: elsewhere

£133

Arrival

30 minutes early

Lateness

Over 15 minutes late risks refusal of entry, with the fee forfeited

Not a risk worth running on a test you can sit only once

FAQ

Frequently asked questions

What does ESAT Mathematics 2 actually cover?

The specification lists eight topics: algebra and functions, sequences and series, coordinate geometry in the (x, y)-plane, trigonometry, exponentials and logarithms, differentiation, integration, and graphs of functions. It also states that all modules assume knowledge of the content of Mathematics 1, and it maps Mathematics 2 to the M and MM topic sets together. The real scope is therefore those eight headings plus the seven Mathematics 1 headings: units, number, ratio and proportion, algebra, geometry, statistics and probability. Only headings are published, not sub-topics.

Do I need to take Mathematics 2?

It depends on the course. Cambridge Engineering (H100), Oxford's Engineering Science and physics routes, and Imperial's Aeronautics, Civil and Environmental, Electrical and Electronic, Mechanical and Physics all specify Mathematics 1, Mathematics 2 and Physics. Imperial Chemical Engineering specifies Mathematics 1, Mathematics 2 and Chemistry. Imperial's MEng Design Engineering takes Mathematics 1 and Mathematics 2 only. Cambridge Natural Sciences, Veterinary Medicine and Chemical Engineering and Biotechnology, Oxford Biomedical Sciences and UCL Electronic and Electrical Engineering are all Mathematics 1 plus any two, with Mathematics 2 a valid pick. Check the Course List row for the exact UCAS code you are applying under.

Can I take Mathematics 2 without Further Maths?

The specification is a content list: it sets out what can be examined, not which qualifications you must have taken, so check your course's own entry requirements and the UAT-UK registration pages for eligibility. What can be observed is that the eight published headings contain none of the topics that usually mark out Further Maths, such as matrices, complex numbers, hyperbolic functions, differential equations or polar coordinates, and that they overlap closely with the pure content of A level Maths. What needs extra work is not new content but fluency by hand without a calculator, refreshing the seven Mathematics 1 topics, multiple-choice technique and speed.

Do Mathematics 1 and Mathematics 2 overlap, and is taking both a waste?

They overlap, by design. The specification states that all modules assume knowledge of Mathematics 1, and maps Mathematics 2 to M plus MM. The two modules therefore share the seven M topics as a foundation. That is leverage rather than waste: solid Mathematics 1 pays into both modules, and a substantial share of your 54 questions rests on the same fundamentals. For a course such as Imperial Design Engineering, where those two modules are the entire test, the leverage is at its maximum.

Can I use a calculator in Mathematics 2?

No. UAT-UK states that no calculator and no dictionary may be used, in either the ESAT or the TMUA. The test is computer based, and the centre provides erasable rough working materials and a pen, which you can ask to have replaced at any point during the test by raising your hand. In practical terms this means common denominators, surd simplification, exact trigonometric values for standard angles, log manipulation and squares and cubes all need to be automatic.

What is a good Mathematics 2 score?

Officially there is no answer, and we are not going to invent one. UAT-UK states that there is no pass or fail score for the ESAT and publishes no grade boundaries; scores are used alongside the rest of your application. What is certain is the mechanism: each module is reported separately on a scale from 1 (low) to 9 (high) to one decimal place, there is no combined total, each module is equated and scaled separately, and appeals against scores are not accepted. The only published score data comes from Imperial, which reports mean raw marks out of 27 among 2025-entry offer-holders and states itself that this is historic data and not indicative of requirements for current or future cycles. Specific thresholds circulating online have no official source, so ask which official page they come from.

Can I change my modules after booking?

Not directly. UAT-UK states that module choices cannot be changed without cancelling and rebooking. More importantly, if you are applying to two or more courses that require the ESAT and one of them offers a free choice of modules, your selection must be dictated by the courses that list compulsory modules, and failing to register for those compulsory modules may invalidate your application to that course. Reconcile every UCAS choice against the official Course List before you complete the booking.

SOURCES

Official sources

MORE GUIDES

Other ESAT preparation guides

FrontierVUE is an independent practice platform. It is not affiliated with or endorsed by UAT-UK, Pearson, OCR, the University of Cambridge, Imperial College London, or any official admissions-test owner.

Put it into practice

72 ESAT papers on FrontierVUE, including 41 Frontier Original mocks built to the current format, every question with a worked solution. The first 2 papers are free.

Practise ESAT papers See pricing