ESAT preparation guide

ESAT Mathematics 1: the seven topics, and what is not in them

Q: Does ESAT Mathematics 1 include trigonometry?

No. Appendix 1 of the official Content Specification lists seven topics for Mathematics 1: Units, Number, Ratio and proportion, Algebra, Geometry, Statistics and Probability. Trigonometry is not among them. It sits in Mathematics 2 as MM4. We searched the Geometry topic word by word for trigonometry, sine, cosine and tangent and found no occurrences. If you are not entered for Mathematics 2, revising trigonometry has no direct value for this test.

Q: What is the difference between Mathematics 1 and Mathematics 2?

Mathematics 1 is the compulsory module with seven topics: Units, Number, Ratio and proportion, Algebra, Geometry, Statistics and Probability. Mathematics 2 is a separate optional module with eight: Algebra and functions, Sequences and series, Coordinate geometry in the (x, y)-plane, Trigonometry, Exponentials and logarithms, Differentiation, Integration, and Graphs of functions. Trigonometry, logs, calculus and graph work all live on the Maths 2 side. The specification also states that every module, Maths 2 included, assumes the Maths 1 content, so the two stack rather than sit side by side. Whether you take Maths 2 is decided by the course you are applying to, not by preference.

Q: Can I use a calculator in Maths 1, and what does the centre provide?

You cannot. The official position is that no calculator and no dictionary may be used, and the FAQ states specifically that calculators are permitted in neither the ESAT nor the TMUA. The centre supplies erasable working material and a pen, described on different official pages as an erasable booklet, an erasable notebook and a whiteboard, and you can raise your hand at any point during the test for a replacement. In practice your mental and written arithmetic speed converts directly into marks, so practise without a calculator from the very start.

Q: Does everyone have to sit Maths 1, or do some courses skip it?

Everyone sits it. The official wording is "All candidates need to sit Maths 1", with most candidates taking two further modules, which is why the test runs to 120 minutes for most people. Even courses that need only two modules in total include it, such as Imperial's MEng Design Engineering (28G3), which takes Mathematics 1 plus Mathematics 2. Note also that module selections cannot be changed without cancelling and re-booking; that if you apply to two courses which both require the ESAT, your selection must follow the one that names compulsory modules; and that you may sit only once per admission cycle, with the October 2026 and January 2027 sittings counting as the same cycle for 2027 entry.

Q: What Maths 1 score is good enough? Is there a pass mark?

There is no pass mark and no published boundary. The official statement is that there is no pass/fail score for the ESAT and that scores are used alongside the rest of your application. Imperial College London, the only university to have published department-level data, says the same thing plainly: there aren't any grade boundaries or pass marks for the ESAT or TMUA, and a high score does not guarantee an offer while a low one does not rule you out. Any figure you see quoted as safe or competitive has no official source, and we will not invent one. What is fixed is how the score is reported: separately for each module, on a 1 to 9 scale to one decimal place, with each module equated and scaled on its own and no combined total. The variable you can actually train is the number of questions you get right.

Q: What if I cannot finish 27 questions in 40 minutes? Guess or leave blank?

Guess. There is no negative marking and each correct answer scores one mark, so leaving a blank is strictly worse than picking something. Three practical habits: in the final minute, fill every unanswered item before you go back to check anything; before guessing, eliminate one or two implausible options, which an order-of-magnitude estimate or a dimensional check will often do on its own; and flag and move on from any question that has run past two minutes without a clear route. Remember too that each module is separately timed with no carry-over and no breaks between modules, so time saved in Maths 1 can only ever be reinvested in Maths 1.

Mathematics 1 is the one module every ESAT candidate sits. The official wording is blunt: "All candidates need to sit Maths 1." Its scope is narrower than most people assume. In Appendix 1 of the official Content Specification, Mathematics 1 has exactly seven topics, numbered M1 to M7: Units, Number, Ratio and proportion, Algebra, Geometry, Statistics and Probability. There is no trigonometry, no calculus and no work on functions and their graphs. All three of those sit in Mathematics 2. Narrow is not the same as easy. The specification says so itself: 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 difficulty in Maths 1 does not come from exotic content. It comes from doing ordinary mathematics quickly, accurately and without a calculator, under a clock that does not wait. This page covers three things: where the boundaries of the seven topics actually fall, why Maths 1 doubles as the foundation for whichever further modules you add, and how to practise for 27 questions in 40 minutes with nothing but the erasable working material the test centre hands you.

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Maths 1 at a Glance

Who sits it: The one module every candidate sits: "All candidates need to sit Maths 1"
Scope: Seven official topics, M1 to M7; no trigonometry, no calculus
Format: 27 multiple-choice questions in 40 minutes; under 90 seconds each by arithmetic
Tools: No calculator, no dictionary; only the erasable working material provided
Scoring: One mark per correct answer, no negative marking; per-module scores from 1 to 9 to one decimal place, no boundaries

Trigonometry, graphs of functions and calculus all sit in Mathematics 2. Figures follow the official Content Specification (for assessment in October 2026 and January 2027) and UAT-UK's official pages.

In short

The official Maths 1 list is seven topics only (Units, Number, Ratio and proportion, Algebra, Geometry, Statistics, Probability); trigonometry and calculus belong to Mathematics 2, not here.
The specification states that every module assumes knowledge of Mathematics 1, so it is not just one module out of three, it is the floor the other two stand on.
27 questions in 40 minutes works out at under 90 seconds each, which is arithmetic and not an official rule; each module is separately timed, so time saved in Maths 1 cannot be carried forward.
No calculator and no dictionary, which makes estimation, cancelling, unit conversion and SI prefixes things you must be able to do without pausing to think.
There is no negative marking and each correct answer scores one mark, so no question should be left blank; scores are reported per module on a 1 to 9 scale to one decimal place, and no grade boundaries are published.

Part 1 of 3

Sections 01 to 04

The official Maths 1 list is seven topics, and trigonometry is not one of them

Appendix 1 of the official Content Specification, the version headed "For assessment in October 2026 and January 2027", breaks Mathematics 1 into seven topics numbered M1 to M7: Units, Number, Ratio and proportion, Algebra, Geometry, Statistics and Probability. Seven, with no eighth. Some third-party material folds trigonometry into Maths 1 regardless. It is not there. Everything below belongs to Mathematics 2.

Trigonometry

MM4 in Mathematics 2

We searched the Geometry topic word by word for trigonometry, sine, cosine and tangent: zero hits

Functions and graphs

MM1 Algebra and functions, plus MM8 Graphs of functions

Differentiation

MM6 in Mathematics 2

Integration

MM7 in Mathematics 2

The cost of getting this wrong is easy to measure. Suppose your combination is Maths 1 with Physics and Chemistry, or Maths 1 with Chemistry and Biology, both permitted where a course asks for Maths 1 plus any two of Biology, Chemistry, Physics and Mathematics 2. In that case you will not sit a single maths module that tests a trigonometric identity or a derivative. Revising to the wrong scope means spending your scarcest resource on a module you are not entered for, while feeling productive the whole time.

The seven topics one by one, and where each boundary falls

	Official topic	Our gloss (not official wording)
M1	Units	Handling units and dimensions, SI prefixes, negative-index notation, dimensional consistency
M2	Number	Integers and fractions, decimals, indices and surds, approximation and estimation, comparing magnitudes fast
M3	Ratio and proportion	Ratios and rates, direct and inverse proportion, percentages, scaling and unit conversion
M4	Algebra	Manipulating and rearranging expressions, equations and inequalities, simultaneous equations, quadratics
M5	Geometry	Length, area and volume, angle relationships, similarity and congruence, properties of plane and solid figures
M6	Statistics	Measures of centre and spread, presenting and reading data from charts
M7	Probability	Single and combined events, independence and mutual exclusivity, systematic listing and tree diagrams

The left column is the official topic heading; the right is our teaching gloss, not official wording. Where the two differ, the PDF wins.

The right way to use this table is as an exclusion list rather than a revision checklist. If you meet a piece of mathematics in someone else's ESAT material that does not fall inside these seven headings, assume it belongs to Mathematics 2 until you have checked the official PDF yourself.

Specifications get revised. The current one states its own scope on the front page: for assessment in October 2026 and January 2027. Open the PDF and read that line yourself before you build a revision plan on top of a copy whose vintage you cannot name.

It is not just a module: every other module assumes it

One sentence in the specification is worth memorising word for word: "All modules will assume knowledge of the content of Mathematics 1." In plain terms, a Physics question is free to lean on proportional reasoning, algebraic rearrangement and unit conversion, and it will not soften the maths just because maths is a separate module. Page 3 of the specification makes this structural with a table of topic tags: the M tags, which are exactly the seven Maths 1 topics, appear in every module you can possibly sit.

Mathematics 1 (the M tags)

Assumed by every module

BiologyDraws on B plus M

B topics
M topics (M1 to M7)

ChemistryDraws on C plus M

C topics
M topics (M1 to M7)

PhysicsDraws on P plus M

P topics
M topics (M1 to M7)

Mathematics 2Draws on M plus MM

MM topics
M topics (M1 to M7)

Tap a branch to unfold

Two practical consequences follow. First, work on Maths 1 has a better return than work on any single other module, because it raises the floor under the others at the same time: in our own teaching, when a student stalls on a Physics question the stall is often about algebraic rearrangement or unit handling rather than about physics. Second, do not treat Maths 1 as the module you can safely deprioritise. Students who decide it looks easy and pour everything into Chemistry or Physics tend to lose marks in those very modules through arithmetic slips and dimensional errors. On a results page that reads as weak science. It is usually weak maths.

Who sits it, and why your module choice is effectively locked

The rule itself is short: "All candidates need to sit Maths 1. Most other candidates need to sit two further modules." Most courses want Maths 1 plus two others, which is why the ESAT runs to 120 minutes for most candidates. Those two further modules are rarely a free choice; the table shows the three typical patterns, and Maths 1 appears in every one of them.

	Pattern	Modules
Cambridge Engineering (H100)	Fixed outright	Mathematics 1, Mathematics 2 and Physics
Cambridge Natural Sciences (BCF0)	Free choice	Maths 1 plus any two of Biology, Chemistry, Physics and Mathematics 2
Cambridge Chemical Engineering and Biotechnology (H810)	Free choice	Maths 1 plus any two of Biology, Chemistry, Physics and Mathematics 2
Oxford Biomedical Sciences (BC98)	Free choice	Maths 1 plus any two of Biology, Chemistry, Physics and Mathematics 2
Imperial MEng Design Engineering (28G3)	Two modules only	Mathematics 1 and Mathematics 2

Under a free choice, Mathematics 2 counts as one of the options, which candidates routinely overlook.

The registration rules that cannot be undone: module selections cannot be changed without cancelling and re-booking the test; if you apply to two or more ESAT courses and one names compulsory modules, your selection must follow that course, or your application to it may be invalid; you may sit only once per admission cycle, the October 2026 and January 2027 sittings count as one cycle for 2027 entry, and registering again under a second account is treated as misconduct. Write out the full list of courses first, then tick the boxes.

Applicants to Cambridge and Oxford are normally required to sit in October, and the only exceptions the official pages name are Cambridge mature colleges with a January admissions deadline and Oxford's Astrophoria Foundation Year; that requirement bites only where the course you are applying to actually requires the test. Applicants to other institutions may choose their sitting, and the official line is that neither session carries an advantage. One last point of confusion: UAT-UK says seven UK universities use one or more of its tests, but only four use the ESAT, namely Imperial College London, Cambridge, Oxford and UCL. UCL requires it for Electronic and Electrical Engineering from September 2027 entry (or September 2028 deferred entry), again as Maths 1 plus any two modules.

Part 2 of 3

Sections 05 to 08

27 questions in 40 minutes: do the arithmetic, but call it what it is

40 minutes

Time allowed per module

27 questions

Multiple-choice questions per module

About 89 seconds

Per question by division; arithmetic, not an official rule

Use the figure as an alarm, not a metronome. If a question has run past two minutes without a clear route to an answer, make a decision: take the slower but certain method, or flag it and move on. Every question is worth exactly one mark, but they will not cost you the same amount of time, and the point of knowing the average is to bank seconds on the routine items so the awkward ones have somewhere to draw from.

Two official rules sharpen this. "Each module is separately timed. If a candidate finishes a module early, the time will not be carried over to the next module." And "there are no breaks between modules or papers of your test." Five minutes saved in Maths 1 cannot be spent on Physics and cannot be spent catching your breath; its only use is inside Maths 1 itself, on the questions you were unsure about.

That leads to a rehearsal step most candidates skip: sit at least one full mock in the real shape, running however many modules you are entered for back to back with nothing in between. If you only ever practise single 40-minute modules and then stop, you will never find out what your accuracy looks like in the back half of the final module, which is exactly where marks tend to go missing.

No calculator: the rule that rewrites how you practise

The official position appears on the test overview page, in the specification and in the FAQ, and it says the same thing each time: the ESAT is a computer-based test, and "you will not be able to use a calculator or dictionary"; the FAQ adds that calculators are permitted in neither the ESAT nor the TMUA. The centre provides erasable working material and a pen, described variously as an erasable booklet, an erasable notebook and a whiteboard, and you can raise your hand at any point for a fresh one. The rule hits Maths 1 harder than any other module, because Number and Ratio and proportion are arithmetic and proportional reasoning by definition. What to drill is unusually concrete.

Estimation and magnitude

Estimate the order of magnitude first, then decide whether an exact value is needed

Where the options are far apart in magnitude, the estimate alone settles it

Cancel before you compute

Simplify the whole expression before touching any arithmetic

The single most reliable time-saver

Know your numbers cold

Squares and cubes, common fraction, decimal and percentage conversions, rough values of simple surds

Recalled, not looked up

Convert units without pausing

Scale factors between length, area and volume

A classic source of avoidable losses

Stay in fractions

Hand-worked decimals are usually slower and more error-prone

Take the calculator off your desk on day one, not in the final week. A question you solved with a calculator has almost no transfer value here, because it bypasses precisely the skill being examined.

SI prefixes and negative-index units: an explicit requirement

One requirement in the specification is unusually explicit: "Candidates will be expected to be familiar with the following SI prefixes when used in connection with any SI unit." What follows is the actual table of prefixes, running from nano- up to giga-, together with the convention for writing units with negative indices; the example the specification gives is velocity written as m s⁻¹. Treat this as an examinable detail of the Units topic rather than as background.

The two ways it shows up in questions

Sometimes a maths question hands you quantities carrying prefixes and expects you to convert before comparing or substituting. More often it appears inside a Physics or Chemistry stem, and those modules officially assume you already have the Maths 1 content.

How to drill it

Learn the prefixes as a number line of powers of ten rather than as a flashcard table, so that milli to micro being three orders of magnitude, and micro to nano being another three, becomes automatic rather than recalled. Then practise reading and writing negative-index units specifically: the convention the specification uses may not match the fraction-line notation in your school textbook, and meeting it for the first time in the test centre costs a chunk of those 89 seconds, on every question that carries units.

No negative marking: three strategies that follow from it

The official line leaves no room for interpretation: your scores are based on the number of correct answers, you do not lose marks for incorrect answers, and "it's worth attempting all questions". The specification puts it in scoring terms: each correct answer scores one mark, no marks are deducted, and results for each module are reported separately. Three things follow directly.

01First

No blanks, ever

Leaving one of 27 unanswered has a strictly lower expected value than picking something. That is arithmetic, not exam technique.

02Second

Final minute: fill first, check second

When the clock reaches the final minute, fill every unanswered item before you go back to check anything. Doing it the other way round is how candidates submit with gaps.

03Third

Eliminate before you guess

Knocking out even one implausible option lifts your odds, and elimination often takes a single order-of-magnitude estimate or a dimensional check rather than a full solution. This is where all that estimation practice actually pays.

One related rule is worth knowing: "You must not share or discuss the test with anyone else." That is a matter of conduct, and it is also why circulating recollections of past questions are unreliable. Treating them as evidence of what is in scope is a bad bet when a published specification exists.

III

Part 3 of 3

Sections 09 to 10

How your Maths 1 score is reported, and why chasing a target number fails

Every module is scored on its own: "Results for each module are reported on a scale from 1 (low) to 9 (high) to one decimal place." You receive a separate score for each module you sit, and there is no aggregate total. ESAT modules are equated and scaled separately, which is a real difference from the TMUA, where the two papers are combined into a single overall score.

Pass mark

None

"There is no pass/fail score for the ESAT"; scores are used alongside the rest of the application

Grade boundaries

None published

Imperial states there aren't any grade boundaries or pass marks for the ESAT or TMUA

Score appeals

Not accepted

Delivery

Matched course by course against your UCAS application and sent automatically

Candidates cannot choose who sees a score

Imperial College London, the one university that has published department-level ESAT data at all, warns alongside those figures that they are historic, that a high score does not guarantee an offer and that a low score does not rule you out. So any claim that some particular number is safe or competitive has no official basis behind it, and we are not going to invent one. What you can control is the number of questions you get right, and what you can train is speed and accuracy.

2026 – 2027Timeline

Nov 26

Dec 26

Jan 27

Feb 27

October sitting results

16 Nov 2026

Results day for the October sitting in the 2027 entry cycle, notified through your UAT-UK account.

January sitting results

8 Feb 2027

Results day for the January sitting in the 2027 entry cycle, notified through your UAT-UK account.

Hard deadline Event WindowOfficially, results arrive roughly four weeks after your sitting; the two dates above are the exact ones.

Narrow is not easy: a workable order for Maths 1 revision

Put the previous sections together and the revision order for Maths 1 is dictated by the rules rather than chosen by taste.

01Step 1

Audit your materials against the seven topics

Remove anything that has drifted in from Mathematics 2: trigonometry, calculus and graphs of functions all go, unless you are actually entered for Maths 2.

02Step 2

Put the calculator away: Number and Ratio first

Use Number and Ratio and proportion for pure hand-calculation work, until cancelling, estimating, converting units and switching between fractions, decimals and percentages happen without hesitating.

03Step 3

Drill Units: SI prefixes and negative indices

The smallest investment with the widest reach, because it resurfaces inside your science modules.

04Step 4

M4 to M7 by weakness, against the clock

Work through Algebra, Geometry, Statistics and Probability in whatever order your own weaknesses dictate, and do it timed. Untimed practice trains a different skill from the one being assessed.

05Step 5

Full-shape mocks, back to back

Run your modules back to back with nothing in between, because the thing you are really rehearsing is your accuracy in the second half of the last module.

One honest note about materials. 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 to all candidates. We are not affiliated with UAT-UK, Pearson or any university, and we do not speak for them. Treat the official specification and preparation materials as your primary source, and third-party material, ours included, as extra volume and explanation on top; where anything conflicts, the official PDF is the one that counts.

FAQ

Frequently asked questions

Does ESAT Mathematics 1 include trigonometry?

No. Appendix 1 of the official Content Specification lists seven topics for Mathematics 1: Units, Number, Ratio and proportion, Algebra, Geometry, Statistics and Probability. Trigonometry is not among them. It sits in Mathematics 2 as MM4. We searched the Geometry topic word by word for trigonometry, sine, cosine and tangent and found no occurrences. If you are not entered for Mathematics 2, revising trigonometry has no direct value for this test.

What is the difference between Mathematics 1 and Mathematics 2?

Mathematics 1 is the compulsory module with seven topics: Units, Number, Ratio and proportion, Algebra, Geometry, Statistics and Probability. Mathematics 2 is a separate optional module with eight: Algebra and functions, Sequences and series, Coordinate geometry in the (x, y)-plane, Trigonometry, Exponentials and logarithms, Differentiation, Integration, and Graphs of functions. Trigonometry, logs, calculus and graph work all live on the Maths 2 side. The specification also states that every module, Maths 2 included, assumes the Maths 1 content, so the two stack rather than sit side by side. Whether you take Maths 2 is decided by the course you are applying to, not by preference.

Can I use a calculator in Maths 1, and what does the centre provide?

You cannot. The official position is that no calculator and no dictionary may be used, and the FAQ states specifically that calculators are permitted in neither the ESAT nor the TMUA. The centre supplies erasable working material and a pen, described on different official pages as an erasable booklet, an erasable notebook and a whiteboard, and you can raise your hand at any point during the test for a replacement. In practice your mental and written arithmetic speed converts directly into marks, so practise without a calculator from the very start.

Does everyone have to sit Maths 1, or do some courses skip it?

Everyone sits it. The official wording is "All candidates need to sit Maths 1", with most candidates taking two further modules, which is why the test runs to 120 minutes for most people. Even courses that need only two modules in total include it, such as Imperial's MEng Design Engineering (28G3), which takes Mathematics 1 plus Mathematics 2. Note also that module selections cannot be changed without cancelling and re-booking; that if you apply to two courses which both require the ESAT, your selection must follow the one that names compulsory modules; and that you may sit only once per admission cycle, with the October 2026 and January 2027 sittings counting as the same cycle for 2027 entry.

What Maths 1 score is good enough? Is there a pass mark?

There is no pass mark and no published boundary. The official statement is that there is no pass/fail score for the ESAT and that scores are used alongside the rest of your application. Imperial College London, the only university to have published department-level data, says the same thing plainly: there aren't any grade boundaries or pass marks for the ESAT or TMUA, and a high score does not guarantee an offer while a low one does not rule you out. Any figure you see quoted as safe or competitive has no official source, and we will not invent one. What is fixed is how the score is reported: separately for each module, on a 1 to 9 scale to one decimal place, with each module equated and scaled on its own and no combined total. The variable you can actually train is the number of questions you get right.

What if I cannot finish 27 questions in 40 minutes? Guess or leave blank?

Guess. There is no negative marking and each correct answer scores one mark, so leaving a blank is strictly worse than picking something. Three practical habits: in the final minute, fill every unanswered item before you go back to check anything; before guessing, eliminate one or two implausible options, which an order-of-magnitude estimate or a dimensional check will often do on its own; and flag and move on from any question that has run past two minutes without a clear route. Remember too that each module is separately timed with no carry-over and no breaks between modules, so time saved in Maths 1 can only ever be reinvested in Maths 1.

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