ESAT Mathematics 1: the seven topics, and what is not in 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. There is no eighth.

Some third-party material folds trigonometry into Mathematics 1. It is not there. Trigonometry is MM4 in Mathematics 2. Functions and their graphs are MM1 and MM8. Differentiation and integration are MM6 and MM7. We searched the Geometry topic of the specification word by word for trigonometry, sine, cosine and tangent, and found nothing.

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 of which are 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.

In the table below, the middle column is the official topic heading. The third column 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.

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 rather than rhetorical. It maps each module onto topic tags: Biology draws on the B topics plus the M topics, Chemistry on C plus M, Physics on P plus M, and Mathematics 2 on M plus MM. The M tags, which are exactly the seven Maths 1 topics, appear in every module you can possibly sit. There is no route through the ESAT that avoids them.

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.

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. Some courses fix them outright, such as Cambridge Engineering (H100), which specifies Mathematics 1, Mathematics 2 and Physics. Others leave them open: Cambridge Natural Sciences (BCF0), Cambridge Chemical Engineering and Biotechnology (H810) and Oxford Biomedical Sciences (BC98) all ask for Maths 1 plus any two of Biology, Chemistry, Physics and Mathematics 2. Note that Mathematics 2 counts as one of the free choices there, which candidates routinely overlook. A few courses need only two modules in total, such as Imperial's MEng Design Engineering (28G3), which takes Mathematics 1 and Mathematics 2. In every one of these cases, Maths 1 is in the list.

Two registration rules bite. First, your module selection cannot be changed without cancelling and re-booking the test. Second, if you are applying to two or more courses that require the ESAT and one of them has a free choice while another names compulsory modules, your selection must follow the course with the compulsory modules, or your application to that course may be invalid. Write out the full list of courses first, then tick the boxes. Doing it the other way round costs a re-booking.

Two more rules are just as irreversible, and they concern which sitting you take. You may sit each test only once per admission cycle, and the 2027 entry cycle counts the October 2026 and January 2027 sittings as one and the same cycle; registering again under a second account is treated as misconduct. 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 worth clearing up. UAT-UK says seven UK universities use one or more of its tests, but only four of them use the ESAT: Imperial College London, Cambridge, Oxford and UCL. Longer lists do circulate, usually because someone has read the roster of UAT-UK universities as a roster of ESAT universities. They are not the same thing. UCL requires the ESAT for Electronic and Electrical Engineering from September 2027 entry (or September 2028 deferred entry), again as Maths 1 plus any two modules.

Each module is 40 minutes and contains 27 multiple-choice questions. Those are the official numbers. Forty minutes is 2400 seconds, which divided by 27 gives roughly 89 seconds a question. That figure is arithmetic. Nowhere does the specification say how long any individual question should take.

So use it 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: however many modules you are entered for, run them back to back with nothing in between. If you only ever practise single 40-minute modules and then stop for tea, 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.

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 across official pages as an erasable booklet, an erasable notebook and a whiteboard, and you can raise your hand at any point during the test to ask for a fresh one.

This 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:

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.

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. It shows up in two ways. 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.

The drill is unglamorous. 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, because the convention the specification uses may not match the fraction-line notation in your school textbook. Meeting that formatting for the first time in the test centre costs you a chunk of those 89 seconds, and it costs it on every question that carries units.

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 for incorrect answers, and results for each module are reported separately.

Three things follow directly. First, no blanks, ever. Leaving one of 27 unanswered has a strictly lower expected value than picking something. That is arithmetic, not exam technique. 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. Third, 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.

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 equated and scaled together into a single overall score.

The part that matters most for planning: "There is no pass/fail score for the ESAT. Scores are typically used alongside other information provided as part of your university application." Imperial College London, the one university that has published department-level ESAT data at all, says alongside it that "there aren't any grade boundaries or pass marks for the ESAT or TMUA", and warns in the same breath that the figures 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.

The procedural facts, for completeness: results arrive roughly four weeks after your sitting, notified through your UAT-UK account. For 2027 entry those dates are 16 November 2026 for the October sitting and 8 February 2027 for the January sitting. Scores are matched course by course against your UCAS application and sent automatically to institutions whose courses require the test. Candidates cannot choose who sees a score, and appeals against scores are not accepted.

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

Start by auditing your materials against the seven topics and removing anything that has drifted in from Mathematics 2. Trigonometry, calculus and graphs of functions all go, unless you are actually entered for Maths 2. Next, put the calculator away and use Number and Ratio and proportion for pure hand-calculation work, with the goal of cancelling, estimating, converting units and switching between fractions, decimals and percentages without hesitating. Then take Units on its own and drill the SI prefixes and negative-index notation, which is the smallest investment with the widest reach because it resurfaces inside your science modules. After that, work through Algebra, Geometry, Statistics and Probability in whatever order your own weaknesses dictate, and do it against a clock. Untimed practice trains a different skill from the one being assessed. Finally, sit full-shape mocks with your modules back to back, 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 the official 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.