Universities · Admissions tests · 2027 entry
The TMUA and ESAT, for Imperial applicants.
What each test is, who sits it, the dates for this cycle, and where the free official practice is. Then an honest list of what our own drills can and cannot do for you.
simplytk is independent: it is not affiliated with, endorsed by or connected to Imperial College London, UAT-UK or UCAS. The practice questions here are original and are not real interview or test questions. Last checked on 10 November 2026.
Start with the official materials.
UAT-UK runs both tests. It says its free materials are all you need, and it does not endorse any paid preparation. That includes this site. So do these first:
- Read the specification for your test, so you know exactly what can come up.
- Work through the past papers, which come with worked answers, under timed conditions.
- Sit the two practice tests on the real test software, so the screen is familiar on the day.
- For TMUA Paper 2, read the Notes on Logic and Proof. Nothing else covers that content as well.
All of it is on UAT-UK's preparation page. Imperial's own guidance is on its admissions tests page.
Test of Mathematics for University Admission
TMUA
Who sits it at Imperial: Economics, Finance and Data Science, Mathematics, Computing, and Mathematics and Computer Science.
Paper 1: Applications of Mathematical Knowledge
20 questions in 75 minutes
AS-level pure maths (algebra and functions, sequences and series, coordinate geometry, trigonometry, exponentials and logarithms, differentiation, integration, graphs) and Higher GCSE maths, applied to unfamiliar problems.
Paper 2: Mathematical Reasoning
20 questions in 75 minutes
The same maths, plus the logic of arguments (if and only if, converse and contrapositive, necessary and sufficient, for all and there exists, negation), proof, and spotting the error in a proof.
Engineering and Science Admissions Test
ESAT
Who sits it at Imperial: Aeronautics, Chemical, Civil, Design, Electrical and Mechanical Engineering, Physics and Life Sciences. Your department fixes the modules.
Mathematics 1
27 questions in 40 minutes
Higher GCSE maths: number, ratio and proportion, algebra, geometry, statistics and probability. Every other module assumes it.
Mathematics 2
27 questions in 40 minutes
AS-level pure maths, the same content list as TMUA Paper 1.
Physics
27 questions in 40 minutes
Electricity, magnetism, mechanics, thermal physics, matter, waves and radioactivity.
Chemistry
27 questions in 40 minutes
Atomic structure, bonding, quantitative chemistry, redox, rates, energetics, organic chemistry and the rest of the published list.
Biology
27 questions in 40 minutes
Cells, inheritance, DNA and gene technologies, enzymes, physiology and ecosystems.
| Department | Modules |
|---|---|
| Electrical and Electronic Engineering (including Electronic and Information Engineering) | Mathematics 1, Mathematics 2 and Physics. |
| Aeronautical Engineering | Mathematics 1, Mathematics 2 and Physics. |
| Mechanical Engineering | Mathematics 1, Mathematics 2 and Physics. |
| Design Engineering | Two modules only: Mathematics 1 and Mathematics 2. |
| Civil Engineering | Mathematics 1, Mathematics 2 and Physics. |
| Chemical Engineering | Mathematics 1, Mathematics 2 and Chemistry. |
| Physics | Mathematics 1, Mathematics 2 and Physics. |
| Life Sciences (Biochemistry, Biological Sciences, Biotechnology and related courses) | Mathematics 1, Chemistry and Biology. |
Dates and fees.
Both tests share the same sittings. A sitting costs £78 in the UK and Ireland and £133 elsewhere. The fee depends on where you sit the test, not where you live. A bursary covers the whole fee for eligible UK candidates and has to be approved before you book. Bursary rules.
12 to 16 October 2026
First TMUA and ESAT sitting
The October test window. Imperial accepts either sitting, and you can sit each test only once in a cycle.
16 November 2026
October test results released
Scores for the October sitting appear in your UAT-UK account. Universities receive them directly.
7 December 2026
Access arrangements deadline for the January sitting
18:00. Apply before this if you need extra time or other adjustments in the test.
14 December 2026
Bursary deadline for the January sitting
18:00. The bursary covers the whole test fee for eligible UK candidates, and it has to be approved before you book.
21 December 2026
Booking closes for the January sitting
18:00. After this you cannot book the TMUA or ESAT for 2027 entry.
4 to 8 January 2027
Second TMUA and ESAT sitting
The last test window for 2027 entry.
8 February 2027
January test results released
Scores for the January sitting appear in your UAT-UK account.
UAT-UK's key dates. The rest of the cycle, including the UCAS deadline, is on the Universities page.
What our drills train, and what they do not.
The drills on simplytk were built for the online tests employers send, not for these exams. None of them teaches the syllabus, and none is a mock paper. What they do train is the layer underneath: arithmetic without a calculator, reading data quickly, and careful reasoning against a clock. Use them as a warm-up beside the official papers, not in place of them.
One difference to keep in mind: a few drills take a mark off for a wrong answer. The TMUA and ESAT never do, so in the real test answer every question.
- Mental MathsFree
Trains: Fast, accurate arithmetic with no calculator: products, decimals, fractions and percentages. Both tests ban calculators, and slow arithmetic is where the time goes.
Does not cover: Algebra, calculus or anything else on the syllabus.
- Fast FractionsFree
Trains: Moving between fractions and decimals without thinking, which the number and ratio questions lean on.
Does not cover: Problem solving: it is a fluency drill and nothing more.
- SequencesFree
Trains: Spotting the rule behind a run of numbers quickly.
Does not cover: The sequences and series content itself: nth terms, arithmetic and geometric series, and the binomial expansion.
Trains: Reading a table carefully under time pressure, choosing the right base for a percentage, and estimating to rule options out.
Does not cover: Maths beyond GCSE number work. The questions are business tables.
Trains: Careful reading of statements with all, some and none, and deciding what must follow from them.
Does not cover: TMUA Paper 2's own logic: converse and contrapositive, necessary and sufficient conditions, negation, and finding the error in a proof. Use the official Notes on Logic and Proof for those.
- ProbabilityFree
Trains: Quick probability with dice, cards and conditional questions.
Does not cover: It goes beyond the GCSE probability the tests set, in the style of trading interviews, and it takes a mark off for a wrong answer, which the tests do not.
- Fermi EstimationFree
Trains: Estimating with round numbers and powers of ten, which is how you check an answer when there is no calculator.
Does not cover: Any test content. It is more use for the interview than for the tests.
Applying for Economics, Finance and Data Science? The interview comes after the test. Practise the interview, or go back to every stage of the application.