ESAT Worked Solutions

The Engineering and Science Admissions Test (ESAT) is a computer-based admissions test set by UAT-UK, a collaboration between Imperial College London and the University of Cambridge, and delivered by Pearson VUE at test centres worldwide. It is used by Imperial College London, the University of Cambridge, the University of Oxford and UCL for a range of engineering and science courses.

It replaced the older ENGAA and NSAA papers, and at Oxford it replaces the Physics Aptitude Test (PAT) for Engineering Science, Physics, Physics and Philosophy, and Biomedical Sciences. If you sat mock papers labelled ENGAA or NSAA, they remain useful practice — the ESAT draws on the same material.

How the test is built

• Five modules exist: Mathematics 1, Mathematics 2, Physics, Chemistry and Biology.
• Mathematics 1 is compulsory for everyone. You then sit two further modules — usually three modules and 120 minutes in total.
• Each module is 40 minutes and 27 multiple-choice questions, separately timed. That is roughly 89 seconds per question, which is the single most important number on this page.
• No calculator and no formula sheet. Every arithmetic step has to be done by hand, which is why method choice matters more than raw ability.
• No negative marking. There is no penalty for a wrong answer, so never leave a question blank — a guess is strictly better than nothing.
• Each module is scored 1.0 to 9.0, reported to one decimal place. There is no pass mark; universities interpret the scores alongside the rest of your application.

When it is sat

There are two sittings in the cycle: 12–16 October 2026 and 4–8 January 2027. If you are applying to Cambridge or Oxford you must sit the October test. Imperial applicants may use either window. You must register in advance — failing to register for a test your course requires can invalidate the application, and no university will make an exception for it.

Securing an offer requires rapid pattern recognition and execution under pressure. The worked solutions on this site focus on the fastest correct route to each answer, because at 89 seconds a question the method you choose decides the score more often than the mathematics you know.

Mathematics 1 is fixed. The two remaining choices are where candidates lose marks before the test even begins — and you cannot change your modules on test day, so the decision is made at booking.

Many courses specify which modules you must take. Where they do, there is no choice to make: take what the course names. Check your own course page before booking, because these requirements are revised between cycles.

Imperial College London

Imperial names the required modules by department:

University of Cambridge

The ESAT is required for Engineering, Natural Sciences, Chemical Engineering and Biotechnology, and Veterinary Medicine. Engineering applicants take Mathematics 1, Mathematics 2 and Physics. Natural Sciences applicants choose the two optional modules that match the subjects they intend to study. Cambridge applicants must sit the October test.

University of Oxford

Oxford uses the ESAT for Engineering Science, Physics, Physics and Philosophy and Biomedical Sciences, in place of the PAT. Oxford applicants sit the October test. Past PAT papers remain worthwhile preparation for interview even though the test itself has changed.

If you genuinely have a free choice

• Take Mathematics 2 if you are able to. It is pure mathematics with no statistics and no probability at all, it overlaps heavily with Mathematics 1, and preparation for one improves the other. It is also the module where a strong candidate can most reliably separate themselves.
• Pick the science you are furthest ahead in, not the one you enjoy most. The syllabus is fixed and shallow; what varies is how much of it you have already met.
• Check the overlap with your A-level timetable. A module whose content you are covering in class in September is far cheaper to prepare than one you finished last year.
• Do not choose a module because it looks easier. Scores are reported per module and read in context; there is no advantage in an easy module you have not prepared.

Module requirements and test dates are set by the universities and change between admissions cycles. Treat everything above as a starting point and confirm it against the official pages linked at the foot of this page before you book.

The questions candidates and parents ask most often, answered from the official specification and the universities' own pages rather than from impression. Every answer is expanded on somewhere above.

Requirements, dates and scoring are set by UAT-UK and the universities and are revised between cycles. Confirm anything you are about to act on against the official sources below.

Everything on this page is written from the documents below. Where a preparation site and an official page disagree, the official page wins — and requirements are revised between admissions cycles, so check these before you book anything.

The test itself — UAT-UK

• About the ESAT — structure, scoring, test dates, registration deadlines and the list of universities that use it.
• ESAT Content Specification (PDF) — the definitive syllabus. Appendix 1 lists every assessable sub-topic, and is the document the tables above are counted from.
• Preparation materials — official subject guides, plus the full archive of ENGAA and NSAA past papers from 2016 to 2023 with answer keys. These are the closest thing to real past papers that exists.
• ESAT Guide: Mathematics 1 (PDF) and Notes on Mathematics for Mathematics 2 (PDF) — the two documents that matter most for the practice sets on this page.

The universities

• Imperial College London — ESAT. The clearest of the three on module requirements: it names the modules department by department, and it is the only one of Cambridge, Oxford and Imperial that lets you sit the January window.
• University of Cambridge — admissions tests. Lists which courses require the ESAT; the individual course pages carry the module detail.
• Oxford — Engineering Science and the ESAT and Oxford Physics — the ESAT. The Physics department page also keeps the PAT past papers online, which remain useful preparation even though the PAT itself has been replaced.
• UCL also uses the ESAT for some courses. Its requirements are listed on the individual UCL course pages rather than in one place, so start from the course you are applying to.

External links open in a new tab and are maintained by the universities and UAT-UK, not by this site. If one of them contradicts anything written here, follow the official page and please let me know so it can be corrected.