ESAT preparation
Original mock papers for the ESAT Mathematics 1, Physics and Mathematics 2 modules, with full worked solutions and diagrams. They are written to be harder and longer than the real thing, so the real test feels roomy.
How to use these papers
A good routine: sit a module timed in ESAT Drill (27 questions, 40 minutes, no calculator; Sets C, D and E have all three modules most engineering and physics applicants sit), then go through every question with its worked solution, including the ones you got right. Use topic practice to drill whatever cost you the most marks.
ESAT mock papers
Newest first, free for everyone. Each paper is a full module: 27 questions in 40 minutes. The numbers are difficulty ratings on the site's 4.5 to 9.0 scale.
ESAT Set E
A full ESAT sitting with extra weight on functions, graphs and integration: graphs to read cleverly, areas found by symmetry and rearrangement, and physics built on gradients and areas under graphs.
ESAT Set D
Pitched between Sets A and B: varied papers with several unfamiliar problems that need a strategy found on the spot. Now with a Physics module, so the set is a full ESAT sitting.
ESAT Set C
Pitched between Sets A and B, with the most unfamiliar-format problems of any set: new rules, processes and puzzles to reason about from scratch. Includes a Physics module.
ESAT Set B
Far harder than Set A: long, wordy multi-step problems, strictly within the ESAT specification. Built for candidates who found Set A comfortable.
ESAT Set A
The first ESAT set: quick to state, and a good first timed attempt.
How the ESAT works
The Engineering and Science Admissions Test is set by UAT-UK and used by Cambridge, Oxford, Imperial and UCL for engineering, physics, natural sciences and related courses. From 2026 (for 2027 entry) Oxford uses it too, for courses including Engineering Science and Physics. Check each course page for the modules it needs, and the official ESAT page for dates and rules.
Mathematics 1 covers number, ratio, algebra, geometry, statistics and probability, at GCSE Higher and a little beyond. Physics covers electricity, magnetism, mechanics, thermal physics, matter, waves and radioactivity at GCSE level, applied in unfamiliar contexts; the mocks take g = 10 N kg−1. Mathematics 2 covers A-level pure: algebra and functions, sequences and series, coordinate geometry, trigonometry, exponentials and logarithms, differentiation, integration and graphs.
Practice tools
ESAT Drill
A full module under exam conditions: answer grid, flags, a 40-minute clock, then marking and every worked solution.
Topic practice
Pick topics such as geometry, probability or integration; questions come one at a time with the solution straight after.
TMUA papers
For harder Mathematics 2 practice: TMUA Paper 1 covers the same A-level pure content at a higher level.