Free · 15 questions · About 20 minutes

ESAT Diagnostic

Fifteen mock ESAT questions written for this site, five each from Mathematics 1, Mathematics 2 and Physics. You get a score the moment you finish, a breakdown by module, and a link to the full worked solution for every question you got wrong.

Questions drawn from the free samples published on this site · No calculator, no formula sheet · Scored in your browser

Not sure where to start? 7 places to go

Start with your question

Why visitors arrive: You want to know how ready you actually are for the ESAT, without paying for a mock or booking anything.

Your question: How good am I at the ESAT right now, and what should I fix first?

You may also be asking

  • How many questions is it and how long does it take?
  • Are these real ESAT questions?
  • Will it predict my ESAT score?
  • Do I have to give my email to see the result?
  • What do I do about the questions I got wrong?

Where to go next

  • What it is: a 15-question sample of the ESAT, built from the same sample questions and worked solutions published free on this site.
  • What it tells you: which of the three modules is currently weakest, and which specific questions to go and read.
  • What it does not tell you: a predicted ESAT score. Fifteen questions cannot do that, and this page will not pretend otherwise.
  • Cost: nothing, and no account. Your email is asked for once, after the result, and the result is already on screen by then.
  • Next sitting: 12 to 16 October 2026. Cambridge and Oxford applicants must sit the October test.

Sit the diagnostic

[01] Before you start

  • 15 questions, five from each of Mathematics 1, Mathematics 2, Physics.
  • Roughly 20 minutes. The real test allows about 89 seconds a question. A timer runs, but nothing cuts you off.
  • No calculator, no formula sheet, exactly as on the day.
  • Every question is a real one from the sample questions published on this site, and every one you miss links straight to its worked solution.
  • Your score is yours. It is worked out in your browser and shown immediately. Sending it to yourself by email is optional and comes after the result.

How this is put together

[01] Published questions only

Nothing written for the quiz

Every one of the fifteen is lifted verbatim from the sample questions already published here, each with a full worked solution. Nothing was written to make the diagnostic look good, and nothing sits behind a signup.

[02] Balanced by module

Five, five and five

Mathematics 1 is compulsory for every candidate. Mathematics 2 and Physics are the two most commonly required options. Equal weight means the module comparison is a fair one.

[03] Timed, not gated

89 seconds is the number

The real test gives about 89 seconds per question. A clock runs so you can see your pace against that, but nothing cuts you off and running over does not affect the score.

Read how every solution on this site is checked before it is published, or go straight to the complete ESAT hub.

What a 15-question sample can and cannot do

Being straight about this matters more than the marketing would suggest, because acting on a bad signal costs a candidate weeks.

  • Module scores are usable. Five questions per module is a coarse instrument, but the gap between five out of five and one out of five is real information, and it is the fastest way to find out which module is quietly costing you the most.
  • Topic rows are a pointer, not a verdict. Most topic groups carry one or two questions. Treat a weak row as a suggestion about what to open first, not as evidence that the topic is a weakness.
  • Speed here is not speed on the day. You are sitting fifteen questions at a desk you chose, not twenty-seven under exam conditions in a test centre. To practise against a countdown, sit a practice set: every question in the practice sets can be taken as a timed test on its own page, marked the moment you finish.
  • There is no predicted grade. ESAT modules are scored 1.0 to 9.0 and the scaling is not published. Anyone converting fifteen questions into a predicted band is guessing.

Your answers and your email

  • Your answers stay in your browser. The diagnostic is scored on your own device and your answers are not sent anywhere unless you ask for the result by email.
  • Unfinished attempts are saved locally. If you close the tab part way through, your progress is kept in your browser's own storage on that device only, and you can pick up where you left off.
  • Email is optional and comes last. The score, the breakdown and every solution link are on screen before you are asked for anything.
  • If you do give it, the address is used to send the result and the ESAT preparation list, and for nothing else. See the privacy policy.

For individual preparation. These questions are free for a candidate working on their own. They are not licensed for a school, college or tutoring provider to print and run with a class, to republish or resell, or to fold into a course sold by another provider. A school sitting a timed mock is welcome to the free sample pack, which comes with mark schemes and a syllabus reference, and a paper written for your own candidates and used nowhere else is a commissioned pack.

About this work

Lucas Rey, aerothermal systems engineer and academic tutor.

  • University of Oxford: DPhil Researcher, Thermofluids Institute.
  • University of Cambridge: Alumnus.
  • Rolls-Royce: Sponsored researcher (High-pressure turbine programme).

This site documents peer-reviewed research, open curriculum, and premium STEM mentorship in one interconnected portfolio.

Full biography & services · Contact

Where to go from here

Every paper, practice set and guide on this site is free to read. These are the things worth doing next.

The diagnostic and the practice sets linked above are free and stay free. One-to-one places are limited and taken by application, not by the hour.