A Free ESAT Mock Paper, Every Module
Lucas Rey · Oxford DPhil · Cambridge MRes
All five modules, the first 10 questions of each, with the full worked solutions, mark schemes, answer sheets and invigilator instructions. 23 documents, no sign-up. Every question here is a real one from a commissioned paper, shown in full.
- What it is: a full ESAT mock sitting: Mathematics 1, Mathematics 2, Physics, Chemistry, Biology.
- Format: 27 multiple-choice questions per module, 40 minutes each, no calculator, exactly as the UAT-UK content specification sets out.
- How much of it is here: the first 10 questions of every module, in full. Each file is the length of the real one, so you can see how long a commissioned paper runs; past question 10 the pages carry a note rather than questions.
- Cost: free, and free to use with your own students. Not for resale or republication.
- Calibration: question length and diagram share are measured against the 648 official ENGAA and NSAA questions UAT-UK publishes, not against our own opinion of what a question should look like.
Download the pack
Every document is a PDF, watermarked as a sample. Start with the invigilator instructions if you are setting it as a mock.
Mathematics 1
- Question paper: the first 10 questions, laid out exactly as the full paper is
- Answer sheet: a separate grid, so the paper can be reused and marking is mechanical
- Mark scheme: the keys and nothing else, so marking needs no subject knowledge
- Worked solutions: every question re-derived, every wrong option explained
Mathematics 2
- Question paper: the first 10 questions, laid out exactly as the full paper is
- Answer sheet: a separate grid, so the paper can be reused and marking is mechanical
- Mark scheme: the keys and nothing else, so marking needs no subject knowledge
- Worked solutions: every question re-derived, every wrong option explained
Physics
- Question paper: the first 10 questions, laid out exactly as the full paper is
- Answer sheet: a separate grid, so the paper can be reused and marking is mechanical
- Mark scheme: the keys and nothing else, so marking needs no subject knowledge
- Worked solutions: every question re-derived, every wrong option explained
Chemistry
- Question paper: the first 10 questions, laid out exactly as the full paper is
- Answer sheet: a separate grid, so the paper can be reused and marking is mechanical
- Mark scheme: the keys and nothing else, so marking needs no subject knowledge
- Worked solutions: every question re-derived, every wrong option explained
Biology
- Question paper: the first 10 questions, laid out exactly as the full paper is
- Answer sheet: a separate grid, so the paper can be reused and marking is mechanical
- Mark scheme: the keys and nothing else, so marking needs no subject knowledge
- Worked solutions: every question re-derived, every wrong option explained
Whole pack
- Covering letter: what the pack is, how it was checked, and what it does not do
- Invigilator instructions: how to run the sitting, so you do not have to invent it
- The whole extract, one document: all 22 documents in one bookmarked PDF, in reading order
Want the whole paper?
The pack above stops at question 10 because the rest of it belongs to the school it was written for. A commissioned pack is 27 questions in every module, with the same worked solutions, mark schemes, answer sheets and invigilator instructions, drawn fresh from the bank, recorded against your school and issued to nobody else.
- Written by researchers in engineering, physics and mathematics at Oxford and Cambridge.
- Checked question by question before it is issued, against the same rules every question in this extract was held to.
- Unseen. Your questions are published nowhere, including on this page.
- Ready to sit: printed pack, answer sheets, mark scheme, invigilator instructions.
How these papers are made
Who writes the questions, and how they are checked
Our researchers write them. Doctoral researchers and recent graduates in engineering, physics and mathematics at Oxford and Cambridge, who have sat these papers themselves and teach the subjects. Every question in this pack was written by one of them.
Then every question is checked by software we developed ourselves, in house, for exactly this work: fixed rules where an answer has to be exact, and AI where the question needs judgement. This is the part we would point at first. Someone reading 135 questions is sharp on the first and tired by the hundredth; the checks are not. On every question, every time a paper is built, they:
- work the question out again from scratch, without being told the intended answer, and have to arrive at the same one
- confirm no second option is also correct
- confirm every wrong option is one a student could really reach, and name the mistake that gets them there
Nothing goes into a paper until it has passed all of it. That is why the worked solutions can tell a student what reasoning led them to C, rather than only that the answer was B.
What this pack does, and what it does not
A mock paper that overstates its own fidelity is worse than one that admits its limits, so here are both, measured rather than asserted.
Measured against the official papers
- Question length is matched to the published distribution per module, not to a single average. Real modules differ enormously: Mathematics 1 a median of 32 words, Mathematics 2 a median of 22 words, Physics a median of 64 words, Chemistry a median of 56 words, Biology a median of 80 words.
- Diagram share in the published papers runs Mathematics 1 16%, Mathematics 2 4%, Physics 28%, Chemistry 9%, Biology 45%. A flat target would put four diagrams in a paper that really carries one and starve another of two thirds of its own, so this pack is built to the per-module share rather than an average.
- What this pack actually carries: Mathematics 1 5 of about 4, Mathematics 2 0 of about 1, Physics 7 of about 7, Chemistry 3 of about 3, Biology 10 of about 12.
Where it differs from the real test
- Option counts vary, as they do on the real paper. This pack runs 44 questions with 5, 34 questions with 6, 15 questions with 7, 42 questions with 8, so a blind guess pays about 16 percent here against roughly 14 percent across the official questions. Closer than a five-option paper, which pays 20, but still read a raw mark as a slight overestimate.
- It is on paper, which is what makes it usable in a classroom. You can print it, sit a whole cohort under timed conditions, and mark it in the room the same afternoon, with no device and no account for anyone. The real ESAT is sat on screen at a Pearson test centre, so a printed mock trains the mathematics and the pacing but not the interface. Use the official on-screen practice at least once for that, or one of the free timed modules on this site, which run in the browser and mark themselves.
- The worked solutions go further than the published papers do. The historic ENGAA and NSAA papers ship an answer key and nothing else, and while the official specimen tests do explain their answers, no full-length paper in the current format shows its working. So every solution here, the named error behind every wrong option included, is work the official material does not offer at this length. The honest consequence is that how much effort a question demands is calibrated against our own reference papers rather than against theirs, because theirs do not show it. Question length and diagram share, above, are measured against UAT-UK directly.
How it was checked
Every question was independently re-derived from its own stem, its key confirmed as uniquely correct, and each wrong option traced to a specific error that produces that exact value. The pack is then checked mechanically against the specification: question counts, timing, syllabus placement, calculator-free arithmetic, unit notation, and that no answer appears anywhere in a question paper.
One thing worth saying plainly: nobody has read this pack cover to cover in one sitting. The verification is automated checks plus independent per-question review, which is a real method with a real limit, and the limit is better stated than implied.
Frequently asked questions
Are there any ESAT past papers?
No. The ESAT was first sat in 2024 and UAT-UK has not released a past paper for it. What the official site publishes is five subject guides and the 16 historic ENGAA and NSAA papers, 2016 to 2023, each with an answer key, with a note in the papers where a question falls outside the ESAT specification. Those predecessor papers are the closest thing to official practice that exists, and everything else you will find online is a copy of them.
What about the official ESAT specimen questions?
They exist and you should sit them, but they are short. Pearson VUE hosts a specimen test and a sample exam for each of the five subjects, both running in the real on-screen test player, and the specimen tests explain the answer to every question. What they do not give you is a full-length timed sitting: this pack is that, on paper, at the official 27 questions in 40 minutes.
Can I use ENGAA and NSAA past papers to prepare for the ESAT?
Yes, and you should: the ESAT draws on the same material. Two limits are worth knowing. They are in the old format rather than the current five modules of 27 questions in 40 minutes, and they ship an answer key with no worked solutions, so a question you get wrong tells you only that you were wrong. This pack is written in the current format, and every question is worked.
Where can I get free ESAT practice papers with worked solutions?
Here, and without an account. This is an extract from a commissioned pack: the first 10 questions of each of the 5 modules, 23 documents in all, with the worked solutions in full. There is no sign-up, no email address to give and nothing to pay. The full paper carries 27 questions per module and is written for one school at a time.
Is this an official ESAT paper?
No, and no unofficial paper should claim to be. It is written independently by Lucas Rey, an Oxford engineering doctoral researcher, and calibrated against the official material rather than against an opinion: question length and diagram share are measured against the 648 questions UAT-UK publishes. The section above sets out where it differs from the real test.
Can a school set this as a timed mock?
Yes, and it is built for that. The pack includes invigilator instructions, separate answer sheets so papers can be reused, and a mark scheme that is keys only, so marking needs no subject knowledge. It is free to use with your own students. It is not for resale or republication.
Will my students have seen these questions before?
Possibly, because this pack is published, and that is exactly why only one is ever given away. A commissioned pack is drawn from a bank, recorded against your school, and issued to nobody else and published nowhere.
Commissioning an unseen pack
This pack is published, so your students may have seen it. A commissioned pack is different: its questions are drawn from a bank, recorded against your school, and never issued to anyone else or published here. That is the whole point of an unseen paper, and it is why only one pack is ever given away.
Papers are built to the same specification, in your school's name, dated to your sitting, and delivered as the same 23 documents.
Where to go from here
Everything on this page is free and stays free. These are the three things worth doing next.
- Take the 15-question ESAT diagnostic - Twenty minutes, scored instantly, with a worked solution for every question you miss
- Follow the dated preparation plan - Every ESAT page on this site, sequenced backwards from the October sitting
- Sitting another admissions test as well? - TMUA, PAT, MAT and STEP each have their own preparation page and free practice
- Join the ESAT preparation list - One email a week from June to October, and nothing else
- Enquire about one-to-one preparation - For candidates who want the gap closed rather than mapped
One-to-one places are limited and taken by application, not by the hour.