CALIBRATED PRACTICE ESAT
ESAT 2027 entry · booking closes 28 September 2026

MEET EVERY TRAP HERE,
NOT IN THE EXAM.

Every wrong option in these papers was built to catch one specific mistake, and the worked solution names it. All 135 of them.

Start with a complete mock paper, free.

One full ESAT Mathematics 1 paper with every worked solution. Not an extract, not a sample. 27 questions, 40 minutes, no calculator.

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One question, as the book treats it
MATHEMATICS 1 · PAPER 2 · Q14 WORKED SOLUTION

A right pyramid has a square base of side 6 cm and a perpendicular height of 4 cm. What is its total surface area, in cm2?

ROUTE

The slant height is not given and is not the same as the height. Get it from the right triangle on the apothem first, then everything else follows.

STEPS

1  apothem = 6 / 2 = 3

2  l = √(32 + 42) = 5

3  4 triangles = 4 × ½ × 6 × 5 = 60

4  base = 36, total = 96

TRAP

84 is what you get if you use 4 as the slant height instead of the perpendicular height. It is the single most common way to lose this question.

FASTER

3, 4, 5 is the first triple to test whenever a pyramid gives you an even base and a whole height. You should not be reaching for Pythagoras here.

The problem

THERE ARE NO ESAT PAST PAPERS.

The test is new. UAT‑UK publishes a content specification and a small number of specimen questions, and that is the whole official supply. For Oxford applicants it is worse still: the PAT is gone, so the archive everyone used to revise from no longer describes the exam you are sitting.

Which leaves one real risk. The most common way to walk into the ESAT under‑prepared is to have practised on questions that were easier than the real ones, and to have no way of knowing it.

Read: what the ESAT actually is
The mechanism

THREE THINGS NOBODY ELSE PRINTS.

01

A NAMED TRAP

Every wrong option was written to catch one specific error, and the solution tells you which one. You find out why you got it wrong, not just that you did.

“84 is what you get if you use 4 as the slant height instead of the perpendicular height.”

02

A ROUTE LINE

One sentence before any algebra, telling you how to see the question. The gap between a strong candidate and a weak one is usually the first ten seconds, not the working.

“Resolve along the slope, not along the ground.”

03

A FASTER NOTE

Wherever a genuine shortcut exists it is written down rather than assumed, and where none does the page does not pretend otherwise. The real module gives you roughly 89 seconds a question, so the long way round is not available to you.

“Power is the bridge between the two sides here, not the turns ratio.”

The series

FIVE FULL PAPERS PER MODULE, WITH EVERY SOLUTION IN THE SAME VOLUME.

Cambridge Engineering candidates sit Mathematics 1, Mathematics 2 and Physics. That is all three volumes.

ESAT Mathematics 1: Five Full Mock Papers — front cover
Papers
5 × 27 = 135
Named traps
135 of 135
Route line
135 of 135
Worked solution
135 of 135

Compulsory for every ESAT candidate, whatever the course. Start here.

Buy on Amazon · £19.99
ESAT Mathematics 2: Five Full Mock Papers — front cover
Papers
5 × 27 = 135
Named traps
135 of 135
Route line
135 of 135
Worked solution
135 of 135

Required for Cambridge Engineering, and taken by many candidates as one of their two optional modules.

Buy on Amazon · £19.99
ESAT Physics: Five Full Mock Papers — front cover
Papers
5 × 27 = 135
Named traps
135 of 135
Route line
135 of 135
Worked solution
135 of 135

Required for Cambridge Engineering. Commonly taken by physics and engineering applicants elsewhere, so check your course page.

Buy on Amazon · £19.99

Not affiliated with, endorsed by or connected to UAT-UK or any university. No official examination material is reproduced.

Before any of it was a book

SAT IN DRAFT BY REAL STUDENTS.

These papers were written for Carl's own students and used in real lessons long before they were typeset. Offer holders at Oxford, Cambridge and Imperial sat them in draft, and independent admissions consultants read them.

I had been getting questions right without knowing why, which turns out to be the dangerous kind of right.
Amelia Offer holder · Biomedical Sciences, Oxford
The shortcuts are the bit I use most. I was doing everything the long way and running out of time.
Ahmed Offer holder · Chemical Engineering, Imperial
The first paper was a shock. That was the point. I would much rather have had that shock in October than in the exam.
Matvei Offer holder · Physics, Oxford
Who wrote them

Carl Morris has tutored since 2008 and holds an MChem from the University of Oxford. He was Principal of a DfE‑registered tutorial college in Oxford and is Vice President of The Tutors' Association.

And what is checked, every build
  • Every answer key solved cold, with the key withheld
  • Every question mapped to a published specification heading
  • No single-step questions, and no two options of equal value
  • Four to eight options a question, so elimination will not save you
Common questions

ESAT QUESTIONS, ANSWERED PROPERLY.

What is the ESAT?

The Engineering and Science Admissions Test is a computer-based admissions test run by UAT-UK and used by the University of Cambridge, Imperial College London, the University of Oxford and UCL. Every candidate sits Mathematics 1, and most sit two further modules chosen from Biology, Chemistry, Physics and Mathematics 2 according to the course applied for. Each module is 27 multiple-choice questions in 40 minutes, taken without a calculator, and each is scored separately from 1 to 9 to one decimal place.

Has the ESAT replaced the Oxford PAT?

Yes, for 2027 entry. Oxford has moved to UAT-UK tests, and applicants for Physics and for Physics and Philosophy now sit the Engineering and Science Admissions Test (ESAT) rather than the Physics Aptitude Test (PAT). Practically, this means the PAT past-paper archive no longer describes the exam being sat: the ESAT is multiple choice, sharply time-limited at roughly 89 seconds a question, and taken without a calculator, where the PAT was a longer written paper.

Are there any ESAT past papers?

No. UAT-UK publishes a content specification and a small set of specimen questions, and does not release past papers. That is why practice material has to be written to the published specification and the real format, and why it matters whether that material was calibrated for difficulty or simply written to look plausible.

Which ESAT modules do I need?

Mathematics 1 is compulsory for every candidate sitting the Engineering and Science Admissions Test (ESAT), and most courses add two further modules, set or chosen by the course itself. Engineering and physics courses almost always take Mathematics 2 and Physics alongside it, chemistry and life-science courses tend to swap in Chemistry or Biology, and a small number take only one further module. Check your own course page before booking, because modules cannot be changed on test day.

The full course-by-course table, university by university →

When is the ESAT in 2026?

Booking for the October sitting of the Engineering and Science Admissions Test (ESAT) closes at 6pm BST on 28 September 2026, with the test running from 12 to 16 October and results on 16 November. A second sitting runs from 4 to 8 January 2027, booking closing on 21 December 2026 and results on 8 February 2027. Access arrangements and bursaries close earlier still, on 14 and 21 September, which is the deadline candidates most often miss.

Every deadline for both sittings →

How do you prepare for a test with no past papers?

By practising on questions written to the published specification at the real length and the real time pressure, and by making every mistake diagnosable. A practice question that tells you only whether you were right teaches you very little; one that names the specific error the wrong option was built to catch tells you what to fix. That, plus sitting complete 40-minute papers rather than untimed question sets, is most of the preparation.

SIT ONE PAPER
BEFORE YOU DECIDE.

A complete ESAT Mathematics 1 mock paper with every worked solution, free. If it is not harder than what you have been practising on, you have lost nothing but 40 minutes.

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