The ESAT specification, module by module
The ESAT is built from separate modules, each with its own specification. Knowing exactly which modules you need, and what each one covers, is the first step to preparing efficiently.
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How the modules work
The Engineering and Science Admissions Test is run by UAT-UK and used by Cambridge and Imperial for courses such as Engineering and Natural Sciences. It has five modules: Mathematics 1, Mathematics 2, Physics, Chemistry and Biology. Mathematics 1 is compulsory for everyone. You then take two further modules, chosen by the course you apply for. Engineering applicants, for example, typically take Mathematics 2 and Physics.
Each module has 27 multiple-choice questions in 40 minutes, so three modules take about two hours. Modules are timed separately: finishing one early does not give you extra time on the next. Calculators are not allowed. Each module is reported on its own scale, so universities can see your performance in each area. Check the official course requirements and the latest specification before you start, as details can change.
Mathematics 1
Mathematics 1 tests core mathematics, largely at GCSE level with some early A level material. Topics include number, ratio and proportion, algebra, sequences, geometry and measures, graphs, statistics and probability. The questions are not hard individually, but with 27 questions in 40 minutes you have under 90 seconds each, so fluency matters more than anything. Many strong students lose marks here through rushing and arithmetic slips.
Mathematics 2
Mathematics 2 goes further into pure A level mathematics: algebra and functions, sequences and series, coordinate geometry, trigonometry, exponentials and logarithms, and differentiation and integration. Questions often combine topics or ask you to reason about graphs and functions rather than run through a standard method.
Physics
The Physics module covers mechanics, electricity, waves, energy, matter and radioactivity, at GCSE and A level standard. The emphasis is on applying principles to unfamiliar situations, interpreting information and handling algebra, rather than recalling facts. Expect to rearrange equations symbolically and to estimate.
Chemistry and Biology
Natural Sciences and some medical or life science courses ask for Chemistry or Biology instead of, or as well as, Physics. These modules follow the same format and test GCSE and A level content applied to new contexts, such as balancing equations and calculating moles in Chemistry, or interpreting experimental data in Biology. This site focuses on maths and physics tutoring, so if your course needs Chemistry or Biology, use the official specification and practice materials for those modules.
How scores are used
Universities look at your ESAT results alongside your predicted grades, personal statement, school reference and, for Cambridge, interviews. There is no pass mark. A strong result in the modules most relevant to your course helps, but no single number decides an application. Focus on doing your best in each module rather than chasing a target score.
Example questions by module
These are original questions in the style of the ESAT, written to show what each module asks for.
Mathematics 1: ratio
Red and blue counters are in the ratio 3 : 5. After 12 red counters are added, the ratio is 1 : 1. How many counters were there at the start?
- Let red = 3k and blue = 5k. Then 3k + 12 = 5k, so k = 6.
- Start: 18 + 30 = 48 counters.
Mathematics 1: probability
Two fair dice are rolled. What is the probability that the total is 9?
- Pairs: (3, 6), (4, 5), (5, 4), (6, 3), which is 4 of 36.
- 1/9.
Mathematics 2: a function
f(x) = 2x + 3 and g(x) = x². Solve f(g(x)) = g(f(x)).
- f(g(x)) = 2x² + 3 and g(f(x)) = 4x² + 12x + 9.
- 2x² + 3 = 4x² + 12x + 9 gives x² + 6x + 3 = 0, so x = −3 ± √6.
Mathematics 2: an area
Find the area enclosed between y = x² and y = 2x.
- They meet at x = 0 and x = 2. Area = ∫02 (2x − x²) dx = [x² − x³/3] = 4 − 8/3.
- 4/3.
Physics: energy and power
A 1.2 kW motor lifts a 60 kg load at constant speed. If the motor is 75% efficient, how fast does the load rise? (g = 10 m/s²)
- Useful power = 0.75 × 1200 = 900 W = mgv.
- v = 900/(60 × 10) = 1.5 m/s.
Physics: circuits
Three identical 6 Ω resistors are connected with two in parallel and the third in series with that pair. The supply is 18 V. Find the current through the series resistor.
- Parallel pair: 3 Ω. Total: 9 Ω.
- I = 18/9 = 2 A.
Working without a calculator
ESAT numbers are designed to work out neatly, often using g = 10 m/s². If your arithmetic becomes messy, re-read the question; you may have made a slip. Keep algebra symbolic until the last step, and cancel before multiplying. Learn square numbers, common surds, and exact trigonometric values, and practise estimating: rough answers can often rule out three of the options at once.
Turning the specification into a plan
- Confirm the modules your course requires on the university's admissions page.
- Download the official specification for each of your modules and mark every topic as secure, shaky or new.
- Prioritise Mathematics 1 fluency early, because every module depends on fast algebra.
- Revise shaky topics, then practise timed sets of 27 questions in 40 minutes.
- Use official practice papers last, under real timings, and keep an error log by topic.
Common mistakes
- Preparing for the wrong modules; check your course first.
- Under-estimating Mathematics 1; it is a speed test.
- Practising with a calculator.
- Spending too long on one question; with 40 minutes per module, move on and come back.
Practice questions
Try each one before opening the answer.
Q1. How many modules do most ESAT candidates take, and which one is compulsory?
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Q2. Roughly how long do you have per question in an ESAT module?
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Q3. A car accelerates uniformly from rest to 20 m/s in 4 s. How far does it travel?
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Frequently asked questions
Which universities use the ESAT?
Cambridge and Imperial use it for a range of engineering and science courses. Requirements vary by course and can change, so always check the course page.
Is the ESAT harder than A level?
The content is mostly GCSE and A level, but the time pressure and unfamiliar question styles make it feel harder. Practice under timed conditions closes most of that gap.
Key takeaways
- Mathematics 1 is compulsory; most candidates take two more modules.
- Each module: 27 questions, 40 minutes, no calculator.
- Mathematics 1 rewards speed and accuracy.
- Mathematics 2 and Physics reward applying ideas to new situations.
- Plan revision from the official specification for your modules.