What is the ESAT?
The ESAT is the admissions test many applicants take for engineering and science at Cambridge and Imperial. Here is how it works and how to prepare.
On this page
- The ESAT in one paragraph
- Who needs it
- The modules
- What the maths and physics modules cover
- How is it scored?
- When do you take it?
- How to prepare
- Should you get an ESAT tutor?
- How the ESAT differs from school exams
- Mathematics 1 style examples
- Mathematics 2 style examples
- Physics style examples
- Working without a calculator
- Timing strategy
- Common mistakes
- Practice questions
- Frequently asked questions
- Key takeaways
- Where to go next
The ESAT in one paragraph
The Engineering and Science Admissions Test (ESAT) is a computer-based, multiple-choice test that checks how well you apply school maths and science to unfamiliar problems. It replaced Cambridge's earlier engineering and natural sciences admissions tests, and it is run by UAT-UK, the testing organisation set up by Cambridge and Imperial.
Who needs it
Cambridge and Imperial use the ESAT for courses such as Engineering, Natural Sciences and related science degrees. Requirements differ by course and can change from year to year, so check the admissions page for the exact course you are applying to.
The modules
The ESAT is made up of separate modules:
- Mathematics 1
- Mathematics 2
- Physics
- Chemistry
- Biology
You take the modules your course asks for, usually three. Engineering applicants, for example, typically take Mathematics 1, Mathematics 2 and Physics. Each module is a short, timed set of multiple-choice questions, and calculators are not allowed, so fast and accurate working matters.
What the maths and physics modules cover
- Mathematics 1: core GCSE and early A level maths, such as algebra, geometry, graphs and basic calculus.
- Mathematics 2: more demanding pure maths, closer to A level, including functions, trigonometry, sequences and calculus.
- Physics: mechanics, electricity, waves, energy and other GCSE and A level physics topics, applied to new situations.
How is it scored?
Each module is scored on a scale from 1.0 to 9.0. There is no pass mark. Universities compare your scores with other applicants for the same course.
When do you take it?
The ESAT is usually offered in autumn and early in the new year, and you need to register in advance. Dates and deadlines change every year, so check the UAT-UK website early.
How to prepare
- Check which modules you need for your course before you start.
- Make your core maths automatic. Mathematics 1 rewards speed, and every module leans on algebra.
- Practise without a calculator from the start.
- Use the official practice papers on the UAT-UK website, under real timings.
- Keep an error log and revisit the topics behind each mistake.
Should you get an ESAT tutor?
A tutor is most useful when you are aiming for a very competitive course, are short on time, or keep losing marks to timing. One-to-one sessions let you focus on the maths and physics question types that slow you down.
How the ESAT differs from school exams
At school, you usually know the type of question before you see it. In the ESAT, each question is short but unfamiliar, and you have little time. The test rewards students who understand the ideas well enough to apply them quickly, without a calculator, and who can see shortcuts. The content itself is mostly GCSE and A level, so preparation is about speed, accuracy and confidence rather than learning new topics.
Mathematics 1 style examples
These are original questions written in the style of each module, not official ones.
Example 1: simultaneous equations
Solve 2x + 3y = 12 and x − y = 1.
- From the second, x = y + 1. Substitute: 2y + 2 + 3y = 12, so y = 2 and x = 3.
Example 2: percentages
A price rises by 20% and then falls by 20%. What is the overall change?
- 1.2 × 0.8 = 0.96, so a 4% decrease. A common trap is to answer “no change”.
Example 3: surds
Simplify (3 + √2)(3 − √2).
- Difference of two squares: 9 − 2 = 7.
Mathematics 2 style examples
Example 4: geometric series
Find the sum to infinity of 8 + 4 + 2 + …
- a = 8, r = ½. S = a/(1 − r) = 16.
Example 5: stationary points
Find the x-coordinates of the stationary points of y = x³ − 3x.
- dy/dx = 3x² − 3 = 0, so x = ±1.
Example 6: trigonometric equations
How many solutions does 2cos²x = 1 have for 0° ≤ x < 360°?
- cos x = ±1/√2, giving x = 45°, 135°, 225°, 315°: four solutions.
Physics style examples
Example 7: free fall
A stone is dropped from rest from a height of 45 m. How long does it take to land? (g = 10 m/s²)
- s = ½gt²: 45 = 5t², so t = 3 s. The numbers are chosen to avoid a calculator.
Example 8: circuits
Two 6 Ω resistors in parallel are connected in series with a 3 Ω resistor across a 12 V supply. Find the current from the supply.
- Parallel pair = 3 Ω; total = 6 Ω. I = 12/6 = 2 A.
Example 9: energy
A 2 kg ball is dropped from 5 m. Find its speed just before landing, ignoring air resistance. (g = 10 m/s²)
- mgh = ½mv², so v = √(2gh) = √100 = 10 m/s. The mass cancels.
Working without a calculator
ESAT numbers are usually chosen to work out neatly, so if your arithmetic becomes messy, check whether you have taken a wrong turn. Learn squares up to 20², common surds, and the trigonometric values for 30°, 45° and 60°. Practise estimating: often only one of the answer options is the right size, so a rough estimate can confirm your answer or rule out others.
Timing strategy
Each module is short and fast-paced. Work through quickly, skipping any question that will take too long, and come back if time allows. There is no penalty for wrong answers, so answer every question. After practice papers, look at how long each question took you; most students find a few topics consistently slow them down, and fixing those has a big effect on the score.
Common mistakes
- Preparing for the wrong modules; check your course requirements first.
- Relying on a calculator during practice.
- Neglecting Mathematics 1 because it looks easy; it is a speed test.
- Not reviewing mistakes after practice papers.
Practice questions
Try each one before opening the answer.
Q1. Rearrange v² = u² + 2as to make a the subject.
Show answer
Q2. A wave has frequency 50 Hz and wavelength 4 m. Find its speed.
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Q3. Find the gradient of the line through (1, 2) and (4, 11).
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Q4. A 60 W lamp is on for 10 s. How much energy does it transfer?
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Frequently asked questions
Which ESAT modules should I take?
It depends on your course. Engineering applicants usually take Mathematics 1, Mathematics 2 and Physics; science courses vary. Check the university's admissions page for the exact course.
Is the ESAT the same as the old ENGAA and NSAA?
It replaced them. The style is similar, multiple choice and calculator free, but the modular structure is new, so use ESAT practice materials first.
How long should I prepare?
Many students start two to three months before the test. If your maths needs strengthening, starting earlier helps.
Key takeaways
- The ESAT tests fast application of GCSE and A level maths and science.
- Choose modules by your course requirements.
- No calculator: practise mental arithmetic and estimation.
- Answer every question; there is no penalty for guessing.
- Use official practice papers and keep an error log.
Where to go next
Read about the TMUA, or revise the maths and physics behind the ESAT.