ESAT Preparation
ESAT Question Bank
Practice the way the ESAT actually tests you — topic-by-topic questions, full mock papers, and worked solutions for Maths 1, Maths 2, Physics, Chemistry and Biology. Built by Oxbridge and Imperial graduates.
What's Inside
Everything you need to prepare for the ESAT
Every ESAT module
Maths 1, Maths 2, Physics, Chemistry and Biology — matched to the modules your course requires.
Real exam style
27-MCQ, 40-minute module format with the no-calculator, time-pressured style the ESAT uses.
Worked solutions
Every question has a full, method-led solution — not just the answer key.
Timed mock papers
Sit full modules under exam conditions and see where your time goes.
Difficulty grading
Questions tiered from entry to stretch so you can ramp up to exam-day standard.
Built by specialists
Written and checked by Oxbridge and Imperial graduates who sat these tests.
The Numbers
ESAT facts, cited
Sources: UAT-UK (the body that delivers the ESAT) plus Cambridge, Imperial, UCL and Oxford admissions guidance, cross-checked in May 2026. Full 2027-entry dates and details are released by UAT-UK from April 2026.
Module Breakdown
The five ESAT modules, explained
Everyone sits Mathematics 1; you then take two further modules chosen for your course. Each module is 40 minutes, 27 multiple-choice questions, and no calculator is allowed.
Mathematics 1
Compulsory for every candidate. Tests fast, accurate handling of core pure maths.
- Algebra and manipulation
- Graphs and coordinate geometry
- Sequences and series
- Trigonometry
- Probability and statistics
Sat by every ESAT candidate, whatever the course.
Mathematics 2
A further-maths-flavoured module, required by Cambridge Engineering and Oxford Physics-family courses.
- Advanced algebra
- Differentiation and integration
- Logarithms and exponentials
- Mechanics-style reasoning
Physics
Mechanics, electricity, waves and energy, with fast unit and dimensional work at its core.
- Mechanics and motion
- Electric circuits
- Waves and light
- Energy and work
Chemistry
Physical, inorganic and organic chemistry, leaning on moles, bonding and reaction reasoning.
- Moles and quantitative chemistry
- Atomic structure and bonding
- Energetics
- Organic reaction reasoning
Biology
Cells, biochemistry, genetics, physiology and ecology, testing quick recall and clean application.
- Cell biology
- Biochemistry
- Genetics
- Physiology and ecology
Difficulty Grading
How we grade difficulty
Every question is banded so you can ramp up deliberately: lock in method at Foundation, calibrate to exam standard at Standard, then separate yourself at Stretch.
Consolidates core methods so technique and unit-handling become fast and automatic.
Pitched at genuine exam difficulty and pace, where you build reliable scoring.
Harder items for top-end separation, with traps and multi-step reasoning.
Sample Questions
See how the ESAT actually tests you
A sample question from each module. Press "Show worked solution" to see the full method, not just the answer. Try them as you would on the day: no calculator, against the clock.
Mathematics 1
Pure maths everyone sits: algebra, graphs, sequences, trigonometry and probability, all without a calculator.
The line L passes through the points (1, 4) and (3, 10). What is the equation of L?
- y = 2x + 2
- y = 3x + 1
- y = 3x − 1
- y = 2x + 1
- y = 6x − 2
Show worked solution
Answer: B · y = 3x + 1
Gradient = (10 − 4) / (3 − 1) = 6 / 2 = 3.
Using y − 4 = 3(x − 1) gives y = 3x + 1. Check the second point: 3(3) + 1 = 10. ✓
The quadratic x2 + kx + 9 = 0 has exactly one (repeated) real root. What are the possible values of k?
- k = 3 only
- k = 6 only
- k = ±3
- k = ±6
- k = ±9
Show worked solution
Answer: D · k = ±6
A repeated root means the discriminant b2 − 4ac = 0.
Here a = 1, b = k, c = 9, so k2 − 4(1)(9) = 0, giving k2 = 36.
Therefore k = ±6. The trap is to keep only the positive root.
A fair six-sided die is rolled twice. What is the probability that the sum of the two rolls is a prime number?
- 5 / 12
- 1 / 3
- 15 / 36
- 1 / 2
- 13 / 36
Show worked solution
Answer: C · 15 / 36
Possible sums run from 2 to 12. The prime sums are 2, 3, 5, 7 and 11.
Count the ordered outcomes for each: 2 → 1 way, 3 → 2, 5 → 4, 7 → 6, 11 → 2. Total favourable = 1 + 2 + 4 + 6 + 2 = 15.
Probability = 15 / 36 (which is also 5 / 12, but option C is written in the unsimplified form the question matches).
Mathematics 2
Further-maths-flavoured module: more advanced algebra, calculus, logarithms and mechanics-style reasoning.
Given that log2 x + log2 (x − 2) = 3, what is the value of x?
- x = 2
- x = 4
- x = 6
- x = 8
- x = −2 or 4
Show worked solution
Answer: B · x = 4
Combine the logs: log2 [x(x − 2)] = 3, so x(x − 2) = 23 = 8.
Then x2 − 2x − 8 = 0, which factorises as (x − 4)(x + 2) = 0.
x = 4 or x = −2. Reject x = −2 because log of a negative number is undefined. So x = 4.
The curve y = x3 − 6x2 + 9x has a local maximum at x = a and a local minimum at x = b. What is the value of a + b?
- 2
- 3
- 4
- 5
- 6
Show worked solution
Answer: C · 4
Differentiate: dy/dx = 3x2 − 12x + 9 = 3(x2 − 4x + 3) = 3(x − 1)(x − 3).
Stationary points at x = 1 and x = 3. The cubic rises, falls, then rises, so the maximum is at x = 1 (a = 1) and the minimum at x = 3 (b = 3).
a + b = 1 + 3 = 4. You do not even need to test which is which, since the question only asks for the sum.
Physics
Mechanics, electricity, waves and energy, with an emphasis on fast unit work and dimensional reasoning.
A ball is dropped from rest and falls freely for 2 seconds. Taking g = 10 m s−2 and ignoring air resistance, how far does it fall?
- 10 m
- 20 m
- 40 m
- 5 m
- 80 m
Show worked solution
Answer: B · 20 m
Use s = ut + ½at2 with u = 0, a = 10 m s−2, t = 2 s.
s = 0 + ½ × 10 × 22 = ½ × 10 × 4 = 20 m.
The common error is forgetting the factor of ½ and writing 40 m (option C).
Two resistors, 3 Ω and 6 Ω, are connected in parallel. What is the combined resistance of the pair?
- 9 Ω
- 4.5 Ω
- 2 Ω
- 0.5 Ω
- 18 Ω
Show worked solution
Answer: C · 2 Ω
For parallel resistors, 1/R = 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2.
So R = 2 Ω. A useful check: the combined value of parallel resistors is always smaller than the smallest individual resistor, here 3 Ω.
A 0.5 kg trolley moving at 4 m s−1 collides with a stationary 1.5 kg trolley and they move off together. What is their common velocity immediately after the collision?
- 1 m s−1
- 1.5 m s−1
- 2 m s−1
- 3 m s−1
- 4 m s−1
Show worked solution
Answer: A · 1 m s−1
Conserve momentum: total before = total after.
Before: 0.5 × 4 + 1.5 × 0 = 2 kg m s−1.
After: combined mass = 0.5 + 1.5 = 2 kg, moving at v, so 2v = 2, giving v = 1 m s−1.
Chemistry
Physical, inorganic and organic chemistry: moles, bonding, energetics and reaction reasoning at speed.
How many moles of oxygen molecules (O2) are present in 64 g of oxygen gas? (Relative atomic mass of O = 16.)
- 1 mol
- 2 mol
- 4 mol
- 0.5 mol
- 32 mol
Show worked solution
Answer: B · 2 mol
Molar mass of O2 = 2 × 16 = 32 g mol−1.
Moles = mass / molar mass = 64 / 32 = 2 mol.
The trap is using the atomic mass 16 (giving 4 mol) instead of the molecular mass 32.
Which of the following best explains why the boiling point of water is much higher than that of hydrogen sulfide (H2S), despite both being group-16 hydrides?
- Water has stronger covalent O–H bonds
- Water molecules hydrogen-bond to one another
- Water has a larger relative molecular mass
- Oxygen is more metallic than sulfur
- Water is a smaller molecule with weaker forces
Show worked solution
Answer: B · Water molecules hydrogen-bond to one another
Boiling point depends on the strength of intermolecular forces, not the strength of the covalent bonds inside the molecule.
Oxygen is highly electronegative and small, so O–H bonds allow strong hydrogen bonding between water molecules. H2S cannot hydrogen-bond effectively, so it boils far lower despite having a higher molecular mass.
Biology
Cells, biochemistry, genetics, physiology and ecology, testing quick recall and clean application.
Which of the following structures is found in a typical plant cell but NOT in a typical animal cell?
- Mitochondrion
- Ribosome
- Cell-surface membrane
- Cellulose cell wall
- Nucleus
Show worked solution
Answer: D · Cellulose cell wall
Mitochondria, ribosomes, the cell-surface membrane and the nucleus are common to both plant and animal cells.
A cellulose cell wall is a feature of plant cells (and absent from animal cells), which is the distinguishing structure here.
In humans, a man with blood group AB and a woman with blood group O have children. Which blood groups are possible in their offspring?
- A or B only
- AB or O only
- A, B, AB or O
- O only
- AB only
Show worked solution
Answer: A · A or B only
The father (AB) passes on either IA or IB. The mother (O) is genotype ii, so she always passes on i.
Offspring genotypes are therefore IAi (group A) or IBi (group B).
So children can be group A or group B only. AB and O are not possible.
These are our own original practice questions, written to illustrate the ESAT style. They are not reproductions of real past-paper or copyrighted exam questions.
Your Prep Plan
An ESAT preparation timeline
Build coverage first, move into timed module practice, then rehearse full sittings under exam conditions.
6 months out
Pick modules, map the spec
Choose your modules and check the specification against your school syllabus. Prioritise topic coverage before speed.
3 months out
Start timed module practice
Begin timed, module-by-module practice and log mistakes by type: knowledge gap, setup error, algebra slip or misread.
1 month out
Full timed sittings
Shift to full 120-minute runs under strict timing, rehearsing guessing discipline, pacing and recovery after hard patches.
Final week
Light review, check logistics
Review formulas, common traps and your error log rather than cramming. Confirm ID, travel and your booked modules.
Choose Your Package
Three ways to prepare
Start with self-paced practice, add full mocks and walkthroughs, or work 1-to-1 with an Oxbridge tutor.
Question Bank
one-off payment
Self-paced practice with full worked solutions.
- Full topic-by-topic question bank
- Step-by-step worked solutions
- Difficulty-graded questions
- Access on any device
Complete Prep
one-off payment
Everything in the bank, plus timed mocks and video walkthroughs.
- Everything in Question Bank
- Full timed mock papers
- Video walkthroughs of hard questions
- Performance tracking by topic
- Exam-day strategy guide
Tutored
from / hour, incl. tutoring
Complete Prep plus 1-to-1 sessions with an Oxbridge tutor.
- Everything in Complete Prep
- 1-to-1 sessions with an Oxbridge tutor
- Personalised study plan
- Marked practice with written feedback
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