Cambridge interview questions
138 original questions in 18 subjects, 90 free to practise here. Choose your subject, think out loud against the clock, take a hint only when stuck, then mark your own thinking against six habits tutors listen for.
4 Medicine questions. Pick one below, or start with the first.
Why does your heart rate go up when you stand up quickly?
A test for a disease is right 99% of the time. One person in 1,000 has the disease. Someone tests positive. How likely is it that they have it?
Should people who smoke wait longer for heart surgery than people who do not?
Why is there still no vaccine for the common cold?
A library's rule says: 'No food or drink in the reading room.' Which of these break the rule? A bottle of water. Chewing gum. Glucose tablets a reader with diabetes needs. A sealed sandwich in a bag.
A by-law says: 'No vehicles in the park.' Does it ban a bicycle? A child's electric toy car? An ambulance answering a call? A tank mounted as a war memorial?
I write to you: 'I will buy your bike for £100. If I hear nothing, I will take it as a yes.' You say nothing. Do we have a contract?
Two people fire at their victims, meaning to kill. One misses because of a sudden gust of wind; the other kills. Should they be punished equally?
A man injures his partner while sleepwalking. Should he be guilty of a crime?
Parliament passes a law today making something a crime and says it applies to anyone who did it last year. Is that acceptable?
Suppose theft is defined as 'dishonestly taking property belonging to another, intending to deprive them of it permanently'. Is each of these theft? You borrow a neighbour's ladder without asking, meaning to return it the next day, and do. You take a library book without checking it out, meaning to return it after your exams. You take a friend's concert ticket, use it, and give the used ticket back.
A shop's window shows a television labelled £20. It is a mistake: it should say £2,000. You go in and ask to buy it at £20. Should the shop have to sell it to you? Give reasons each way.
You walk past a lake and see a stranger drowning. A lifebuoy hangs right beside you. Should the law make it a crime not to throw it?
Suppose a simple rule says a will is valid only if 'signed by the person making it', and consider only that rule. Which of these should count? Ann, whose hand is injured, makes an X. Ben, too ill to write, asks his carer to sign his name while he watches. Cara types her name at the end of an email setting out her wishes.
In an earlier case, a shop was held responsible when a customer tripped on a loose carpet the shop had known about for a week. Now a customer slips on a floor mopped two minutes earlier, with a 'wet floor' sign up. Does the earlier case mean the shop is responsible again?
At what age should a child be held criminally responsible for shoplifting? Should a 12-year-old be treated like an adult?
A law says: 'Anyone who sells alcohol to a person under 18 commits an offence.' A shop sells to a 16-year-old who shows a convincing fake ID saying they are 19. Should the shop be guilty?
50! means 50 × 49 × 48 × … × 2 × 1. How many zeros are at the end of 50!? Talk me through how you would find out without multiplying it out.
What is the last digit of 7²⁰²⁶? Tell me how you know without working the number out.
In how many ways can you cover a 2 by 10 strip of squares with 1 by 2 dominoes, with no gaps or overlaps?
Is there a largest prime number? Convince me either way.
Sketch the graph of y = x e⁻ˣ. Talk me through what you check as you go.
Which is bigger, 2¹⁰⁰ or 3⁶³? No calculator. Show me how you would decide.
Sketch the graph of y = x / (1 + x²). Describe it to me as you go: where it crosses the axes, what happens for large x, and where it turns.
Show that n³ − n is divisible by 6 for every whole number n.
Break a stick of length 1 at two points chosen independently and uniformly along its length. What is the probability that the three pieces can form a triangle?
Is √2 + √3 rational? Convince me.
Without a calculator, which is bigger: e^π or π^e?
Let a₁ = 1 and aₙ₊₁ = aₙ + 1/aₙ. Is a₁₀₀ bigger than 14?
Put n points on a circle and join every pair with a straight chord, with no three chords meeting at one point inside. Into how many regions is the disc cut? Try n = 1 to 5 first.
A uniform ladder leans against a smooth wall, with its foot on rough ground. What stops it sliding down? How steep must it be so that it does not slip?
Estimate how long a 2 kW kettle takes to bring 1 litre of water from 20 °C to boiling. Then tell me why the real time is longer.
A 1,200 kg car travelling at 30 m/s brakes steadily and stops in 60 m. What is the average braking force? What happens to the stopping distance if the car is going twice as fast?
A spinning top stays upright, but the same top falls over at once when it is not spinning. Why?
You have two identical springs, each with stiffness k. How stiff is the pair when hung one below the other, and when hung side by side sharing a load?
Estimate the power you produce running up one flight of stairs. Choose your own numbers and tell me what you are ignoring.
Estimate the power a cyclist needs to ride at 10 m/s on a flat road with no wind.
A wooden plank 200 mm wide and 25 mm thick spans a stream. Is it stiffer laid flat, or on its edge? By how much?
A ladder circuit repeats forever: each section has a 1 Ω resistor along the top rail, then a 1 Ω rung across to the bottom rail. What is the resistance between the two terminals at the start?
You pour a hot cup of tea and want to drink it as hot as possible in ten minutes. Should you add the cold milk now, or just before you drink?
A car drives round a circular track of radius 100 m, banked at 10° to the horizontal. At what speed does it need no friction at all to stay on its path?
What is the longest vertical straw you could drink water through, however hard you suck?
A ball is dropped from 2 m and each bounce reaches 80% of the height before. How far does it travel in total before it stops?
A ball is thrown straight up and caught at the same height. Allowing for air resistance, does it take longer going up or coming down?
You see a flash of lightning and hear the thunder 6 seconds later. How far away was the strike? What did you assume?
Why does a straw in a glass of water look bent at the surface? Which way does it look bent, and why?
A mountain top is closer to the Sun than the valley below. Why is it colder?
A 60 W bulb is designed for a 230 V supply. What current does it draw and what is its resistance? Two of them are then connected in series to the same supply: what happens?
Estimate the mass of the air in this room. Is the answer more or less than you expected?
Why is the sky blue in the middle of the day, but the sun looks red at sunset?
Roughly how many atoms are there in a human body?
An ice cube floats in a glass of water filled exactly to the brim. When the ice melts, does the glass overflow?
Two balls start together from rest at the same height. One rolls along a straight sloping track to a point lower down; the other along a track with a gentle dip in the middle, below the straight one, rising again to the same end point. Which arrives first?
A geostationary satellite stays above the same point on the equator. How far from the centre of the Earth must it orbit?
Two incandescent filament bulbs rated 60 W and 100 W at 230 V are connected in series across 230 V. First model each resistance as fixed at its rated operating value and use dissipated power as a proxy for brightness. Which dissipates more power? What might change for real bulbs?
Why do councils spread salt on icy roads? Would it still work on a very cold night, at −25 °C?
A city sets a maximum rent below today's market rent for every flat. What happens? Who gains and who loses?
A football club sells out every home match, yet it does not raise ticket prices. Is it being irrational?
The government puts a tax of 50p on every cup of coffee sold, collected from the cafés. Who really pays it?
A shop cuts the price of a game from £10 to £8 and weekly sales rise from 100 to 130. How price-sensitive are buyers, and did revenue go up?
Two passengers sit side by side on the same flight. One paid £60 and the other £300. Why does this happen, and is it bad for passengers?
Your savings account pays 4% a year while prices rise by 10%. Are you better or worse off after a year, and by roughly how much?
Water is essential to life and diamonds are not. Why do diamonds cost far more?
A beach is 1 km long, with sunbathers spread evenly along it. Two cafés, with the same prices, each choose a spot to win as many customers as they can. Everyone walks to the nearer café, and splits evenly when the two are equally near. Where do the cafés end up?
Should a national museum charge for entry? Give the economic case each way.
In a recession, households become worried and all decide to save more. Does total saving in the economy rise?
A café cuts its coffee from £3.00 to £2.50, and sales rise from 200 to 260 cups a day. Each cup costs 80p to make, and the café's other costs stay the same. Did revenue rise? Did profit rise?
After a storm destroys many homes, the country's GDP rises over the next year as they are rebuilt. Is the country better off?
You have 9 coins that look the same. One is slightly heavier. With a balance scale, what is the smallest number of weighings that always finds it?
A list holds whole numbers. Every number appears exactly twice, except one, which appears once. How do you find it, using only a fixed amount of extra memory?
How can a computer check whether a positive whole number is a power of two in a single step, without a loop?
How many squares of any size can you find on an 8 by 8 chessboard? Then generalise.
On a 4 by 4 grid of squares, you walk along the lines from the bottom-left corner to the top-right corner, moving only right or up. How many different routes are there?
You have two ropes. Each takes exactly an hour to burn, but they burn unevenly, so half a rope need not take half an hour. With a lighter, how do you measure exactly 45 minutes?
You climb a staircase of 10 steps, taking 1 or 2 steps at a time. How many different ways are there to reach the top?
I think of a whole number from 1 to 1,000. You may ask yes or no questions. How many questions do you need, in the worst case, to be sure of finding it?
A corridor has 100 closed lockers. Person 1 opens every locker. Person 2 toggles every 2nd locker, person 3 every 3rd, and so on up to person 100. Which lockers are open at the end?
A list holds every whole number from 1 to n except one, in a random order. How would you find the missing number, using very little extra memory?
A robot starts at (0, 0) facing north on an endless grid. F moves it one square forward, L and R turn it 90° left or right on the spot. It repeats the program FFRFFL forever. Does it stay inside some fixed region, or wander off?
On an island, knights always tell the truth and knaves always lie. A says: 'B is a knave.' B says: 'A and I are the same kind.' What are A and B?
Three pegs, and n discs of different sizes stacked on the first peg, largest at the bottom. Move them all to the third peg, one disc at a time, never putting a larger disc on a smaller one. How many moves does it take?
Is it ever right to break a promise? Give me your view, then the best case against it.
A friend hiding in your house is being chased by someone who wants to hurt them. The pursuer asks you where your friend is. May you lie?
A computer program answers every question about a story exactly as a person would. Does it understand the story?
Do we owe anything to people who will be born in 200 years' time?
Is a tax on sugary drinks a fair way to improve health?
Two people drive home equally drunk. One hits a child who runs into the road; the other meets no one and gets home safely. Is the first more to blame?
A machine scans your body, destroys it, and builds an exact copy on Mars from new atoms. The copy has all your memories. Did you travel to Mars, or did you die?
Can you know that you are not dreaming right now?
Is it wrong to break a promise to someone who has died?
Is a law that is never enforced still a law?
Suppose we gave each voter extra votes for passing a test on politics. Would decisions improve? Would it be fair?
A runaway tram will kill five people unless you switch it to a side track, where it will kill one. Most people say switch it. A surgeon could save five dying patients by taking the organs of one healthy visitor. Almost everyone says no. Is there a real moral difference?
A machine scans you, destroys your body, and builds an exact copy on Mars, with all your memories. Did you survive the trip?
Should the voting age for UK general elections be 16?
A city gives every adult resident £1,000 a year, with no conditions. Who gains, who pays, and what might change?
'Every swan I have ever seen is white, so all swans are white.' Is that good reasoning? What about 'The sun has risen every day, so it will rise tomorrow'?
Should voting be compulsory, with a small fine for not voting?
A mug of tea cools from 80 °C to 60 °C in 10 minutes in a room at 20 °C. Roughly how long does it take to cool from 60 °C to 40 °C?
Why are an elephant's legs so much thicker, for its size, than a deer's?
A drug's level in the blood halves every 6 hours. A patient takes the same dose every 6 hours. What happens to the level over a few days?
How would you estimate the number of fish in a lake without draining it?
What do you notice about this poem?
Does it matter what an author meant, if the meaning is not in the text?
Can a film be better than the novel it adapts?
Who is telling this story, and should we trust them?
What can this source tell a historian, and what can it not?
Is it ever right for a historian to call an event inevitable?
You can keep only one kind of evidence about everyday life in an English town in 1750: tax records, private diaries, or court records. Which would you keep?
Two historians read the same evidence and reach different conclusions about why an event happened. Does that mean one of them is wrong?
A study finds that people who drink more coffee live longer. Should everyone drink more coffee?
People shown a list of 20 words tend to remember the first few and last few best. Why might that be, and how could you test your explanation?
How could you find out whether babies a few months old can tell the difference between one object and two?
Can happiness be measured?
Water boils at 100 °C, but hydrogen sulfide, H₂S, a heavier molecule, is a gas at room temperature. Why?
Dissolving ammonium nitrate in water makes the beaker cold. If it takes in heat, why does it dissolve at all?
Roughly how many water molecules are in a glass of water? If you poured that glass into the sea and let it mix completely, how many of its molecules would be in the next glass you scooped out?
Why does ice float? What would lakes be like if it did not?
On a tall sunflower, the leaves near the top are smaller and thicker than the leaves near the ground. Why might that be?
A bacterium divides every 20 minutes. Starting from one cell with plenty of food, roughly how long before the colony would weigh as much as the Earth? Why does that never happen?
On islands, small mammals such as rodents often evolve to be larger than their mainland relatives, while large mammals such as elephants have evolved to be smaller. Why might both happen?
Is a virus alive?
Why are so many of the world's largest cities on a coast or a big river?
In many older British industrial cities, the poorer districts are in the east and the richer ones in the west. Can you suggest why?
Is a flood a natural disaster?
A county wants to build a new onshore wind farm. How would you decide where it should go?
How would you say 'The wolf saw the farmer'? What does this language use instead of word order?
Was ancient Athens a democracy?
How can we know anything about the lives of ordinary people in the Roman world?
Is it fair to judge ancient writers by modern values?
Why are so many large medieval churches and cathedrals tall and narrow, while many modern supermarkets are low and wide?
Choose a building or space you pass often. What works about it, and what would you change?
Should a new building in a historic town copy the style of the old buildings around it?
Two rooms have exactly the same floor area. One feels calm and spacious and the other feels cramped. What might make the difference?
Why does a flat in central London cost several times more than an identical flat 100 miles away?
Should the government allow building on the green belt to tackle the housing shortage?
A town wants to cut traffic in its centre. Compare a congestion charge with closing roads to cars.
A new railway station makes nearby homes more valuable. Who should pay for the station?
How Cambridge interviews run
- Cambridge's main interview period is 7 to 18 December 2026. Most invitations go out in November.
- Whether you interview online or in person depends on your college.
- Most applicants have one or two interviews, lasting 35 minutes to an hour in total. Some have three or four.
- In maths and science interviews you may be asked to show your working, so practise saying each step as you go.
Rehearse out loud before December
Problems in your subject, answered out loud on the page. Take hints when stuck, answer the follow-ups, and see how your thinking comes across. 12 months of access. No offer is promised.
Oxbridge Interview Rehearsal: two subjects
£249 once. No VAT is charged.
Introductory price £249 until 31 December, then £399.
Rehearse every problem in two subjects you choose, with hints, follow-ups and Mia's marks, for 12 months.
- All 8 problems in each of your two subjects, chosen after you pay
- Hints when you are stuck, then the tutor's follow-up questions
- Mia's marks on up to 60 attempts a day, within a fair-use allowance for each interview season: thinking aloud, using hints, checking, reasoning
- Your next problem picked from your weakest skill
- Your latest 300 attempts saved, with re-attempts side by side
Access for 12 months, until 6 November 2027. Choose your subjects after paying, on a free account. Full refund within 14 days, for any reason.
By paying you agree to our Terms and get access straight away, which ends your 14-day cancellation right. Your full refund within 14 days, for any reason, still applies.Oxbridge Interview Rehearsal: all subjects
£349 once. No VAT is charged.
Introductory price £349 until 31 December, then £499.
Every problem in all seven subjects, for joint courses and for practising beyond your own subject.
- All 56 problems: Maths, Computer Science, Engineering, Physics, Economics, Law and PPE
- Hints when you are stuck, then the tutor's follow-up questions
- Mia's marks on up to 60 attempts a day, within a fair-use allowance for each interview season: thinking aloud, using hints, checking, reasoning
- Your next problem picked from your weakest skill
- Your latest 300 attempts saved, with re-attempts side by side
Access for 12 months, until 6 November 2027. Use it on a free account. Full refund within 14 days, for any reason.
By paying you agree to our Terms and get access straight away, which ends your 14-day cancellation right. Your full refund within 14 days, for any reason, still applies.Questions
What questions do Cambridge interviewers ask?
Expect questions about your subject that go beyond what you have studied, often with something to work on: a problem, a passage or some data. Be ready to talk about anything in your personal statement too.
Are these real Cambridge interview questions?
No. Every question here is our own, written in the same style. Cambridge does not publish the questions it will ask.
When are Cambridge interviews in 2026?
The main period is 7 to 18 December 2026. Winter pool interviews are in mid to late January 2027.
How should I practise?
Out loud, against a clock, on questions you have not seen. Say your first idea early, test it on an example and check it before you move on.
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