Natural Sciences interview questions

Natural Sciences interviews at Oxford and Cambridge

Natural Sciences interview questions to practise

Say your first thoughts out loud or type them, then compare with how a strong answer goes. These questions are our own, written in the style tutors use.

1. Question 1

   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?

   What it shows a tutor: Whether you model a situation before calculating, and check the answer against intuition.

   Your first thoughts, as you would say them
   Show a strong answer
   How a strong answer goes

   1. It is not another 10 minutes: tea cools faster when it is much hotter than the room. A sensible model is that the rate of cooling is proportional to the gap above room temperature.
   2. Then the gap falls by the same fraction in equal times. The gap went from 60 to 40 degrees, a factor of 2/3, in 10 minutes.
   3. Now it needs to go from 40 to 20 degrees, a factor of 1/2. That is a bigger fractional drop, so it takes longer than 10 minutes.
   4. The time is 10 × ln 2 / ln 1.5. ln 2 is about 0.69 and ln 1.5 is about 0.41, so about 17 minutes.
   5. Check: two more steps of 2/3 would take the gap from 40 to about 18, just past 20. So a little under 20 minutes is right.

   A tutor might then ask: If you add cold milk, is it better to add it straight away or just before you drink it, if you want the tea as cool as possible?

   The usual wrong turn: Assuming a steady rate. Say the model you are using before you use it.

2. Question 2

   Why are an elephant's legs so much thicker, for its size, than a deer's?

   What it shows a tutor: Scaling arguments: how area and volume change at different rates.

   Your first thoughts, as you would say them
   Show a strong answer
   How a strong answer goes

   1. Imagine scaling an animal up by a factor of 2 in every length. Its volume, and so its weight, goes up by 2³ = 8.
   2. The strength of a bone depends on its cross-sectional area, which only goes up by 2² = 4.
   3. So the stress in the bones, weight divided by area, doubles. Scale up enough and the bones would break.
   4. To keep stress the same, a larger animal needs bones that are thicker in proportion to its length: legs like pillars.
   5. It also suggests an upper limit on the size of land animals. A related scaling argument, surface area against weight, explains why a mouse can survive a fall that would kill a horse: the mouse has far more air resistance for its weight.

   A tutor might then ask: Whales are far heavier than elephants. What lets them get away with it?

   The usual wrong turn: Saying elephants are heavy so they need strong legs. The point is how weight and strength scale differently with size.

3. Question 3

   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?

   What it shows a tutor: Turning words into a sequence, finding its limit, and saying what it means.

   Your first thoughts, as you would say them
   Show a strong answer
   How a strong answer goes

   1. Call the dose D. Just after the first dose the level is D. After 6 hours it is D/2, then the next dose takes it to D + D/2.
   2. Next peak: half of 1.5D plus D, which is 1.75D. Then 1.875D. Each peak gets closer to something.
   3. If the peak settles at P, then P = P/2 + D, so P = 2D. The level just before each dose settles at D.
   4. So the level rises over the first day or so and then swings steadily between D and 2D, a steady state.
   5. Doctors use this: if the first dose needs to work at once, they can give a larger loading dose of 2D to start at the steady state immediately.

   A tutor might then ask: What happens if the patient takes the dose every 12 hours instead?

   The usual wrong turn: Saying the drug builds up forever. Ask whether the extra each time shrinks.

4. Question 4

   How would you estimate the number of fish in a lake without draining it?

   What it shows a tutor: Designing a measurement and naming the assumptions behind it.

   Your first thoughts, as you would say them
   Show a strong answer
   How a strong answer goes

   1. Catch a sample, say 100 fish, mark them harmlessly and release them.
   2. Wait for them to mix back in, then catch another sample, say 200 fish. Suppose 10 are marked.
   3. If the second sample is representative, marked fish are the same fraction of the lake as of the sample: 100 / N = 10 / 200, so N is about 2,000.
   4. Then the assumptions: marks do not fall off, marked fish are no easier or harder to catch, fish mix evenly, and none are born, die or leave between catches.
   5. Each can be tested. Repeat the estimate a few times and see if it is stable, or catch in different parts of the lake.

   A tutor might then ask: If marked fish were easier to catch the second time, would your estimate be too high or too low?

   The usual wrong turn: Giving the method without the assumptions. The assumptions are where the science is.

Oxford interview dates, December 2026

All Oxford interviews are online. Your invitation gives your own times.

What tutors are listening for

• Thinking aloud

  Both universities say they want to hear how you work things out, not a memorised answer.

• Using a hint

  Tutors expect to help. What matters is what you do with a prompt or an objection.

• Checking

  Test your answer on a simple case, an example or a counterexample, and fix slips out loud.

More for your application

• Cambridge Natural Sciences acceptance rate
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