How to approach an Oxbridge interview question
An interview is a mock tutorial. They already have your grades — now they want to see how you think when you don't know the answer. Nobody expects a polished result; they're watching the route you take. This is the method, and it works for every subject.
What they're actually testing
- How you think, not what you can recall.
- Whether you can apply familiar knowledge to an unfamiliar problem.
- Whether you reason out loud and make your assumptions explicit.
- Whether you take a hint and adapt gracefully when challenged.
- Genuine curiosity — going somewhere with the problem yourself.
The method
A real question ramps up in stages. Work it like this:
Unpack the question
Say it back in your own words and pin down exactly what's being asked — and what's ambiguous. This buys honest thinking time and stops you answering the wrong question. If a term is undefined, define it out loud.
Think out loud
Silence tells the tutor nothing. Narrate everything, including “I'm not sure yet, but here's what I'd try…”. The transcript of your reasoning is the thing being marked — not the final number.
State your assumptions
Especially for estimation: “let me assume a person is 70 kg and a floor is 3 m…”. Making and defending simplifying assumptions is a graded skill, not a cop-out. Flag which ones you'd revisit.
Start with the simple case
Try a small number, a sketch, a limiting case, or n = 1, 2, 3. Footholds and patterns come from the easy end. A concrete example almost always unlocks the general problem.
Use what you already know
Deploy your A-level toolkit — calculus, Newton's laws, a reaction mechanism, supply and demand — on this unfamiliar problem. Reason from first principles rather than reaching for a memorised result.
Sanity-check
Check units, limiting cases, and orders of magnitude: does the answer feel right? Spotting and fixing your own mistake impresses far more than never making one.
Take the hint, then extend
A hint is a gift — build on it, don't ignore it or crumble. A challenge (“are you sure?”) is a probe, not a verdict: defend or revise calmly. Once you've cracked it, offer the generalisation before you're asked.
The method in action
“How thick would a sheet of paper be if you could fold it in half 50 times?”
Unpack & assume. Each fold doubles the thickness. I'll take a sheet as about mm m — I should state that, since the answer depends on it.
Small case. After folds the thickness is . One fold → 0.2 mm; ten folds → about 10 cm. Already growing fast.
Compute. , so the thickness is m.
Sanity-check. m is about 100 million km — roughly two-thirds of the way to the Sun. Absurd-sounding, but that's the point: exponential growth is wildly unintuitive, and the check confirms the arithmetic rather than refuting it.
Extend (the follow-up). “So why can't you actually fold paper more than ~7 times?” Because the area halves each fold too — you'd need exponentially more length and force. The interesting physics is in the constraint, not the number.
By subject
Maths & Computer Science
Rigour first: try small cases, conjecture a pattern, then prove it — and hunt for counterexamples. State definitions precisely.
Physics & Engineering
Model it: list assumptions, work from first principles, then check with dimensions, limiting cases and orders of magnitude. Estimate boldly.
Chemistry
Reason from mechanism and structure. Explain a trend from principles rather than stating it; weigh thermodynamics against kinetics.
Biology
Be hypothesis-driven: propose an explanation, then say how you'd test it. Reason from principles and interpret the data in front of you.
Economics
Think at the margin. Weigh trade-offs and second-order effects, and reach for a diagram or a derivative to make the argument precise.
What sinks strong candidates
Now put it into practice.
140 real-style questions with model reasoning — then have a Cambridge student grill you.