Maths Interview-style Questions

Note: Oxford and Cambridge do not publicly release any interview questions because they often reuse questions across application cycles. Below are interview-style questions of suitable difficulty that will help you prepare for your Oxbridge interview.

Question 1

Draw graphs of y = sin(1/x), y = x·sin(1/x), y = x^3·sin(1/x)

Hint: Look for asymptotes, intercepts, stationary points, and end behaviour.

Question 2

Twenty balls in an urn: 5 red, 5 green, 5 yellow, 5 blue. Three drawn without replacement. Find P(exactly one red), P(all three different colours), P(blue balls > yellow balls drawn)

Question 3

Consider a square. We want to fill it with rectangles in ratio 2:1. For what values of n can we fill the square with exactly n rectangles?

Question 4

A fair coin is tossed repeatedly. Let t be when we first see three consecutive heads, s when we first see four consecutive heads. What is P(s = t + 1)? What is P(s = t + 9)?

Question 5

Starting with 1, 2, ..., n, replace any two terms x and y with x+y+xy. Repeat until one remains. What do you get?"

Interview Tips

  • Think out loud: The interviewer will be assessing your ability to think through complex problems. They can only do this if they know your thought process.

  • Be familiar with your syllabus: The interviewer can ask you a question from any topic you have been taught already in your A level/IB syllabus.

  • Practice: There is no better way to prepare than to practice.

For comprehensive guidance, visit our Oxbridge Interview Guide.