Preparing for Maths Interviews

These pages are designed to help you prepare for a maths interview, with a focus on problem solving techniques.  Different colleges will run interviews in slightly different ways, and we recommend that you also have a look at the relevant college website to get more information on how that college organises the interview process.  There is some general information about interviews on the Cambridge Maths Faculty website, including some Frequently Asked Questions. 

In the video below Dr. Ron Reid-Edwards explains everything you need to know about Maths Interviews.

Resources to help you practice

One of the most popular resources for interview preparation is the “TBO Problem Solving booklet”, which is a collection of 151 "interview style" questions.  There is also a solutions booklet, which usually only shows one possible method for each question, but for many problems there will be a variety of methods that can be used.  More interview style questions can be found on our "Useful topics for interview preparation" and "Other Interview Preparation Material" pages.

Example Interview Question

As an example, consider the question:

Determine whether the equation $x^4 +2x^3 + 3x^2 +2x + 1 =0$ has any real solutions.

(This is Question 38 in the TBO booklet, with a slight edit).

Try this problem for yourself before watching the video below to see some of the possible methods discussed.  

More advice for interviews

Solving problems in an interview situation is different to solving them in a classroom or at home, and one of the main differences is that you will be talking about the problem at the same time as trying to solve it.  One of the most important things to practise is “talking out loud” as you are working through a problem.  You could do this with a group of other students preparing for interview, perhaps taking turns, but equally as good is talking to your cat/dog/teddy bear as you write.

When practising problem solving for interviews, make sure that you don’t look at an “answer” too soon.  If you get stuck then take some time out and then try again later.  In an interview situation, interviewers will expect you to get stuck, and when necessary will give hints and suggestions to help you towards the next step.  For other problem solving tips see our Guide to Problem Solving page.

There is more advice in preparing for interviews given in the Advanced Maths Support Programme's SUMS magazine. 

We will be running an interview preparation webinar on Wednesday 25th November 2026, where we will give some more problem solving hints and tips as well as answering your questions!  Registrations for this webinar will open early in November.