A Mathematics Interview for Oxford

By Isabelle Zeidler

Do you feel as though an air of mystery surrounds the Oxford maths interview process? I certainly did – so here’s a rough outline of what to expect.

The first thing to note is that the tutors in your interview want to assess whether you are teachable, rather than whether you already know all of the content. This means they will continue to push questions past the point of your understanding, and instead will assess how you ask questions and react to the hints and ideas that they provide you.

The general format is as follows: whilst it is slightly different per applicant, it is typical that you will have two interviews with one college and another interview with another college. Do not worry about who you have your interviews with - they are from the same bank of questions regardless. They also generally will split these three interviews into one specifically focused on applied maths, although this is still not quite as specialised as you might have met at school. The questions in the interview aren’t necessarily hard content (so it’s alright if you didn’t pick that applied module at school), but instead tricky applications or problem-solving required on more basic concepts from GCSE.

For example, you may use GCSE probability extrapolated to infinite iterations, so you need to apply integration and theories here. My (hardest) interview question was a theoretically easy idea of an ant walking along a string (mechanics), but you were then required to form and solve simultaneous differential equations in a few forms. This cross-topic approach to questions means that you must ensure you become very comfortable with skills such as integration, simultaneous equations, general algebraic manipulation and differentiation (particularly in optimisation questions).

Another vital skill which interviewers always appreciate is sketching graphs. You may sometimes receive concrete questions on sketching graphs, such as sketching the exponent of the sine of x, or you can use this to buy yourself time when you meet a hard question. This helps you to visualise the question - and show that you understand it - while you can think about a few approaches in the back of your mind.

To practise this, you can make up a few functions by combining powers, exponents, logs and trigonometry in different formats. You need to always look at the same four features – x intercept, y intercept, turning points and asymptotes (which also includes activity at + - infinity). You can check your answers in Desmos.

How else might you prepare? I suggest looking at the TBO problem-solving books, STEP I or STEP II questions or some easier BMO questions. Here, you should imagine you are explaining your working to someone else as you answer the questions, and you could ask ChatGPT for some support if you get stuck. Ensure that you only do STEP II questions which cover A-level maths content, not further maths content, as this is the only content which is specifically targeted in your interview.

I'd like to end on the most important comment – you must talk your way through your interview. They want to hear you talk through different approaches that you have thought about, why some of them might not work – essentially, you should never stop talking! This allows them to have a look into the way that you think and hopefully see your curious, problem-solving mind.

I look back on my interviews with a smile on my face! While stressful at first, I ended up really enjoying all of them, and the opportunity to work through problems with such bright minds is very exciting. Get this enjoyment across to give yourself the best chance, and good luck!