Cambridge Mathematics: Tips & Questions for Interview

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maths cambridge interview questions

Cambridge University maths interview questions are notoriously difficult. This article guides candidates on how to best prepare for the Cambridge Mathematics interview, with guides on past Cambridge Maths interview questions, interview tips, mock examples and real experiences from students who have sat the Cambridge Mathematics Panel Interview.

This article is from a collection of accounts from Oxbridge applicants.

What is the Cambridge Mathematics Interview structure?

During the Cambridge interview period, candidates are most likely to have two mathematics interviews. This will depend on the college – some colleges may opt for a single, longer, interview. The Cambridge Mathematics interviews are likely to last 20 to 40 minutes. The university will inform candidates ahead of time how many interviews they will have, and the length of each particular interview.

During the Cambridge interview maths questions are the primary type of question. The focus is on solving mathematical problems, so that the interviewers can assess a candidate’s mathematical potential. Although there is no pre-interview assessment for Mathematics at Cambridge, a college may give candidates a short written assessment prior to interviews, which admissions tutors will discuss during the interview. These will be similar style questions as STEP, so preparing for STEP with STEP past papers is useful in preparing for interview. Candidates can also call our team to enquire about STEP tutoring. Looking at the example Cambridge interview maths questions below will also be extremely helpful in preparing for any written assessments candidates may be given. The Cambridge Mathematics website has links to some sample Cambridge University maths interview questions from Downing College, and three from Trinity College: Test 1, Test 2, and Test 3.

cambridge interview questions math
Practise maths Cambridge interview questions prior to interview

What are the Cambridge Mathematics interview dates?

The Mathematics interviews at Cambridge for entry in 2025 will be taking place sometime from early to mid December 2024. The exact dates vary, depending on the college that interviews candidates. To find out the interview dates for the college they applied to (which will likely be where they are interviewed), candidates can check the college’s website for further information. Specific dates will also be emailed to you in November, if candidates are successfully admitted to interviews.

Specific information will be emailed to successful applicants closer to the time. All applicants to Trinity College based in the UK will be interviewed in-person.

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Cambridge University Maths Interview Questions Examples

Here are some general and specific Cambridge math interview questions for candidate to practise prior to interview.

  • General Cambridge Maths interview questions:
    • Why did you choose to pursue Mathematics at university?
    • What is it about Cambridge that appeals to you?
    • Is there anything about the Mathematics course at Cambridge that particularly appeals to you? Why do you want to study Mathematics at Cambridge specifically, rather than somewhere else?
    • Questions about my Oxbridge Maths personal statement

Specific Cambridge Maths interview questions

  • Divisibility: Is n3-n divisible by 6 if n is an integer?
  • Proof by contradiction: Prove that when the solutions to z2=x2 + y2 are whole numbers, it cannot be that x and y are both odd.
  • Colouring a cube: I want to paint the 6 faces of a cube 6 different colours (with each face being painted one colour). How many different ways can I do this? What if I wanted to paint them 5 different colours?
  • Cutting pizza: How many slices of pizza can I get if I cut it n times?
  • Delivering water: I live in the desert, and I am in charge of delivering water to four different towns. These towns all lie on the same straight line. To successfully deliver all of the food, I must visit every town in turn, and return to my house between each visit. Where should I place my house so that I drive the shortest possible distance? I can build as many roads as needed, so this is not an issue.
  • Square roots: Can you prove that 3 is irrational?
  • Birthdays: There are 40 people in a room. What is the probability that two of them have the same birthday?
  • Prime factors: Can you prove that any integer is either itself a prime number, or can be expressed in terms of prime factors?
  • Dropping my shoes: I drop my shoes from the top of a building. Can you form the basic equations to describe the motion of my shoes? At time t, the stone has speed v and experiences a resistance of magnitude mv (where is a constant). The initial speed of the stone is u. Can you find an expression for v at time t?
maths interview questions cambridge
Maths interview questions Cambridge

Further Cambridge Math Interview Questions

  • Ant’s journey: An ant is standing on the vertex of a cube. It wanted to reach the opposite vertex, and can only walk along the faces of the cube. What is the quickest route the ant could take?
  • Questions about identifying sequences (such as a geometric sequence) and finding the sum to infinity.
  • Questions involving showing you a graph and asking for a discussion on it – talking about the minimum and maximum points, inflection points, etc. They may ask you to try and provide an equation that would produce the graph.
  • Questions giving you an equation and asking you to manipulate it (e.g., differentiate/integrate it) and sketch it.
  • Mechanics questions – such as asking you to calculate the velocity of an object at time t.
  • Statistics and probability questions.

Insider Guides: Cambridge Mathematics Interview

What happens on the day of your Cambridge Mathematics interview? 

I had in person interviews. My interviews occurred on one day – I had two Mathematics interviews, with roughly a two hour break in between them. Each of the interviews lasted about 30 minutes, but it was such a friendly environment that it actually felt much quicker than that!

What do you have to bring to your Cambridge Mathematics interview?

Make sure you follow the guidance about what ID you are expected to bring, as they’ll want to make sure they’re interviewing the right person! Otherwise, don’t worry too much about what to bring, particularly if your interview is in person. While it’s nice to feel prepared and bring your own stationary, they will definitely have spares you can borrow so don’t worry too much! With regards to calculators, I think the interviews tend to be non-calculator, but they will likely tell you if you need to bring one!

If your interviews are online, then do make sure you have your own stationary (pens and paper) on hand, as you will almost definitely need this! 

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What is the interview setting and how long is it?

I had two different Mathematics interviews in different rooms. The first was a nice office with some sofas/armchairs, and the second one was a classroom environment. As I stated before, both of my interviews were roughly 25-30 minutes long.

What are the Cambridge Mathematics interviewers like? 

In my experience, the interviewers ranged from friendly to professional. None of them were particularly cold or stand-offish, so I felt quite comfortable in my Cambridge Mathematics interviews. Just remember that they want you to succeed as well! It’s helpful if you have the mentality of you and the interviewer working together to solve the Maths problem, rather than you against the interviewer! When asking maths interview questions Cambridge tutors will be looking for you to explain your thought process and will support you in finalising an answer.

The Interview

The Maths Cambridge interview questions are very set. They will have pre-prepared follow up questions to advance the questioning process on each question. However, if you seem to be struggling at a particular point in your answer, they will ask leading/prompting questions for you to consider, in an effort to help you reach the answer. Do not feel bad if you do need some hints! This gives the interviewers an opportunity to see how you can use new information and unfamiliar concepts to work towards an answer. In fact, the Cambridge Mathematics website states that interviewers try to ask questions that you will get stuck on, so that they can test this ability!

maths interview questions cambridge

What are the best tips for planning my trip for my Cambridge Mathematics Interview?

There isn’t a dress code, although a lot of students do wear suits. This can help you feel more comfortable, but it is by no means essential – they will not judge you on your appearance so don’t worry about getting new clothes! The Cambridge Mathematics website says that you should wear whatever you are comfortable in. (Personally, when I did my interview, I turned up with a suitcase from my overnight stay, and my taxi had been cancelled so I was wearing jeans that I had just run across the city in!) 

If your interviews are in person, you could consider staying overnight. There are lots of budget options available in the city if the college will not provide you with accommodation. It can be helpful for you to find the college you are interviewing at the night before, so you know where you’re going. This can save some stress on the actual day!

Are there any academic or challenging Mathematics questions at the Cambridge Interview?

All of the formal questions I was asked were academic Mathematical questions. They were quite challenging. Generally speaking, they will likely test you on the first year of A level Mathematics. There will also be some content from the first year of A level Further Mathematics. The questions are normally designed to take the knowledge they expect you to know and get you to apply it in novel ways.

Are there any personality, work experience or extracurricular based Mathematics questions at the Cambridge Interview? 

In my experience, the interview wasn’t focused on any personality, work experience or extracurricular questions. I wasn’t asked about my personal statement either. The purpose of the Cambridge Mathematics Interview is to allow you to demonstrate your Mathematical capabilities, regardless of your experience or previous opportunities. For this interview, it is enough that you are capable, passionate about Mathematics, and can demonstrate this clearly! As such, you don’t need to worry that your lack of previous Mathematical achievements might hold you back.

Top Tips for the Cambridge Mathematics Interview

  1. Try not to panic too much! You will give a much better performance if you are calm and able to think clearly
  2. Work through your answer out loud! The interviewers aren’t going to be able to help you if you’re doing all the work in your head. 
  3. If your interview is in person, make sure you get there with lots of time to spare. You want to allow time for your travel to go wrong and for you to find the right room. If it is online, make sure that you can connect to the interview about 15 minutes beforehand. You don’t want to be stressed right before your interview, and you definitely don’t want to be late or miss it! 
  4. It’s okay if you get stuck – the questions are designed to be challenging and to push you. What the interviewers are most interested in is how you handle unfamiliar situations. 
  5. Make sure you sleep and eat properly before the interview so you know you’re giving yourself the best chance you can.
  6. Practise with others – you can practise your answers with family and friends. You can also contact us to see how we can help with Oxbridge Mathematics interview tutoring.

Top Tips for the “Why Cambridge” interview question

  1. Consider what really drew you to the university – is it the city itself, a famous alumni, or something particular about the educational system that appeals to you? Perhaps a combination of these things? There are many unique things about Cambridge University – pinpoint a few things that make you want to study there.
  2. You must also consider the subject itself – why Mathematics in particular at Cambridge? Do some research into the course before your interview. Find out about the various options available to study, and see if any of these appeal to you. You can also look into the academics that might be teaching you. Mentioning particular courses you want to study, or particular academics you look up to, will show that you have decided to apply to Mathematics at Cambridge not just because of the prestige and reputation, but because you genuinely have interest in the course itself!

My Favourite Things about Studying Mathematics at Cambridge University

Here are some favourite aspects about Cambridge from successful applicants:

  • The collegiate system: this gives you a lively social life and allows you to meet so many people right at the start of your university experience. You will be living with and studying with these people, and there will be so many events that are put on for your college specifically.
  • Tutorial/supervisions: one unique thing about Cambridge (and Oxford) is the supervision system. You will be given regular sessions with your tutor and at maximum one or two other students – this will be your mode of study, rather than larger classes as most other universities have. This is a great opportunity, as it lets you have a far more personal academic relationship with leading academics in the field, and you can learn a lot more from them.
  • The city itself is beautiful – and central Cambridge is a lively university town. 

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