So you’ve got an interview for Mathematics at Cambridge! To help you prepare we’ve compiled some of the best advice from real Mathematics applicants who went to interview so you can get all the top tips in one place.
If you’re looking to learn more about the course from Cambridge themselves you can do so from their website 🔗, and you can find advice from us on how to prepare an Mathematics application here 🔗 🌟.
For entry in previous years, some colleges required applicants for Mathematics to do a written assessment at the interview, and applicants were given details in their invitation letter for the interview. For candidates interviewed overseas, a written Maths assessment was administered by the overseas interviewing team.
For the most up-to-date information on entry requirements to the Mathematics course at Cambridge, do visit the undergraduate admissions page for the course 🔗 🌟.
You will be asked mathematical questions, and are expected to talk through your answers with the interviewers. You will receive paper and writing materials to help this process. A common theme across our interview testimonials is that interviewers would start off with a question on a topic within the scope of the Mathematics (or Further Mathematics) A level syllabus, then introduce extensions to that initial question to stretch the interviewee’s abilities.
What mathematical topics might you be faced with in the interview? We’ve looked at all the testimonials on our website given by past Mathematics applicants - here is what they have mentioned.
- Calculus: differentiation, integration, differential equations
- Graphs: graph-sketching, graph theory, graph properties. One applicant to Clare College (Full interview here 🔗) suggested to “practice sketching and analysing lots of interesting graphs”. While practising, use sites like Desmos 🔗 to check your answers.
- Probability
- Geometry
- Proof questions
- Logic questions
- Mathematical induction
- Trigonometry
- Fibonacci sequences
- Coordinates
- Combinatorics
- Mechanics
- Dynamics
- Complex numbers
- Sequences
- Game theory - though the candidate, an applicant to Churchill College (Full interview here 🔗), remarked that it was “completely off-syllabus” and no prior knowledge was expected of them.
You might be faced with odd questions, such as this applicant:
“The last question was about a maths concept that they do not expect a high schooler to know or have seen. Then they gave me a few mathematical constructs and asked me to determine, according to the given rules, whether they do or do not satisfy the given condition.” - applicant to Sidney Sussex College. Full interview here 🔗.
It is important to remain calm and answer what you can.
If you have an at-interview written assessment, your interview might involve questions about your solutions to the assessment. You may be asked to go through or explain your solutions to the interviewers. You may also be given the chance to re-attempt any unfinished or incorrectly-answered questions. These re-attempts are often guided by the interviewers.
You might get questions linked to your personal statement, though not all interviewees would get such questions. Be sure to only tell the truth in your statement, and fully understand what you include in it.
“I think it's worth just doing a lot of challenging mathematics, wherever it's from, whether it be UKMT (United Kingdom Mathematics Trust) challenge papers, Olympiads, STEP questions etc. The actual content doesn't matter too much, just practise thinking about challenging problems.” - applicant to Homerton College. Full interview here 🔗.
“Maths is all about practice, the more you practice the better you will get and the more confident you will feel.” - applicant to Jesus College. Full interview here 🔗.
Almost all the testimonials from applicants to the Mathematics course at Cambridge recommend practising mathematics questions in preparation for your interview, especially since this practice would be useful for the STEP (Sixth Term Examination Paper) and your at-interview test (if applicable). Some interviewees recommend practising under timed conditions.
Here are the resources mentioned by our testimonials:
- The STEP website 🔗 🌟
- The NRICH website 🔗
- The STEP Support Programme 🔗 🌟 (and a - guide 🔗 on how to use it well)
- A list of STEP questions with solutions at Underground Mathematics 🔗
- The book “Advanced Problems in Mathematics: Preparing for University” by Stephen Siklos, available legally and for free as PDF at OpenBook Publishers 🔗
- STEP preparation threads on student forums, such as The Student Room, for useful tips and information.
- Attending outreach STEP events held by universities. The 2021 STEP Prep Day at Robinson College, Cambridge, will be held on Saturday 18 September. Applications close 3 September. Details are available here 🔗 🌟, and the registration form can be found here 🔗.
- STEP past papers, available at stepdatabase.maths.org 🔗
- The University of Oxford’s Maths Admissions Test past papers, available on their website 🔗
- British Mathematical Olympiad past papers available at Maths.org 🔗
- The United Kingdom Mathematics Trust website 🔗
-The Advanced Mathematics Support Programme 🔗 🌟
- Drfrostmaths.com 🔗
- Artofproblemsolving.com 🔗
- Specimen at-interview test papers, available on the Trinity College subject page for Mathematics 🔗
Books - try to borrow them from a library!
- “A Mathematical Olympiad Primer” and “A Mathematical Olympiad Companion” by the United Kingdom Mathematics Trust.
- "A Concise Introduction to Pure Mathematics" by Martin Liebeck.
A Scottish applicant also specifically mentioned past papers from the Scottish Qualifications Authority (SQA) 🔗:
“For people doing Scottish qualifications: Advanced Higher Applied Maths/mechanics is pretty easy if you're already doing maths and physics and it looks good. I had to teach it to myself because my school didn't do it but SQA past papers were great.” - applicant to Sidney Sussex College. Full interview here 🔗.
“It's worth getting some sort of practise speaking about maths before the interview, either in a mock interview if you can find someone to do that for you, or just explaining your thought process aloud to yourself. Having to explain to someone else how you are going about approaching a problem when you are stuck is a key part of the interview, but it's not a skill you really get to practise much elsewhere.” - applicant to Sidney Sussex College. Full interview here 🔗.
“Do try to talk through your solutions with someone, e.g. a friend, because the interviewers are looking for you to be able to explain how you solved a question. If you do get the chance to have a mock interview with a teacher, focus on responding to advice and hints - the interviewers are looking whether or not you can turn a little hint into a little bit of progress.” - applicant to Sidney Sussex College. Full interview here 🔗.
“Practice asking good questions if you are stuck - an interviewer will be very happy to help you if you ask an intelligent question or explain where it is that you are struggling, and they would far prefer this to someone who sits struggling in silence - or maybe even someone who just whizzes through the questions with very little communication.” - applicant to Jesus College. Full interview here 🔗.
“Although I heard it a million times before my interview, I didn't really believe that the interviewers aren't there to catch you out, but it's true! The interviewers are not there to catch you out. They don't expect you to understand degree-level maths yet, nor are they going to ask you questions which are impossible to answer. They are there to provide key information (such as a definition or a formula) in case you forget. They want to see how you approach hard problems so remember to talk out loud when you're thinking!” - applicant to Queens College. Full interview here 🔗.
“I remember misunderstanding what one of the questions meant, but once I had asked for clarification I made progress on the problem, so there's no harm in asking this. [...] If I was stuck on what to say [the interviewers] sometimes gave a small hint to put me in the right direction, or to think differently about a problem.” - applicant to Emmanuel College. Full interview here 🔗.
“If you forget something (e.g. a formula), just ask. It's not a memory test. [...] If [the interviewers] say "How about using this method?", then USE THAT METHOD.” - applicant to St Catharine’s College. Full interview here 🔗.
“The interviewer will always want to push you so that it becomes difficult or you don’t know what to do, so that they can see how you learn and think when doing something fairly unfamiliar.” - applicant to Jesus College. Full interview here 🔗.
“Don't worry about your English! I know this doesn't apply to everyone but I was really nervous about having to talk in English with native speakers but it was completely fine.” - applicant to Pembroke College. Full interview here 🔗.
“Don't panic if you think it went horribly, as you've probably done much better than you realise and I think maths and science students tend to be more pessimistic about their performance. The interviewers are looking for someone who has a real passion for learning and can solve new situations with the same content you learn in A-Level, so just try different approaches that you already know about and talk about the approaches you're using.” - applicant to Sidney Sussex College. Full interview here 🔗.
If you would like to read the accounts of Mathematics applicants in full, we have many testimonials in the Interviews section 🔗 of our website. You can find non-course specific information about the interview and how to prepare a Cambridge application here 🔗, and the Cambridge University YouTube channel also has a video 🔗 about the interview process. And if you’d like help preparing for the STEP, we have just the guide 🔗 for you.