8+ weeks
Rebuild core technique and definitions
- Review algebra, functions, vectors, graph sketching and proof basics.
- Keep a short notebook of definitions you can explain aloud.
- Use Oxford practice problems and TMUA-style questions for timed drills.
Free Interview Resources
Oxford Mathematics Interview Questions
Free practice questions, preparation advice, and expert insights for Mathematics interviews at Oxford.
2-3 interviews · tutorial-styleFormat
Sample Oxford Mathematics Interview Questions
Real Mathematics interview questions in the style Oxford asks. Try answering each one aloud before you reveal the hint.
01A ladder leans against a vertical wall with its foot on the ground. As it falls, what curve is traced by the midpoint of the ladder?
Problem-Solving
mid
A ladder leans against a vertical wall with its foot on the ground. As it falls, what curve is traced by the midpoint of the ladder?
Problem-Solving
Hint
Model the wall and floor as perpendicular axes and use the fixed length of the ladder.
02How many ways are there to cover a 2 by n rectangular grid with 2 by 1 domino tiles?
Problem-Solving
mid
How many ways are there to cover a 2 by n rectangular grid with 2 by 1 domino tiles?
Problem-Solving
Hint
Work out the first few cases and then separate arrangements according to how the leftmost part of the rectangle is tiled.
03Find the complete set of values of x satisfying both inequalities below.
Problem-Solving
entry
Find the complete set of values of x satisfying both inequalities below.
Problem-Solving
Hint
Draw a sign chart for each product, then intersect the two solution sets.
04Two lines each meet the same quadratic curve at exactly one point. Find b minus c.
Problem-Solving
hard
Two lines each meet the same quadratic curve at exactly one point. Find b minus c.
Problem-Solving
Hint
For each line, substitute into the quadratic and use the condition for exactly one intersection.
05For how many values of a does the equation below have exactly two distinct real solutions?
Problem-Solving
hard
For how many values of a does the equation below have exactly two distinct real solutions?
Problem-Solving
Hint
Consider when the linear factor root overlaps with roots from the quadratic, and when the quadratic has repeated or real roots.
Tutorial-style interviews with subject-specific problems, often involving unfamiliar material.
Oxford interviews typically take place at the college you applied to. You will usually have two or three interviews of around 20-30 minutes each, sometimes at different colleges if you are pooled. The atmosphere is meant to resemble a tutorial: the interviewer gives you a problem and watches how you reason through it.
20-30 minutes per interview2-3 interviews, sometimes at different colleges
- -Expect to be given a passage, diagram, or problem you have not seen before and asked to think through it.
- -Interviewers at Oxford will often push you until you get stuck. This is deliberate and is designed to see how you handle difficulty.
- -Oxford tutorials involve deep 1-to-1 discussion, so showing you can engage in academic conversation is key.
Invitation → Decision: the interview timeline
Interview Invitation
Late Nov
Arrival to Interview
Early Dec
Technical Question
Mid Dec
Decision
Early Jan
Interview Invitation
Late Nov
Arrival to Interview
Early Dec
Technical Question
Mid Dec
Decision
Early Jan
Problem-Solving
2 questions01Find the shortest distance from the origin to the line below.
mid
Hint
Write the squared distance from the origin as a function of t, then minimise it.
02Without evaluating the integrals directly, rank the four integrals below in order of size.
hard
Hint
Use inequalities between sine, cosine, and tangent on the interval before comparing integrands.
Conceptual
5 questions01Given that q has roots 2, -3 and 1, what could q be? Give at least two possible polynomials of different degrees.
entry
Hint
Start with the factor theorem, then think about what you can multiply by without changing the listed roots.
02If x minus 2 is a factor of p(x), what must p(2) be, and why?
entry
Hint
Substitute x=2 into the factor and connect that to the product form of a polynomial.
03What does it mean for a function to be one-to-one, and why can a function not be one-to-many?
entry
Hint
Separate the definition of a function from the extra property of injectivity.
04For which values of k does the quadratic equation have exactly two real solutions? Explain the role of the discriminant.
mid
Hint
Write the discriminant and interpret positive, zero, and negative cases.
05Prove the AM-GM inequality for two positive real numbers, then explain how averaging two unequal terms affects a fixed-sum product.
hard
Hint
Begin from a square such as (sqrt(a)-sqrt(b))^2 and then interpret equality.
Personal Statement-Based
3 questions01Tell us about an area of mathematics you have studied. What was the main idea, and where did your understanding become more precise?
entry
Hint
Choose a topic you can explain clearly and be ready to define one term carefully.
02Your application mentions doing mathematics beyond the curriculum. Pick one problem or resource and explain the idea that made it interesting.
entry
Hint
Focus on one example and show how it changed how you think, rather than listing activities.
03Choose a theorem, proof, or mathematical idea from your personal statement and explain it as if the interviewer has not read the same source.
mid
Hint
State the problem, define the objects involved, and give the key step rather than trying to recite everything.
Curveball
3 questions01Sketch all points (x, y) satisfying f(x)=f(y) for the function below.
hard
Hint
Use symmetry and the periodic structure of cosine; start with easy families of solutions.
02Suppose A is a 2 by 2 matrix and A to the power n is zero for some n at least 2. Prove that A squared is zero.
hard
Hint
Use determinants first, then use the trace-determinant identity given for a 2 by 2 matrix.
03Use the recursion below to generate infinitely many integer solutions to u squared minus 2v squared equals 1, then explain how it gives rational approximations to square root 2.
hard
Hint
First verify that the transformation preserves u^2-2v^2, then look at u/v.
6 weeks
Turn practice into spoken reasoning
- Solve unfamiliar problems while narrating each choice of method.
- After each problem, write one sentence on what the key idea was.
- Practise accepting hints and restarting without treating that as failure.
4 weeks
Build interview-style flexibility
- Mix problem-solving, conceptual and curveball questions in one session.
- Ask yourself what changes if a parameter, domain or assumption is altered.
- Prepare two personal-statement topics you can explain mathematically.
2 weeks
Run realistic mocks
- Do short online mock interviews with no notes except working paper.
- Practise checking boundary cases and saying when a first approach has failed.
- Review the common mistakes you have made in practice and attach one corrective habit to each.
Final week
Consolidate and reduce friction
- Revisit solved questions and explain the reasoning without reading your notes.
- Prepare your video-call setup and working space.
- Sleep normally and keep the last practice sessions short and precise.
Unlock the full guide
- The full Mathematics question bank, by category, with hints
- A week-by-week preparation roadmap
- The common mistakes that cost offers - and how to avoid them
Free Resource
The Complete Oxford Mathematics Interview Guide
Enter your email to unlock the full question bank, worked approaches, a week-by-week prep roadmap, and the mistakes that cost offers.
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Other Oxford Subjects
Further Reading
Recommended Resources
Book
Numbers and Proofs
by R. B. J. T. Allenby
Oxford Mathematical Institute practice-problem guidance recommends it as helpful for studying key mathematical concepts and methods.
Book
Mathematical Techniques
by D. W. Jordan and P. Smith
Referenced by Oxford Mathematical Institute practice-problem materials for students strengthening core techniques.
Book
Fermat's Last Theorem
by Simon Singh
Good for mathematical storytelling, but applicants should be ready to explain one mathematical idea rather than only the narrative.
Book
The Music of the Primes
by Marcus du Sautoy
Accessible enrichment for number theory and mathematical curiosity; best used with follow-up notes on examples and definitions.
Website
Oxford Mathematical Institute TMUA page
by Oxford Mathematical Institute
Central page for Oxford-specific TMUA dates, format and preparation advice.
Website
UAT-UK TMUA test information
by UAT-UK
Gives test structure, timing, scoring and official preparation information.
Course
Oxford Mathematical Institute TMUA support webinars
by Oxford Mathematical Institute
Weekly problem-solving and admissions support with a particular focus on TMUA and interviews (summer 2026 onwards).
Tool
Oxford Mathematical Institute Practice Problems
by Oxford Mathematical Institute
Good for consolidating technique and preparing to explain mathematical reasoning aloud.
Tool
STEP Support Programme foundation modules
by STEP Support Programme
Oxford suggests these modules may be useful for candidates seeking additional problem-solving practice.
Frequently Asked Questions
The UCAS code is G100. The official Oxford page is headed Mathematics / Mathematics and Statistics because admission is joint at first and students choose between the Mathematics and Mathematics & Statistics routes after the fourth term.
No. For this cycle, Oxford Mathematics applicants take the TMUA. Oxford Mathematical Institute says the MAT will not take place for the 2026 admissions round and applicants will take TMUA instead.
Oxford lists the TMUA test dates as 12-16 October 2026. Registration opens on 1 June 2026, booking opens on 20 July 2026, and the booking deadline is 28 September 2026 at 6pm UK time.
Oxford lists A*A*A at A-level, with A*s in Mathematics and Further Mathematics if Further Mathematics is available. For the IB, Oxford lists 39 including core points with 766 at HL, with the 7 in Higher Level Mathematics.
Oxford describes Mathematics as required and Further Mathematics as highly recommended. The course page says most students who read Mathematics have taken both Mathematics and Further Mathematics or an equivalent combination.
No. Oxford's Mathematics course page says applicants do not need to submit written work for this course.
The Mathematical Institute says candidates generally have one or two interviews in their first-choice college and at least one at another college, with each interview lasting about 25 minutes. Exact formats vary by college.
Yes. Oxford says shortlisted applicants for this cycle will have online interviews in December, and the Mathematical Institute says Mathematics interviews are online via video call for all candidates.
No. Oxford Mathematical Institute says there is no TMUA pass mark; the score is used together with UCAS information and school-background context when deciding whom to shortlist.
No college should be treated as an easy route. Oxford says reallocation is normal, open applications are treated without preference or disadvantage, and each college interviews roughly the same number of applicants for each place.