Oxbridge Maths Interview Preparation: Problems and Practice

In short

Oxbridge maths interviews are academic problem-solving conversations held by Oxford colleges and Cambridge Colleges for mathematics applicants, after the TMUA in October. Oxford interviews are online, about 25 minutes each, in December; Cambridge's main interview period for 2027 entry is 7 to 18 December 2026, with most applicants having one or two interviews totalling 35 minutes to an hour. Both say they want to see how you think. Modern Age Coders runs live online interview practice with original problems, in a group of 15 to 20 or 1-on-1.

Where to start

Three courses for an Oxbridge maths applicant

Problem solving beyond the syllabus, the admissions-test and STEP mathematics that sits around the interview, and the Further Maths Cambridge requires.

Maths Olympiad & Competition Course course thumbnail

OIP / 01

Olympiad and competition maths

Unfamiliar problems every week, the closest thing to an interview a course can give.

Open the syllabus →

OIP / 02

TMUA and STEP preparation

The test before the interview and the papers in the offer; Cambridge says STEP work also prepares you to interview.

Open the syllabus →

OIP / 03

A Level Further Maths

Cambridge requires it of A Level applicants; interview problems often lean on it.

Open the syllabus →

Oxford and Cambridge side by side

What are Oxford and Cambridge maths interviews like?

Both are short, mathematical and held in December. Oxford interviews every shortlisted mathematician online, at two colleges at least; Cambridge decides online or in person College by College, and its Faculty describes the interview in one line: maths, followed by some more maths.

Mathematics interviews for 2027 entry, from each university's own pages (read 31 October 2026)
	University of Oxford	University of Cambridge
Admissions test first	TMUA, October sitting (12 to 16 October 2026)	TMUA, October sitting; registration deadline 28 September 2026
When	"Interviews occur in December."	Main period 7 to 18 December 2026; winter pool mid to late January 2027
Where	Online via video call for all candidates	Online or in person, depending on College and course
How many	One or two at the first-choice college, at least one at another	Most applicants 1 or 2; some 3 or 4
How long	About 25 minutes each	35 minutes to an hour in total (University); about 20 to 40 minutes (Faculty)
What happens	Talk about maths studied, technique, curve sketching, a problem, a new definition	Mathematical problems with guidance; some Colleges add a written assessment
Who is interviewed	Shortlisted applicants	Historically 75% to 80% of Mathematics applicants

Oxford, in its own words

The Mathematical Institute lists four things an interview may do: ask about an area of mathematics you have studied, look closely at a point of technique or curve sketching, set a problem and ask you to talk through your thinking, or give you a definition and ask you to work out its consequences.

It adds a line worth pinning above the desk: tutors are "not mind-readers", so a candidate who works in silence gives them nothing to assess.

Cambridge, in its own words

The Faculty says there are no trick questions and that interviews mostly cover numbers, sequences, integrals and graph sketching, sometimes probability and basic mechanics. Applicants to Mathematics with Physics always get at least one mechanics question.

Cambridge also says the number of interviews, and their timing, say nothing about how strong a candidate is. Families who read meaning into a single interview or a late slot can stop.

Sources: the Oxford Mathematical Institute interviews page and undergraduate study page; the University of Cambridge interviews page; the Cambridge Faculty of Mathematics admissions FAQ and how to apply; all read 31 October 2026. We are not connected with either university or any college.

What the interviewers are looking for

What do Oxbridge maths interviewers want to see?

How you think when the answer is not obvious. Cambridge's Faculty says an instant solution mostly shows you have seen a problem before, while getting stuck and using a hint shows potential. That turns the usual exam instinct upside down.

What each source says it is assessing, quoted from the pages read on 31 October 2026
Source	In its words
Oxford Mathematical Institute	"We are trying to see how you think when you do Mathematics."
Cambridge Faculty of Mathematics	"All we are interested in is your ability to tackle mathematical problems."
Cambridge Faculty of Mathematics	"we will always ask some questions where you will get stuck somewhere"
University of Cambridge	Interviews assess understanding of the subject, readiness for high-level study, and "your ability to think critically and independently"
University of Cambridge	On the day, interviewers "are interested in how you work out your answers and how you think"; you may ask them to explain anything you do not understand

Why being stuck is the point

The Faculty FAQ spells out the logic. If a candidate solves a problem straight away, the interviewers learn that the candidate can solve that problem, "and perhaps that you have seen it before". If the candidate gets stuck, a hint follows, and the interviewers see whether it can be used.

So the hint is not a penalty. A student who takes a hint, says what it changes and moves on is showing exactly the quality the interview exists to find.

Why rehearsed answers fail

Cambridge forbids sharing interview questions, and the university says paid preparation companies "do not have access to any exclusive information". Lists of supposed past questions are therefore unofficial at best.

Even a genuine past question would not help much. Recognising a problem removes the very thing interviewers are trying to watch: a mind meeting something new.

What the universities say about paid preparation. Cambridge's interviews page states that some companies offer interview preparation for a fee, that these services are not endorsed by the University, and that all official guidance is free. That includes us. Oxford's Mathematical Institute says the main preparation is doing mathematics, lots of it, on and near the syllabus. What a class can add is a teacher who sets fresh problems and gives hints the way an interviewer would.

Quotations from the Oxford Mathematical Institute interviews page, the Cambridge Faculty of Mathematics admissions FAQ, and the University of Cambridge preparing for your interview and admission tests pages, read 31 October 2026.

Five problems of ours

What kind of problems come up in an Oxbridge maths interview?

Problems that start inside A Level and leave it quickly: a curve to sketch, a claim about whole numbers, a new definition, an integral to compare, a short probability. The five below are ours, written for this page in the areas Cambridge and Oxford name. None is a reported interview question. Each comes with the hints we would give, in order.

Our five interview-style problems, with hint ladders
Our problem	Hint 1	Hint 2	Where it leads
Sketch y = x / (1 + x²).	What happens when x is replaced by −x?	What happens for very large x?	An odd curve through the origin, peaking at (1, 1/2), dipping to (−1, −1/2), flattening towards 0
Show that n³ − n is divisible by 6 for every integer n.	Factorise it fully.	What is true of any three consecutive integers?	n(n − 1)(n + 1) holds a multiple of 2 and a multiple of 3
Call a number a staircase number if it is a sum of two or more consecutive positive integers. Which numbers are staircase numbers?	List 1 to 16. Which fail?	Write the sum of k terms starting at a as one fraction.	Exactly the numbers that are not powers of 2
Which is larger: the integral of sin x or of sin² x, from 0 to π?	Where does sin x lie on that interval?	Compare a number between 0 and 1 with its square.	sin² x ≤ sin x there, so the first is larger: 2 against π/2
A metre stick is broken at a uniformly random point. What is the expected length of the longer piece?	If the break is at x, how long is the longer piece?	Use symmetry about the middle.	3/4 of a metre

The curve

The derivative of x / (1 + x²) is (1 − x²) / (1 + x²)², zero at x = ±1. But a good candidate sketches before differentiating: oddness, the origin and the behaviour at infinity give the shape, and the derivative only pins the turning points.

The extension

An interviewer who sees n³ − n done quickly will push: is n⁵ − n always divisible by 30? It is. It factorises as n(n − 1)(n + 1)(n² + 1), which handles 2 and 3, and checking n = 0 to 4 modulo 5 shows a factor of 5 every time.

The stick

If the break is at x, the longer piece is the larger of x and 1 − x. By symmetry assume x is at least 1/2, where x is uniform on [1/2, 1]. Its average is the midpoint, 3/4. Saying "by symmetry" out loud, and justifying it, is half the marks an interviewer would give.

All five problems, hints and solutions are ours, written on 31 October 2026, in the topic areas the Cambridge Faculty of Mathematics lists (numbers, sequences, integrals, graph sketching, probability) and the activities the Oxford Mathematical Institute describes (curve sketching, a problem talked through, a new definition explored). They are not reported or reconstructed interview questions, which Cambridge prohibits sharing.

One problem, narrated

How do you think out loud in a maths interview?

By saying what you are trying, why, and what you notice, in short sentences, while you work. Here is our staircase problem as a strong candidate might talk it through, with the two moments where an interviewer would usually step in.

Restate it. "So I want numbers that are sums of at least two consecutive positive whole numbers, like 9 = 4 + 5 or 9 = 2 + 3 + 4."
Try small cases and say what happens. "3 is 1 + 2, 5 is 2 + 3, 6 is 1 + 2 + 3, 7 is 3 + 4. I can't make 1, 2 or 4. Let me check 8: no. 16? Also no."
Name the pattern as a guess, not a fact. "The failures so far are 1, 2, 4, 8, 16. My guess is that powers of 2 are exactly the ones that fail, but I haven't shown anything yet."
Find a general form, with or without the hint. "A run of k terms starting at a adds up to k(2a + k − 1)/2. So twice the number is k times (2a + k − 1)." An interviewer might offer this step if the candidate is circling.
Notice the parity. "k and 2a + k − 1 differ by 2a − 1, which is odd, so one of them is odd and the other even. Both are at least 2. So twice the number has an odd factor bigger than 1, which means the number itself does."
Close both directions. "A power of 2 has no odd factor above 1, so it can't be a staircase number. For the other direction I'd need to build a run for any number with an odd factor; could I try that with 12?" Here the interviewer may hint: use the odd factor as the length of the run.

What made that strong

The candidate guessed in public and labelled the guess as a guess. They wrote the general sum before trying to prove anything with it. When they reached the harder direction they said so plainly and offered a concrete case instead of going quiet.

Nothing in it needs mathematics beyond Year 12. What it needs is the habit of narrating, which most students have never been asked to practise.

Finishing the construction

For 12 the odd factor is 3, so try a run of three centred on 12 / 3 = 4: that gives 3 + 4 + 5 = 12. In general a number with an odd factor m above 1 can be written as m terms centred on its quotient by m, or, when that run dips below 1, as a shorter run made by cancelling negative and positive terms.

An interviewer would not expect every detail of that last step in 25 minutes. They would expect the candidate to see the idea, test it, and say what still needs checking.

The narration is ours and illustrates the advice in Cambridge's interview preparation page to "think about how you might show or explain the way you worked out a problem", and the Oxford Mathematical Institute's suggestion to practise explaining A Level ideas aloud.

From the TMUA to an offer

When are Oxbridge maths interviews for 2027 entry?

December 2026 for both. Cambridge's main period is 7 to 18 December 2026 and invitations mostly go out in November; Oxford's Mathematical Institute says interviews occur in December. Decisions for October applicants arrive in January 2027.

The 2027-entry route for a mathematics applicant, from the Oxford and Cambridge pages
Stage	Oxford	Cambridge
UCAS application	By 15 October, 6pm UK time	By 15 October
Admissions test	TMUA, 12 to 16 October 2026	TMUA, October sitting
Extra form	None named on the Institute page	My Cambridge Application, listing the maths topics you have covered
Interview invitations	After shortlisting	Mostly November, some early December
Interviews	December, online	7 to 18 December 2026; winter pool mid to late January 2027
Offers	Conditional, on A Level or equivalent grades	Conditional, typically including grades 1 in STEP 2 and STEP 3
Share made offers	Not read by us	Around 30% of all Mathematics applicants in previous years (Faculty)

Tell Cambridge what you have covered

The Faculty asks applicants to list the mathematics topics in their qualifications on My Cambridge Application, because this "will help interviewers ask appropriate questions". A student on a course that has not yet reached complex numbers should say so.

It is also the place to mention any lack of help with STEP at school. Cambridge says applicants in that position are not disadvantaged and that free support follows an offer.

Get the technology right

Cambridge says mathematics applicants may need to share workings, sometimes with a stylus and tablet on a shared whiteboard, and that Colleges may run a tech check. Practise writing mathematics on that setup before the day, not during it.

For any online interview: a quiet room, a charged device, working camera and microphone, and pen and paper within reach. Cambridge lists all of these.

Dates and stages from the Oxford Mathematical Institute undergraduate study and interviews pages and the Cambridge interviews page and Faculty admissions pages, read 31 October 2026. The central Oxford admissions site refused our request that day and was not retried, so Oxford shortlisting figures are not given here.

Eight weeks to December

Four stages before the interview

Our suggested plan from the October test to the December interviews. It assumes Year 13 school work continues alongside, as it must.

Our interview practice plan
When	Stage	You are ready to move on when
Late October	1. Problems, untimed and alone	You have tried twenty unfamiliar problems and written down where each one stalled
Early November	2. Problems aloud, on your own	You can talk through a whole problem to a recording without long silences
Mid November	3. Problems aloud, with a stranger	Someone who does not know you sets problems and gives hints, and you use them
Early December	4. Two mock interviews	Two 25-minute sessions on screen with a shared whiteboard, then a rest

If the invitation comes late

Cambridge says the timing of an invitation says nothing about the candidate. Skip stage 1 and go straight to talking problems through.

One honest mock with a stranger is worth more than ten solo sessions in the last week.

If you are in Year 12

Do lots of problems on and near the syllabus, as Oxford advises, and start STEP-style questions slowly. Cambridge says STEP preparation doubles as interview preparation.

Explain one A Level idea a week to someone at home. It feels odd, and it is the cheapest practice there is.

The full list

What we teach an Oxbridge maths applicant

Three groups: problem solving for the interview, the school mathematics it stands on, and the tests around it.

I

Problem solving

For the interview itself

OIP / P / 01

Olympiad and competition maths

Fresh problems, weekly.

Open the syllabus

OIP / P / 02

Problem solving and algorithms

For Mathematics and Computer Science applicants.

Open the syllabus

OIP / P / 03

Statistics and probability

The probability that sometimes appears.

Open the syllabus

II

The school mathematics

Years 12 and 13

OIP / S / 01

A Level Further Maths

Required of A Level applicants at Cambridge.

Open the syllabus

OIP / S / 02

A Level Maths

Pure and mechanics in depth.

Open the syllabus

OIP / S / 03

IB Mathematics

Analysis and Approaches HL applicants.

Open the syllabus

III

The tests around it

October and June

OIP / T / 01

TMUA and STEP preparation

Before and after the interview.

Open the syllabus

OIP / T / 02

Competitive programming

For Computer Science interview problems.

Open the syllabus

OIP / T / 03

University mathematics

A first look at first-year topics.

Open the syllabus

How practice runs

Live interview practice through November and December

Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays.

Weekday evenings

A new problem, solved aloud in turns.

Weekend mornings

Mock interviews on a shared whiteboard.

1-on-1

Full 25-minute mocks with a teacher you have not met.

Unseen problems

Every problem is new to the student; recognising one defeats the exercise.

Hints on purpose

Teachers hold back, then hint, the way an interviewer would.

Narration marked

Feedback covers what the student said, not only what they wrote.

Groups of 15 to 20

Students watch each other think aloud, which teaches the habit fast.

Whiteboard practice

Writing mathematics on a tablet or shared board, before the real day.

No offer promised

We are not endorsed by either university and we promise no place.

Student work

What our students have made

A few of the mathematics, coding and machine-learning projects our students have published. The student labs hold the rest.

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Fees

Oxford and Cambridge charge nothing for interviews, and Cambridge says all official guidance is free. Our practice classes are optional and billed monthly; most interview students join for six to eight weeks and stop in December.

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Interview questions

What Oxbridge maths applicants and parents ask

What happens in an Oxbridge maths interview?

You are given mathematical problems and asked to work on them aloud while one or two interviewers watch and offer hints. Oxford also mentions curve sketching, points of technique and exploring a new definition.

Are Oxford maths interviews online?

Yes. The Oxford Mathematical Institute says interviews are online via video call for all candidates, in December, at the first-choice college and at least one other.

How long is a Cambridge maths interview?

The Faculty of Mathematics says an interview typically lasts about 20 to 40 minutes. The University says most applicants have one or two interviews totalling 35 minutes to an hour, with some having three or four.

When are Cambridge interviews in 2026?

Cambridge gives the main interview period as 7 to 18 December 2026, with invitations mostly sent in November. Winter pool interviews take place around mid to late January 2027.

How many Cambridge maths applicants get an interview?

The Faculty of Mathematics says that historically between 75% and 80% of applicants have been invited to interview, and that around 30% of all applicants have ultimately received conditional offers.

Where can I find Oxbridge maths interview questions?

Not from the universities: Cambridge says sharing interview questions is strictly prohibited. Practise on unfamiliar problems instead, such as STEP questions, problem books and the original problems on this page.

Is it bad to get stuck in a Cambridge maths interview?

No. The Faculty says it will always ask some questions where you get stuck, and that seeing how you use a hint helps it judge mathematical potential.

Do I need interview coaching for Oxford or Cambridge?

The universities say no special training is needed and that paid services have no exclusive information. Practice with someone who does not know you, as Cambridge suggests, is the part a class can supply.

What topics come up in Cambridge maths interviews?

The Faculty lists numbers, sequences, integrals and graph sketching, sometimes probability and some basic mechanics. Mathematics with Physics applicants always get at least one mechanics question.

When are your classes held?

Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays.

Are you linked to Oxford or Cambridge?

No. Modern Age Coders is independent and is not endorsed by the University of Oxford, the University of Cambridge or any college, and we have no inside information about interviews.

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Related pages in this guide

Part of the guide: UK university admissions: maths tests and computing applications

Admissions tests and interviews

Computer science applications

More guides: UK maths exam boards and specification codes · UK maths year by year, Reception to Year 11 · UK selective school maths tests: 7+, 11+, 13+ and 16+ · UK maths enrichment, competitions and able pupils

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Say which university and course you applied for and whether you have an invitation yet. The free class gives you one of our problems to work aloud, with hints when you need them, and tells you honestly how your narration comes across.

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Three courses for an Oxbridge maths applicant

Olympiad and competition maths

TMUA and STEP preparation

A Level Further Maths

What are Oxford and Cambridge maths interviews like?

Oxford, in its own words

Cambridge, in its own words

What do Oxbridge maths interviewers want to see?

Why being stuck is the point

Why rehearsed answers fail

What kind of problems come up in an Oxbridge maths interview?

The curve

The extension

The stick

How do you think out loud in a maths interview?

What made that strong

Finishing the construction

When are Oxbridge maths interviews for 2027 entry?

Tell Cambridge what you have covered

Get the technology right

Four stages before the interview

If the invitation comes late

If you are in Year 12

What we teach an Oxbridge maths applicant

Problem solving

Olympiad and competition maths

Problem solving and algorithms

Statistics and probability

The school mathematics

A Level Further Maths

A Level Maths

IB Mathematics

The tests around it

TMUA and STEP preparation

Competitive programming

University mathematics

Live interview practice through November and December

Unseen problems

Hints on purpose

Narration marked

Groups of 15 to 20

Whiteboard practice

No offer promised

What our students have made

NutriLife

Misti

GuardianX

SkyCast

Fees

Rated 4.9 across 547 Google reviews

What Oxbridge maths applicants and parents ask

What happens in an Oxbridge maths interview?

Are Oxford maths interviews online?

How long is a Cambridge maths interview?

When are Cambridge interviews in 2026?

How many Cambridge maths applicants get an interview?

Where can I find Oxbridge maths interview questions?

Is it bad to get stuck in a Cambridge maths interview?

Do I need interview coaching for Oxford or Cambridge?

What topics come up in Cambridge maths interviews?

When are your classes held?

Are you linked to Oxford or Cambridge?

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Mathematical Olympiad for Girls

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Related pages in this guide

Admissions tests and interviews

Computer science applications

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