See exactly where you stand — a short, adaptive set of TMUA-style questions, plus worked practice questions, a guide to sitting a full mock, and everything you need to know about the real test.
Start your free TMUA checkTwo 75-minute papers, 20 multiple-choice questions each — but the two papers reward very different things.
Content covered is roughly AS-level, but the questions aren’t testing whether you know the content — they’re testing whether you can use it somewhere you haven’t seen it before. Pattern-matching from familiar questions doesn’t work; the paper is built so it can’t.
This is the paper that catches most students out, because elementary logic and formal proof aren’t usually taught explicitly at school. Expect questions on the structure of an argument, what a proof actually establishes, and spotting where reasoning breaks down.
Three TMUA-style questions to try before the full check — two in the style of Paper 1, one in the style of Paper 2. They are written by us, not taken from an official paper. Give each one a couple of minutes before you read the answer: the real test allows 75 minutes for 20 questions, under four minutes each.
Question. How many distinct real solutions does the equation (x² − 5x)² − 2(x² − 5x) − 24 = 0 have?
Answer: E. Expanding gives a quartic, which is the slow route. Instead let u = x² − 5x: the equation becomes u² − 2u − 24 = 0, so (u − 6)(u + 4) = 0. Then x² − 5x = 6 gives (x − 6)(x + 1) = 0, and x² − 5x = −4 gives (x − 1)(x − 4) = 0. That is four solutions, −1, 1, 4 and 6, all different. Seeing a repeated block and substituting for it is exactly the “use it somewhere new” skill Paper 1 rewards.
Question. The graph of y = 3x² − 2kx + k, where k is a real constant, lies entirely above the x-axis. What is the complete set of possible values of k?
Answer: B. The quadratic has a positive leading coefficient, so it lies entirely above the axis exactly when it has no real roots: the discriminant (2k)² − 4(3)(k) = 4k(k − 3) must be negative, which happens for 0 < k < 3. C is the trap. At k = 0 the graph is y = 3x², which touches the axis at the origin, so it is not entirely above it; k = 3 fails the same way. Most lost marks on questions like this come from the boundary, not the algebra.
Question. Which value of the integer n is a counterexample to the statement “if n² + n is divisible by 4, then n is divisible by 4”?
Answer: A. A counterexample to “if P then Q” must make P true and Q false. At n = 3, n² + n = 12, which is divisible by 4, but 3 is not — so the statement fails. At n = 5 and n = 6 the hypothesis is false (30 and 42 are not multiples of 4), so those values say nothing about the statement. At n = 4 and n = 8 both parts are true, which is consistent with it. Choosing a value where the conclusion fails but forgetting to check the hypothesis is the classic slip. Our TMUA logic and proof notes cover this and the other Paper 2 skills in full.
Want to know how you would do across the whole test, not three questions? The free readiness check adapts to your answers and maps both papers topic by topic.
The TMUA is the shared maths admissions test for Cambridge, Imperial, Warwick, UCL, LSE and Durham, with Oxford using it for Maths, Computer Science and their joint honours courses. Seven universities in total — check your specific course’s entry requirements, since not every maths-adjacent course at each university requires it.
Registration accounts opened 1 June 2026. Booking for the October sitting closed on 28 September 2026; the test runs 12–16 October 2026 (TMUA on 15 or 16 October in China, Hong Kong and Macau), with results on 16 November 2026. The January sitting runs 4–8 January 2027 (8 January in China, Hong Kong and Macau): booking opens at 3pm on 26 October 2026 and closes at 6pm UK time on 21 December 2026; access-arrangement applications close on 7 December and bursary applications on 14 December. January is not available to Cambridge or Oxford applicants, apart from mature applicants to a Cambridge mature college with a January deadline and applicants to an Oxford foundation-year programme with a January deadline, and you can sit the TMUA only once in an admissions cycle. Cost is £78 (UK/Republic of Ireland) or £133 (international). Results are released on 8 February 2027 for the January sitting (16 November 2026 for October), as one score on a 1.0–9.0 scale — there’s no pass/fail score. Always confirm exact dates directly with UAT-UK, as these shift between cycles.
A short, adaptive set of TMUA-style questions — then a Fraley tutor takes the picture it builds and drives the plan.
An overall band — where you stand right now, free immediately.
A topic-by-topic readiness picture across both papers.
A prioritised plan — the order to close the gaps, and why.
About 15–25 questions, 20–30 minutes, all multiple choice — nothing to upload. Share your email to unlock the full route, and a Fraley tutor turns it into focused lessons aimed at your target.
Start your free TMUA checkTMUA-style practice questions, written by our own team — not affiliated with any exam board.
UAT-UK and Pearson provide genuinely good free preparation materials — use both alongside our check.
Specimen tests (with explained answers) and timed practice tests built from real past papers are both free via the official UAT-UK preparation page, alongside the test specification and dedicated notes on logic and proof for Paper 2. We’re independent of UAT-UK and Pearson — our check adds an adaptive, personalised read on where you stand and what to prioritise next, but it doesn’t replace sitting the real specimen materials.
Our check is a diagnostic, not a mock: it is shorter, and it adapts to you. For a full mock, use the real thing — UAT-UK publishes every paper from 2016 to 2023 free, with worked answers, in its archive of TMUA past papers, and its specimen and practice tests run in the same on-screen test player you will use at the test centre.
What a mock mark does and does not tell you. UAT-UK’s own practice tests show you which answers were right but deliberately give no score. The 1.0–9.0 scale is set each year from how that cohort performed, with the median fixed at 4.5 and the 90th percentile at 7.0, so there is no fixed conversion from a raw mark out of 20 to a TMUA score. UAT-UK also cautions that practice performance will not necessarily match performance under exam conditions. Use raw marks to compare yourself with yourself, paper against paper, and use the pattern of lost marks to decide what to work on next.
We classified every question in the published TMUA papers from 2016 to 2023. The result: Paper 2 is 43.8% pure reasoning, and Paper 1 concentrates two-thirds of its questions into just four topics. Full topic tables for both papers — useful context once you know your readiness map.
Not sure how to actually answer the reasoning questions? Our TMUA logic and proof notes explain Paper 2 with worked examples for necessary vs sufficient conditions, negating quantifiers, choosing a proof method, and spotting a flawed proof.
Switching from the MAT? Oxford retired it after 2025 — here is what changed, and what your MAT preparation is still worth.
Our topic priority calculator runs the same style of analysis across GCSE, A-Level and IB papers, board by board.
Our tutors have sat the TMUA themselves and studied at the universities that set it. See our full entrance exam tutoring page for STEP and ESAT preparation too, and how we teach TMUA prep alongside A-Level Further Maths.
Is this the real TMUA?
No. The free check uses TMUA-style questions written by our own team — it is not affiliated with UAT-UK, Pearson VUE or any exam board, and it is not a substitute for the official specimen and practice tests. It exists to give you an honest, adaptive read on your readiness, fast.
How long does the free check take?
About 15–25 multiple-choice questions, roughly 20–30 minutes. It adapts as you go, so you spend your time on questions near your actual level rather than working through a fixed paper.
How do I sit a full TMUA mock test?
Use the official papers: UAT-UK publishes every TMUA paper from 2016 to 2023 free, with worked answers, in its archive of past papers. Sit Paper 1 then Paper 2, 75 minutes each, back to back, with no calculator and no formula sheet, and answer every question — wrong answers cost nothing.
Can I turn a practice-test mark into a TMUA score?
Not reliably. The 1.0–9.0 scale is set each year from how that cohort performed, with the median fixed at 4.5 and the 90th percentile at 7.0, which is why UAT-UK’s own practice tests give no score. Compare your raw marks with your own earlier attempts instead, and look at which kinds of question you are losing.
What do I get at the end?
An overall readiness band, a topic-by-topic map across both papers, and a prioritised route — the order to close the gaps, and why. The band and map are free immediately; share your email to unlock the full route.
When can I register for the real TMUA, and what does it cost?
For the 2026/27 cycle, registration accounts opened 1 June 2026. Booking for the October sitting closed on 28 September 2026; the test runs 12–16 October 2026 (TMUA on 15 or 16 October in China, Hong Kong and Macau), with results on 16 November 2026. The January sitting runs 4–8 January 2027 (8 January in China, Hong Kong and Macau): booking opens at 3pm on 26 October 2026 and closes at 6pm UK time on 21 December 2026; access-arrangement applications close on 7 December and bursary applications on 14 December, and results follow on 8 February 2027. January is not available to Cambridge or Oxford applicants, apart from mature applicants to a Cambridge mature college with a January deadline and applicants to an Oxford foundation-year programme with a January deadline, and you can sit the TMUA only once in an admissions cycle. The test costs £78 for UK/Republic of Ireland candidates and £133 internationally. Always confirm exact dates and deadlines directly with UAT-UK, as these can shift between cycles.
Does this replace the official practice materials?
No — use both. UAT-UK and Pearson provide free specimen tests (with explained answers) and timed practice tests built from real past papers, and we’d recommend working through those regardless. Our check adds something they can’t: an adaptive read on exactly where you personally stand, and a prioritised plan for what to do next.
What happens after the check?
The check earns the picture; a Fraley tutor turns your route into focused lessons aimed at your target. You’ll be invited to book a free intro meeting, already pre-filled with your diagnosed profile, so the first conversation starts from where you actually are. Or book a free intro meeting directly.
“…helped her secure her place at UCL!”
“Alex was very knowledgeable beyond the course… he helped me prepare for my admissions exam.”
Take the free check, or go straight to a free 20-minute intro meeting. No obligation, no pressure.
Start your free TMUA check Book a Free Intro Meeting