TMUA preparation guide

The TMUA revision plan: from registration to results

You sit the TMUA once per admissions cycle, and that single rule shapes everything about how to prepare: plan backwards from the official dates, sit your mocks before you book, and revise in three phases. This guide puts the official 2027-entry timeline, the free official materials and a week-by-week revision structure in one place, so every step from opening an account to reading your score lands on an actual date in your calendar.
Papers
28
Questions
827
Free to try
2
In short
  • Oxbridge applicants must, as a rule, sit in October, and every candidate gets exactly one sitting per admissions cycle: there is no retake for a better score.
  • Plan backwards from the official dates: October booking closes at 6pm UK time on 28 September, so your first full timed mock belongs in mid-September at the latest.
  • Revise in three phases: secure the Section 1 mathematics, then the Paper 2 logic and proof material, then full papers under timed, back-to-back conditions.
  • Everything essential is free from UAT-UK: the Content Specification, the Notes on Logic and Proof, and the 2016-2023 past papers with worked answers.
  • Calibrate with the official score distribution for October 2025 (typical candidates around 4.5, roughly 10% above 7.0), and remember the scale changed in 2024, so older numbers do not transfer.
01

The 2027-entry timeline: every date that matters

Before you plan a single revision session, put the official dates in your calendar. The TMUA runs twice per admissions cycle, and for 2027 entry the key dates (all UK time, as published by UAT-UK) are:
MilestoneOctober sittingJanuary sitting
Booking opens20 July, 3pm26 October, 3pm
Booking deadline28 September, 6pm21 December, 6pm
Test window12-16 October 20264-8 January 2027
Test days in mainland China, Hong Kong and Macau15 or 16 October8 January
Results released16 November 20268 February 2027
Registration is a two-step process: create an account on the UAT-UK website, then book a test slot through Pearson VUE. The test costs £78 in the UK and Republic of Ireland and £133 everywhere else, including China. Candidates in mainland China, Hong Kong and Macau cannot pick freely within the window: in those regions the TMUA runs only on 15 or 16 October, and only on 8 January in the second window. The booking deadline is a hard cut-off, so do not leave account setup and payment to the final week.
02

One sitting per cycle: choose it deliberately

UAT-UK's rule is unambiguous: "you can only sit once within an admissions cycle", and the official guidance adds that neither session carries any advantage. This single rule reshapes the whole plan. There is no sitting the October test as a trial run and going again in January for a better score: the paper you submit is the only score you get.
How to choose:
  • Applicants to Cambridge or Oxford must, as a rule, take the October sitting. The only exceptions are applicants to Cambridge mature colleges with the January admissions deadline, and applicants to Oxford's Astrophoria Foundation Year.
  • Applicants to the other universities that use the TMUA (Imperial, LSE, Warwick, UCL and Durham) may choose either sitting. January buys almost three extra months of preparation, but results only arrive on 8 February 2027.
  • Once released, scores are sent automatically to the institutions in your UCAS application that require the test, matched course by course; you cannot choose which of them see your score.
For non-Oxbridge applicants the real question is therefore not "which sitting is easier" but "will I be at my target level before the booking deadline of the sitting I choose". That is why this plan front-loads mock exams, as covered below.
03

The free official materials: download everything first

UAT-UK's own preparation advice is a single sentence: read the test specification, read the Notes on Logic and Proof, and answer practice papers under timed conditions. All of it is free. Download the full set before you begin:
  • The Content Specification. The current version applies to the October 2026 and January 2027 sittings. It defines Section 1 (the mathematical knowledge shared by both papers) and Section 2 (the logic and proof scope specific to Paper 2), and it is the only authoritative answer to "is this topic examinable".
  • Notes on Logic and Proof. An official booklet written for Paper 2, aimed at candidates who have not yet met theorems and proofs in their maths classes. If formal logic is new to you, this is your textbook.
  • Past papers, 2016 to 2023. The official preparation-materials page hosts Paper 1, Paper 2, worked answers and an answer key for every year from 2016 to 2023, plus an early specimen set. These come from the paper-based era, but the specification and question style carry through, and they remain the core practice material.
  • The Explanation of Results. UAT-UK publishes an official score-distribution document for every sitting, which is how you calibrate expectations (more on this below).
One warning worth flagging on day one: there is no formulae booklet, and candidates are expected to recall every relevant formula. Build memorisation into the plan from the start rather than discovering the gap in the final week.
04

The framework: three phases, planned backwards

The structure of the test dictates the order of revision. Paper 1 (Applications of Mathematical Knowledge) draws only on the Section 1 mathematics; Paper 2 (Mathematical Reasoning) draws on the same mathematics plus the Section 2 logic and proof material. Section 1 is therefore the shared foundation, and the Paper 2 material sits on top of it. That gives a three-phase plan:
  1. Phase one: close the Section 1 gaps. Work through the AS level pure content and the Higher Level GCSE content, fix weak topics, and start committing formulae to memory.
  2. Phase two: Paper 2 logic and proof. Study the Section 2 specification alongside the Notes on Logic and Proof, then practise past Paper 2s by question type.
  3. Phase three: timed full papers. Sit the 2016-2023 papers under real conditions, 75 minutes per paper and the two papers back to back, to train pacing and decision-making.
Schedule it backwards. Fix phase three against the test window (12-16 October), fix your first full mock against the booking deadline (28 September), and let phases one and two fill whatever time remains. If you start late, compress each phase rather than deleting one: the three phases target three different ways of losing marks (not knowing the content, arguing loosely, and running out of time), and skipping any of them shows up directly in the score.
05

Phase one: secure the Section 1 knowledge

The official line on content level is that the TMUA is based on Higher Level GCSE mathematics or AS level mathematics. The specification splits Section 1 in two. Part 1 is almost all AS level pure maths, organised into eight topics: algebra and functions, sequences and series, coordinate geometry, trigonometry, exponentials and logarithms, differentiation, integration, and graphs of functions. Part 2 is almost all Higher Level GCSE material: units, number, ratio and proportion, algebra, geometry, statistics and probability.
How to work through this phase:
  • Audit yourself against the specification line by line, not against a textbook's contents page. Candidates coming from non-UK curricula should pay particular attention to differences in terminology and notation, and to GCSE topics such as statistics and probability that are easy to skip.
  • Write a one-page formula card for each topic as you finish it. With no formulae booklet, the trigonometric identities, the laws of logarithms and the rules of differentiation and integration all have to live in your head.
  • Practise without a calculator from day one. Calculators and dictionaries are banned in the test, so build fluency in unaided arithmetic, especially simplifying fractions, surds and logarithms.
  • Work topic by topic at this stage, checking each one against matching past-paper questions; full timed papers can wait.
The exit test for phase one is simple: you can honestly tick every Section 1 line in the specification, and you can reproduce your formula cards from memory. If you cannot, stay in phase one.
06

Phase two: logic and proof for Paper 2

Paper 2's official brief is to test mathematical thinking: understanding and constructing mathematical arguments. The Section 2 content is genuinely small, and a focused two to three weeks covers it systematically:
  • The language of logic (Arg1 to Arg4). True and false; and, or (meaning inclusive or), not; the four conditional forms: if A then B, A if B, A only if B, and A if and only if B; the converse and the contrapositive of a statement, and how their truth relates to the original; the terms necessary and sufficient; the quantifiers for all, for some (meaning for at least one) and there exists; and negating statements built from any of these.
  • Proof (Prf1 to Prf5). The specification lists four types of proof: direct deductive proof, proof by cases, proof by contradiction, and disproof by counterexample. Mathematical induction is not on that list, so do not spend revision time on it for this test. Beyond the four types, you are expected to deduce implications from given statements, make and justify conjectures from small cases, rearrange shuffled statements into a correct proof, and handle problems that need a sophisticated chain of reasoning.
  • Spotting errors (Err1 and Err2). Identifying mistakes in purported proofs and knowing the classic invalid steps; the specification's own examples are concluding b = c from ab = ac, and concluding A = B from sin A = sin B.
The specification also states explicitly that symbolic notation and formal truth tables are not required. A sensible order: read the Notes on Logic and Proof first, then work through the 2016-2023 Paper 2s sorted by the question types above, returning to the relevant specification line every time you get one wrong.
07

Phase three: full papers at test pace

The final phase does one thing only: complete full papers under the real constraints. Those constraints are:
  • Twenty questions in 75 minutes per paper. That works out at roughly 3 minutes 45 seconds per question, which is arithmetic rather than an official rule, but it carries the point: any question that absorbs more than five minutes is borrowing time from the others.
  • Both papers back to back. The papers are taken one after the other, 2 hours 30 minutes in total, and no official document mentions a break in between. Run the two-paper sequence in full at least two or three times to train concentration in the second half.
  • No negative marking. Questions across the two papers carry equal weight, wrong answers cost nothing, and the official advice is to attempt every question. Build the habit in practice: bank the questions you can do, return to the hard ones with whatever time remains, and never leave a blank.
  • Test-day working conditions. No calculator and no dictionary; test centres provide erasable sheets or a whiteboard with a pen, and you may not bring your own materials. Do at least a few papers working on a whiteboard or a single sheet, to get used to constrained working space.
After each paper, debrief against the official worked answers. Sort every dropped mark into one of three causes: a knowledge gap, a loose argument, or a time problem, and feed each back into phase one material, phase two material or pacing drills respectively. This is also the phase for getting comfortable on screen, since the live test is computer-based: practise timed papers in a computer-based interface where you can.
08

Sit your mocks before you book

Because you sit only once per cycle, mocks are not just practice: they are the evidence on which you make decisions. Working backwards, booking for the October sitting closes at 6pm on 28 September, so your first full timed mock should happen no later than mid-September. That mock answers two questions:
  1. Should you book October at all? Oxbridge applicants have no choice; October it is. But if you are applying elsewhere and the mock lands well below your target state, you can sit in January instead (booking opens 26 October and closes 21 December), buying almost three months to close the gap.
  2. How far off are you? Calibrate against the official Explanation of Results. For October 2025, UAT-UK's own wording is that typical candidates score around 4.5 and roughly 10% of candidates score above 7.0. The same official pages say plainly that the tests are designed to be challenging, and that candidates should not expect to score as highly as they do in school exams, even with top school grades.
Two calibration traps are worth naming. First, old-scale targets: the score scale changed in 2024, and Durham states that a 6.5 from 2023 equates to a 5.0 from 2024 onwards, so numbers in older forum threads mostly live on the wrong scale. Second, hunting for a pass mark: UAT-UK publishes no grade boundaries at all, and universities use the score in very different ways (Durham, for instance, publishes that 5.0 or above brings automatic eligibility to be considered for a reduced offer). The right use of a mock score is tracking your own trajectory, not chasing rumours.
09

A week-by-week plan you can copy (October sitting)

Taking the October sitting as the example, allow roughly twelve weeks from late July. Starting later means compressing each phase proportionally, but keep the mock milestones where they are:
WeekApproximate datesFocus
Week 1late JulyBook early once booking opens on 20 July; download the specification, the Notes and the past papers; first self-audit against the specification
Weeks 2-4early to mid AugustPhase one: the eight Part 1 topics one by one, a formula card per topic, with the GCSE-level topics woven in
Weeks 5-7late August to early SeptemberPhase two: the Notes on Logic and Proof, Arg1 to Arg4 and the four proof types; past Paper 2s sorted by question type
Week 8mid SeptemberFirst full mock: both papers back to back, timed, no calculator; calibrate honestly
Week 9late SeptemberPatch the weakest areas; confirm booking details before the 28 September deadline
Weeks 10-11late September to early OctoberPhase three: a timed full paper every two to three days, with a debrief after each
Week 12final weekOne last full mock early in the week; after that only formula cards, logic definitions and the error log, and sort out your sleep
Keep one fixed debrief slot per week, sorting the week's errors into knowledge, reasoning and timing. And ration the papers: the official archive covers eight years (2016 to 2023), so do not burn complete sets during phase one; whole papers belong to phase three, under the clock.
10

Test week, test day and what happens after

Test week is about subtraction. Nothing new goes in at this stage, and nothing new should. Keep exactly three things in rotation: reproducing your formula cards, the Section 2 definitions (the contrapositive, necessary versus sufficient, and negating quantified statements deserve the most repetitions), and the recurring error types flagged in your log.
Re-check the test-day rules once more:
  • No calculator and no dictionary, and there is no formulae booklet;
  • Rough working goes on the erasable sheets or whiteboard and pen provided at the centre, and you may not take your own materials in;
  • The two papers run one after the other, 2 hours 30 minutes in total, and no official document mentions a break, so prepare your concentration for one continuous session.
Results follow on 16 November 2026 for the October sitting and 8 February 2027 for the January sitting, released through your UAT-UK account. Scores go automatically to the institutions in your UCAS application that require the test, matched course by course; nothing needs submitting by hand, and you cannot choose who sees the score. Two final rules are worth knowing in advance so that results day holds no procedural surprises: UAT-UK publishes no grade boundaries, and it does not accept appeals against scores. If the number disappoints, the lever is your application strategy and the rest of your file, not a remark request.
FAQ

Frequently asked questions

When do I register for the TMUA for 2027 entry?
Create an account on the UAT-UK website first; booking opens at 3pm UK time on 20 July 2026. Booking for the October sitting closes at 6pm on 28 September; for the January sitting it opens on 26 October and closes on 21 December. Places are booked through Pearson VUE, and the test costs £78 in the UK and Republic of Ireland and £133 elsewhere.
Can I sit the TMUA twice and use the better score?
No. UAT-UK allows one sitting per admissions cycle, so October and January are alternatives, not two attempts. Officially neither session carries an advantage, and your score is sent automatically to the universities in your UCAS application that require the test.
How long does TMUA preparation take?
The framework in this guide allows roughly twelve weeks: about four on Section 1 knowledge, about three on Paper 2 logic and proof, and the rest on timed full papers with debriefs. If you start later, compress each phase proportionally, but protect the mid-September full mock, because it also informs your booking decision.
Where do I find TMUA past papers, and are the old ones still useful?
The official preparation-materials page hosts free papers for every year from 2016 to 2023, each with Paper 1, Paper 2, worked answers and an answer key, plus an early specimen. They date from the paper-based era while the live test is now computer-based, but the specification and style carry through; save whole papers for timed use in the final phase.
I have never studied logic. How do I prepare for Paper 2?
The official Notes on Logic and Proof is written precisely for candidates who have not met theorems and proofs in class. Read it first, then study the Section 2 terms (Arg1 to Arg4) and the four proof types against the specification, then practise past Paper 2s by question type. Symbolic notation and truth tables are explicitly not required, and mathematical induction is not on the specification's list.
What can I take into the TMUA, and is there a break?
Calculators and dictionaries are banned, and there is no formulae booklet. Rough working goes on the erasable sheets or whiteboard and pen provided by the centre, and you may not bring your own materials. The two papers are taken one after the other, 2 hours 30 minutes in total, and no official document mentions a break between them.
When do TMUA results come out, and how do universities get them?
For 2027 entry, results are released on 16 November 2026 for the October sitting and on 8 February 2027 for the January sitting, through your UAT-UK account. Scores are sent automatically, course by course, to the institutions in your UCAS application that require the test; you cannot choose who sees them, UAT-UK publishes no grade boundaries, and score appeals are not accepted.

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Put it into practice

28 TMUA papers on FrontierVUE, including 10 Frontier Original mocks built to the current format, every question with a worked solution. The first 2 papers are free.