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.
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TMUA Revision at a Glance
Sittings
One sitting per cycle: October or January, not both; Oxbridge applicants must, as a rule, sit in October
October deadlines
Booking closes 6pm UK time on 28 Sep; test window 12-16 Oct; results on 16 Nov
The framework
Roughly twelve weeks in three phases: Section 1 maths, then Paper 2 logic and proof, then timed full papers
First full mock
By mid-September at the latest; it also informs the booking decision
Core materials
All free from UAT-UK: the Content Specification, the Notes on Logic and Proof, and the 2016-2023 past papers with worked answers

All dates are UAT-UK's published schedule for 2027 entry, UK time.

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.
I

Part 1 of 3

Sections 01 to 04

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 the timeline below covers every 2027-entry milestone from booking opening to results day, all UK time as published by UAT-UK.
2026 – 2027Timeline
Jul 26
Aug 26
Sep 26
Oct 26
Nov 26
Dec 26
Jan 27
Feb 27
October booking opens
20 Jul, 3pm
Book early once booking opens: create a UAT-UK account first, then book a slot through Pearson VUE.
October booking deadline
28 Sep, 6pm
A hard cut-off: no October bookings are accepted afterwards, so do not leave account setup and payment to the final week.
October test window
12-16 Oct
In mainland China, Hong Kong and Macau the test runs only on 15 or 16 October.
October results
16 Nov
January booking opens
26 Oct, 3pm
January booking deadline
21 Dec, 6pm
January test window
4-8 Jan 2027
In mainland China, Hong Kong and Macau the test runs only on 8 January.
January results
8 Feb 2027
Hard deadline Event WindowAll times are UK time as published by UAT-UK; candidates in mainland China, Hong Kong and Macau cannot pick freely within the window.

How to register

Two steps: create a UAT-UK account, then book through Pearson VUE

Fee (UK and Ireland)

£78

Fee (elsewhere, incl. China)

£133

Test days in the China region

Fixed at 15 or 16 October and at 8 January

No free choice within the window for mainland China, Hong Kong and Macau

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. There is no sitting October as a trial run and going again in January: the paper you submit is the only score you get.
Applying to Oxford or CambridgeApplying elsewhere (Imperial, LSE, Warwick, UCL, Durham)
Which sittingMust, as a rule, take the October sittingEither sitting is allowed
Exceptions and trade-offsThe only exceptions: applicants to Cambridge mature colleges with the January deadline, and to Oxford's Astrophoria Foundation YearJanuary 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 four items below before you begin.

The Content Specification

The only authoritative answer to "is this topic examinable"

The current version applies to the October 2026 and January 2027 sittings and defines Sections 1 and 2

Notes on Logic and Proof

The official booklet written for Paper 2

Aimed at candidates who have not yet met theorems and proofs in class; if formal logic is new to you, this is your textbook

Past papers, 2016 to 2023

Paper 1, Paper 2, worked answers and an answer key for every year, plus an early specimen set

From the paper-based era, but the specification and question style carry through; still the core practice material

The Explanation of Results

The official score-distribution document for every sitting

The calibration tool; see the section on mocks

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 the shared foundation, the Paper 2 material sits on top of it, and that gives a three-phase plan.
01Phase 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.
02Phase 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.
03Phase three

Timed full papers

Sit the 2016-2023 papers under real conditions, 75 minutes per paper and 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.
II

Part 2 of 3

Sections 05 to 08

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 into two parts, covering the topics below.

Part 1

Almost all AS level pure maths, in eight topics

Algebra and functions, sequences and series, coordinate geometry, trigonometry, exponentials and logarithms, differentiation, integration, graphs of functions

Part 2

Almost all Higher Level GCSE material

Units, number, ratio and proportion, algebra, geometry, statistics and probability

Audit yourself against the specification, not a textbook
Candidates 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 you finish
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; full timed papers can wait
Check each finished topic against matching past-paper questions, and save complete papers for the later phases.
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. Here it is, block by block.
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
  • 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. 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.
Two boundaries worth memorising: mathematical induction is not on the specification's list of proof types, so do not spend revision time on it for this test; and the specification 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. There are four of them.

Pace per paper

Twenty questions in 75 minutes, roughly 3 minutes 45 seconds each

The average is arithmetic, not an official rule; any question over five minutes is borrowing time from the others

Back to back

One paper after the other, 2 hours 30 minutes in total

No official document mentions a break; run the full sequence at least two or three times to train second-half concentration

Marking

No negative marking; equal weight for every question across both papers

The official advice is to attempt everything: bank what you can do, return to the hard ones, never leave a blank

Working conditions

No calculator or dictionary; only erasable sheets or a whiteboard and pen are provided

No materials of your own; do a few papers on a whiteboard or 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. 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.
01Question 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.
02Question 2

How far off are you?

Calibrate against the official Explanation of Results. For October 2025, typical candidates score around 4.5 and roughly 10% 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 grades.
Calibration trap one: targets on the old scale
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 and cannot be adopted as targets.
Calibration trap two: 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.
III

Part 3 of 3

Sections 09 to 10

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.
01Week 1 · late July

Book and stock up

Book early once booking opens on 20 July; download the specification, the Notes and the past papers; first self-audit against the specification.
02Weeks 2-4 · early to mid August

Phase one: Section 1

The eight Part 1 topics one by one, a formula card per topic, with the GCSE-level topics woven in.
03Weeks 5-7 · late August to early September

Phase two: logic and proof

The Notes on Logic and Proof, Arg1 to Arg4 and the four proof types; past Paper 2s sorted by question type.
04Week 8 · mid September

First full mock

Both papers back to back, timed, no calculator; calibrate honestly.
05Week 9 · late September

Patch gaps, confirm booking

Patch the weakest areas; confirm booking details before the 28 September deadline.
06Weeks 10-11 · late September to early October

Phase three: timed full papers

A timed full paper every two to three days, with a debrief after each.
07Week 12 · the week before the test

The final week

One last full mock early in the week; after that only formula cards, logic definitions and the error log, and sort out your sleep.
Two standing disciplines: keep one fixed debrief slot per week, sorting the week's errors into knowledge, reasoning and timing; and ration the papers, since the official archive covers only eight years (2016 to 2023). 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.

October results

16 November 2026

Released through your UAT-UK account

January results

8 February 2027

Released through your UAT-UK account

Score delivery

Sent automatically to the institutions in your UCAS application that require the test

Matched course by course; nothing to submit by hand, and no choosing 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.
SOURCES

Official sources

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