United Kingdom · Year 13 · 12 to 16 October 2026 and 4 to 8 January 2027

TMUA preparation: the Test of Mathematics for University Admission

The TMUA looks like a maths test and is half a logic test. Its first paper asks you to apply school mathematics in unfamiliar ways; its second, Mathematical Reasoning, asks whether a statement follows, whether a condition is necessary or sufficient, and where an argument breaks. Both papers are 75 minutes for 20 multiple-choice questions, with no calculator. Cambridge, Imperial, Oxford and Warwick use it, among others, for mathematics, computer science and some economics courses. This page sets out the format and windows for 2027 entry from those universities' own admissions pages, explains how the scaled score works, works through the kind of logic Paper 2 tests with examples of our own, and is honest about how much preparation the universities say you need.

Book the free first class Book a priority demo Try the Paper 2 logic lesson Ask on WhatsApp

Live teaching since 2020 · 10,000+ students · TMUA facts from Imperial, Cambridge, Warwick and Oxford pages

In short

The TMUA (Test of Mathematics for University Admission) is a computer-based admissions test run by UAT-UK at Pearson VUE centres. It has two papers, Applications of Mathematical Knowledge and Mathematical Reasoning, each with 20 multiple-choice questions in 75 minutes, no calculator, and no marks lost for wrong answers. Imperial lists seven universities that use it for some courses: Imperial, Cambridge, Durham, LSE, UCL, Oxford and Warwick. Windows for 2027 entry are 12 to 16 October 2026 and 4 to 8 January 2027. Modern Age Coders runs live online TMUA classes, in groups of 15 to 20 or one-to-one.

Where to start

Three courses for a TMUA candidate

One for the test, and the two A Levels its questions draw on.

TMUA and STEP Preparation (Oxford MAT Now TMUA) course thumbnail

TP / 01

TMUA course

Sixth formers aged 16 to 18: both papers, the logic of Paper 2, and timed sets.

Open the syllabus →
A-Level Maths course thumbnail

TP / 02

A Level Maths

Paper 1 lives mostly in AS-level and GCSE Higher content, plus some of the full A Level.

Open the syllabus →
A Level Further Maths course thumbnail

TP / 03

A Level Further Maths

Not needed for the TMUA, but expected for many of the courses that set it.

Open the syllabus →

The two papers

What is on the TMUA, and how long is it?

Two papers of 75 minutes, each with 20 multiple-choice questions, two and a half hours in total. Imperial and Warwick describe Paper 1 as applying mathematics in new situations and Paper 2 as reasoning and simple ideas from elementary logic.

TMUA format, from the Imperial, Warwick and Cambridge admissions pages (read 31 October 2026)
Paper 1Paper 2
NameApplications of Mathematical KnowledgeMathematical Reasoning
What it assessesYour ability to apply your knowledge of mathematics in new situationsYour ability to deal with mathematical reasoning, and simple ideas from elementary logic
Questions20 multiple-choice20 multiple-choice
Time75 minutes75 minutes
AidsNo calculator or dictionaryNo calculator or dictionary
Wrong answersCost nothingCost nothing
ContentSection 1 of the content specificationSections 1 and 2; Section 2 covers logic and proof

The content is school mathematics

Oxford's Mathematical Institute summarises the content specification as mathematics "usually taught at AS-level or Higher Level GCSE, plus a small number of topics from the full A-level Mathematics". There is no Further Maths in it, which is why the test can be set to applicants from many school systems.

What makes it hard is the setting. A Paper 1 question rarely announces its topic; a student has to recognise that a question about areas is really about a quadratic, or that a sequence question is really about inequalities.

Paper 2 is the unusual one

The second section of the specification applies only to Paper 2, Oxford says, and covers logic and proof: what a statement means, what follows from it, and how arguments go wrong. Most A Level courses touch these ideas lightly, if at all.

Cambridge and Warwick both recommend reading the specification and the notes on Logic and Proof that UAT-UK publishes. For most applicants, those notes are the single most useful document, and they are free.

Pacing, our arithmetic from the published format
MeasureValueWhat it means
Time per question75 minutes / 20 = 3 minutes 45 secondsA question that has taken six minutes is costing another
Marks lost for a wrong answerNone, per Cambridge and ImperialNever leave a blank; a guess cannot lower the score
Our two-pass planFirst pass about 50 minutes, second about 25Answer what is quick, flag and guess the rest, then return to the flags

Sources: Imperial College London TMUA page, the University of Warwick admissions tests page, the University of Cambridge TMUA page and the Oxford Mathematical Institute TMUA page, read 31 October 2026. The UAT-UK website could not be reached from our side that day, so no fact here is taken from it directly. Pacing and the two-pass plan are ours. We are not connected with UAT-UK, Pearson VUE or any university named.

Who asks for it

Which universities require the TMUA?

Imperial lists seven: Imperial, Cambridge, Durham, LSE, UCL, Oxford and Warwick, for certain courses in mathematics, economics and computer science. Each university decides which of its courses require it, so the course page is the authority.

Courses that use the TMUA, from each university's own admissions page where we could read it (31 October 2026)
UniversityCoursesRequired or optionalWindow
University of CambridgeComputer Science, Economics, MathematicsRequiredOctober; January only for mature applicants in the January round
University of OxfordMathematics, Computer Science and joint honoursRequired (it replaced the MAT from 2026)October only
Imperial College LondonDepartment of Computing, including joint Mathematics and Computer Science; Department of Mathematics; BSc Economics, Finance and Data ScienceRequiredOctober or January
University of WarwickComputer Science (G400, G403, GN42) and Discrete Mathematics (G190, G4G3)Required, except for contextual offersOctober or January
University of WarwickMathematics (G100, G103)TMUA or STEPOctober or January
University of WarwickEconomics; Mathematics and Statistics, MORSE, Data ScienceOptionalOctober or January
Durham, LSE, UCLSome mathematics, economics or computer science coursesNamed as users by Imperial; check each course pageNot verified by us

Sit it once

A student applying to several of these universities takes the test once per cycle. Imperial says "Only your first test score will be considered", and Warwick says it accepts the results from one test in each admissions cycle. A student who sits in October cannot sit again in January to improve.

Because Oxford and Cambridge require the October window, anyone applying to either must sit in October, and that score is the one every other university sees too.

Read the course, not the list

Warwick shows why. Computer Science requires the TMUA; Mathematics accepts TMUA or STEP; Economics and Statistics make it optional, with Warwick saying applicants who skip it are not at a disadvantage for Statistics. The same university, four different rules.

For computer science applicants, note that Warwick excludes Computer Systems Engineering (G406, G408) from the requirement. Course codes matter, and each university lists them.

Course lists from the Cambridge, Imperial and Warwick pages above, and the Oxford Computer Science how to apply page. Durham's admissions tests page refused our request on 31 October 2026 and we did not retry it; LSE and UCL are named as Imperial lists them.

Dates for 2027 entry

When is the TMUA in 2026 and 2027?

There are two windows: 12 to 16 October 2026 and 4 to 8 January 2027. Booking for October closed on 28 September 2026; booking for January opened on 28 October 2026 and closes on 21 December 2026 at 18.00 UK time.

TMUA windows and deadlines for 2027 entry, from Imperial's TMUA page
Window 1Window 2
Test dates12 to 16 October 20264 to 8 January 2027
China, Hong Kong and Macau15 to 16 October 2026 only8 January 2027 only
Booking opens20 July 2026, 15.00 UK time28 October 2026, 15.00 UK time
Booking closes28 September 2026, 18.00 UK time21 December 2026, 18.00 UK time
Access arrangement requests1 June to 14 September 20265 October to 7 December 2026
Who must use itAll Oxford and Cambridge applicantsOthers who did not sit in October
  1. Create a UAT-UK account. Imperial says one account is enough even for a student who sits more than once across cycles.
  2. Apply for a bursary first, if eligible. UK candidates in financial need can sit free, but Imperial says the bursary must be approved before booking.
  3. Request access arrangements in their window. Rest breaks or extra time are available for learning difficulties, disabilities, sensory impairments and medical conditions.
  4. Book the date and the Pearson centre. Imperial says the fee depends on the test centre location, not on nationality or residence.
  5. Sit the test. Two 75-minute papers on screen, no calculator or dictionary.
  6. Wait for the university. Warwick releases Mathematics decisions in batches from November and sets its final threshold around April.

Windows, booking times and access arrangement dates from Imperial's TMUA page; the October requirement for Oxford and Cambridge from Imperial and Cambridge; Warwick's decision timing from its admissions tests page; all read 31 October 2026. Fees are set by UAT-UK and are not printed here.

Paper 2, ours

How do you answer TMUA Paper 2 logic questions?

By reading the statement before doing any mathematics. Most Paper 2 errors are not calculation errors; they are a converse taken for the original, a condition called sufficient when it is only necessary, or a proof accepted because its conclusion is true. These four examples are ours, written for this page.

Converse and contrapositive

Take "if n is a multiple of 6, then n is even". True. Its converse, "if n is even, then n is a multiple of 6", is false: n = 4. Its contrapositive, "if n is odd, then n is not a multiple of 6", is true, and always agrees with the original.

Necessary or sufficient

Is x > 2 sufficient for x2 > 4? Yes: any x above 2 has a square above 4. Is it necessary? No: x = −3 gives x2 = 9 without x > 2. The exact condition is x > 2 or x < −2.

Negating "for all"

The negation of "every student passed some test" is not "no student passed any test". It is "some student passed no test". Swap each quantifier and negate what is left.

Our flawed proof. Claim: x2 ≥ x for every real number x. "Proof": x2 − x = x(x − 1). If x ≥ 1, both factors are at least zero, so the product is too. If x ≤ 0, both factors are at most zero, so the product is at least zero. Therefore x2 ≥ x always.

Where it fails

Each case is argued correctly. The error is in what is missing: the cases x ≥ 1 and x ≤ 0 do not cover the numbers strictly between 0 and 1. There, x is positive and x − 1 is negative, so the product is negative. Try x = 1/2: x2 = 1/4, which is less than 1/2. The claim is false.

Paper 2 questions of this kind usually offer options such as "the proof is correct", "the error is in line 2" or "the error is that a case is omitted". Reading each line for truth will not find this mistake; asking "have all possibilities been covered?" will.

A Paper 1 contrast

Paper 1 rewards spotting structure quickly. Our example: the roots of x2 − 6x + k = 0 differ by 2. Find k. Call the roots r and r + 2; their sum is 6, so 2r + 2 = 6 and r = 2. The roots are 2 and 4 and k is their product, 8. No quadratic formula needed.

In the test, that is a forty-second question if the student thinks about sum and product first and a four-minute one if they do not. The time saved goes to a Paper 2 question that needs it.

Six practice questions of our own, with answers
#Our questionAnswer
1True or false: x2 − 4x + 5 > 0 for every real x.True: it equals (x − 2)2 + 1
2What is the least value of x2 − 6x + 13, and where?4, at x = 3
3What is the sum of the first 20 odd numbers?400
4True or false: if ab is irrational, then at least one of a and b is irrational.True: its contrapositive is that two rationals multiply to a rational
5How many integers n satisfy n2 < 50?15: from −7 to 7
6Is "n2 is a multiple of 4" necessary, sufficient, both or neither for "n is even"?Both, for integers n

All examples and practice questions are ours, written on 31 October 2026, and are not TMUA questions. UAT-UK publishes official practice papers, and Warwick's Mathematics Institute publishes walkthroughs of selected past questions; Oxford also ran free TMUA webinars in the summer of 2026, with recordings.

Scores and preparation

How is the TMUA scored, and what is a good score?

Scores run from 1 to 9 to one decimal place, with no pass mark and no grade boundaries. Universities read them alongside the rest of the application, and only Warwick, among the pages we read, has published anything like a figure.

What the universities say about TMUA scores (read 31 October 2026)
SourceWhat it says
ImperialScores are "reported on a scale that runs from 1 (low) to 9 (high)", "recorded to one decimal place" and "statistically equated" across test versions; the TMUA gives a single overall score
ImperialA high score does not mean an application will succeed, and a low score does not mean it will fail
WarwickFor 2025 entry, "the majority of offers were made to applicants with a TMUA score of 5.0 and above" for Mathematics, with some below 5.0 after holistic assessment
WarwickComputer Science: the exact requirement is set once all results are in and "will not be published"
WarwickStatistics and related courses: offers may be met by 5.0 in TMUA, or grade 2 in any STEP, or by A Level or IB grades
CambridgeThere is no pass or fail; the final score is based on the number of correct answers

What the universities say about preparing

Cambridge and Warwick use the same sentence, and it belongs on any page selling TMUA classes: "there is no need to take a preparation course or to do much preparation beyond familiarising yourself with the test format and style of questions." Both recommend the specification and the Logic and Proof notes.

There is also free structured help. Warwick points to MEI, an education charity, which runs a free online TMUA course for Year 13 students at state-funded schools, academies and colleges.

Where a class still helps

A student whose school course never mentioned contrapositives or necessary conditions may find Paper 2 genuinely new, and some international curricula reach AS-level topics in a different order. A few weeks of teaching can close that gap faster than reading alone.

Some students simply work better with a teacher and a group. That is a fair reason too, provided nobody pretends the test needs coaching to pass. It has no pass mark, and we promise no score.

Score statements from Imperial's Understanding your ESAT and TMUA scores page and Warwick's and Cambridge's admissions pages, read 31 October 2026. Warwick's 5.0 describes its own 2025 offers and is not a requirement elsewhere.

A route to the October window

Four stages before the test

Our suggested order for a Year 12 student sitting next autumn, compressed for anyone sitting in January 2027. Each stage ends with something the student can do, not a date.

Our TMUA plan
WhenStageThe sign it is secure
Year 12, spring1. AS-level pure in placeAlgebra, coordinate geometry, sequences, logs and basic calculus are automatic
Year 12, summer2. Logic and proof learnedCan state the converse, contrapositive and negation of any statement without hesitating
Year 13, early autumn3. Untimed official practiceGets most questions right with no clock, and knows why the wrong ones were wrong
Final four weeks4. Timed papers, two passesFinishes both papers with no blanks and time to check the flagged questions

If January is the window

Booking is open until 21 December 2026. Spend the first fortnight on the Logic and Proof notes and the rest on timed practice papers.

Remember that a January score cannot be used for Oxford or Cambridge. It is the right window only for applicants who are not applying to either.

If the test is next October

Use Year 12 to make A Level pure fluent and to learn logic properly. Neither needs test papers yet.

Applicants also sitting STEP for Cambridge or Warwick will find the two complement each other: the TMUA rewards speed and precision, STEP rewards stamina and depth.

The full list

What we teach a TMUA candidate

Four groups, sorted by the course the student is applying for.

I

The test

Both papers

TP / T / 01

TMUA, MAT and STEP preparation

Logic, proof and timed sets.

Open the syllabus

TP / T / 02

Olympiad and competition maths

Harder problems for spare evenings.

Open the syllabus

TP / T / 03

Quantitative reasoning

Fast multiple-choice technique.

Open the syllabus
II

Mathematics applicants

A Level and IB

TP / M / 02

A Level Further Maths

Expected by most courses that set the TMUA.

Open the syllabus

TP / M / 03

IB Mathematics

For Diploma students applying in the UK.

Open the syllabus
III

Computer science applicants

Cambridge, Imperial, Oxford, Warwick

TP / C / 01

Problem solving and algorithms

Reasoning about programs.

Open the syllabus

TP / C / 03

Cambridge A Level Computer Science

For 9618 students.

Open the syllabus
IV

Economics applicants

Cambridge, Imperial, Warwick

TP / E / 01

Statistics and probability

The mathematics of economic data.

Open the syllabus

TP / E / 02

Business and finance mathematics

Growth, interest and optimisation.

Open the syllabus

TP / E / 03

Data analytics mathematics

Working with real datasets.

Open the syllabus

How lessons run

Live TMUA classes through the autumn and winter

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

Logic and content, after sixth form.

Weekend mornings

Full timed papers, both halves.

1-on-1

A single applicant with a single gap.

Statements first

Every Paper 2 lesson starts by rewriting a statement three ways before any algebra.

The clock, later

Accuracy without time pressure comes first; the 3 minutes 45 seconds arrive in the final weeks.

Error log

Each wrong answer is labelled: content gap, misread statement or pacing.

Groups of 15 to 20

Wrong answers are compared openly, which is how logic errors become visible.

Original questions

We write our own practice; students sit UAT-UK's papers themselves.

No score promised

The TMUA has no pass mark and we promise no number on its scale.

Student work

What our students build

A selection of projects our students have published in maths, code and machine learning. See the student labs for more.

NutriLife AI nutrition coach project screenshot

AI and ML

NutriLife

An AI nutrition coach that reads what you eat and works you toward a target.

by Bhavya · Open it

Misti AI chatbot for maths and coding screenshot

AI and ML

Misti

A chatbot that answers mathematics and programming questions, built and deployed by a student.

by Harshit · Open it

GuardianX AI internet safety assistant screenshot

AI and ML

GuardianX

An assistant that helps a young person recognise unsafe situations online.

by Vivaan · Open it

SkyCast weather forecast application screenshot

Web app

SkyCast

A weather forecasting site with live conditions for any location.

by Krish

Fees

Fees

The test fee goes to UAT-UK and depends on the test centre; bursaries exist for UK candidates in financial need. Our classes are billed monthly with nothing to join, and most TMUA students stop after their window.

Free first class

USD 0

no card required

  • A free first class
  • Five Paper 2 statements, read together
  • No card details
Book it

Group batch

USD 100

a month, billed in US dollars

  • Groups of 15 to 20
  • A steady teacher
  • Timed sets reviewed
  • Monthly, cancel when done
Start here

One to one

USD 150

a month, billed in US dollars

  • One student, one teacher
  • Built on the error log
  • For a near window
Enquire

What families say

Rated 4.9 across 547 Google reviews

Verbatim reviews from our Google business profile.

★★★★★

"The one step solution for my son. Modern Age Coders make learning coding so simple that kids love it. The teachers explain complex concepts clearly with practical exercises and interactive content."

Ria Mukherjee

Parent

★★★★★

"Modern Age Coders has been a game-changer for me. I struggled to grasp IT concepts and coding before joining, but their classes transformed everything. I can now confidently write complex programs with ease."

Samriddha Mondal

Student

★★★★★

"One of the most wonderful education centres out there. Education is not limited to school syllabus but focuses on skill development."

Vansh Agarwal

Student

★★★★★

"My child Dhairya is really enjoying the Modern Age Coders classes. This is his first online class and he eagerly looks forward to it. I can already see his improvement, and the teachers are very cooperative."

Sonam Oswal

Parent of Dhairya

★★★★★

"Modern Age Coders have wonderful teachers who teach in a clear, easy and practical way. The teacher boosts students' confidence and inspires them to learn without hesitation."

Sonu Goyal

Parent

★★★★★

"I highly recommend this computer coding class! The teachers are incredibly knowledgeable and passionate about coding."

Ritu Kedia

Parent

TMUA questions

What TMUA candidates and parents ask

What is the TMUA?

The Test of Mathematics for University Admission, a computer-based admissions test administered by UAT-UK at Pearson VUE centres. Universities use it for certain mathematics, computer science and economics courses.

How long is the TMUA?

Two and a half hours: two papers, each of 75 minutes with 20 multiple-choice questions. Paper 1 is Applications of Mathematical Knowledge and Paper 2 is Mathematical Reasoning.

When is the TMUA for 2027 entry?

Imperial lists two windows: 12 to 16 October 2026 and 4 to 8 January 2027. Booking for January opened on 28 October 2026 and closes on 21 December 2026 at 18.00 UK time.

Which universities use the TMUA?

Imperial lists Imperial, Cambridge, Durham, LSE, UCL, Oxford and Warwick. Each decides which courses need it, so check the course page; at Warwick, for example, it is required for Computer Science and optional for Economics.

Can I use a calculator in the TMUA?

No. Cambridge and Warwick say you will not be able to use a calculator or dictionary, and Oxford says no calculators are permitted for the test.

Is there negative marking in the TMUA?

No. Cambridge and Imperial say you do not lose marks for wrong answers, so it is worth answering every question, even with a guess.

What is a good TMUA score?

Scores run from 1 to 9 to one decimal place and there is no pass mark. Warwick says most of its 2025-entry Mathematics offers went to applicants scoring 5.0 or above, but that figure is Warwick's own and not a target elsewhere.

Can I take the TMUA twice?

Only once per admissions cycle counts. Imperial says only your first test score will be considered, and Oxford and Cambridge applicants must sit the October window.

Do I need a TMUA tutor?

Cambridge and Warwick say there is no need for a preparation course beyond knowing the format and question style. A class helps most when logic and proof are new, or when a student wants a teacher to practise with.

What days are classes on?

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 connected with UAT-UK?

No. Our classes are entirely separate from UAT-UK, Pearson VUE and every university on this page. Students register and book the test themselves.

Related pages

Other pages for TMUA applicants

The school courses the test draws on, and pages for computer science applicants.

A Level Maths tuition online

Paper 1 content, taught at depth.

IB Maths tuition online

For Diploma students heading to UK universities.

Further Maths tuition online

Often expected alongside the test, never examined in it.

OCR A Level Computer Science H446

For computer science applicants on the OCR course.

AQA A Level Computer Science 7517

The AQA route, paper by paper.

Maths tuition in London

For families near LSE, UCL and Imperial.

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

Start here

Book a free TMUA class

Say which window you are sitting and which courses you are applying for. The free class reads five Paper 2 statements with you and shows where your reasoning is solid and where it slips.

Before booking, you can browse our courses or read about how we teach.

WhatsApp us · +91 91233 66161 · connect@modernagecoders.com

Lessons are live from India at a time fixed in UK time. WhatsApp tends to be the quickest way to reach us from a UK number.

Nothing to pay and no card; we answer once to set a time.

Want a class sooner? Book a priority demo

A priority demo is a full class of about 45 to 60 minutes. After the class the mentor sends a written skill report and a personal learning roadmap on WhatsApp. If you enrol, the demo fee is adjusted against your first month's fee. Share your demo Order ID with us on WhatsApp and we take it off.

Book a priority demo

Keep exploring Modern Age Coders

Related courses and guides

Learn more

Free resources

From the blog

Start here

Free classPriority demoCall us