TMUA Guide 2026: Complete Guide for 2027 University Entry

The Test of Mathematics for University Admission, usually shortened to TMUA, is used by selected UK universities for mathematically demanding degrees.

You may need to take it when applying for courses such as:

• Mathematics

• Computer Science

• Economics

• Statistics

• Data Science

• Econometrics

• Actuarial Science

• Joint Mathematics courses

The TMUA does not reward the memorisation of advanced techniques for their own sake.

Instead, it assesses whether you can:

• Apply familiar mathematics in unfamiliar situations

• Identify efficient solutions

• Interpret mathematical statements precisely

• Follow and construct logical arguments

• Recognise errors in reasoning

• Work accurately without a calculator

• Make sensible decisions under time pressure

The test lasts two hours and 30 minutes. It contains two papers of 20 multiple-choice questions, with 75 minutes allowed for each paper. There is no calculator, no formula booklet and no penalty for incorrect answers.

For 2027 university entry, the two TMUA windows are:

• 12 to 16 October 2026

• 4 to 8 January 2027

Most Oxford and Cambridge applicants must take the October sitting.

This guide explains:

• Who needs to take the TMUA

• Which universities use it

• The test format

• What appears in Papers 1 and 2

• How TMUA scoring works

• What counts as a good score

• The 2026 and 2027 dates

• Registration, fees and bursaries

• How to prepare effectively

• What to expect on test day

• Common mistakes to avoid

For an overview of other tests, read Complete Guide to University Admissions Tests .

What Is the TMUA?

TMUA stands for:

Test of Mathematics for University Admission

It is a computer-based admissions test administered through University Admissions Tests UK, commonly called UAT-UK.

UAT-UK is a collaboration between Imperial College London and the University of Cambridge. Its tests are delivered through Pearson’s international network of professional test centres.

The TMUA is used to assess mathematical thinking and reasoning for selected courses at universities including:

• University of Cambridge

• Durham University

• Imperial College London

• London School of Economics and Political Science

• University of Oxford

• UCL

• University of Warwick

Not every Mathematics, Economics or Computer Science course at these universities requires the test. Some make it compulsory, some recommend it and others provide alternative routes. You must check the individual course page before registering.

What Does the TMUA Assess?

The TMUA assesses whether you can use school-level Mathematics flexibly.

It focuses on:

• Mathematical knowledge

• Problem-solving

• Logical reasoning

• Mathematical proof

• Interpretation of statements

• Efficient use of familiar methods

• Identification of flawed arguments

UAT-UK describes the content as Mathematics normally covered within Higher Level GCSE and AS-level Mathematics courses. The challenge comes from applying that knowledge to unfamiliar problems rather than learning a large amount of additional content.

Is TMUA an A-Level Mathematics Test?

Not exactly.

Much of the mathematical content overlaps with Higher GCSE and AS Mathematics, including:

• Algebra

• Functions

• Graphs

• Sequences

• Coordinate geometry

• Trigonometry

• Exponentials and logarithms

• Differentiation

• Integration

• Geometry

• Probability

• Statistics

Paper 2 also assesses mathematical logic and proof, which may be less familiar from standard school examinations.

The questions are designed to make you think rather than repeat a familiar method.

You may recognise every topic in a question but still need to decide:

• Which information matters

• Which method is most efficient

• Whether a statement is always true

• Whether one example proves or disproves a claim

• Whether an argument follows logically

Who Needs to Take the TMUA?

You need to take the TMUA when it is compulsory for one or more of your chosen courses.

You might also choose to take it when a university recommends the test or uses a strong score to make reduced offers.

Check:

1. The university

2. The exact degree

3. The course code

4. The intended entry year

5. Whether TMUA is required or optional

6. Whether October or January is permitted

7. Whether STEP can be used as an alternative

Failing to take a compulsory admissions test can make your application ineligible for consideration.

Which Universities Use the TMUA?

Cambridge TMUA Requirements

For 2027 entry, Cambridge requires the TMUA for:

• Computer Science

• Economics

• Mathematics

Most Cambridge applicants must take the test during the 12 to 16 October 2026 window.

Cambridge Computer Science

All applicants to Cambridge Computer Science must take the TMUA.

The test helps the university assess mathematical reasoning alongside:

• Academic results

• Predicted grades

• Subject preparation

• The wider application

• Interview performance

• Contextual information

Computer Science applicants should not assume that A-level Computer Science preparation is more important than Mathematics. The Cambridge course has demanding mathematical entry requirements as well as the TMUA.

Cambridge Economics

All applicants to Cambridge Economics must take the TMUA.

The test is particularly relevant because university Economics contains substantial mathematical and statistical content.

Applicants should still check:

• A-level or equivalent Mathematics requirements

• College requirements

• Interview arrangements

• Qualification-specific conditions

Cambridge Mathematics

All applicants to Cambridge Mathematics must take the TMUA during the application stage.

Cambridge Mathematics applicants may also need STEP as a condition of an offer. TMUA and STEP perform different roles:

TMUA	STEP
Taken during the application process	Normally taken after an offer
Multiple-choice	Extended mathematical solutions
Two papers of 75 minutes	Three-hour written papers
Used to support selection	May be included in offer conditions

Do not assume that taking TMUA removes the need to prepare for STEP.

Read STEP Guide if you are applying for Cambridge Mathematics.

Oxford TMUA Requirements

Oxford has changed its Mathematics and Computer Science admissions testing for 2027 entry.

The previous Mathematics Admissions Test, or MAT, is no longer used. Applicants to Oxford Mathematics, Computer Science and related joint courses now take the TMUA.

Courses using TMUA include:

• Computer Science

• Computer Science and Philosophy

• Mathematics

• Mathematics and Statistics

• Mathematics and Computer Science

• Mathematics and Philosophy

All standard Oxford applicants must use the October sitting and complete both TMUA papers.

Oxford Mathematics

Oxford uses TMUA scores to support interview shortlisting.

The Mathematical Institute explains that it cannot interview every applicant and uses the test to help identify approximately three applicants per available place for interview.

Your score is not considered in isolation. Oxford also considers:

• Academic record

• Predicted or achieved grades

• Subject combination

• Contextual information

• Interview performance

Oxford Computer Science

Oxford Computer Science applicants must take TMUA.

The university uses the score alongside evidence of:

• Mathematical ability

• Independent thinking

• Ability to understand unfamiliar ideas

• Enthusiasm for the subject

Further Mathematics is highly relevant to Oxford’s entry requirements where it is available at your school.

Oxford Joint Courses

A joint course containing Mathematics or Computer Science may also require TMUA.

Do not assume that a Philosophy, Statistics or joint course uses a different test. Check the exact Oxford course page.

Imperial College London TMUA Requirements

For 2027 entry, Imperial requires TMUA for undergraduate courses within:

• Department of Computing

• Department of Mathematics

• Imperial Business School’s Economics, Finance and Data Science degree

Joint Mathematics and Computing courses are included within the Computing requirement.

Imperial Mathematics

Applicants to Imperial Mathematics courses must take TMUA.

The university uses the result alongside the rest of the application rather than treating it as a standalone pass or fail examination.

Imperial Computing

Applicants to Imperial Computing courses, including joint Mathematics and Computing programmes, must take TMUA.

This includes specialist computing routes where the course page identifies TMUA as compulsory.

Imperial Economics, Finance and Data Science

Applicants to the BSc Economics, Finance and Data Science must take TMUA.

The course also requires strong advanced Mathematics preparation, including A-level Mathematics at the specified grade or an accepted equivalent.

Imperial applicants can normally choose either the October or January test window.

LSE TMUA Requirements

LSE uses TMUA differently across its courses.

For September 2027 entry, the test is compulsory for:

• BSc Economics

• BSc Econometrics and Mathematical Economics

It is recommended, but not compulsory, for several other quantitative degrees, including courses in:

• Mathematics and Economics

• Financial Mathematics and Statistics

• Mathematics with Data Science

• Data Science

• Economics and Data Science

• Actuarial Science

A strong optional score may make an application more competitive, but applicants to these recommended-test courses can still be considered without taking TMUA.

LSE accepts either the October or January sitting, although it recommends the first window where possible because applicants are likely to have a wider choice of appointments and locations.

UCL TMUA Requirements

For the 2027 admissions cycle, UCL requires TMUA for:

• Economics BSc

• Economics with a Year Abroad BSc

UCL considers the result alongside the applicant’s academic record, UCAS application and evidence of suitability for its quantitative Economics programme.

Do not confuse UCL’s TMUA requirements with its other admissions tests.

For 2027 entry:

• Economics uses TMUA.

• Selected Computer Science courses use TARA.

• Electronic and Electrical Engineering uses ESAT.

Warwick TMUA Requirements

Warwick’s TMUA policy is course-specific.

Warwick Computer Science

The current Warwick admissions guidance states that TMUA is required for applicants to courses including:

• Computer Science BSc

• Computer Science MEng

• Computer Science with Business Studies

• Discrete Mathematics BSc

• Discrete Mathematics MEng

Applicants eligible for Warwick’s contextual offer arrangements may be treated differently.

Warwick Mathematics

Applicants to Warwick Mathematics normally need to take either:

• TMUA

or

• STEP

Warwick assesses the TMUA score alongside predicted grades, GCSEs and contextual information. Its 2027 offer guidance indicates that a strong TMUA score can support the standard Mathematics offer, while applicants using STEP receive a STEP condition.

Warwick Economics

TMUA is optional for Warwick Economics courses.

A strong result may be used as an additional admissions factor or lead to a reduced offer for selected courses. Applicants who do not take the test remain eligible for consideration.

Warwick Statistics, MORSE and Data Science

TMUA is optional for several Warwick courses in:

• Mathematics and Statistics

• MORSE

• Data Science

Offers may provide different ways to meet the requirements, such as:

• A specified TMUA score

• A STEP grade

• Higher qualification grades

Check the individual 2027 course page because the alternatives vary.

Durham TMUA Requirements

Durham is listed by UAT-UK as one of the universities using TMUA for selected courses.

The exact requirement must be checked on the current Durham course page because the test may be:

• Compulsory

• Recommended

• Limited to selected mathematical degrees

• Used as one factor within a wider assessment

Do not register only because Durham appears on the participating-university list. Confirm that your precise course requires the test.

TMUA Test Format

The TMUA contains two papers.

TMUA paper	Questions	Time	Main focus
Paper 1	20 multiple-choice questions	75 minutes	Applications of Mathematical Knowledge
Paper 2	20 multiple-choice questions	75 minutes	Mathematical Reasoning

The papers are taken one after the other.

The full test therefore contains:

• 40 questions

• 150 minutes

• An average of 3 minutes and 45 seconds per question

There is no scheduled break between the papers.

Are Calculators Allowed?

No.

You cannot use a calculator or dictionary.

You should be comfortable with:

• Fraction arithmetic

• Surds

• Exact values

• Algebraic simplification

• Powers and roots

• Ratios

• Estimation

• Mental arithmetic

• Standard form

• Common trigonometric values

Is There a Formula Booklet?

No.

The official specification states that candidates are expected to understand and recall the relevant formulae.

Create a formula and facts checklist during preparation, but focus on understanding where each relationship comes from and when it applies.

Is There Negative Marking?

No.

Every question carries equal weight and incorrect answers do not lose marks. You should therefore attempt all 40 questions.

Where you cannot solve a problem completely:

1. Eliminate impossible options.

2. Test a simple case.

3. Estimate the likely value.

4. Make the best available choice.

5. Move on.

Leaving a question blank removes any chance of gaining the mark.

TMUA Paper 1 Explained

Paper 1 is called:

Applications of Mathematical Knowledge

It assesses whether you can apply mathematical knowledge in unfamiliar situations.

You will complete:

• 20 multiple-choice questions

• In 75 minutes

• Without a calculator

Paper 1 uses the mathematical content in Section 1 of the official specification.

TMUA Paper 1 Topics

The specification includes areas such as:

• Algebra and functions

• Sequences and series

• Coordinate geometry

• Trigonometry

• Exponentials and logarithms

• Differentiation

• Integration

• Graphs

• Number

• Ratio and proportion

• Geometry

• Statistics

• Probability

The official specification should be treated as the complete content boundary. Do not assume that every topic in your full A-level Mathematics course can appear. Equally, check that you have not overlooked Higher GCSE material such as bounds, geometry or statistical graphs.

Algebra and Functions

You should be comfortable with:

• Index laws

• Surds

• Quadratic equations

• The discriminant

• Completing the square

• Simultaneous equations

• Linear and quadratic inequalities

• Factor and remainder theorems

• Algebraic division

• Function notation

• Modulus and square-root functions

TMUA questions frequently reward manipulation before calculation.

Before expanding everything, ask:

• Can the expression be factorised?

• Can common factors be cancelled?

• Can I substitute the answer choices?

• Is there a symmetry?

• Can I compare signs?

• Can I use the discriminant?

Sequences and Series

The specification includes:

• Formulae for the nth term

• Simple recurrence relations

• Arithmetic series

• Finite geometric series

• Infinite geometric series

• Binomial expansion for positive integer powers

Practise interpreting how a sequence behaves rather than only substituting into formulae.

A question might ask:

• Whether a sequence increases

• Whether it converges

• Which term first meets a condition

• Whether a proposed formula works for every term

• How a recurrence behaves after several steps

Coordinate Geometry

You may need to work with:

• Straight-line equations

• Gradients

• Parallel and perpendicular lines

• Circles

• Tangents

• Chords

• Circle theorems

• Intersections

Draw a quick diagram where it helps.

A rough sketch can reveal:

• Which points are possible

• Whether a gradient should be positive

• Whether a line intersects a circle

• Whether an answer has the right scale

Trigonometry

Relevant preparation includes:

• Sine and cosine rules

• Triangle area

• Radians

• Arc length

• Sector area

• Exact values

• Trigonometric graphs

• Identities

• Simple trigonometric equations

Keep answers in exact form unless a decimal is specifically needed.

Without a calculator, recognising values such as:

• sin 30°

• cos 60°

• tan 45°

must be automatic.

Exponentials and Logarithms

You should understand:

• Exponential graphs

• Laws of logarithms

• Solving exponential equations

• Manipulating expressions before applying logarithms

• Growth and decay

The specification does not require every advanced logarithmic technique from a full A-level course, so follow the official boundaries carefully.

Differentiation

You may need to use differentiation to understand:

• Gradients

• Tangents and normals

• Rates of change

• Stationary points

• Maximum and minimum points

• Increasing and decreasing functions

• Graph shape

Do not differentiate automatically.

First ask whether a quicker method is available through:

• Symmetry

• Completing the square

• Comparing values

• Factorisation

• Testing answer options

Integration

Relevant skills include:

• Definite and indefinite integration

• Areas between a curve and an axis

• The Fundamental Theorem of Calculus

• Combining integrals

• The trapezium rule

• Simple differential equations within the specification

Check whether the question asks for:

• A definite integral

• A geometric area

• A signed area

• A total area

These are not always the same.

Graphs

You should recognise and interpret graphs of:

• Linear functions

• Quadratics

• Cubics

• Trigonometric functions

• Exponentials

• Logarithms

• Square-root functions

• Modulus functions

You should also understand:

• Transformations

• Roots

• Intercepts

• Turning points

• Intersections

• Increasing and decreasing regions

• How algebraic solutions connect to graph intersections

Sketching a rough graph is often faster than carrying out a long calculation.

Probability and Statistics

The specification includes topics such as:

• Tables and charts

• Histograms

• Cumulative frequency

• Averages

• Quartiles and interquartile range

• Scatter graphs

• Correlation

• Probability rules

• Possibility spaces

• Tree diagrams

• Conditional probability

Be careful with words such as:

• Independent

• Mutually exclusive

• At least

• Exactly

• Given that

• Neither

• Both

Small wording changes can completely alter the calculation.

How to Approach TMUA Paper 1

Look for Structure

TMUA questions are often easier when you recognise the underlying structure.

Ask:

• Is this really a quadratic?

• Is there an invariant quantity?

• Is the relationship proportional?

• Can I express everything using one variable?

• Is there a useful graph?

• Can I simplify before substituting?

Use Answer Choices Strategically

The options are part of the question.

You may be able to:

• Substitute each option

• Eliminate answers with incorrect signs

• Check units or scale

• Use a special value

• Test a boundary case

• Compare parity

• Approximate the result

This is not cheating or avoiding Mathematics. It is efficient multiple-choice reasoning.

Avoid Unnecessary Calculation

If the options are widely separated, an estimate may be enough.

If only one answer is positive, you may only need to determine the sign.

If the question asks which statement is always true, one counterexample can eliminate an option.

Check the Domain

A proposed answer may fail because it assumes:

• A denominator is non-zero

• A square root is defined

• A logarithm has a positive argument

• A length is positive

• An angle lies in the correct interval

Domain restrictions are a common source of attractive wrong answers.

TMUA Paper 2 Explained

Paper 2 is called:

Mathematical Reasoning

It assesses whether you can understand, analyse and construct mathematical arguments.

You will complete:

• 20 multiple-choice questions

• In 75 minutes

• Without a calculator

Paper 2 draws on the mathematical content from Paper 1 and the additional logic and proof material in Section 2 of the specification.

What Mathematical Logic Do You Need?

You should understand the meaning of:

• True and false

• And

• Or

• Not

• If A, then B

• A if B

• A only if B

• A if and only if B

• Converse

• Contrapositive

• Necessary

• Sufficient

• For all

• For some

• There exists

• Negation

You are not expected to use formal symbolic notation or complete formal truth tables.

“If A, Then B”

Suppose:

If a number is divisible by 4, then it is even.

Here:

• Being divisible by 4 is sufficient for being even.

• Being even is necessary for being divisible by 4.

The converse is:

If a number is even, then it is divisible by 4.

This is false.

The contrapositive is:

If a number is not even, then it is not divisible by 4.

This is true whenever the original statement is true.

A statement and its contrapositive are logically equivalent. A statement and its converse are not.

Necessary and Sufficient Conditions

A condition is sufficient when it guarantees the outcome.

A condition is necessary when the outcome cannot occur without it.

For example:

Being divisible by 6 is sufficient for being divisible by 3.

However:

Being divisible by 6 is not necessary for being divisible by 3.

The number 9 is divisible by 3 but not by 6.

Questions may hide these relationships inside unfamiliar algebraic or geometric statements.

Negating Statements

Negation means writing what must be true when the original statement is false.

For example:

Original statement:

Every student solved the problem.

Negation:

At least one student did not solve the problem.

The negation is not:

No student solved the problem.

Similarly:

Original statement:

There exists a positive integer with property P.

Negation:

No positive integer has property P.

Careful negation is essential in Paper 2.

Converse and Contrapositive

For the statement:

If A, then B

the converse is:

If B, then A

the contrapositive is:

If not B, then not A

A common Paper 2 mistake is assuming that the converse follows automatically from the original statement.

Types of Proof

The official specification includes:

• Direct proof

• Proof by cases

• Proof by contradiction

• Disproof by counterexample

You may need to:

• Follow a proof

• Identify a missing step

• Rearrange steps into the correct order

• Find an error

• Decide which conclusion follows

• Select a valid counterexample

• Complete a chain of reasoning

The specification also includes recognising common invalid deductions.

Direct Proof

A direct proof begins with known information and uses valid steps to reach the conclusion.

For example, to prove that the sum of two even integers is even:

• Let the integers be 2m and 2n.

• Their sum is 2m + 2n.

• This equals 2(m + n).

• Since m + n is an integer, the sum is even.

Proof by Cases

A proof by cases separates the problem into every possible category.

For example, an integer may be:

• Even

• Odd

If the statement is proved in both cases, it is proved for every integer.

The cases must cover all possibilities.

Proof by Contradiction

A proof by contradiction:

1. Assumes that the statement to be proved is false.

2. Follows the consequences of that assumption.

3. Reaches an impossibility.

4. Concludes that the original statement must be true.

Be careful to identify the exact negation of the original statement.

Disproof by Counterexample

To disprove a universal claim, one counterexample is enough.

Claim:

Every prime number is odd.

Counterexample:

2 is prime and even.

You do not need to list several counterexamples.

However, one example supporting a universal statement does not prove it.

How to Approach TMUA Paper 2

Read Every Word

Logical questions depend on precise wording.

Watch for:

• All

• Some

• Exactly

• At least

• At most

• Only if

• If

• If and only if

• Necessary

• Sufficient

• Must

• May

• Cannot

Do not replace the written statement with a looser version in your head.

Test Small Cases

Small examples can help you:

• Disprove a statement

• Identify a pattern

• Check whether the converse holds

• Find an overlooked condition

• Eliminate answer options

However, several successful examples do not prove that a statement is always true.

Use examples to generate or test ideas, then decide whether a general argument is needed.

Search for Counterexamples

When asked whether a statement is always true, actively try to break it.

Test:

• Zero

• One

• Negative values

• Equal values

• Extreme values

• Boundary cases

• Simple fractions

• Degenerate geometric cases

Many false statements appear convincing because they work for ordinary examples.

Check Every Division

A proof may divide by an expression that could equal zero.

For example, from:

ab = ac

you cannot always conclude:

b = c

unless you know that a is not zero.

The official specification specifically identifies unjustified cancellation as a common proof error.

Separate “May Be True” From “Must Be True”

A conclusion may be possible without being logically necessary.

TMUA questions often ask what follows from the information.

The correct answer must be guaranteed, not merely plausible.

TMUA Dates for 2027 Entry

October 2026 Sitting

Stage	Date
UAT-UK accounts, bursaries and access requests open	1 June 2026 at 3pm
Test booking opens	20 July 2026 at 3pm
Access-arrangement request deadline	14 September 2026 at 6pm
Bursary request deadline	21 September 2026 at 6pm
Test booking closes	28 September 2026 at 6pm
Test window	12 to 16 October 2026
Results released	16 November 2026

January 2027 Sitting

Stage	Date
Access and bursary applications reopen	5 October 2026 at 3pm
Test booking opens	26 October 2026 at 3pm
Access-arrangement request deadline	7 December 2026 at 6pm
Bursary request deadline	14 December 2026 at 6pm
Test booking closes	21 December 2026 at 6pm
Test window	4 to 8 January 2027
Results released	8 February 2027

UAT-UK does not accept bookings after the published deadlines.

Which TMUA Sitting Should You Take?

Oxford Applicants

Standard Oxford applicants must take TMUA in October.

The January sitting is available only for specified exceptions, including eligible Oxford Astrophoria Foundation Year applicants using its January application route.

Cambridge Applicants

Most Cambridge applicants must take the October sitting.

Eligible mature applicants applying to a mature College through the January application round may be able to use the January sitting.

Imperial, LSE, UCL, Durham and Warwick Applicants

Applicants to other participating institutions can normally choose either October or January, subject to the individual course’s policy.

There is no official scoring advantage to either sitting. UAT-UK states that you may take the test only once within the admissions cycle.

Should You Choose October or January?

October may be preferable when:

• You want the widest choice of appointments.

• You are applying to Oxford or Cambridge.

• You want the result earlier.

• Your preparation can be completed by autumn.

• You want more certainty during the application process.

January may be preferable when:

• Your chosen courses permit it.

• You need more preparation time.

• Your school has not yet covered relevant content.

• October clashes with several other admissions tests.

• You are not applying to Oxford or Cambridge.

Do not treat January as a retake opportunity.

Can You Sit TMUA Twice?

No.

You may take TMUA only once during the 2027 admissions cycle.

Attempting to sit in both October and January, including through a second account, is treated as misconduct.

How Much Does TMUA Cost?

For the 2027 admissions cycle:

Test location	Fee
UK or Republic of Ireland	£78
Other countries	£133

The fee is based on the location of the test centre rather than your nationality or home address.

Is There a TMUA Bursary?

Yes.

UK applicants in financial need may apply for a UAT-UK bursary covering the full cost of the test.

Apply before selecting and booking TMUA.

UAT-UK cannot reimburse candidates who pay before applying for a bursary. Bursary applications can take up to five working days to review.

How to Register for TMUA

Step 1: Create a UAT-UK Account

Create your account using details that match:

• Your photographic identification

• Your UCAS application

• Your official school records

Your full name must exactly match the identification you intend to present on test day.

Step 2: Check Your Courses

Before choosing the test, confirm:

• Which courses require TMUA

• Whether the test is compulsory or optional

• Which sitting is permitted

• Whether STEP is accepted instead

• Whether you are applying to Oxford or Cambridge

Step 3: Apply for a Bursary

Complete the bursary application before selecting TMUA.

Once you have selected or paid for the test, a bursary cannot be applied retrospectively.

Step 4: Apply for Access Arrangements

Request access arrangements before booking.

You may need to provide:

• A school or college letter

• A diagnostic assessment

• Medical evidence

• Confirmation of your normal way of working

• Details of existing examination arrangements

Approved arrangements cannot be added to an existing booking.

Step 5: Select TMUA

Add the test to your UAT-UK account.

TMUA does not have optional modules. Every candidate takes both papers.

Step 6: Book Through Pearson

Choose:

• Test centre

• Date

• Time

Book early because local appointments may become limited.

In the UK, UAT-UK advises candidates to contact Pearson if no appointment is available within 40 miles, although some applicants in remote areas may still need to travel further.

Step 7: Add Your UCAS Personal ID

Add your UCAS Personal ID when it becomes available.

This helps UAT-UK match your result to the relevant courses on your application.

How Is TMUA Scored?

You receive one overall TMUA score.

It is reported:

• On a scale from 1.0 to 9.0

• To one decimal place

The score is statistically equated so that candidates taking different versions or sittings can be reported on a common scale.

You do not receive a separate publicly reported Paper 1 and Paper 2 score.

Is There a Pass Mark?

No.

UAT-UK does not set a pass or fail score.

Universities decide how to use the result alongside the rest of your application.

What Is a Good TMUA Score?

There is no universal good score.

A competitive result depends on:

• The university

• The degree

• The applicant cohort

• Whether the test is compulsory

• Whether it is optional

• How heavily it is weighted

• Your academic record

• Contextual information

• Interview performance

A score considered helpful for an optional LSE course might not be enough for Oxford interview shortlisting.

Warwick reports that, in its previous admissions cycle, most Mathematics offers went to applicants with a score of 5.0 or above, although some lower-scoring applicants received offers after holistic assessment. This is a Warwick example, not a universal threshold.

Do not assume that:

• 5.0 guarantees an offer.

• A score below 5.0 makes every application unsuccessful.

• Last year’s threshold will remain the same.

• Different universities apply identical cut-offs.

How Many Correct Answers Do You Need?

UAT-UK does not publish a fixed conversion that applies permanently.

Your raw number of correct answers is converted to the scaled score using statistical equating.

The conversion can vary according to the live test versions and applicant performance.

Unofficial online score converters should therefore be treated cautiously.

Use practice percentages to monitor progress, not to predict an exact official score.

How Do Universities Use TMUA Scores?

A university may use TMUA to:

• Decide who is invited to interview

• Rank eligible applicants

• Compare students with similar grades

• Assess mathematical preparation

• Make reduced offers

• Add context to an application

• Decide between TMUA and STEP offer routes

• Support holistic selection

The same score can have different implications at different universities.

Oxford

Oxford uses TMUA to help shortlist Mathematics and Computer Science applicants for interview.

A strong score helps, but it does not guarantee an interview or offer.

Cambridge

Cambridge uses TMUA within the selection process for Mathematics, Computer Science and Economics.

The test is considered alongside academic evidence and, where relevant, interview performance.

Imperial

Imperial uses TMUA for Mathematics, Computing and Economics, Finance and Data Science.

The result provides evidence of mathematical reasoning and is assessed with the wider application.

LSE

For compulsory-test courses, TMUA forms part of the selection process.

For recommended-test courses, a good score may strengthen the application, but not taking it does not automatically make the application ineligible.

Warwick

Warwick’s use varies by department.

It can be:

• Compulsory

• Optional

• An alternative to STEP

• Part of a reduced-offer route

Check the current course requirements rather than applying one Warwick policy to every degree.

When Are TMUA Results Released?

For 2027 entry:

• October results are released on 16 November 2026.

• January results are released on 8 February 2027.

Results are made available through your UAT-UK account.

Do You Send Your Result to Universities?

No manual submission is normally required.

UAT-UK automatically sends the score to participating universities where your UCAS course officially uses TMUA.

Universities that are not official users of the test do not automatically receive the result.

Do You Enter TMUA on UCAS?

You should ensure that your UAT-UK and UCAS information matches, including your personal details and UCAS Personal ID.

You do not normally type your TMUA score into the qualifications section of your application.

How Long Should You Prepare for TMUA?

A preparation period of around eight to twelve weeks may suit many applicants.

You may need longer when:

• You have gaps in AS Mathematics

• You have not studied logic and proof

• You are balancing several admissions tests

• You have not practised non-calculator Mathematics recently

• You are applying for highly competitive Mathematics courses

• You need to rebuild confidence with algebra

Starting earlier does not mean completing full papers immediately.

The most effective sequence is:

1. Read the specification.

2. Diagnose weak topics.

3. Learn the logic material.

4. Practise questions without time pressure.

5. Introduce timed sets.

6. Complete full papers.

7. Practise both papers consecutively.

Read How to Prepare for an Admissions Test for a general preparation framework.

Ten-Week TMUA Preparation Plan

Week 1: Understand the Test

• Confirm that your courses require TMUA.

• Read the official specification.

• Read the Notes on Mathematics.

• Read the Notes on Logic and Proof.

• Complete a small selection of Paper 1 and Paper 2 questions.

• Start an error log.

• Register for the test.

Do not judge your potential from your first score.

The diagnostic is meant to show what needs work.

Week 2: Audit Mathematical Knowledge

Create a checklist for:

• Algebra

• Functions

• Sequences

• Coordinate geometry

• Trigonometry

• Logarithms

• Calculus

• Graphs

• Geometry

• Probability

• Statistics

Label each area:

• Confident

• Needs revision

• Not yet studied

Repair the largest gaps first.

Week 3: Strengthen Algebra

Focus on:

• Surds

• Indices

• Quadratics

• Inequalities

• Simultaneous equations

• Factorisation

• Algebraic division

• Functions

Practise simplifying before calculating.

Week 4: Strengthen Graphs and Calculus

Focus on:

• Graph transformations

• Intersections

• Roots

• Stationary points

• Gradients

• Areas

• Exponentials

• Logarithms

• Trigonometric graphs

Use sketches to support reasoning.

Week 5: Learn Logic and Proof

Work through:

• Necessary and sufficient

• Converse

• Contrapositive

• Negation

• Quantifiers

• Direct proof

• Proof by cases

• Contradiction

• Counterexamples

• Proof errors

Complete Paper 2 questions without strict timing until the language becomes familiar.

Week 6: Introduce Timed Sets

Complete groups of:

• Five Paper 1 questions

• Five Paper 2 questions

Use a target of approximately 18 to 20 minutes for each set.

Review every question afterwards.

Week 7: Complete Timed Papers

Complete one 75-minute paper at a time.

Record:

• Raw score

• Questions left unanswered

• Questions guessed

• Time used

• Error types

• Topics needing revision

Do not immediately complete the second paper unless you are deliberately practising endurance.

Week 8: Improve Weak Areas

Use the evidence from your timed work.

For example:

• Revisit inequalities if you repeatedly miss domain restrictions.

• Review contrapositive reasoning if you confuse it with the converse.

• Practise geometric diagrams if coordinate questions take too long.

• Review conditional probability if tree diagrams cause errors.

Week 9: Complete Full TMUA Mocks

Complete both papers consecutively:

• Paper 1: 75 minutes

• Paper 2: 75 minutes

• No calculator

• No formula booklet

• No unscheduled break

• Computer-based practice where possible

Review the full test over one or two later sessions.

Week 10: Consolidate

• Revisit your error log.

• Reattempt difficult questions.

• Review formulae and exact values.

• Complete short timed sets.

• Confirm identification and travel.

• Protect sleep.

• Reduce intensive practice before test day.

Official TMUA Preparation Materials

UAT-UK provides free resources including:

• Test specification

• Notes on Mathematics

• Notes on Logic and Proof

• Specimen tests

• Practice tests

• Historic TMUA papers

• Worked answers

• Answer keys

• Pearson test-player practice

The historical papers remain useful because UAT-UK states that the content specification and question style have remained unchanged despite the move to computer-based testing.

Which Past Papers Should You Use First?

A sensible order is:

1. Specimen material

2. Older past papers for learning

3. Middle-year papers for timed practice

4. Recent official practice tests near the real assessment

Do not use every recent paper at the beginning.

Save enough untouched material for realistic full mocks.

How Should You Review a TMUA Paper?

For every incorrect question, record:

• The topic

• The first incorrect step

• Whether the problem was knowledge or reasoning

• Why your chosen option looked attractive

• The quickest correct method

• What you will check next time

Also review correct answers.

You may have:

• Guessed correctly

• Used an unnecessarily long method

• Misunderstood the reasoning

• Taken too much time

• Been unable to explain why the other options were wrong

Do You Need Paid TMUA Coaching?

No.

UAT-UK provides the official materials free of charge and recommends focusing on the test specification, logic and proof notes, and timed practice.

LSE and Warwick similarly state that applicants do not need a specialist preparation course and should focus on familiarising themselves with the format and question style.

Paid support may offer:

• Additional structure

• Tutoring

• Extra questions

• Accountability

• Feedback

Before paying, check that the provider:

• Uses the current two-paper format

• Uses the 1.0 to 9.0 score scale

• Reflects the current specification

• Does not introduce unnecessary Further Mathematics

• Provides accurate worked solutions

• Does not claim access to live questions

• Does not guarantee offers or scores

Paper 1 Preparation Strategies

Make Algebra Automatic

You should be able to manipulate expressions without using most of your attention.

Practise:

• Factorising

• Cancelling

• Rearranging

• Substitution

• Completing the square

• Working with surds

• Using index laws

This frees your attention for the unfamiliar part of the problem.

Use Special Values

When a statement claims to apply to all values, test:

• 0

• 1

• -1

• A fraction

• A large value

• A boundary value

A single contradiction can eliminate an answer.

Sketch Graphs

A rough graph can answer questions about:

• Number of roots

• Signs

• Intersections

• Turning points

• Increasing and decreasing behaviour

• Possible parameter values

Your sketch does not need to be beautiful. It needs to reveal the structure.

Estimate

Estimation is useful when:

• Options are far apart

• Only the order of magnitude matters

• Exact arithmetic is cumbersome

• You want to check a result

• The question asks for the closest value

Work Backwards From Options

Where appropriate:

1. Substitute the possible answers.

2. Check which satisfies the conditions.

3. Eliminate the rest.

This can be faster than deriving the result from scratch.

Paper 2 Preparation Strategies

Translate Every Statement

Rewrite statements in your own precise language.

For example:

A only if B

means:

If A is true, B must be true.

It does not mean:

If B is true, A must be true.

Practise Negations

Create your own examples using:

• Every

• Some

• At least one

• Exactly one

• No

• If

• Only if

Then write the logical negation.

Search for Hidden Assumptions

A proof may assume:

• A variable is non-zero

• A function is one-to-one

• A square root can be negative

• Two angles with the same sine are equal

• A pattern from small cases always continues

• The converse of a true statement is true

These are classic TMUA traps.

Separate Evidence From Proof

Checking ten examples may provide evidence.

It does not prove a statement about every possible value.

Ask:

Why must this continue?

If you cannot answer, the argument may be incomplete.

Use Counterexamples Efficiently

You do not need to search randomly.

Try values likely to expose a weakness:

• Zero for division problems

• Negative numbers for inequalities

• Fractions for integer-looking patterns

• Equal values for strict inequalities

• Boundary values for geometric claims

TMUA Time Management

You have an average of:

3 minutes and 45 seconds per question.

This is more generous than the average time in some other admissions tests, but individual TMUA questions can require substantial thought.

Suggested Timing Checkpoints

Time used	Approximate progress
15 minutes	Questions 1 to 4
30 minutes	Questions 5 to 8
45 minutes	Questions 9 to 12
60 minutes	Questions 13 to 16
Final 15 minutes	Complete questions 17 to 20 and review

This is only a starting framework.

Some candidates prefer to:

1. Complete accessible questions first.

2. Flag harder questions.

3. Return with the remaining time.

When Should You Move On?

Move on when:

• You have no clear starting point.

• Your working has become very long.

• You have repeated the same approach.

• You are choosing between options without progress.

• The question is taking time needed elsewhere.

Enter a provisional answer before moving on because there is no negative marking.

Do Not Rush the First Questions

The test is not necessarily arranged in strict difficulty order.

An early question may be hard, and a later question may be straightforward.

Do not let one difficult opening question damage the rest of the paper.

Access Arrangements

UAT-UK offers access arrangements for candidates with:

• Learning differences

• Disabilities

• Sensory impairments

• Medical conditions

• Mental health conditions that affect testing

Possible arrangements include:

• Extra time

• Pause-the-clock rest breaks

• Separate invigilation

• Reader or recorder

• Approved medical items

• Coloured overlay

• Other justified adjustments

Extra time is normally awarded at 25% where appropriate, although individual applications are assessed using supporting evidence.

Apply Before Booking

You must apply for access arrangements before selecting and booking the test.

UAT-UK cannot add arrangements to an existing appointment.

Applications may take up to ten working days to review, and non-standard requests may take longer.

Evidence Requirements

If you are currently in education, evidence may include a signed letter from your school or college confirming:

• Your condition or learning difference

• Your normal way of working

• Existing examination arrangements

• The percentage of extra time

• Any requirement for separate invigilation

School arrangements do not transfer automatically. You must complete the UAT-UK process.

International TMUA Applicants

TMUA is delivered through international Pearson test centres.

Candidates sitting outside the UK and Republic of Ireland pay £133.

Book early because availability can vary considerably between countries.

China, Hong Kong and Macau

For test security reasons, TMUA is offered on restricted dates in China, Hong Kong and Macau.

For the 2027 admissions cycle, the available dates are:

• 15 or 16 October 2026

• 8 January 2027

Oxford and Cambridge applicants must still use the October window unless a published exception applies.

What Happens on TMUA Test Day?

TMUA is taken at a Pearson professional test centre.

UAT-UK advises candidates to arrive approximately 30 minutes before the appointment.

You may be refused entry if you arrive more than 15 minutes late, and your fee may be lost.

What to Bring

Bring:

• Original, valid photographic identification

• Pearson appointment confirmation

Your identification must meet the current UAT-UK policy.

Your name must match the name used for your booking.

At the Test Centre

You should expect to:

• Check in

• Present identification

• Store personal belongings

• Complete security checks

• Be assigned a computer

• Receive an erasable notebook and pen

Check that the pen works before the test begins.

Items Not Normally Permitted

You cannot normally take items such as:

• Phone

• Watch

• Calculator

• Notes

• Books

• Personal stationery

• Food

• Drink

Approved comfort aids and disability-related items follow separate rules.

All candidates may take non-digital earplugs, subject to inspection, without applying for access arrangements.

Breaks

There is no scheduled break between Paper 1 and Paper 2.

If you leave the room without approved pause-the-clock breaks, your test time continues.

Practise both papers consecutively at least once before the real test.

What If Something Goes Wrong?

Report any problem immediately.

Examples include:

• Computer failure

• Excessive noise

• Fire alarm

• Illness during the test

• Incorrect access arrangements

• Keyboard or mouse problems

• Serious disruption

Ask for an incident reference before leaving the centre.

UAT-UK states that it will not normally take action when a disruption is reported only after the test and was not raised at the centre.

What If You Are Ill Before the Test?

Follow the current rescheduling and special-consideration policy.

If you sit the test without reporting the problem, you are normally declaring yourself fit to test.

Applicants who are not applying to Oxford or Cambridge may be able to move from October to January where appointments and deadlines allow.

Common TMUA Mistakes

Preparing for MAT Instead of TMUA

Oxford Mathematics and Computer Science applicants now take TMUA for 2027 entry.

Old MAT problems may still develop useful skills, but MAT registration rules, structure and scoring do not apply.

Assuming Every Mathematics Course Requires TMUA

Requirements differ by university and course.

Assuming TMUA Is Optional Everywhere

It is compulsory for several courses, including Oxford, Cambridge, Imperial, UCL and LSE programmes.

Taking the Wrong Sitting

Most Oxford and Cambridge applicants must sit in October.

Treating January as a Retake

You can take TMUA only once during the cycle.

Ignoring Paper 2

Strong school Mathematics grades do not automatically produce strong logical reasoning.

Learning Advanced Further Mathematics Instead of the Specification

The test is based mainly on Higher GCSE and AS Mathematics.

Using a Calculator During Practice

Calculators are not allowed.

Forgetting Formulae

There is no formula booklet.

Leaving Answers Blank

There is no negative marking.

Completing Past Papers Without Reviewing Them

Practice only helps when you understand your errors.

Memorising Worked Solutions

You need to reproduce the reasoning independently in a new problem.

Confusing Converse and Contrapositive

A statement is equivalent to its contrapositive, not necessarily its converse.

Proving by Example

Several supporting examples do not prove a universal statement.

Missing Domain Restrictions

Check denominators, square roots, logarithms and geometric conditions.

Applying for a Bursary After Paying

Bursaries must be approved before booking.

Booking Before Access Arrangements Are Approved

Adjustments cannot be added afterwards.

Arriving With Incorrect Identification

You may be refused entry and lose the fee.

TMUA Registration Checklist

•  I have checked every chosen course.

•  I know whether TMUA is compulsory or optional.

•  I know whether I must take October or January.

•  I know whether STEP is an alternative.

•  I have created a UAT-UK account.

•  My name matches my photographic identification.

•  My details match my UCAS application.

•  I have applied for a bursary where eligible.

•  I have requested access arrangements where required.

•  My arrangements were approved before booking.

•  I have selected TMUA.

•  I have booked a Pearson appointment.

•  I have saved the confirmation.

•  I have added my UCAS Personal ID.

•  I know the result-release date.

TMUA Preparation Checklist

•  I have read the official specification.

•  I have read the Notes on Mathematics.

•  I have read the Notes on Logic and Proof.

•  I have audited every Paper 1 topic.

•  I am confident with non-calculator arithmetic.

•  I know the required formulae.

•  I understand necessary and sufficient conditions.

•  I understand converse and contrapositive.

•  I can negate quantified statements.

•  I recognise direct proof.

•  I recognise proof by contradiction.

•  I can find counterexamples.

•  I can identify invalid cancellation and other proof errors.

•  I use an error log.

•  I have completed timed Paper 1 practice.

•  I have completed timed Paper 2 practice.

•  I have completed both papers consecutively.

•  I practise using the computer interface.

•  I attempt every question.

•  I know when to move on.

•  I have protected time for my main qualifications.

TMUA Test-Day Checklist

•  Correct test date

•  Correct appointment time

•  Correct test-centre address

•  Travel planned

•  Arrival planned for 30 minutes early

•  Valid original photographic identification

•  Name matches the booking

•  Pearson confirmation

•  Access arrangements shown correctly

•  Test rules read

•  No calculator packed

•  Timing plan for both papers

•  Strategy for difficult questions

•  Incident-reporting process understood

Frequently Asked Questions About TMUA

What Does TMUA Stand For?

TMUA stands for Test of Mathematics for University Admission.

How Long Is the TMUA?

TMUA lasts two hours and 30 minutes.

It contains two 75-minute papers.

How Many Questions Are in TMUA?

There are 40 questions:

• 20 in Paper 1

• 20 in Paper 2

All questions are multiple-choice.

What Is TMUA Paper 1?

Paper 1 is Applications of Mathematical Knowledge.

It assesses your ability to apply familiar Mathematics in unfamiliar situations.

What Is TMUA Paper 2?

Paper 2 is Mathematical Reasoning.

It assesses logic, proof, mathematical arguments and the identification of reasoning errors.

Are Calculators Allowed?

No.

You cannot use a calculator or dictionary.

Is There a Formula Booklet?

No.

You must know and understand the relevant formulae.

Is There Negative Marking?

No.

Incorrect answers do not lose marks, so attempt every question.

How Is TMUA Scored?

You receive one overall score from 1.0 to 9.0, reported to one decimal place.

Do You Receive Separate Paper Scores?

No separate Paper 1 and Paper 2 scores are normally reported to candidates.

You receive one overall TMUA result.

Is There a Pass Mark?

No.

Each university decides how to use your score.

What Is a Good TMUA Score?

There is no universal good score.

Your competitiveness depends on the university, course and annual applicant cohort.

Is 5.0 a Good TMUA Score?

It may be useful for some courses.

Warwick reports that most Mathematics offers in its previous cycle were made to applicants with 5.0 or above, but some applicants below 5.0 also received offers. Other universities may use very different standards.

Do You Need Further Mathematics for TMUA?

No.

TMUA itself is based primarily on Higher GCSE and AS Mathematics content.

However, your university course may separately require or strongly prefer Further Mathematics.

Is TMUA Harder Than A-Level Mathematics?

TMUA generally uses less advanced content than a full A-level Mathematics course, but the questions are unfamiliar and reasoning-focused.

Strong A-level performance does not guarantee a high TMUA score without practice.

Which Cambridge Courses Require TMUA?

For 2027 entry:

• Computer Science

• Economics

• Mathematics

Which Oxford Courses Require TMUA?

Oxford uses TMUA for Mathematics, Computer Science and related joint courses, including Mathematics and Computer Science and Mathematics and Philosophy.

Does Oxford Still Use MAT?

No.

Oxford Mathematics and Computer Science applicants use TMUA for 2027 entry.

Which Imperial Courses Require TMUA?

Imperial requires TMUA for courses in:

• Mathematics

• Computing

• Economics, Finance and Data Science

Which LSE Courses Require TMUA?

For 2027 entry, it is compulsory for:

• Economics

• Econometrics and Mathematical Economics

It is recommended for several other quantitative courses.

Which UCL Courses Require TMUA?

For 2027 entry:

• Economics BSc

• Economics with a Year Abroad BSc

Does Warwick Require TMUA?

It depends on the course.

It is compulsory or normally required for selected Computer Science and Mathematics routes, while it is optional for several Economics and Statistics courses.

Can You Take TMUA and STEP?

Yes.

You may need TMUA during the application process and STEP as an offer condition.

Warwick also allows STEP as an alternative route for selected Mathematics applicants.

Can You Take TMUA and ESAT?

Yes, if different courses require them.

You must register and pay for each test separately unless a bursary covers the fees.

Can You Take TMUA and TARA?

Yes, where your university choices require both tests.

Can You Take TMUA Twice?

No.

You can sit it only once in the 2027 admissions cycle.

Can You Take TMUA in January?

Yes, if your chosen university permits the January sitting.

Most Oxford and Cambridge applicants must take it in October.

Is January Easier Than October?

No official advantage applies to either window.

Scores are equated onto the same reporting scale.

When Are the Results Released?

• October sitting: 16 November 2026

• January sitting: 8 February 2027

Do Universities Receive Your Score Automatically?

Yes, where the course on your UCAS application is an official TMUA user.

Do You Need Paid Coaching?

No.

UAT-UK provides free preparation resources, specifications and past papers.

Are Old TMUA Papers Still Useful?

Yes.

UAT-UK states that the content specification and question style remain unchanged despite the test becoming computer-based.

Can You Get Extra Time?

Possibly.

Apply for access arrangements with evidence before booking.

Is There a TMUA Bursary?

Yes.

Eligible UK candidates can receive a bursary covering the full test fee. Apply before selecting or paying for the test.

Can International Applicants Take TMUA?

Yes.

TMUA is available through international Pearson test centres.

The international fee is £133.

Can You Take TMUA at Home?

TMUA is normally taken in person at a Pearson test centre.

Follow UAT-UK guidance if exceptional circumstances affect your access to a centre.

What Happens If You Miss the Booking Deadline?

UAT-UK does not accept late bookings.

If your course requires TMUA, your application may be invalid without it.

Does a High TMUA Score Guarantee an Interview?

No.

Universities consider the result alongside other parts of the application.

Can a High TMUA Score Make Up for Lower Grades?

Possibly to a limited extent, depending on the university.

It does not normally replace:

• Required subjects

• Minimum academic grades

• English language conditions

• Other compulsory qualifications

What If You Get a Low TMUA Score?

Do not assume that every application is unsuccessful.

A university may:

• Consider your complete academic profile

• Apply contextual information

• Use the score as one factor

• Offer a STEP route

• Give less weight to TMUA

• Consider an optional score only when helpful

Check how each university uses the test before making assumptions.

Final Thoughts on TMUA

TMUA is challenging because it asks you to think carefully with Mathematics that appears familiar.

Success depends less on learning advanced new topics and more on becoming excellent at:

1. Manipulating core Mathematics accurately

2. Recognising efficient methods

3. Interpreting logical language

4. Testing claims with examples and counterexamples

5. Following and evaluating proofs

6. Working without a calculator

7. Managing two demanding papers

8. Attempting every question

Begin with the official specification and the Notes on Logic and Proof.

Repair genuine knowledge gaps, then spend most of your preparation applying that knowledge to unfamiliar problems.

Use past papers carefully, review every mistake and practise both papers under realistic conditions.

Most importantly, check the admissions rules before booking.

TMUA can be compulsory, optional or one of several possible routes depending on the university and course. The right preparation starts with knowing exactly how your chosen universities will use your result.