TMUA preparation guide

TMUA vs STEP: One Screens, One Seals the Offer

TMUA and STEP are two very different maths tests in the UK admissions cycle: TMUA is a 2-hour-30-minute computer-based multiple-choice test sat at the start of the application season, while STEP is a long-form written exam the following June that decides whether a conditional offer is met. For Cambridge Mathematics from 2027 entry they are not alternatives: every applicant sits TMUA before interview, and STEP 2 and 3 still form the offer condition. This page lines the two tests up, role by role.

Practise 28 TMUA papers (2 free)Full TMUA guide

Papers: 28
Questions: 827
Free to try: 2

Quick answer

Role: TMUA screens before interview; STEP is the offer condition
Format: Two 20-question MCQ papers vs long questions, best six count
When: TMUA in October and January; STEP the following June
Results: A 1.0-9.0 scale with no boundaries vs grades S to U with published boundaries

For Cambridge Maths from 2027 entry you need both: TMUA guides interview invitations, and grade 1 in each of STEP 2 and 3 sits in the typical offer.

In short

Cambridge Maths from 2027 entry uses both: every applicant sits TMUA pre-interview (October 2026 sitting), and the typical offer still asks for grade 1 in both STEP 2 and STEP 3.
The formats are opposites: TMUA is a 2h 30m on-screen test of two 20-question multiple-choice papers scored on a 1.0-9.0 scale with no boundaries; STEP is two 3-hour written papers where your best six of 12 questions count, graded S to U with published boundaries.
The timelines barely overlap: TMUA sits in October (with a January window) at the start of the cycle, while STEP is taken the following June with results in mid-August, deciding the offer itself.
Oxford also switched to TMUA from 2026 (the MAT is discontinued), making TMUA the shared first gate for Oxbridge maths; sensible prep runs TMUA first, then STEP.

Roles: why this is not a choice

It is tempting to treat TMUA and STEP as substitutes, and under Cambridge's new Mathematics rules that is a costly misreading. From 2027 entry, every applicant sits TMUA before interview invitations go out, while STEP 2 and 3 remain in the typical offer: the two tests guard opposite ends of the process. In the faculty's own words: "All applicants are now required to take the Test of Mathematics for University Admission (TMUA) as part of a preliminary assessment to help guide our invitations for interview." (University of Cambridge, Faculty of Mathematics)

Cambridge Maths, 2027 entry

Two maths test gates

TMUA: pre-interviewOctober 2026, on screen

Required of all applicants
Guides interview shortlisting
Historically 75%-80% get interviewed

STEP: offer conditionWritten papers the following June

Typical offer: grade 1 in each of STEP 2 and 3
Mid-August results decide the place

Tap a branch to unfold

Oxford moved the same way: from 2026 Oxford uses the TMUA and the MAT is discontinued. Official wording: "From 2026, Oxford will use the TMUA. The MAT will not take place, and all applicants for Mathematics or Computer Science (including joint honours courses) will take the TMUA instead." (University of Oxford, Mathematical Institute) The MAT ran from 2007 to 2025. TMUA is now the shared first gate for Oxbridge maths, while STEP remains the final gate of a Cambridge Maths offer.

Format head-to-head: MCQ on screen vs long-form on paper

Almost every design choice runs in opposite directions: TMUA rewards hitting 20 multiple-choice questions reliably inside each 75-minute paper, while STEP rewards turning six long questions into complete, rigorous written solutions over 3 hours. The table lines up who runs each test, what you sit, how it is scored and what it costs.

	TMUA	STEP
Role	Early-cycle screening (guides Cambridge Maths interview invitations)	Offer condition (Cambridge Maths typical offer: grade 1 in each of STEP 2 and 3)
Run by	UAT-UK (a non-profit set up in 2023 by Imperial College London and the University of Cambridge)	OCR (from 2024, also part of Cambridge)
Delivery	Computer-based MCQ via around 5,500 Pearson VUE test centres worldwide	Handwritten long-form papers, sat on two separate days
Length	2h 30m in total: two back-to-back papers, 75 minutes and 20 questions each	3 hours per paper, 12 questions (8 pure, 2 mechanics, 2 probability and statistics), best six count
Scoring	A single 1.0-9.0 score, both papers equated together, median anchored at 4.5	20 marks per question out of 120, graded S, 1, 2, 3 or U
Aids	No calculator or dictionary	No formula booklet since 2019
Sittings	Two windows a year, October and January	June each year, results in mid-August
Fees	£78 at UK centres, £133 elsewhere	£102.50 in the UK, £142.25 outside

TMUA details follow UAT-UK's current official pages; STEP details follow OCR's.

TMUA pacing

20 questions in 75 minutes

Two back-to-back papers, 2h 30m in total

TMUA marking

No negative marking

Only correct answers count, so attempt every question

STEP question weight

20 marks a question

Full marks for a correct answer by any method

STEP totals

Best six answers count

Out of 120 per paper

Scoring: a cohort scale vs published boundaries

A TMUA score is relative: the scale is set on each cohort, with the median anchored at 4.5 and roughly 10% of candidates above 7.0, floored at 1.0 and capped at 9.0, with no pass mark. STEP works the other way round: grade boundaries are published every year, and the 2025 boundaries are below. Different reporting logic calls for different target-setting.

4.5

TMUA median anchor

7.0

About 10% score above this

120

STEP full marks per paper

Best answers counted in STEP

	STEP 2 (9470)	STEP 3 (9475)
S (Outstanding)	92	86
1 (Very Good)	75	61
2 (Good)	61	49
3 (Satisfactory)	35	27

Official 2025 grade boundaries out of 120, from OCR's Explanation of Results for STEP 2025.

In UAT-UK's own words, "UAT-UK does not provide any grade boundaries or a pass mark" and "we do not accept appeals of test scores" (UAT-UK). STEP boundaries, by contrast, are published each year, and for Cambridge, copies of answer booklets are sent directly to the admissions team for borderline decisions. Neither test has an official safe score, so ignore numbers circulating online.

Timeline: September booking to results the following August

The two tests sit at opposite ends of the cycle: TMUA in October at the start (a January window exists, but Oxford and Cambridge applicants are expected to sit in October), and STEP the June after offers land. The timeline below uses the 2027 entry cycle; the hard deadlines are TMUA's two booking cut-offs.

2026 – 2027Timeline

Sep 26

Oct 26

Nov 26

Dec 26

Jan 27

TMUA window 1 booking deadline

Hard deadline

Closes 18:00 UK time; Cambridge Maths applicants must book by this date

TMUA test window 1

Expected for Oxbridge

Candidates in mainland China, Hong Kong and Macau sit TMUA on 15 or 16 October only

TMUA window 2 booking deadline

Hard deadline

Closes 18:00 UK time

TMUA test window 2

Mainland China, Hong Kong and Macau candidates sit on 8 January only; Cambridge mature applicants in the January round use this window

Hard deadline Event WindowSTEP falls outside this window: it is sat in June with results in mid-August, as the flow below shows.

01By 28 Sep 2026

Book the TMUA

Window 1 booking closes 18:00 UK time on 28 September 2026

0212-16 October

Sit TMUA in October

Results go automatically via UCAS matching to institutions that require the test; you cannot choose who sees them

Interview and offer

A Cambridge Maths typical offer asks for grade 1 in each of STEP 2 and 3, which puts STEP on your calendar

042026 as the example

Sit STEP the following June

In 2026, STEP 2 was sat on 4 June and STEP 3 on 10 June, 3 hours each

0513 August in 2026

Results in mid-August

Released at 8am on 13 August 2026; results reach universities via UCAS, and Cambridge also receives answer booklets directly for borderline decisions

Prep paths: TMUA first, then STEP

Run your prep in two legs: drill timed multiple-choice work for TMUA through the autumn, then switch to STEP's long-form writing the moment the October sitting ends, and keep going until June. Here is what the two question banks on this site hold.

TMUA past papers (2015-2023, incl. 2 official specimens)

971

TMUA questions in total (plus 10 original mocks)

111

STEP past papers (1987-2025)

1,532

STEP questions in total

Using the TMUA bank

The site holds 18 TMUA past papers (2015-2023, including 2 official specimen sets) plus 10 original mock sets, 971 questions in total; the two most recent past papers per subject are free to try, and every question carries a full worked solution with a Chinese translation. Start with timed full papers in the TMUA past paper bank, then work through the Paper 1 guide and Paper 2 guide.

Using the STEP bank

The site holds 111 STEP past papers (1987-2025), 1,532 questions in total. The Cambridge Maths faculty's official STEP Support Programme also offers free preparation material. Start writing out full solutions from the STEP past paper bank, alongside the STEP 2 guide, STEP 3 guide and the grades guide.

Sequencing the two tracks

Make TMUA the autumn priority; see the registration and dates guide for booking details. After the October sitting, move onto STEP: STEP 2 draws on A Level Mathematics plus AS Further Mathematics, and STEP 3 on A Level Mathematics plus A Level Further Mathematics, so pace it against your Further Maths coursework. This site is not affiliated with UAT-UK, OCR or any university.

FAQ

Frequently asked questions

Does Cambridge Maths really require both TMUA and STEP?

Yes. From 2027 entry every applicant sits TMUA pre-interview (October sitting, booked by 28 September 2026), while STEP remains the offer condition, with grade 1 in each of STEP 2 and 3 in the typical offer. Cambridge frames TMUA as a way to identify candidates unlikely to be competitive rather than to pick only likely offer-holders, and historically 75%-80% of applicants have been invited to interview.

How are TMUA and STEP scores reported, and are there boundaries?

TMUA reports a single score from 1.0 to 9.0 on a cohort-referenced scale, with the median anchored at 4.5 and about 10% of candidates above 7.0; there are no grade boundaries or pass mark, and score appeals are not accepted. STEP is marked out of 120 per paper and graded S, 1, 2, 3 or U, with boundaries published every year: in 2025 the grade 1 boundary was 75 for STEP 2 and 61 for STEP 3.

Does STEP 1 still exist, and what does STEP look like now?

No. STEP 1 was discontinued from 2021; its last actual sitting was 2019, with the 2020 paper cancelled in the pandemic. Today STEP means STEP 2 and STEP 3: 3 hours and 12 questions each (8 pure, 2 mechanics, 2 probability and statistics), with your best six answers counting. STEP 2 draws on A Level Mathematics plus AS Further Mathematics, STEP 3 on A Level Mathematics plus full A Level Further Mathematics.

Where are the two tests sat, and what do they cost?

TMUA is computer-based, delivered through around 5,500 Pearson VUE centres worldwide, with official fees of £78 at UK centres and £133 elsewhere; candidates in mainland China, Hong Kong and Macau sit window 1 on 15 or 16 October only. STEP is a handwritten exam costing £102.50 in the UK and £142.25 outside, with results passed to universities via UCAS.

SOURCES

Official sources

MORE GUIDES

Other TMUA preparation guides

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

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