TMUA vs STEP: Two Very Different Maths Tests
One decides whether you get an offer. The other decides whether you keep it. Here's what actually separates them — and why practising for one is poor practice for the other.
If you are applying for maths at a top UK university, you will probably meet both of these tests.
They sound similar. They are not.
Here is the short version:
The TMUA helps decide whether you get an offer. STEP decides whether you keep it.
Everything else follows from that one difference.
They happen at completely different times
This is the part students most often get wrong.
The TMUA comes first. You sit it in October of Year 13, before universities have made any decisions. Your score is part of what they look at when deciding who to interview and who to offer.
STEP comes last. You sit it in June of Year 13, alongside your A levels, after you already hold an offer. It is a condition of that offer, like an A*.
So they are not two versions of the same hurdle. They sit at opposite ends of the application.
What the papers actually look like
TMUA
- Two papers, 75 minutes each (2 hours 30 in total)
- 20 multiple-choice questions per paper
- Taken on a computer, at a Pearson VUE test centre
- No calculator
- Paper 1 is about applying maths you already know
- Paper 2 is about reasoning — proof, logic, spotting a flawed argument
That works out at under four minutes per question.
Nobody ever sees your working. Only the answer counts.
STEP
- Two papers, STEP 2 and STEP 3, sat on separate days
- Three hours each
- 12 questions per paper — 8 pure, 2 mechanics, 2 statistics
- You answer up to six, and only your best six count
- Each question is marked out of 20, so 120 marks per paper
- Handwritten, in an exam hall
- No calculator
That works out at roughly thirty minutes per question.
Here, the working is the mark. A right answer with no argument behind it scores very little.
(STEP 1 was discontinued back in 2020, so ignore any advice that mentions it.)
Side by side
| TMUA | STEP | |
|---|---|---|
| When | October of Year 13 | June of Year 13 |
| What it decides | Whether you get an offer | Whether you meet the offer |
| Length | 2 × 75 minutes | 2 × 3 hours |
| Questions | 20 multiple choice per paper | 12 per paper, answer 6 |
| Format | On screen | Handwritten |
| Time per question | Under 4 minutes | About 30 minutes |
| Calculator | No | No |
| Result | A score from 1.0 to 9.0 | A grade: S, 1, 2, 3 or U |
| Rewards | Speed and accuracy | Depth and stamina |
| Your working | Never seen | Is the whole mark |
How the results are reported
TMUA gives you a number between 1.0 and 9.0, where 9.0 is the top.
There is no pass or fail. It is just a score, and each university decides what it wants to see. You do not lose marks for wrong answers, so there is never a reason to leave one blank.
STEP gives you a grade: S, 1, 2, 3 or U, with S at the top.
Offers name the grade. Cambridge maths offers, for example, usually ask for a grade 1 in both STEP 2 and STEP 3.
Who needs which one
Universities requiring the TMUA (2027 entry)
- Cambridge — Maths, Computer Science, Economics
- Oxford — Maths, Computer Science and their joint courses
- Imperial — Maths and Computing
- Warwick — Maths, Computer Science, Discrete Maths (recommended for several others)
- Durham — Maths
- LSE — Economics and Econometrics (recommended for several others)
- UCL — Economics
Oxford’s move to the TMUA is new. It replaced the MAT, so older guides will point you at the wrong test.
Universities requiring STEP
In practice, Cambridge.
Imperial and Warwick both used to use STEP and have since moved across to the TMUA. Plenty of other departments still suggest STEP papers as good practice, but they do not make it a condition.
And if you are applying to Cambridge for Maths?
You will sit both. The TMUA in October, then STEP the following June.
Course requirements do change year to year, so always check the course page before you plan around this.
The trap: they need different kinds of practice
Here is the thing almost nobody tells you.
The content overlaps a lot. Proof, number theory, logic, sequences, combinatorics — the same ideas turn up in both. Working on one genuinely builds the maths you need for the other.
The skills do not overlap at all.
The TMUA rewards you for finding the short route, ruling out three options quickly, and moving on. Getting stuck for ten minutes is a disaster.
STEP rewards the opposite. It rewards sitting with one problem for half an hour, trying something, watching it fail, and trying again — then writing the whole argument down so a marker can follow it.
So a student who only grinds multiple-choice questions gets fast and gets stuck. A student who only does STEP questions is thorough and runs out of time.
Use TMUA questions to build content. Use STEP questions to build stamina. Don’t expect either to prepare you for the other.
A sensible timeline
Year 12 — Build the maths. Work through proof, algebra and sequences properly. It is far too early to worry about test technique.
Summer before Year 13 — Start the free STEP Support Programme foundation modules. Begin timed TMUA practice.
September — TMUA practice becomes the priority. Full papers, strictly timed.
October (12th–16th, 2026) — Sit the TMUA. Booking closes 28 September. Results come back 16 November. There is also a January sitting for some courses.
December to January — Interviews and offers.
January onwards — If your offer includes STEP, this is when the real work starts. Entries open in early March and close in early May, so make sure your school or an exam centre has registered you.
June — STEP 2 and STEP 3, on separate days.
August — STEP results arrive on A level results day.
Free things worth using
The STEP Support Programme is run by Cambridge and costs nothing. It is genuinely the best starting point, and the discussion after each question is worth more than a worked answer.
Past papers for both tests are freely available and are the only practice that really counts.
And for the official detail — dates, fees, what each university actually asks for — go to UAT-UK for the TMUA and the Cambridge Faculty of Mathematics for STEP.
The one thing to remember
The TMUA is a sprint. STEP is a long walk uphill.
They test the same maths in almost opposite ways, and the students who do well in both are the ones who noticed that early.