Quick answer
The TMUA and STEP are different tests: the TMUA is two 75-minute multiple-choice papers sat in October before you apply, while STEP is long written-proof papers sat the following summer as a conditional offer. STEP is significantly harder, and most applicants only sit the TMUA. CrackTMUA gets you TMUA-ready fast with 400+ questions and 18+ timed mocks. Compare all the tests.
"TMUA or STEP?" is a question that usually rests on a false assumption: that you pick one. For most applicants the two are not alternatives at all. They are different tests, sat at different points in the application cycle, doing completely different jobs. The TMUA screens you before you apply; STEP tests you once you already hold an offer. This guide explains exactly what each one is, how the formats and difficulty compare, who sits which (and when), and why a single Cambridge maths applicant may well meet both.
Key fact
The cleanest way to hold these apart: the TMUA is a pre-application screening test (multiple-choice, October, no calculator). STEP is a conditional-offer test (written proofs, the following summer, well beyond A-level). They sit at opposite ends of the cycle, so "TMUA vs STEP" is rarely a choice between two routes to the same place.
What the TMUA is
The TMUA (Test of Mathematics for University Admission) is a pre-application admissions test for maths, computer science and economics courses. It is run by UAT-UK, a joint venture between the University of Cambridge and Imperial College London, and delivered on-screen at Pearson VUE test centres. It moved to that provider in 2024, having previously been run by Cambridge Assessment through 2023.
The format is fixed and tight: two papers, 75 minutes each, 20 multiple-choice questions per paper, so 40 questions in total. There is no calculator and no formula booklet on either paper.
- Paper 1, Applications of Mathematical Knowledge, is essentially pure maths at roughly AS-level, but applied indirectly. The challenge is spotting the quick method rather than grinding through a signposted procedure.
- Paper 2, Mathematical Reasoning, tests logic, proof, the difference between necessary and sufficient conditions, counterexamples and spotting the flaw in a faulty proof. Most A-level students have never formally met this, which is why it rewards deliberate practice. Our Paper 2 logic and proof guide breaks the skills down.
Each paper is reported on a scale from 1.0 to 9.0 in 0.1 steps. There is no negative marking, so you should answer every question. As a rough guide, around 4.5 is the median score, 6.5 and above is upper tier, and 7.5 and above is exceptional.
What STEP is
STEP (the Sixth Term Examination Paper) is a different animal entirely. Rather than a pre-application screening test, it usually appears inside a conditional offer: some Cambridge and Warwick maths offers require you to achieve a given STEP grade. You sit it in the summer after your A-level exams, typically in June.
STEP is written, not multiple-choice. Each paper runs around three hours, and the questions are long, open-ended, and demand full worked solutions with rigorous proofs. You choose a subset of questions to attempt and write out complete arguments by hand. The content starts at A-level and reaches well beyond it, and a single question can take a long time to crack. Of the common UK maths admissions tests, STEP asks for the deepest sustained problem-solving.
Tip
If your Cambridge or Warwick offer mentions a STEP grade, that is a condition you meet next summer, not a test you sit this autumn. Get the TMUA out of the way first as part of the application, then turn to STEP once you hold the offer. Trying to prepare for both at once, a year early, spreads you thin.
TMUA vs STEP at a glance
| TMUA | STEP | |
|---|---|---|
| Purpose | Pre-application screening test | Condition inside an offer |
| Format | Multiple-choice | Written long-answer and full proofs |
| Structure | 2 papers, 75 min each, 20 questions each (40 total) | Long papers, around 3 hours each |
| Calculator | Not allowed | Not allowed |
| Where | On-screen at Pearson VUE test centres | Written, at your school or a centre |
| When sat | October, before you apply | The following summer, after A-levels |
| Content level | Roughly AS-to-A-level, applied indirectly | A-level and well beyond |
| Scoring | 1.0 to 9.0 per paper, no negative marking | Graded S / 1 / 2 / 3 / U per paper |
| Difficulty | Harder than A-level; rewards speed and clean reasoning | The most demanding of the common maths tests |
Which is harder?
STEP, comfortably, and it is not especially close. The two tests are hard in different ways, but STEP is harder on almost every axis that matters.
The TMUA is harder and more indirect than a standard A-level paper, and the Paper 2 reasoning genuinely catches people out, but the underlying content stays close to the AS and early A-level syllabus. Its difficulty comes from speed, abstraction and unfamiliar question styles, not from advanced material. Crucially, it is multiple-choice: you never have to construct and write a full argument, only pick the right option quickly.
STEP removes that safety net. The content goes well beyond A-level, the questions are open-ended, and you must build complete, watertight proofs and sustain them over a page or more, under time pressure, with no options to choose from. That is a different order of challenge. If you want the honest difficulty ranking of every UK maths test, our is the TMUA hard guide places the TMUA above A-level but firmly below STEP.
A taste of the reasoning gap
Descriptions only go so far. The clearest way to feel the difference is to attempt a real TMUA reasoning question, then imagine being asked to write out a full proof of the same idea by hand, with no options to choose from. That second task is roughly the leap from the TMUA to STEP. Have a proper go at this one before you reveal the solution:
Notice what the TMUA asks: follow the logic, judge what must be true, and select. STEP would hand you a blank page and ask you to justify every line. Same reasoning muscle, far heavier load.
Who sits which, and when
The two tests slot into different stages of the same cycle, so plenty of applicants meet both.
- You sit the TMUA if you are applying for maths or computer science at Oxford or Cambridge, maths or computing at Imperial, economics at LSE or UCL, or computer science at Warwick, among others. It is taken in October, before applications close. For the full list, see which universities require the TMUA.
- You sit STEP if your offer requires it, which is the case for some Cambridge and Warwick maths offers. You take it the following summer, after your A-level exams, to meet a grade condition.
So the honest answer to "TMUA or STEP" for a Cambridge maths applicant is usually both, in sequence: the TMUA in October as part of the application, then STEP the next summer as part of the offer. They are not competing options. Always confirm the exact requirement on your specific course's admissions page, because universities adjust these year to year, and do not assume a course uses STEP unless its own page says so.
How preparing for each differs
Because the tests do different jobs, the preparation looks different too.
For the TMUA, you are training fluency and pattern recognition: fast calculator-free arithmetic, recognising question types, and drilling the Paper 2 reasoning that has no A-level equivalent. Volume on real, well-explained questions under the clock is what moves the needle, and you want this sorted before you apply in October. CrackTMUA is built precisely for this stage: an interactive bank of 400+ questions (including 100+ original trap-based ones) with in-depth worked solutions, filterable by paper, topic and difficulty, plus 18 full timed mocks. The free tier gives you 10 questions a day; Premium unlocks everything for £37 one-time, with 12 months of access.
For STEP, the work is slower and deeper: long, open-ended problems, full written proofs, and building the stamina to sustain a single argument over an extended time. STEP preparation is its own discipline, with its own past papers and support, and it happens later, once you hold an offer. The two preparations rarely overlap on a single timeline, which is another reason not to treat them as a head-to-head choice.
Where to go from here
If you are at the application stage, your immediate test is the TMUA, and the earlier you start on real questions the further ahead you will be. STEP, if it applies to you at all, is next summer's problem and forms part of an offer you do not yet hold.
For the wider picture, including how the retired MAT and the science-focused ESAT fit in, see our full TMUA vs MAT vs STEP vs ESAT comparison. To get straight into the work, start with the Paper 2 logic and proof skills, since that reasoning is both the most underprepared part of the TMUA and the closest the test comes to STEP-style thinking.
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