TMUA Past Papers: Where to Find Them and How to Use Them
Every student preparing for the TMUA eventually hits the same wall: there aren't enough past papers. The test has existed since 2016, but the number of publicly available papers is surprisingly small, and it shrank further when UAT-UK took over administration in 2024. Here's where to find what exists and how to make the most of it.
What's available
The TMUA was originally run by Cambridge Assessment Admissions Testing from 2016 to 2023. During that period, Cambridge published past papers and mark schemes for most years. When UAT-UK (a collaboration between Cambridge and Imperial, administered by Pearson VUE) took over in 2024, the old papers remained available but new papers have not been released publicly.
The UAT-UK website (esat-tmua.ac.uk) hosts the current specification and some official practice materials. The Cambridge Assessment archive still has older papers, though navigating to them isn't always straightforward.
In total, you're looking at roughly 8–10 years of papers with two papers per year, giving you somewhere between 320 and 400 questions. That sounds like a lot, but once you've gone through them in practice — some for learning, some for timed conditions — you'll find yourself running out faster than expected.
How to use past papers effectively
Don't do them all at once. Ration them. Here's the approach that works best.
Phase 1: Learning mode.Take the older papers (2016–2020) and work through them untimed, with the mark scheme open. The purpose isn't to test yourself — it's to learn what TMUA questions look and feel like. Study the solutions. Notice how the questions require insight rather than routine computation. Notice how the distractors correspond to common mistakes. Build your sense of what “TMUA-style thinking” means.
Phase 2: Practice mode.Take the 2021–2022 papers and do them under light time pressure — give yourself 90 minutes per paper instead of 75. Check your answers afterwards, and for every question you got wrong, write down what went wrong and what the correct approach was. Keep a log of your mistakes by topic.
Phase 3: Mock mode.Save the most recent papers (2023 and anything from 2024 onward if available) for full timed mocks under exam conditions. 75 minutes, no breaks, no checking. These are your best indicator of how you'll perform on the real thing, so don't waste them until you're ready.
Phase 4: You've run out. This is where most students end up three to four weeks before the exam, having done all the past papers and wanting more practice. You have a few options.
When you run out of past papers
MAT past papers are useful for Paper 1 practice. Oxford's Mathematics Admissions Test (which is being replaced by the TMUA from 2027) tested similar mathematical thinking skills. The multiple choice questions especially overlap in style. The longer MAT questions are less relevant since the TMUA is entirely multiple choice.
For Paper 2, there's less crossover from other tests. The logic and proof content is fairly unique to the TMUA. You can practise with discrete mathematics textbooks, logic puzzles, and proof-based exercises, but these won't match the exact TMUA format.
The other option is purpose-built practice material. This is why we created tmua.study— to solve the problem that every TMUA student faces. The platform generates original questions that are calibrated to match recent TMUA papers in style, difficulty, and format. Every question goes through a multi-stage quality check to make sure it's accurate and feels like the real thing. You can filter by paper, topic, and difficulty, take full timed mocks, and never run out of material.
Things to watch out for
The TMUA has changed over the years. The 2016–2019 papers have a slightly different flavour to the 2022–2024 papers — the more recent exams tend to have more argument-analysis questions on Paper 2 and more questions that combine multiple topics on Paper 1. Weight your preparation toward the newer papers.
The scoring system also changed in 2024 when UAT-UK took over. Scores from 2024 onward are roughly 1–1.5 points lower on the 1.0–9.0 scale compared to the same raw performance in earlier years. This doesn't affect your preparation, but be aware of it when comparing score benchmarks — a 6.0 in 2024 is not the same as a 6.0 in 2022.
Don't memorise past paper answers. The point of practice is to train your thinking process, not to recognise specific questions. If you find yourself remembering the answer to a question rather than solving it, that paper has lost its value for you — you need fresh material.
The key takeaway
Past papers are your most valuable preparation resource, but they're limited. Use them strategically — learning first, then practice, then full mocks. When you run out, supplement with MAT papers for Paper 1 and purpose-built TMUA practice (like tmua.study) for both papers. The goal is to arrive at exam day having done enough quality practice that no question style surprises you.