Quick answer
The core of any good TMUA prep is the official UAT-UK specimen and past papers plus the official notes on logic and proof for Paper 2. Everything else is a supplement. A few honest extras help once you have exhausted those: worked-solution videos, and harder problems from the MAT and STEP. Start with the past papers.
There is no shortage of TMUA "resources" online, and most of them are noise: thin question packs, paywalled mocks of dubious quality, and revision notes that just restate the A-level syllabus. The truth is that the materials worth your time form a short list, and almost all of the value sits in the official ones. This guide ranks the genuinely useful resources, official-first, with an honest one-line verdict on each, so you can spend your prep time on the things that move your score rather than collecting links.
Key fact
The single most important rule: the official past papers are scarce and irreplaceable, so they are the centre of your prep, not background reading. Everything else exists to fill the gaps between them. Use free supplements to build skills, and save the real papers for timed mocks.
The official resources (start here, always)
If you only used the materials below and nothing else, you would still be well prepared. These are written by the people who set the exam, so they define the question style, difficulty and phrasing more accurately than any third party can.
The UAT-UK specimen papers and past papers. This is the core of TMUA preparation, full stop. The official sittings (2016 onwards under Cambridge Assessment, plus the newer UAT-UK papers) are the only questions guaranteed to match the real style, difficulty and indirect phrasing. They are limited in number, which makes them precious. Do not burn through them carelessly. Our past papers guide explains which papers exist, where to find them and how to ration them across your timeline. Verdict: non-negotiable, and the single best resource by a wide margin.
The official notes on logic and proof. UAT-UK publish a short set of notes covering the logic, reasoning and proof content that Paper 2 assumes and most schools never teach: implication, converse and contrapositive, necessary versus sufficient conditions, proof by contradiction and disproof by counterexample. Most applicants have never met this material formally, so it is the highest-leverage thing you can read before touching Paper 2. Verdict: essential, and short enough to work through in an afternoon. If you are unsure why Paper 2 matters so much, Paper 1 vs Paper 2 breaks down the difference.
The official specification and notes on the mathematical content. Less exciting, but it tells you exactly what is examinable so you do not waste time revising things that never appear. The TMUA draws almost entirely on the AS and early A-level syllabus, and the specification confirms it, which is reassuring: you are not learning new content so much as learning to apply familiar content quickly and indirectly. Skim it once early so your revision stays in scope, then return to it only if a past-paper question makes you wonder whether a topic is fair game.
A common mistake is to treat these official documents as background reading and dive straight into questions. Resist that. An hour spent on the logic notes and the specification at the start of your prep saves you days of confusion later, because so much of what makes the TMUA feel hard is unfamiliarity with its conventions rather than the maths itself.
Video resources: worked solutions worth watching
Past papers are far more useful when you can see how a strong solver actually thinks, not just the final answer. A worked solution shows you the slick observation that turns a four-minute slog into a thirty-second one, and that is most of what Paper 1 rewards.
r2drew2 (YouTube). Long-standing, thorough worked solutions to TMUA past papers, going through questions methodically. Genuinely useful for seeing the reasoning step by step when a question has stumped you. Verdict: a strong free companion to the past papers.
Jaymin Shah (YouTube). Clear walkthroughs of TMUA papers and problem types, well explained and easy to follow. A good second voice when one explanation has not clicked. Verdict: worth watching alongside r2drew2.
A word of caution on video: it is easy to watch a solution, nod along, and convince yourself you could have done it. You almost certainly could not have, yet. Always attempt the question fully and give up only after a real struggle, then watch. Passive watching builds false confidence, not skill. The most valuable moment in any walkthrough is the instant the solver spots the trick that collapses the problem, so pause there, rewind, and ask whether you would have seen it. That habit, repeated over dozens of questions, is what trains the pattern recognition the exam rewards under time pressure.
Harder practice: where to go once past papers run low
The official papers are limited, so disciplined students run out of fresh ones before exam day. When that happens, the answer is not random worksheets. It is harder, structurally similar material from neighbouring admissions tests, used to sharpen the same skills.
MAT multiple-choice questions (Q1). The Oxford MAT (retired after 2024) opened with ten multiple-choice questions that are close cousins of TMUA Paper 1: short, pure, calculator-free, and rewarding a clever observation over brute force. The longer MAT questions are too proof-heavy to be representative, but that first multiple-choice section is excellent extra Paper 1 practice and there is a large back catalogue of it. Verdict: the best source of extra Paper-1-style questions once official papers are gone.
STEP foundation and easier STEP questions. STEP is harder than the TMUA and mostly long-form proof, so it is not a like-for-like substitute. But the STEP Foundation modules and the gentler early questions are good for building the proof and reasoning muscle that Paper 2 leans on. Use them to get comfortable with rigour, not to mimic the exam format. Verdict: useful for Paper 2 reasoning stamina, not for format practice.
Both of these are stretch material. If you are still shaky on the official papers, they are a distraction. Reach for them only once the real papers are no longer fresh.
Try a real question
No roundup beats sitting an actual official question, so here is one from the past papers we keep banging on about. Have a proper go before you reveal the worked solution:
CrackTMUA: a free interactive question bank
In the interest of being straight with you: this is our site, so weigh the recommendation accordingly. What we actually offer for free is a question bank of the official past papers, made interactive, with full worked solutions for every question. Instead of a PDF and a separate answer key, you attempt each question in the browser, reveal a complete written solution, and filter by paper, topic and difficulty so you can drill a weak area directly. The free bank covers the official questions with worked solutions; it does not pretend to add questions that are not real.
We will not oversell it. The official PDFs are free and you should use them, and the YouTube channels above are excellent. CrackTMUA exists to make the official material easier to work through and to put a proper solution next to every question, which the bare PDFs do not. The honest gap it fills is friction: the official papers ship as a question PDF and a separate, often terse mark scheme, so working through them means flipping between documents and reconstructing the reasoning yourself. Having an attempt box, an instant reveal and a full written solution in one place keeps you in the flow and makes a study session less of a chore. If a clean interface and an explanation for every question saves you time, it is worth a look. If you are happy with PDFs and a notepad, the official papers alone will serve you well, and that is a perfectly good way to prepare.
How to combine them (a sensible order)
Resources only help if you use them in the right order. A rough sequence that works for most applicants:
| Resource | What it is | Best for |
|---|---|---|
| Official past papers (UAT-UK) | The real exams, scarce and authoritative | Timed mocks and the truest difficulty read |
| Official logic and proof notes | Short notes on Paper 2 reasoning | Learning the proof content schools skip |
| r2drew2 and Jaymin Shah (YouTube) | Free worked-solution walkthroughs | Seeing the slick method after you have tried |
| CrackTMUA question bank | Interactive past papers with full solutions | Drilling by topic with a solution per question |
| MAT Q1 multiple-choice | Short, pure, calculator-free problems | Extra Paper-1 practice once papers run low |
| STEP foundation questions | Gentler long-form proof problems | Building Paper 2 reasoning stamina |
The order matters more than the list. Start with the logic notes so Paper 2 is not a mystery, build skills on free walkthroughs and the question bank, and ration the official past papers for timed mocks near the exam. Then, only if you run dry, reach for MAT and STEP material. For the full timeline, see how to prepare for the TMUA.
What you can safely ignore
Plenty of paid "TMUA courses" and question packs promise the world. Be sceptical. The honest test for any non-official resource is simple: does it teach the slick, calculator-free methods the exam actually rewards, and are its questions calibrated to the real difficulty? Most fail one or both. Before paying for anything, exhaust the official papers, the logic notes and the free walkthroughs, because that combination already covers the vast majority of what you need.
One genuinely worthwhile skill that no single resource hands you is mental and by-hand arithmetic under time pressure, since the exam bans calculators entirely. That is a habit you build across every question you do, and our calculator-free techniques guide collects the shortcuts worth drilling.
And if you are still deciding how much of all this you actually need, our honest take on whether the TMUA is hard will help you size the job before you start.
Practise the real TMUA, free
Work through every official past paper as an interactive question bank, with instant worked solutions, trap-spotting and progress tracking. No PDFs.