Quick answer
The most useful free TMUA resource is CrackTMUA's free tier: 10 interactive questions a day with full worked solutions, plus a specimen mock and these guides, at no cost. Use it alongside the official UAT-UK past papers and Physics and Maths Tutor, which are also free. For the full list including paid options, see best TMUA resources.
You do not have to spend a penny to prepare well for the TMUA. The most important material of all, the questions written by the people who set the exam, is completely free, and a surprising amount of genuinely useful supporting material is too. This guide is an honest list of the resources that cost nothing, what each is good for, and how to actually use them. We sell a paid platform, so recommending free things might seem odd, but the truth matters more: if you use the free resources below properly, you are most of the way there already.
Key fact
Almost everything that genuinely moves your TMUA score is free. The official past papers, the official answers and the official logic notes cost nothing, and they are the single most valuable thing you can practise with. Paid tools add convenience, structure and extra questions, but they are supplements to the free core, not replacements for it.
The official past papers and answers (free, and the most important)
Start here, always. The official TMUA past papers are published free by UAT-UK and Cambridge, and they are the best practice questions that exist because they are the only ones written to the exact specification, difficulty and indirect phrasing of the real exam. No third party can fully replicate that.
What you get for free:
- The specimen paper, the cleanest illustration of the format, and a sensible first contact with the test.
- Every past sitting, two papers of 20 multiple-choice questions each, sat in 75 minutes per paper with no calculator. That runs to a deep back catalogue of genuine questions.
- The official answer keys and worked answers, so you are never left guessing why an option was correct.
The pre-2024 papers were marked slightly differently and reported three grades rather than one, but the questions themselves are completely valid practice, so do not skip them. For the full list of which papers exist, where to download the originals and how to ration them across your timeline, see our TMUA past papers guide.
Tip
The official papers are scarce, so treat them as gold. Build your skills on the free supplements below, and save a handful of complete, unseen papers for timed full mocks in the final weeks. Burning through them early, untimed, wastes your most valuable free resource.
The official logic, proof and content notes (free)
Alongside the papers, UAT-UK publish short notes on logic and proof and a specification for the mathematical content, both free. The logic notes are the highest-leverage free read before you touch Paper 2: implication, converse and contrapositive, necessary versus sufficient, proof by contradiction and disproof by counterexample. Most applicants have never met this material formally, and it is exactly what makes Paper 2 feel alien. An afternoon with these notes removes a lot of that. If you are unsure why Paper 2 deserves the attention, Paper 1 vs Paper 2 explains the split.
The specification is duller but useful: it tells you exactly what is examinable, so you do not waste time revising things that never appear. The reassuring takeaway is that the TMUA draws almost entirely on the AS and early A-level syllabus you already know.
Physics & Maths Tutor (PMT): free papers and solutions
Physics & Maths Tutor (PMT) is a free revision site that hosts the TMUA past papers and their solutions in one tidy place. It does not replace the official source, but it is genuinely convenient: the papers and worked answers are organised together and easy to download, which saves the hunting around that the official pages sometimes need. If you find the official site fiddly, PMT is a clean free mirror to fall back on.
Use it the same way you use the official PDFs: attempt a paper properly, then study the solutions, especially for the questions you got wrong or got right by luck. The value is in the worked method, not the score.
Free worked-solution videos
Past papers teach you far more when you can watch how a strong solver actually thinks, not just read the final answer. There are free worked-solution videos on YouTube that walk through TMUA past papers question by question, showing the slick observation that turns a four-minute grind into a thirty-second move. That clever step is most of what Paper 1 rewards, and seeing it modelled repeatedly trains the pattern recognition you need under time pressure.
One honest warning: it is easy to watch a solution, nod along, and convince yourself you could have done it. You probably could not have, yet. Always attempt the question fully and give up only after a real struggle, then watch. The most valuable second of any walkthrough is the instant the solver spots the trick that collapses the problem, so pause there and ask whether you would have seen it. Passive watching builds false confidence, not skill.
To find good ones, search precisely: "TMUA 2022 paper 1 solutions" rather than a vague "TMUA help", swapping in the year and paper you are working on. Prefer full-paper walkthroughs over single-question clips, because they keep the difficulty progression intact and are usually from someone who has sat the whole thing rather than cherry-picked the easy parts. And always check the video's final answer against the official answer key before you trust the method, because anyone can upload a confidently wrong solution and there is no quality control on YouTube.
Try a real one, free, right now
Theory only goes so far. Here is a genuine official past-paper question, free to attempt in your browser. Give it a proper go before you reveal the worked solution:
CrackTMUA's free tier
Full disclosure: this is our site. But our free tier is genuinely free and genuinely useful, so it belongs on an honest list. With no payment and no card you get:
- 10 practice questions a day, drawn from official past papers and our own original questions, each with a full step-by-step worked solution that names the trap and shows the fastest method.
- The specimen mock, sat in a replica of the real on-screen interface, so you can feel the format before exam day.
- All of these guides, free to read, covering scoring, syllabus, strategy and university requirements.
That is a real amount of free practice. To be straight about what is paid: Premium (a one-time £37 for 12 months of access, never a subscription and never "lifetime") unlocks the full 400+ question bank including 100+ original trap-based questions, 18+ full timed mocks, the SM-2 spaced-repetition engine, the predicted TMUA band with topic-by-topic analytics, and the community. The predicted band and the full bank are premium, so we will not pretend otherwise. But you can prepare seriously on the free tier, and our practice questions guide shows how to get the most from it.
The free toolkit at a glance
| Free resource | What it is | Best for |
|---|---|---|
| Official past papers and answers (UAT-UK / Cambridge) | The real exams plus answer keys, free to download | Timed mocks and the truest difficulty read |
| Official logic and proof notes | Short notes on Paper 2 reasoning | Learning the proof content schools skip |
| Physics & Maths Tutor (PMT) | Free mirror of the papers and solutions | A tidy, convenient place to grab papers |
| Free worked-solution videos | Walkthroughs of past-paper questions | Seeing the slick method after you have tried |
| CrackTMUA free tier | 10 questions a day, specimen mock, free guides | Daily interactive drilling with inline solutions |
The order matters more than the list. Read the free logic notes first so Paper 2 is not a mystery, build skills on free walkthroughs and daily questions, and ration the official past papers for timed mocks near the exam. For the full timeline, see how to prepare for the TMUA, and for the honest take on paid extras worth their price, our best resources roundup is the companion to this page.
How to use the free stuff well
Free does not mean effective on its own. A few habits separate students who improve from those who just collect links:
- Study the worked answer for every question, even the ones you got right. The official route is often faster than yours, and that efficiency is exactly what a no-calculator, four-minutes-a-question test rewards.
- Keep a short log of every mistake and its reason: a topic gap, a careless slip, a trap, or a method you did not know. Patterns appear fast and tell you what to drill next.
- Practise by topic first, then by difficulty, then add the clock. Doing all three at once early on just teaches you to panic.
- Protect the official papers. They are the one free resource you cannot get more of, so do not waste them on casual untimed runs.
Get that loop right and the free resources above will carry you a long way, whatever the forums say about how hard the TMUA is.
Practise the real TMUA, free
Drill 400+ questions, every official past paper plus 100+ original, trap-based ones, each with a full worked solution, then sit full mocks in a replica of the real exam screen. Spaced repetition and a predicted band included. No PDFs.