What's new

Small but overdue. On the free tier, Quiz mode used to say nothing about your daily allowance until you had already run out, and then only as a one-line error.

Three things are better. You can now see how many of your 10 free questions are left while you are still building the quiz, along with when the next lot arrive. If you ask for more questions than you have left, it tells you up front how long the quiz will actually be, instead of quietly handing you a shorter one. And if you are out for the day, you get a proper panel with the countdown rather than a red sentence.

One detail worth knowing: the daily allowance resets at midnight UTC, which in British summer time is 1am, not midnight. We now show you the real time in your own timezone rather than guessing.

Also fixed. If your connection dropped at the exact moment a quiz answer was being marked, that question used to be recorded as wrong. It is now left out of the score entirely and labelled, so a dropped connection can never tell you that a correct answer was wrong. And the quiz now returns you to the top of the page on each new question, instead of leaving you parked at the button you just pressed.

Three new guides. TMUA question types walks through all six formats the exam actually uses, with a real past-paper example of each: the standard single-answer questions, the complete-set-of-values ones that punish stopping early, multi-statement questions, spot-the-error questions, theorem validity, and pure deduction puzzles. How much practice you need puts honest numbers on preparation, including the arithmetic most people avoid: the entire official back catalogue is about 360 questions, which covers maybe half of a serious total. And the diagnostic test explains how to find your starting level in about ten minutes instead of burning a past paper to do it.

Now the less good news, which you deserve to hear plainly.

On 24 July we tightened how worked solutions are served, so that signed-out visitors see the question and the first step rather than the whole method. That change caught something it was never meant to touch: the interactive question boxes inside our guides. For ten days, if you were not signed in and you answered one of those correctly, it told you "Not quite", left the answer letter blank, and showed a multi-step solution labelled "Step 1/1".

So if a guide told you that you got a question wrong since 24 July, there is a real chance you got it right. Sorry. That is a bad way to meet a maths site, and we should have caught it sooner.

It is fixed. The question boxes in guides are back to what they always were: pick an answer, see whether you got it, read the complete worked solution, no account needed. The guide boxes and the practice pages now run on completely separate code, so tightening one can never quietly break the other again.

Nothing else changed. The free tier is the same: 10 questions a day, and questions you have already attempted stay open forever.

A full 40-question mock, Paper 1 and Paper 2, built to sit above every real TMUA paper ever released.

The numbers. Mock 7 averages 6.6 on our 1 to 9 difficulty scale, with 18 of its 40 questions at band 7 or above and a genuine 8.0 ceiling. For comparison, a typical real paper averages 5.9 with about 17% of questions at band 7, the hardest real paper (2021) averages 6.2, and our own Mock 6 averages 6.4. Sit Mock 7 when you want to find out what breaks, not to feel good.

We wrote the rules down before writing the questions. The difficulty targets, the format mix and the answer-key spread were all pre-registered first, specifically so a weak question could not be argued through afterwards. Every one of the 40 answers was then re-derived from scratch, independently of whoever wrote it.

Then we tried to break it. All 40 questions went to blind reviewers who saw the question and the options and nothing else: no answer, no difficulty, no clue which were ours. Mixed in with them were 56 real past-paper questions, so a reviewer had no way to tell our work from the official material, and we could measure how hard each reviewer marks before believing anything they said about ours.

Five questions came down as a result, and none went up. Four of them because a reviewer found a shortcut we had missed: one can be settled by testing a single value, one by recalling a standard constant, one because a specific small case exposes the whole thing in about twenty seconds. A question you can crack in under a minute is not a band-7 question, whatever the intended method was, so those are now rated for the shortcut rather than the intention.

Two other things we fixed while we were in there.

• A question appeared in both Mock 4 and Mock 5 with the same numbers and the same answer. If you sat both, the second one was a free mark that also flattered your predicted band. Mock 5's copy has been replaced.
• Four worked solutions in Mock 3 told you that the right answer was a mistake, because the explanation named the wrong option letter. If you got one of those right and then read the solution, it said you were wrong. That is fixed.

Mock 7 is included with Premium alongside every other CrackTMUA mock and every official past paper.

Some housekeeping on how solutions are served, and one honest change to the free tier.

The fix behind the scenes. Full worked solutions used to be reachable in ways they shouldn't have been. That's tightened up: signed-out visitors now see the question, the options, and the first step of the method, then sign up free to see the rest and the answer. Nothing you were relying on changes.

The free tier, stated plainly. Free accounts can practise 10 questions a day (unchanged) and open full worked solutions for up to 20 questions a day. Questions you've already attempted stay open forever, so revising never costs you anything. It's a fair-use limit to stop the whole bank being scraped, and almost nobody doing real revision will ever reach it.

Premium is unchanged: unlimited everything. If you ever hit a wall that feels wrong, tell us on the contact page.

A big content day. Nothing here changes scoring or your data, it just makes more of the site useful.

Each past-paper guide now links all 40 of its questions. Open the 2019 guide, say, and there is a Q1 to Q20 list for both papers, each going straight to that question. No more scrolling the bank to find question 17.

Nine new guides. The ones we think you will actually use:

• The hardest TMUA paper, every year ranked. We rated all 320 released questions on one difficulty scale, so we can finally answer this properly. It was 2021, and 2023 was the gentlest by a distance.
• TMUA worked solutions. One page linking every solution for every released paper, plus what separates a real worked solution from an answer key.
• TMUA past papers 2024 and 2025. Short version: they were never released, and anyone selling them is mislabelling something. The guide explains why and what to use instead.
• TMUA vs ESAT, for anyone weighing Cambridge or Imperial courses across the two tests.
• TMUA for Maths degrees, the missing sibling of our Computer Science and Economics pages.
• Score conversion, test centres, community papers, and why Oxford replaced the MAT round out the set.

We also rebuilt the tutor guide with honest cost numbers, turned the preparation guide into a proper 12-week plan to the October sitting, and went deeper on practising by topic.

If you spot anything wrong in any of them, use the report button or the contact page. We fix fast.

Some of this is embarrassing to write. We would still rather you knew.

Mock 4 could be beaten by guessing. On Paper 1, 19 of the 20 correct answers were option A. On Paper 2, 18 of 20. Picking A every time, without reading a single question, scored 37 out of 40. The cause was mundane: whoever built it wrote the correct answer first and added the wrong ones after, and nobody ever looked at the pattern. Real past papers avoid this because their options are usually in ascending order, so the answer lands in a different place each time.

Every paper has been checked and rebalanced. No CrackTMUA paper now has more than about 30% of its answers in any one position, which is where the real papers sit. We did not touch the official past papers: their option order is part of the real exam, not something for us to tidy.

• Mock 4 has a real hard section now. Five of its questions were rated as top-decile but were nothing of the sort. They are replaced with genuinely hard new ones, and Mock 4's Paper 2 goes from an average difficulty of 4.9 to 5.9.
• Nine more free questions. The replaced questions were not thrown away. They are sound questions that were simply labelled too hard, so they are now free CrackTMUA Originals. The free question pool grows from 42 to 51, and its hardest question goes from 7.0 to 7.5.
• Find-the-error questions now work properly. Every one of them offers "the proof is correct" as an option, and none of them tells you up front that the proof is broken. Deciding whether anything is wrong at all is the hardest part of that question type, and we were giving it away on 13 questions.
• One worked solution named the wrong option. A Paper 2 negation question had its explanation pointing at option A when the answer is option B, with the letters swapped throughout. The answer was always right; the explanation was not. Fixed.
• The difficulty label on each mock now means something. "Harder than real" used to trigger on a round number that sat above every real paper, so nothing could earn it honestly. It is now measured against the real papers themselves, and requires beating the hardest of them on both average difficulty and the share of genuinely hard questions.

If you sat Mock 4 before today, your score still stands. Nothing was re-marked.

A difficulty rating is only worth anything if it is honest. So we checked ours properly, against the only benchmark that matters.

What we did. All 642 questions went to independent reviewers who could not see our labels. Critically, each batch was more than half real past-paper questions, mixed in, so a reviewer had no way to tell our questions from the official ones. We then calibrated every batch against those real questions. That is the difference between "we think this is a 7" and "this sits where a real 7 sits".

What we found. The bank is in good shape. Every series came back within half a band of its existing rating, and our questions are no more open to a lucky shortcut than the official ones. Our newest material, Mock 6 and the free original questions, came out best.

What we changed. 25 questions had their difficulty lowered. Not one was raised. They were concentrated in the harder end of our older mocks, where a few questions were labelled as top-decile without genuinely earning it. Mock 4 accounted for eight of them.

What this means for you.

• Your predicted band may have moved slightly, without you doing anything. The band is worked out from the difficulty of the questions you answered, so re-rating those questions re-rates the estimate. Nothing about your performance changed and no answer was re-marked.
• Two mocks now show a gentler label on the mocks page. Same questions, more honest description.
• No question was removed, edited or made easier. Only the number describing it moved.

We would rather tell you the rating was too generous than let it flatter you before the real exam. If you are wondering why your band shifted, tap the small i on the Predicted band card and it explains this there too.

Our hardest mock yet, five hard free questions, and an honesty pass on our own ratings.

• CrackTMUA Mock 6 - a full 40-question mock (Paper 1 + Paper 2) that sits above the hardest papers ever set. It averages 6.4 on our 1 to 9 difficulty scale, and 13 of its 40 questions are band 7 or above. For comparison: the 2021 paper averages 6.2, the 2022 paper 6.2, and a typical real paper 5.9. Our own Mocks 1 to 5 sit between 4.9 and 5.7. Sit Mock 6 when you want a genuine stress test rather than a confidence builder.
• Five hard original questions, free - two Paper 1 and three Paper 2, free to attempt with the full worked solution, and two of them are embedded to try directly in the hardest TMUA questions guide with no account needed.
• We put our own new questions through a blind audit, and lowered ten of them. Independent reviewers who could not see our labels rated every question alongside real past-paper questions of known difficulty, and a separate adversary tried to beat each one with a shortcut. Where our rating sat above what the evidence supported, we lowered it: ten questions came down, some by a full band and a half. None went up. A difficulty number is only useful if it is honest, and we would rather under-promise it.
• Honest confidence ranges on mock results - the estimated band range used to be a fixed plus-or-minus 0.5 whatever you did. It is now the real range from the model, which is wider after a single paper than after both. A band of 8.0 or above also now says what it means against the cohort, and flags that an estimate that high rests on very few comparable data points.

Premium unlocks Mock 6 alongside every other CrackTMUA mock and past paper.

Corrected 31 July. This entry originally said Mock 6 averaged 6.2 and sat "level with" the hardest real papers. That number was simply wrong, and it undersold the paper. Recomputed from the bank, Mock 6 shipped at 6.5 and two later re-ratings brought it to 6.4. Either way it is harder than every real paper, not level with them. None of the questions changed.

A fresh full mock, and a clearer read on how hard each one is.

• CrackTMUA Mock 5 - a brand-new full mock (Paper 1 + Paper 2), calibrated to match the difficulty and question mix of a real TMUA sitting, including the reasoning-heavy Paper 2 formats. Every question was independently re-solved and double-checked before it went live.
• Difficulty labels on the mocks page - each mock now shows how it compares to a real past paper - "Gentle start", "Exam-realistic" - with the exact numbers on tap. No more guessing which mock to sit next.
• More free practice questions, including our first graph questions - new original questions added to the free sampler, among them graph-reading questions where you work straight from the diagram - so there is more to work through before you decide to upgrade.
• For schools - teachers can now get a custom class plan for a whole group of students from the new "For schools" page.

Premium unlocks Mock 5 alongside every other CrackTMUA mock and past paper.

The mock exams got a serious upgrade, so you can use them the way that suits where you are in your prep.

• Sit both papers back-to-back - pick "Both" on any mock to run the full exam in one go: Paper 1, a short breather, then Paper 2. Your predicted band is worked out across both, exactly like a real result.
• Practice mode - prefer to learn as you go? Switch a mock to practice mode for the same questions untimed, with the full worked solution after each one. Your answers still feed your progress and spaced-repetition deck.
• Re-open any past sitting - every mock you have sat is now listed on your dashboard and on the mocks page, so you can jump back into the full breakdown and review whenever you want.
• Send your misses to review - one tap on the results screen adds every question you got wrong to your review deck, so they come back on the days you are about to forget them.
• Practise your weak topics - the results screen now links straight into targeted practice on the exact topics you slipped on.

Free users get all of this on the specimen mock. Premium unlocks it across every CrackTMUA mock and past paper.

Your predicted TMUA band now weighs more than right-vs-wrong. It factors in how fast you answer (the real exam is timed), how recently you practised, whether you've covered both papers and a spread of topics, and it counts fresh attempts more than spaced-review ones.

• Tap the i on the Predicted band card to see exactly how it's worked out.
• We tell you when we're not sure - if there isn't enough reliable data yet, we ask for a few more questions instead of guessing a number.
• Still deliberately conservative - the band leans low for real exam conditions, because we would rather you beat it than miss it.

The predicted band is a Premium feature, so your free practice is unchanged.

We put the whole question bank through an independent blind expert review to make our 1 to 9 difficulty ratings as accurate as possible.

• We would rather under-promise than over-promise - where a question was rated a touch high (mostly routine "apply a formula" questions, and a few in our newest mock), we nudged it down to match how hard it genuinely is. The real reasoning questions stay hard.
• Your practice is unchanged - same questions, same worked solutions, same spaced repetition. Only the difficulty label is tightened, so your predicted band reflects reality rather than flattering it.

Mock 4 is live for Premium - a fourth full original mock (40 questions across Paper 1 and Paper 2), pitched deliberately a notch harder than the real test for when you want to stress-test your preparation.

• Harder, but honest - fewer gentle openers and a fuller run of demanding mid-to-late questions, with a genuine top-end tail. It is a step up from a real sitting, not an inflated one.
• Every answer re-solved - each question was independently re-solved from scratch to confirm the key, and each worked solution names the trap and the fastest route.
• Sit it timed - both papers run in the Pearson VUE-style simulator with the 75-minute clock, then feed your predicted band and review deck like everything else.

That makes four full original mocks and over 175 original questions, alongside every official past paper. Find it in the mocks list.

We have added 10 brand-new original questions to the free question bank - no account or payment needed, and every one comes with a full worked solution.

• Five Paper 1 problems - covering surds, arithmetic series, logarithms, circle geometry and turning points, each with a common trap built in and explained.
• Five Paper 2 problems - necessary versus sufficient conditions, counterexamples, divisibility, multi-statement reasoning and a spot-the-flawed-proof question, the exact reasoning styles Paper 2 rewards.
• Learn from every attempt - the worked solutions name the trap and the fastest method, not just the answer.

That doubles the free original sampler. Practise them now in the question bank - free users get 10 questions a day.

Working through the official past papers just got a lot easier, both in the question bank and in the guides.

• Filter practice by year - the question bank now has a Year filter, so you can drill a single official past paper (2016 to 2023) or mix several at once. Perfect for sitting one specific year as a timed run.
• A guide for every past paper - new in-depth breakdowns of each year's paper from 2016 to 2023, and the specimen paper, each with its difficulty, the topics it covered, a standout question and real questions to try with full worked solutions. Plus a hardest questions roundup and a practice by topic hub that links straight to the questions.
• A rebuilt guide library - the Guides section is reorganised into clearer, intent-based sections (past papers, universities and requirements, scoring, preparation, exam strategy and more) with a "start here" row and a quick jump-nav, so you can find the right guide fast.

All of it is free: practise 10 questions a day and read every guide without an account.

A brand-new Mock 3 is live for Premium, adding 40 original questions (Paper 1 and Paper 2) built to real exam-day difficulty, not an inflated version of it.

• Fresh and exam-realistic - every question is a new problem type, distinct from Mocks 1 and 2, with the difficulty spread of a genuine sitting: gentle openers rising to a proper reasoning tail.
• Checked hard - every answer key was independently re-solved from scratch and confirmed, and every worked solution names the trap and the fastest method.
• Sit it timed - both papers run in the Pearson VUE-style simulator with the 75-minute clock, then feed your predicted band and review deck like everything else.

That takes CrackTMUA to three full original mocks and over 120 original questions, alongside every official past paper. Find it in the mocks list.

Practice on your terms with the new Quiz mode. Instead of scrolling the whole question bank, build a focused set and work through it one question at a time.

• Choose your questions - filter by topic, difficulty, paper and source, then pick how many you want.
• Set the pace - add a per-question timer to train exam speed, or leave it untimed to focus on method. Premium unlocks adaptive pacing that scales the time to each question's difficulty, plus total-time budgets, fully custom per-difficulty timing, and longer quizzes.
• Instant or test mode - reveal the worked solution after each question, or hold all feedback until a scorecard at the end.

Every question counts toward your normal daily practice and feeds your predicted band and review deck, exactly like the bank. Tap a quick-start preset or build your own, from the top menu or your dashboard.

Every question you get wrong now becomes a flashcard, scheduled by FSRS, the modern spaced-repetition algorithm and a step beyond the older SM-2 method most tools still use. It brings each one back at the moment you are about to forget the fix.

• A dedicated Review page - work through your due questions one at a time, with the full worked solution and an Again / Hard / Good / Easy rating that shows the next interval under each button.
• Tuned to your exam date - nothing is scheduled past your sitting, so every card fits inside your prep window.
• See your history - each card shows when you first got it wrong, how many times you have reviewed it, and how long you tend to spend.
• Retention analytics - Premium adds a review-workload forecast and a measure of how much you are truly holding on to.

Free accounts get 5 reviews a day; Premium removes the cap. Find Review in the top menu, or on your dashboard when cards are due.

New members now start with a short, interactive setup that turns your goals into a personal game plan.

• Pick your universities - choose everywhere you might apply and watch your target band take shape from real admissions expectations.
• Set your sitting - October or January, with a live countdown to test day.
• Find your starting point - an optional short diagnostic that adapts to your answers and gives you a provisional starting band, powered by the same model as your predicted band.
• Your game plan, always in view - the dashboard now leads with your targets, your countdown, and your start-to-target trajectory, which sharpens as you practise.

Already signed up? Set or update your plan any time from Settings, under "Your study plan".

A second full CrackTMUA mock - 40 brand-new original questions (Paper 1 + Paper 2), written and independently checked in the same style as the real test.

• Deliberately tougher at the top end - Paper 2's hard tail reaches genuine band-8 reasoning: quantifier logic, must-be-true analysis, and consistency puzzles that cannot be cracked by testing a few values.
• Every question has a full worked solution that names the trap each wrong option is built on.
• Find it in Practice under the CrackTMUA Mock 2 paper sets (Premium).

Two quick, free tools to help you make sense of your TMUA prep, no account needed.

• Score calculator - enter your raw marks from each paper for a rough estimate of your band on the 1.0 to 9.0 scale. It is upfront that there is no official raw-to-band table, so the number is a ballpark, not a result.
• University eligibility checker - pick your university to see the TMUA score it looks for, whether the test is required or recommended, and how to get there.

Find them both under Tools in the top menu.

We expanded the free guides library with in-depth pages covering far more of what TMUA applicants actually search for.

What is new:

• Every TMUA university - dedicated guides for Imperial, LSE, Warwick, Durham and UCL, alongside Oxford and Cambridge, plus a "which universities require the TMUA" overview.
• Is the TMUA hard? and What is a good TMUA score? - straight answers, with the post-2024 scoring change explained.
• TMUA for Economics and TMUA for Computer Science - exactly which universities need the test for each subject.
• Topic-by-topic deep dives - dedicated guides for the trickier areas (logarithms, sequences and series, coordinate geometry, integration, Paper 2 logic and proof, and more), each with a worked example you can try.

Every guide now opens with a quick-answer summary, so the key facts are right at the top. All free, no account needed.

We launched a full community - a place to ask about specific questions, swap strategy, and compare notes with other TMUA applicants.

What you can do:

• Ask about any question - post a question thread and mark an accepted answer, with full Markdown and LaTeX math support so your working renders properly.
• Upvote, build reputation, and earn badges as you help other people out.
• Private messages - DM other members, with a notification bell so you never miss a reply or a mention.
• Tied to the question bank - every practice question has its own "Discuss this question" space.

Set your username in Settings, under "Community profile", then jump in.

Your progress dashboard got a complete rebuild, designed around one headline number: a predicted TMUA score that updates every time you practise.

Here is what is now tracked:

• Predicted score and band - instead of a plain "percent correct", we fit a proper ability model to your attempts (the same family of item-response models used by real admissions tests). Hard and easy questions count differently, the estimate sharpens the more you do, and it comes with a confidence range.
• Strengths and weak spots by topic - a clear breakdown of which topics are pulling your score up and which are dragging it down.
• Timing and pace - how long you spend per question and whether speed is costing you accuracy.
• Accuracy and progress over time - watch the trend line move as you improve.
• Your full attempt history - every question you have done, how you answered, and how long it took.

The full dashboard is part of Premium. Free accounts get a live preview so you can see what gets tracked.

We've since made it even better: free accounts now see more up front - your accuracy by difficulty, accuracy by paper, and how much of the question bank you've covered, right at the top. And Premium gained three new cards: a predicted-band trajectory (watch your band climb over time), an exam-time projection (could you finish a full paper inside the clock?), and a mock-vs-practice readiness gap.

Premium now includes a complete, timed mock exam - a full Paper 1 and Paper 2 pair - that runs in an interface modelled on the real Pearson VUE exam environment, so practice feels like the real thing.

• Take it timed, to rehearse pacing under pressure, or untimed to work through it carefully.
• Every question comes with the same full worked solution as the rest of the bank.

More mocks are on the way.

We finished adding every official TMUA paper from 2016 to 2023, plus the specimen paper - over 350 real past-paper questions in total.

• Each question has a full, step-by-step worked solution with trap-spotting commentary, not just an answer key.
• Every paper was checked against the original source PDFs for fidelity, including the figures and the maths.
• Free accounts get a set number of questions a day; Premium removes the daily cap.

We launched a free library of TMUA strategy guides - proper, in-depth articles rather than thin blog posts.

They cover scoring and band targets, the syllabus, how Paper 1 and Paper 2 differ, calculator-free technique, and the TMUA requirements for Cambridge, Imperial, Warwick, LSE, Durham and more. Several include an interactive worked example you can try right in the page.