How to Prepare for the TMUA in 16 Weeks (a Realistic Plan)

16 weeks back from the 12-16 October 2026 window means starting in the week of 22 June. Budget 8-10 hours a week, roughly 140 hours total. The shape: two weeks of diagnosis, six weeks of content and technique, four weeks on Paper 2 logic, three weeks of timed mocks, one week of taper. Most plans fail not from too few hours but from spending them re-reading notes.

Table of contents

• Why 16 weeks and not 6
• Weeks 1-2: diagnose before you prescribe
• Weeks 3-8: content and technique
• Weeks 9-12: the Paper 2 logic block
• Weeks 13-15: timed mocks, done properly
• Week 16: taper
• The re-reading trap
• No formula book: spaced repetition or suffer
• Frequently asked questions

Intro

The TMUA is 40 questions in 150 minutes with no calculator: Paper 1 on applications of mathematical knowledge, Paper 2 on mathematical reasoning and logic, 75 minutes and 20 questions each. That is under four minutes a question on material that is mostly AS-level in content but emphatically not AS-level in style. The constraint you are training against is not knowledge. It is retrieval speed, comfort with unfamiliar question framing, and a body of logic content that A-level never teaches you. A 16-week plan works because those three things improve on different timescales, and a plan that ignores the difference wastes hours on the wrong one.

Why 16 weeks and not 6

You can prepare for the TMUA in six weeks. But six-week plans force you to run content repair, logic learning and mock practice simultaneously, and the logic content in particular does not compress well. Necessary versus sufficient conditions, contrapositives and counterexample-hunting need repeated exposure spread over weeks before they feel automatic under time pressure. Cramming them in September means you will still be translating "P is necessary for Q" into an implication arrow mid-exam, which costs 40 seconds per logic question on a paper where 40 seconds is a lot.

The other reason: the 2024 and 2025 papers shifted style. They are wordier and more applied than the pre-2023 papers, with more reading per question. Adjusting your pacing to that takes mock cycles, and mock cycles take calendar weeks.

Sixteen weeks from the 12-16 October window puts your start in late June. If you are reading this later than that, keep the block structure below and shrink the content block first; the logic block and the mock block earn their time most directly. Key admin point before any of this: registration opens 20 July and closes 28 September. Book in July.

Weeks 1-2: diagnose before you prescribe

Do not start with a textbook. Start by finding out what is actually broken. Sit our free diagnostic, or a recent full past paper untimed, and sort every error into one of three bins:

1. Content: you did not know the maths.
2. Technique: you knew the maths but took six minutes or picked an approach that buried you in algebra.
3. Style: you misread the question, fell for a trap option, or could not parse a logic statement.

Your bin ratios decide where your hours go. A student with 70% content errors needs a different 16 weeks from one with 70% style errors, and most students confidently misdiagnose themselves before seeing the data. Roughly 6 hours a week is enough for this fortnight.

Weeks 3-8: content and technique

The long block: six weeks, 8-10 hours a week, working through the specification topic by topic with the emphasis weighted by your diagnostic. Two rules keep this block honest.

Rule one: practice questions outnumber notes ten to one. For each topic, the loop is: attempt questions, fail somewhere specific, read exactly the bit of theory that fixes the failure, re-attempt. Reading the chapter first feels safer and teaches less.

Rule two: train calculator-free arithmetic from day one. Surd manipulation, fraction arithmetic, powers of 2 and 3, sin and cos of the standard angles. The TMUA gives you nothing, and slow arithmetic is the most common hidden tax on Paper 1.

End each week with a 10-question mini-set, mildly timed (say 45 minutes), to keep contact with exam pressure without committing to full mocks early. The TMUA Pro question bank sorts questions by topic and difficulty and tells you why each wrong option is wrong, which shortens the failure-diagnosis loop considerably. The free PDF guides cover the highest-yield Paper 1 techniques if you want the unpaid route.

Weeks 9-12: the Paper 2 logic block

Four dedicated weeks, because this is the content A-level never gave you. The syllabus here is small but unfamiliar: implication and its converse, necessary and sufficient conditions, contrapositive, negating quantified statements, counterexamples, and judging the validity of short arguments. Small syllabus, but the questions are precise and the trap options are built from exactly the errors untrained students make.

Work through the material systematically rather than ad hoc. Our Logic course is free and built for this block, and we have a full written walkthrough of the core ideas with worked examples in TMUA Paper 2 Logic: Necessary vs Sufficient, Contrapositive and Counterexamples. Keep Paper 1 ticking over with two mixed mini-sets a week so the earlier block does not decay.

By the end of week 12 you should be able to translate any "necessary/sufficient" sentence into an implication arrow in under ten seconds. That single skill is worth multiple marks.

Weeks 13-15: timed mocks, done properly

Now, and not earlier, full timed mocks become the core activity. Two full papers a week, sat in one sitting where possible, under real conditions: 75 minutes per paper, no calculator, no pausing, same time of day as your booked slot. If past papers are your mock source, weight them towards 2024 and 2025: the new format post explains why older papers undersell the current reading load.

The mock itself is half the work. The other half is the review, which should take as long as the sitting:

• Re-bin every error into content, technique or style, and watch how the ratios move week to week.
• For every question that took over five minutes, find the faster route, even if you got it right.
• Keep a one-page error log. Before each new mock, read it. This is the cheapest score improvement available and almost nobody does it. The ten errors that fill most of these logs are catalogued in 10 TMUA Mistakes That Cost Marks Under Time Pressure.

Auto-marked mocks with per-topic analytics, six of them, are part of TMUA Pro; the analytics matter here because week-on-week trend data is what tells you whether the plan is working. If your mock scores plateau for two consecutive weeks on the same error type, that is the signal to get targeted help rather than grind harder; a couple of 1-1 sessions with a Cambridge student tutor on your specific weak area is the efficient fix at this stage.

Why not start mocks in week 5? Because early mocks mostly measure problems you already know you have, at the cost of two prime hours plus review time. Mocks earn their hours once the content and logic blocks have given them something to measure.

Week 16: taper

The final week is maintenance, not improvement. One light half-paper early in the week, daily 20-minute formula and error-log reviews, and nothing new after the 5th of October. The goal is arriving at your Pearson VUE slot with fast recall and no fatigue. Cramming a new topic in the last four days has roughly zero expected value and nonzero panic value.

The re-reading trap

The most common failure mode in self-directed TMUA prep is not laziness. It is hours spent re-reading notes and re-watching explanations, which feels like work and produces almost nothing. Recognising a worked solution is a different mental act from producing one under time pressure, and the exam only pays for the second. The fix is mechanical: every study session ends with attempted questions, closed-book, and your notes exist to be retrieved from memory, not re-read. If a session contained no retrieval, it did not count.

No formula book: spaced repetition or suffer

The TMUA provides no formula booklet. Trig identities, log laws, binomial expansion, geometric series sums, the lot must be in your head, retrievable in seconds. The reliable way to get there is spaced repetition: a small deck of formula cards (30-50 covers it), reviewed daily at first, then at stretching intervals. Ten minutes a day from week 3 onwards makes the whole problem disappear by September. Starting in October does not; spacing is the active ingredient.

Related reading

• TMUA 2026: Key Dates, Registration and the 28 September Deadline
• TMUA Paper 2 Logic: Necessary vs Sufficient, Contrapositive and Counterexamples
• What TMUA Score Do You Need for Cambridge, Imperial and LSE?

Closing

Sixteen weeks, 140 hours, four blocks: diagnose, build, logic, mocks. The plan is not clever and does not need to be. What separates the students who hit 6.5 from the ones who stall at 5.0 is rarely the plan itself; it is whether the hours inside it were retrieval and timed practice or re-reading and hope. Start with the diagnostic, be honest about the bins, and let the error data steer everything after that.

Frequently asked questions

How long do I need to prepare for the TMUA? 16 weeks at 8-10 hours a week, roughly 140 hours total, is a realistic budget for a student with solid AS maths aiming at a competitive score. You can compress to 8-10 weeks by raising weekly hours, but the logic content in Paper 2 needs calendar time to settle, not just hours.

When should I start doing timed TMUA mocks? Around week 13 of a 16-week plan, so roughly three to four weeks before the test. Earlier than that, untimed and partially timed work fixes more per hour. Later than that, you have no time to act on what the mocks reveal.

Is there a formula book in the TMUA? No. The TMUA provides no formula booklet and no calculator. Everything you would normally look up, trig identities, log laws, the binomial expansion, sum formulae, has to be in your head and retrievable at speed.

Are old TMUA past papers still useful? Yes for content, with a caveat for style. The 2024 and 2025 papers became wordier and more applied than the pre-2023 papers. Use old papers to train technique, but calibrate your pacing and reading load against the recent style.

How many hours a week is enough? 8-10 focused hours a week over 16 weeks is the budget this plan assumes. Fewer hours can still work if every hour is active practice rather than note-reading, which is where most self-directed prep quietly fails.

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Sources: UAT-UK TMUA test specification and published 2026 dates. Last updated 2026-06-10.