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Targeted practice

TMUA Practice by Topic: Every Topic, With Questions

Practise the TMUA one topic at a time. Jump straight to real questions on algebra, calculus, trigonometry, logic and every other topic, each with full worked solutions. Free.

Past Papers & Practice Updated 7 Jul 2026 6 min read

Quick answer

The most efficient way to raise a TMUA score is to practise one topic at a time, drilling your weak areas until they are automatic, rather than doing whole papers on repeat. Paper 1 covers algebra, coordinate geometry, calculus, logarithms, sequences, trigonometry, functions, inequalities and statistics; Paper 2 adds logic, proof, number theory and counting. On CrackTMUA you can filter the free question bank to any topic and get a full worked solution on every question. The links below jump straight to each one.

Doing whole past papers is the right way to finish your TMUA preparation, but it is a poor way to improve in the middle of it. When you sit a full paper, your weakest topic gets three or four questions and then disappears, which is nowhere near enough to fix it. The faster route, the one strong candidates rely on, is targeted practice: pick the topic that is costing you marks and drill it, question after question, until the method is automatic. This guide is a directory for exactly that. Each topic below links straight to real TMUA questions on it, with full worked solutions, plus the in-depth guide that teaches the topic.

Key fact

Whole papers tell you where you are weak; topic practice is how you fix it. Identify your worst two or three topics, drill them in focused blocks until they stop costing you marks, then return to full timed papers. This is the middle phase of the proven three-phase method, and it is where most of the score gain happens.

Why practising by topic works

Deliberate practice beats general practice because it concentrates your effort where the return is highest. A student who does ten mixed papers spreads their attention thinly across everything, including the topics they already have. A student who spends the same time drilling the three topics they keep getting wrong closes the exact gaps that are holding their score down. The maths is stable and the question styles repeat, so once a topic clicks, it tends to stay fixed.

Topic practice also fits the TMUA's structure. Paper 1 is applications of standard maths, so its topics map cleanly onto the A-level content you already know. Paper 2 is reasoning, so its "topics" are as much about logical technique as about content. Filtering to one at a time lets you feel that difference and train each properly. Here is a representative Paper 1 question to show the level; try it, then use the directory below to drill whichever topic you need:

Paper 1 topics: applications of maths

These are the pure-maths topics that make up Paper 1 and appear on Paper 2 too. Click "Practise" to jump straight to real questions on that topic in the free bank, and "Learn" for the full in-depth guide.

TopicPractiseLearn the topic
Algebra & SurdsPractiseSurds & indices guide
Indices, Logarithms & ExponentialsPractiseLogarithms guide
Coordinate GeometryPractiseCoordinate geometry guide
TrigonometryPractiseTrigonometry guide
DifferentiationPractiseDifferentiation guide
IntegrationPractiseIntegration guide
Sequences & SeriesPractiseSequences & series guide
Functions, Transformations & GraphsPractiseGraphs & transformations guide
InequalitiesPractiseInequalities guide
Statistics & ProbabilityPractiseCounting & probability guide

Algebra and surds is the single most common topic across the papers, so it is usually the highest-value place to start. If your foundations there are shaky, everything else gets harder, because algebra sits underneath every other topic.

Paper 2 topics: reasoning

Paper 2 layers logic and proof on top of the content above, and these "topics" are really techniques. They are the most under-practised part of the TMUA and, because the toolkit is finite, the most trainable.

TopicPractiseLearn the topic
Logic & QuantifiersPractisePaper 2: logic & proof
Number Theory & DivisibilityPractiseProof techniques guide
Sets & CountingPractiseCounting & probability guide

Logic and quantifiers is by far the largest Paper 2 category, and it is where the most gettable marks hide, precisely because so many candidates neglect it. If you do nothing else with your topic practice, drill this one. For the full method, see Paper 2: logic and proof and TMUA proof techniques.

How much practice each topic has

One of the reasons topic practice works so well on CrackTMUA is depth: because the bank combines every official past paper with a large set of original questions, most topics have enough questions to drill properly, not just the handful you would get from a single paper. The pools are not equal, and knowing that helps you plan.

The deepest pools are the ones that appear most often on the real test. Logic and quantifiers is the single largest, since it underpins the whole of Paper 2, followed closely by algebra and surds, which turns up everywhere on Paper 1. Functions and graphs, trigonometry, sequences and series, coordinate geometry, inequalities, differentiation, integration and logarithms all have substantial pools of their own, comfortably enough for focused, back-to-back practice. Number theory and the counting topics are smaller but concentrated on Paper 2, and statistics is the smallest, reflecting how lightly the TMUA tests it.

The practical takeaway is to spend your time in proportion to both your weakness and the topic's weight. There is little value in over-drilling statistics, which might give you one question on the day, and enormous value in getting fluent at algebra and Paper 2 reasoning, which shape a large share of your score. Filter to a topic, set a difficulty range you can handle, and work upward.

How to use topic practice

Topic practice works best inside a plan, not on its own:

  • Diagnose first. Do a paper or two, or a diagnostic, and note which topics you consistently miss. Those are your targets. Guessing your weak spots is worse than measuring them.
  • Drill in blocks. Take one topic and do a run of questions on it back to back, easy to hard, reading the worked solution each time. Doing them in a cluster builds the pattern recognition that scattered practice never quite delivers.
  • Mix back in. Once a topic stops costing you marks, fold it back into mixed practice and full papers so you can still switch between topics on demand, which is what the real exam requires.
  • Filter by difficulty too. Within a topic, start at a difficulty you can handle and climb. The bank lets you set a difficulty range as well as a topic, so you can push your ceiling deliberately.

This is the middle phase of the three-phase past-paper method: familiarise, then drill by topic, then sit timed papers. For the full plan around it, see how to prepare for the TMUA, and for the complete topic list with what each one contains, the TMUA syllabus guide.

Practise any topic free

Every topic above links straight into the CrackTMUA question bank, filtered to that topic, with a full worked solution on every question that names the trap and the fastest method. You can narrow further by paper and difficulty, and your attempts, flags and weak topics are tracked so you always know what to drill next.

It is free at 10 questions a day, and premium is a one-time £37 for 12 months if you want the whole library, every official paper plus 100+ original questions and 18+ full mocks, with no daily cap. Pick your weakest topic from the tables above and start there, or open the full practice bank and set your own filters. To see what a good bank should offer, read what a TMUA question bank needs.

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.

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Frequently asked questions

On CrackTMUA you filter the question bank to a single topic (and optionally a paper and difficulty range), then work through real past-paper and original questions on just that topic, each with a full worked solution. The topic links in this guide jump straight to each filtered set. It is free at 10 questions a day.

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