TMUA 2022 Past Paper: Questions, Topics & Worked Solutions

The 2022 TMUA is the paper to save for when you want to know whether you are really ready. It was one of the last sittings run by Cambridge Assessment before UAT-UK took over, and by our own difficulty rating it is one of the tougher recent papers, with a top end that includes some of the hardest questions in the whole archive. That makes it far more useful as a late-stage stress test than as a first attempt. This guide breaks down what the 2022 paper covered, where its difficulty really sat, and the question that separated the strongest candidates, and it lets you try real 2022 questions with full worked solutions.

What the 2022 TMUA paper looked like

Like every TMUA sitting, 2022 was two separate papers taken on the same day:

That is 40 questions in two and a half hours, all multiple-choice, all calculator-free, with no negative marking, so you should answer every question. The two papers combine into a single score on the 1.0 to 9.0 scale. Here is a Paper 2 opener from 2022, a gentle way in that still asks you to think about a curve rather than just crunch it:

How hard was the 2022 paper?

This is what defines 2022. On CrackTMUA's own 1 to 9 difficulty rating (our calibration of every question, not an official statistic, since the exam board does not publish per-question data), the 2022 paper sits among the hardest of the recent sittings. Its questions reach the very top of our scale, and its average difficulty is higher than gentler years such as 2023. In practice that means the ramp is steeper and the final few questions on each paper are genuinely punishing.

That has a clear implication for how you use it. Do not make 2022 your first full paper; you will spend too long stuck and learn the wrong lesson about your own ability. Instead, build your timing on a gentler paper such as 2023 first, then bring 2022 out as a late rehearsal to see whether you can hold your pace when the questions bite.

One number matters more than the difficulty rating: there is no negative marking. A blank and a wrong answer score the same, so guess on anything you cannot finish rather than leave it empty, especially on a hard paper like this one where you are more likely to run short of time. Remember too that the exam board does not publish grade boundaries, so there is no fixed raw mark that guarantees a grade; scores are scaled each sitting. For what a competitive score looks like, see what counts as a good TMUA score and how scoring works.

Topics tested in the 2022 paper

The 2022 paper covered the full breadth of the syllabus. Paper 1 drew on algebra and surds, coordinate geometry, differentiation and integration, indices and logarithms, sequences and series, trigonometry, functions and graphs, inequalities, and a little statistics. Paper 2 layered logic, proof and number theory on top, testing whether you can reason about statements rather than just compute answers.

What made 2022 hard was not exotic content; it was how tightly the harder questions combined familiar ideas. The lesson holds for every year: no chapter is safe to skip, but the reasoning of Paper 2 is the part most candidates under-prepare. For the full topic map, see the TMUA syllabus guide, and for the reasoning half specifically, Paper 2: logic and proof.

Paper 1 vs Paper 2 in the 2022 paper

The two 2022 papers are hard in different ways, and it is worth feeling that difference for yourself. Paper 1 dresses up maths you recognise so that the obvious method is slow and a clever observation is fast. Here is a mid-paper Paper 1 question from 2022; the whole thing collapses if you spot the right property of the logs instead of grinding:

Paper 2 removes the calculation almost entirely and asks whether an argument holds: which statement must be true, which deduction is valid, where a printed proof breaks. In a hard year like 2022 that reasoning is where the toughest marks live, and it is exactly the part most candidates neglect. If the reasoning style is new to you, drilling it in clusters is far more effective than meeting it cold. Our guide to Paper 1 vs Paper 2 breaks down how to approach each.

The standout question of 2022

Every paper has a hardest question, and 2022's is a genuine one: we rate it at the very top of our difficulty scale. It looks like a routine "find the set of values" question and hides a careful, multi-stage argument about how two shaped polynomials interact. Do not expect to crack it in the four minutes you would have on the day; sit with it, and read the worked solution carefully, because seeing the key idea is how you learn to spot the same move next time:

If you found that brutal, you are in good company; questions at this level are what separate a 6.5 from an 8.0, and only a handful of them exist across all the papers. The single most reliable way to get better at them is deliberate practice on well-explained hard questions, which is what a good bank gives you and a PDF does not. Our roundup of the hardest TMUA questions collects the toughest of them in one place.

How to actually use the 2022 paper

Doing the paper once and checking your score wastes it. Use the same three-phase method that works for every past paper, but treat 2022 as advanced material:

• Familiarise on an easier paper first. Get the format and pacing solid on a gentler year, then come to 2022 already comfortable with the basics.
• Drill by topic. Pull the harder 2022 questions apart by topic and difficulty, mixing them with the same question types from other years so you build pattern recognition rather than memorising one paper.
• Sit it timed, late. Save a clean run of 2022 for a strictly timed mock close to the exam: 75 minutes per paper, no calculator, rough paper only. If you can hold your pace here, you can hold it on the day.

The review is where the marks actually come from. For every question you got wrong, identify the specific move you missed, a faster method, a trap option, or a misread quantifier on Paper 2, and note it. On a hard paper those insights are worth the most, because the same handful of moves recur across every sitting. The full progression is laid out in our complete TMUA study plan, and how many timed papers to sit is covered in the mock exams guide.

Practise the 2022 paper free

The clumsy way to study the 2022 paper is a question booklet in one file and an answer key in another. The better way is interactive. On CrackTMUA the entire 2022 paper is a filterable question bank: every question has an instant, in-depth worked solution that names the trap and the fastest method, you can jump straight to the 2022 questions or mix them with other years, and your attempts, flags and weak topics are tracked so you know what to review.

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. The best next step is simply to start: open the 2022 questions in the practice bank and try a few, or read the complete past-papers guide for how the full collection fits together.

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