TMUA 2023 Past Paper: Questions, Topics & Worked Solutions

The 2023 TMUA is one of the most useful papers to study, and not only because it is recent. It was the final sitting run by Cambridge Assessment before UAT-UK and Pearson VUE took over in 2024, and by our own difficulty rating it is the gentlest of the recent papers, which makes it the natural place to sit your first complete, timed paper without being buried. This guide breaks down exactly what the 2023 paper covered, how hard each part was, and the one question that separated the strong candidates, and it lets you try real 2023 questions with full worked solutions before you commit to a full sitting.

What the 2023 TMUA paper looked like

Like every TMUA sitting, 2023 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 are combined into a single score on the 1.0 to 9.0 scale. If you are new to the format, our overview of what a TMUA question actually looks like is worth a read first.

Here is the opening question from the 2023 Paper 1. It is a very typical opener: everything in it is first-year A-level content, and the difficulty is purely in doing it cleanly and quickly by hand. Give it a real attempt before you reveal the solution:

How hard was the 2023 paper?

This is where 2023 stands out. 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 2023 paper is the most approachable of the recent sittings. Its questions span roughly our 3.5 to 7.0 band, and unlike 2021 and 2022 it contains no questions we rate at the very top of the scale. In plain terms: there is no single monster question, and the ramp from easy to hard is gentler than usual.

That has a practical consequence. If you have done a lot of topic practice but never sat a full, timed paper, 2023 is the one to start with. You get the genuine experience of pacing 20 questions in 75 minutes without the demoralising effect of a near-impossible question near the end. Save the tougher 2021 and 2022 papers for when your timing is already solid.

One number matters more than the difficulty rating: there is no negative marking. A blank and a wrong answer score the same, so on the 2023 paper, as on every TMUA, you should put something down for all 40 questions even if it is a last-second guess. Candidates lose easy marks every year by leaving the final few questions blank when they ran out of time. Budget your 75 minutes so you at least see every question.

None of this means 2023 is easy in absolute terms. The average TMUA score sits around 4.5 and only about 15% of candidates score above 6.5, so "gentle for the TMUA" is still a demanding paper by any normal standard. Remember too that the exam board does not publish grade boundaries, so there is no fixed raw mark that guarantees a given grade; scores are scaled each sitting. For what those numbers mean where you are applying, see what counts as a good TMUA score and how scoring works.

Topics tested in the 2023 paper

The 2023 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.

The lesson of looking across the topics is the one that holds for every year: no chapter is safe to skip, but the reasoning of Paper 2 is the part most candidates under-prepare. The maths content is standard; the reasoning style is what feels unfamiliar. For the full topic-by-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 2023 paper

The two 2023 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; the difficulty is speed and slickness. Here is a mid-difficulty Paper 1 question from 2023. Notice how it defines its own condition and then asks you to work with it, a very TMUA move:

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. That is a genuinely different muscle, and it is why candidates who only revise content freeze on Paper 2. If the reasoning style is new to you, the fastest way to make it feel normal is to drill it in clusters rather than meet it cold on the day. Our guide to Paper 1 vs Paper 2 breaks down how to approach each.

The standout question of 2023

Every paper has a hardest question, and it is worth studying because it shows you the ceiling. In 2023 that ceiling sat lower than usual, which is exactly why the paper feels manageable. The toughest question we identify on the 2023 paper is this Paper 2 reasoning problem. 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 hard, that is completely normal. The gap between a 6.5 and a 7.5 lives in a small handful of questions like it, and the single most reliable way to close that gap is deliberate practice on well-explained hard questions, which is precisely what a good bank gives you and a PDF does not.

How to actually use the 2023 paper

Doing the paper once and checking your score wastes it. Use the same three-phase method that works for every past paper:

• Familiarise first. If the format is still new, work through the 2023 questions untimed and read the worked solution for every one, including the questions you got right, because the fastest method is often not the one you used.
• Then drill by topic. Once the style is familiar, stop doing whole papers and practise by topic and difficulty, mixing 2023 questions with other years so you build pattern recognition across sittings.
• Then sit it timed. Save a clean run of the 2023 paper for a strictly timed mock: 75 minutes per paper, no calculator, rough paper only. Review every question you missed or spent too long on, and write down the one insight that would have made it faster.

The review is where the marks actually come from. For every question you got wrong, do not just read the answer and nod; identify the specific move you missed, whether that was a faster method, a trap option you fell for, or a misread quantifier on Paper 2, and note it. The same handful of moves recur across every sitting, so a mistake understood on the 2023 paper is a mark saved on the day. A student who does the 2023 paper once with a proper review learns more than one who rushes through three papers and only checks the score.

Because 2023 is the gentlest recent paper, it works best as an early timed mock rather than a final one, and as a useful calibration checkpoint: if your timing and accuracy hold up here, you are ready to take on the harder years. Keep a tougher paper such as 2022 in reserve for your last rehearsal before the real thing. 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 2023 paper free

The clumsy way to study the 2023 paper is a question booklet in one file and an answer key in another. The better way is interactive. On CrackTMUA the entire 2023 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 2023 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 2023 questions in the practice bank and try a few, or read the complete past-papers guide for how the full collection fits together.

Frequently asked questions