Quick answer
The 2016 TMUA was the first-ever live sitting: two 75-minute papers of 20 multiple-choice questions each, no calculator, scored 1.0 to 9.0, run by Cambridge Assessment. Paper 1 tests applications of maths, Paper 2 tests reasoning. By our difficulty rating it was a mid-difficulty paper, and despite being the oldest it is still fully representative of the current test. You can work through the real 2016 questions free on CrackTMUA, each with a full worked solution.
The 2016 TMUA is where the archive begins: it was the first live sitting of the test, run by Cambridge Assessment, and it set the template that every paper since has followed. Do not dismiss it as out of date. The format, syllabus and question style are unchanged, so a 2016 paper trains exactly the same skills as a 2023 one, and on our difficulty rating it is a solid mid-difficulty paper worth a full sitting. This guide breaks down what the 2016 paper covered, how hard it really was, and the question that separated the strongest candidates, and it lets you try real 2016 questions with full worked solutions.
Key fact
The 2016 paper set the format that has held ever since: two 75-minute papers of 20 multiple-choice questions, no calculator, scored 1.0 to 9.0. Paper 1 is applications of mathematical knowledge; Paper 2 is mathematical reasoning. Nothing on it goes beyond AS and early A-level content.
What the 2016 TMUA paper looked like
Like every TMUA sitting since, 2016 was two separate papers taken on the same day:
| Paper | What it tests | Questions | Time |
|---|---|---|---|
| Paper 1 | Applications of Mathematical Knowledge | 20 | 75 minutes |
| Paper 2 | Mathematical Reasoning (logic, proof, deduction) | 20 | 75 minutes |
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 the very first question of the very first TMUA Paper 1, a binomial-expansion problem that rewards careful, by-hand algebra:
How hard was the 2016 paper?
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 2016 paper is a solid mid-difficulty sitting. Being the first paper, its style is slightly more classical than later years, but the demands are familiar: quick, accurate, calculator-free work on Paper 1 and careful reasoning on Paper 2. Its hardest questions are demanding without reaching the very top of our scale.
One number matters more than the difficulty rating: there is no negative marking. A blank and a wrong answer score the same, so put something down for every question even if it is a last-second guess. 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 2016 paper
The 2016 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, number theory and some counting on top, testing whether you can reason about statements rather than just compute answers.
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. The maths content is standard; the reasoning style is what feels unfamiliar. For the full topic map, see the TMUA syllabus guide, and for the reasoning half, Paper 2: logic and proof.
Paper 1 vs Paper 2 in the 2016 paper
The two 2016 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 2016, a coordinate-geometry problem where a normal to a curve leads you to chase an intersection:
Paper 2 removes the calculation almost entirely and asks whether an argument holds. It 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, 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 2016
The question that defines the 2016 paper is a Paper 2 reasoning problem in the multi-statement format: you are given a quadratic and several statements about it, and you must decide which combination is true. It is a clean example of what Paper 2 is really testing, not whether you can solve the quadratic, but whether you can reason precisely about what does and does not follow. 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:
If you found that hard, that is completely normal. Multi-statement questions reward testing each claim on its own rather than trusting the first that looks right, a discipline you build with practice. The single most reliable way to get there is deliberate practice on well-explained questions, which is what a good bank gives you and a PDF does not.
How to actually use the 2016 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. Work through the 2016 questions untimed and read the worked solution for every one, including those you got right; the older style is still fully representative.
- Then drill by topic. Once the style is familiar, practise by topic and difficulty, mixing 2016 questions with other years to build pattern recognition.
- Then sit it timed. Save a clean run of the 2016 paper for a timed mock: 75 minutes per paper, no calculator, rough paper only.
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. The same handful of moves recur across every sitting, which is exactly why the oldest paper is still worth your time. 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 2016 paper free
The clumsy way to study the 2016 paper is a question booklet in one file and an answer key in another. The better way is interactive. On CrackTMUA the entire 2016 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 2016 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 2016 questions in the practice bank and try a few, or read the complete past-papers guide for how the full collection fits together.
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.