TMUA Paper 1: what every past paper says about where your marks actually are

Most TMUA advice is folklore: "do lots of past papers", "logs come up a lot", "watch out for the weird ones at the end". We wanted something better, so we classified all 180 questions from every released TMUA Paper 1 — the Specimen and the 2016–2023 papers — by primary topic and by difficulty on a 1–5 scale.

This is the question bank our students train on. Here is what it says.

Where the questions actually come from

Classified by primary topic, the 180 questions break down like this:

Topic	Questions	Share
MM4 Trigonometry	29	16%
MM1 Algebra and functions	28	16%
MM7 Integration	26	14%
MM2 Sequences and series	24	13%
MM5 Exponentials and logarithms	19	11%
MM6 Differentiation	19	11%
MM3 Coordinate geometry	14	8%
MM8 Graphs of functions	11	6%
GCSE-strand topics (M1–M7)	10	6%

Two conclusions jump out.

First: four topics carry more than half the paper. Trigonometry, algebra and functions, integration, and sequences and series account for 107 of 180 questions — roughly 60%. If your preparation time is limited, this is the ordering it should follow. A student who is genuinely sharp in those four strands walks into the exam with most of the paper already familiar.

Second: the "pure GCSE" strands are a rounding error — as primary topics. Units, ratio, basic number work: only 10 questions in eight papers lead with them. But be careful with that conclusion. GCSE-strand ideas appear constantly as secondary skills inside harder questions — a probability wrapper around a circle problem, a geometry fact buried in a coordinate question. You don't revise M1–M7 as topics; you keep them warm as reflexes.

The difficulty distribution is not what students expect

On our 1–5 scale (5 being the hardest questions ever set):

Difficulty	Questions	Share
2	15	8%
3	87	48%
4	66	37%
5	12	7%

There are almost no easy questions — nothing in eight years rated 1 — and very few monsters. 85% of the paper lives at difficulty 3–4. The exam is not designed to be finished by racing through trivial questions and gambling on brutal ones; it is a long sequence of medium-hard questions, each disguised just enough that a memorised method won't fire automatically.

This has a direct training consequence. The marginal mark for most candidates is not in learning more theory — the syllabus is deliberately thin — it is in reducing the cost of the disguise: recognising, quickly, which familiar structure a question is hiding.

What a difficulty-4 question actually tests

Take this one, from 2019 (Paper 1, Question 18), rated 4 in our bank:

Find the shortest distance between the curve $y = x^2 + 4$ and the line $y = 2x - 2$.

No single step is hard. The question tests whether you choose the right frame: the shortest distance from a curve to a line occurs where the tangent to the curve is parallel to the line. Differentiate, set $\frac{dy}{dx} = 2x = 2$, get the point $(1, 5)$, then compute the perpendicular distance to $2x - y - 2 = 0$:

$$d = \frac{|2(1) - 5 - 2|}{\sqrt{2^2 + (-1)^2}} = \frac{5}{\sqrt{5}} = \sqrt{5}.$$

A student who has "done differentiation" and "done coordinate geometry" as separate chapters often cannot do this question in ninety seconds, because the join between the chapters is exactly what was never trained. Our bank tags this question under both topics for precisely that reason — cross-topic joins are where TMUA hides its difficulty: 7 of our 12 difficulty-5 questions carry two or more topic tags, as do more than half of the difficulty-4 questions.

How to use this in your preparation

1. Weight your time like the paper weights its marks. Trigonometry, algebra, integration, sequences — in that order of priority, to genuine fluency, before anything else.
2. Train at difficulty 3–4, deliberately. Sets of medium-hard questions against the clock beat both gentle textbook exercises and heroic struggles with the hardest past questions.
3. Practise the joins, not just the topics. After finishing a topic, seek out the questions that combine it with something else. That's where the paper discriminates.
4. Keep GCSE skills warm as reflexes, not as revision topics.

Our students work through this bank sorted by topic and difficulty, with problem sets built for exactly the joins above. If you'd like your preparation to run on the data rather than the folklore, book a consultation — twenty minutes is enough to map where your marks are.