Difficulty D1–D5 · reasoning, construction, insight
Difficulty measures how much reasoning, construction and insight a question demands — not how advanced
the topic is. It counts the real decisions you must make and how deep each one goes. A question where you must
construct the route yourself rates higher than one that executes a named technique, however long that technique runs.
No official question is a D1: the exam starts at D2 and tops out at D5.
Mean difficulty by year
Papers have drifted harder: both P1 and P2 trend upward after 2018.
Difficulty mix by year (all 40 Qs/yr)
The D4+D5 share grows from about half the paper in 2018 to 80% in 2023.
Topics map by primary subtopic tag
Each question is counted once under its primary subtopic. Main = Paper-1 maths (MM1–MM8),
Reasoning = Paper-2 logic/proof (Arg/Prf/Err), Foundations = GCSE-assumed material that still headlines the odd question.
Strand share by year
Reasoning holds ~⅕ of each year (7–9 of 40 questions — almost entirely in Paper 2).
Strand split by paper
P2 is roughly half Reasoning, half maths re-used as proof material.
Topic × year heatmap
Cell = number of questions whose primary subtopic sits in the topic that year (both papers). Hover for the P1/P2 split and mean difficulty.
Syllabus map
Width of each block = how many of the 320 questions touch that subtopic (primary or secondary tag).
Colour = mean difficulty of those questions (cool then hot). Very thin subtopics are grouped as "+N smaller subtopics" — hover to see them.
≈D3 when it appears≈D4≈D4.7+
Skills 99 distinct skills
The skill layer is where "what to revise" lives. The scatter answers the two student questions at once:
how often does a skill appear (x) and how hard are the questions that use it (y). Bubble = one skill, sized and shaded by frequency, coloured by home strand.
Frequency × difficulty — every skill
Top-right = common and hard (priority revision). Bottom-right = common but routine (bankable marks). Fainter bubbles appear less often. Hover any bubble; the most interesting ones are labelled.
Top-40 skill × year heatmap
Appearances per year (a question can use several skills); counts printed in each cell.
All skills — sortable
Click a column header to sort; type to filter. "Hard share" = % of its questions rated D4 or D5.
Skill network which skills get tested together
Nodes = skills (≥4 appearances); an edge means the two skills were needed in the same question at least twice.
TMUA rarely tests one skill in isolation. The co-occurrence graph falls into five stable skill-packs: the Algebra engine, Logic & proof, Curves & geometry, Trig & graph reading, and Integration. The strongest single pairing: exact trig values × trig equations, 13 questions. A typical question chains 3 skills — revise combinations, not checklists.
Use the tabs to view one skill-pack at a time. Node size = frequency · colour = pack · drag to rearrange · hover a node to see its details on the right.
Question formats 7 formats
Beyond plain single-answer MCQ, TMUA leans on reasoning formats — multi-statement ("which of I, II, III…"),
necessary/sufficient, spot-the-error proofs, counterexamples. These are heavily concentrated in Paper 2 and are, on average, harder than single-answer questions.
Format mix by year
Format profiles
Position in paper Q1 → Q20
Mean difficulty at each question number. Both papers ramp broadly upward — but the second chart shows the real story: Paper 1's whole curve shifted up ~0.4 (Q1 now averages D3.3 — the warm-up is gone), while Paper 2 shifted less (~0.24) and mostly in its closing run — Q16–20 now average D4.7–5.0, and its opener actually got gentler.
All-time curve
Two eras compared
Dashed = 2016–20 · solid = 2021–23 · shading = gap where recent ≥ early. P1 shift ≈ +0.37 everywhere; P2 ≈ +0.24, concentrated at Q16–20.
Skill dictionary 99 skills defined
Every skill, in plain words: what it means, how it differs from lookalikes, and where it shows up.
Search, filter by topic, or sort — then open a card. Buttons jump to real example questions that use that skill.
n× = how many of the 320 official questions (2016–2023) used the skill.
Skills often appear outside their home topic — completing the square turns up inside circle questions, for example.
Example questions 30 real questions
Real TMUA questions, shown exactly as set (answers deliberately not shown — try them). Difficulty and skill tags are ours.