Everything below is drawn from the official UAT-UK specification, paraphrased as a tick-box checklist. Work through it honestly: mark each row green (fluent), amber (slow) or red (avoiding it), then revise red first. Every code links to a topic hub with drills.
Paper 1 checklist: MM1–MM8
Paper 1 tests mathematical thinking — fluent school maths without a calculator. The eight core strands:
- MM1 — Algebra & functions
Polynomials, factorising, completing the square, surds, inequalities, function notation and inverses.
- MM2 — Sequences & series
AP/GP nth terms and sums, convergence intuition, sigma notation, binomial expansion for positive integer powers.
- MM3 — Coordinate geometry
Lines, circles, parabolas; gradients, intersections, tangents; sketching from equations.
- MM4 — Trigonometry
Exact values, identities (Pythagorean, double-angle awareness), graphs, solving equations in ranges.
- MM5 — Exponentials & logarithms
Index and log laws, solving exponential equations, sketching growth/decay.
- MM6 — Differentiation
First principles intuition, standard derivatives, stationary points, tangents/normals, optimisation.
- MM7 — Integration
Indefinite and definite integrals, area under curves, kinematics (displacement/velocity).
- MM8 — Graphs & transformations
y = af(bx+c)+d, reflections, symmetry, asymptotes, interpreting unfamiliar plots.
Paper 1 applied strands
Alongside MM1–MM8, Paper 1 draws on applied checkpoints many schools label M1–M7 (number, measure, geometry and data). In our bank these live under three hubs:
- M-Num — Number, ratio & estimation
Fractions, percentages, standard form, bounds, degree-of-accuracy traps and Fermi-style estimation under time pressure.
- M-Geo — Geometry, mensuration & vectors
Angle facts, Pythagoras, area and volume, similarity, basic vectors and locus reasoning — often fused with coordinate geometry.
- M-Stat — Statistics & probability
Averages, cumulative frequency intuition, Venn diagrams, tree diagrams and conditional probability phrased as short word problems.
Paper 2 checklist: Arg / Prf / Err
Paper 2 tests reasoning and logic. Questions split into three families:
- ARG — argument analysis. Identifying conclusions, assumptions & flaws, inference and quantitative reasoning.
- PRF — proof logic. Direct proof, contrapositive & contradiction, necessary & sufficient, quantifiers and induction.
- ERR — error spotting. Finding the first invalid step and repairing arguments. Full method in the Paper 2 logic guide.
How to use this checklist
First, read what the TMUA is if you have not already. Then sit a full mock cold and map every miss back to a row above. Drill red topics in /practice (five questions at a time), browse the question bank for coverage, and re-mock fortnightly. Compare the papers in Paper 1 vs Paper 2 so you split revision time sensibly, and check how to prepare for 4, 8 and 12-week plans built around this list.
How to use this checklist in 7 days
A checklist only works if you turn ticks into timed evidence. Here is a one-week routine that converts the rows above into a genuine study plan. Day 1: grade every Paper 1 row green, amber or red without touching a textbook — honesty now saves weeks later. Then start where marks compound fastest: algebra. Attempt exemplar TMUA-P1-MM1-002 closed-book in under four minutes, mark it harshly, and rewrite the full solution from scratch in an error log. If it felt easy, confirm with a second exemplar, TMUA-P1-MM1-003; if it felt slow, note exactly which step wobbled (factorising? surds? function notation?) and drill that micro-skill for twenty minutes.
Day 2: repeat the process for calculus, the other high-leverage strand. Work through TMUA-P1-MM6-001 untimed first, writing every differentiation step out in full, then re-attempt it timed the same evening — fluency means getting it right twice, not once. Day 3: pick your reddest applied strand (usually number estimation or probability) and drill five questions in one timed set. Day 4: switch papers and meet Paper 2 properly: read the logic and proof guide section on converse versus contrapositive before attempting anything, so the new vocabulary beds in before any time pressure.
Day 5: sit a five-question MM1 drill in /practice?topic=MM1 under strict conditions: no calculator, phone in another room, scrap paper only. Day 6: review the whole week's error log, redo every miss from a blank page, and re-grade the checklist — greens should have multiplied. Day 7: sit half of a full mock (one paper, 75 minutes) to bank exam-day habits early, then convert your raw mark with the score calculator. Repeat the cycle fortnightly and this checklist stops being a poster and becomes a plan.
What is out of scope
Complex numbers, matrices, differential equations, Box plots beyond GCSE interpretation, and formal set-theory notation do not appear. Mechanics beyond basic kinematics (suvat via calculus) is not tested. If a resource teaches you content far beyond AS-level, it is not TMUA revision — come back to this checklist and to the FAQ before spending more hours.
Common slip & diagram reading
| Slip | What happens | Fix in 30 seconds |
|---|---|---|
| Common slip: revising favourite greens | Polishes fluent MM topics weekly while red ARG/PRF rows sit untouched, so mocks plateau at the same band for a month | Grade every row green-amber-red after each mock and drill reds first in five-question sets before any green comfort work |
Diagram description: imagine a syllabus grid for this guide. Eight MM1–MM8 cards form the top two rows with green-amber-red dots in their corners, three applied M-Num, M-Geo and M-Stat cards sit beneath them, and three wider ARG, PRF and ERR bands anchor the bottom with icons for arrows, proof steps, and magnified faulty lines. A red-first arrow sweeps from the bottom bands upward to the reddest MM card, showing revision priority flows from weakness rather than fondness. The habit is to re-dot the grid after every mock and let the reddest card choose tomorrow's drill, not nostalgia.