Original practice material written in the style of the Test of Mathematics for University Admission, for the October 2026 and January 2027 sittings. Everything here is free to download and print.
New: the Future Mathematicians course. Self-marking TMUA and STEP lessons, timed to the real papers. Open your Year 12 Maths, Year 13 Maths or Further Maths course in the Student Hub: Lesson 1 of each course is a free taster, and the full course is £10 a week.
Start here. Download the Prep Plan and pick your track: Track A if you sit in October (Oxford and Cambridge applicants must), Track B for January. The plan tells you which resource to use in which week. Book the test through your UAT-UK account before the deadline.
The resources
Plan
Prep Plan · October and January
Week-by-week for both sittings, key dates and booking deadlines, the habits that move the score, and how to use the error log in our lessons.
The logic Paper 2 expects: implication and its phrasings, converse / inverse / contrapositive, negation and nested quantifiers, proof methods, where "proofs" go wrong, and an eight-question practice set with answers.
Six ten-minute sets: algebra, functions and graphs, sequences and series, trig / exponentials / logs, calculus, and logic. Short-answer on purpose, answers and key steps at the back.
Both papers in the real format: 20 multiple-choice questions, 75 minutes each, no calculator. Do it in one sitting once you have done the drills, and record answers on the grid at the back.
Quick answers for both papers, then the key step for every question and a "don't lose the easy marks" list. Redo each wrong answer before you read its solution.
FormatTwo papers of 20 multiple-choice questions, 75 minutes each. On screen at a Pearson VUE centre. No calculator. No penalty for wrong answers, so answer everything.
Paper 1Applications of mathematical knowledge: GCSE Higher and AS content used in unfamiliar ways.
Paper 2Mathematical reasoning: the same maths, but you judge whether statements are true, arguments valid, or where a proof breaks.
Official materialThe specification, past papers and Notes on Logic and Proof are free on the UAT-UK website. Check dates and deadlines in your own UAT-UK account.
Doing the test with us
Bring your error log to the Q&A slot at the start of any Maths lesson.
Common TMUA mistakes will be added to this page as they come up.
Stuck on a question? Use the "Stuck on a question?" button on the Student Hub.