TMUA
Twelve sets of original mock papers with solutions, timed drills and a question bank rated by difficulty.
Kevinvariant
Oxbridge admissions test prep for the TMUA and ESAT, and olympiad prep: original papers with full solutions, and tools for practising them properly. A little every day adds up.
Choose your path
ESAT
Original Mathematics 1 and Mathematics 2 mocks: 27 questions in 40 minutes, no calculator, with worked solutions.
Olympiad
Original mock olympiad papers, written solutions to real competitions, and geometry you can drag.
Practise and compete
Race a bot, duel a friend, take on the problem of the week, and earn levels, badges and coins.
How it works
What the difficulty numbers mean, which papers are free, and how the newest sets are unlocked.
New this term
ESAT mock Set E: Mathematics 1, Physics and Mathematics 2
The newest ESAT set, with extra functions, graphs and integration: 27 varied questions in 40 minutes per module, unfamiliar problems that need a new strategy on the spot, and diagrams throughout. Set A is the warm-up and Set B the hardest.
Smart Practice: questions that fit your level
FreeTMUA
Each question is chosen to suit your level as it changes. At the end you see an estimate of your level, your strongest and weakest topics, and what to practise next.
Confidence calibration
FreeTMUA
TMUA has no negative marking, so knowing when you are guessing matters. Say Guess, Unsure or Sure before each answer is checked, and Progress shows whether your confidence matches your results.
Trap Map: the mistake behind each wrong answer
FreeTMUA
When a wrong option in Drill, the question bank or Review comes from a common mistake, the site names that mistake. Your most frequent traps collect on the Progress page, each with a short drill to clear it.
UKMT Senior Mathematical Challenge 2026: full solutions
FreeOlympiad
Solutions to all 25 problems, with every diagram redrawn in tkz-euclide. No code or account needed.
TMUA mock Set K
Heavy computation next to short questions that turn on a single idea, with olympiad techniques hidden inside AS content.
See Set KWin a code in an Instagram challenge, or use coins in the Shop.
TMUA mock Set L
The newest and hardest set: both papers rate above every earlier paper.
See Set LWin a code in an Instagram challenge, or use coins in the Shop.
How it works, in brief
One difficulty scale
Every question is rated from 4.5 to 9.0, and every paper on the same scale.
Solid4.5 to 5.9Hard6.0 to 7.4Severe7.5 to 9.0
Almost everything is free
- Free TMUA Sets A to D, the ESAT mocks, every tool and every olympiad paper, with no account needed.
- Locked TMUA Sets E onwards. Unlock them with a code from an Instagram challenge, or with coins in the Shop (every locked set except J).
The book
Beyond the Incenter
A modern monograph on olympiad geometry, from the triangle's five centres to projective geometry, radical axes and spiral similarity.
About the book Sample chapter
Recommended elsewhere:
Arolf Math, built by a friend of the site: targeted AMC 10 and 12 practice, from foundational problems up to AIME-qualifying level, with timed exam modes.