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The TMUA Diagnostic

Fifteen questions drawn from both papers, scored the moment you finish, with your applications score and your reasoning score reported separately. The gap between those two numbers is usually the most useful thing a candidate learns about their own preparation.

Read this first

The TMUA questions behind this page were drafted with AI assistance

They are not the same thing as the ESAT material on this site. Every ESAT question is written by one member of the group and sat under timed conditions by another before it is published, to the standard set out on the quality assurance page. These questions have not been through that process.

What was checked: All 40 answer keys in the TMUA corpus were checked by computer algebra, for correctness and for being the only correct option.
What was not checked: difficulty calibration against the real paper, whether each wrong option matches a mistake candidates actually make, and the wording of the explanations.
Use them as: extra practice on the right topics. Not as a predictor, and not as a substitute for real past papers.
Found an error? Please tell me at lucasrey.eng@gmail.com and it will be fixed or withdrawn.

Why the two scores are reported apart

Paper 1 asks you to apply mathematics you already know. Paper 2 asks you to reason about it: to negate a statement correctly, to say what a counterexample has to do, to tell a necessary condition from a sufficient one, and to find the single invalid step in an argument that looks fine. Those are different skills, and school teaches the first far more than the second.

A candidate who is fluent at the first and shaky at the second is the normal case rather than the exception. One score across all fifteen questions would hide that, so this one does not report it.

Sit the diagnostic

[01] Before you start

15 questions, drawn from both papers: Paper 1: applications, Paper 2: reasoning.
A timer runs and nothing cuts you off. Work at the pace you would want to sit the real thing at, and see what that costs you in accuracy.
Every question comes from the mock papers published on this site, and every one you miss links straight to its worked solution.
Watch the gap between the two papers. A candidate well ahead on Paper 1 and behind on Paper 2 is the normal case, and that gap is usually the most improvable thing about their preparation.
Your score is yours. It is worked out in your browser and shown immediately. Sending it to yourself by email is optional and comes after the result.

The diagnostic is interactive and needs JavaScript. The questions it draws on are all published as full worked solutions, so nothing here is behind the script: