Free prep tools

Elevate Your Test Performance

Get high-yield admissions resources for free. Baseline your score with our diagnostic engine or grab our comprehensive math technique handbook.

Prep Handbook

Free PDF Download

A 30-page blueprint detailing logical reasoning shortcuts,Necessary/Sufficient triggers, and key calculus identities.

TMUA Paper 2 Logic walkthroughs
ESAT Speed-math calculators
Worked examples of common pitfalls

Diagnostic Test

20-Question Baseline Test

Take a mock checkpoint diagnostic. Assess your score across logical logic patterns and algebra difficulty tiers.

Scored across 6 core syllabus areas
Provides instant estimated Elo rating
Revealing detailed topic analysis report

What the Diagnostic Covers

Our questions match the timing, format, and logical pitfalls of the real UK university admissions papers.

Sample TMUA Paper 2 Question

A student claims: “If $n$ is an integer and $n^2$ is divisible by 4, then $n$ must be divisible by 4.” Which of the following numbers acts as a counterexample to disprove this claim?

n = 2 (since 2² = 4 is divisible by 4, but 2 is not)

n = 4 (since 4² = 16 is divisible by 4, and 4 is divisible by 4)

n = 8 (since 8² = 64 is divisible by 4, and 8 is divisible by 4)

There is no counterexample; the student's statement is mathematically true.