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Update: 120 new TMUA questions reviewed and pushed to the database: 5th July 2026

Live examples: ESAT examples

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Drafted in the distinct style and subject matter of TMUA (pure maths & logic) or ESAT (maths, physics, chemistry, biology), trained on every real past paper, then checked and modified by Oxford students. Example TMUA and example ESAT questions shown here alternate every month.

Example ESAT problems

Physicsmechanics
The graph shows the trajectory of a projectile of mass 2m, launched from level ground. Air resistance is negligible.

At the instant when the projectile is at x = 60 m, it breaks into two fragments of equal mass. Immediately after the break-up, one fragment is instantaneously at rest.

What is the speed of the other fragment immediately after the break-up?

Take g = 10 m sβˆ’2^{-2}.

Projectile trajectory

height / m
05101520020406080scroll to zoom Β· dbl-click reset

horizontal displacement / m

Trajectory of the projectile before it breaks up.
A10510\sqrt{5} m sβˆ’1^{-1}
B20220\sqrt{2} m sβˆ’1^{-1}
C20520\sqrt{5} m sβˆ’1^{-1}
D4040 m sβˆ’1^{-1}
E5050 m sβˆ’1^{-1}
Mathsgeometry
A circle has centre O and radius 10 cm.

AB is a chord of the circle with AB = 12 cm.

The tangents to the circle at A and B meet at T.

A smaller circle lies inside triangle TAB. It is tangent to TA and TB, and is externally tangent to the original circle.

What is the radius of the smaller circle?
A circle with chord AB, tangents at A and B meeting at T, and a smaller circle tangent to both tangents and to the original circle.

A circle with chord AB, tangents at A and B meeting at T, and a smaller circle tangent to both tangents and to the original circle.

A11 cm
B2019\dfrac{20}{19} cm
C109\dfrac{10}{9} cm
D54\dfrac{5}{4} cm
E32\dfrac{3}{2} cm

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Access every multiple-choice question from every past NSAA and TMUA paper. ENGAA papers are also included, since ENGAA and NSAA cover the same material. Timed exam mode or question-by-question practice.

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2,000+ pre-reviewed questions
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Generatively expanding question database
2,000+ pre-reviewed questions
Every NSAA Β· TMUA Β· ESAT past paper built in
100% full worked solutions
1 week free trial
Unlimited question generation, checked by Oxford students
Any topic Β· Any subject Β· Any difficulty
Created at New College, Oxford
Questions reviewed and modified by Oxford students
Best value: less than half the price of competitors
Generatively expanding question database

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Updates

  • 30 Jun 2026Fixed TMUA 2022 images not rendering
  • 30 Jun 2026Fixed TMUA 2022 Paper 2 Q18 missing table figure
  • 30 Jun 2026Fixed LaTeX \neq (and similar commands) rendering as garbage in quick mode
  • 30 Jun 2026Fixed KaTeX rendering on 8 TMUA questions
  • 30 Jun 2026Fixed issue with legacy subscriptions β€” all new subscriptions now correctly assigned to Basic or Elite tier
  • 3 Jul 2026Fixed ESAT sessions occasionally serving TMUA-only topics (e.g. proof and logic)
  • 3 Jul 2026Referral bonus increased to 2000 XP per friend referred
  • 4 Jul 2026Added per-topic selection for TMUA in Quick Mode, matching ESAT
  • 4 Jul 2026Fixed questions failing to generate when at the AI token limit
  • 4 Jul 2026Resolved backend downtime causing question generation failures