OpenTMUA

Education should be open.

A free collection of open-source questions in the style of the TMUA. Built by a student, for students.
No account. No paywall.

Start practising → PAPER 1 · MATHEMATICAL THINKING

Q. Algebra Original · OpenTMUA

x and y are positive integers such that x² − y² = 45. How many possible values of x are there?

x² − y² = (x−y)(x+y) = 45. Factor pairs of 45: (1,45), (3,15), (5,9) — each gives an integer (x,y). That's 3 values of x.

Harder questions Focussing on the later, harder questions in the TMUA.

Original questions Written in the style of the TMUA, not lifted from past papers.

No account Nothing to sign up for. Open the practice tab and start.

WHAT'S COVERED

Two papers, two skills

Containing questions that cover content from both papers. The bank is growing question by question, in the open.

PAPER 1

Applying maths you already know to unfamiliar, multi-step problems — algebra, functions, sequences, and proof-adjacent reasoning.

IN PROGRESS

PAPER 2

Evaluating mathematical arguments — spotting flawed logic, necessary vs. sufficient conditions, and reading proofs critically.

IN PROGRESS

OpenTMUA is a static site and a JSON question bank — nothing more. If you can write a good problem, you can contribute one.

View on GitHub Contribute a question