Euclid

The Euclid Mathematics Contest, run by the Faculty of Mathematics at the University of Waterloo, has been held since the 1970s. Aimed primarily at Grade 12 students, it is often called the 'TOEFL of mathematics'. In each of the past five years, more than 20,000 students from 2,000 schools have taken part, including around 8,000 international candidates — the majority from China.

Thanks to Waterloo's reputation in mathematics and the rigour of the Euclid standard, the contest has become a key reference for Canadian, British and American universities when assessing international applicants' mathematical ability, admission eligibility and scholarship awards — Waterloo's Faculty of Mathematics explicitly 'strongly recommends' that applicants take the Euclid, and lists it as a requirement for its entrance scholarships.

The exam is a 2.5-hour paper-based test with 10 problems worth 100 points in total. It mixes short-answer questions with full-solution problems: some require only the final answer, while others demand complete written reasoning — marks are awarded for method and steps, so a wrong final answer can still earn strong partial credit. Calculators without internet, storage or computer-algebra-system features are permitted.

The syllabus covers equations and inequalities, elementary functions, polynomials, exponentials and logarithms, trigonometry, sequences and series, permutations and combinations, elementary number theory, and plane and analytic geometry. Each year, the top 25% of candidates receive a Certificate of Distinction from the University of Waterloo (recent cut-offs around 66-69 points), while the top 2.5% are named on the Honor Roll (around 87+ points).