As the registration deadline for the first half of 2026 approaches, high school students around the world are preparing for this grand mathematical feast. Organized by the University of Waterloo in Canada, this competition is known as the "TOEFL of the Math World." It is not only widely recognized for its high value but also attracts countless math enthusiasts due to its rigorous assessment standards and challenging content.
I. Basic Contest Information (2026 Season)
| Item | Details |
|---|---|
| Organizer | CEMC, University of Waterloo, Canada |
| Registration Deadline | March 5, 2026 (Schools are advised to complete registration 1–2 weeks in advance) |
| Exam Date | • North & South America: March 31, 2026 (Tuesday) • Other regions (including China): April 1, 2026 (Wednesday) |
| Exam Format | Paper-based offline exam (organized by authorized test centers) |
| Duration | 2.5 hours |
| Question Types & Scoring | 10 short-answer questions, total 100 points • Some questions contain sub-questions (a)(b) • Full solution process required (answers alone receive no credit) |
| Score Release | 5–6 weeks after the exam (expected mid-to-late May 2026) |
II. Target Audience
Goal-Oriented Students:
Planning to apply to Canada's Top 5 universities (University of Toronto, UBC, McGill, Waterloo, McMaster).
Interested in applying to Waterloo's Mathematics, Computer Science, Engineering, Actuarial Science, or Business programs.
Hoping to leverage contest results for undergraduate scholarships (Waterloo has clear scholarship thresholds for Euclid scores).
Profile Enhancers:
Students in Grades 10–12 who want to add a high-value academic credential to their applications to UK, US, and Canadian schools.
Students with a solid math foundation (equivalent to Chinese Grade 12/Canadian Grade 12 level) who have not participated in advanced competitions like AIME.
Value Seekers:
Compared to AIME (average score only 4–5/15), achieving 75+ in Euclid is more attainable, and its recognition in Canada is extremely high.
III. Exam Content & Weight Distribution
The knowledge points of the Euclid contest are highly stable, focusing on core high school mathematics + logical expression:
| Module | Weight | High-Frequency Topics |
|---|---|---|
| Plane Geometry & Analytic Geometry | ≈35% | Triangle properties, Power of a Point theorem, coordinate method for area calculation, vector applications, ratio and proportion proofs |
| Algebraic Operations | ≈30% | Equation solving, inequalities, function properties, sequences (arithmetic/geometric), polynomials (factorization, relationship between roots and coefficients) |
| Combinatorics & Probability | Always tested | Fundamental counting principles, probability models (often combined with number theory/algebra, appearing in Q5–Q10) |
| Trigonometry | ≈1 question | Trigonometric identity transformations, solving triangles (a strength for Chinese students) |
| Number Theory | 1–2 questions | Prime numbers, GCD/LCM, modular arithmetic, Diophantine equations (mostly in Q9–Q10) |
| Functions & Logarithms | Interspersed | Inverse functions, composite functions, change of base formula for logarithms |
Question Features:
- Calculus, complex numbers, and solid geometry are not tested.
- Emphasis on process writing: even if the answer is wrong, clear logic can earn partial credit.
- Highly integrated final problems: Q8–Q10 often combine 2–3 modules (e.g., "sequences + number theory," "geometry + algebra").
IV. Answer Strategies by Question Type (Step‑by‑Step Breakthrough of the 10 Questions)
Q1–Q4: Foundational Questions (Goal: Perfect Score)
Features: Direct application of formulas, mainly computational.
Strategies:
- Strengthen speed training; aim to complete the first 4 questions within 10 minutes.
- If English reading is challenging, preview the questions from the past 5 years' exams in advance and build up high‑frequency expressions.
Q5–Q7: Intermediate Questions (Goal: Score 70%+)
Features: Require simple modeling or case classification.
Strategies:
- Sub‑questions are independent: if stuck on (a), skip to (b) directly.
- Avoid brute‑force calculation: complicated equations always have a clever method (symmetry, substitution, factorization).
- Write standard solutions: even when stuck, write down the given conditions and the direction of your attempts.
Q8–Q10: Final Challenging Questions (Goal: Snatch Process Points)
Features: Highly integrated, requiring deep thinking.
Strategies:
- Prioritize securing correctness for the first 7 questions before tackling the final problems.
- Write down key steps clearly, e.g., "Let the common ratio be r," "By the Pythagorean theorem…".
- Time allocation: ≤15 minutes per question; if time runs out, stop and return to check the foundational questions.
