The Euclid Mathematics Contest (Euclid), organized by the University of Waterloo in Canada, is one of the most influential high school math competitions in the world. It holds particularly high value when applying to top Canadian universities (such as the University of Toronto, UBC, and Waterloo) as well as STEM/Economics programs in the UK and US. Renowned for "emphasizing thinking, not tricks, and stressing application," it is often called the "SAT of the math world." Below, we comprehensively break down key preparation points for the 2026 Euclid contest from four dimensions: contest features, award structure, question format, core test points, and preparation strategies.
I. Three Distinctive Features of the Euclid Contest
1. Moderate Difficulty to Win an Award – Top 25% Earn a Certificate
Simple and direct award structure: Only the Certificate of Distinction is awarded, given to the top 25% of participants globally.[reference:0]
High actual award rate: Due to the large number of Asian participants and their generally high level, Chinese students can usually secure a spot in the top 25% by scoring 70+ out of 100.[reference:1]
Low psychological pressure: No need to obsess over the last problem; the key is zero mistakes on basic problems and high scores on intermediate ones.[reference:2]
Compared to other competitions (e.g., AMC12 requires top 5% to qualify for AIME), Euclid is far more friendly to "non-Olympiad students."[reference:3]
2. Humanized Scoring: Process‑Based Point Protection Mechanism
Partial credit for partial work: Even if the final answer is incorrect, writing key steps (e.g., correctly setting up an equation, drawing an auxiliary line, establishing a recurrence relation) can still earn 1–3 points.[reference:4]
Avoids the "all or nothing" trap: For example, on a geometry proof problem, writing the criteria for triangle similarity can earn points even if the full derivation is incomplete.[reference:5]
Encourages attempting: Even if you cannot solve the whole problem, make sure to jot down relevant formulas or ideas![reference:6]
3. Limited Scope of Knowledge – No Calculus Required
Low mathematical tool requirements: Only needs knowledge up to middle school / Grade 9-10 math level; does not involve derivatives, integrals, matrices, complex numbers, or other advanced content.[reference:7]
Focus on core abilities: The emphasis is on logical reasoning, model abstraction, and flexible application, not "how many formulas you know."[reference:8]
Some problems have a "brain teaser" flavor: For instance, 2024 Question 3 revealed hidden symmetry through simple algebraic manipulation.[reference:9]
Suitable for: Students who have studied high school math but have not systematically trained for Olympiads can still aim for high scores based on a solid foundation.[reference:10]
II. Question Structure & Scoring Strategy (10 Questions / 150 Minutes)
| Question No. | Difficulty Level | Target Strategy | Score Proportion |
|---|---|---|---|
| Questions 1–7 | Basic & Intermediate | Aim for perfect score with careful, standardized steps | ≈60–70 points |
| Questions 8–9 | Intermediate to High | Key point-differentiating area; require integrating multiple knowledge points and mastering case analysis and reverse thinking | ≈20–25 points |
| Question 10 | High difficulty / Innovation | For top-tier participants; often blends number theory, combinatorics, and algebra; requires constructive thinking | ≈10 points |
Core Strategy:
- If your goal is top 25% (≈70 points) → ensure perfect score on Q1–7 + secure half the points on Q8–9.[reference:11]
- If your goal is top 5% (≈85+ points) → Q8–9 need near‑perfect scores, and aim for process points on Q10.[reference:12]
III. In-depth Analysis of Test Points: 3 Major Modules
Module 1: Foundational Modules (70% of Score, Cornerstone for Stable Points)
| Sub‑module | Weight | Core Content | Preparation Points |
|---|---|---|---|
| Algebra | 30% | Equations/inequalities (including radical/ rational forms), function graphs (exponential/logarithmic), algebraic identity transformations | Pay attention to domain restrictions and substitution techniques; many lost points on 2025 Q1 due to ignoring domain constraints[reference:13] |
| Geometry | 35% | Plane geometry (congruence/similarity, power of a point theorem, area), analytic geometry (equations of lines/circles) | A strong area for Chinese students! But standardized writing is needed, e.g., "By the perpendicular chord theorem, we get …" must cite the basis.[reference:14] |
| Trigonometry | 5% | Basic definitions, identities (sin²x+cos²x=1), graph properties | Usually only one problem; just memorize the formulas.[reference:15] |
Module 2: Advanced Modules (30% of Score, Key to High Scores)
| Sub‑module | Weight | Core Content | Typical Question Types |
|---|---|---|---|
| Number Theory | 10% | Prime numbers, GCD/LCM, congruences, divisibility | 2024 Q10: prime factorization → deduce divisibility pattern → rigorous proof[reference:16] |
| Combinatorics & Probability | 20% | Permutations and combinations (categorization, stars and bars method), classical probability, recursive thinking | 2025 Q7: "probability + sequence" synthesis; need to master symmetry simplification and complementary counting.[reference:17] |
IV. Two Major Proposition Trends in Recent Years
Trend 1: Cross‑disciplinary Integration
Pure single‑module problems are decreasing; more problems require cross‑field linkage:[reference:18]
Using algebraic methods to solve geometric optimization (e.g., setting variables to construct functions and find extrema);[reference:19]
Using number theory to analyze combinatorial structures (e.g., modular arithmetic to determine permutation parity);[reference:20]
Probability + sequences, geometry + trigonometry have become the norm.[reference:21]
Trend 2: Improved Mathematical Reading Comprehension
Problem statements often embed real‑world scenarios (environmental protection, economics, population growth);[reference:22]
Test‑takers must first abstract the mathematical model from the text:[reference:23]
Example: 2025 Q8 described "city population grows by 5% annually" → recognize it as a geometric sequence and establish a recurrence relation;[reference:24]
Key abilities: Information extraction → model recognition → mathematical transformation.[reference:25]
