As one of the “world’s three high school math competitions” alongside the US AMC and UK BMO, the Euclid Contest is organized by the University of Waterloo, Canada. Its features of high recognition, stable question types, and process-focused scoring have made it an academic benchmark eagerly pursued by STEM applicants worldwide. But how difficult is it really? Is it accessible to everyone, or reserved only for geniuses? This article will help you accurately assess your suitability for the Euclid Contest and how to prepare efficiently, based on three dimensions: difficulty distribution, core competencies tested, and student profiles.
I. Overall Difficulty: Moderately High, Emphasizing “Depth” Over “Speed”
Stable Knowledge Scope: Closely aligned with Grade 12 and earlier curriculum, no out-of-syllabus content.
Highly Standardized Question Types: 10 non-multiple-choice questions, each with 2–3 sub-questions, progressing gradually.
The Core Difficulty Is Not “Difficulty” but “Attention to Detail”:
You must write a complete solution process.
Skipping steps or making unsupported derivations → Even if the answer is correct, you may receive 0 points.
Clear process and logical rigor → Even if the answer is wrong, you can still score high marks.
II. Difficulty Progression of the 10 Questions: A Three-Tiered Design for Precise Stratification
| Question | Difficulty | Target Group | Preparation Strategy |
|---|---|---|---|
| Questions 1–7 (Basic to Intermediate) | Basic to Intermediate | All participants | Must secure full marks! This is the key to obtaining the Certificate of Distinction (Top 25% globally). The topics cover algebra, functions, geometry, trigonometry, sequences, etc. With a solid foundation and standardized steps, you can basically get them all right. |
| Questions 8–9 (Intermediate to Advanced) | Advanced | Those aiming for the top 5% | The key scoring zone! Requires integrating knowledge from multiple modules (e.g., geometry + algebra, number theory + functions), emphasizing skills and modeling abilities. It is recommended to intensively practice past papers from the last 5 years and summarize high-frequency models. |
| Question 10 (High Difficulty) | Very High | Those aiming for the top 1% | A top-tier selection problem! Often involves innovative constructions, recursive optimization, or in-depth number theory, testing mathematical intuition and creativity. Those aiming for the top 1% must conquer it; others can try to gain experience. |
III. Who Is the Euclid Contest For?
1. Grade Level and Foundation
Main Participant Grades: 11–12 (Junior–Senior years)
Can Challenge Across Levels: Math-excellent students in grades 9–10 (must have completed core content such as functions, trigonometry, geometry)
Minimum Foundation Requirement: School math score ≥ 90 points, proficient in high school core modules
2. Competency Profile (The Most Critical Factor)
Proficient in logical derivation and step-by-step writing: All 10 questions require written solutions; the process is more important than the answer.
Does not rely on “tricks” or elimination methods: 2.5 hours for only 10 questions, ample time, suitable for deep thinkers.
Proficient in English reading and writing: The test paper is entirely in English, and you need to express your problem-solving logic clearly in English (no literary flair required, but accuracy is needed).
Pursues rigor and organization: Suitable for students who like to “explain clearly” rather than just aiming for correct answers.
3. Not Suitable For:
Those accustomed to multiple-choice questions and guessing by elimination
Those who have difficulty writing in English or organizing logical statements
Students who only want to practice problems without writing out the process
IV. Academic Value: Not Just Canada, but a “Universal Currency” for Global STEM Applications
| Application Direction | Value of Euclid |
|---|---|
| Canadian Undergraduate (Top Choice) | Officially referenced by the University of Waterloo, University of Toronto, UBC, and others; 70+ is the baseline for popular majors, 85+ offers priority admission + scholarships. |
| UK G5 / US Top 30–50 | A powerful supplement to the AMC, especially suitable for those who have not taken the AMC or whose AMC scores are average. |
| Those Seeking Profile Enhancement | 2–3 months of systematic training can help you target the global top 25%, offering extremely high cost-effectiveness. |
Unique Advantage: Compared to the AMC’s “speed battle”, Euclid is more like a “mathematical essay writing”, better reflecting a student’s academic rigor and depth of thought — exactly the qualities valued by universities like Oxford, Cambridge, MIT, CMU, etc.
Frequently Asked Questions
How difficult is it, honestly?
Moderately high, and difficult in a specific way: the syllabus stays within the senior secondary curriculum with no out-of-syllabus content, so the challenge is depth rather than reach. The paper gives 2.5 hours for ten questions, which is generous by contest standards. What it does not give is credit for reasoning you did not write down.
How is the paper structured by difficulty?
In three tiers. The early questions are answerable with secure school technique and should be completed rather than rushed. The middle band requires choosing an approach without prompting. The last two or three combine areas and demand extended written reasoning, and most scripts separate there rather than at the start.
Who is it actually for?
Primarily students in their final two years, though strong students in Grades 9 and 10 regularly write it with the core modules in place. The more useful filter is not the year but the disposition: the paper rewards a student willing to write out a derivation step by step, and penalises one who prefers to jump to the answer.