Category: Blog

I. 2025 Euclid Core Data Snapshot

Metric	Data
Average Score	54.8 / 100
Top 25% (Distinction)	≥68 points
Top 5% (Honour Roll)	≈85+ points (referencing recent years)
Number of Participants	Over 20,000 globally (steady growth)
Exam Duration	2.5 hours, 10 long-answer questions

Key Interpretation: The average score is similar to previous years, but competition in the high-score range has intensified, reflecting an overall improvement in the skill level of participants. A score of 68 only places you in the top quarter; to be competitive for top-tier universities, you need 85+.

II. 2025 Knowledge Point Distribution and Difficulty Trends

Module	Weight	2025 Exam Characteristics	Difficulty Change
Probability & Combinatorics	25% (largest weight!)	Lock combination password problems, counting with multiple constraints	⬆️ Significantly increased; requires casework + inclusion-exclusion principle
Functions & Equations	21%	Functional equations + integration of exponents and logarithms	⬆️ Highly comprehensive; requires deep understanding of function properties
Sequences	13%	Complex arithmetic sequence operations, recurrence relations	➖ Stable, but increased computational load
Number Theory	10%	Palindromes + divisibility + casework	⬆️ Increased depth of thinking; not a rote problem type
Plane Geometry	14%	Complex composite figures (e.g., hexagon formed by right and equilateral triangles)	⬆️ Complex figures requiring auxiliary lines and integration of multiple theorems
Exponents & Logarithms	8%	Basic operations + solving equations	➖ Stable; an area of strength for Chinese students
Trigonometry	5%	Identities transformations + practical applications	➖ Stable; often combined with other modules
Analytic Geometry	4%	Coordinate system trajectories, vector applications	➖ Low weight, but can create score gaps

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III. Comparison of the Last Three Years (2023–2025): The Evolution of Question-Setting Ideas

Algebra: From "Operations" to "Structural Understanding"
2023: Focused on basic applications like systems of equations and averages.
2024–2025: Saw the introduction of functional equations (e.g., f(x+y)=f(x)f(y)), requiring mastery of deriving function properties, not just substituting to solve.

Geometry: From "Single Figure Calculations" to "Composite Configurations"
2023–2024: Focused on isolated triangles and circle problems.
2025: Featured a hexagon composed of multiple special triangles, requiring identification of substructures and step-by-step calculations, testing spatial decomposition skills.

Combinatorics & Number Theory: From "Template Problems" to "Open Modeling"
2025 Lock Combination Problem: "A 4-digit password, the first digit ≠ 0, digits are not repeated, and satisfies a+b=c+d" → requires enumeration + constraint filtering + symmetry optimization, no fixed formula.

IV. Award Value and Relevance for Top-Tier University Applications

Direct Benefits
University of Waterloo: Honour Roll (Top 5%) qualifies for an entrance scholarship of up to CAD $5,000; Euclid scores carry high weight in admissions for Math/CS programs.
Top North American Universities: MIT, Stanford, CMU, among others, explicitly encourage submitting Euclid scores in their application systems; can serve as core material for Common App "Honors" or "Additional Info" sections.

Long-term Value
Forging Logical Thinking: Euclid emphasizes rigorous derivation and clear expression, aligning well with university-level research.
Connecting Competition Backgrounds: A high Euclid score enables a seamless transition to AMC12/AIME, BMO, COMC; forming a "Canada + United States + United Kingdom" multi-system competition chain, enhancing application resilience.

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.

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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.