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The Euclid Mathematics Contest, hosted by the Faculty of Mathematics and Computer Science at the University of Waterloo in Canada, is one of the world's most influential high school mathematics competitions. Due to its high academic standards, strong connection to university academics, and direct reference value for University of Waterloo undergraduate admissions, it is hailed as the "SAT of the mathematics world" and the "golden stepping stone for Canadian STEM applications."

This article will systematically analyze the Euclid Contest's format characteristics, question type distribution, difficulty gradient, award settings, and provide a phased award-winning preparation strategy to help you move from foundation building to high-score breakthroughs, efficiently preparing for the April 2026 exam.

I. Basic Format of the Euclid Contest

Item	Details
Organizer	University of Waterloo, Canada (CEMC)
Exam Format	Written exam (paper-based or computer-based, depending on the test center)
Exam Duration	2.5 hours (150 minutes)
Number of Questions	10 long-answer questions, each containing 2–3 sub-questions
Total Score	100 points (10 points per question, marks awarded for steps)
Question Type Requirements	Short answer + full solution questions: Must write the complete reasoning process; answers alone receive no points.
Exam Language	English (Chinese can be used for rough work/drafts, but the final answer must be in English)

Key Features:

The first 5 questions are basic, the last 5 are advanced, with difficulty increasing in a stepped manner.

The most challenging problems (Questions 9–10) often involve Olympiad-level thinking, distinguishing top students.

High weight on step-by-step marks: "Write down whatever you know" to score points.

II. Six High-Frequency Core Question Types (Based on Past Papers from the Last 10 Years)

Euclid questions cover core high school mathematics areas. The following six types appear almost every year:

Question Type	Core Content	Score Proportion	Student Pain Points
1. Logarithms & Exponents	Rules of operation, change of base formula, exponential equations	≈15–20 points	Confusing logarithm properties, neglecting domain restrictions
2. Functions & Equations	Polynomials, quadratic functions, solving equations, function graphs	≈15 points	Neglecting case discussions, incomplete solutions
3. Analytic Geometry	Line/circle equations, distance formula, calculating intersection points	≈10–15 points	Calculation errors, unclear geometric meaning
4. Trigonometry	Simplification, proving identities, solving trigonometric equations	≈10–15 points	Weak area for most students, confusion with formula memorization
5. Sequences & Series	Arithmetic/geometric, recurrence relations, summation techniques	≈10 points	Difficulty modeling recurrences, limited summation methods
6. Circle Geometry	Circle power theorems, tangent properties, angle relationships	≈10 points	Inability to construct auxiliary lines, rigid application of theorems

Question Trends: In recent years, there has been an increase in cross-module comprehensive questions, such as "using trigonometry to solve geometric optimization problems" or "sequences + function iteration."

III. Analysis of Question Difficulty Gradient (Layering of 10 Questions)

Question Numbers	Difficulty Level	Ability Requirements	Target Score
Questions 1–5	Basic Questions	Mastery of in-class knowledge + basic computation	Goal: All correct (50 points)
Questions 6–8	Intermediate Questions	Flexible application + multi-step reasoning	Goal: Get 6–8 points per question
Questions 9–10	Advanced/Challenging Questions	Innovative thinking + Olympiad techniques	Goal: Secure sub-question (1) (2–4 points each)

Key to Winning Awards:

Aim to securely score over 70+ points on the first 8 questions, and strive for step marks on the last 2 questions → A total score of 80+ = Top 5% globally!

IV. Award Settings and Value

Award	Description	Value
Certificate of Distinction	Awarded to students scoring in the top 25% globally.	An important credential for applications to top Canadian universities like Waterloo, U of T, UBC.
Honour Rolls	Divided into three lists: Canadian (Official/Informal) and International.	For international students, making the Honour Rolls demonstrates顶尖 mathematical ability.
Contest Medal	Awarded to the top-scoring student at each participating school.	The highest honor within the school.
Plaque + Cash Prize	Top 5 in Canada: $500 CAD; Ranks 6–15: $200 CAD.	Only applicable to Canadian official participants.

Value for University Applications:

University of Waterloo: Euclid scores are directly used in admissions evaluations for Engineering, CS, and Math programs.

UK/US Institutions: Can serve as supplementary material demonstrating academic ability in STEM fields (especially suitable for students without AMC scores).

Global Recognition: Complements AMC 12 and AIME, showcasing rigorous mathematical literacy.

The Euclid Mathematics Contest is an international mathematics competition for high school students hosted by the University of Waterloo in Canada. Renowned for its high academic standards, strong connection to university academics, and significant reference value for University of Waterloo undergraduate admissions, it is hailed as the "TOEFL of the mathematics world." This article will provide a detailed analysis of the Euclid Contest's registration methods, core advantages, difficulty range, and phased preparation strategies to help you prepare efficiently for the April 2026 exam.

I. Euclid Contest Registration Methods

1. Unified School Registration

Applicable Students: Students whose schools are official in-person test centers for Euclid.

Process: Registration is organized and handled uniformly by the school. Individual self-registration is not supported.

Recommendation: Consult your school's math teacher or the teacher in charge of competitions directly for more information.

For local students in Canada: You can register directly through your school.

2. Registration via Institution Agent

Applicable Students: Students whose schools are not Euclid Contest test centers.

Process: Register through an authorized institution partnered with the contest.

Recommendation: Add and consult teachers from relevant institutions for information and to obtain registration eligibility.

We are an officially authorized test center and can provide代理 registration services.

II. Why You Must Choose Euclid?

1. Canada's "TOEFL of Mathematics," Highly Recognized by Top Universities

Reference for North American University Admissions: Excellent performance significantly enhances competitiveness when applying to top institutions like the University of Waterloo, University of Toronto, UBC, McGill, and others.

High Global Recognition: Especially suitable for students without AMC scores, serving as supplementary material demonstrating academic ability in STEM fields.

2. Direct Link to Scholarships

Priority for Entrance Scholarships at the University of Waterloo: High-scoring students have the opportunity to receive substantial scholarships, achieving "furthering studies through competition, earning scholarships through competition."

3. Moderate Difficulty, Extremely High Cost-Effectiveness

Focus on Logical Thinking: Unlike some contests that emphasize out-of-syllabus knowledge, Euclid places greater importance on logical thinking, problem-solving steps, and mathematical expression.

Easy to Score with Systematic Training: As long as students undergo systematic training, most can achieve outstanding results, making it suitable for the vast majority of high school students aiming for success.

III. Euclid Difficulty Range and Benchmarking

1. Overall Difficulty Positioning

Falls between AMC 10 and AMC 12, significantly lower than AIME, slightly higher than the later part of AMC 10, and lower than the most challenging AMC 12 problems.

Difficulty Curve: Gentle at the start, steep at the end, with a sharp increase —

Questions 1–5: "Gimme questions," solvable with a solid foundation.

Questions 6–8: "The dividing line," require flexible application of in-class knowledge.

Questions 9–10: "The master zone," test Olympiad-level thinking and techniques.

2. Knowledge Scope

Covers core high school mathematics areas: Algebra, Geometry, Number Theory, Combinatorics, Functions, Trigonometry, etc.

No Calculus/Linear Algebra: However, the depth of exploration of basic concepts and the integration across modules far exceed in-class requirements.

Typical Question Types: Exponential and logarithmic operations, solving functions, analytic geometry, trigonometric simplification, sequence recurrence relations, circle geometry problems, etc.

IV. Euclid Preparation Tips: Phased Strategy

Phase 1: Foundation Building

1. Quickly Scan and Master Knowledge Points

Core Resource: Past papers and solutions from the University of Waterloo official website.

Task: Quickly review core high school math knowledge points to ensure no knowledge gaps.

2. Intensively Practice the First 8 Questions of Past Papers

Goal: Master the logic of basic question types and improve accuracy in reading questions.

Task: Carefully work through the first 8 questions of past papers from 2015-2020, while memorizing mathematical English vocabulary.

3. Create a Categorized Error Log

Mark Error Causes: Such as fuzzy concepts, calculation mistakes, unclear problem-solving thought process, etc.

Targeted Breakthrough: Conduct specialized practice for weak modules (e.g., geometric auxiliary line construction).

Phase 2: Ability Strengthening

1. Focus on Comprehensive Question Types

Target Question Numbers: Past paper questions 6-9.

Method: Refine core models like substitution methods, case discussions, forming general problem-solving approaches.

2. Tackle Difficult Modules

Key Focus: Tackle challenging areas like Number Theory, Combinatorics.

Task: Combine practice with questions from similar contests to enhance problem-solving ability in complex scenarios.

3. Standardize English Solution Steps

Requirement: Ensure derivations are clear to avoid losing points on process.

Structure: Write the solution process following the "Given → Reasoning → Conclusion" format.

Phase 3: Final Sprint (March 26 – Exam Day)

1. Full Mock Exams to Adapt to the Pace

Task: Use past papers from the last 5-10 years for timed mock exams (150 minutes), simulating the exam environment.

Time Allocation: Control the time for questions 1-7 within 90 minutes, leaving enough time for the most challenging problems.

2. Score-Grabbing Strategy for Challenging Problems

Priority: Tackle the first two sub-questions of question 10.

Task: Organize your thoughts, list relevant formulas, and strive for every possible point.

3. Review and Optimize Test-Taking Strategy

Compare with Scoring Guidelines: Identify issues in steps and time allocation.

Optimization Strategy: Adjust the order of answering and time management based on mock exam performance.