Category: Blog

I. Euclid Contest Registration

1. School Registration
Applicable: Students whose schools are official Euclid offline test centers.
Process: Registration organized by the school; individual registration is not supported.
Tip: Consult your school's math teacher or contest coordinator for details. Canadian students can register directly through their schools.

2. Agency Registration
Applicable: Students whose schools are not Euclid test centers.
Process: Register through an authorized contest agency partner.
Tip: Contact the teachers of relevant agencies to inquire and secure registration eligibility. (We are an authorized test center and can act as an agency for registration.)

II. Why Choose Euclid?

1. The "TOEFL of the Mathematics World" in Canada, Highly Recognized by Top Schools
North American Admissions Edge: Excellent scores significantly boost competitiveness when applying to top institutions like the University of Waterloo, University of Toronto, UBC, and McGill. High Global Recognition: Especially suitable for students without AMC scores, serving as supplementary proof of academic ability in STEM fields.

2. Direct Link to Scholarships
University of Waterloo Admission Scholarships: High scorers have the chance to win substantial scholarships, achieving both "admission through contest" and "funding through excellence."

3. Moderate Difficulty, Excellent Value for Effort
Emphasis on Logical Thinking: Unlike some contests that focus on out-of-syllabus content, Euclid emphasizes logical reasoning, problem-solving steps, and mathematical expression. Structured Training Yields Success: With systematic preparation, most students can achieve impressive results, making it ideal for the majority of high school students aiming high.

III. Euclid Difficulty & Comparison

1. Overall Difficulty Level
Positioned between AMC10 and AMC12, significantly lower than AIME, slightly harder than the later part of AMC10 and less challenging than the final problems of AMC12. The difficulty curve is gentle at first and steep later. Questions 1–5 are "easy points" for those with a solid foundation. Questions 6–8 are the "watershed," requiring flexible application of in-class knowledge. Questions 9–10 are the "high-achiever zone," testing Olympiad-level thinking and skills.

2. Knowledge Scope
Covers core high school math: Algebra, Geometry, Number Theory, Combinatorics, Functions, Trigonometry, etc. No Calculus/Linear Algebra: However, the depth of conceptual exploration and cross-module integration goes far beyond the standard curriculum. Typical questions involve exponential and logarithmic operations, function solving, analytic geometry, trigonometric simplification, recurrence relations, and circle geometry.

IV. Euclid Exam Prep: A Phased Strategy

Stage 1: Foundation Building

1. Quickly Review Knowledge Points
Core Resource: Past papers and solutions from the official Waterloo website. Task: Quickly review core high school math concepts, ensuring no knowledge blind spots.

2. Thoroughly Practice First 8 Questions of Past Papers
Goal: Master the logic of basic question types and improve reading comprehension. Task: Thoroughly work through the first 8 questions of past papers from 2015-2020, while memorizing English math vocabulary.

3. Maintain a Categorized Mistake Log
Annotate Error Causes: e.g., vague concepts, calculation errors, unclear thinking. Targeted Remediation: Conduct specialized training for weak areas (e.g., geometric auxiliary line construction).

Stage 2: Skill Enhancement

1. Focus on Integrated Problem Types
Target Questions: Past paper questions 6-9. Method: Refine core models like substitution and case classification to develop versatile problem-solving approaches.

2. Conquer Difficult Modules
Key Focus: Tackle challenging areas like Number Theory and Combinatorics. Task: Expand training with problems from similar contests to enhance problem-solving ability in complex scenarios.

3. Standardize English Solution Writing
Requirement: Ensure derivations are clear to avoid losing step-by-step points. Structure: Use a "Given → Reasoning → Conclusion" framework for your solutions.

Stage 3: Pre-exam Sprint (March 26 – Exam Date)

1. Full-length 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 test environment. Time Allocation: Aim to complete questions 1-7 within 90 minutes, leaving ample time for the challenging final problems.

2. Strategy for Scoring on Challenging Problems
Priority: Tackle the first two sub-questions of Question 10. Task: Organize your thoughts and list relevant formulas to secure every possible point.

3. Review and Optimize Exam Strategy
Cross-check with Rubrics: Correct any issues in steps or time management. Optimized Strategy: Adjust your answering order and time management based on mock test performance.

This article systematically explains the six core modules of Euclid, recent trends in question design, high-scoring preparation strategies, and final-sprint suggestions to help you prepare efficiently and aim for the top 5% (Distinction) or even top global rankings.

I. Core Characteristics of the Euclid Contest

Exam Date: Annually in April (April 2, 2026)

Exam Duration: 2.5 hours

Question Format: 10 long-answer questions (some with sub-parts), total 100 points

Language: English (mathematical symbols are universal, low language barrier)

Target Grade: Grade 12 and below (equivalent to China's Grade 11–12)

Value for Applications:

University of Waterloo (Mathematics/CS): Euclid scores directly used for scholarship assessment.

University of Toronto, UBC: Strongly encouraged to submit, especially for Mathematics, CS, and Engineering programs.

UK / US universities: Serves as a powerful supplement to AMC/AIME, demonstrating mathematical breadth.

II. Six Core Modules & Recent Question Trends

Module	Weight	Key Focus	2025–2026 New Trends
1. Algebra & Equations	30%–40% (largest weight)	Polynomial factorization, exponential & logarithmic operations, inequalities, function properties	Triple fusion problems involving "functions + exponents + inequalities"; high-degree symmetric factorization appears more frequently
2. Geometry	≈30%	Plane geometry (circles, triangles), analytic geometry (coordinate systems, vectors)	Increased graphical complexity; requires synthesis of Pythagorean theorem, similarity, power of a point; constructing auxiliary lines is key
3. Trigonometry	10%–15%	Identity transformations, graph analysis, applications of law of sines/cosines	Often combined with algebra (e.g., solving trigonometric equations); an area of strength for Chinese students
4. Probability & Combinatorics	10%–15%	Counting principles, conditional probability, recursive counting	Proportion increasing; often appears in Questions 5–7 or as final problems; frequently intersects with number theory/sequences
5. Number Theory	5%–10%	Prime numbers, divisibility, factorization, modular arithmetic	Problem contexts more complex (e.g., palindromic numbers + prime determination); mostly appears in Questions 9–10
6. Sequences & Recursion	Frequent in final problems	Arithmetic/geometric sequences, term derivation, summation, second-order linear recurrence	Appears in the last four questions; often as the final challenge; some years integrated with geometry/combinatorics

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III. Four High-Score Preparation Modules (Essential for Distinction)

1. Algebra & Equations (Over 1/3 of Total Points)

Key Focus:

Factorization of high-degree polynomials (techniques for symmetric/palindromic polynomials)

Absolute value / fractional inequalities

Exponential and logarithmic equations (change of base, same-base conversion)

Function graph transformations (translation, scaling, reflection)

Past Paper Focus:

Questions 1, 3, 6 from 2019–2024. Master techniques like "splitting and adding terms" and "completing the square".

2. Geometry (25% of Points, Often a Score Differentiator)

Core Tools:

Similar triangles, power of a point theorem, Ptolemy's theorem

Coordinate methods (setting points, vectors, parametric equations)

Auxiliary line models (midpoints of chords, cyclic quadrilaterals, angle bisectors)

Strategy: If stuck with pure geometry, switch decisively to analytic geometry (coordinate system calculations).

3. Number Theory & Combinatorics (Most Flexible)

High-Frequency Topics:

Modular equations (ax ≡ b mod m)

Fermat's Little Theorem for simplifying large exponent modular arithmetic

Inclusion–exclusion principle, recursive counting (e.g., staircase climbing variants)

Problem-Solving Techniques:

"Enumerate small cases → identify pattern → generalize proof" — especially effective for difficult combinatorics problems.

4. Sequences & Recursion (Staple of Final Problems)

Essential Models:

Arithmetic / geometric sequence summation

Second-order linear homogeneous recurrence (characteristic equation method)

Fractional recurrence, periodic sequences

Final-Problem Strategy:

Even if you cannot fully solve, write down the recurrence relation + first few terms + conjecture the general term to earn step-by-step points.

IV. Sprint Phase Preparation Suggestions

1. Timed Mock Exams with Past Papers

Work through past 5 years' papers (2021–2025) strictly within 2.5 hours.

Focus on time allocation: first 6 questions ≤60 minutes; reserve ample time (≥90 minutes) for the last 4 questions.

2. Categorized Error Review

Create an error log and categorize mistakes:

Calculation errors: → Strengthen scratch paper discipline

Conceptual errors: → Supplement solution models (e.g., "seeing a circle and a tangent → recall the tangent-chord theorem")

Knowledge gaps: → Return to textbooks / topic-specific drills

3. Specialized Final-Problem Practice

Intensively study 1–2 final problems (Questions 9–10) per week; summarize:

Common integration patterns (e.g., "sequences + inequalities")

Standardized solution flows (Assume → Derive → Prove → Answer)

Techniques for earning step-by-step points (even if the final answer is wrong, a clear process can still earn ≥60% of the points)

4. Train Standardized Solution Writing

Euclid awards points step by step. Ensure you:

Clearly state assumptions and definitions

Maintain logical coherence throughout derivations

Box the final answer

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.

I. Why Is Everyone Rushing to Take It? Three Core Advantages

1. High Recognition: Globally Respected by Top Universities

Canada: The University of Waterloo, University of Toronto (UofT), UBC, and others officially consider Euclid scores for admissions and scholarship decisions. For CS/Math/Engineering programs, 70+ is the baseline, and 85+ offers priority admission + scholarships.

UK/US: MIT, Stanford, Oxford, Cambridge, and others, while not requiring it, highly regard its academic rigor. It serves as a strong complement to the AMC.

Australia, New Zealand, Singapore, Hong Kong: The University of Sydney, University of Melbourne, NUS, and others also consider it strong proof of mathematical ability.

2. Moderate Difficulty: Achieving Distinction in 2–3 Months is Entirely Feasible

Stable knowledge scope: The contest covers core high school math content (algebra, geometry, trigonometry, sequences, probability, etc.) without exceeding the standard curriculum.

Structured question format: 10 long-answer questions. The first 7 are basic to intermediate—mastering them secures 60+ points.

Clear award thresholds:

Top 25% (Distinction) ≈ 68 points → Equivalent to solving the first 7 questions correctly + partial points from question 8.

Top 5% (Honour Roll) ≈ 85 points

Top 1% ≈ 95 points

Comparison with AMC: The top 5% in AMC 12 requires 100+ points (out of 150), with a fast-paced format and low margin for error. Euclid offers ample time (2.5 hours for 10 questions), making it better suited for students who prefer deep thinking.

3. Efficient Preparation: Individual Competition + Fast Results + Process Equals Ability

No need to form teams: It’s an individual contest, allowing you to prepare at your own pace.

Fast results: Scores are released 4–6 weeks after the exam, just in time for RD/UC application deadlines.

Direct skill development:

Enhances English reading comprehension and academic writing skills.

Develops rigorous logical expression and step-by-step solution habits.

Improves the ability to break down and model complex problems.

Ideal for:

Students with strong in-school math performance but limited contest experience.

Students who didn't perform well on the AMC and are looking for an alternative path.

Applicants targeting CS/Math/Engineering programs in Canada.

II. Awards: The Distinction Certificate is the "Gold Standard"

Award	Global Percentage	Application Value
Certificate of Distinction	Top 25%	Most practical and cost-effective; can be directly listed on the Common App.
Honour Roll	Top 5%	Top-tier honor, key for Waterloo scholarships.
School Champion / Regional Award	School/Region	Background supplement, demonstrates leadership.
Participation Certificate	All candidates	Can be used as an activity record.

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III. Final Sprint Suggestions: Past Papers + Standardized Approach = High Score

1. Intensively practice past 5 years of papers, imitating the logic of official solutions.

Solve problems without time limits → analyze errors → compare with official marking schemes.

Focus on learning:

Which key phrases must be included (e.g., "By the Pythagorean Theorem...")

How to avoid point deductions for skipping steps.

English mathematical expression templates (e.g., "Let x be...", "Therefore, we conclude that...").

Remember: Over 50% of Euclid points come from the process! Being able to solve a problem does not guarantee scoring points.

2. Full-length mock exams + scientific answering strategy.

Goal allocation:

First 7 questions: Ensure full marks (≈60 points).

Questions 8-9: Aim for partial points.

Question 10: Attempt if time permits; otherwise, prioritize reviewing the first 7 questions.

Principle: Secure foundational points before tackling difficult problems.

IV. Three Key Points for Pre-Exam Skill Improvement

1. Strengthen your English math vocabulary.

Master high-frequency terms such as "quadratic," "congruent," "logarithm," "perpendicular" to avoid reading obstacles.

2. Train your ability to interpret complex problem descriptions.

When faced with long problem statements, use diagrams, tables, and variable annotations to extract key information.

3. Memorize core formulas and theorems.

Be able to recall formulas such as the law of cosines, geometric series sum, and change of base for logarithms effortlessly.

However, many candidates lose points due to unfamiliarity with the exam format and scoring rules. This article provides a detailed explanation of Euclid's exam details, pre-exam preparation points, and common high-frequency pitfalls to help you secure a high score!

I. Exam Format Explained: Process Weighs More Than Answers

Paper Structure

Total Questions: 10 long-answer questions

Points per Question: 10 points

Total Score: 100 points

Sub-question Distribution: Each question contains 2–4 sub-questions of varying difficulty

Question Types

Type	Icon	Features	Scoring Criteria
Short Answer	[Lightbulb]	Only final answer needed	Even if the answer is incorrect, partial points may be awarded if the steps are reasonable
Full Solution	[Handwriting]	Full solution process must be written	Scored step by step; unclear process may result in point deductions even if the answer is correct

Permitted Tools

✅ Allowed: Scientific calculators without programming or internet capabilities

❌ Prohibited: Graphing calculators, CAS systems, and other advanced devices

II. Pre-Exam Tips: Details Determine Success or Failure

Stationery Essentials

Black ink pen

2B or HB pencil

Compass

Triangle ruler

Basic functional calculator

Note: Calculators must comply with regulations; otherwise, they will not be allowed into the exam room.

Exam Instructions

Before the exam starts, be sure to read all instructions on the question paper to ensure you understand the question requirements, answer specifications, and scoring criteria.

Time Allocation: 150 minutes to complete 10 questions — proper time management is crucial.

Answer Filling

Answer Location: All answers must be handwritten in the official Answer Booklet provided.

Matching Question Numbers: Write each answer in the designated box in the Answer Booklet; answers placed in the wrong location may not receive marks.

Complete Steps: For questions labeled "full solution required", provide a complete solution process including all key mathematical steps and written explanations.

Scratch Paper: You may complete detailed calculations on scratch paper before neatly transcribing the final answer.

III. High-Frequency Pitfalls Reminder: Avoid Common Mistakes

1. Non-standard Solution Process

Manifestation: Skipping steps, failing to cite theorems or supporting evidence — even if the answer is correct, points may be deducted.
Countermeasure: Provide clear reasoning for each step and minimize skipped steps.

2. Neglecting Boundary Conditions

Manifestation: Overlooking multiple solutions in geometry problems, domain restrictions in functions, etc.
Countermeasure: Carefully check boundary conditions for each problem to ensure nothing is missed.

3. Calculation Errors

Manifestation: Algebraic manipulation, logarithmic operations, geometric side-length calculations account for over 30% of total point loss.
Countermeasure: Practice calculations regularly and cultivate careful habits.

IV. Pre-Exam Sprint Strategy: Efficient Score Improvement

Simulate Real Exam Pace

Action: Complete 1–2 sets of recent past papers strictly within contest time (150 minutes).
Goal: Adapt to the exam pace and improve time management skills.

Re-do Mistakes from Past 3 Years' Papers

Analyze Error Causes: Misguided thinking / calculation errors / knowledge gaps.
Targeted Remediation: Summarize high-frequency topics and organize corresponding solution templates.

Stay Calm, Perform at Your Best

Mindset Adjustment: Stay calm during the exam. Don't panic when facing difficulty — tackle simpler problems first to gradually build confidence.

V. Euclid Pre-Exam Sprint Course: Short-Term, Efficient Award Pursuit

Course Highlights

Focus on Four Core Areas: High-frequency topics, answer standards, problem-solving techniques, time allocation.

Instruction Language: Bilingual (Chinese/English) or full English.

Class Size: 1-on-1 (due to the approaching contest).

Why Choose Our Team of Instructors?

Proficient in Contest Strategy: Years of tutoring experience, familiar with question trends.

Understand Students: Pinpoint students' weaknesses with personalized guidance.

Master Question Trends: Help you quickly improve problem-solving skills within a limited time.

I. These Three Types of Students Are Particularly Suited to Participate in Euclid!

First Type: “High Achievers” Who Want to Test Their International Level

Your grades in school math are stable (e.g., an A or 90+), but you’re uncertain where you stand on the international stage.

You want to objectively assess your math ability through an authoritative, fair, and globally ranked competition.

Euclid provides a detailed global percentile ranking, letting you clearly know whether you are in the top 10%, 25%, or 50%.

Second Type: “College Applicants” Targeting STEM/CS/Economics

You plan to apply to the University of Waterloo, the University of Toronto, UBC in Canada, or top G5/Top30 STEM schools in the UK and US.

You need to prove in your personal statement that “I not only can take exams but also think rigorously.”

A top 25% Euclid certificate = golden endorsement for STEM applications, especially favored by Waterloo’s Math/CS programs; high scorers can directly win scholarships.

Third Type: “Potential Students” with a Good Foundation but Weak Expression and Integration Skills

You can work out problems correctly in practice, but you skip steps, have disorganized logic, and are afraid to tackle the final challenging problems.

Teachers often comment: “Your thinking is right, but the process is non‑standard, which hurts you on exams.”

Euclid precisely trains these abilities: connecting knowledge points, expressing ideas in English logical connectors, and completing every derivation step fully.

II. What Does Euclid Test? How Difficult Is It?

Knowledge coverage: core high school content, no out‑of‑syllabus material.
Algebra (functions, equations, inequalities), Geometry (triangles, circles, similarity, analytic geometry), Number Theory (modular arithmetic, divisibility), Combinatorics (counting, probability), Trigonometry, and Logarithms.

Key characteristic: “The easy questions are truly easy; the final problems are not basic at all!”

Questions	Difficulty	Proportion	Goal
Questions 1–3	Basic	≈30%	Must get full marks (carefulness is enough)
Questions 4–7	Medium	≈40%	Key breakthrough point (requires proficient application)
Questions 8–10	Challenging	≈30%	Differentiating tier (emphasizes logic + innovation)

Question 10 is often open‑ended, possibly involving function iteration, geometric construction, number theory proofs, requiring in‑depth analysis and clever thinking. But! If you do well on the first 7 questions, 68–70 points will safely get you into the top 25% – no need to stubbornly crack the final problems!

III. Authoritative Answers to Common Questions

Q1: Can I participate without any contest experience?
✅ Absolutely! Euclid does not test tricky Olympiad problems; all the knowledge points come from the high school curriculum. As long as your math foundation is solid (e.g., having completed Pre‑Calculus), a systematic 2–3 month preparation makes it entirely feasible to sprint for the top 25%.

Q2: How should I choose between Euclid and the AMC?

Dimension	Euclid	AMC12
Difficulty	Medium (emphasizes process)	Higher (emphasizes skills + speed)
Question format	All long‑answer (10 big questions)	All multiple‑choice (25 questions)
Best suited for	Most high‑achieving students	Students with rich contest experience
Prestige recognition	Top Canadian + strong Commonwealth	Strong among US Top30 colleges
Recommendation	Average foundation → prioritize Euclid; strong foundation → prepare for both

Q3: How do Chinese students register?
Students from partner schools: register through the school.
Non‑partner school students / independent candidates: register through officially authorized test centers.
Confirmed cities: Shanghai, Beijing, Shenzhen, Guangzhou, Hangzhou, Chengdu, Changsha.
(Centers in Wuhan, Chongqing, Xi’an, etc. are to be announced; keep an eye on the University of Waterloo’s official website or authorized institutions for updates.)

Q4: How much does winning an award help my application?
University of Waterloo: the top 25% significantly increases admission chances; a score of 80+ qualifies you to apply for scholarships.
University of Toronto / UBC: serves as supplementary evidence of academic ability, enhancing the competitiveness of STEM applications.
UK/US institutions: although not mandatory, it sets you apart from ordinary applicants and demonstrates rigorous thinking.

Q5: With zero contest experience, can I go for the top 25%?
Absolutely! The first 7 questions (70 points) only require a solid foundation plus standardized steps. What you need is not a “flash of inspiration” but a “step‑by‑step approach.” Every year, many ordinary students succeed in winning awards through systematic training.

This article compiles the 2026 season's key timeline, exam focus, participation advice, and strategic value, helping you plan precisely and efficiently strive for a high score!

I. 2026 Euclid Mathematics Contest Key Timeline (Must Remember!)

Item	Date	Notes
Exam Date	North/South America: March 31, 2026 (Tuesday) Other regions (including China): April 1, 2026 (Wednesday)	Globally unified questions; Chinese candidates take it 1 day later
Registration Deadline	February 25, 2026	⚠️ Individual registration not accepted! Must be submitted through schools or authorized educational institutions
Registration Method	Organized by school / Registered through authorized training institution	Institution channels often close earlier (e.g., before Feb 20), be sure to confirm early
Exam Format	Offline paper-based written test, entirely in English, 150 minutes	Test papers are collected after the exam and cannot be taken away

Suitable for: Students in grades 10–12 worldwide (high school years 1–3), especially those planning to apply to STEM majors such as mathematics, computer science, engineering, and physics.

II. Exam Content & Module Weights (Based on Recent Years' Analysis)

Euclid covers the core content of Canadian Grade 12 Mathematics, roughly equivalent to senior high school content + some pre-university knowledge in China. There is no out-of-syllabus content, but comprehensive application is heavily emphasized.

Core Modules and Weightings:

Module	Weight	Key Topics
Probability & Combinatorics	≈25%	Permutations and combinations (addition/multiplication principle); classical probability; grouping/coloring problems; introduction to expectation
Functions & Equations	≈21%	Properties and graphs of linear, quadratic, exponential, and logarithmic functions; solving equations (including relationships between roots of cubic equations, remainder theorem); connections between function zeros and equations
Sequences & Series	≈13%	Arithmetic/geometric sequences: general term and sum; recurrence relations; analysis of monotonicity and boundedness
Geometry & Analytic Geometry	≈15%	Plane geometry proofs; properties of circles; coordinate method; vector applications
Trigonometry	≈10%	Graph transformations; law of sines and cosines; trigonometric identities
Number Theory & Algebra	≈10%	Divisibility, modular arithmetic, factorization, inequalities
Other (Sets, Logic, etc.)	≈6%	Basic logical reasoning; set operations

Trend insight: In recent years, the final challenging problems (Q9–10) often integrate functions + sequences + inequalities or geometry + algebra, emphasizing cross-module modeling skills.

III. Grade-Specific Participation Suggestions: Scientific Planning, Step-by-Step Progression

Grade	Positioning	Goal	Preparation Advice
Grade 9 (Freshman)	Trial & Familiarization	Get acquainted with question types, adapt to English exam environment	Focus on the first 6 questions; master basic functions, equations, and elementary geometry
Grade 10 (Sophomore)	Systematic Award Pursuit	Achieve Certificate of Distinction (≥80 points)	Cover all modules comprehensively; strengthen probability/combinatorics and functions/equations
Grade 11 (Junior)	Peak Sprint	Strive for Honor Roll (≥90 points), create application highlights	Specialize in challenging problem types; enhance solution rigor and speed
Grade 12 (Senior)	Address Weaknesses	Supplement application materials, aim for scholarships	Even if not taken before, can still aim for Distinction as a supplement

Golden window: Grades 10–11 are the best period to aim for awards—ample time, comprehensive knowledge, and application materials not yet finalized.

IV. Why Is Euclid Highly Recommended?

1. Hard Currency for Prestigious North American Admissions

University of Waterloo: Directly used for evaluating admissions to Math, CS, and Engineering programs; high scores can lead to entrance scholarships.

University of Toronto, UBC, McGill: Acts as a core proof of academic ability.

U.S. Ivy League & Top 30: Although not required, a score of 90+ can significantly enhance STEM application competitiveness.

UK G5: Admissions tutors for Oxford/Cambridge Engineering/CS programs highly regard its logical rigor.

2. Unique Value in Developing Core Skills

Compared to AMC (multiple-choice, emphasis on speed and tricks), Euclid focuses on full-solution questions, stressing logic and expression.

Mathematical modeling ability: Transforming text into symbols and equations.

Rigorous reasoning skills: Each step requires justification.

Academic writing in English: Describing mathematical ideas using standardized language.

However, with a surge in the number of participants and fluctuations in question difficulty, how can you accurately grasp cutoff trends, efficiently earn step marks, and secure a spot in the top 25% or even aim for the Distinction (top 5%)? This article provides a comprehensive breakdown for you[reference:2].

I. Recent Participation Trends and Cutoff Scores (2019–2025)

1. Continuous Increase in Participants, Intensifying Competition

Year	Number of Participants	Trend
2019	≈22,000	Baseline
2024–2025	>27,000	⬆️ Over 20% growth in 5 years

Impact: The expansion of the candidate pool leads to increased competition pressure at the top (top 2.5%) and upper-middle (top 25%) levels, reducing the margin for error[reference:3].

2. Award Cutoff: 68–69 Points Become the "New Benchmark"

The Euclid contest is out of 100 points, consisting of 10 big questions (some with sub-questions). The top 25% receive the Certificate of Distinction, which is the key indicator that most prestigious schools focus on[reference:4].

Year	Top 25% Cutoff	Average Score	Difficulty Assessment
2021–2022	68	≈53–54	Medium
2023	65	51	⚠️ Most difficult in recent years (abstract final problems)
2024	69	54+	Return to normal
2025	68	54+	Stable, slightly challenging

Key Conclusions[reference:5]:
- 68–69 points = The stable award threshold in recent years; equivalent to completely solving 7 big questions (including some sub-questions).
- If aiming for Waterloo's Math/CS programs, it is recommended to aim for 80+ points (top 5%).

3. School Champion (School Medal): 54 Points May Secure Domination

Cutoff: Fluctuates in the range of 51–56 points; in 2024–2025, it was 54 points[reference:6].
Practical Significance: Being top in your school does not mean a high global rank (54 points is only about the top 50% level); however, it can serve as an academic benchmark within your school, helping with recommendation letters or scholarship applications[reference:7].

II. Core Grading Principle of Euclid: Process > Result

This is the "invisible trap" that Chinese students are most likely to fall into! No process = loss of points![reference:8]

Even if the answer is correct, lacking key derivation steps might only earn you 1–2 points (out of a 10-point question). Conversely, if the process is complete and logically clear, you can still get 6–8 points even if the calculation is wrong[reference:9].

Four Tips for Earning Step Marks:

1. Write in Full English + Use Logical Connectors: Use standard mathematical expressions; avoid "obviously," "it is easy to see," "so the answer is..." (graders cannot tell if you truly understand)[reference:10].

2. Standard Answer Format: Write all answers in the designated area of the official answer booklet, matching question numbers; present solutions step by step[reference:11].

3. Compliant Calculator Use: Allowed: basic scientific calculators (no CAS, no storage, no internet); Prohibited: Directly inputting equations to solve → Must write algebraic steps manually; Numerical calculations may use a calculator, but you must indicate "using calculator"[reference:12].

4. Never Leave Tough Questions Blank! Fill with Effective Steps: Even if you can't solve, write down the given conditions; define variables; draw diagrams/auxiliary lines; list relevant formulas. These can earn you 1–3 points, which can accumulate[reference:13]!

I. Core Exam Details: Rules Determine Success or Failure

1. Exam Paper Structure

Total number of questions: 10 long-answer questions

Total score: 100 points (10 points per question)

Question distribution:

Each question contains 2–4 sub-questions, with difficulty increasing (a → b → c → d)

First 5 questions are basic, next 5 gradually increase, last 2 are challenging final problems

2. Question Type Identification and Answer Requirements

Icon	Type	Answer Requirements	Scoring Focus
[Lightbulb Icon]	Short Answer	Only final answer required, but it is recommended to show key steps	As long as the process is reasonable, points can be earned, even if the final answer is wrong
[Handwritten Icon]	Full Solution	Must write complete derivation process	Points given step by step; correct answer with no process may result in 0 points

3. Permitted Tools

✅ Allowed: Scientific calculators without programming or internet capabilities (e.g., Casio fx-991ES)

❌ Prohibited:

Graphing calculators (e.g., TI-84)

Calculators with CAS (Computer Algebra System) functionality (e.g., TI-Nspire CX CAS)

Mobile phones, smartwatches, or any electronic devices

Recommendation: Check in advance whether your calculator model is compliant to avoid it being confiscated at the exam venue.

II. Pre-exam 24-Hour Ultimate Preparation Checklist

1. Packing Your Bag (Complete the Night Before)

Place in a transparent pencil case, double-check:

Admission ticket (printed in advance, clear information)

Valid ID (ID card / passport, must match registration)

Black ink pen (primary), 2B/HB pencil

Compass, ruler, triangle, eraser

Compliant scientific calculator (with fresh batteries)

Transparent pencil case (no labels, no compartments)

❌ Strictly prohibited: Mobile phone, scratch paper (provided by exam venue), correction tape, or stationery with storage function.

2. State Adjustment

No staying up late: Ensure at least 7 hours of sleep; a clear mind is essential for logical rigor.

No new problems: On the last day, only review your error notebook + core formulas + standard answer writing paradigms from past papers.

Eat a good breakfast: Avoid low blood sugar affecting your thinking.

Arrive early: Arrive at least 40 minutes in advance to familiarize yourself with the environment and ease nervousness.

3. Exam Hall Strategy

First 3 minutes before the exam starts: Read exam instructions, confirm question type icons.

Quickly skim the entire paper: Understand the focus of Questions 9–10 (often number theory, functional equations, geometry proofs) to be mentally prepared.

Recommended time allocation:

First 5 questions: ≤30 minutes (Goal: get them all correct, secure 50 points)

Questions 6–8: ≤60 minutes (Moderate difficulty, aim for ≥7 points each)

Questions 9–10: Remaining 30 minutes (Choose sub-questions you can tackle, don't force completion)

Handling being stuck: If you spend more than 10 minutes on a problem without progress → Skip it immediately and secure foundational points first!

III. High-scoring Answer Techniques: How to "Write" Your Way to Process Points?

1. Full Solution Questions Must "Tell a Story"

Don't just list formulas! Connect your thoughts with a logical chain:

Incorrect example: "x = 5"

Correct example: "Let the side length of the square be x, then the area is x². According to the problem, x² = 25. Taking the square root of both sides gives x = 5 (discarding the negative root because length must be positive)."

2. Make Good Use of the "Let... Since... Therefore..." Structure

Let: Define variables

Since / Because: Cite known conditions or theorems

Therefore / Hence: Draw conclusions

3. Memorize High-frequency English Math Terms

Although a dictionary is allowed, looking up words takes time! Be sure to master:

algebra, geometry, function, equation, polynomial, sequence, series

logarithm, exponent, trigonometric, identity, theorem, proof

probability, permutation, combination, integer, prime, factorization

IV. Six Major Pitfalls and Countermeasures

Pitfall 1: No process written → Even if the answer is right, you lose step points.
Countermeasure: Write every step, even if simple.

Pitfall 2: Using logical leaps → Grader cannot follow your reasoning.
Countermeasure: Use "Because... Therefore..." as connecting threads.

Pitfall 3: Misreading the question type → Not knowing whether to write a full solution or just the answer.
Countermeasure: Before answering, check the icon type.

Pitfall 4: Stuck on a single problem → Squandering time and missing easy points from later foundational problems.
Countermeasure: Apply the "10-minute rule" – if no progress, skip and return later.

Pitfall 5: Calculator misoperation → Wrong key presses cause answer errors.
Countermeasure: Re-check critical calculation steps by doing them manually or re-entering.

Pitfall 6: Incomplete final answer → For example, forgetting to write the units or not discarding extraneous roots.
Countermeasure: In the final 5 minutes, check that answers fully satisfy the problem conditions.

V. Self-Check Quick List

Are all items in the transparent pencil case complete? (Especially the calculator and admission ticket)

Have you memorized the English math terms for key modules?

Have you planned your time allocation for the 150 minutes?

Do you understand that "full solution questions must show process"?

Do you know how to use "Let... Since... Therefore..." to construct logical steps?

Have you arrived at the exam venue at least 40 minutes early to calm down?