Category: Blog

Below is a comprehensive guide regarding score inquiry timelines, official channels, award categories, and post-exam planning.

I. Score Inquiry Time: Expected Mid-to-Late May

Score Release Cycle: 4–6 weeks after the contest
2026 Exam Date (outside North America): April 1, 2026
Expected Inquiry Period: May 15 – May 30, 2026

As of today (April 24, 2026), the earliest release date is still approximately 3 weeks away. Please wait patiently.

II. Official Score Inquiry Channel (The Only Authoritative Entry Point)

Step-by-Step Instructions:

Navigation Path: Left menu bar → Contests → Results → Find Euclid on the right and click to enter.

Login Query: Enter the School ID and Password (both provided by the school's contest coordinator).

Individual account registration for score checking is not supported (must go through school registration channel).

After login, you can view detailed information including: personal score sheet, total score, global ranking percentile, and award status.

III. Award Categories and Historical Score Reference

Official Award System:

Award	Description
Certificate of Distinction	Top 25% globally (2025 cutoff: 68 points)
Honour Rolls	Separated into Canadian Official/Non-Official + International Regions, for top scorers
Contest Medal	School champion award (one per school)
Plaque + Cash Prize	Top 5 in Canada: 500 CAD; 6th–15th: 200 CAD

2025 Data Reference:

Number of Participants: 27,092

Average Score: 54.8 / 100

Distinction Cutoff: 68 points

Honor Roll (Top 5%): ≥ 90 points

IV. Three Major Post-Exam Pathways (Choose Based on Performance)

Path 1: Excellent Performance (Top 25% and Above)

Recommended Actions:
- Prepare for AMC10/12 (November 2026)
- Train for BMO or AIME
Target Majors: Pure Mathematics, Theoretical Physics, CS (AI/Theoretical direction), Financial Engineering
Application Targets: G5 universities, Ivy League, Waterloo CS Co-op

Path 2: Average Performance (Top 25% – 50%)

Recommended Actions:
- Strengthen weak areas (such as geometry proofs, number theory)
- Transition to UKMT-SMC (October) or Australian AMC (September)
Major Shift: Electronic Engineering, Data Science, Applied Mathematics, and other "application-focused" fields

Path 3: Below Expectations (No Award)

Recommended Actions:
- Cut losses promptly; avoid stubbornly pursuing advanced math competitions
- Shift to areas of strength such as Physics Bowl, Chemistry Olympiad, Business Case Competition
- Strengthen in-school curriculum, solidify foundation, and prepare thoroughly for IB/AP/A-Level final exams

I. Why Do These Three Types of Students Particularly Need to Participate in Euclid?

Type 1: Students with good grades but an unclear understanding of their own level.

"I always score 95+ in school, but where do I rank nationwide or globally?"
Euclid provides a global uniform benchmark: In 2025, 27,092 participants worldwide with an average score of 54.8, requiring 68 points to reach the top 25%.
It is not a test where "high scores come from mere practice," but a comprehensive assessment of logic, rigor, and mathematical intuition.
A single participation allows you to clearly position yourself: Are you a "top student at school" or an "international contender"?

Type 2: Students aiming for STEM, Computer Science, or Economics.

"Who doesn't have A* in the applicant pool? Why choose you?"
These majors demand extremely high levels of mathematical modeling, abstract reasoning, and precise expression.
The Euclid certificate serves as an invisible advantage for top Canadian universities such as the University of Waterloo, the University of Toronto, and UBC.
More importantly, its underlying logic aligns with that of Oxford MAT, Cambridge STEP, and TMUA—all emphasizing process, proof, and critical thinking.
A top 25% scorecard is more persuasive than ten statements of "I'm strong in math."

Type 3: Students who can solve problems but cannot "write solutions" (a common pain point for A-Level/IB students).

Skipping steps in homework and providing only answers in exams may yield short-term gains but plants long-term pitfalls. University interviews require in-person deductions, personal statements demand descriptions of thought processes, and research calls for written proofs.
Euclid forces you to articulate a complete logical chain, serving as the ultimate training ground for academic writing skills.
It tests not just "whether you can solve" but "whether you can explain clearly."

II. Is Euclid Worth It? Two Key Data Points

Indicator	2025 Data
Global Participants	27,092
Average Score	54.8 / 100
Distinction (Top 25%)	68 points
Honor Roll (Top 5%)	≥ 90 points

Conclusion: It is not a "free-points contest"—the average score of only 55 indicates it is properly discerning. But it is also not "exclusive to geniuses"—with systematic preparation, reaching the top 25% is entirely achievable.
Extremely cost-effective: One exam simultaneously builds skills, secures validation, and clarifies direction.

III. Post-Exam Alignment: Three Types of Students, Three Paths

1. Aim for Top 2.5%+ (Honor Roll Level)

Characteristics:
- Can handle most of Q8–Q10;
- Proofs are logically rigorous and written in a standardized manner;
- Demonstrates curiosity and analytical skills when facing new problems.
Talent Recognition: A genuinely rigorous STEM prospect with an integrated triad of abstract thinking, mathematical intuition, and precise expression.
Recommended Next Steps:
- Major Directions: Pure Mathematics, Theoretical Physics, Computer Science (AI/Theoretical), Financial Engineering.
- Advanced Competitions: Immediately begin AMC10/12 → AIME; aim for BMO (British Mathematical Olympiad) or COMC (Canadian Open Mathematics Challenge).
- Target Universities: G5 (Oxbridge, Imperial, UCL), Ivy League, MIT, Stanford, Waterloo CS Co-op.
- Admissions Test Preparation: Focus on Oxford MAT/Cambridge STEP/TMUA as core goals; Euclid is just the starting point.

2. Solidly Secure Top 25% (Distinction Level)

Characteristics:
- First 7 questions are mostly correct with proficient computation;
- Q8–Q10 are completely unfathomable or can only solve part (a);
- Can use formulas to solve problems but lacks deep deductive ability.
Talent Recognition: An excellent "user of mathematical tools," but not a "creator of mathematical ideas."
Recommended Next Steps: Immediately pivot and switch lanes! Leverage the Euclid Distinction certificate to prove a solid STEM foundation. Starting in April, pivot to applied-science competitions such as Physics Bowl, BPhO, and Chemistry Olympiads.
- Major Direction Adjustment: Avoid the "intense competition hell" of pure mathematics and theoretical physics; shift to Electronic Engineering, Mechanical Engineering, Materials Science, and Computer Applications (e.g., Software Engineering, Data Science).

3. High Probability of No Award

Characteristics:
- Struggles even with the first 4 questions;
- Gives up immediately upon seeing proof questions;
- Feels frustrated, anxious, and doubtful after the exam.
Talent Recognition: Rationally face reality: the high-intensity STEM track is not where you shine.
Recommended Next Steps: Cut losses in time; do not stubbornly persist. Do not force yourself to aim for BMO, STEP, or AMC12—that is a path to becoming cannon fodder. Shift to advantageous tracks:
- Humanities & Social Sciences (PPE, International Relations, Psychology);
- Business Management (Marketing, Strategy, Entrepreneurship—avoiding Financial Engineering/Actuarial Science);
- Art & Design (Interaction Design, Digital Media, Architecture).
Core Strategy: Use your existing standardized test scores + the Euclid participation experience (demonstrating courage) + authentic passion projects to craft a differentiated application story.

I. Official Attitude: Explicit Recognition, Encouraged Mention

Directly quotable in the Personal Statement (PS): Universities such as Cambridge, Imperial College London, and UCL explicitly allow applicants to describe their Euclid participation in their PS as evidence of academic enthusiasm and ability.

Not mandatory but strongly recommended: Although it is not a rigid entrance exam like MAT/STEP, the top 25% (Certificate of Distinction) is regarded as "proof of mathematical potential" and can significantly enhance the persuasiveness of your personal statement.

Key insight: In an applicant pool with increasingly homogeneous grades, Euclid contest results serve as an efficient signal for admissions officers to quickly identify students who are "logically rigorous, articulate clearly, and academically proactive."

II. Why Do G5 Favor Euclid? Three Core Reasons

1. Question Type Highly Matches British Academic Tradition

Dimension	Euclid	AMC (for comparison)
Question Type	Full solution questions (10 in total)	All multiple-choice (25 questions)
Scoring Focus	Process > Result, emphasizes logical derivation and standardized writing	Speed + Technique, result-oriented
Alignment with Oxbridge	⭐⭐⭐⭐⭐ (matches entrance test/interview requirements)	⭐⭐ (only reflects breadth of problem-solving)

2. Content Goes Straight to Oxbridge Entrance Tests

MAT (Oxford's Mathematics Admissions Test): About 50% of the content involves algebra, functions, geometry, and number theory—highly overlapping with Euclid's core test points.

STEP (Cambridge's Mathematics Admissions Test): Emphasizes proofs and constructions; Euclid's final challenging problems (like recursive functions and combinatorial proofs) serve as excellent practice.

TMUA (required by Warwick/LSE, etc.): Logical reasoning and problem modeling skills can also be strengthened through Euclid preparation.

Synergy in preparation: Preparing for Euclid means simultaneously building a foundation for MAT/STEP—two for one.

3. Demonstrates "Depth of Academic Exploration"

What G5 admissions officers value most is not "what you have learned," but "how you have gone beyond the syllabus to explore the subject."

Euclid requires flexible application of high school knowledge to complex situations.

Encourages independent modeling, case analysis, and critical reflection.

Demonstrates the independent learning and problem-solving abilities needed for university.

III. Action Guide for Students of Different Grades

Grades 9–10: Plan Ahead, Engage in Multiple Competitions

Goal: Accumulate experience, identify strengths and weaknesses.

Actions:

Complete 1–2 sets of recent Euclid past papers from recent years to diagnose "knowledge gaps" vs. "lack of contest techniques."

Simultaneously prepare for UKMT-SMC/BMO (British system) and AMC10/12 (American system) to build a diversified competition background.

Make use of the "contest season" from September to January (Australian AMC, SMC, AMC10/12, IMC, etc.) to make steady progress.

Grade 10 (Just Taken Euclid): Review and Level Up

Goal: Extract methodology from practical experience and advance to higher-level competitions.

Actions:

Analyze points lost: Was it due to non-standard process? Weak modeling skills? Or insufficient progress on final problems?

Focus on addressing weaknesses during the summer break (e.g., analytic geometry, probability and counting).

Start preparing for AMC12 or BMO to tackle higher difficulty.

Turn your competition experience into Personal Statement material (e.g., "Through Euclid, I learned how to use mathematical language to clearly articulate an idea").

Grades 11–12: A Key Weapon for Targeting G5

Goal: Use high-scoring certificates to boost your application.

Strategies:

If your target is mathematics/CS/engineering, the top 25% in Euclid is the baseline threshold; the top 5% is even more competitive.

Combine Euclid with MAT/STEP preparation, creating a dual guarantee of "contest + entrance test."

Be specific about your competition takeaways in your Personal Statement (avoid vague claims like "I improved my math skills").

I. 2026 Exam Features: Steady with Changes, Emphasis on Process & Modeling

Stable structure: 10 long‑answer questions, 100 points total. All questions require handwritten solutions; no multiple‑choice or fill‑in‑the‑blank.

Clear difficulty gradient:

Questions 1–4: Basic level (algebra, equations, introductory geometry).

Questions 5–7: Intermediate comprehensive problems (probability & counting, function properties, analytic geometry).

Questions 8–10: Challenging high‑level problems (recursive functions, combinatorial construction, abstract proofs) — extremely difficult to crack.

Core topics covered: Algebraic operations, analytic geometry, probability & counting, comprehensive geometry, polynomial theory. All are within the high school syllabus, but the emphasis is on knowledge transfer and model building.

Trends: Continues the direction of “text → mathematical model,” with moderate computation but extremely high demands on case classification, range constraints, and logical rigor.

II. Major Points of Point Loss: Missing Process & Weak Modeling

1. Non‑standard solution writing

A large number of candidates write only the final answer and omit key steps (e.g., equation simplification, geometric derivation, probability enumeration).

Consequence: Even if the final answer is correct, they lose many steps points because the process is missing.

Countermeasure: Develop the habit of “every step has a basis” and use English logical connectors (Let, Since, Therefore) to link ideas.

2. Insufficient ability to convert text into mathematical model

When faced with word problems (e.g., distance, percentages, dice probability, area optimization), they cannot quickly extract conditions and set up equations or inequalities.

Typical sticking points: Defining recursive functions, geometric extremum problems, digit counting.

Countermeasure: Train specifically on “modeling word problems” by extracting common scenarios from NYT articles and CEMC past papers.

3. Inadequate case classification

In problems such as integer solutions, peak permutations, and obtuse triangle determination, frequent mistakes include missing cases, extraneous solutions, and range errors.

Countermeasure: Create a “checklist of cases” and verify boundary conditions after solving.

III. Summary of Historical Cutoff Scores

Based on official and authoritative institutional data:

Year	Top 25% Cutoff	Top 5% (Honor Roll)
2023	65	87
2024	69	89

IV. What to Do After the Contest: Turn Your Contest Experience into Application Assets

1. Organize your contest experience to create strong Personal Statement (PS) material

G5 and US universities allow you to mention your contest experience in the personal statement / Common App essay. It is recommended to summarise from the following perspectives:

Preparation duration and methods (e.g., “I intensively practiced two sets of past papers each week, focusing on analytic geometry”).

Difficulties overcome (e.g., “Transitioning from skipping steps to full derivation — enhancing logical rigor”).

Exam hall strategy (e.g., “Time allocation: 90 minutes for the first 6 questions, 60 minutes for the last 4”).

Deeper understanding of mathematics or your intended major (e.g., “Euclid made me realize that mathematics is the language for modeling the world”).

2. Save your scores and certificates promptly

Scores are expected to be released in mid‑to‑late May 2026 (3–4 weeks after the contest).

Log in to the CEMC official website to download your PDF certificate.

Scan and archive with a standardised filename (e.g., Euclid2026_ZhangSan_85.pdf).

If used for UCAS, ensure it is uploaded in the “Qualifications” or “Additional Info” section.

V. Subsequent Academic Planning: The Euclid Contest Is Only the Starting Point

If your goal is Oxbridge, G5, or US Top 30 universities, proceed with the following schedule:

Time	Key Tasks
2026 May – June	Crunch time for A‑Level / IB / AP final exams; your school grades are the foundation.
2026 June – August	Determine your intended major and target universities; research admissions test requirements.
2026 August – September	Start preparing for MAT / STEP / TMUA (required for Oxford/Cambridge Math/CS); simultaneously prepare the first draft of your UCAS personal statement.
26 October 2026	UCAS deadline for Oxford, Cambridge, and medical programmes.
14 January 2027	Regular UCAS deadline for most undergraduate programmes (earlier than previous years).

I. Key Changes in the 2026 Euclid Contest

1. Major adjustments in content distribution:
- The algebra section has reached its highest proportion in recent years: functions, equations, polynomials, sequences, and other algebraic content run throughout the paper, particularly dominating questions 7–10.
- Permutations & combinations and analytic geometry are significantly reduced: traditional high-frequency topics such as complex combinatorial counting and conic section problems in coordinate systems have almost disappeared.
- Changes in the assessment of trigonometry: no standalone trigonometric equation problems appeared; instead, they were integrated into composite function contexts, emphasizing conceptual understanding over mechanical solving.
Trend interpretation: Euclid is shifting from "broad coverage" to "deep exploration," with algebraic thinking and logical rigor becoming the keys to high scores.

II. Question-by-Question Style Analysis

First 5 Questions: Steady with Changes, Foundation is King

Following the style of previous years, they mainly tested:
- Algebraic operations and proportional applications (e.g., speed, concentration problems)
- Parabola vertex and axis of symmetry properties
- Prime factorization and base-10 expansion
- Basic probability (classical probability, independent events)
Although they are foundational, computational details are prone to errors; you must secure full marks on the first 5 questions.

Questions 6–8: Sudden Style Shift, Difficulty Spike

Question 6:
Combines logarithms and composite functions: no longer directly asks to solve logarithmic equations, but requires understanding the structure and reasoning using logarithmic monotonicity and domain restrictions.
Skills required: awareness of function composition + flexible use of logarithmic properties.

Question 7:
A traditional algebra synthesis problem involving inequalities and parameter discussions, but no traps; it's a "conquerable" medium-level problem.

Question 8 (the biggest difficulty this year!):
- Part (a): Tests the Inscribed Angle Theorem and the Right Triangle Altitude Theorem; no tangents are examined, and auxiliary lines need to be constructed.
- Part (b): Uniquely combines the triangle inequality and the floor function, requiring students to have relatively rich experience in handling the floor function.
Overall difficulty: Significantly higher than previous year's question 8, becoming a key differentiator between Distinction (top 25%) and Honor Roll (top 5%).

Questions 9–10: Final Tough Problems Remain, Algebra and Combinatorics as Main Tracks

Question 9 (Algebra final problem):
- Part (a): Simple graph analysis, easy points.
- Part (b): Tests understanding of polynomial roots, requiring a good grasp of Vieta's formulas and their applications.
- Part (c): Requires the ability to analyze solutions of quadratic Diophantine equations, demanding a relatively high level of number theory.

Question 10 (Combinatorics final problem):
- Part (a): Small-scale enumeration, intuitive.
- Parts (b) and (c): Relatively traditional permutations and combinations problems; constructing a recursive function for n solves them.
Although it is combinatorics, the thinking is more algebraic, reflecting the trend of "algebraization of combinatorics."

III. Difficulty and Cutoff Predictions

Indicator	2026 Trend
Overall difficulty	Higher than 2024–2025, especially questions 8 and 9 raising the bar
Distinction cutoff	Expected around 68 points
Honor Roll cutoff	Expected around 90 points

IV. Preparation Suggestions for 2027 and Beyond

1. Solidify the Six Fundamental Modules

Ensure no blind spots in:
- Exponents and logarithms (including applications in composite functions)
- Functions and systems of equations (including cubic equations, Vieta's formulas)
- Trigonometry (properties, graphs, identities)
- Sequences (arithmetic/geometric, recursion, summation)
- Counting and probability (permutation and combination models, expectation)
- Elementary number theory (divisibility, modular arithmetic, Diophantine equations)

2. Strengthen Two Core Areas of Attack

Area	Key Focus Points
Plane Geometry	- Inscribed angles, tangent-chord angles, Altitude Theorem - Auxiliary line construction (perpendiculars, medians, similar triangles) - Integration with algebra (e.g., coordinate method, vectors)
Counting & Probability	- Recursive modeling (state transitions) - Inclusion-Exclusion Principle, introduction to generating functions - Problems integrating with sequences/inequalities

3. Special Plan for Final Problems

Questions 7–8: Practice 2 medium-to-high difficulty problems each week, focusing on multi-knowledge point integration.
Questions 9–10: Develop strategies based on target awards:
- Pursuing Distinction: Ensure parts (a) and (b) of question 9 and parts (a) and (b) of question 10 are correct.
- Pursuing Honor Roll: Must conquer question 8(b), question 9(c), and question 10(c); systematic study of elementary number theory and advanced recursion techniques is recommended.

I. Why Do Oxbridge G5 Universities Value the Euclid Contest So Much?

1. Assessment of "Mathematical Expression" and "Logical Rigor"

Unlike multiple-choice competitions like the AMC, the Euclid Contest features a significant number of full-solution questions. The evaluation focuses not only on the final result but also on the process: examiners award points based on the completeness of the solution steps and the rigor of the logic. This assessment style is highly consistent with Oxbridge interviews and admissions tests like the MAT/STEP—elite universities do not want "calculators" who can only do drills; they seek students who can express mathematical thinking clearly and logically.

2. Bridging the "Depth of Thinking" Required at the University Level

The last two questions (Q9, Q10) of the Euclid Contest are extremely difficult, often requiring strong creativity and a deep understanding of the essence of mathematics. This design aims to screen for students who possess "sustained resilience" when facing unknown and complex problems—a quality essential for the demanding STEM coursework at G5 universities.

3. Authoritative "Academic Endorsement"

The University of Waterloo holds an excellent reputation in the global mathematics community. For G5 admissions officers, the Euclid Contest serves as a globally standardized and highly credible benchmark. Earning a Certificate of Distinction (top 25% globally) is a powerful academic credential in itself.

II. How to Leverage Your Euclid Results?

Many students simply file away their certificates after the contest, which is a significant waste of this resource. Below is the proper way to leverage your results:

1. Include It in the UCAS System

When filling out your UCAS application, you can enter your Euclid award in the "Extra-curricular activities" or "Awards" section. This is particularly beneficial if you are applying for Mathematics, CS, Engineering, or Physics, as strong contest results can significantly enhance your academic competitiveness.

2. Mention It in Your Personal Statement

This is the most valuable way to use your results. Instead of simply stating "I participated in the Euclid Contest and won an award," describe:

Specific intellectual growth: Detail your logical reasoning process when tackling a challenging full-solution problem.

Transferable skills: Explain how the logical abilities honed through the competition have helped you better understand advanced A-Level/IB concepts.

3. Use It as a Tool for "Borderline Admission"

Special for the University of Waterloo: If you apply to its Mathematics or Computer Science programs, your Euclid score directly influences borderline admission decisions and entrance scholarships. For reference by G5 universities: If your predicted grades are on the borderline, a strong Euclid score could be the deciding factor that leads an admissions officer to issue an offer.

4. Use It as Preparation for Admissions Tests (MAT/STEP/TMUA)

The assessment style of the Euclid Contest (a mix of short-answer and full-solution questions) is very similar to the additional admissions tests required by top UK universities, such as Cambridge's STEP and Oxford's MAT. The problem-solving mindset and mental resilience you develop while preparing for Euclid can be seamlessly transferred to these high-stakes university assessments.

III. Summary: What Score Should You Aim For?

For applications to general prestigious universities: Earning a Certificate of Distinction (top 25% globally) is a solid foundation, demonstrating strong mathematical literacy. For those aiming for G5 universities, the Ivy League, or competitive programs at Waterloo: Your target should be a score of 85+ (typically the top 5% or higher). This score is sufficient to prove to admissions officers that you possess top-tier logical reasoning and mathematical communication skills.

I. 2026 Euclid Contest In-Depth Difficulty Review

1. Questions 1–6: Foundation Points – Must Be Secured

Content Covered: Algebraic operations, linear/quadratic equations, basic number theory (divisibility, modular arithmetic), introductory analytic geometry (lines, circles), and simple applied problem modeling.
Difficulty Level: Comparable to in-class AP Precalculus / A-Level Maths – considered "easy points."
Target Score: 55–60 points (out of approximately 60). This is the absolute foundation for achieving Distinction (top 25%).
Key Reminder: Any mistake could directly cost you an award. Ensure zero computational errors.

2. Question 7: Difficulty Jumps – Abstract Thinking Emerges

Topics: Logarithmic functions + piecewise function iteration.
Challenge: Requires understanding the domain transfer and range constraints of nested functions, demanding a complete logical chain.
Typical Pitfall: Ignoring piecewise conditions, leading to an expanded solution set.

3. Questions 8–10: The "Arena" for Top Competitors

Question	Core Topics	Difficulty Analysis
Q8	Geometric properties of circles + number theory counting	Part (b) combines triangle side-length inequalities with the floor function, requiring construction of inequality systems and enumeration of feasible solutions – extremely prone to missing solutions.
Q9	Cubic polynomials + Diophantine equations	Involves factorization, the Rational Root Theorem, and integer solution constraints. Heavy computation and complex steps – one mistake can ruin the entire solution.
Q10	Brand new "internal peak" combinatorics	Defines a new concept, "internal peak," requiring on-the-spot understanding and construction of recurrence relations or dynamic programming models. No set pattern to follow – highly creative.

II. 2026 Euclid Contest Score Predictions

Due to the increased difficulty of the last three questions, and despite the relative stability of the first six questions, the number of high-scoring candidates is likely to decrease. The Distinction cutoff is expected to drop slightly.

Award	2025 Cutoff	2026 Estimated Cutoff	Explanation
Distinction (Top 25%)	68	65–67	Q8–Q10 lower the mean for high-scoring segment.
Honor Roll (Top 5%)	≈80	78–80	Almost no one scored full marks on Q10.
Perfect Score (100)	Very few	Extremely unlikely	Q10 is a completely new type of problem, making a perfect score very difficult.

Official Release: CEMC typically releases official cutoffs and results 5–6 weeks after the exam (i.e., mid-May 2026).

III. Post-Exam Golden Planning Guide

Phase 1: Before Results (April–Mid-May) – Consolidation & Expansion

Synchronize with In-Class Knowledge: The topics tested in Euclid (functions, polynomials, trigonometry, sequences, analytic geometry, number theory, etc.) heavily overlap with AP Calculus, IB HL Math, and A-Level Further Math. Strike while the iron is hot to avoid forgetting.

Plan Next Competitions:
Lower grades (G9–G10): Prepare for AMC10/12, Kangaroo Math, CEMC Fryer/Galois/Hypatia.
Upper grades (G11–G12): If you did well, consider challenging AIME or the Canadian COMC.

Phase 2: After Results (Late May Onward) – Precise Positioning

Save Your Results: Log in to the CEMC official website to download your PDF certificate and archive it with standardized naming.

Adjust Your Academic Strategy Based on Score:

Score Type	Recommended Direction
Top 2.5%+ (≥85)	Aim for pure mathematics, theoretical physics, theoretical CS; consider preparing for advanced competitions like BMO or Putnam.
Steady Top 25% (65–75)	Suitable for applied science and engineering fields such as engineering, electronics, materials, data science – a "lane-changing advantage."
No Award (<60)	Timely pivot to humanities, social sciences, business (non-quantitative tracks), art & design, etc., leveraging other strengths.

To break into the top 5% or even the top 1% globally in the Euclid contest, a solid foundation in regular math classes is far from enough. You need a precise "knowledge point map" and a flexible set of "exam hall game theory."

I. Core Knowledge Points: "Compulsory Courses" for High Scorers

The distribution of questions in Euclid follows a highly consistent pattern: Questions 1-6 are basic and intermediate levels, questions 7-8 are the "divide," and questions 9-10 are the zone where top-tier competitors contend. To consistently achieve a high score of 85+, you must master the following modules:

1. Advanced Algebra and Functions (Algebra & Functions)

Algebra is the lifeblood of the Euclid contest, permeating almost all of the problems.
Core points: Polynomial division, the Remainder Theorem, advanced applications of Vieta's formulas.
High score requirements: Proficiency in manipulating logarithms and exponential equations, especially in comprehensive problems involving complex function graph transformations and optimization (using discriminants or the AM-GM inequality).

2. Analytic Geometry and Trigonometric Functions (Geometry & Trigonometry)

Euclid has a strong preference for combining circle properties with trigonometric functions.
Core points: Law of Sines, Law of Cosines, sum-to-product formulas.
High score requirements: Proficiency in using analytic methods (coordinate systems) to solve plane geometry problems. You must also be familiar with "contest-level" geometry concepts like the Power of a Point theorem and Ptolemy's theorem, which are often needed for geometry problems in questions 8-9.

3. Combinatorics and Probability (Counting & Probability)

This module is highly flexible in its questioning.
Core points: Stars and bars method, the Inclusion-Exclusion Principle, conditional probability.
High score requirements: The ability to handle complex dynamic counting problems, especially probability models that often appear in the last two questions and require solving with recurrence relations.

4. Elementary Number Theory (Number Theory)

Although not as deep as in the AMC, it appears every year.
Core points: Divisibility analysis, congruences, greatest common divisor and least common multiple, prime factorization.
High score requirements: Mastery of the Euclidean algorithm and its inverse operations, and understanding fundamental number theory tools such as Bézout's identity.

II. Exam Hall Strategies: How to Maximize Your Score

The Euclid contest is 150 minutes long, consists of 10 long-answer questions, and is worth a total of 100 points. Its unique feature is that it includes both "answer-only" questions and "full-solution" questions.

1. Master the Scoring Logic of "Full-Solution" Questions

The final few questions in Euclid typically require you to write out a complete proof or solution steps.
Strategy: Examiners award points step-by-step. Even if you don't get the final answer correct, if your logical framework is correct, you've written down the core equations, and you've proven the key propositions, you can still earn 60%–80% of the points. Never leave a blank space. Even if you only write down the given conditions and your line of reasoning, do so.

2. Adhere to a Strict "Writing Standard"

As the exam is manually graded, clear logical expression is crucial.
Strategy: Use connective words like "Because/Therefore" to outline the logical chain. For geometry problems, be sure to briefly describe how you constructed your auxiliary lines. For algebra problems, clearly define your variables. A neat, presentable answer sheet can significantly improve the "impression score" from the grader.

3. Apply the "Asymmetrical Principle" of Time Allocation

Questions 1-6 (within 45 minutes): Aim for "zero errors." These questions form the foundation for winning any award. Answer them quickly and accurately, and don't waste too much scrap paper on them.
Questions 7-8 (45 minutes): Approach these steadily. These two questions determine whether you will receive a certificate (Distinction). Reserve enough time for a thorough logical breakdown.
Questions 9-10 (60 minutes): These are for deep strategic play. They usually have 2-3 sub-questions, with the first often being a guide. Even if you can't solve the final part, make sure to securely earn the points from the first part.

4. Make Good Use of "Specialization" and "Estimation"

When dealing with multiple-choice or fill-in-the-blank style questions, if the algebraic expression is too abstract:
Strategy: Try substituting special values (like 0, 1, or extreme geometric positions) to find patterns. This "informal" method is very efficient for the first half of the Euclid contest.

III. Preparation Advice for the 2027 Season

Practice with past papers is the only shortcut: The style of Euclid questions is very consistent. It is recommended to go through the past 10 years' past papers at least twice, especially questions 7-10.

Strengthen your English expression: Many students are strong in math but cannot accurately describe their logical reasoning in English. It is recommended to read the Full Solutions officially released by the University of Waterloo and mimic their style of expression.

Mindset building: The Euclid contest is a contest of "patience." 150 minutes is a long time, and the last two questions may leave you completely puzzled. However, staying calm and continuously trying to find a breakthrough by analyzing small-scale data is often the key to success.

For many students aiming for prestigious schools but facing time constraints in their preparation, the most pressing questions are: Where exactly does its value lie? And if you only have 1-2 months for short-term preparation, how can you focus your efforts effectively to break into the top 25% and win an award?

I. The Euclid Mathematics Contest: Three Dimensions of Its Value

1. A "Special Admission Ticket" to the University of Waterloo: The University of Waterloo's Faculty of Mathematics and its Computer Science department enjoy a stellar reputation in North America. Euclid scores are an important reference indicator for the university's admissions and scholarship awards. If your goal is to major in Mathematics or CS at Waterloo, Euclid is almost a "must-have."

2. An "Invisible Plus" for Top-Tier Universities: The format of the Euclid exam (including both short-answer and full-solution questions) is very similar in logic to the written tests (like MAT, STEP) for Oxford and Cambridge in the UK. Therefore, the Euclid Distinction certificate (top 25% globally) is highly regarded by G5 universities and US Ivy League schools. It demonstrates to admissions officers that you can not only "compute correctly" but also "explain clearly."

3. A Distinctive "Proof of Ability": Unlike the high-intensity multiple-choice format of the US AMC, Euclid emphasizes the logic of the solution process and writing standards. This assessment of "mathematical communication skills" offers a unique differentiating advantage in profile enhancement.

II. Short-Term Prep: Three Core Strategies to Reach the Global Top 25%

To rank among the top 25% of tens of thousands of participants worldwide, you typically need a score of around 68-72 points (varies slightly depending on the difficulty of the current year). In the short term, you don't need to solve all the difficult problems; instead, you should aim to "maximize your returns."

1. Prioritize: "Grind" Questions 1 to 8

Euclid has 10 long-answer questions, each worth 10 points. Difficulty increases with the question number:

• Questions 1-6: Foundational & Advanced levels. Primarily extensions of in-class math. For short-term prep, you must ensure you secure these 60 points without any loss.

• Questions 7-8: Medium to Difficult levels. These are the critical ones for breaking into the top 25%. If you can score half the points on these two questions, combined with the foundational points from the earlier ones, you'll have safely crossed the award threshold.

• Questions 9-10: Extremely Difficult levels. For short-term prep, it's recommended to only attempt the first part of these and use the remaining time to double-check your answers on earlier questions.

2. Master the High-Frequency "Deadly Triangle" of Topics

The topic distribution in Euclid is highly concentrated. Short-term intensive preparation should focus on these three high-yield areas:

• Geometry & Trigonometry: Properties of circles, the law of sines and cosines, and trigonometric identities appear almost every year. Mastering these formulas and their variations can secure at least 20-30 points.

• Analytic Geometry: Setting up coordinate systems to solve plane geometry problems is a common and efficient approach in Euclid.

• Polynomials & Logarithms: Mastering Vieta's formulas, the remainder theorem, and basic logarithmic properties will help. These typically appear in questions 5-7, offering high value for the effort.

3. Grasp the Unspoken Rules for "Full-Solution Questions"

The last few questions in Euclid require you to write out solution steps, with points awarded per step.

Tip: Even if you can't compute the final answer, make sure to write out the key theorem applications, the transformation of given conditions, and a clear logical chain. In Euclid's marking logic, you earn points for each correct step. Clear, neat English mathematical expression can help you gain an extra 3-5 points, which often makes the difference in reaching the 25% certificate threshold.

III. Exam Hall Strategy: The 150-Minute Time Game

A short-term test-taker's strategy should follow the principle of "unbalanced time allocation":

• First 45 Minutes: Clear Questions 1-6. Aim for speed and accuracy. Don't get bogged down on details here; save time.

• Middle 60 Minutes: Aggressively attack Questions 7-8. This is your "point-grabbing zone." You need to calmly derive and try different approaches (like combining algebraic and geometric methods).

• Final 45 Minutes: Review & attempt the first parts of difficult questions. Check Questions 1-6 for any careless mistakes, then try to solve the relatively easier first parts of Questions 9-10.

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However, let's peel back that mysterious veil and discuss a very practical question: Is Euclid suitable for so-called "average students"? If your foundation is average, is it possible to "turn the tables" and aim for an award through preparation?

1. Demystifying: Is Euclid Really Only for "Geniuses"?

First, let’s define the "average student": In this context, it refers to students who excel in regular math classes, have decent logical thinking skills, but haven't undergone systematic Olympiad training.

The conclusion is: Euclid is very suitable for the "average student" to get started.

Three reasons:

Extremely gentle difficulty curve: Euclid consists of 10 long-answer questions. The first 5-6 questions are essentially at an advanced regular math level. As long as you have a solid grasp of high school math basics, scoring points is not difficult.

No "tricky, obscure, or overly difficult" bias: Unlike the occasional highly technical problems in the American AMC series, Euclid's questions are designed to be very "gentle." It values your depth of understanding of concepts and logical expression, rather than testing your IQ ceiling.

Broad award coverage: As long as you rank in the top 25% globally (usually scoring around 60-70 points), you will receive a Certificate of Distinction. For an average student, achieving this certificate through effort offers great value for money.

2. The "Three Major Hurdles" for Average Students Preparing for Euclid

Although suitable, average students aiming for a high score (85+) in Euclid must overcome three major hurdles:

1. The "Context Barrier" of English Proficiency

Euclid is not purely about mathematical calculations; it includes extensive background descriptions. If you don’t understand the logical qualifiers in the questions (e.g., "exactly," "distinct," "at most"), even strong math skills will be useless.

2. The Logical Writing of "Full Solutions"

This is the area average students find most unfamiliar. The later parts of Euclid require writing complete solution steps. Students accustomed to Chinese multiple-choice and fill-in-the-blank questions that "only look at the final answer" often lose significant points due to imprecise steps.

3. The "Breadth" of Knowledge Points

Euclid involves some topics that are not deeply explored in regular Chinese high school curricula, such as advanced trigonometric identities, basic number theory, and recurrence relations.

3. From Beginner to Award Winner: A Four-Step Preparation Method

If you decide to participate in the Euclid contest for the 2026 season, it is recommended to follow this pace for your preparation and improvement:

Phase 1: Eliminate Knowledge Gaps (Solidify Your Foundation)

Average students should not start by tackling the last two questions.

Key areas to focus on: Geometry (properties of circles, applications of trigonometric functions), Algebra (polynomial theorems, logarithms and exponents), and Combinatorics.

Action: Use past syllabi to fill in any missing knowledge points. Ensure you can achieve 100% accuracy on the first six questions during practice.

Phase 2: Targeted Attack (Elevate Your Thinking)

Once you can consistently solve the first six questions, set your sights on questions 7-9.

Core Training: Try solving the same problem using different methods. Euclid favors testing the intersection of knowledge points, such as using geometric methods to solve algebraic optimization problems.

Action: Practice "translating" mathematical language and learn to construct rigorous English solution processes using logical connectors like "Because/Therefore."

Phase 3: Timed "Mock" Tests with Past Papers (Exam Hall Experience)

The Euclid exam duration is 150 minutes, which truly tests your endurance.

Action: Use past papers from the last 10 years and simulate the exam under strict timing. Learn how to allocate your physical and mental energy within the 150 minutes.

Review: Focus on the official "Full Solutions." Compare your steps with the official ones and learn their logic of expression.

Phase 4: Strategic "Reinforcement" and "Letting Go"

For average students, the final part of question 10 is typically reserved for the global top 1%.

Action: In the week before the exam, review formula sheets and memorize high-frequency academic vocabulary. In the exam hall, if you have no idea about question 10, spend your time checking the details of the first eight questions to ensure you "don't lose a single point you deserve."

4. The Value After Winning an Award: The Path to "Gilding" for Average Students

For average students, Euclid results serve two major purposes:

An "Admission Ticket" to the University of Waterloo: As long as you apply to Waterloo's Mathematics, Computer Science, or Engineering programs, Euclid is a mandatory entry requirement. An excellent score significantly increases your chances of admission and qualifies you for substantial entrance scholarships.

"Hard Currency" for Profile Enhancement: Compared to the fiercely competitive AMC, a Euclid certificate effectively demonstrates your logical expression abilities and academic potential when applying to prestigious Commonwealth universities (such as the University of Toronto, McGill, and even Oxford/Cambridge/G5).

Scan the QR Code to Get Free Past Paper Solutions from 1998-2025 + Essential Formulas + Categorized Question Banks!

1998-2025 Past Papers

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