Category: Blog

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.