The Euclid Mathematics Contest is organized by the University of Waterloo in Canada. It is one of the most influential high school mathematics contests globally, holding particularly high value when applying to top Canadian universities (like the University of Toronto, UBC, Waterloo) and for science/engineering/economics programs in the UK and US. Known for "emphasizing thinking over tricks, with strong practical application," it is often called the "SAT of Mathematics."
The following provides a comprehensive breakdown of the key points for preparing for the 2026 Euclid Contest from four dimensions: contest features, award setting, question structure, core topics, and preparation strategies.
I. Three Distinct Features of the Euclid Contest
1. Moderate Award Difficulty: Top 25% Wins an Award
Simple Award Setting: It only offers a Certificate of Distinction, awarded to the top 25% of participants globally.
High Actual Award Rate: Due to high participation and skill level among many Asian students, Chinese students can typically secure a place in the top 25% with a stable score of around 70+ (out of 100).
Lower Psychological Pressure: There's no need to struggle desperately with the last question. The focus is on zero errors in basic questions + high scores in mid-level questions.
Compared to other contests (e.g., AMC12 requires top 5% for AIME), Euclid is more friendly to "non-olympiad students."
2. Humanized Scoring: Partial Marks Protection Mechanism
Partial marks for steps: For some questions, even if the final answer is wrong, writing key steps (e.g., setting up the correct equation, drawing auxiliary lines, writing recurrence relations) can still earn 1–3 points.
Avoids the "all or nothing" trap: For example, in a geometry proof, points can be earned for writing the criteria for similar triangle determination, even without completing the entire derivation.
Encourages attempt: Even if you can't solve the problem completely, write down relevant formulas or ideas!
3. Limited Topic Scope: No Calculus
Low mathematical tool requirement: Only requires mathematics up to the high school sophomore level, not involving advanced content like derivatives, integrals, matrices, or complex numbers.
Core competency-oriented: The focus is not on "how many formulas you know," but on logical reasoning, model abstraction, and flexible application skills.
Some problems have a "brain teaser" quality: e.g., the 2024 Question 3 revealed hidden symmetry through simple algebraic manipulation.
Suitable for: Students who have learned high school mathematics but haven't undergone systematic olympiad training can aim for high scores with a solid foundation.
II. Question Structure and Scoring Strategy (10 Questions / 150 minutes)
| Question Numbers | Difficulty Level | Target Strategy | Score Proportion |
|---|---|---|---|
| 1–7 | Basic & Intermediate | Steady and sure, aim for full marks (Accurate calculation + Standard procedure) |
≈60–70 points |
| 8–9 | Medium-High Difficulty | Key for score differentiation Requires integrated use of multiple topics, mastery of case analysis, reverse thinking |
≈20–25 points |
| 10 | High-Difficulty Innovative Question | For top contestants Often integrates number theory + combinatorics + algebra, requires constructive thinking |
≈10 points |
Core Strategies:
If the goal is top 25% (≈70 points) → Ensure all questions 1–7 are correct + secure about half the points from questions 8–9.
If the goal is top 5% (≈85+ points) → Need near-perfect scores on questions 8–9, and strive for partial marks on question 10.
III. In-Depth Topic Breakdown: 3 Major Modules
Module 1: Foundation Module (70%, Foundation for Stable Scores)
| Sub-module | Proportion | Core Content | Preparation Key Points |
|---|---|---|---|
| Algebra | 30% | Equations/Inequalities (including radical, fractional), Function Graphs (Exponential/Logarithmic), Algebraic Identity Transformation | Pay attention to variable domains, substitution techniques; many lost points on 2025 Q1 due to ignoring range. |
| Geometry | 35% | Plane Geometry (Congruence/Similarity, Power of a Point Theorem, Area), Analytic Geometry (Line/Circle Equations) | An area of strength for Chinese students! But requires standardized writing, e.g., must state the basis like "by the Chord Perpendicular Bisector Theorem...". |
| Trigonometry | 5% | Basic Definitions, Identities (sin²x+cos²x=1), Graph Properties | Usually 1 question, mastering the formulas is sufficient. |
Module 2: Extension Module (30%, Key for High Scores)
| Sub-module | Proportion | Core Content | Typical Question Types |
|---|---|---|---|
| Number Theory | 10% | Prime Numbers, GCD/LCM, Congruence, Divisibility | 2024 Q10: Prime Factorization → Derive Divisibility Rules → Rigorous Proof |
| Combinatorics & Probability | 20% | Permutations & Combinations (Case Enumeration, Stars and Bars), Classical Probability, Recurrence Thinking | 2025 Q7: "Probability + Sequence" combined; requires mastery of symmetry simplification, complementary set thinking. |
IV. Two Recent Question Trends
Trend 1: Cross-Topic Integration
Purely single-topic questions are decreasing. More questions require cross-domain linkage:
Using algebraic methods to solve geometry optimization problems (e.g., setting variables to build functions to find extremes).
Using number theory to analyze combinatorial structures (e.g., using modular arithmetic to determine permutation parity).
Probability + Sequences, Geometry + Trigonometry have become common.
Trend 2: Enhanced Mathematical Reading Comprehension
Problem statements often embed real-world scenarios (environmental protection, economics, population growth).
Candidates must first abstract the mathematical model from the text:
Example: 2025 Q8 described "city population growing 5% annually," requiring recognition as a geometric sequence and establishing a recurrence relation.
Key ability: Information extraction → Model recognition → Mathematical transformation.
Categorized Exercise Book + Competition Prep Book
