The Euclid Mathematics Contest, organized by the University of Waterloo, Canada, is one of the most influential high school math competitions world-wide. It carries significant weight, especially when applying to top Canadian universities (such as University of Toronto, UBC, Waterloo) as well as STEM programs in the UK and US. Its biggest characteristic is not simply "calculating the correct answer", but "writing a clear, rigorous, and complete reasoning process". This article systematically covers exam details, scoring rules, pre-exam preparation, and answer strategies to help you avoid common traps and maximize your scoring potential.
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 |
Skipping steps, making baseless assertions, or breaking logical flow → Even if the answer is correct, you may receive 0 points;
Clear steps, logical consistency, reasonable attempts → Even if miscalculated, you can still get 6–8 points per question.
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?
