In the tide of applying to prestigious overseas universities, transitioning to an international track, or enhancing academic backgrounds, the Euclid Mathematics Contest, hosted by the University of Waterloo in Canada, has long been hailed as the “TOEFL of the mathematics world” due to its official endorsement and high value.
The philosophy behind the Euclid’s problem-setting is fundamentally different from that of the Chinese Gaokao and its mock exams. As long as you follow a precise phased strategic plan and master a scientific preparation approach, students with an average foundation in Chinese mathematics can successfully win a global award.
I. Why Can Students with “An Average Foundation in Chinese Mathematics” Still Succeed in the Euclid?
To overcome fear, we must first recognize the two completely different underlying logics in the core assessment of Chinese high school mathematics and the Canadian Euclid Contest:
The essence of Chinese high school mathematics is “high-pressure, large-volume problem-solving and speed testing”: Chinese high school mathematics (whether in the Gaokao system or various mock exams) places extreme emphasis on computational volume, complex classification discussions, and various tricky composite functions and conic section deformation problems. If your thinking is not fast enough, or if you are not good at grinding through extremely difficult problems under time pressure, your school grades will naturally appear “average.”
The essence of the Euclid Contest is “light on formulas, heavy on logic, with a smooth gradient”: The Euclid gives you 150 minutes to solve 10 long-answer questions (100 points total), providing ample time. More importantly, the difficulty of the questions increases in a strictly stepwise manner. Questions 1 to 7 are foundational to intermediate, testing topics (such as basic quadratic equations, similar triangles, and basic analytic geometry) that, from the perspective of Chinese high school students, are not only not difficult but could even be described as “extremely friendly.”
Core Winning Formula: The cutoff for the Euclid’s global top 25% (Distinction) has historically been stable at around 65–70 points. This means you do not need to tackle the final Questions 9 and 10, which are designed to identify top-tier geniuses. As long as you leverage the solid foundational skills of a Chinese high school student to secure the first 7 questions (securing a base of 70 points), even if you only write down the first few core steps on the last three questions to earn scattered process marks, you will have already firmly crossed the global award line!
II. Say No to Blind Practice! A Three-Phase “Dark Horse Comeback” Preparation Plan for the Euclid
To help students with an average foundation avoid detours, we have tailored a phased scientific preparation roadmap for you:
1. Comprehensive “Full-Subject Gap-Filling” to Bridge International Test Discrepancies: 4–5 Months Before the Exam
Core Task: Although Chinese high school mathematics is solid, there is about a 20% “misalignment” in test points with the Euclid, which must be addressed first.
Specific Execution: Focus your efforts on conquering the three major golden areas that are not heavily emphasized in Chinese high school but are consistently tested in the Euclid:
- Logarithms and Exponential Operations: Master the change of base formula for logarithms and solving logarithmic equations.
- Combinatorics and Probability: Systematically learn the binomial theorem, the principle of inclusion-exclusion (PIE), and non-repetitive, non-omissive counting methods.
- Advanced Trigonometric Transformations: Become thoroughly proficient in applying the sine rule and cosine rule to geometric figures.
2. Targeted Practice on “Questions 1–7” to Meticulously Polish Your Foundation: 2–3 Months Before the Exam
Core Task: Students with an average foundation should not start by tackling Questions 9 and 10 of the full past papers. Your goal is a 100% conversion rate on the first 7 questions.
Specific Execution: Categorize and retrieve Euclid past papers from the last 10 years, and practice the first 7 questions by module, such as “Algebraic Equations,” “Analytic Geometry,” and “Summation of Sequences.” Every time you get a question wrong, reflect in your error notebook: Did I get stuck because I didn’t understand the English problem statement, or did I make a mistake in formula transformation? Ensure that the first 70 points of the exam are securely in your pocket.
3. Full-Length Timed Mock Exams and Special Training in “Full English Academic Writing Standards”: 1 Month Before the Exam
Core Task: Adapt to the 150-minute exam pressure and bridge the gap from “being able to solve the problem” to “being able to write a full-mark solution process.”
Specific Execution: The latter half of the Euclid paper consists of full-graded long-answer questions, where errors in the process will be severely penalized. Force yourself to simulate a closed-book exam, writing your answers in full English strictly according to the official high-scoring templates. Train yourself to use rigorous mathematical connectors. At the same time, figure out your time management strategy: aim to clear the first 7 questions within 60–70 minutes, leaving a full 80 minutes to tackle Question 8 and the first parts of Questions 9 and 10, aggressively picking up process marks.
III. Essential Tips for Dark Horse Award Winners: A Guide to Avoiding Pitfalls in Full English Long-Answer Writing
Students with an average foundation are most likely to encounter pitfalls in the full-graded (long-answer) section during the third phase of preparation:
⚠ Fatal Writing Pitfall: Jumping Logic and Lack of Connective Words
Chinese students are accustomed to the fast pace of “calculating on scratch paper and directly writing the core formulas and final answers on the answer sheet.” However, the Euclid is marked by human evaluators who place great emphasis on Communication Skills (academic communication and reasoning ability).
How to Avoid: Even if your final numerical answer is completely correct, if you omit the intermediate algebraic derivation steps, the examiner will mercilessly deduct 2–3 process marks. Remember: when writing long-answer questions, always assume the examiner is a “beginner who knows nothing.” Every new variable you introduce must be clearly defined; every geometric theorem you use must state its prerequisites. Present your complete chain of thought in a standardized, rigorous manner. This is your absolute guarantee for securing all the process marks on Questions 5 to 8.
Frequently Asked Questions
Can a student with an average school record do well here?
It happens more often than parents expect, because the two systems test different things. A domestic curriculum trains fast, accurate technique against familiar question types. This paper asks for reasoning written out for a reader, which is a skill most students have never been graded on. That resets the field somewhat: being average at one does not predict being average at the other.
Which gaps usually need closing first?
Two. The first is topic coverage where the syllabuses differ — some areas that appear on this paper get lighter treatment in a domestic classroom. The second, and larger, is written English mathematical argument: connective words, stated assumptions, a visible line of reasoning. The second gap is the one students underestimate, and it is the one that costs marks on every long-answer question.
What does a realistic plan look like?
Three phases. Close the topic gaps first, while there is still time to learn rather than revise. Then move to whole problems written out in full, marked against worked solutions rather than answer keys. Finally sit timed papers to build pace. Students who invert this — starting with timed papers — usually build speed on top of an argument style that will not score.