On the international mathematics competition track for academic profile enhancement, the Euclid Mathematics Contest, organized by the University of Waterloo in Canada, has long been hailed as the “golden key” to STEM program applications.
Faced with this high-value international competition, many students and parents are hesitant: “Is the Euclid really difficult to prepare for? If the goal is not just participation, but to achieve a high score and aim for the global top 1%, what exactly should we do?”
This article will provide you with the most in-depth difficulty analysis and high-scoring strategies.
I. Is the Euclid Contest Difficult to Prepare For? A Polarized Difficulty Curve
In the competition community, there is a classic saying about the Euclid: “Easy to win an award, extremely difficult to get a high score.” Its difficulty curve does not rise gradually, but instead shows a steep polarization.
1. Why is it said that “winning an award is not particularly difficult”?
If your goal is to obtain the official Certificate of Distinction (Top 25% globally), the preparation difficulty is relatively manageable.
- High Knowledge Overlap: 70% of the Euclid’s test points overlap heavily with the mathematics of Grade 10 and Grade 11 (Algebra, Geometry, Trigonometry) as well as international curricula (AP Pre-Calculus, IB Math HL).
- Lenient Cutoff Scores: The exam is worth 100 points in total. In previous years, scoring around 70 points was enough to secure a Top 25% certificate. This means that as long as you have a solid foundation in school mathematics and avoid losing marks on the first 7 questions (each worth 10 points), you can easily cross the threshold.
2. Why is it said that “achieving a high score (Top 5% or 1%) is extremely difficult”?
When your goal enters the high-score range of 85 points or even 90 points and above, the Euclid instantly becomes “hell mode.”
- Olympiad-Level Difficulty in the Last 3 Questions: Questions 8, 9, and 10 typically no longer test concrete arithmetic, but introduce highly abstract functional equations, advanced number theory, and complex combinatorics. These problems have no direct analogue in standard textbooks.
- Strict Human Marking Standards: The Euclid includes a large number of “Full-Solution” questions, requiring complete English argumentation steps. The examiners are mathematics professors from the University of Waterloo. Any logical leaps, non-standard notation, or lack of clear explanation will be mercilessly penalized. “Correct answer, but deducted for steps” is a common pitfall in the high-score range.
II. How to Achieve a High Score? Four Core Strategies
To break through the bottleneck and achieve a high score in the exam, you must do the following four things correctly in your preparation:
1. Train in “Rigorous Mathematical English Writing (Communication)”
The Euclid is an exam about “reasoning.” From now on, when practicing long-answer questions, never just write a list of formulas and a final number.
- High-Score Action: Standardize the use of mathematical connective words. For example, use “Assume” to introduce variables, use “Since… Therefore…” to explain causal relationships, and use “Case 1 / Case 2” to demonstrate the completeness of your classification discussion. Turn your solution into a logically rigorous and well-structured “mathematical essay.”
2. Conquer High-Frequency “Cross-Module Composite” Problems
Recent trends show that high-score questions increasingly favor “cross-disciplinary combinations.”
- High-Score Action: Focus on targeted practice of composite problems such as “Geometry + Analytic Geometry + Probability” or “Sequences + Number Theory.” For example, in a coordinate system of analytic geometry, use advanced trigonometric functions to derive a general formula for the area of a polygon. When reviewing, try to connect the knowledge networks of Algebra, Geometry, and Number Theory, and avoid memorizing formulas in isolation.
3. Master “Advanced Mathematical Tools” for the Last 3 Questions
To break through Questions 8–10, relying solely on high school knowledge will be very painful. You need to equip yourself with some competition-level “dimensionality-reduction weapons” in advance.
- High-Score Action: Systematically supplement your knowledge of elementary number theory (such as congruence equations, the Chinese Remainder Theorem, Wilson’s Theorem) as well as recurrence relations and dynamic programming concepts in combinatorics. These tools will allow you to instantly see the underlying logic of abstract algebraic derivations.
4. Practice “Staged Time Allocation” and “Point-Scavenging Tactics”
The 150-minute exam time may seem ample, but poor allocation can easily lead to a collapse in the second half.
- High-Score Action:
- First 45 minutes: Rush through Questions 1–5, aiming for 100% accuracy to save time for later.
- Minutes 45–90: Steadily tackle Questions 6 and 7.
- Final 60 minutes: Switch to “point-scavenging mode” for difficult problems. Faced with Questions 9 and 10, even if you cannot produce a complete final proof, be sure to solve part (a) (which usually involves plugging in numbers to verify a model) and write down the core formulas and boundary conditions you used in part (b). In the Euclid arena, scavenging just 3 process points can advance your ranking by several percentage points at the provincial or global level.
Frequently Asked Questions
Is the Euclid difficult to prepare for?
The honest answer is that the difficulty curve is polarised rather than steep. Reaching an award is achievable for a student with a solid school foundation and a season of focused work. Reaching a high score is a different problem, because the last few questions ask for sustained multi-step reasoning written out in full. Most students find that the gap between those two outcomes is larger than they expected.
What separates a high score from an award?
Writing. Students who reach the award band usually get there on the earlier questions, which are answerable with school-level technique. Students who reach the high bands do so by collecting partial marks on questions they did not fully finish, and partial marks only exist where the argument is legible. Training the writing is the cheapest available route from one band to the next.
How long should preparation take?
Plan in seasons rather than weeks. A student starting from a solid school foundation typically needs the months from late spring through to the sitting, with the summer used for topic gaps and the winter for whole timed papers. Compressing it into the final six weeks is possible but tends to produce speed without the writing habit, which is the part the paper actually marks.