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For many students aiming for prestigious schools but facing time constraints in their preparation, the most pressing questions are: Where exactly does its value lie? And if you only have 1-2 months for short-term preparation, how can you focus your efforts effectively to break into the top 25% and win an award?

I. The Euclid Mathematics Contest: Three Dimensions of Its Value

1. A "Special Admission Ticket" to the University of Waterloo: The University of Waterloo's Faculty of Mathematics and its Computer Science department enjoy a stellar reputation in North America. Euclid scores are an important reference indicator for the university's admissions and scholarship awards. If your goal is to major in Mathematics or CS at Waterloo, Euclid is almost a "must-have."

2. An "Invisible Plus" for Top-Tier Universities: The format of the Euclid exam (including both short-answer and full-solution questions) is very similar in logic to the written tests (like MAT, STEP) for Oxford and Cambridge in the UK. Therefore, the Euclid Distinction certificate (top 25% globally) is highly regarded by G5 universities and US Ivy League schools. It demonstrates to admissions officers that you can not only "compute correctly" but also "explain clearly."

3. A Distinctive "Proof of Ability": Unlike the high-intensity multiple-choice format of the US AMC, Euclid emphasizes the logic of the solution process and writing standards. This assessment of "mathematical communication skills" offers a unique differentiating advantage in profile enhancement.

II. Short-Term Prep: Three Core Strategies to Reach the Global Top 25%

To rank among the top 25% of tens of thousands of participants worldwide, you typically need a score of around 68-72 points (varies slightly depending on the difficulty of the current year). In the short term, you don't need to solve all the difficult problems; instead, you should aim to "maximize your returns."

1. Prioritize: "Grind" Questions 1 to 8

Euclid has 10 long-answer questions, each worth 10 points. Difficulty increases with the question number:

• Questions 1-6: Foundational & Advanced levels. Primarily extensions of in-class math. For short-term prep, you must ensure you secure these 60 points without any loss.

• Questions 7-8: Medium to Difficult levels. These are the critical ones for breaking into the top 25%. If you can score half the points on these two questions, combined with the foundational points from the earlier ones, you'll have safely crossed the award threshold.

• Questions 9-10: Extremely Difficult levels. For short-term prep, it's recommended to only attempt the first part of these and use the remaining time to double-check your answers on earlier questions.

2. Master the High-Frequency "Deadly Triangle" of Topics

The topic distribution in Euclid is highly concentrated. Short-term intensive preparation should focus on these three high-yield areas:

• Geometry & Trigonometry: Properties of circles, the law of sines and cosines, and trigonometric identities appear almost every year. Mastering these formulas and their variations can secure at least 20-30 points.

• Analytic Geometry: Setting up coordinate systems to solve plane geometry problems is a common and efficient approach in Euclid.

• Polynomials & Logarithms: Mastering Vieta's formulas, the remainder theorem, and basic logarithmic properties will help. These typically appear in questions 5-7, offering high value for the effort.

3. Grasp the Unspoken Rules for "Full-Solution Questions"

The last few questions in Euclid require you to write out solution steps, with points awarded per step.

Tip: Even if you can't compute the final answer, make sure to write out the key theorem applications, the transformation of given conditions, and a clear logical chain. In Euclid's marking logic, you earn points for each correct step. Clear, neat English mathematical expression can help you gain an extra 3-5 points, which often makes the difference in reaching the 25% certificate threshold.

III. Exam Hall Strategy: The 150-Minute Time Game

A short-term test-taker's strategy should follow the principle of "unbalanced time allocation":

• First 45 Minutes: Clear Questions 1-6. Aim for speed and accuracy. Don't get bogged down on details here; save time.

• Middle 60 Minutes: Aggressively attack Questions 7-8. This is your "point-grabbing zone." You need to calmly derive and try different approaches (like combining algebraic and geometric methods).

• Final 45 Minutes: Review & attempt the first parts of difficult questions. Check Questions 1-6 for any careless mistakes, then try to solve the relatively easier first parts of Questions 9-10.

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However, let's peel back that mysterious veil and discuss a very practical question: Is Euclid suitable for so-called "average students"? If your foundation is average, is it possible to "turn the tables" and aim for an award through preparation?

1. Demystifying: Is Euclid Really Only for "Geniuses"?

First, let’s define the "average student": In this context, it refers to students who excel in regular math classes, have decent logical thinking skills, but haven't undergone systematic Olympiad training.

The conclusion is: Euclid is very suitable for the "average student" to get started.

Three reasons:

Extremely gentle difficulty curve: Euclid consists of 10 long-answer questions. The first 5-6 questions are essentially at an advanced regular math level. As long as you have a solid grasp of high school math basics, scoring points is not difficult.

No "tricky, obscure, or overly difficult" bias: Unlike the occasional highly technical problems in the American AMC series, Euclid's questions are designed to be very "gentle." It values your depth of understanding of concepts and logical expression, rather than testing your IQ ceiling.

Broad award coverage: As long as you rank in the top 25% globally (usually scoring around 60-70 points), you will receive a Certificate of Distinction. For an average student, achieving this certificate through effort offers great value for money.

2. The "Three Major Hurdles" for Average Students Preparing for Euclid

Although suitable, average students aiming for a high score (85+) in Euclid must overcome three major hurdles:

1. The "Context Barrier" of English Proficiency

Euclid is not purely about mathematical calculations; it includes extensive background descriptions. If you don’t understand the logical qualifiers in the questions (e.g., "exactly," "distinct," "at most"), even strong math skills will be useless.

2. The Logical Writing of "Full Solutions"

This is the area average students find most unfamiliar. The later parts of Euclid require writing complete solution steps. Students accustomed to Chinese multiple-choice and fill-in-the-blank questions that "only look at the final answer" often lose significant points due to imprecise steps.

3. The "Breadth" of Knowledge Points

Euclid involves some topics that are not deeply explored in regular Chinese high school curricula, such as advanced trigonometric identities, basic number theory, and recurrence relations.

3. From Beginner to Award Winner: A Four-Step Preparation Method

If you decide to participate in the Euclid contest for the 2026 season, it is recommended to follow this pace for your preparation and improvement:

Phase 1: Eliminate Knowledge Gaps (Solidify Your Foundation)

Average students should not start by tackling the last two questions.

Key areas to focus on: Geometry (properties of circles, applications of trigonometric functions), Algebra (polynomial theorems, logarithms and exponents), and Combinatorics.

Action: Use past syllabi to fill in any missing knowledge points. Ensure you can achieve 100% accuracy on the first six questions during practice.

Phase 2: Targeted Attack (Elevate Your Thinking)

Once you can consistently solve the first six questions, set your sights on questions 7-9.

Core Training: Try solving the same problem using different methods. Euclid favors testing the intersection of knowledge points, such as using geometric methods to solve algebraic optimization problems.

Action: Practice "translating" mathematical language and learn to construct rigorous English solution processes using logical connectors like "Because/Therefore."

Phase 3: Timed "Mock" Tests with Past Papers (Exam Hall Experience)

The Euclid exam duration is 150 minutes, which truly tests your endurance.

Action: Use past papers from the last 10 years and simulate the exam under strict timing. Learn how to allocate your physical and mental energy within the 150 minutes.

Review: Focus on the official "Full Solutions." Compare your steps with the official ones and learn their logic of expression.

Phase 4: Strategic "Reinforcement" and "Letting Go"

For average students, the final part of question 10 is typically reserved for the global top 1%.

Action: In the week before the exam, review formula sheets and memorize high-frequency academic vocabulary. In the exam hall, if you have no idea about question 10, spend your time checking the details of the first eight questions to ensure you "don't lose a single point you deserve."

4. The Value After Winning an Award: The Path to "Gilding" for Average Students

For average students, Euclid results serve two major purposes:

An "Admission Ticket" to the University of Waterloo: As long as you apply to Waterloo's Mathematics, Computer Science, or Engineering programs, Euclid is a mandatory entry requirement. An excellent score significantly increases your chances of admission and qualifies you for substantial entrance scholarships.

"Hard Currency" for Profile Enhancement: Compared to the fiercely competitive AMC, a Euclid certificate effectively demonstrates your logical expression abilities and academic potential when applying to prestigious Commonwealth universities (such as the University of Toronto, McGill, and even Oxford/Cambridge/G5).

Scan the QR Code to Get Free Past Paper Solutions from 1998-2025 + Essential Formulas + Categorized Question Banks!

1998-2025 Past Papers

Categorized Question Booklets + Preparation Books