Below is an introduction to the Euclid competition rules, the knowledge points tested, and preparation strategies. Click to view the detailed descriptions.
Euclid Mathematics Competition Rules
2026 Competition Dates (Updated):
North and South America: March 31, 2026
Outside North and South America: April 1, 2026
1. Eligibility
High school students in any grade may participate. Most participants are in Grades 9–12.
2. Competition Format
Duration: 2.5 hours
Venue: Online (requires a computer with a camera and a mobile device)
Participation: Individual, paper‑and‑pencil exam
3. Exam Content
Total Score: 100 points
Number of Questions: 10 questions (short‑answer and full‑solution), each with 2–3 parts
Language: Full English paper
Part 1 contains relatively straightforward questions designed to test students’ basic mathematical knowledge and skills.
Part 2 includes more complex problems that assess students’ advanced mathematical understanding, creative thinking, and ability to solve sophisticated problems.
4. Scoring Rules
Each question usually has 2–3 parts.
At the beginning of each question, it is labeled as either short answer (only the answer is required) or full solution (a complete solution process is needed).
It is important to note that full‑solution questions do not require an overly elaborate presentation. Students can earn most of the marks by presenting clear reasoning, answering the question properly, and ensuring that steps are written on the answer sheet rather than on scratch paper. Conversely, poorly presented solutions may result in significant mark deductions. Most questions are at the high school level, while the final few questions challenge students with advanced mathematical abilities.
5. Important Notes
Calculators are permitted, and most calculators can be used except those with the following functions: internet access; data storage; computer algebra systems; communication with other devices; or dynamic geometry software.
The University of Waterloo will award a Certificate of Distinction to students whose final scores place them in the top 25% of all participants.
6. Release of Results
Results are typically announced in late May, when the official organizing committee publishes the cut‑off scores and the list of award winners.
7. Awards
Individual Awards
Certificate of Distinction: Awarded to students who rank in the top 25% of all participants worldwide.
Contest Medal: Presented by the CEMC to the top student at each school.
Honour Rolls: High‑scoring students are recognized in separate honour rolls for
Canadian official contestants
Canadian unofficial contestants
international contestants
Plaque: The top 5 official Canadian contestants receive a plaque and a CAD 500 prize.
The 6th–15th ranked official Canadian contestants receive a CAD 200 prize.
Team Awards
Schools may optionally participate in the team ranking, which is based on the sum of the scores of the top 3 official contestants from the school.
In Canada, three levels of team awards are available: Zone, Provincial, and National.
Canadian schools may be awarded:
Canadian Championship Plaque
Provincial Championship Plaques
Zone Championship Certificates
Euclid Exam Topics / Knowledge Points Tested in the Euclid Competition
The knowledge points tested in the Euclid Mathematics Competition mainly focus on the following areas: basic algebraic operations and sequences, polynomials, plane geometry, analytic geometry, equation solving, number theory, combinatorics and probability, trigonometric identities and trigonometric functions, and logarithms.
The Euclid places greater emphasis on testing students’ mathematical reasoning, so it has relatively high requirements for the clarity and completeness of their solution processes.
Algebra Section
Algebraic operations and solving equations account for approximately 30% of the Euclid Mathematics Competition. These questions mainly assess students’ abilities in algebraic manipulation and equation solving. In addition, there are occasionally some relatively less common topics such as sequences and polynomials.
Geometry Section
In the Euclid Mathematics Competition, plane geometry and analytic geometry account for a relatively high proportion of the total score, approximately 35%. Geometry questions mainly involve calculating areas or side lengths, as well as proving area divisions, proportional relationships between side lengths, or size relationships.
Trigonometry
In the Euclid Mathematics Competition, problems involving trigonometric identities, trigonometric functions, or solving trigonometric equations usually appear in questions 7 to 9, and are often referred to as “bonus questions” for Chinese students. Chinese students are generally very familiar with these two types of problems, so they have a clear advantage when dealing with these calculation‑oriented questions. However, in most cases, if a logarithm question appears, it is unlikely that a trigonometry question will also appear.
Combinatorics and Probability
Combinatorics and probability are mandatory topics. They usually appear in questions 5–7, or in question 10 in combination with other topics.
Number Theory Section
Number theory questions do not appear very often in the Euclid Mathematics Competition. They are frequently combined with counting problems and are usually placed in question 9 or 10.
Key Points for Preparing for the Euclid Competition
I. Clarify the Exam Rules
Composition of the Exam / Structure of the Questions
The Euclid exam consists of 10 main questions, each worth 10 points, for a total of 100 points.
Questions 1–8 each consist of 2–3 sub‑questions that are not related to one another, essentially forming around twenty independent problems.
Questions 9–10 each consist of 2–4 sub‑questions that are interconnected.
Composition of the Exam Paper
Each sub‑question of the 10 main questions is marked with either a “light bulb” or a “handwritten” symbol. For questions 1–8, each light‑bulb sub‑question is generally worth 3 points, and the remaining points are allocated to the final handwritten sub‑question. For questions 9–10, points are distributed according to the number of sub‑questions.
For questions marked with a “light bulb” symbol, providing the correct answer alone is sufficient for full marks. If the answer is incorrect but the steps are correct, partial credit may still be awarded for the working shown.
For questions marked with a “handwritten” symbol, points are awarded based on the steps shown. Providing only the correct answer without any reasoning will result in a deduction. To receive full marks, all reasoning and logical arguments must be presented completely and clearly.
II. Develop a Study Strategy
Building a strong foundation is essential
Make sure you have a solid grasp of fundamental mathematical knowledge, including algebra, geometry, number theory, and other relevant areas. Review your high school math curriculum, with a special focus on content related to competitions. You can use textbooks, video lectures, and other resources to reinforce your understanding of basic concepts, theorems, and methods.
Practice past papers to improve problem‑solving skills
Doing a large number of practice problems is an effective way to enhance your problem‑solving abilities. Choose targeted problem sets or competition question banks that cover all the key topics and question types tested in the competition. Gradually increase the difficulty level to build your capacity for solving complex problems. At the same time, focus on understanding the mathematical principles and reasoning behind each question, rather than simply memorizing answers.
Take mock exams to sharpen test‑taking skills
Participating in mock exams allows you to simulate the real competition environment, helping you adapt to the time constraints and pressure in advance. After each mock exam, carefully analyze your paper to identify areas where your problem‑solving is weak, adjust your study strategy promptly, and strengthen training on those weaknesses. Through continuous mock exams, you can improve your test‑taking skills and answer efficiency.
Address weaknesses with targeted practice
During your preparation, pay close attention to filling knowledge gaps and resolving any doubts or misunderstandings in a timely manner. Seek help from teachers, classmates, or by joining study groups or tutoring courses. At the same time, focus on reflecting on and summarizing your mistakes, identifying their root causes, and addressing them to avoid repeating similar errors.
III. Use a calculator wisely
In the Euclid Competition, students are allowed to bring a calculator (which must not have programming, graphing, internet communication, or storage capabilities), so it is important to make sure you have an appropriate calculator ready. Although a calculator is permitted, the Euclid does not feature problems that rely purely on heavy computation. However, some simpler questions may still be solved through straightforward calculation. Therefore, it is essential to learn how to use your calculator effectively for verification and solving equations.
