Most parents first hear about the Euclid Mathematics Contest through their child’s school, or through another parent whose Grade 12 student has just written it. The name is familiar; what it actually represents — and why a strong result matters as much as it does — is less well understood. This guide explains what the Euclid Mathematics Contest is, how it works, what results look like, and why it has earned a reputation as the most significant mathematics credential available to a Canadian high school student.
What is the Euclid Mathematics Contest?
The Euclid Mathematics Contest is a senior-level mathematics competition for Grade 12 students, run by the Centre for Education in Mathematics and Computing (CEMC) at the University of Waterloo. It is the flagship competition in the CEMC series — the same series that begins with the Gauss Contest in Grades 7 and 8 and runs through Pascal, Cayley, and Fermat in Grades 9 to 11.
The contest was first held in the 1970s. It has grown from around 300 participants annually in its early years to more than 20,000 students from approximately 2,000 schools worldwide, including around 8,000 international participants each year. Canadian students make up the core of the competition; it is also written internationally, with Chinese students making up the largest group outside Canada.
The contest takes place in April each year and is written at school through registered CEMC centres.
What makes the Euclid different from every other CEMC contest
Every other competition in the CEMC series — Gauss, Pascal, Cayley, Fermat — is multiple choice. Students select from five options. The Euclid is fundamentally different: it requires full written solutions.
Students must construct complete mathematical arguments, show every step of their reasoning, and communicate their thinking clearly in writing. Partial marks are awarded for correct reasoning even when a final answer is wrong. This means the contest does not just test whether a student can get the right answer — it tests whether they can think mathematically and explain why.
This is why the Euclid carries a weight that no other pre-university mathematics assessment in Canada matches. A strong result demonstrates not just content knowledge but genuine mathematical maturity.
| Feature | Gauss / Pascal / Cayley / Fermat | Euclid Mathematics Contest |
|---|---|---|
| Format | Multiple choice | Full written solutions |
| Partial marks | No | Yes |
| Time | 60 minutes | 150 minutes |
| Questions | 25 | 10 (with multiple parts) |
| What it tests | Speed and accuracy | Reasoning and communication |
| University relevance | Developmental | Direct admissions weight |
The Euclid Mathematics Contest format
The contest consists of 10 questions, each with multiple parts — typically labelled (a), (b), and (c). The structure is designed deliberately:
- Part (a) of each question is accessible to well-prepared students
- Part (b) requires more sustained reasoning
- Part (c) is designed to challenge the strongest students nationally
The total marks available is 100. Students have 150 minutes. Calculators are permitted for numerical calculations, but all mathematical steps must be shown and justified in writing.
The difficulty progression within each question — and across the 10 questions — means that most students will complete the early parts of most questions, while only a small number will complete all parts of the hardest questions. This graduated structure is intentional: it produces a meaningful spread of scores that distinguishes between strong, very strong, and exceptional students.
Euclid Mathematics Contest results and recognition
Average scores and what they mean
The average score in the 2024 Euclid Contest was 54.3 out of 100. This reflects the contest’s design — it is intended to challenge even well-prepared students, and a score significantly above the average represents a genuinely strong mathematical performance.
The 2025 results followed a similar pattern. Top-scoring students were recognised on the Honour Roll, with results published on the CEMC website. Students may opt out of having their names publicly listed while still receiving recognition through their school.
Certificates of Distinction
Among all participants, the top 25% of students receive a Certificate of Distinction. This is the primary recognition for strong performers who do not reach the Honour Roll. For university applications, a Certificate of Distinction signals that a student placed in the top quarter of a national and international competition — a meaningful credential alongside a transcript.
Honour Roll
The Honour Roll recognises the highest-scoring students nationally. Students listed on the Honour Roll receive a prize of $200 from the CEMC; students who receive a plaque — the highest individual recognition — receive $500. Honour Roll students are typically those whose scores place them among the strongest mathematics students in Canada for their year.
Awards summary
| Recognition | Criteria | Prize |
|---|---|---|
| Certificate of Distinction | Top 25% of all participants | Certificate |
| Honour Roll | High-scoring students by region | $200 |
| Plaque | Top individual performers | $500 |
Why the Euclid Mathematics Contest matters for university admissions
The University of Waterloo is Canada’s leading university for mathematics, computer science, and engineering. Its Faculty of Mathematics is among the most selective in the country, and competition for entrance scholarships is significant.
While the Euclid Contest is not required for admission to the Faculty of Mathematics at the University of Waterloo, strong performance can help a student earn admission. To be considered for a Faculty of Mathematics entrance scholarship, applicants are strongly encouraged to participate in at least one of the Canadian Senior Mathematics Contest or the Euclid Contest during the school year in which they are applying.
In practice, this means the Euclid is effectively a required component of a competitive application to Waterloo Mathematics, Computer Science, or Engineering. A student who does not write it — or who writes it but performs poorly — is at a disadvantage compared to applicants who have a strong result to present.
Beyond Waterloo, the Euclid result is recognised by other North American universities as evidence of mathematical ability. The contest results have gained widespread recognition among North American universities, sometimes described informally as the ‘TOEFL of Mathematics’ for competitive mathematics programmes.
What a strong Euclid result signals to universities
A student who scores well above the average on the Euclid has demonstrated:
- Mastery of advanced high school mathematics content across all major topic areas
- The ability to construct and communicate complete mathematical arguments
- Performance under timed, high-stakes conditions without multiple choice support
- A level of mathematical maturity that distinguishes them from peers who have only been assessed through curriculum-based examinations
None of these things are easily demonstrated through a transcript alone. This is why admissions teams at selective programmes pay attention to Euclid results in a way they do not for most other extracurricular achievements.
What the Euclid Mathematics Contest tests
The Euclid draws on the full scope of the Ontario Grade 12 mathematics curriculum and beyond. The main topic areas that appear consistently across past papers:
| Topic area | What appears in Euclid problems |
|---|---|
| Algebra and equations | Polynomial equations, systems of equations, algebraic manipulation |
| Functions | Transformations, composite functions, inverse functions |
| Trigonometry | Identities, equations, sine and cosine rules, triangle problems |
| Sequences and series | Arithmetic and geometric sequences, summation problems |
| Combinatorics | Counting, permutations and combinations, probability |
| Geometry | Circle theorems, coordinate geometry, proof-based problems |
| Number theory | Divisibility, primes, modular arithmetic |
| Logarithms and exponents | Laws of logarithms, exponential equations |
No single past paper tests all of these equally. The topic mix varies year to year, which is part of what makes preparation challenging — students cannot predict which areas will be emphasised and must be competent across all of them.
The hardest Euclid problems (typically parts (b) and (c) of questions 8–10) require students to combine multiple topic areas in a single solution and to reason through unfamiliar problem structures. This is what distinguishes the Euclid from curriculum examinations: the problems are not testing whether students have memorised content, but whether they can use it flexibly.
The Euclid Mathematics Contest in the context of Canadian math competitions
The CEMC series is not the only mathematics competition available to Canadian students. Here is how the Euclid sits relative to other options:
| Competition | Level | Format | Who it suits |
|---|---|---|---|
| Euclid Mathematics Contest | Grade 12 | Full written solutions | Top Canadian high school students |
| Canadian Senior Mathematics Contest (CSMC) | Grade 11–12 | Mixed format | Strong students below Euclid level |
| AMC 10/12 | Grade 10/12 | Multiple choice | Students seeking US university recognition |
| AIME | Invitation only (from AMC) | Short answer | Elite problem solvers |
| Canadian Mathematical Olympiad (CMO) | Invitation only | Proof-based | National team selection |
For most Canadian students aiming for competitive university programmes in mathematics or computer science, the Euclid is the most accessible and most directly useful competition at the senior level. The AMC/AIME pathway is more relevant for students targeting US universities specifically; the CMO is a national elite competition for a very small number of exceptional students.
The Euclid Mathematics Contest and the CEMC ladder
The Euclid does not exist in isolation. The CEMC series is designed as a development pathway from Grade 7 onward, with each contest building the reasoning skills and problem-solving habits that the next level requires.
Students who begin writing CEMC contests in Grade 7 (Gauss) and continue through Pascal (Grade 9), Cayley (Grade 10), and Fermat (Grade 11) arrive at the Euclid with several years of contest experience behind them. They understand how contest problems are structured, how to manage time across questions of varying difficulty, and how to write solutions clearly under pressure.
Students who write the Euclid without this background are not at a disadvantage in terms of content knowledge — but they are often less prepared for the problem-solving style and the communication demands. This is why the CEMC explicitly positions the earlier contests as preparation for the Euclid, and why many educators and parents who are thinking about university admissions start their children in the contest series well before Grade 12.
For a full overview of the CEMC contest series and how each competition connects, see our Waterloo Math Competition guide.
How to read your child’s Euclid result
When Euclid results are released, students receive a score out of 100 and information about their standing relative to other participants.
Score below average (~54): The student completed the accessible parts of most questions but struggled with the sustained reasoning required for later parts. This is a common result and does not indicate a poor mathematical ability — it indicates that the contest-specific skills of constructing complete solutions need further development.
Score around 60–70: The student is performing above average and likely received a Certificate of Distinction. This is a solid result for a student who has not had intensive contest preparation.
Score above 80: The student is in Honour Roll territory. This is a strong result nationally and will be noticed in university applications to competitive programmes.
Score above 90: Exceptional. A small number of students nationally reach this level each year. This level of performance is typically the result of years of contest preparation and exceptional mathematical ability.
How Think Academy Canada supports students preparing for the Euclid Mathematics Contest
Think Academy Canada works with high-performing students from Grade 1 through Grade 12. For students targeting the Euclid, the preparation pathway starts much earlier than Grade 12 — building the algebraic fluency, geometric reasoning, and problem-solving habits that the contest requires.
Our approach starts with a diagnostic. Every new student completes a free assessment and receives a personalised feedback report showing where their mathematical skills currently sit. For students in Grades 9 to 11 who are building toward the Euclid, the report identifies the specific areas — whether that is functions, trigonometry, combinatorics, or written reasoning — that need the most development.
The Euclid is written in April each year. Students who begin structured preparation in Grade 10 or 11 — working through the CEMC ladder and building problem-solving fluency alongside their curriculum work — are significantly better placed than those who begin in the months before the contest.
For a full preparation guide including topic-by-topic strategy and past paper analysis, see our Euclid Math Contest preparation guide.
FAQ
What is the Euclid Mathematics Contest?
The Euclid Mathematics Contest is a senior mathematics competition for Grade 12 students, run by the CEMC at the University of Waterloo. It consists of 10 questions requiring full written solutions, takes 150 minutes, and is written in April each year. It is the most prestigious and widely recognised mathematics competition for Canadian high school students.
How is the Euclid Mathematics Contest different from other CEMC contests?
All other CEMC contests (Gauss, Pascal, Cayley, Fermat) are multiple choice. The Euclid requires full written solutions, awards partial marks for correct reasoning, and takes 150 minutes rather than 60. It directly affects university admissions decisions in a way that the earlier contests do not.
What is a good score on the Euclid Mathematics Contest?
The average score in 2024 was 54.3 out of 100. The top 25% of students receive a Certificate of Distinction. Scores above 80 are Honour Roll territory and represent exceptional national performance.
Does the Euclid Mathematics Contest affect university admissions?
Yes, directly for University of Waterloo. Strong performance supports admission and is strongly encouraged for entrance scholarship consideration to the Faculty of Mathematics. The result is also recognised by other North American universities as evidence of mathematical ability.
Who should write the Euclid Mathematics Contest?
Grade 12 students with strong mathematics backgrounds who are considering university programmes in mathematics, computer science, or engineering — particularly at the University of Waterloo. Students who have worked through the CEMC ladder from Gauss onward are the most naturally prepared.
How many students write the Euclid Mathematics Contest each year?
More than 20,000 students from approximately 2,000 schools worldwide write the Euclid each year, including around 8,000 international participants. Canadian students make up the majority of participants.
What topics does the Euclid Mathematics Contest cover?
The Euclid covers algebra, functions, trigonometry, sequences and series, combinatorics, geometry, number theory, and logarithms and exponents. The topic mix varies year to year. Problems require combining multiple areas in a single solution.
What is the Certificate of Distinction for the Euclid?
The Certificate of Distinction is awarded to the top 25% of all Euclid participants. It is issued by the University of Waterloo and serves as a credential in university applications.
Can Grade 11 students write the Euclid Mathematics Contest?
The Euclid is designed for Grade 12 students. Some exceptional Grade 11 students write it as a stretch goal, but the mathematical content assumes a near-complete high school mathematics background. Grade 11 students are more typically directed to the Fermat Contest.
How does the Euclid Mathematics Contest relate to the AMC?
The AMC (American Mathematics Competitions) is a US-based series with a different format and pathway. The Euclid is more directly relevant for students targeting Canadian universities, particularly Waterloo. Students targeting US universities may prefer the AMC/AIME pathway; students targeting Canadian programmes should prioritise the Euclid.
How do I prepare my child for the Euclid Mathematics Contest?
Preparation is most effective when it begins well before Grade 12, through the CEMC contest ladder and structured problem-solving practice. For a full preparation guide, see our Euclid Math Contest preparation guide.
Does Think Academy Canada offer Euclid preparation?
Yes. Think Academy Canada works with students from Grade 1 through Grade 12, with structured programmes for CEMC contest preparation including the Euclid. A free diagnostic assessment and personalised feedback report are available for any student.
About Think Academy Canada Think Academy Canada is a K-12 mathematics tutoring programme, part of TAL Education Group. We work with motivated students across Canada from Grade 1 through Grade 12, with a focus on Ontario curriculum, EQAO, and competition mathematics including CEMC contests (Gauss, Pascal, Cayley, Fermat, Euclid) and AMC. All lessons are delivered online. Follow us on Instagram at @thinkacademyca.
