What Is the Canadian Open Mathematics Challenge?
The Canadian Open Mathematics Challenge (COMC) is the premier national mathematics competition administered by the Canadian Mathematical Society (CMS). It serves as the primary gateway into the Canadian mathematical olympiad pathway, which leads through the Canadian Mathematical Olympiad (CMO) and ultimately to selection for the International Mathematical Olympiad (IMO) team.
The COMC is written each fall, typically in late October or early November, by students in Grades 7 through 12 across Canada and internationally. There is no entry fee for most participants writing through their school. Students who score in the top tier of the COMC are invited to write the Canadian Senior Mathematics Contest (CSMC) or the Repechage competition, with the strongest performers advancing to the CMO.
What Is the Format of the COMC Exam?
The COMC is 2.5 hours long and consists of three parts with increasing difficulty and point value:
| Part | Questions | Format | Points Each |
|---|---|---|---|
| Part A | 4 questions | Short answer, no justification required | 4 points |
| Part B | 4 questions | Short answer with brief justification | 6 points |
| Part C | 4 questions | Multi-part, full solution required | 10 points |
The maximum score is 120 points. Part A problems are accessible to strong Grade 10 students. Part C problems require mathematical creativity, careful proof writing, and comfort with olympiad-style reasoning that typically takes years to develop. A score of 36 to 48 (mostly correct on Parts A and B) is a solid performance for a first-time writer in Grade 11. Scores above 72 are exceptional and competitive for national recognition.
Who Should Write the COMC?
The COMC is best suited to students in Grades 10 through 12 who have completed or are currently taking a strong mathematics course. This includes students in Ontario’s Advanced Functions (MHF4U), IB Math Analysis and Approaches (either level), or AP Calculus. Students do not need calculus to succeed on the COMC, but they should be comfortable with algebraic manipulation, geometric reasoning, and mathematical argumentation.
According to experienced educators, students who have competed in the AMC 10 or AMC 12 and scored above 90 are well positioned for the COMC. Students who have not yet competed in any math contest should consider starting with the AMC 8 or AMC 10 to build foundational contest skills before attempting the COMC.
What Mathematical Topics Appear on the COMC?
The COMC draws primarily from the following areas, none of which require calculus:
- Algebra: Polynomial equations, inequalities, systems of equations, sequences and series, functional equations
- Number theory: Divisibility, modular arithmetic, prime factorization, Diophantine equations
- Combinatorics: Counting principles, permutations and combinations, inclusion-exclusion, pigeonhole principle
- Geometry: Euclidean plane geometry including circle theorems, similar triangles, area and perimeter relationships, coordinate geometry
- Functions and graphs: Piecewise functions, absolute value, floor and ceiling functions, and recognizing graphical patterns
Students who are only strong in curriculum-based algebra and calculus will find COMC problems unfamiliar, particularly in combinatorics and number theory. These topics are rarely covered in school curricula but are central to olympiad mathematics. Targeted practice is necessary.
How Does the COMC Compare to the AMC and the Euclid Contest?
These three competitions serve different purposes and test somewhat different skills:
- AMC 10/12: 30 multiple-choice questions in 75 minutes, administered by the Mathematical Association of America. Speed and accuracy on well-defined problem types are emphasized. Strong AMC performance is also recognized by some American universities. The AMC is excellent for building contest fluency before attempting the COMC.
- Euclid Contest (CEMC): 10 questions with multi-part answers, administered by the Centre for Education in Mathematics and Computing at the University of Waterloo. The Euclid focuses more on Grade 12 curriculum content and is explicitly used in Waterloo’s admission process. It is less proof-intensive than the COMC.
- COMC: Tests deeper mathematical creativity and proof-writing ability. A strong COMC score is the most rigorous signal of mathematical talent among these three contests, and a top score is a meaningful differentiator in university applications to research-oriented programs.
What Is the Recommended Preparation Timeline for the COMC?
A 12-week preparation timeline beginning in August for an October exam works well for most students. Based on our work with students at top private schools, the following structure is effective:
- Weeks 1 to 3: Diagnose gaps using one or two past COMC papers from the CMS website. Identify which of the four topic areas are weakest. Begin targeted review of number theory and combinatorics, as these are the topics least covered in school.
- Weeks 4 to 6: Work through Art of Problem Solving (AoPS) resources for competition combinatorics and number theory. The AoPS forums also contain detailed solutions to past COMC problems, which are valuable for understanding proof structure.
- Weeks 7 to 9: Return to past COMC papers and attempt Part B questions under timed conditions. Practice writing out brief justifications in complete sentences. Mathematical communication on Part B and Part C is scored, not just the final answer.
- Weeks 10 to 12: Attempt full timed COMC practice exams from past years. Review Part C problems even if you cannot solve them. Understanding the structure of olympiad solutions develops pattern recognition that helps on future problems.
How Does COMC Performance Affect University Applications?
A strong COMC score is recognized by Canadian universities, particularly those with competitive mathematics and engineering programs. The University of Waterloo explicitly reviews contest performance as part of admissions to Mathematics and Computer Science programs. Students who advance to the CMO or achieve a score in the national top tier on the COMC have a distinct advantage in applications to programs where mathematical aptitude is central.
Beyond admissions, COMC preparation builds problem-solving skills that transfer directly to first-year university mathematics, particularly in proof-based courses. Students who have written the COMC seriously are better prepared for courses in linear algebra and real analysis than students who have only completed curriculum-based coursework.
If your child is preparing for the COMC and wants expert guidance on olympiad-style problem solving, contact Polaris Tutors to connect with a tutor who has deep competition mathematics experience. You can also visit our areas of practice to learn about our contest math support programs.
Frequently Asked Questions
Does writing the COMC affect a student’s chance of being considered for the IMO?
Yes. The pathway to Canada’s IMO team begins with the COMC. The top COMC scorers are invited to the CMO, and CMO performance determines IMO team selection. The IMO team consists of 6 students, making it extraordinarily competitive. However, participating seriously in the COMC at any level builds the problem-solving foundation relevant to the full olympiad pathway.
Are past COMC papers available for practice?
Yes. The Canadian Mathematical Society publishes past COMC exams and complete solutions on the official CMS competition website. Papers going back more than a decade are available at no cost. These are the most valuable practice resource, supplemented by AoPS forums where detailed discussion of specific problems can be found.
What is a realistic score target for a first-time COMC writer?
For a Grade 11 student writing the COMC for the first time with solid school mathematics, a score between 24 and 40 out of 120 is a realistic baseline. Students who have done any contest preparation targeting Part B and C problem types can realistically aim for 40 to 60. Scores above 72 are typically achieved by students who have been preparing specifically for olympiad mathematics for at least one to two years.
Can Grade 9 or 10 students write the COMC?
Yes. There is no grade restriction for the COMC. Students in Grade 9 or 10 who are mathematically advanced and have already demonstrated strong performance on junior contests such as the AMC 8 or CEMC Cayley may benefit from writing the COMC as a learning experience, with realistic expectations about score. The exposure to olympiad-style problems at a younger age is valuable regardless of score outcome.