The Canadian Open Mathematics Competition is one of the most significant contests a Canadian high school student can enter. It is the primary gateway to the Canadian Mathematical Olympiad — and for students aiming at top universities, a strong COMC math contest result is a credential that stands out. But it is also genuinely hard. This guide covers everything students and parents need to know: what the COMC is, how it works, what it takes to do well, and how to build a preparation plan that produces results.
What Is the COMC Math Contest?
The COMC (Canadian Open Mathematics Competition) is an annual national mathematics contest run by the Centre for Education in Mathematics and Computing (CEMC) at the University of Waterloo. It is open to all Canadian high school students and is one of the most challenging and prestigious competitions in the Canadian mathematics calendar.
Unlike earlier CEMC contests such as the Gauss, Cayley, Fermat, or CIMC, the COMC is not grade-specific — it is open to any student in Grades 9 through 12. In practice, most competitive participants are in Grade 11 or 12, and the contest difficulty reflects that.
The COMC is also the primary qualification route to the Canadian Mathematical Olympiad (CMO) — the national olympiad that selects Canada’s team for the International Mathematical Olympiad (IMO). Top COMC scorers receive invitations to the CMO, making the COMC a critical stepping stone for students with olympiad ambitions.
For a full overview of where the COMC fits within the Canadian competition landscape, see our math competitions in Canada guide.
COMC Math Contest Format and Eligibility
Who can enter? Any Canadian high school student in Grades 9–12 can enter the COMC math contest. There is no minimum grade requirement, though the difficulty level means most successful participants are in the senior secondary years.
When is it held? The COMC math contest takes place each year in late October or early November. Schools register through the CEMC website and students write at school during a designated session.
Format at a glance:
| Feature | Detail |
|---|---|
| Duration | 2.5 hours |
| Part A | 4 questions — answer only, 1 mark each |
| Part B | 4 questions — answer only, 2–4 marks each |
| Part C | 4 questions — full solution required, 4 marks each |
| Calculators | Not permitted |
| Negative marking | None |
Total: 40 marks
The three-part structure is intentional. Part A is accessible — designed to reward careful, accurate mathematical thinking without requiring advanced techniques. Part B raises the difficulty. Part C demands full written solutions with logical reasoning shown, and is where the contest truly differentiates top performers from the rest.
How the COMC Math Contest Is Scored
Part A: Four questions, 1 mark each. Answer only — no working required. Maximum: 4 marks.
Part B: Four questions, worth 2 to 4 marks each depending on difficulty. Answer only. Maximum: 12 marks.
Part C: Four questions, 4 marks each. Full written solutions required. Partial credit is awarded — a well-reasoned incomplete solution will earn more marks than a correct answer with no working. Maximum: 16 marks (with an additional 8 bonus marks available for exceptional solutions at the highest difficulty).
Why Part C is decisive. Students who can reliably score full marks on Parts A and B but cannot write clean, logical solutions in Part C will plateau around the 75th percentile. The ability to construct a complete mathematical proof — not just find the right answer — is what separates COMC qualifiers for the CMO from strong-but-non-qualifying performers.
What Topics Does the COMC Cover?
The COMC is not a curriculum test. It draws on senior secondary mathematics but extends well beyond what any Canadian provincial curriculum covers. Students who prepare only from school material will find the harder questions in Parts B and C significantly more challenging than expected.
Algebra and Functions Polynomial equations, systems, inequalities, and functional equations. COMC problems often require algebraic creativity — recognising structure and substituting cleverly rather than grinding through standard methods.
Number Theory Divisibility, modular arithmetic, prime factorisation, and Diophantine equations. Number theory is frequently the most unfamiliar area for students who haven’t specifically studied contest mathematics.
Geometry Euclidean geometry — triangle properties, circle theorems, area relationships, and coordinate geometry. COMC geometry problems often require elegant constructions rather than coordinate bashing. Our guides to special triangles in trigonometry and tangent lines to a circle cover two of the most tested geometric concepts.
Combinatorics Counting arguments, the pigeonhole principle, graph theory basics, and combinatorial proofs. These problems are often the most creative and least amenable to formula application.
Sequences and Inequalities Arithmetic and geometric sequences, telescoping sums, and classical inequalities (AM-GM, Cauchy-Schwarz at the harder end).
Proof Writing This is not a separate topic but a cross-cutting skill. Part C requires students to write rigorous, logically ordered solutions. Students who have only practised finding answers — not writing proofs — will consistently lose marks in Part C even when their mathematical instincts are correct.
What Score Do You Need to Do Well?
Score distributions vary by year, but as benchmarks:
| Result | Approximate Score |
|---|---|
| Top 50% of participants | 10+ / 40 |
| Certificate of Distinction (top 25%) | 18+ / 40 |
| Invitation to write the CMO | ~28–32+ / 40 (top ~50 students nationally) |
| Perfect score | 40 / 40 (rare — typically fewer than 5 students nationally) |
The CMO qualification threshold is not a fixed number — it is determined annually based on the national score distribution. In competitive years, the cutoff can be higher. Students aiming at CMO qualification need to be scoring reliably in Parts A and B and earning meaningful partial credit across all four Part C questions.
How to Prepare for the COMC
Preparation for the COMC requires sustained, structured work over months — not a few weeks of past paper practice. The students who score well on the COMC are almost always students who have been building contest mathematics skills for a year or more.
1. Build the Prerequisites First The COMC is significantly harder than the Euclid Mathematics Contest and the CIMC. Students who have not yet competed in those contests, or who found them difficult, should build their contest foundation there before targeting COMC seriously.
2. Study Each Topic Area Systematically Contest mathematics topics — particularly number theory and combinatorics — require dedicated study, not just exposure to problems. Build a structured preparation plan that covers each major topic area before attempting past papers. Our study schedule guide gives a framework for building consistent preparation habits.
3. Learn to Write Full Solutions Part C is where the COMC is won and lost. Practice writing complete, logically ordered solutions with every step justified — not just finding the answer. This is a skill that requires deliberate practice: solving a problem is not the same as writing a solution that a marker can follow and award full credit for.
4. Work Through Past Papers Under Timed Conditions CEMC publishes past COMC papers with full solutions. Work through these under timed, exam-like conditions. After each paper, review every question — including the ones you got right — and study the official solution to identify more elegant approaches.
5. Study Olympiad Problem-Solving Techniques For students targeting CMO qualification, basic contest preparation is not enough. Specific olympiad techniques — proof by contradiction, mathematical induction, the extremal principle, invariants, and modular arithmetic — need to be in the toolkit before attempting the hardest Part C questions. Our proof by contradiction guide is a starting point for one of the most important of these techniques.
6. Get Expert Guidance The gap between a student who self-studies from answer keys and one who works with an instructor experienced in olympiad mathematics is significant at the COMC level. Knowing the right approach to an unfamiliar problem type — and having someone who can explain why a solution works, not just what the answer is — is the difference between plateauing and improving.
How Think Academy Can Help
Think Academy Canada has helped students prepare for the full range of CEMC and AMC competitions, from the Gauss and Cayley at the intermediate level through to the Euclid and COMC at the senior level. Our instructors have competed at the national and international level and understand exactly what the COMC rewards — and where students most commonly leave marks on the table.
Our COMC preparation approach:
- Topic-by-topic curriculum covering all major COMC areas — algebra, number theory, geometry, and combinatorics — with contest-specific problem types at each level of difficulty
- Part C solution writing practice with instructor feedback on logical structure, not just mathematical correctness
- Past paper review sessions where students understand why the official solution works, not just what the answer is
- Progress checkpoints against realistic COMC scoring benchmarks so students and parents have a clear picture of trajectory
Whether your child is entering the COMC for the first time and wants a strong baseline result, or is specifically targeting CMO qualification, structured preparation with expert guidance produces measurably better outcomes than self-study alone.
COMC vs. Other Senior Math Contests
| Contest | Level | Key Difference |
|---|---|---|
| Fermat | Grade 10 | Multiple choice only |
| Euclid | Grade 12 | Full solutions, university admissions relevance |
| AMC 10 / AMC 12 | Grades 10–12 | US competition series, AIME pathway |
| COMC | Grades 9–12 | CMO qualification route, proof writing required |
| CMO | Invitation only | National olympiad, IMO selection |
The COMC is the most prestigious open-entry contest in Canada. Unlike the Euclid — which has university admissions relevance for Waterloo applicants specifically — the COMC is a pure competition credential, with the CMO invitation as its highest reward.
Students who are also participating in the AMC series should note that the COMC and AMC 12 take place in the same autumn window and require overlapping but distinct preparation. For guidance on navigating multiple contests, see our math competitions in Canada guide.
Frequently Asked Questions
What is the COMC? The Canadian Open Mathematics Competition — an annual national contest run by CEMC at the University of Waterloo, open to all Canadian high school students in Grades 9–12, and the primary qualification route to the Canadian Mathematical Olympiad.
How hard is the COMC? Significantly harder than the Euclid, CIMC, or any multiple-choice CEMC contest. Part C questions require full written proofs at a level comparable to early olympiad problems. Students who have not studied contest mathematics specifically will find the harder questions very challenging.
Can Grade 9 students enter the COMC? Yes. There is no grade restriction. In practice, most strong performers are in Grade 11 or 12, but motivated younger students who have built strong contest foundations through the Gauss, CIMC, and Euclid series can perform well.
Does the COMC help with university admissions? Indirectly, yes. A strong COMC result — particularly a CMO invitation — is a meaningful credential for university applications, especially for mathematics and computer science programmes. Waterloo’s mathematics faculty, in particular, pays close attention to competition results. It is not a formal admissions criterion, but it signals mathematical ability in a way that grades alone cannot.
When should my child start preparing for the COMC? At least six months before the October contest date — ideally longer. Students aiming at CMO qualification typically build contest mathematics skills over multiple years, starting with intermediate contests and progressing upward. A student beginning COMC preparation in September for an October contest is starting too late for meaningful improvement.
Is a calculator allowed? No. Like all CEMC contests, the COMC does not permit calculators. Mathematical reasoning and algebraic technique are more important than computational speed.
See our related guides: math competitions in Canada · Euclid math contest guide · Fermat math contest guide · CIMC math contest guide · AMC 10 guide · AMC 12 guide · Waterloo math competition guide · proof by contradiction guide · math enrichment guide
The COMC rewards the students who prepared earliest. Start now.
