--- title: "How to Prepare for the Canadian Open Mathematics Challenge (COMC)" description: "COMC format, topics, a 12-week prep plan, how it compares with the AMC and Euclid, and how a strong score can help university applications." url: https://bosenacademics.com/blog/comc-prep-guide/ published: 2026-04-09T10:00:00Z updated: 2026-11-12T17:05:00Z section: "Math and computing contests" publisher: Bosen Academics (https://bosenacademics.com) --- # How to Prepare for the Canadian Open Mathematics Challenge (COMC) **The short answer:** The COMC is a 2.5-hour national contest run by the Canadian Mathematical Society each fall, with a maximum of 80 points. It is the entry point to the path toward the Canadian Mathematical Olympiad and the IMO team. A 12-week plan starting in August, built on past papers and olympiad-style combinatorics and number theory, works well for most students. ## What is the Canadian Open Mathematics Challenge? The Canadian Open Mathematics Challenge (COMC) is the main national math competition run by the Canadian Mathematical Society (CMS). It is the first step on Canada's olympiad pathway, which continues through the Canadian Mathematical Olympiad (CMO) and ends with selection for the International Mathematical Olympiad (IMO) team. The COMC is open to students of any grade, in Canada and abroad, and they write it each fall (October 29 in 2026). To count as official participants, students must be under 19 on June 30 of the contest year and be in full-time school. Roughly the top 100 qualifying students in the Competitive Division, which is for students in Canada and Canadian citizens abroad, are invited to write the CMO (or the Junior CMO) in March. The old Repechage competition has been discontinued. ## What does the COMC exam look like? The exam runs 2.5 hours and has three parts, each harder and worth more than the last: | Part | Questions | Format | Points Each | |---|---|---|---| | Part A | 4 questions | Short answer, no justification required | 4 points | | Part B | 4 questions | Short answer; partial marks for correct work shown | 6 points | | Part C | 4 questions | Multi-part, full solution required | 10 points | The top score is 80 points, and calculators and other electronic devices are not allowed. Strong Grade 10 students can handle Part A. Part C calls for mathematical creativity, careful proof writing and comfort with olympiad-style thinking, which usually takes years to build. For a Grade 11 student writing for the first time, 24 to 32 points (mostly correct on Parts A and B) is a solid showing. A score above 48 is exceptional and competitive for national recognition. ## Who should write the COMC? The contest suits students in Grades 10 through 12 who have finished, or are taking, a strong math course. That includes Ontario's Advanced Functions (MHF4U), IB Math Analysis and Approaches at either level, and AP Calculus. Calculus is not needed to do well, but students should be at ease with algebra, geometric reasoning and building a mathematical argument. Experienced educators say that students who have written the AMC 10 or AMC 12 and scored above 90 are in a good position for the COMC. Anyone who has not yet entered a math contest should begin with the AMC 8 or AMC 10 to develop basic contest skills first. ## Which math topics show up on the COMC? Most problems come from the areas below, and none of them needs 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, the pigeonhole principle - **Geometry:** Euclidean plane geometry, including circle theorems, similar triangles, area and perimeter relationships and coordinate geometry - **Functions and graphs:** piecewise functions, absolute value, floor and ceiling functions, and spotting patterns in graphs A student whose strength is limited to curriculum algebra and calculus will find the COMC unfamiliar, especially in combinatorics and number theory. Schools seldom teach these topics, yet they sit at the heart of olympiad math, so targeted practice is a must. ## How does the COMC compare with the AMC and the Euclid? The three contests have different goals and test somewhat different skills: - **AMC 10/12:** 25 multiple-choice questions in 75 minutes, run by the Mathematical Association of America. It stresses speed and accuracy on well-defined problem types, and some American universities also recognize strong results. It is a good way to build contest fluency before taking on the COMC. - **Euclid Contest (CEMC):** 10 multi-part questions mixing short answers and full solutions, run by the Centre for Education in Mathematics and Computing at the University of Waterloo. It leans more on Grade 12 curriculum content, and writing it (or the CSMC) is required for some Waterloo entrance scholarship decisions. - **COMC:** tests deeper mathematical creativity and proof-writing. Of the three, a strong COMC score is the most demanding signal of mathematical talent, and a top result stands out in applications to research-oriented programs. ## What is a good preparation timeline for the COMC? For an October exam, a 12-week plan that starts in August suits most students. Based on what tends to work at top private schools, here is a sensible structure: 1. **Weeks 1 to 3:** Find your gaps with one or two past COMC papers from the CMS website, and note which of the four topic areas is weakest. Start reviewing number theory and combinatorics, since school covers them least. 2. **Weeks 4 to 6:** Use Art of Problem Solving (AoPS) material on competition combinatorics and number theory. The AoPS forums also hold detailed solutions to past COMC problems, which help in understanding how a proof is built. 3. **Weeks 7 to 9:** Go back to past COMC papers and try Part B questions against the clock. Practise writing brief justifications in full sentences, because partial marks in Parts A and B and every mark in Part C reward the communication of reasoning, not only the final answer. 4. **Weeks 10 to 12:** Sit full timed COMC practice exams from earlier years. Study the Part C problems even if you cannot solve them, since knowing how olympiad solutions are put together builds the pattern recognition that pays off later. ## How does a COMC result affect university applications? Canadian universities, especially those with competitive math and engineering programs, recognize a strong COMC score as evidence of mathematical ability. The University of Waterloo does not require any contest for admission, but its Faculty of Mathematics asks applicants on its Supplementary Information Form which math contests they have written, and applicants can list their COMC results as well. Students who reach the CMO or finish in the national top tier on the COMC have a strong credential in programs where mathematical aptitude is central. COMC preparation also builds problem-solving skills that carry straight into first-year university math, especially proof-based courses. Students who have taken the COMC seriously arrive better prepared for linear algebra and real analysis than those with only curriculum coursework behind them. If your child is preparing for the COMC and wants expert help with olympiad-style problem solving, [book a free consultation with Bosen Academics](https://bosenacademics.com/consultation/) to be matched with a tutor who has deep competition math experience. You can also browse our [tutoring subjects](https://bosenacademics.com/tutoring/) to see our contest math support. ## Frequently asked questions ### Does the COMC affect a student's chance of reaching the IMO? Yes, because the route to Canada's IMO team starts at the COMC. Top scorers are invited to the CMO, and CMO results decide IMO team selection. The team has only 6 students, so it is extremely competitive, but serious COMC work at any level builds skills useful along the whole olympiad path. ### Can students practise with past COMC papers? Yes. The Canadian Mathematical Society posts past COMC exams with full solutions on its competition website, going back more than a decade and free of charge. They are the best practice material, and the AoPS forums add detailed discussion of individual problems. ### What is a realistic score goal for a first-time COMC writer? A Grade 11 student with solid school math who is writing for the first time can expect a baseline of about 16 to 27 out of 80. Students who have already practised Part B and C style problems can aim for 27 to 40. Scores above 48 usually come from at least one to two years of olympiad-focused preparation. ### Can Grade 9 or 10 students write the COMC? Yes, there is no grade restriction. Advanced students in Grade 9 or 10 who have done well on junior contests such as the AMC 8 or CEMC Cayley can write it as a learning experience with realistic expectations. Meeting olympiad-style problems early is valuable whatever the score. ## Tutoring from Bosen Academics One-on-one tutoring from certified teachers and subject experts with master's and PhD degrees, in person in North York, Toronto, or online. Book a free consultation: https://bosenacademics.com/consultation/