COMC Preparation Course: Canadian Open Mathematics Challenge Training

Half the marks are in the last four problems

The Canadian Open Mathematics Challenge is run by the Canadian Mathematical Society, which calls it Canada's premier national mathematics competition. It is the open entry point of the Canadian olympiad structure, written internationally rather than only in Canada, and it is open to any student in Grade 12 or below.

The paper is two and a half hours for 80 marks in three parts. Part A is four questions at 4 marks, Part B is four at 6 marks, and Part C is four full-solution problems at 10 marks each. In Parts A and B the final answer is what is required, though work shown can earn partial marks when the answer is wrong. In Part C the complete argument must be written out.

Those numbers decide how to prepare. Part C alone is 40 of the 80 marks, so it is worth as much as the rest of the paper put together, and a single Part C problem outweighs two Part A questions.

The section most students leave blank

In our experience the commonest avoidable loss on this paper is not a wrong answer but an untouched Part C. Students see four longer problems that ask for proof, judge them out of reach, and spend the remaining time rechecking Parts A and B. They have capped themselves at half marks to protect a handful.

Often those problems are not out of reach. They usually need one idea rather than advanced machinery, and a student who has practised starting — writing down what is given, trying a small case, drawing the configuration — finds a reasonable share of them open up. Four weeks of this course are given to that: not to new mathematics, but to the discipline of beginning, and then of writing what was found so a marker can award it.

Topic coverage

Algebra underpins everything and comes first: factoring, surds, inequalities and systems, worked to the fluency the paper assumes rather than the fluency school requires.

Number theory covers divisibility, modular arithmetic, primes and digit problems. These are taught as competition problems from the start, because a student who has only met modular arithmetic as a clock analogy will not get far with a contest problem built on it.

Geometry works triangles, circles, similar figures and areas, with attention to the configurations that recur year after year. Combinatorics covers systematic counting, pigeonhole, invariants and recursion, where a clear idea beats heavy calculation.

Time as a strategic decision

With 40 marks sitting in four long problems, spreading two and a half hours evenly across twelve questions is usually the wrong choice. Students who secure Parts A and B quickly and then commit the bulk of the remaining time to Part C score better than students of equal ability who simply work through in order and run out of clock.

We practise this explicitly in the closing weeks, including the uncomfortable decision to abandon a Part C problem that is not yielding. It is far easier to settle in advance than in the room.

What a strong result leads to

This is the question parents usually want answered first. The top scorers, on the order of a hundred students, are invited to the Canadian Mathematical Olympiad or the Junior CMO in March, and the CMO is the qualifier for Canada's IMO team. A group of leading students is also selected to write the APMO as Team Canada, and the top female contestants go forward for EGMO selection.

Qualifying scores are set each year and move, so we do not publish a target mark. Anyone quoting a fixed cutoff is quoting one particular year.

How the classes run

Sessions are live and online, one-on-one or in small groups of two to six. Students write solutions during the session and have them critiqued immediately, which is considerably more useful than submitting work and receiving a score days later.

The final weeks are full past papers under timed conditions, with written work marked to contest standard, so a student knows what their argument is actually worth before it counts.

What a year of preparation actually looks like

Parents reasonably ask what thirty weeks buys. For most of that time it looks unremarkable: a student works a handful of problems, gets some wrong, and finds out why. Progress in competition mathematics is not visible week to week, and a student who expects it to be often concludes too early that they are not suited to this.

What changes over a year is the response to an unfamiliar problem. A student beginning this course typically reads a hard problem, recognises nothing, and stops. A student finishing it reads the same problem, still recognises nothing, and starts anyway: tries a small case, draws the figure, writes down what is given. That shift is the real outcome, and it transfers well beyond this contest.

Who this suits

Students with solid Class 9 algebra and geometry. Competition experience helps but is not required; what matters is willingness to be marked strictly on presentation, which is the part most students resist and most need.

Dates, qualifying scores and the exact arrangements for international candidates are set by the Canadian Mathematical Society and change between cycles. Check cms.math.ca for the current year rather than relying on details reproduced on a coaching page.