Competitions · Mathematics · COMC
COMC, the Canadian Open Mathematics Challenge.
Twelve questions in two and a half hours, run by the Canadian Mathematical Society. It is Canada’s principal national mathematics competition and the qualifying round for the Canadian Mathematical Olympiad - and candidates in China who reach the Canadian line are invited to that second round too.
At a glance
What the contest is, and who sits it.
The Canadian Mathematical Society runs COMC to promote mathematical research, improve mathematics teaching in Canadian schools, and find the students who will represent Canada internationally. ASDAN China has hosted it in China since 2018.
- Organiser
- The Canadian Mathematical Society (CMS)
- Who can enter
- High-school students in any year. There is no strict grade requirement, but the paper is pitched at high-school and CEGEP mathematics with some questions beyond it, so it is not advised for younger students
- Format
- An individual written paper in three parts, twelve questions in all. Marks are awarded for correct working, not only for the final answer
- Duration
- 2 hours 30 minutes
- Marks
- 80 in total
- Language
- English
- Calculators
- Not permitted, in any form
- Where
- In person, either at a school partnered with the organiser or at a public test centre. Hanlin is an officially authorised centre
- When
- Late October. The 2025 paper was sat on Thursday 30 October, 17:00-19:30
- What it qualifies for
- The Canadian Mathematical Olympiad, either directly or through a repechage round
- In China
- More than a thousand students from over 113 international schools and key high schools took part in the first year ASDAN hosted it
The paper
Three parts, rising sharply in weight.
Half the paper’s marks sit in its last four questions, and those are built like Euclid’s long problems - three linked sub-parts where an earlier result is the way into the next.
| Part | Questions | Marks each | Total | What it asks |
|---|---|---|---|---|
| Short answer | 4 | 4 | 16 | Reachable for anyone with a sound mathematical foundation, and including some straightforwardly gettable marks |
| Challenge | 4 | 6 | 24 | Requires some competition mathematics, but manageable for a student who has entered contests before |
| Full solution | 4 | 10 | 40 | Usually three linked sub-parts each, where the earlier conclusions feed the later ones. Strong analysis and logical reasoning, set out in writing |
Marks follow the working. A correct chain of reasoning earns credit even where the final answer does not arrive, which is why the last four questions are worth attempting even when they cannot be finished.
Syllabus
What the questions are built on.
Most of the paper sits on the secondary and CEGEP curriculum, with a minority of questions reaching past it.
Geometry and trigonometry
Euclidean and analytic geometry, and trigonometry taken as far as functions, graphs and identities. Geometry questions here reward willingness to switch between a synthetic and a coordinate treatment of the same figure.
Functions and equations
Exponential and logarithmic functions, functional notation, systems of equations, and polynomials - including the relationships among the roots of quadratic and cubic equations, and the remainder theorem.
Sequences and counting
Sequences and series, simple counting problems, the binomial theorem, and probability. These frequently appear inside the challenge section rather than as questions in their own right.
Elementary number theory
Divisibility tests, counting the divisors of a number, and simple Diophantine equations. As on most contests of this kind, number theory is where a memorised technique pays for itself most directly.
What follows
The route from COMC to the Canadian team.
COMC is a selection round, and the selection continues well past it. About eighty students reach the Canadian Mathematical Olympiad each year.
The top fifty go straight through
Canadian-national students placing in the top 50 advance directly to the Canadian Mathematical Olympiad. Candidates in China who pass the Canadian cutoff are also invited to the second round and ranked alongside Canadian entrants.
A repechage for 51st to 125th
Students ranked 51 to 125 qualify for the CMO Qualifying Repechage. The top twenty to twenty-five there also advance to CMO, which is what brings the final field to roughly eighty.
Prize money and the national team
Students reaching honourable mention or above at CMO receive between CAD $500 and $2,000 and become eligible for the Canadian national team. CMS typically selects six students for the team that competes at the International Mathematical Olympiad.
The route to EGMO
A strong COMC result can also qualify a female candidate for the Canadian women’s mathematics team, which competes at the European Girls’ Mathematical Olympiad. That is a separate selection from the IMO team.
China-region awards
Four award bands.
The China region awards on percentile. Separately, global awards are given against fixed cutoffs set by the organising committee each year.
Preparation
How Hanlin prepares students for COMC.
Fifty of the eighty marks require written mathematics, and the paper allows no calculator at all. Both facts shape how a candidate should train for it.
Writing linked sub-parts
The four ten-mark questions each run as three connected sub-parts, so part (a) is usually the key to part (c). Students practise recognising that structure and writing up each part so the marker can follow the chain.
Banking the first eight
Forty of the eighty marks sit in the short-answer and challenge sections. Securing those quickly is what buys the time to write proper solutions to the long questions, and it is where a realistic award target is built.
Arithmetic without a calculator
No calculating aid of any kind is allowed for two and a half hours. Students who have prepared for contests that permit one need to rebuild mental and written arithmetic before the paper, not during it.
Euclid as the nearest neighbour
The long questions are close in style to the later Euclid problems, so past papers from both contests reinforce each other. Students often prepare for the two in the same season.
Why Hanlin
Preparation for COMC at Hanlin is taught by full-time subject tutors, on a course tier chosen by placement paper rather than by year group.
Programme formats
Five ways this is taught.
Group size is the whole difference between these. It decides how much of the tutor's attention a student gets and how far the course can bend to them, so it is worth choosing rather than accepting.
| Format | Group size | What it suits |
|---|---|---|
| One-to-one | One student | Content, pace and emphasis set by what this student actually needs rather than by a syllabus. The only format that can be rebuilt mid-course. |
| Small group | Three to eight | Opens at three. Frequent discussion, and the tutor can slow down or move on according to what the group has absorbed. Most students chasing a higher award are taught in this one. |
| Class | Eight to twelve | Taught by the subject lead or a medal coach. Less back-and-forth, so it suits a student who will say when something is unclear. |
| Large class | Ten to twenty | For students in the middle of the placement range, and a way to try a competition before committing. Students often move to a small group or to one-to-one afterwards. |
| Past-paper class | No cap | Past papers worked through in sequence in the weeks before the sitting. Free to students already enrolled. |
Course length for COMC is set after a placement paper. The gap between where a student is and what the paper asks for is what the course has to close, and that gap is not the same for two students in the same year group.
How it runs
Six steps, four people on your side.
The same process for every student, so that nothing depends on one tutor remembering to do it.
Step 1Pre-course assessment
A placement paper before anything is booked, so the course tier is chosen on evidence rather than on a year group.
Step 2Tutor matching
A subject tutor is matched to the result, and their full background is provided before you agree to it.
Step 3Plan and group
A study group opens with four people on one student: the tutor, a planner, a supervisor and an academic manager.
Step 4Scheduled teaching
The teaching office sets the timetable around the competition date and school term, and teaching begins.
Step 5After-class reports
What was covered, and how the student handled it, reported after every lesson.
Step 6Homework follow-up
The teaching assistant and the form teacher both check that homework is done, which is where most preparation quietly fails.
Free resource pack
Past papers and preparation pack
The same material our own COMC students work from. Scan the code, say what you need, and an advisor sends it.
Tell an advisor which competition and year group, and the material comes back the same day. Free, and you do not have to enrol in anything. If we do not already hold what you need, we will go and find it.
- PDFPast papers, every year the organiser has released
- PDFWorked solutions, where the organiser publishes them
- PDFThe syllabus on one page - every topic, and how heavily it is examined
- PDFEntry checklist and the dates for the current cycle
Teaching team
Who would teach it.
Three of the twenty-two tutors on the published Hanlin roster - the ones whose subject this is.
Dr Zhang
PhD in theoretical mathematics from the University of Rochester and a postdoctoral fellow at the Shanghai Center for Mathematical Sciences at Fudan. An AMC-accredited coach, ASDAN-accredited for DMM and ITCCC, and an accredited UKMT BMO2 and PUMaC coach. His students have gone on to read mathematics and physics at Harvard, MIT, Princeton, Caltech and Cambridge.
Dr Zhuang
PhD in mathematics from the University of Denver, working in mathematical logic, after a first degree in applied mathematics at Southeast University. A repeat conference speaker on his research, with three years lecturing and assisting on undergraduate mathematics at Denver.
He
A Cambridge master's after a computer science degree with a mathematics minor at the University of Nebraska-Lincoln, and a US high school GPA of 4.13. Six years overseas and teaches entirely in English, across AMC, Math League, AP Computer Science and AP Calculus.
Student results
What Hanlin students got.
Taken from Hanlin's published record of student honours and rewritten in English. Figures are as the organisers reported them.
COMC
- 20212 students reached the Canadian Mathematical Olympiad winter camp
The full record, across every subject and year, is on the student honours page.
Where it is taught
Hanlin learning centres.
Teaching runs from Hanlin's own centres in Shanghai, Shenzhen, Chengdu and Hangzhou, and online for students elsewhere.
Talk to an advisor
Everything Hanlin does for COMC, in one conversation.
Entry, planning, coaching and the past papers. An advisor will tell you which of these a student actually needs, including when the answer is none of them.
Competition entry and planning
Which competitions suit this student, in what order, and by when - then we handle the registration, including the ones that can only be entered through a school or a centre.
Competition coaching
Taught by full-time subject tutors, on a course tier chosen by placement paper rather than by year group.
International curriculum tutoring
IB, AP, A-Level, IGCSE and the US high school curriculum, taught alongside school and timed around the exam calendar.
Competition past papers, free
A large library of past papers, mark schemes and syllabus breakdowns across every competition on this site. No charge and no enrolment.
Scan to add an advisor
Say which competition or course you are asking about. Replies in Chinese or English.
Or call +86 21 6352 6630FAQ
COMC, briefly answered.
What students and families ask before entering.
Can middle-school students enter COMC?
There is no strict grade requirement, but the questions are pitched at high-school and CEGEP mathematics and some reach beyond it. The organisers recommend it for high-school students.
How is the paper structured?
Twelve questions in three parts, out of 80 marks: four short-answer questions at 4 marks, four challenge questions at 6 marks, and four full-solution questions at 10 marks. Marks are awarded for correct working, not just the final answer.
What score is needed for an award?
By percentile in the China region: gold for the top 10%, silver the top 25%, bronze the top 35%, and a regional excellence award for a further 20% in each region.
Can Chinese students qualify for the Canadian Mathematical Olympiad?
Candidates in China who pass the Canadian cutoff are invited to the second round and ranked against Canadian entrants. Chinese nationals cannot take a place on the Canadian national team, but reaching that standard is authoritative evidence of ability in its own right.
What is the repechage round?
Students placing 51st to 125th qualify for the CMO Qualifying Repechage. The top twenty to twenty-five in that round also advance to the Canadian Mathematical Olympiad, bringing the CMO field to around eighty students.
Can I use a calculator?
No. No calculating device of any kind is permitted, for the full two and a half hours.
Where is COMC sat?
In person, either at a school partnered with the organiser or at a public test centre. Hanlin is an officially authorised centre, so independent candidates can sit it without going through their own school.
Is there a route to an international olympiad?
Yes, through CMO. Students reaching honourable mention or above there receive prize money and become eligible for the Canadian team, and a strong COMC result can separately qualify a female candidate for the Canadian team at EGMO.
Related
Other olympiad-route contests.
Papers students commonly enter in the same season as COMC.
COMC enquiries
Fifty of the eighty marks are written mathematics.
COMC rewards students who can set out a linked argument and work without a calculator for two and a half hours. Tell us the year group and what contests the student has already sat, and an advisor will map the October entry.