COMC Cheat Sheet 2026

The 30 highest-yield COMC facts, distilled from real exam questions. Print it, save it as a PDF, or study it here — free, no sign-up.

1. If gcd(a, b) = 6 and lcm(a, b) = 60, what is the product ab? → 360
2. In an arithmetic sequence, the sum of the 3rd and 7th terms is 26, and the sum of the 4th and 8th terms is 30. What is the common difference? → 2
3. What is the minimum grade level required to participate in the Canadian Open Mathematics Challenge (COMC)? → Grade 7
4. How are geometry problems typically presented in the COMC? → Solving for angles and areas in shapes
5. In how many ways can 8 people be split into two unlabeled groups of 4? → 35
6. How are points typically distributed in the COMC? → Harder questions carry more points
7. If a/b = 3/4 and a + b = 28, what is the value of a − b? → −4
8. What is the smallest positive integer that has exactly 5 positive divisors? → 16
9. How are schools recognized in the COMC? → For highest average scores among participants
10. How should professionals apply communication and documentation in daily practice? → Consistently integrate best practices into every aspect of professional work
11. How is a tiebreaker determined when multiple students achieve the same score? → Difficulty level of questions answered correctly
12. How many ways can a committee of 3 people be chosen from a group of 12? → 220
13. The Fibonacci sequence is F₁=1, F₂=1, Fₙ=Fₙ₋₁+Fₙ₋₂ for n ≥ 3. What is F₁₀? → 55
14. What is the value of (1 + √3)(1 − √3)? → −2
15. What is the coefficient of x² in the expansion of (1 + x)⁵? → 10
16. How many positive divisors does 360 have? → 24
17. What is the sum of the first 20 positive odd integers? → 400
18. Are students outside Canada allowed to participate in the COMC? → Yes, if their school is registered and approved
19. Which type of mathematical problem involves finding unknown values using equations? → Algebra
20. How many diagonals does a regular octagon have? → 20
21. How should challenges in continuing education requirements be addressed? → Apply systematic problem-solving, seek expert guidance when needed, and document decisions
22. What is the primary criterion for scoring written response questions? → Clarity, reasoning, and correctness of the solution
23. What is the remainder when 2026² is divided by 10? → 6
24. A function f defined for positive reals satisfies f(x/y) = f(x) − f(y) for all x, y > 0, and f(4) = 2. What is f(64)? → 6
25. What quality assurance measure supports industry best practices? → Regular self-assessment, peer review, and adherence to established standards
26. Let g(x) = x² − 3 and f(x) = 2x + 1. For how many integer values of x does f(g(x)) = g(f(x))? → 0
27. What quality assurance measure supports applied methods and techniques? → Regular self-assessment, peer review, and adherence to established standards
28. What quality assurance measure supports assessment and evaluation? → Regular self-assessment, peer review, and adherence to established standards
29. How is the COMC structured to challenge advanced students? → By including challenging problems requiring creative thinking
30. If two fair six-sided dice are rolled, in how many ways can the sum equal 7? → 6