The Canadian Open Mathematics Competition (COMC) 2025 has been written. Results have been distributed. For students and families now looking at those results — whether the outcome was stronger than expected, weaker, or somewhere in between — this guide covers what the COMC 2025 score actually means, how to use the past paper as a preparation tool, and what the most effective path to the 2026 contest looks like.
For a complete overview of the COMC — what it is, who should write it, how it is structured, and what a strong result leads to — see our COMC math contest guide.
What the COMC 2025 Results Mean
Understanding the COMC Score
The COMC is scored out of 84 marks across three parts:
| Part | Questions | Marks per question | Total |
|---|---|---|---|
| Part A | 4 | 4 marks each | 16 |
| Part B | 4 | 6 marks each | 24 |
| Part C | 4 | 10 marks each (partial credit) | 44 |
| Total | 12 | 84 |
Part A and B answers require only a final numerical answer — no working shown. Part C requires full written solutions with complete reasoning, and partial credit is awarded for meaningful progress toward a solution.
What Different Score Ranges Mean
Score 60–84 (top performers): This range typically places a student in contention for an invitation to write the Canadian Mathematical Olympiad (CMO). The exact cut-off varies by year — contact the Canadian Mathematical Society for the specific COMC 2025 threshold. Students in this range have demonstrated exceptional mathematical ability and should be actively preparing for the CMO pathway.
Score 40–59 (strong performers): A solid COMC result. Students in this range are performing well above average and have real potential to improve into the top tier with structured preparation. The gap between 50 and 70 on the COMC is addressable — it typically reflects specific technique gaps in Part C proof-writing rather than fundamental ability limitations.
Score 20–39 (developing): This is a meaningful competition result — the COMC is a genuinely difficult contest and most student participants score in this range. The most useful question is not “is this score good?” but “which specific parts of the paper caused the most difficulty, and what do those difficulties point to?”
Score below 20: The COMC may not yet be the right contest for this student’s current level. Building stronger foundations through the Cayley, Fermat, and COMC Part A before targeting Part B and C performance is the right development path. See our math competitions in Canada guide for the full ladder.
The CMO Invitation Threshold
Top COMC 2025 performers are invited to write the Canadian Mathematical Olympiad — Canada’s most prestigious high school mathematics competition. The exact score threshold varies by year and is determined by the Canadian Mathematical Society after results are tabulated.
If your child is in the score range that might qualify, contact the CMS directly for confirmation. See our Canadian Mathematical Olympiad guide for what the CMO involves and how to prepare.
How to Use the COMC 2025 Past Paper
The COMC 2025 paper and official solutions will be published on the CEMC website at cemc.uwaterloo.ca following the competition. Working through the past paper — systematically, not just reviewing the answers — is the highest-leverage preparation activity available before the 2026 contest.
Step 1: Score by Part, Not Just Total
Record separately:
- Part A score (out of 16)
- Part B score (out of 24)
- Part C score (out of 44)
A student with 12/16 on Part A, 10/24 on Part B, and 0/44 on Part C has a very different preparation need from a student with 16/16, 20/24, and 8/44. The total score (22 vs 44) doesn’t capture this distinction; the part-by-part breakdown does.
Step 2: Categorise Every Non-Full-Credit Question
For each question where you did not score full marks, identify the reason:
Topic gap: The relevant mathematical technique or content area was unfamiliar.
Approach gap: You knew the content but could not identify how to apply it to this specific problem.
Execution gap: You identified the right approach but made an error in carrying it through.
Part C proof gap: You had the right idea but could not write it as a complete, rigorous mathematical argument.
Each category has a different fix. Topic gaps require content study. Approach gaps require more varied problem exposure. Execution gaps require careful checking habits. Proof gaps require deliberate proof-writing practice.
Step 3: Re-attempt Before Reading Solutions
For every problem you did not fully solve: attempt it again, fresh, without any hints. Spend at least 20 minutes on each Part B problem and 30–45 minutes on each Part C problem before consulting the official solution.
This is the most uncomfortable step and the most valuable one. The struggle of re-attempting a problem without solution access is what builds the mathematical resilience that improves competition performance.
Step 4: Study Solutions for Both Correct and Incorrect Answers
Read the official solution for every problem — including ones you answered correctly. Your approach may have been correct but less elegant than the official solution. Understanding the cleanest approach to each problem type builds the mathematical intuition that makes future problems easier.
For Part C solutions in particular: read not just what the solution does but why each step was taken. Ask: how would I have known to try this approach from the problem statement? The answer to that question is more valuable than the solution itself.
The COMC 2025 Paper: Topic Areas to Review
Without access to the specific 2025 paper, the following topic areas are consistently tested across COMC past papers and warrant systematic review for any student preparing for COMC 2026:
Part A (Accessible — computational and algebraic)
Algebra: Solving systems, manipulating expressions, working with sequences. Number theory: Divisibility, remainders, properties of integers — often accessible versions of deeper results. Geometry: Area calculations, similar triangles, coordinate geometry. Counting: Systematic counting, basic combinatorics.
Part A problems should be solved quickly and accurately. A student who struggles with Part A has foundational gaps that will compound in Parts B and C. See our Grade 11 Functions Ontario guide and math order of operations guide for foundational content.
Part B (Intermediate — requires mathematical insight)
Number theory: Modular arithmetic, prime properties, Fermat’s Little Theorem applications. Combinatorics: Pigeonhole principle, counting with restrictions, graph theory. Algebra: Functional equations, polynomial properties, rational root theorem applications. Geometry: Circle theorems, angle chasing, area and length relationships.
Part B requires recognising which technique applies, not just executing a known procedure.
Part C (Advanced — full proofs required)
Proof techniques: Mathematical induction, proof by contradiction, contrapositive arguments. Inequalities: Cauchy-Schwarz, AM-GM, Jensen’s inequality. Number theory: Divisibility proofs, Fermat’s Little Theorem, integer properties. Combinatorics: Existence proofs, extremal arguments, pigeonhole principle.
Part C proof-writing requires both mathematical content knowledge and the specific skill of constructing and expressing a complete rigorous argument.
Building a COMC 2026 Preparation Plan
The COMC is typically held in late October or early November. That gives students who wrote the COMC 2025 approximately 11–12 months before the next contest — more than enough time to make meaningful improvement.
Phase 1: Review and Diagnosis (Now — 1 month)
Complete the COMC 2025 paper analysis described above. Identify your three most significant topic/technique gaps. Build a targeted list of what to work on — specific, not vague. “Improve proof-writing” is vague; “practise modular arithmetic divisibility proofs using the template in our induction guide” is specific.
Phase 2: Systematic Topic Building (Months 2–6)
Work through the identified gaps systematically. For each topic:
- Read the relevant guide and understand the technique
- Work through 10–15 problems on that topic specifically
- Practise in competition format (timed, without notes)
For Part C specifically: write out complete proof arguments for every practice problem, even when you could get the answer more informally. Proof-writing is a specific expressive skill that improves with deliberate practice.
Key resources:
- CEMC past papers for all contests (Cayley, Fermat, COMC) at cemc.uwaterloo.ca
- Art of Problem Solving for topic-specific practice
- Think Academy’s competition programme for structured expert-guided preparation
Phase 3: Past Paper Practice (Months 7–10)
Work through COMC past papers from recent years — 5–8 years is a good range. For each paper:
- Sit it under timed conditions (2.5 hours, no aids)
- Score by part immediately after
- Complete the full analysis described in the review section above
- Re-attempt unsolved problems before reading solutions
Phase 4: Consolidation (Final 4–6 weeks)
Focus on Part C specifically — this is where the most improvement is possible and where preparation time pays off most directly. Practise proof-writing under contest conditions. Review all techniques that appeared in past Part C problems. Ensure Part A performance is automatic (these marks should not be lost to carelessness).
The COMC as a Stepping Stone: What Comes Next
The COMC sits in the middle of the Canadian competition mathematics pathway. Understanding what it leads to — and what it requires as a foundation — is essential for planning.
What the COMC builds on:
- Cayley Contest (Grade 10) and Fermat Contest (Grade 11) — the immediate predecessors in the CEMC series
- AMC 10 and AMC 12 — strong parallel preparation, different format
- Strong MCR3U and MHF4U content (Ontario), Math 30-1 (Alberta) — curriculum foundations
What the COMC leads to:
- CMO invitation — for top performers, the gateway to Canada’s national olympiad
- Euclid Contest — taken in parallel (Grade 12); the two contests together provide a comprehensive picture of a student’s senior competition mathematics level
- University of Waterloo Faculty of Mathematics — COMC performance is considered in admissions, particularly for students applying to mathematics, computer science, and combinatorics programmes
For the Euclid preparation connection, see our Euclid math contest guide and Euclid past contests guide.
How Think Academy Supports COMC Preparation
Think Academy Canada works with students preparing for the COMC at every level — from students targeting a strong Part A and B performance to those working toward Part C solutions and CMO qualification.
Our COMC preparation programme:
Diagnostic-led: Every student begins with an assessment identifying specific gaps across Part A, B, and C topic areas — so preparation time is targeted at the problems most likely to improve the score.
Proof technique development: Part C requires complete, rigorous written proofs. Think Academy builds proof-writing as a specific skill — including the mathematical induction, contradiction, contrapositive, and inequality techniques that appear most frequently in COMC Part C.
Past paper review: Our instructors work through COMC past paper solutions with students, explaining not just what the solution does but how to recognise the right approach from the problem statement — the skill that cannot be extracted from reading solutions alone.
The CMO pathway: For students whose COMC performance suggests potential for the CMO, Think Academy’s programme builds toward the mathematical depth the CMO demands. See our Canadian Mathematical Olympiad guide.
Frequently Asked Questions
When are COMC 2025 results released? COMC results are typically distributed to schools within several weeks of the contest date (late October/early November). Contact your school’s mathematics department or competition coordinator if you have not received results.
Where can I find the COMC 2025 past paper and solutions? The COMC 2025 paper and official solutions will be published on the CEMC website at cemc.uwaterloo.ca following the contest. Navigate to Contests → COMC → Past Contests.
What score on COMC 2025 qualifies for the CMO? The CMO invitation threshold varies by year. Top COMC performers are considered, but the exact cut-off is determined by the Canadian Mathematical Society after results are tabulated. Contact the CMS directly for the 2025 threshold.
My child scored lower than expected on COMC 2025. What should we do? Work through the past paper analysis described in this guide — score by part, categorise every error, and identify the specific topic or technique gaps that produced the most lost marks. A lower-than-expected COMC result is almost always addressable with structured preparation targeting those specific gaps.
How different is COMC 2026 likely to be from COMC 2025? The format and scoring are consistent year to year. Topic areas vary, but the core areas (algebra, number theory, combinatorics, geometry) are always represented across the four parts. Preparation built on past papers is directly applicable to the next contest.
How long before COMC 2026 should preparation start? Starting now — the day after receiving COMC 2025 results — is the optimal time. This allows a full 11–12 months of preparation, which is enough time for substantial improvement across all three parts.
See our related guides: COMC math contest guide · Canadian Mathematical Olympiad guide · Euclid math contest guide · Euclid past contests guide · math induction proof guide · proof by contradiction guide · contrapositive math guide · Cauchy-Schwarz inequality guide · pigeonhole principle guide · Fermat’s Little Theorem guide · math competitions in Canada
