The Fermat Math Contest is the senior contest in the University of Waterloo’s Pascal–Cayley–Fermat (PCF) series, written each February by Grade 11 students and ambitious younger students across Canada. Run by the Centre for Education in Mathematics and Computing (CEMC), the contest is a 60-minute, 25-question challenge that demands genuine mathematical thinking, not curriculum recall. For students aiming at competitive university programs — particularly Waterloo’s Math, Computer Science, and Engineering faculties — a strong Fermat result is one of the cleanest signals on a Canadian application. This guide covers the format, the difficulty curve, registration deadlines, Fermat Math Contest past papers (including 2025 and 2024), and a structured Fermat Math Contest practice plan built around what the top scorers actually do.
What is the Fermat Math Contest?
The Fermat Contest is the most advanced of the three PCF contests, designed for students in Grade 11 or below. It sits above the Pascal (Grade 9) and Cayley (Grade 10) and serves as a natural bridge to the Euclid Contest, which Grade 12 students write later in the spring as part of Waterloo’s admissions process.
Each year, more than 80,000 students worldwide register for one of the three PCF contests. The Fermat draws the strongest cohort: students who have either been preparing for years through programs like Think Academy, or who are naturally drawn to mathematical problem-solving and want to test themselves against a national benchmark.
The contest is not a school exam. It rewards careful reading, the ability to abandon a wrong approach quickly, and a deep enough toolkit to recognise familiar structures hiding inside unfamiliar problems. Students who treat it as “harder algebra homework” tend to score around the median. Students who treat it as a problem-solving exercise tend to break into the top quartile.
Who is eligible to write the Fermat?
| Contest | Eligible grade | Typical age |
|---|---|---|
| Pascal | Grade 9 or below | 13–14 |
| Cayley | Grade 10 or below | 14–15 |
| Fermat | Grade 11 or below | 15–16 |
A student can write only one of the three PCF contests in a given school year. Strong Grade 10 students sometimes write the Fermat instead of the Cayley if they have been preparing competitively, but they cannot write both.
Fermat Math Contest format and scoring (2025/2026 update)
The CEMC has updated the PCF format recently, so older preparation guides are out of date. Here is the current structure.
Structure
- 25 questions total, split into three parts of increasing difficulty
- Parts A and B: traditional multiple choice (A, B, C, D, or E)
- Part C: each answer is a whole number from 0 to 99 (newer format, no longer multiple choice)
- 60 minutes of working time
- Score out of 150
- Written at school on paper or online through the CEMC Contests Online platform
- Some calculators permitted (no internet access, no CAS, no communication features)
Scoring breakdown
| Section | Questions | Points per correct answer | Total available |
|---|---|---|---|
| Part A | 10 | 5 | 50 |
| Part B | 10 | 6 | 60 |
| Part C | 5 | 8 | 40 |
| Total | 25 | — | 150 |
There is no penalty for a wrong answer, but each unanswered question is worth 2 points, to a maximum of 10 unanswered questions (20 points). This makes blank-management a real strategic decision: on Fermat specifically, where Part C is materially harder than on Pascal or Cayley, the top scorers often leave one or two Part C questions blank deliberately.
What topics show up?
The Fermat covers content common to Grade 9–11 curricula across Canadian provinces. The most frequent areas are:
- Algebra: quadratic equations, systems, sequences and series, functional equations, inequalities
- Geometry: triangles, circles, similarity, area ratios, coordinate geometry, 3D solids
- Number theory: divisibility, modular arithmetic, prime factorisation, integer equations
- Counting and probability: structured casework, simple recursion, probability trees
- Logical reasoning: combined word problems that pull from two or more topics
Fermat Part C is meaningfully harder than Cayley Part C. The problems often require a non-obvious first step — a substitution, a transformation, or a way of reframing the problem — before the algebra or geometry becomes tractable. This is the gap students need to bridge between strong school performance and competitive contest performance.
Fermat Math Contest 2026 dates and registration
The 2026 Fermat Contest was written on Wednesday, 25 February 2026 in North and South America. The CEMC has published the tentative 2027 date as Wednesday, 24 February 2027, with the practice contest opening earlier in the month through the CEMC Contests Online platform.
Key deadlines for Canadian schools
| Item | Typical timing |
|---|---|
| Registration deadline | Late January |
| Practice contest opens | Early February |
| Contest day | Last Wednesday of February |
| Results published | March (preliminary), then mid-March (final) |
| Solutions posted publicly | By mid-May on the CEMC website |
Students cannot register directly. Schools register them through the CEMC Contest Supervisor Portal. If a child’s school does not offer the Fermat, parents can ask a nearby school to host the student as a guest writer. The per-student fee is set by each school; CEMC’s base charge is roughly $5–$10 per participant. Think Academy can help you register.
Fermat Math Contest 2025: a strong recent benchmark
The Fermat Math Contest 2025 was written on Wednesday, 26 February 2025, and is now one of the most important papers for current preparation. It uses the same Part C format as 2023 and 2024 (whole-number answers 0–99), and its difficulty calibration sits very close to what students writing the next Fermat should expect.
A few observations from the 2025 paper:
- Part A stayed accessible, with the opening questions testing simple arithmetic and basic algebraic substitution. Strong students cleared Part A in under 12 minutes, which is the pace top scorers aim for.
- Part B leaned heavily on geometry, including a triangle area-ratio problem that rewarded students who knew how to split a triangle using parallel lines and similar triangle relationships. This is exactly the kind of toolkit that separates Fermat-ready students from Cayley-ready ones.
- Part C was demanding but fair. Question 23 involved a perfect-square calendar-year problem (the kind of integer-equation reasoning Fermat increasingly favours), and question 25 combined casework with a counting argument that required spotting a clean invariant.
Approximate topic distribution from 2025:
| Topic | Approximate number of questions |
|---|---|
| Algebra and equations | 7 |
| Geometry (plane and coordinate) | 8 |
| Number theory and divisibility | 4 |
| Counting and probability | 3 |
| Logic and pattern recognition | 3 |
The signal from 2025: the geometry weighting has crept up slightly compared with 2023 and 2024. Students preparing for the next Fermat should spend proportionally more practice time on triangle similarity, area ratios, and coordinate-geometry problems than they might have a few years ago.
Fermat Math Contest 2024: what to learn from it
The Fermat Math Contest 2024 was written on Tuesday, 27 February 2024, and is one of the most useful papers for current preparation because its calibration matches what students see today. A few observations:
- Part A was forgiving by Fermat standards. Question 1 was a simple expression evaluation, and questions 2–5 stayed accessible to any motivated Grade 11 student. This is where strong scorers bank points fast and free up time for Part C.
- Part B introduced classic algebra–geometry crossover problems, including a coordinate-geometry question requiring students to find a line satisfying multiple area constraints. Students who had practised similar 2022 and 2023 problems recognised the structure immediately.
- Part C reached its hardest at question 25, a sequence problem that combined modular arithmetic with combinatorial reasoning. Most top scorers spent 12–15 minutes on it; those who skipped it and consolidated Parts A and B often scored higher overall.
Approximate topic distribution from 2024:
| Topic | Approximate number of questions |
|---|---|
| Algebra and equations | 8 |
| Geometry (plane and coordinate) | 7 |
| Number theory and divisibility | 4 |
| Counting and probability | 3 |
| Logic and pattern recognition | 3 |
The lesson from 2024 is simple: students who lock down 90% of Parts A and B almost always finish in the top quartile, even if they get only one or two Part C questions right. Front-of-paper accuracy matters more than back-of-paper heroics.
Fermat Math Contest past papers: where to find them and how to use them
Fermat Math Contest past papers are the single most valuable preparation resource, and they are all available free from the CEMC. Here is how to find them and how to actually use them.
Where to find Fermat past papers
- CEMC Past Contests archive — official papers, solutions, and results for every Fermat going back over a decade. Located on the CEMC Resources page.
- CEMC Problem Set Generator — builds custom sets of past Fermat, Cayley, and Pascal problems filtered by topic. Useful for targeted weak-area practice.
- CEMC Math Courseware — structured free lessons that map directly to the topics tested on the Fermat.
- Think Academy’s Fermat problem library — curated by difficulty and topic, with worked solutions in our app.
Which years to prioritise
Not every past paper is equally valuable. The Part C format changed around 2022, so older papers feel slightly different. We recommend this order:
| Priority | Year | Why |
|---|---|---|
| 1 | 2025 Fermat | Most recent paper; matches current difficulty exactly |
| 2 | 2024 Fermat | Same format, geometry-balanced |
| 3 | 2023 Fermat | Tough Part C; good stretch test |
| 4 | 2022 Fermat | First year of new Part C format |
| 5 | 2019 Fermat | Pre-format-change but excellent algebra |
How to actually use past papers
Most students treat past papers as a checklist: do the paper, mark it, move on. That is the slow path. Here is the faster one.
- Sit one paper fully timed, 60 minutes, no help.
- Mark it the same day, using the official CEMC solutions.
- Redo every question you got wrong, without looking at the solution first.
- Read the official solution, even for questions you got right. The CEMC frequently shows two different methods, and the second method is often where the real learning sits.
- Tag every mistake by type: concept gap, careless arithmetic, time pressure, misread the question.
- Build a personal error log that grows across all papers. After 5–6 papers, patterns emerge that show you exactly where to focus.
The post-mortem on a single paper should take longer than the paper itself. Ninety minutes to two hours per paper is normal at the serious preparation level.
Fermat Math Contest practice: a 12-week preparation plan
This is the structured Fermat Math Contest practice plan we recommend at Think Academy Canada for students targeting the top 25% or higher.
Weeks 1–2: Diagnose and benchmark
- Sit one past paper under timed conditions (the 2022 paper works well as a baseline).
- Mark it and record three numbers: total score, score by Part (A/B/C), and topics where mistakes clustered.
- Set the target: Certificate of Distinction (top 25%), top 10%, or top 1% (school medal candidate). The plan changes meaningfully at each level.
Weeks 3–6: Build topic foundations
Spend two weeks each on the two weakest topics from the diagnostic. Rotate through:
- Algebra (quadratics, systems, sequences)
- Geometry (similarity, area ratios, coordinate geometry)
- Number theory (divisibility, modular arithmetic)
- Counting and probability (casework, simple recursion)
Use a mix of the CEMC Problem Set Generator (custom topic sets from past PCF problems) and the CEMC Courseware modules. Twenty focused minutes a day beats two hours on Sunday.
Weeks 7–10: Past paper rotation
Aim for one full past paper per week, building from easier to harder.
| Week | Paper to attempt | Why |
|---|---|---|
| 7 | 2022 Fermat | Newer Part C format introduction |
| 8 | Fermat Math Contest 2023 | Hardest Part C in recent memory |
| 9 | Fermat Math Contest 2024 | Geometry-balanced, current difficulty |
| 10 | Fermat Math Contest 2025 | Most recent benchmark; closest to next paper |
After each paper, run the post-mortem described above.
Weeks 11–12: Refine and rehearse
- Two more past papers in fully timed conditions.
- Build a personal cheat sheet of formulas and techniques the student keeps forgetting. Not allowed in the contest, but the act of building it cements the content.
- Practise the blank-answer strategy: on every paper, decide in advance which 1–3 questions to leave blank to bank the 2-point unanswered marks.
- Run one final paper in the actual time slot you will write the real contest in. Body clock matters.
Why the Fermat matters for Canadian students
Strong Fermat results carry weight in three concrete ways.
- Waterloo admissions and the Adjusted Admission Average. The University of Waterloo’s Math and Computer Science faculties explicitly track CEMC contest performance. A Certificate of Distinction (top 25%) on the Fermat is a meaningful data point on a Canadian application; a top-school medal is significantly stronger. Strong Fermat scorers are also better positioned to do well on the Euclid in Grade 12, which directly affects scholarship offers.
- Pipeline to invitational contests. Top Fermat scorers can be invited to the Canadian Open Mathematics Challenge (COMC) and other invitationals, which feed into the Canadian Mathematical Olympiad (CMO) pipeline. For students aiming at top US universities, this trail of contest results is one of the most legible signals of mathematical ability.
- Transferable problem-solving skills. The thinking habits the Fermat builds — careful reading, structured casework, recognising when an approach is dead — transfer directly to physics, computer science, engineering, and any field that rewards problem-solving over recall.
For students writing the AMC 10 or AMC 12 the same year, Fermat preparation overlaps significantly. The algebra, geometry, and number-theory toolkits are nearly identical, though the AMC papers are 75 minutes for 25 questions and the AMC 12 reaches harder problems than the Fermat.
How the Fermat fits in the broader Waterloo contest family
The CEMC runs the country’s largest network of math contests. The Fermat is one stop on a longer journey.
| Grade | Recommended contest | Notes |
|---|---|---|
| 7 | Gauss 7 | Friendly entry point; multiple choice, online |
| 8 | Gauss 8 | Same format, one step harder |
| 9 | Pascal | First of the PCF series |
| 10 | Cayley | Middle of the PCF series |
| 11 | Fermat | This guide |
| 11–12 | Euclid | Full-solution contest; matters directly for Waterloo admissions |
For deeper dives, see our complete Waterloo Math Competitions guide, our Cayley Math Contest guide, our Pascal Math Contest guide, our Euclid Math Contest preparation guide, and our Gauss Math Contest guide.
How Think Academy Canada supports Fermat preparation
Think Academy is the international arm of TAL Education Group, one of the largest education companies in the world. Our Canadian programs are built around a carefully paced math curriculum, an online interactive platform built specifically for math, and gamified rewards that keep students engaged across the full school year rather than burning out in a six-week sprint.
For Fermat preparation specifically:
- A curriculum that runs ahead of provincial standards. Most provinces give students five years of high school math to reach the level the Fermat tests. Think Academy students reach the same level a year or more earlier, which is why our Grade 10 students regularly write the Fermat and place in the top quartile.
- Online-first delivery. Unlike in-person providers, our students learn from anywhere in Canada with the same teachers and the same curriculum. This matters in a country where in-person centres cluster in a handful of cities.
- A built-in interactive system. Lessons, homework, replays, and feedback all live in one app. Parents see what was taught, what was marked, and where their child stood that week.
- Free resources before you commit. Fermat past papers, a free math evaluation, and access to our problem library are available before signing up for a paid program.
- Teachers who mark homework personally. Every homework set is reviewed by the teaching team, not auto-graded by software.
We charge for the package, not for individual lessons, and we expect families to stay with us for years. That long arc is what produces durable mathematical skill — and the kind of Fermat result that opens doors at Waterloo and beyond.
Frequently asked questions
What is the Fermat Math Contest?
The Fermat Math Contest is a 60-minute, 25-question mathematics competition for students in Grade 11 or below, run annually by the University of Waterloo’s CEMC. It is the senior contest in the Pascal–Cayley–Fermat series and is written by tens of thousands of students worldwide each February.
When is the Fermat Math Contest written?
The contest is held on the last Wednesday of February. The 2026 contest was written on 25 February 2026; the tentative date for the 2027 contest is 24 February 2027.
How is the Fermat Math Contest scored?
It is scored out of 150. Part A questions are worth 5 points each, Part B questions 6 points each, and Part C questions 8 points each. There is no penalty for wrong answers, and each unanswered question is worth 2 points, up to a maximum of 10 blanks.
How hard is the Fermat Math Contest?
Part A is accessible to any strong Grade 11 student. Part B requires real problem-solving and is where most students lose points. Part C is genuinely difficult and is where the top scorers separate from the rest. The median score is usually around 60–75 out of 150.
What’s the difference between the Fermat and the Cayley?
The Cayley is for Grade 10 students and the Fermat is for Grade 11 students. Both follow the same format and scoring, but Fermat problems demand a deeper toolkit, especially in Part B and Part C, where algebra and geometry crossover problems are more common.
Where can I find Fermat Math Contest past papers?
The full archive is on the CEMC Past Contests page, with problems, solutions, and results for the last decade. The 2024 and 2023 Fermat papers are the most relevant for current preparation because they use the latest Part C format.
How should my child practise for the Fermat?
The most effective approach is structured: 4–6 weeks of topic-by-topic foundation work using the CEMC Problem Set Generator, followed by 4–6 weeks of timed past papers with detailed post-mortems on every mistake. Our 12-week plan above breaks this down week by week.
What calculator can my child use?
A basic scientific calculator is allowed. Calculators with internet access, communication features, or computer algebra system (CAS) capabilities — for example the Casio ClassPad 300, HP Prime, or TI-Nspire CAS — are not permitted.
Can my child write the Fermat if they’re in Grade 10 or earlier?
Yes. The Fermat is open to any student in Grade 11 or below. Strong Grade 10 students often write the Fermat instead of the Cayley if they have been preparing seriously, but they can only write one of the three PCF contests in a given year.
About Think Academy Canada
Think Academy Canada, part of TAL Education Group, supports K–12 students with structured math programs built around an online interactive platform, gamified learning, and teachers who personally mark every homework set. Our curriculum runs ahead of the provincial standards and is designed to prepare students for both school excellence and Canadian math competitions, including the Gauss, Pascal, Cayley, Fermat, and Euclid contests.
