The Fermat Contest is the Grade 11 member of CEMC's Pascal, Cayley and Fermat trio, and for many students it is the last multiple-choice contest before the written Euclid in their final year. The format has not changed since Grade 9, but the math has, and so has the pressure of the clock: CEMC's own 2026 statistics show most Fermat writers leaving the final questions untouched. This page lays out the 2027 contest from CEMC's pages, reads the 2026 results booklet question by question, gives a three-pass plan for spending the sixty minutes, offers six problems we wrote with full solutions, and shows how Fermat leads to the Hypatia, the CSMC and the Euclid.
Live online teaching since 2020 · 10,000+ students · six Grade 11 problems on this page, all our own
Quick answer
The Fermat Contest is CEMC's Grade 11 math contest from the University of Waterloo: twenty-five questions, mostly multiple choice, sixty minutes, out of 150, written at school on Tuesday 23 or Wednesday 24 February 2027 in the Americas, with entry only through the school. Modern Age Coders prepares Grade 11 students for it live online, in a batch or one to one, in the Waterloo Math Contests course, Gauss to Euclid.
Courses for Grade 11
Three courses we pair with a Fermat year
Contest preparation first, then the deeper problem solving the last questions demand, then the senior school math that Fermat and, a year later, Euclid are built on.
One CEMC page covers Pascal, Cayley and Fermat together. Here are the Fermat details, as that page and the cover of the 2025 Fermat booklet read on 22 October 2026.
Who and when
CEMC: "Students in Grade 11 are eligible to write the Fermat Contest." For official results, "The Fermat Contest may be written by any participant in Grade 11 or below," so a strong Grade 10 student may write Fermat instead of Cayley.
In North and South America the 2027 contest runs on Tuesday, February 23, 2027 and Wednesday, February 24, 2027, and each school uses one of the two days. Schools in Canada must order by Tuesday, February 9, 2027.
The paper itself
Twenty-five questions: ten in Part A, ten in Part B, both with five lettered options, and five in Part C, each with a whole-number answer from 0 to 99. The total is 150.
The 2025 booklet tells writers: "When your supervisor tells you to begin, you will have 60 minutes of working time." It also warns that "Diagrams are not drawn to scale. They are intended as aids only." Measuring a diagram with a ruler is not a method.
Fermat 2027: the remaining practical points, from CEMC's contest page and the 2025 Fermat booklet (read 22 October 2026)
Topic
Detail
Marks per question
5 in Part A, 6 in Part B, 8 in Part C; a wrong answer loses nothing; a blank gains 2, for no more than 10 blanks
Paper or online
The school chooses when it orders; a paper Fermat is sent back to CEMC to be marked
Calculators
Some are permitted; devices with a computer algebra system or internet access are among those that are not
One per year
Pascal, Cayley and Fermat are a group, and a student writes only one of them in a school year
After the paper
Writers are asked not to discuss the problems or solutions online for 48 hours
Awards
A Certificate of Distinction for the top 25%; a Contest Medal for each School Champion who reaches the medal cutoff, with two medals in a tie
Sources: CEMC, Pascal, Cayley and Fermat Contests and the cover of CEMC's 2025 Fermat Contest booklet, read 22 October 2026. Modern Age Coders works independently of CEMC and the University of Waterloo.
The hour
Where the Fermat hour runs out, and a plan for spending it
CEMC's 2026 results booklet shows, for every Fermat question, the share of counted contestants who left it blank. Read down the column and the shape of the hour appears: by the last five questions, a majority had stopped writing answers.
Fermat 2026, from question 15 on: share leaving each question blank and share answering it correctly, from CEMC's 2026 PCF Results booklet (Fermat statistics page: 14670 contestants, average mark 88.77). No answers are reproduced.
Question
Left blank
Answered correctly
15
35.96%
29.97%
19
41.59%
29.14%
20
49.58%
25.99%
21
60.4%
17.27%
22
51.06%
22.33%
23
69.92%
7.33%
24
79.41%
4.10%
25
80.34%
1.55%
Two things stand out, and the reading is ours. First, question 22 was answered correctly more often than question 21, and left blank less often. Order on the paper is a guide to difficulty, not a rule, and a student who stops at 21 may walk past a question they could have done. Second, the blank column passes 50% at question 21. For most Grade 11 writers, the contest is decided by how well they use the first forty minutes.
Our three-pass plan for the 60 minutes of a Fermat paper (ours, not CEMC's)
Pass
Clock
What the student does
1. Sweep
Minutes 0 to 25
Questions 1 to 15 in order. Anything that will clearly take more than three minutes gets a mark in the margin and is skipped.
2. Scout
Minutes 25 to 30
Read all five Part C questions, and questions 16 to 20, without solving. Choose the two or three that look most approachable.
3. Spend
Minutes 30 to 55
Work the chosen questions, Part C first if one looked open, then the skipped ones from pass 1.
Close
Minutes 55 to 60
Count blanks. Up to ten earn 2 each, so guess only where at least two Part B options are already ruled out.
Why scout before spending
A Part C question is worth 8 marks, more than a Part B question at 6. If one of the last five happens to suit a student, finding it in minute 26 instead of never is the cheapest 8 marks on the paper.
Scouting also stops the most common Fermat failure we see: fifteen minutes lost on question 18 while an easier question 22 waits unread.
Practising the plan
We rehearse the passes with a timer on short sets from November, so by February the switch from sweep to scout happens without thinking.
After each timed paper the student writes down where the minutes went. Two or three papers later, most students find that their time was not short; it was spent on the wrong questions.
Strong wrong answers
When most Fermat writers chose the same wrong option
The results booklet also prints how many contestants chose each option in Parts A and B. In 2026 two Fermat questions in the first half had one wrong option that pulled in a large share of the field.
Two 2026 Fermat questions with a strong wrong option, from CEMC's 2026 PCF Results booklet. Letters and answers are not reproduced.
Question
Chose the correct option
Chose the most popular wrong option
9
56.19%
31.32%
10
30.15%
58.51%
On question 10, a single wrong option drew 58.51% of the counted contestants, almost twice the 30.15% who chose the correct one. We will not guess at what that question asked, and we do not reproduce it, but the pattern is one every contest teacher knows: an option that matches the first, quick reading of a question. The habit that protects against it is cheap. Before filling in a circle, the student asks what the question would have to say for the quick answer to be right, and whether it says that.
Re-read the final sentence. Is it asking for the number, its square, the difference, the remainder?
Test an extreme. Put in 0, 1 or a very large value and see whether the chosen option still makes sense.
Distrust the diagram. The booklet says diagrams are not drawn to scale, so an angle that looks like 90 degrees has to be proved to be one.
Estimate first. A rough size for the answer rules out options that are ten times too big or too small.
These four habits are ours, and they cost about fifteen seconds a question. Over twenty multiple-choice questions that is five minutes, and in our experience it is the best five minutes a Fermat writer can spend.
Six practice problems
Six Fermat-style problems, written by us, solved in full
Every problem here is our practice problem, not a CEMC problem. Our teachers wrote them for Grade 11 students, and none is copied from or modelled on a past Fermat. Two sit at Part A level, two at Part B level and two in Part C, with answers from 0 to 99. We checked each answer in Python by brute force or substitution before publishing.
F1.Our practice problem, not a CEMC problem. Part A level. If f(x) = 2x - 3, what is the value of f(f(4))? (A) 5 (B) 7 (C) 9 (D) 11 (E) 13
Worked solution. Work from the inside out. f(4) = 2(4) - 3 = 5, then f(5) = 2(5) - 3 = 7, answer (B). Option (A) is the inside value only, the most common slip on composition questions: stopping one step early.
F2.Our practice problem, not a CEMC problem. Part A level. If 2x + 3 = 4x - 1, what is the value of x? (A) 1 (B) 2 (C) 4 (D) 5 (E) 7
Worked solution. Write both sides with base 2: 4x - 1 = (22)x - 1 = 22x - 2. Equal powers of 2 have equal exponents, so x + 3 = 2x - 2 and x = 5, answer (D). Check: 28 = 256 and 44 = 256.
F3.Our practice problem, not a CEMC problem. Part B level. In an arithmetic sequence, the 3rd term is 14 and the 8th term is 39. What is the 20th term? (A) 94 (B) 96 (C) 99 (D) 104 (E) 109
Worked solution. From the 3rd term to the 8th there are 5 steps, and the terms rise by 39 - 14 = 25, so the common difference is 5. From the 8th term to the 20th there are 12 more steps: 39 + 12 x 5 = 99, answer (C). Counting steps, not terms, avoids the off-by-one error that leads to (D), 104.
F4.Our practice problem, not a CEMC problem. Part B level. A function f satisfies f(x) + 2f(1/x) = 3x for every non-zero real number x. What is f(2)? (A) -1 (B) 0 (C) 1 (D) 2 (E) 3
F4 · our worked solutiontext
f(x) + 2f(1/x) = 3x ... (1)
Replace x by 1/x everywhere:
f(1/x) + 2f(x) = 3/x ... (2)
Double (2): 2f(1/x) + 4f(x) = 6/x
Subtract (1): 3f(x) = 6/x - 3x
So f(x) = 2/x - x
f(2) = 2/2 - 2 = -1
Check in (1) with x = 2: f(2) + 2f(1/2) = -1 + 2(4 - 1/2) = -1 + 7 = 6 = 3 x 2
The answer is (A), -1. Substituting x = 2 alone gives one equation with two unknowns, f(2) and f(1/2). The idea is to substitute 1/x as well, which gives a second equation, and then solve the pair. This trick appears in Fermat-level function questions often enough to be worth practising until it is automatic.
F5.Our practice problem, not a CEMC problem. Part C level. For how many integers n with 1 ≤ n ≤ 99 is n2 - 1 a multiple of 24? Give a whole number from 0 to 99.
Worked solution. Write n2 - 1 = (n - 1)(n + 1). If n is odd, n - 1 and n + 1 are consecutive even numbers, so one of them is a multiple of 4 and their product is a multiple of 8. If n is not a multiple of 3, one of n - 1 and n + 1 is, so the product is a multiple of 3. Together: when n is odd and not a multiple of 3, n2 - 1 is a multiple of 24. Conversely, if n is even then n2 - 1 is odd, and if 3 divides n then 3 does not divide n2 - 1, so both conditions are needed. Count from 1 to 99: there are 50 odd numbers, and of those the odd multiples of 3 are 3, 9, 15 and so on up to 99, which is 17 numbers. The answer is 50 - 17 = 33.
F6.Our practice problem, not a CEMC problem. Part C level. Two fair six-sided dice are rolled. The probability that the product of the two numbers rolled is a multiple of 6 can be written as p/q in lowest terms. What is p + q?
F6 · our worked solutiontext
Complement: products that are NOT multiples of 6
Product misses the factor 2 -> both dice odd: 3 x 3 = 9 pairs
Product misses the factor 3 -> neither die is 3 or 6: 4 x 4 = 16 pairs
Misses both 2 and 3 -> both dice in {1, 5}: 2 x 2 = 4 pairs
Not a multiple of 6: 9 + 16 - 4 = 21 pairs
Multiple of 6: 36 - 21 = 15 pairs
Probability 15/36 = 5/12, so p + q = 5 + 12 = 17
The answer is 17. Counting the complement is easier here: a product fails to be a multiple of 6 when it misses the factor 2 or the factor 3, and inclusion and exclusion stops the four pairs that miss both from being counted twice. A direct count, listing all 15 good pairs, makes a good check.
Working the six as a mini paper
Allow fourteen minutes and use the three passes: F1 to F3 quickly, then read F5 and F6 before choosing between F4 and a Part C problem.
Score it with the contest marks: 5 for F1 and F2, 6 for F3 and F4, 8 for F5 and F6. The maximum is 38.
The ideas inside
Composition and bases (F1, F2) are Part A habits. Counting steps (F3) and substituting 1/x (F4) are the kind of single idea Part B rewards.
F5 and F6 both turn on the factors 2 and 3, from two different directions: divisibility of a product, and the complement of a probability. Spotting the shared structure is the point.
Grade 11 math
The Grade 11 math the Fermat paper rests on
CEMC writes Fermat on curriculum common to all the provinces. Below is our own map of what that means in practice for a Grade 11 student, not a CEMC list.
Topics on a Fermat paper and how we teach them (our analysis)
Substitution as a tool, as in F4: choose the input that creates a second equation
Exponents and powers
Equations with powers, comparing large numbers, last digits
Rewriting with a common base before anything else
Sequences
Arithmetic and geometric sequences, sums, recursive rules
Counting steps between terms, and writing out the first five terms
Trigonometry
Right-triangle ratios, special angles, the sine and cosine laws
Exact values of sine and cosine for 30, 45 and 60 degrees, and when to use each law
Counting and probability
Dice, cards, arrangements, complements
Choosing between a direct count and the complement before starting
Number theory
Divisibility, remainders, factoring numbers like n squared minus 1
Factoring first, then testing small cases, as in F5
Two provinces as examples
In Ontario, the Grade 11 university math course is MCR3U, Functions. It is the prerequisite for MHF4U, Advanced Functions, so the function work Fermat rewards feeds straight into Grade 12.
In British Columbia, Grade 11 students take Pre-calculus 11 or Foundations of Mathematics 11. Pre-calculus 11, with its quadratic functions and trigonometry, is the closer match for a Fermat paper.
February comes early in the course
The contest falls in February, when a semestered Grade 11 course may have only just started. A student whose functions course runs in the second semester may meet some Fermat topics in our classes first.
That is one reason we spend November and December on functions and sequences: by February the student has them, whatever the school timetable.
2026 results
Fermat 2026: averages, cutoffs and what results look like
CEMC lists the Fermat average and cutoffs for 2026 on its contest page. These are the Fermat figures only, never added to Pascal or Cayley.
Fermat 2026, from CEMC's contest page (read 22 October 2026)
Measure
Fermat 2026
Average (mean)
88.9
Certificate of Distinction cutoff
102
School Medal Champion cutoff
88
Maximum possible score
150
Number of contestants
17 959
Reading the cutoff
Our arithmetic: the 2026 Certificate of Distinction line of 102 is 68 percent of 150 (102 / 150). That is a lower share than the Pascal and Cayley lines, and our reading is that it matches the blank rates above: the Grade 11 paper asks the most of its writers, so the top quarter begins lower.
CEMC also prints "Student rankings" in its results booklet, so a student can see where a score places among all contestants, and that is more useful than the raw number.
Names, rankings and opting out
The 2025 Fermat cover says that "The name, grade, school and location, and score range of some top-scoring students will be published on our website, cemc.uwaterloo.ca."
CEMC's rules let a student decline that: participants consent to having their names in public results "unless they choose to opt out". A family that prefers privacy should raise it with the school's contest supervisor.
The rule is the same for every CEMC contest: a school orders, and its students write. A Grade 11 family's part is a timely conversation.
November 2026: ask the head of math whether the school will order the 2027 Fermat, and on which February day it will run.
December 2026: if the school has never ordered from CEMC, an application for a school account is needed, and CEMC reviews it by hand, which can take up to three weeks.
January 2027: if the school will not order, look for a nearby school willing to let your child sit the paper there, as CEMC suggests.
By Tuesday, February 9, 2027: the order for a school in Canada must be in.
Contest day: the student writes at the ordering school, supervised in person, on paper or online as the school chose.
We prepare students; we cannot enter them or host the paper. The full entry rules are on CEMC's How contests work page.
The plan
A Grade 11 plan, November 2026 to February 2027
Our plan, month by month, for a student starting in November and writing on Tuesday 23 or Wednesday 24 February 2027, with two live classes each week.
Our month-by-month Fermat plan (not a CEMC schedule)
Month
Math focus
Contest skill
Practice
November 2026
Functions, composition, functional equations
The sweep: questions 1 to 15 at three minutes or less
Part A of two past Fermat papers, timed
December 2026
Exponents, sequences, the factors of n squared minus 1
Elimination and the four trap checks
Part B of two past papers; F1 to F4 above
January 2027
Trigonometry, counting, probability
The scout: choosing among Part C questions
Two full papers under the three-pass plan; F5 and F6
February 2027 (to the 22nd)
No new topics
Calm blank counting in the last five minutes
One final full paper, then the mistakes list only
First CEMC contest
Aim for a clean sweep of Part A and half of Part B. Try the scout in every timed paper.
Wrote Cayley last year
Your Cayley mistakes are the starting list. The goal moves to Part C.
Euclid in view
Add one written solution a week from December, ready for Hypatia and the Euclid.
After Fermat
From Fermat to Hypatia, the CSMC and the Euclid
Grade 11 is the year a CEMC student moves from choosing answers to writing them. Everything in the table is from CEMC or Waterloo; the last column is our advice.
The written contests open to a Grade 11 student, from CEMC's and the University of Waterloo's pages (read 22 October 2026)
Contest
What the organizer says
Our advice
Hypatia (Grade 11), Wednesday, April 7, 2027
"Students in Grade 11 are eligible to write the Hypatia Contest." Each solution is judged on completeness, clarity and presentation, and "a correct solution, poorly presented, will not earn a full score for that problem."
The natural partner to Fermat: the same grade, every step written out
CSMC (Grades 11 and 12)
"Students in Grades 11 and 12 and CÉGEP students are eligible to write the CSMC." Marked out of 60; most problems use curriculum "up to and including the final year of secondary school."
The 2026 sitting is on Wednesday, November 18, 2026, and CEMC's ordering deadline for it is Thursday, October 22, 2026, the day this page was written; for most readers it is a Grade 12 plan
Euclid (final year)
CEMC: "Many students seeking to achieve a strong score in their final year of secondary school write the Euclid one or more times in previous years." The 2027 date is Tuesday, April 6, 2027 in the Americas.
Worth writing in Grade 11 as a rehearsal, if the school will enter a Grade 11 student
What Waterloo says, in its own words: its Supplementary Information Form "asks about any Waterloo mathematics contests you've participated in", and writing the CSMC or the Euclid "is not required for admission, but writing one of these contests is required for some Faculty of Mathematics scholarships." Fermat is not one of the two contests named there. Its value in Grade 11 is as preparation for them, and as a contest worth writing for its own sake. We make no promise about any scholarship, admission or result.
Past Fermat papers, and the booklets most students never open
CEMC posts every recent Fermat paper with solutions, and its results booklets too. Students use the first; almost nobody uses the second, which is a mistake.
Past papers
CEMC's past contests, solutions and results page has the Fermat papers of recent years. We use them whole and timed from January 2027, and part by part before that.
The Problem Set Generator also draws on past Fermat questions, which makes it useful for a holiday fortnight of mixed practice.
Results booklets
The booklet for each year shows how many students chose each option on each question. After a timed past paper, we have the student compare their own blanks and errors with the national pattern for the same paper.
A question that 80% of contestants left blank and the student also left blank is no cause for worry. A question most contestants answered correctly and the student missed is the one to study.
Solutions are read after a genuine attempt, never before, and the student explains CEMC's solution back in their own words. That one rule turns an old paper from a quiz into a lesson.
Starting point
Four kinds of Fermat writer we meet
Our labels, used to plan from the first class.
Where Grade 11 students tend to start (ours)
Type
What it looks like
1. The newcomer
Strong at school math, has never written a CEMC contest
2. The sprinter
Fast through Part A, stuck by question 16, never reaches Part C
3. The perfectionist
Accurate but slow; leaves points on the table by refusing to skip
4. The planner
Uses the passes, finds the open Part C question, counts blanks at the end
For parents
Types 2 and 3 are the most common, and both are fixed by the same thing: practising the hour, not just the math.
A Fermat score is only one February afternoon. Ask your child what they would do differently next time; that answer tells you more.
For students
Read all of Part C by minute 30, every time, even when it feels like a waste.
If a question has taken four minutes and you can see no way in, mark it and move on. You can come back.
Further courses
Nine courses for a Grade 11 problem solver
All taught live online, with the same teacher every week, in a group or privately, wherever in Canada a student lives.
A weather forecasting site with live conditions for any location.
by Krish
Fees
Fees
Whatever CEMC charges is paid by the school with its order. Our monthly fee is for teaching alone, with no term contract, so stopping after the February 2027 paper is simple.
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From Grade 11 families
Fermat Contest: what families ask
What is the Fermat Contest?
It is CEMC's math contest for Grade 11, from the University of Waterloo. Students have 60 minutes for 25 questions worth 150 marks: twenty with five lettered options and five with a whole-number answer from 0 to 99.
When is the Fermat Contest in 2027?
The Americas window is two days long, Tuesday, February 23, 2027 or Wednesday, February 24, 2027, with the school choosing its day. Canadian schools order by Tuesday, February 9, 2027.
Can a Grade 10 student write Fermat?
Yes. CEMC says the Fermat Contest may be written by any participant in Grade 11 or below, so a Grade 10 student working ahead can choose it. They would then not write Cayley that year, because only one of Pascal, Cayley and Fermat is allowed per school year.
How many students leave Fermat questions blank?
Many. In CEMC's 2026 results booklet, over half of the counted Fermat contestants left question 21 blank, and about four in five left questions 24 and 25 blank. That is why we teach a time plan as well as the math.
What was the Fermat cutoff in 2026?
CEMC lists a 2026 Fermat average of 88.9, a Certificate of Distinction cutoff of 102 and a School Medal Champion cutoff of 88, out of 150, with 17 959 contestants.
Does the Fermat Contest matter for University of Waterloo admission?
Waterloo names the CSMC and the Euclid, not Fermat, as the contests required for some Faculty of Mathematics scholarships, and says neither is required for admission. Fermat is good preparation for both. We make no admission or scholarship promises.
Should my child write Hypatia as well as Fermat?
If they enjoy Fermat, yes. Hypatia is CEMC's Grade 11 full-solution contest, on Wednesday, April 7, 2027 in the Americas, and it trains the written reasoning the Euclid asks for a year later.
Can a student write the Euclid in Grade 11?
CEMC welcomes motivated students in lower grades and says many students write the Euclid one or more times before their final year. Whether a Grade 11 student can sit it depends on the school ordering it for them.
How do we enter the Fermat Contest?
Through the school, which orders it from CEMC; students cannot enter themselves. A student whose school says no can, as CEMC suggests, ask a different school in the area to let them sit the paper there.
When are Fermat classes?
Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays. We work in Eastern time and confirm each class in your province's time.
Read next
Related pages
More for Grade 11 students in Canada who are thinking about contests and university math.
In the first class your child does two Fermat-style questions we wrote and a short timed sweep, with a teacher watching how they spend the minutes. You hear which of the four types they are and what we would change before February 2027.
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