Categories
Math All Contests Math Contests - Problems and Discussion

Introduction to Canadian Math Contest

(Revised in August 20, 2026)

Have you heard about the Canadian Math Contests? It is certainly for those talented in math and logic to show their ability, and a good opportunities for those who love the challenges.

For a student to participate in a contest, talk to the school one attends, or talk to us (Jonah’s Math Corner). Be sure to have a current enrollment in a secondary school (junior, high school) — or sometimes elementary school, located in Canada.

Check your grade too — if it says grade 9, then all students in grade 10 and higher cannot write that contest. A students in lower grade are allowed to participate in contests for higher grade (only if he or she feels confident), but not the other way round.

If you are looking at very selective competitions, then COMC (Canadian Open math challenge) is the contest to participate (typically held in October). The very best performed students can earn an entry to represent Canada for the IMO (International Math Olympiad) through further selective process.

Students in grade 9/10/11 may look for CIMC (Canadian Intermediate Contest) and CSMC (Canadian Senior Math Contest) — here Senior means “Senior High School” — Both are held in November on the same time, but no one is allowed to participate in both (just choose one of them).

Keep reading for information about different Contest series, detailed as follows: 

1) Junior math contests (have to be under grade 9 to participate): the most popular is the Gauss contest for grades 7 & 8, organized by U. of Waterloo. Gauss is very popular that some school teachers enrolled all of their students to participate.

There are some grade 9 contest – see the mid-level and high-school level contests, as the challenge is already close to high levels.

If you live in Alberta, then both U. of Calgary and U. of Alberta have set up challenges for Junior students.

2) Mid-level and High-school level Contests — the main stage for the middle school math challenge. University of Waterloo has organized 3 series respectively for grade 9, 10 and 11. The contests questions appears typically in multiple-choice format.

Series I: PCF contest: Pascal for grade 9, Cayley for grade 10 and Fermat – for grade 11.

Questions in PCF appear in multiple-choice format.

Series II: FGH contest: Fryer – for grade 9, Galois – for grade 10 and Hypatia – for grade 11.

No multiple-choice question in FGH series. All answers have to be worked out by participants. In any of these series, there will be two types of questions, one will ask participants for answers only, and the other type will ask students to write full solutions. Each contests is 75 minutes long.

Series III: CIMC – Canadian Intermediate Math Contests (for grade 9/10) and CSMC – Canadian Senior Math Contests (for grade 11/12). The format is similar to FGH, however, the level of challenge is in general higher, and students are provided with 2 hours time to answer.

4) Selective Contests for those best talents in math: Canadian Math Society have a challenge series for those who want to participate in Math Olympiad. The first step is the COMC (Canadian Open Math Challenge). It is selective, so only COMC is open to students; all following contests in the series, like CMO (Canadian Math Olympiad) and IMO (International Math Olymiad), are by-invitation ONLY.

5) Popular Math Contests: Math Kangaroo, started in Europe and becoming popular across world, is organized by Math Kangaroo company. Their are 6 age groups and each group bracket two grades, like grades 1-2, grades 3-4, .. .. According to the organizer’s claim, the purpose of the contest is to challenge students in a playful setting; instead of academic, it aims at developing mental powers and flexibility.

5) Other Contests: besides those mentioned, we occasionally will register students in Regional Math League of Canada or US – some contests are online only – save students the cost and time to travel.

Jonah’s math corner can serve as a site to supervise students to write the math contests. If you have any question, just talk to us.

Categories
Algebra Equations (incl. Inequalities) Math Modelling

Pairing up with a Perfect Match

Math starts from the simple and goes a long way.

In this post, we will start from “pairing up” like 1 + 4 = 2 + 3 = 5 but there is a long way to go so that we learn the sets, working on the sets, pairing-up, observing and developing conditions for a perfect pair-up.

Pairing up for a Perfect Match

 

Categories
Math Contests - Problems and Discussion Math Junior (G9 and under)

Sample Questions for Gauss Contests


Questions chosen from previous Gauss contests
Gauss contests are organized by the Centre of Education for
Math and Computing, University of Waterloo


Problem 1

In the addition shown, P and Q each represent single digits, and the sum is 1PP7. What is P + Q?

(A) 9 (B) 12 (C) 14 (D) 15 (E) 13

Problem 2

In the right-angled triangle PQR, we have that PQ = QR. The three segments QS, TU and VW are perpendicular to PR, and the segments ST and UV are perpendicular to QR, as shown. What fraction of triangle PQR is shaded?

(A) 3 ⁄ 16 (B) 3 ⁄ 8 (C) 5 ⁄ 16 (D) 5 ⁄ 32 (E) 7 ⁄ 32

Problem 3

A box contains a total of 400 tickets that come in five colors: blue, green, red, yellow, and orange. The ratio of blue to green to red tickets is 1 : 2 : 4. The ratio of green to yellow to orange tickets is 1 : 3 : 6. What is the smallest number of tickets that must be drawn to ensure that at least 50 tickets of the same colour have been selected?

(A) 50 (B) 246 (C) 148 (D) 196 (E) 115

Problem 4

Greg, Charlize, and Azarah run at different but constant speeds. Each pair ran a race on a track that measured 100 m from start to finish. In the first race, when Azarah crossed the finish line, Charlize was 20 m behind. In the second race, when Charlize crossed the finish line, Greg was 10 m behind. In the third race, when Azarah crossed the finish line, how many metres was Greg behind?

(A) 20 (B) 25 (C) 28 (D) 32 (E) 40

Problem 5

In right-angled, isosceles triangle FGH, segment FH = √̅8. Arc FH is part of the circumference of a circle with centre G and radius GH. The area of the shaded region is

(A) π – 2; (B) 4 π – 2 (C) 4 π – (1 ⁄ 2) √̅8 ; (D) 4 π – 4 (E) π – √̅8