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Canadian Mathematical Olympiad & Junior Olympiad (CMO/CJMO)

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The Canadian Mathematical Olympiad (CMO) is Canada’s premier national advanced mathematics competition.

Competitors require an invitation from the Canadian Mathematical Society in order to participate.

The Canadian Junior Mathematical Olympiad (CJMO), also by invitation only, is held at the same time for students up to grade ten.  The CJMO is not as challenging as the CMO, however some problems may appear in both competitions.

These 3-hour competitions are held each March at a selected time and date.  All official participants write at the same time and are proctored by their local school faculty or staff.

The top students at the CMO can readily expect great scholarship and recruitment offers from universities. They will also be short-listed for the selection for Team Canada at the International Mathematical Olympiad!

CMO Trophy
2023
Earlier
Prizes
Invitations
Eligibility
Sponsors

2023 Olympiads

Status Update:

Competition results are now released!  Congratulations to Warren Bei of Rockridge Secondary School in West Vancouver, BC for earning Gold in the CMO and to Perry Dai of University of Toronto Schools in Toronto, ON for earning Gold in the CJMO.

Please read our Media Release.

See the details below.

CMO 2023

Photo of Warren Bei (2023)
CMO 2023 Champion: Warren Bei
 
Congratulations to  Warren Bei who attends Rockridge Secondary School in West Vancouver, BC!
 
Warren has earned this year’s CMO Cup and the top prize of $2,000 cash!
Rank Name School
Gold Medal Warren Bei Rockridge Secondary (West Vancouver, BC)
Silver Medal Andrew Wen Phillips Academy (Andover, MA, USA)
Bronze Medal Marvin Mao Bergen Country Academies (Hackensack, NJ, USA)
Honourable Mention Emily Ma Marc Garneau Collegiate Institute (Toronto, ON)
Joshua Wang Brookfield Central High School (Brookfield, WI, USA)
Kaixin Wang Magee Secondary School (Vancouver, BC)
Ming Yang Brophy College Preparatory (Phoenix, AZ, USA)

All official competitors live in Canada or are Canadian Citizens or Permanent Residents living abroad.

Statistics

  • Top score: 29/35
  • Lowest score for the top quartile: 14/35
  • Median score: 9/35
  • Competitors: 89 (77 official, 12 unofficial)

Resources

Matthew Brennan Award for Best CMO Solution

[read here for general information about the award]

The 2022 Award goes to Ming Yang of Brophy College Preparatory (Phoenix, AZ, USA) for his solution to problem 3.

The question asked students to prove a geometric inequality, and Ming Yang recasted the claim as a three variable inequality where the variables were shown to sum to 1 by a slick argument involving areas. The solution was finished with a direct application of Jensen’s inequality. The entire solution was just over half a page, and very elegant!

CJMO 2023

Photo of Perry Dai
CJMO 2023 Champion: Perry Dai
 
Congratulations to Perry Dai who attends University of Toronto Schools in Toronto, Ontario!
 
 
Rank Name School
Gold Medal Perry Dai University of Toronto Schools (Toronto, ON)
Silver Medal Raymond Ouyang William Lyon Mackenzie Collegiate Institute (North York, ON)
Honourable Mention Amos Zhang University of Toronto Schools (Toronto, ON)
David Zhang York Mills Collegiate Institute (Toronto, ON)
All official competitors live in Canada or are Canadian Citizens or Permanent Residents living abroad.

Statistics

  • Top score: 24/35
  • Lowest score for the top quartile: 19/35
  • Median score: 15/35
  • Competitors: 17

Resources

How to Earn an Invitation

All students require an invitation from the Canadian Mathematical Society in order to participate.  Typically 75-100 students are invited each year to write the CMO and a further 20 students are invited to write the CJMO.

Invitations are normally sent out in February.

COMC – Canadian Open Mathematical Challenge

The primary way students to come to our attention to be considered for a CMO/CJMO invitation is by doing very well on the Canadian Open Mathematics Challenge (COMC) in October.  We normally invite the top fifty (approx) qualifying COMC students to write the CMO.

CMO Qualifying Repêchage

The next 75 (approx) top qualifying COMC students are invited to write the Repêchage.  This is a “take home” week-long exercise held in February.  Up to twenty students are selected from this group to write the CMO.

CJMO Invitations

After the Repêchage is complete, we select students for the CJMO.  Anyone invited to the CMO is not invited to the CJMO. Remaining Repêchage writers who are in grade ten or less are invited to write the CJMO (normally the maximum is twenty such students).  If additional spots are available, then the best qualifying COMC students in grade ten or less, who didn’t get invited to the CMO or Repêchage, are invited.

Alternate Competitions

By traditional arrangement, the top winners from the Alberta High School Mathematics Competition (Part II) and from le Concours de l’Association Mathématique du Québec (AMQ – secondaire) are invited to write the CMO.

Students we’ve invited to represent Canada at the European Girls’ Mathematical Olympiad (EGMO) or the Asia Pacific Mathematical Olympiad (APMO) are normally also invited.

Preparing for the Olympiads

It is important to emphasize that any student who is invited to write the Olympiads should be aware that success will require mathematics at a higher level than is taught in most schools, and therefore should prepare specifically for the competition.

The CMS has several resources available for competitors.  The most important resource are the publicly-available Problem Sets and Solutions from previous years.

Eligibility

In order to be an official participant, all competitors:

  • must be a Canadian Citizen or Permanent Resident of Canada (but not necessarily residing in Canada currently),
  • must not have formally enrolled at a university or any other equivalent post-secondary institution and must not yet have graduated from high school (or equivalent),
  • must be currently attending school full-time since the start of the current school year,
  • must be less than 20 years old as of June 30 of the year of the Competition.

Additionally, the CJMO requires that competitors must be in grade ten or earlier.

Students who choose to write the Competition agree to allow the CMS to publish their names and schools when announcing contest results. 

CMO 2023

Photo of Warren Bei (2023)
CMO 2023 Champion: Warren Bei
 
Congratulations to  Warren Bei who attends Rockridge Secondary School in West Vancouver, BC!
 
Warren has earned this year’s CMO Cup and the top prize of $2,000 cash!
Rank Name School
Gold Medal Warren Bei Rockridge Secondary (West Vancouver, BC)
Silver Medal Andrew Wen Phillips Academy (Andover, MA, USA)
Bronze Medal Marvin Mao Bergen Country Academies (Hackensack, NJ, USA)
Honourable Mention Emily Ma Marc Garneau Collegiate Institute (Toronto, ON)
Joshua Wang Brookfield Central High School (Brookfield, WI, USA)
Kaixin Wang Magee Secondary School (Vancouver, BC)
Ming Yang Brophy College Preparatory (Phoenix, AZ, USA)

All official competitors live in Canada or are Canadian Citizens or Permanent Residents living abroad.

Statistics

  • Top score: 29/35
  • Lowest score for the top quartile: 14/35
  • Median score: 9/35
  • Competitors: 89 (77 official, 12 unofficial)

Resources

Matthew Brennan Award for Best CMO Solution

[read here for general information about the award]

The 2022 Award goes to Ming Yang of Brophy College Preparatory (Phoenix, AZ, USA) for his solution to problem 3.

The question asked students to prove a geometric inequality, and Ming Yang recasted the claim as a three variable inequality where the variables were shown to sum to 1 by a slick argument involving areas. The solution was finished with a direct application of Jensen’s inequality. The entire solution was just over half a page, and very elegant!

CMO 2022

ZixiangZhou2022
CMO 2022 Champion: Zixiang Zhou
 
Congratulations to  Zixiang Zhou who attends London Central Secondary in London, Ontario!
 
Zixiang has earned this year’s CMO Cup and the top prize of $2,000 cash!
Rank Name School
Gold Medal Zixiang Zhou London Central Secondary (London, ON)
Silver Medal Warren Bei Homeschool (Vancouver, BC)
Bronze Medal Alec Le Helloco Lycée Blaise Pascal (Orsay, France)
Honourable Mention Cordelia Hu Farragut High (Knoxville, TN, USA)
Evan Lu Vincent Massey Secondary (Windsor, ON)
Kevin Min Cupertino High (Cupertino, CA, USA)
Kaixin Wang Magee Secondary (Vancouver, BC)
Jason Zhang Canton High (Canton, MI, USA)

Statistics

  • Top score: 35/35
  • Lowest score for the top quartile: 12/35
  • Median score: 8/35
  • Competitors: 88 (78 official, 10 unofficial)

Resources

Matthew Brennan Award for Best CMO Solution

[read here for general information about the award]

The 2022 Award goes to Marvin Mao of Bergen County Academies (Hackensack, NJ, USA) for his solution to problem 3.

Problem 3 asked students to prove an upper and lower bound involving a game, and Marvin had a clever solution to the upper bound. He changed the rules to make the game easier to analyze, and showed that the new game still satisfies the desired upper bound. The idea to change the game was present in a few papers, but Marvin’s version was the most elegant.

Congratulations, Marvin!

CJMO 2022

ChristopherLi2022
CJMO 2022 Champion: Christopher Li
 
Congratulations to Christopher Li who attends TTmath School and William Berczy Public School in Markham, Ontario!
 
 
Rank Name School
Gold Medal Christopher Li TTmath School and William Berczy Public School (Markham, ON)
Honourable Mention Emily Ma Mark Garneau CI (Toronto, ON)
Joshua Wang Brookfield Central High (Brookfield, WI, USA)
Carol Wu Port Moody Secondary (Port Moody, BC)
Daniel Ye William Lyon MacKenzie CI (Toronto, ON)

Statistics

  • Top score: 26/35
  • Lowest score for the top quartile: 18/35
  • Median score: 15/35
  • Competitors: 22

Resources

CJMO 2023

Photo of Perry Dai
CJMO 2023 Champion: Perry Dai
 
Congratulations to Perry Dai who attends University of Toronto Schools in Toronto, Ontario!
 
 
Rank Name School
Gold Medal Perry Dai University of Toronto Schools (Toronto, ON)
Silver Medal Raymond Ouyang William Lyon Mackenzie Collegiate Institute (North York, ON)
Honourable Mention Amos Zhang University of Toronto Schools (Toronto, ON)
David Zhang York Mills Collegiate Institute (Toronto, ON)
All official competitors live in Canada or are Canadian Citizens or Permanent Residents living abroad.

Statistics

  • Top score: 24/35
  • Lowest score for the top quartile: 19/35
  • Median score: 15/35
  • Competitors: 17

Resources

CMO 2021

CMO 2021

Official Results:
Warren Bei CMO Champion
Congratulations to CMO Champion Warren Bei who is homeschooled in Vancouver, British Columbia! Warren has earned this year’s Canadian Mathematical Olympiad Cup and $2,000 cash!
Canadian Division
PLACECOMPETITOR(S)PRIZE
1stWarren Bei (Vancouver, BC, homeschooled)$ 2000 and the CMO Cup
2ndThomas Guo (Philips Exeter Academy, Exeter, NH, USA) and
Zhening Li (Sir John A. Macdonald Secondary School in Waterloo, ON)
Arvin Sahami (RWS, Richmond Hill World School, Richmond Hill, ON)
Eric Shen (University of Toronto schools, ON)		$ 1000 prize
  
Honourable
Mentions		(listed alphabetically)
Kaylee Ji (Lexington High School, Lexington, MA, USA);
Alec Le Helloco (Lycée Blaise Pascal, Orsay, France);
Kevin Min (Cupertino High School, Cupertino, CA, USA);
Zixiang Zhou (London Central Secondary School, London ON)		$ 300 each

CJMO 2021

CJMO 2021

The 2021 CJMO exam was written at the same time as the CMO – on Thursday, March 11, 2021. There were 20 students competing

Official Results:
CJMO Champions

Congratulations to CJMO Champions Maggie Pang from Marc Garneau C.I. and William Zhao from Windemere Ranch Middle School. 

Canadian Division
PLACECOMPETITOR(S)PRIZE
1stMaggie Pang (Marc Garneau C.I., ON) and
William Zhao  (Windemere Ranch Middle School, CA, USA) 		$ 100
Mentions

Emily Qingle Liu (Marc Garneau C.I., ON),

Raymond Wang (University Transition Program, Vancouver, BC) BC),  and

Richard Zhang (Georges Vanier Secondary School, North York, ON).

 $ 50

CMO 2020

Congratulations to CMO Champion Thomas Guo, a Canadian student who attends Phillips Exeter Academy in Exeter, New Hampshire. 

Thomas earned 2020’s Canadian Mathematical Olympiad Cup and a $2,000 prize!

Canadian Division
PLACECOMPETITOR(S)PRIZE
1stThomas Guo, Phillips Exeter Academy, Exeter, NH$ 2000 and the CMO Cup
2ndZixiang Zhou, London Central Secondary School, London, ON$ 1500 prize
3rdMichael Li, Marc Garneau C.I., Toronto, ON$ 1000 prize
Honourable
Mentions

(listed alphabetically)

Andrew Dong, Centennial Collegiate Vocational Institute, Guelph, ON;

Arvin Sahami, RWS, Richmond Hill World School, Richmond Hill, ON;

Eric Shen, University of Toronto Schools, Toronto, ON;

Edgar Wang, Marianopolis College, Westmount, QC;

Kevin Wan, Marc Garneau C.I., Toronto, ON; 

Daniel Yang, University of Toronto Schools, Toronto, ON

$ 400 each
  • Download and try the 2020 questions.
  • View the official solutions.
  • Read our press release
  • The top score this year was 32/35, the median score was 9/35.
  • A total of 83 students from more than 60 different schools wrote the 2020 CMO.

CJMO 2020

The 2020 CJMO Champion is Richard Zhang of Western Canada H.S., Calgary, AB. Congratulation!

Four other students were recognized with Honourable Mention. They are, in alphabetical order:

  • William Bate (Math Challenge at Western), London, ON;
  • Jason Fang (Prince of Wales Secondary School), Vancouver, BC;
  • George Wang (University of Toronto Schools), Toronto, ON;
  • Haozhe Yang (Walter Murray Collegiate), Saskatoon, SK.
  • The top score this year was 21/35, the median score was 10/35.
  • A total of 19 students from 17 different schools wrote the 2020 CJMO

2020: Exam, solutions

CMO 2019

Congratulations to CMO Champion William Zhao who attends Richmond Hill High School in Richmond Hill!

William earned 2019’s Canadian Mathematical Olympiad Cup and $2,000 cash!

Canadian Division
PLACECOMPETITOR(S)PRIZE
1stWilliam Zhao, Richmond Hill High School, Richmond Hill, ON$ 2000 and the CMO Cup
2ndVictor Rong, Marc Garneau C. I., Toronto, ON$ 1500 prize
3rdHoward Halim, University of Toronto Schools, Toronto, ON$ 1000 prize
Honourable
Mentions		(listed alphabetically)
Michael Li, Marc Garneau C. I., Toronto, ON;
Zhening Li, Sir John A. Macdonald S.S., Waterloo, ON;
Eric Shen, University of Toronto Schools, Toronto, ON;
Edgar Wang, Marianopolis College, Westmount, QC;
Scott Xu, Hon. Vincent Massey S.S., Windsor, ON;		$ 500 each
  • Download and try the 2019 questions.
  • View the official solutions.
  • Read our press release
  • The top score this year was 34/35, the median score was 12.5/35.
  • A total of 86 students from more than 50 different schools wrote the 2019 CMO.

CMO 2018

Congratulations to CMO Champion Victor Rong who attends Marc Garneau C.I. in Toronto!

Victor has earned this year’s Canadian Mathematical Olympiad Cup and $2,000 cash!

Canadian Division
PLACECOMPETITOR(S)PRIZE
1stVictor Rong, Marc Garneau C.I., Toronto, ON$ 2000 and the CMO Cup
2ndHoward Halim, University of Toronto Schools, Toronto, ON$ 1500 prize
3rdWilliam Zhao, Richmond Hill High School, Richmond Hill, ON$ 1000 prize
Honourable
Mentions		(listed alphabetically)
Steven Chow, Albert Campbell C.I., Scarborough, ON;
Andrew Dong, Centennial C. & V.I., Guelph, ON;
Andrew Lin, University Hill S.S., Vancouver, BC;
Victor Wang, Sir Winston Churchill S.S., Vancouver, BC;
Scott Xu, Hon. Vincent Massey S.S., Windsor, ON;
Zixiang Zhou, University Heights P.S., London, ON.		$ 500 each

CMO 2017

Congratulations to CMO Champion Thomas Guo who attends William Berczy Public School in Markham! Thomas has earned this year’s Canadian Mathematical Olympiad Cup and $2,000 cash!

Canadian Division
PLACE COMPETITOR(S) PRIZE
1st Thomas Guo, William Berczy Public School, Markham, ON. $ 2000 and the CMO Cup
2nd Rui Ming Xiong, Western Canada High School, Calgary, AB. $ 1500 prize
3rd Victor Rong, Marc Garneau Collegiate Institute, Toronto, ON. $ 1000 prize
Honourable
Mentions		 (listed alphabetically)
Edward Jiang, Moscrop Secondary School, Burnaby, BC;
Michael Li, Marc Garneau Collegiate Institute, Toronto, ON;
Jason Yuen, Pierre Elliot Trudeau High School, Markham, ON;
William Zhao, Richmond Hill High School, Richmond Hill, ON;
Daniel Zhou, Centennial Collegiate, Saskatoon, SK.		 $ 500 each
  • Download and try the 2017 questions.
  • View the official solutions.
  • Read our press release
  • The top score this year was 31/35, the median score was 10/35.
  • A total of 81 students from 50 different schools wrote the 2017 CMO.

Earlier Olympiads

CMO - Canadian Mathematical Olympiads

2023: Problem Set Solutions Results
2022: Problem Set Solutions Results
2021: Problem Set Solutions Results
2020: Problem Set Solutions Results
2019: Problem Set Solutions Results
2018: Problem Set Solutions Results
2017: Problem Set Solutions Results

CJMO - Junior Olympiads

2023: Problem Set Solutions Results
2022: Problem Set Solutions Results
2021: Problem Set Solutions Results
2020: Problem Set Solutions Results

Older CMO Problem Sets and Solutions

Prizes and Awards

CMO Trophy

Official competitors compete for the right to be named the CMO Champion (or CJMO Champion).   We also recognize the Silver, Bronze and Honourable Mention competitors as appropriate each year.  Typically, this is at least six students for CMO and fewer for CJMO.

The CMO Championship Cup is a full-size trophy that permanently commemorates the Champions.  There is no equivalent for the CJMO.  The Cup is normally loaned to the CMO Champion’s school to display for a year

Prize Money

Each year a pre-budgeted amount is allocated from the Canadian Mathematical Society and its members and sponsors.  Normally, this prize pool is divided up to ensure the CMO Gold medalist gets CAD$2000 (unless there are ties) and Silver, Bronze, and Honourable Mentions also get prize money in decreasing amounts per person.

The CJMO is similar but with considerably smaller cash prizes.

Matthew Brennan Award for Best CMO Solution

Photo of Matthew BrennanIn 2021 the CMS and the mathematical community lost one of our most valuable members.  Matthew represented Canada twice at the International Mathematical Olympiad, earning a bronze medal in 2011 and a gold medal in 2012. He returned to the IMO as deputy leader observer in 2014 and 2017, and was the leader in 2019. Matt was passionate about Olympiad math, and had served on the Canadian Mathematical Olympiad committee since 2014. He also contributed extensively to problem creation and selection.

In Matthew’s honour, the CMS has created the Matthew Brennan Award for Best CMO Solution. It is awarded every year to the student(s) who have written the best solution to a single problem on that year’s CMO. Their solution will be included in the official solutions, and they will receive a monetary prize.

Canadian Mathematical Society
616 Cooper St. 
Ottawa, ON  K1R 5J2, Canada
Telephone: +1 (613) 733-2662

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