International Mathematics Olympiad 2017 Answer Key
Supported by the Actuarial Profession
The Canadian Mathematical Olympiad (CMO) is Canada's premier national advanced mathematics competition. Candidatesrequire an invitation from the Canadian Mathematical Society in order to participate.
The CMS wishes to thank the sponsors and partners who make our competitions program successful.
CMO 2021
Official Results:
Warren Bei CMO Champion
Congratulations to CMO ChampionWarren Bei who is homeschooled in Vancouver, British Columbia! Warren has earned this year's Canadian Mathematical Olympiad Cup and $2,000 cash!
| Canadian Division | ||
|---|---|---|
| PLACE | COMPETITOR(S) | PRIZE |
| 1st | Warren Bei (Vancouver, BC, homeschooled) | $ 2000 and theCMO Cup |
| 2nd | Thomas 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 |
- Download and try the 2021 questions.
- View the official solutions.
- Read our press release
- The top score this year was 29/35, the median score was 9/35.
- A total of 89 students from more than 48 different schools wrote the 2021 CMO.
Matthew Brennan Award for Best CMO Solution
In 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.
This year, the winner of the Matthew Brennan Award for Best CMO solution goes to: Warren Bei
Canadian Junior Mathematical Olympiad (CJMO) 2021
The CJMO is an olympiad style competition for younger students. Like for the CMO, the invitation to the CJMO is based on the results of the COMC and the Repêchage. Invitees will be the top students in grade 10 and below. Invitations to the CJMO will be sent out after the Repêchage has been graded.
The 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 ChampionsMaggie Pang from Marc Garneau C.I. and William Zhao from Windemere Ranch Middle School.
| Canadian Division | ||
|---|---|---|
| PLACE | COMPETITOR(S) | PRIZE |
| 1st | Maggie 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 |
- Download and try the 2021 questions.
- View the official solutions.
Past CJMO exams
Invitation
Eligibility
In order to be eligible to write the CMO and receive prizes, the student:
- must be a Canadian citizen or permanent resident of Canada who is attending school full-time (elementary, secondary, Cégep, or home-schooled) since September of the year prior to the CMO;
- be less than 20 years old as of June 30 of the year of the CMO; and
- must not have written the Putnam Competition.
Students who choose to write the CMO agree to allow the CMS to publish their names and schools when announcing contest results.
Results and Prizes
Official results are posted in two divisions: (1) students competing within Canada (the Canadian division) and (2) students competing abroad (the International division). Actual scores are not displayed publicly but students will be informed of their own scores.
The Championship title, the Cup and the prize money are only awarded to students in the Canadian division.
Prizes (Canadian division only): If there are no ties, the First Prize winner in the Canadian Mathematical Olympiad receives the CMO Cup and $2000. In addition, the Second Prize winner receives a cash prize, the Third Prize winner receives a cash prize and students earning an Honourable Mention (up to six students) receive a cash prize. In the case of ties, prizes are pooled upwards.
Preparing for the CMO
It is important to emphasize that any student who is invited to write the CMO should be aware thatsuccess 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.
Past Exams and Solutions
-
- 2020: Exam, solutions
- 2019: Exam, solutions
- 2018: Exam, solutions
- 2017: Exam, solutions
- 2016: Exam, solutions
- 2015: Exam, solutions
- 2014: Exam, solutions
- 2013: Exam, solutions
- 2012: Exam, solutions
- 2011: Exam, solutions
- 2010: Exam, solutions
- 2009: Exam, solutions
- 2008: Exam, solutions
- 2007: Exam, solutions
- 2006: Exam, solutions
- 2005: Exam, solutions
- 2004: Exam, solutions
- 2003: Exam, solutions
- 2002: Exam, solutions
- 2001: Exam, solutions
- 2000: Exam, solutions
- 1999: Exam, solutions
- 1998: Exam, solutions
- 1997: Exam, solutions
- 1996: Exam, solutions
- 1995: Exam, solutions
- 1994: Exam, solutions
- 1993: Exam
- 1992: Exam
- 1991: Exam
- 1990: Exam
- 1989: Exam
- 1988: Exam
- 1987: Exam
- 1986: Exam
- 1985: Exam
- 1984: Exam
- 1983: Exam
- 1982: Exam
- 1981: Exam
- 1980: Exam
- 1979: Exam
- 1978: Exam
- 1977: Exam
- 1976: Exam
- 1975: Exam
- 1974: Exam
- 1973: Exam
- 1972: Exam
- 1971: Exam
- 1970: Exam
- 1969: Exam
CMO Hall of Fame
Recent CMO Winners
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 | ||
|---|---|---|
| PLACE | COMPETITOR(S) | PRIZE |
| 1st | Thomas Guo, Phillips Exeter Academy, Exeter, NH | $ 2000 and theCMO Cup |
| 2nd | Zixiang Zhou, London Central Secondary School, London, ON | $ 1500 prize |
| 3rd | Michael 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.
Congratulations to CMO ChampionWilliam Zhao who attends Richmond Hill High School in Richmond Hill!
William earned 2019's Canadian Mathematical Olympiad Cup and $2,000 cash!
| Canadian Division | ||
|---|---|---|
| PLACE | COMPETITOR(S) | PRIZE |
| 1st | William Zhao,Richmond Hill High School, Richmond Hill, ON | $ 2000 and theCMO Cup |
| 2nd | Victor Rong,Marc Garneau C. I., Toronto, ON | $ 1500 prize |
| 3rd | Howard 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.
Congratulations to CMO ChampionVictor 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 | ||
|---|---|---|
| PLACE | COMPETITOR(S) | PRIZE |
| 1st | Victor Rong,Marc Garneau C.I., Toronto, ON | $ 2000 and theCMO Cup |
| 2nd | Howard Halim,University of Toronto Schools, Toronto, ON | $ 1500 prize |
| 3rd | William 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 |
- Download and try the 2018 questions.
- View the official solutions.
- Read our press release
- The top score this year was 33/35, the median score was 10/35.
- A total of 79 students from 51 different schools wrote the 2018 CMO.
Congratulations to CMO ChampionThomas Guo who attends Olympiads School in North York, Ontario and 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,Olympiads School, North York, ON and William Berczy Public School, Markham, ON. | $ 2000 and theCMO 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.
Recent CJMO Winners
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
International Mathematics Olympiad 2017 Answer Key
Source: https://cms.math.ca/competitions/cmo/
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