Canadian Mathematics Competition An activity of the Centre for Education in Mathematics and Computing, University of Waterloo, Waterloo, Ontario Concours canadien de math´ ematiques Une activit´ e du Centre d’´ education en math´ ematiques et en informatique, Universit´ e de Waterloo, Waterloo, Ontario 2006 Results Pascal Contest (Grade 9) Cayley Contest (Grade 10) Fermat Contest (Grade 11) 2006 R´ esultats Concours Pascal (9 e ann´ ee – Sec. III) Concours Cayley (10 e ann´ ee – Sec. IV) Concours Fermat (11 e ann´ ee – Sec. V) C.M.C. Sponsors: Chartered Accountants Great West Life and London Life Sybase i Anywhere Solutions C.M.C. Supporters: Canadian Institute of Actuaries Maplesoft c 2006 Waterloo Mathematics Foundation
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2006 Pascal Contest Concours Pascal - CEMC · Nos f´elicitations vont a tous les participants du Concours Pascal, Cayley et Fermat de cette ann´ee. Les Con- Les Con- cours de cette
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CanadianMathematicsCompetition
An activity of the Centre forEducation in Mathematics and Computing,University of Waterloo, Waterloo, Ontario
Concourscanadien demathematiquesUne activite du Centre d’educationen mathematiques et en informatique,Universite de Waterloo, Waterloo, Ontario
The Centre for Education in Mathematics and Computing is proud to once again be the major sponsor of theCanadian Mathematics Competition this year. The year 2006 marks the 44th year of Contests produced by theCanadian Mathematics Competition.
Our congratulations go to all who participated in this year’s Pascal, Cayley and Fermat Contests. This year’sContests were resounding successes, with average of 95.9, 95.9 and 91.4 across the three Contests. The numberof students with perfect papers on the three Contests were 23, 3 and 8. We are very pleased with these results.The overall number of students writing this year’s papers showed a small increase over that from 2005. There wasa healthy increase in International participation this year as well as some very strong results from Internationalschools.
We would like to especially thank the hard-working Problems Committees. Without their insightful and en-tertaining problems, these Contests would not be possible.
We would also like to thank all participants, both teachers and students. We hope that the papers providedyou with some interesting mathematics to think about and play with. Thank you for your continued support!
Lastly, we would like to apologize for the initial difficulties we have had this year in providing results. Wewill soon be undertaking a major review of our marking process to attempt to vastly improve upon this part ofour activities for future years. Again, our apologies.
Le Centre d’education en mathematiques et en informatique a encore une fois le plaisir d’etre un majeur sup-porter du Concours canadien de mathematiques. L’annee 2006 marque la 44e annee de concours produit par leConcours canadien de mathematiques.
Nos felicitations vont a tous les participants du Concours Pascal, Cayley et Fermat de cette annee. Les Con-cours de cette annee retentissaient de succes, avec des moyennes de 95,9, 95,9 et 91,4 a travers les trois Concours.Le nombre d’etudiants possedant un concours parfait etait de 23, 3 et 8. Nous sommes satisfait de ces resultats.L’ensemble du nombre de participants cette annee a montre une petite augmentation comparee a 2005. Il y avaitune bonne augmentation dans la participation internationale cette annee, de meme que quelques resultats treseleves des ecoles internationales.
Nous aimerions surtout remercier les Comites de problemes pour leur dur travail. Sans leurs problemes per-spicaces et amusants, ces Concours ne seraient pas possibles.
Nous aimerions remercier aussi tous les participants incluant les enseignants et les etudiants. Nous esperonsque les concours vous ont offert des mathematiques interessantes qui vous ont amusees et portees a reflechir.Merci pour votre soutien continue!
Dernierement, nous aimerions nous excuser des difficultes initiales que nous avons eu cette annee a vous fournir lesresultats. Nous entreprendrons bientot une revue majeure de notre procede de correction pour tenter largementd’ameliorer cette partie de nos activites pour les annees futures. Encore, nos excuses.
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Enrollment Inscription
Number of schools registered by province /Nombre d’ecoles inscrit par province
Total number of students enrolled / Nombre d’inscriptions individuelles: 91342
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Champions – 2006 Champions – 2006
2006 STUDENT CHAMPIONS AND CHAMPIONSHIP TEAMSPALMARES INDIVIDUEL ET PALMARES PAR EQUIPE 2006
PASCAL CONTEST / CONCOURS PASCAL
STUDENTS /ELEVESStudents are listed in alphabetical order / Les eleves sont nommes en ordre alphabetique
Gold Medals School Location Grade AgeMedailles d’or Ecole Endroit Niveau AgeADRIAN BAR Sir William Mulock S.S. Newmarket, ON 9 14KEVIN CONRAD Prince Arthur J.H.S. Dartmouth, NS 9 14LOUIS HONG Waterloo C.I. Waterloo, ON 9 13PATRICIA JEE Avalon J.H.S. Edmonton, AB 9 14XUELIAN JIANG William Lyon Mackenzie C.I. North York, ON 9 14ALBERT KWON Richview C.I. Etobicoke, ON 9 15SHEN LI E.S. St-Luc Montreal, QC 9 15DI MO Queen Elizabeth H.S. Calgary, AB 8 13ADAM PRINS Turner Fenton S.S. Brampton, ON 9 14YOUBEOM SEO Streetsville S.S. Mississauga, ON 9 14JEFF SHAO Zion Heights J.H.S. North York, ON 9 14MIKE TANG Pleasant View J.H.S. North York, ON 9 15SCOTT WOLDUM Cochrane H.S. Cochrane, AB 9 14YU WU Semiahmoo S.S. Surrey, BC 9 15JONATHAN ZHOU Burnaby North S.S. Burnaby, BC 8 13ZIMU ZHU Richmond Hill H.S. Richmond Hill, ON 9 14
TEAMS / EQUIPES
School Location ScoreEcole Endroit Note
Champion / Premiere: Queen Elizabeth H.S. Calgary, AB 438Waterloo C.I. Waterloo, ON 438
Third / Troisieme Burnaby North S.S. Burnaby, BC 436Zion Heights J.H.S. North York, ON 436
Fifth / Cinquieme University of Toronto Schools Toronto, ON 433
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Champions – 2006 Champions – 2006
2006 STUDENT CHAMPIONS AND CHAMPIONSHIP TEAMSPALMARES INDIVIDUEL ET PALMARES PAR EQUIPE 2006
CAYLEY CONTEST / CONCOURS CAYLEY
STUDENTS /ELEVESStudents are listed in alphabetical order / Les eleves sont nommes en ordre alphabetique
Gold Medals School Location Grade AgeMedailles d’or Ecole Endroit Niveau AgeMIN BAI Western Canada H.S. Calgary, AB 10 16FANG YING CHU College St-Louis Lasalle, QC 10 15BOCHENG CUI Semiahmoo S.S. Surrey, BC 10 16PHILIP DUONG Victoria Park C.I. North York, ON 10 15FREDERIC ELBAZ Maimonide - Campus Parkhaven Cote St Luc, QC 10 15JIMMY HUA Burnaby South S.S. Burnaby, BC 10 15ADAM LESLIE Ashbury College Rockcliffe, ON 10 15YAN LI Dr. Norman Bethune C.I. Scarborough, ON 10 15YENA OH Western Canada H.S. Calgary, AB 10 15VAROON PAREKH Silverthorn C.I. Etobicoke, ON 10 15PHILIP PENG Thornhill S.S. Thornhill, ON 10 15ZHE QUAN Richmond Hill H.S. Richmond Hill, ON 10 16PETER TIAN J.N. Burnett S.S. Richmond, BC 10 15SERGIU TOARCA R.H. King Academy Scarborough, ON 10 15PHILIP VANDERVIES London District Christian S.S. London , ON 10 15HANG XIE St. John’s School Vancouver, BC 10 17ANNIE XU Old Scona Academic H.S. Edmonton, AB 10 16VICK YAO Vincent Massey S.S. Windsor, ON 10 15ANDY ZHAO Vincent Massey S.S. Windsor, ON 10 15
TEAMS / EQUIPES
School Location ScoreEcole Endroit Note
Champion / Premiere: Vincent Massey S.S. Windsor, ON 428Second / Deuxieme Western Canada H.S. Calgary, AB 426
Richmond Hill H.S. Richmond Hill, ON 426Fourth / Quatrieme R.H. King Academy Scarborough, ON 418
Thornhill S.S. Thornhill, ON 418
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Champions – 2006 Champions – 2006
2006 STUDENT CHAMPIONS AND CHAMPIONSHIP TEAMSPALMARES INDIVIDUEL ET PALMARES PAR EQUIPE 2006
FERMAT CONTEST / CONCOURS FERMAT
STUDENTS /ELEVESStudents are listed in alphabetical order / Les eleves sont nommes en ordre alphabetique
Gold Medals School Location Grade AgeMedailles d’or Ecole Endroit Niveau AgeBORIS BRAVERMAN Sir Winston Churchill H. S. Calgary, AB 11 15LIN FEI Don Mills C.I. North York, ON 11 17JIMMY HE Seaquam S.S. Delta, BC 10 15KENT HUYNH University of Toronto Schools Toronto, ON 11 15STEVEN KARP Lord Byng S.S. Vancouver, BC 11 16GYUHYON LEE Waterloo C.I. Waterloo, ON 11 16ALEXANDER REMOROV Waterloo C.I. Waterloo, ON 10 15MAX ZHOU L’Amoreaux C.I. Scarborough, ON 11 16
TEAMS / EQUIPES
School Location ScoreEcole Endroit Note
Champion / Premiere: Waterloo C.I. Waterloo, ON 444Second / Deuxieme University of Toronto Schools Toronto, ON 432Third / Troisieme Western Canada H.S. Calgary, AB 426Fourth / Quatrieme Don Mills C.I. Toronto, ON 424Fifth / Cinquieme Lord Byng S.S. Vancouver, BC 410
Sir Winston Churchill H.S. Calgary, AB 410Upper Canada College Toronto, ON 410
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Champions – 2006 Champions – 2006
2006 FERMAT CONTEST PROVINCIAL CHAMPIONSCHAMPIONS PROVINCIAUX AU CONCOURS FERMAT 2006
Each student below will receive a $200 prize / Chaque etudiant ci-dessous recevrait un prix de 200 $
Province Student School LocationProvince Etudiant Ecole EndroitNL JANE BRODIE Holy Heart of Mary Regional H.S. St. John’sNL IAN PAYNE Pasadena Academy PasadenaNS ETHAN MACAULAY The Halifax Grammar School HalifaxNB NA YIN Fredericton H.S. FrederictonPE YUFENG CHEN Colonel Gray S.H.S. CharlottetownPE MAX LABRECH Souris Regional H.S. SourisQC JEAN MARC CAMPAGNA E.S. des Sources Dollard des OrmeauxQC VINCENT CRETE College Durocher/St-Lambert St-LambertON North MITCH DELLANDREA Bracebridge & Muskoka Lakes S.S. BracebridgeON East ZHAO LIU Glebe C.I. OttawaON Metro LIN FEI Don Mills C.I. TorontoON Metro KENT HUYNH University of Toronto Schools TorontoON Metro MAX ZHOU L’Amoreaux C.I. TorontoON Central ALLAN JIANG Oakville Trafalgar H.S. OakvilleON Central KEVIN LI Glenforest S.S. MississaugaON West GYUHYON LEE Waterloo C.I. WaterlooON West ALEXANDER REMOROV Waterloo C.I. WaterlooMB ALEXANDER HOGEVEENRUTTER J.H. Bruns C.I. WinnipegSK BOBBY XIAO Walter Murray C.I. SaskatoonAB BORIS BRAVERMAN Sir Winston Churchill H.S. CalgaryBC JIMMY HE Seaquam S.S. DeltaBC STEVEN KARP Lord Byng S.S. Vancouver
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Correct Answers Bonnes Rponses
# Pascal Cayley Fermat1 E E B2 B A B3 D A A4 A C C5 B B E6 C D A7 E C C8 A A D9 C C A
10 D B D11 B E A12 C E C13 D D A14 E D B15 E C D16 D A C17 A B D18 C D B19 A D E20 A C B21 E C E22 A A C23 C C E24 B E E25 A A D
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Pascal Contest Concours Pascal
Number of Contestants / Nombre de concurrents: 29753Average mark / Note moyenne: 95.93
Percentage of contestants selecting each option / Pourcentage de concurrents par choix:
Correct % not % correctAnswer/ attempted/ of attemptedBonne % sans % tentatives
Reponse reponse reussies# A B C D E1 E 1.66 0.57 0.68 0.26 96.38 0.46 96.822 B 3.68 84.90 7.14 0.80 2.19 1.29 86.013 D 5.08 7.40 9.33 71.20 2.32 4.67 74.694 A 91.76 4.02 1.45 0.27 0.12 2.40 94.015 B 1.25 80.01 10.08 4.30 0.98 3.38 82.826 C 6.85 2.30 76.36 2.28 10.87 1.35 77.407 E 2.41 0.82 4.31 6.94 82.01 3.52 85.008 A 73.82 3.69 5.10 8.19 2.18 7.01 79.389 C 3.59 2.67 78.99 12.01 1.10 1.65 80.31
10 D 2.84 6.72 1.55 81.58 2.33 4.99 85.8711 B 1.03 85.88 0.88 8.58 2.95 0.67 86.4612 C 3.85 3.93 78.10 3.86 3.08 7.19 84.1513 D 3.44 2.83 3.94 82.80 1.13 5.86 87.9614 E 2.73 1.27 1.59 4.43 85.49 4.48 89.5115 E 6.82 9.75 4.01 5.48 60.18 13.76 69.7816 D 9.94 13.61 31.03 19.66 21.16 4.60 20.6017 A 57.72 9.61 6.22 4.39 5.21 16.85 69.4218 C 2.25 3.99 80.89 5.85 1.21 5.81 85.8819 A 59.00 4.88 5.45 4.87 2.05 23.75 77.3820 A 23.81 7.78 11.61 7.36 17.15 32.28 35.1621 E 7.91 9.09 3.00 4.58 51.68 23.73 67.7622 A 27.37 11.08 5.05 17.25 4.91 34.33 41.6823 C 6.16 9.46 30.64 12.25 17.25 24.25 40.4424 B 5.98 14.85 14.96 15.77 18.36 30.08 21.2425 A 9.58 8.88 8.88 6.90 3.77 61.98 25.20
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Cayley Contest Concours Cayley
Number of Contestants / Nombre de concurrents: 22299Average mark / Note moyenne: 95.86
Percentage of contestants selecting each option / Pourcentage de concurrents par choix:
Correct % not % correctAnswer/ attempted/ of attemptedBonne % sans % tentatives
Reponse reponse reussies# A B C D E1 E 0.81 3.05 0.84 1.30 93.66 0.34 93.972 A 92.84 1.28 4.21 0.16 0.89 0.62 93.423 A 98.03 0.57 0.96 0.19 0.10 0.15 98.174 C 0.43 0.32 98.38 0.49 0.24 0.14 98.525 B 3.44 88.99 0.76 0.66 2.26 3.88 92.596 D 3.26 9.37 1.92 72.41 3.12 9.91 80.387 C 2.18 1.28 90.61 4.46 0.61 0.85 91.398 A 73.64 1.14 19.13 0.74 1.73 3.63 76.419 C 2.35 2.52 87.01 2.39 1.85 3.87 90.52
10 B 5.27 90.17 0.62 1.48 0.65 1.82 91.8411 E 1.32 7.92 5.02 1.36 81.01 3.37 83.8412 E 4.52 7.61 2.85 3.52 73.58 7.92 79.9013 D 3.63 2.08 11.96 67.34 0.86 14.14 78.4214 D 14.59 9.82 2.15 71.59 1.04 0.81 72.1715 C 1.76 2.16 79.56 1.64 1.78 13.09 91.5516 A 55.94 3.97 2.35 8.35 6.97 22.42 72.1117 B 2.56 80.43 1.69 2.42 1.50 11.40 90.7818 D 7.06 13.25 4.98 38.26 2.41 34.04 58.0119 D 0.89 44.23 6.11 39.80 2.92 6.05 42.3620 C 8.39 8.48 32.83 4.81 4.64 40.85 55.5021 C 5.11 4.71 18.68 5.90 4.18 61.41 48.4122 A 31.97 6.79 19.99 9.78 6.91 24.56 42.3823 C 5.66 10.91 11.24 24.28 13.15 34.75 17.2324 E 7.48 13.84 10.15 6.82 6.17 55.55 13.8725 A 7.16 7.10 6.33 6.82 8.32 64.27 20.03
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Fermat Contest Concours Fermat
Number of Contestants / Nombre de concurrents: 17937Average mark / Note moyenne: 91.41
Percentage of contestants selecting each option / Pourcentage de concurrents par choix:
Correct % not % correctAnswer/ attempted/ of attemptedBonne % sans % tentatives
Reponse reponse reussies# A B C D E1 B 0.19 96.34 2.18 0.72 0.38 0.18 96.512 B 0.27 98.65 0.10 0.40 0.15 0.43 99.083 A 94.69 0.32 3.63 0.20 0.85 0.30 94.974 C 0.49 7.05 88.15 0.81 2.49 1.01 89.065 E 1.71 2.90 0.34 0.81 91.84 2.40 94.096 A 96.55 0.51 0.60 0.31 1.27 0.77 97.307 C 1.18 3.02 82.41 7.44 0.99 4.97 86.728 D 1.58 1.20 2.84 90.90 0.67 2.81 93.539 A 76.84 4.02 2.87 7.63 3.28 5.37 81.19
10 D 1.66 23.20 2.10 49.35 7.83 15.86 58.6511 A 64.62 2.79 3.92 4.15 3.28 21.23 82.0412 C 0.93 1.56 93.07 1.51 0.71 2.22 95.1813 A 61.65 2.74 1.53 10.14 8.65 15.29 72.7914 B 11.45 75.45 3.92 1.05 0.65 7.47 81.5415 D 5.81 15.57 9.24 44.17 7.01 18.19 53.9916 C 4.11 7.40 55.57 6.56 6.02 20.35 69.7617 D 1.76 3.61 5.69 65.92 3.99 19.03 81.4218 B 4.46 48.40 4.95 12.53 5.79 23.87 63.5719 E 3.76 5.39 16.07 4.08 44.84 25.86 60.4820 B 5.12 14.45 14.03 18.58 19.70 28.13 20.1021 E 9.27 5.65 8.05 21.75 16.44 38.84 26.8722 C 5.06 11.19 12.51 27.92 10.73 32.59 18.5623 E 6.14 8.37 8.79 7.86 14.19 54.65 31.2824 E 7.47 6.81 5.10 9.01 9.23 62.39 24.5325 D 4.18 6.60 6.39 5.03 4.45 73.34 18.86
N.B. These rankings pertain to ALL contestants, in-cluding international and unofficial contestants /N.B. Ces rangs se rapportent a TOUS concurrents, ycompris les concurrents internationaux et non officiels
Number of three student teams / Nombre d’equipes de trois elevesPascal Contest / Concours Pascal : 1183Cayley Contest / Concours Cayley : 1098Fermat Contest / Concours Fermat : 1060
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CanadianMathematicsCompetition
An activity of the Centre forEducation in Mathematics and Computing,University of Waterloo, Waterloo, Ontario
Concourscanadien demathematiquesUne activite du Centre d’educationen mathematiques et en informatique,Universite de Waterloo, Waterloo, Ontario
2006Results
Pascal Contest(Grade 9)
Cayley Contest(Grade 10)
Fermat Contest(Grade 11)
2006Resultats
Concours Pascal(9e annee – Sec. III)
Concours Cayley(10e annee – Sec. IV)
Concours Fermat(11e annee – Sec. V)
Pascal Contest Honour RollsPalmares pour le concours Pascal
Score/ScoreCity/VilleRank/Rang
School/École
438Waterloo1 Waterloo C.I.
438Calgary 1 Queen Elizabeth H.S.
436Burnaby3 Burnaby North S.S.
436North York 3 Zion Heights J. H. S.
433Toronto5 University of Toronto Schools
432Burnaby6 Burnaby Mountain S.S.
432Vancouver6 Sir Winston Churchill S.S.
432North York6 Crescent School
431Richmond Hill9 Richmond Hill H.S.
430Coquitlam10 Pinetree S.S.
430Vancouver 10 Eric Hamber S.S.
430North York10 Earl Haig S.S.
430Vancouver10 St. George's School
430Delta10 Seaquam S.S.
430North York 10 Marc Garneau C.I.
430Edmonton10 Avalon J.H.S.
430Mississauga10 The Woodlands S.
428Windsor18 Vincent Massey S.S.
427Toronto19 Upper Can Col-Upper School
426Scarborough20 Agincourt C.I.
426Richmond Hill20 Bayview Secondary School
426Nepean20 Bell H.S.
426Port Moody20 Port Moody S.S.S.
426Ottawa20 Lisgar C.I.
426Winnipeg20 St. John's-Ravenscourt School
426Vancouver20 University Transition Program
426Richmond20 Richmond S.S.
425Cochrane28 Cochrane H.S.
424Scarborough29 Sir John A. Macdonald C.I.
424Surrey29 Earl Marriott S.S.
424Victoria29 St. Michael's Univ. School
424Gloucester 29 Colonel By S. S.
424Montreal29 E.S. St-Luc
424North York 29 Pleasant View J.H.S.
2006Pascal Contest/Concours Pascal
Team Honour Rolls/Palmarès d'équipes
Score/ScoreCity/VilleRank/Rang
School/École
422Etobicoke35 Richview C.I.
422Winnipeg35 Acadia J.H.S.
422Surrey35 Semiahmoo S.S.
422Burnaby35 Byrne Creek S.S.
421Montreal39 Academie IBN-SINA
420Guelph40 Centennial C. & V.I.
420Montreal40 College Jean de Brebeuf
420Vancouver40 Magee Secondary School
419North York43 William Lyon Mackenzie C.I.
418Edmonton44 McKernan J.H.S.
418Markham44 Unionville H.S.
418Mississauga44 Lorne Park S.S.
418Etobicoke44 Martingrove C.I.
418Kingston44 Loyalist C.&V.I.
418Toronto44 Danforth Coll & Tech. Inst.
417Mississauga50 Glenforest S.S.
416Ajax51 Pickering H.S.
416Burnaby51 Burnaby South S.S.
416Toronto51 North Toronto C.I.
416Vancouver51 Point Grey Secondary School
416Mississauga51 Erindale S.S.
2006Pascal Contest/Concours Pascal
Team Honour Rolls/Palmarès d'équipes
Grade/Niveau
Location/Endroit
Name/Nam School/École Age/Âge
Group I/Groupe I Scores/Notes 150 - 146BAR ADRIAN 9NewmarketSir William Mulock S.S. 14