2011 Results Euclid Contest 2011 Résultats Concours Euclide

The CENTRE for EDUCATIONin MATHEMATICS and COMPUTING

Le CENTRE d’EDUCATIONen MATHEMATIQUES et en INFORMATIQUE

www.cemc.uwaterloo.ca

2011Results

Euclid Contest

2011Resultats

Concours Euclide

c©2011 Centre for Education in Mathematics and Computing

Competition Organization Organisation du Concours

Centre for Education in Mathematics and Computing Faculty and Staff /Personnel du Centre d’education en mathematiques et informatique

Ed AndersonLloyd AucklandTerry BaeSteve BrownErsal CahitKaren ColeJennifer CoutureSerge D’AlessioFrank DeMaioFiona DunbarMike EdenBarry FergusonBarb ForrestJudy FoxSteve FurinoJohn GalbraithSandy GrahamAngie HildebrandJudith KoellerJoanne KursikowskiBev MarshmanDean MurrayJen NissenJ.P. PrettiLinda SchmidtKim SchnarrJim SchurterCarolyn SedoreIan VanderBurghTroy Vasiga

Problems Committee / Comite des problemes

Serge D’Alessio (Acting Chair), University of Waterloo, Waterloo, ONKathir Brabaharan, Sir John A. Macdonald C.I., Scarborough, ONSteve Brown, University of Waterloo, Waterloo, ONCharlotte Danard, Branksome Hall School, Toronto, ONFiona Dunbar, University of Waterloo, Waterloo, ONGarry Kiziak, Burlington, ONDarren Luoma, Bear Creek S.S., Barrie, ONAlex Pintilie, Crescent School, Toronto, ONLarry Rice, Toronto, ONRoss Willard, University of Waterloo, Waterloo, ON

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Comments on the Paper Commentaires sur les epreuves

Overall CommentsCongratulations to all of the participants in the 2011 Euclid Contest. The average score of 48.0 is about the sameas that of 2010. We were very pleased that a large number of students achieved some success on the early partsof the last few problems on the paper. At the same time, the later parts of these problems managed to challengethe top students even more than last year’s problems. Special congratulations go to the five official contestantswho achieved scores of higher than 90 this year.

We at the Centre for Education in Mathematics and Computing believe strongly that it is very important forstudents to both learn to solve mathematics problems and learn to write good solutions to these problems. Manystudents do a reasonable job of writing solutions, while others still include no explanation whatsoever.

Special thanks go to the Euclid Problems Committee that annually sets the Contest problems and managesto achieve a very difficult balancing act of providing both accessible and challenging problems on the same paper.

To the students who wrote, the parents who supported them, and the teachers who helped them along theway, thank you for your continuing participation and support. We hope that you enjoyed the Contest and relishedthe challenges that it provided. We hope that mathematics contests continue to feed your love for and interest inmathematics.

Specific Comments

1. Average: 9.1This problem was very well done throughout.

2. Average: 9.2This problem was very well done throughout.

3. Average: 8.2Both parts to this problem were quite well done. In part (a), some students chose the wrong combinationof endpoints of the two intervals while trying to maximize the given expression. In part (b), lots of studentssolved for f(x) and g(x) without first substituting x = 2, while many students substituted x = 2 first andthen solved.

4. Average: 6.6In part (a), many students had the correct answer, while some others did not find all of the possible arithmeticsequences or did not count the total number of possible sequences properly. Part (b) had many differentpossible approaches.

5. Average: 4.4Part (a) was fairly well done. Most students set up their solution like our model solution. Some studentsused a divisibility argument to solve the problem. There were many ways to solve part (b). We saw solutionsthat used various constructions, equations of lines, the distance formula, area calculations, and vectors. Themost common solution was to “complete the rectangle”.

6. Average: 3.4Students who understood the question and distance/speed/time relationships did well on part (a). Manystudents fixed the length of AB. Part (b) was done quite well by those who attempted it. Most studentsattacked the problem by discussing the vertices of the trapezoid, rather than the concavity of the parabola.These students broke the problem into two cases: the vertices are on OR and PQ, and the vertices are onOR, OP and QR. The most common mistake made in this question was to consider only one case.

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7. Average: 1.9In part (a), many students found the correct answer, but a large number of students made incorrect assump-tions about the problem or did not seem to have any way to start the problem. Students who did not getthe correct answer rarely had written much to be marked. A common incorrect answer was 55%. Part (b)was done quite well by those who attempted it. For the most part, the written solutions were excellent.

8. Average: 3.0In each of parts (a) and (b), many students obtained the correct answer, but few students showed much orany justification. Very few students attempted part (c), even though it just involved some factoring, withan explanation that both factors 2R+ 1 and 2C + 1 are greater than 1.

9. Average: 2.0In part (a), the most common error was not applying the definition of the greatest integer function correctly(many students rounded up 63.9 to 64). Many students made other computational errors (for example,stating that 2 × 2011 = 4011). In part (b), trial and error seemed to work well for most students, thoughmore elegant solutions narrowed down the choices by using the quadratic formula and verifying the correctanswer. There were only a handful of students that made any progress in part (c).

10. Average: 0.2In part (a), a good number of students found the similar triangles or used the sine law repeatedly to getthe result. In part (b), the most common solutions used the cosine law (Method 3 in the sample solutions)though some students did use the sin 3θ rewriting. Fixing a value for one of the angles (say 30◦), does notprove anything. Very few students attempted part (c).

Please visit our website at www.cemc.uwaterloo.ca to download the 2011 Euclid Contest, plus fullsolutions.

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Commentaires GenerauxFelicitations a tous les participants du Concours Euclide 2011. La note moyenne de 48,0 est presque egale a cellede 2010. Nous avons eu le plaisir de constater que beaucoup d’eleves ont eu du succes dans les premieres partiesdes dernieres questions. De plus, les dernieres parties de ces problemes presentaient un plus grand defi pour lesmeilleurs etudiants que l’annee derniere. Des felicitations speciales vont aux cinq concurrents officiaux qui ontatteint une note superieure a 90 sur 100.

Le Centre d’education en mathematiques et en informatique croit fortement qu’il est tres important pour lesetudiant(e)s d’apprendre a resoudre des problemes de mathematiques ainsi que d’apprendre a ecrire de bonnessolutions a ces problemes. Plusieurs etudiants developpent leurs solutions resonablement bien, tandis que d’autresn’inclus aucune explication avec leurs reponses.

Un grand merci va au comite des problemes du concours Euclide qui rassemble annuellement les problemes duconcours et reussit a accomplir la tache difficile de concevoir des problemes accessibles et stimulants sur le memeexamen.

Un grand merci aux etudiant(e)s qui ont ecrit, aux parents qui les ont soutenus et aux enseignant(e)s qui lesont aides pour votre participation continue et votre soutien. Nous esperons que vous avez apprecie le concours etsavoure les defis qu’il a presentes. Nous esperons que les concours de mathematiques continuent a nourrir votreamour et interet pour les mathematiques.

Remarques particulieres

1. Moyenne: 9,1Toutes les parties du probleme ont ete bien reussies.

2. Moyenne: 9,2Toutes les parties du probleme ont ete bien reussies.

3. Moyenne: 8,2Les deux parties du probleme ont ete assez bien reussies. Dans la partie (a), certains eleves ont utiliseles mauvaises combinaisons d’extremites des intervalles pour determiner la valeur maximale de l’expression.Dans la partie (b), un grand nombre d’eleves ont determine une expression algebrique pour f(x) et une autrepour g(x) sans reporter la valeur de x = 2, alors que d’autres ont reporte la valeur de x = 2 d’abord pourensuite resoudre le systeme d’equations.

4. Moyenne: 6,6Un grand nombre d’eleves ont reussi la partie (a), alors que d’autres ont oublie certaines suites arithmetiques,ou ont mal compte le nombre de suites possibles. La partie (b) pouvait etre resolue de plusieurs faconsdifferentes.

5. Moyenne: 4,4La partie (a) a ete assez bien reussie. La plupart des eleves ont utilise une approche semblable a celle denotre solution modele. Certains eleves ont utilise un argument base sur la divisibilite. La partie (b) pouvaitetre resolue de maintes facons. Les eleves ont utilise des constructions diverses, des equations de droites, laformule de distance, des calculs d’aires et des vecteurs. L’approche la plus commune a ete de completer unrectangle.

6. Moyenne: 3,4Les eleves qui ont compris la question et qui etaient a l’aise avec la relation distance-vitesse-temps ont bienreussi la partie (a). Beaucoup d’eleves ont fixe la distance AB. La partie (b) a ete plutot bien reussie parceux qui ont essaye de la resoudre. La plupart des eleves ont parle des sommets du trapeze plutot que del’ouverture de la parabole vers le haut ou vers le bas. Ces eleves ont considere deux cas, soit que les sommets

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etaient situes sur OR et PQ, ou qu’ils etaient situes sur OR, OP et QR. L’erreur la plus commune etait dene considerer qu’un cas.

7. Moyenne: 1,9Dans la partie (a), un grand nombre d’eleves ont obtenu la bonne reponse, mais beaucoup d’eleves ontsuppose certaines choses a tort ou ne savaient pas commen s’y prendre pour commencer. Les eleves qui ontdonne une mauvaise reponse ont rarement ecrit quoi que ce soit pour qu’on puisse leur accorder des points.La reponse erronee «55 %» etait assez commune. La partie (b) a ete plutot bien reussie par ceux qui onttente de la resoudre. En general, la redaction des solution etait excellente.

8. Moyenne: 3,0Bon nombre d’eleves ont obtenu la bonne reponse dans les parties (a) et (b), sans montrer du travail et sansjustifier. Tres peu d’eleves ont tente de resoudre la partie (c), meme s’il suffisait de factoriser et d’expliquerque chacun des facteurs 2R+ 1 et 2C + 1 est superieur a 1.

9. Moyenne: 2,0Dans la partie (a), l’erreur la plus commune etait de mal utiliser l’expression du plus grand entier (certainsont arrondi 63,9 a 64 au lieu de tronquer). Beaucoup d’eleves ont commis des erreurs de calcul (p. ex., enaffirmant que 2×2011 = 4011). Dans la partie (b), la plupart des eleves ont procede par essais systematiques.Les solutions les plus elegantes ont reduit le nombre de cas a considerer en utilisant la formule pour resoudreune equation du second degre. Une poignee d’eleves ont aborde la partie (c) pour progresser quelque peu.

10. Moyenne: 0,2Un bon nombre d’eleves ont reussi la partie (a) en utilisant des triangles semblables ou la loi des sinus. Dansla partie (b), les eleves ont surtout utilise la loi du cosinus (3e methode de notre solution), bien que certainsont developpe sin 3θ. On ne prouve rien en attribuant une valeur particuliere a un angle (p. ex. 30◦). Trespeu d’eleves ont essaye de resoudre la partie (c).

Veuillez visiter notre site Web a www.cemc.uwaterloo.ca pour telecharger le Concours Euclide 2011,avec solutions completes.

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Champions – 2011 Champions – 2011

STUDENTS / ELEVESStudents are listed in alphabetical order. / Les eleves sont nommes en ordre alphabetique.

Plaques Jonas Chin Piere Elliott Trudeau H.S. Markham, ONJames Rickards Colonel By S.S. Gloucester, ONMariya Sardarli Strathcona Composite H.S. Edmonton, ABHunter Spink Western Canada H.S. Calgary, ABDaniel Spivak Bayview S.S. Richmond Hill, ON

Each plaque winner receives a $500 cash prize from the Centre for Education in Mathematicsand Computing. /Chaque eleve qui recois une plaque recevra aussi un prix de 500 $ du Centre d’education enmathematiques et en informatique.

Book Prizes/ Yuzhou Chen Sir John A. Macdonald C.I. Scarborough, ONPrix en livres Anqi Dong Walter Murray C.I. Saskatoon, SK

Heinrich Jiang Vincent Massey S.S. Windsor, ONDong Won Kang North Toronto C.I. Toronto, ONVictor Liu Dr. Norman Bethune C.I. Scarborough, ONChang Su Western Canada H.S. Calgary, ABSusan Sun West Vancouver S.S. West Vancouver, BCHenry Heng Tang Bayview S.S. Richmond Hill, ONChao Wang Sir John A. Macdonald C.I. Scarborough, ONJason Wang Dover Bay S.S. Nanaimo, BCZexua Wang A.Y. Jackson S.S. North York, ONHantian Xu Point Grey S.S. Vancouver, BCFranklin Yang Don Mills C.I. North York, ONEric Zhan University of Toronto Schools Toronto, ONHan Chao Zhao Dr. Norman Bethune C.I. Scarborough, ON

TEAMS / EQUIPESChampion/Premiere: Western Canada H.S. Calgary, ABSecond/Deuxieme: Bayview S.S. Richmond Hill, ONThird/Troisieme: Sir John A. Macdonald C.I. Scarborough, ONFourth/Quatrieme: Dr. Norman Bethune C.I. Scarborough, ONFifth/Cinquieme: A.Y. Jackson S.S. North York, ON

University of Toronto Schools Toronto, ON

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Enrollment Inscription

Number of students registered by province /Nombre d’etudiants inscrit par province

Enrollment/Inscription

NL 191NS 239NB 146PE 30QC 299ON 9396MB 310SK 185AB 483BC 2691NT 1International 2727

Total 16748

There were 1279 schools enrolled. / 1279 ecoles etaient inscrites.

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Student Rankings Classements des eleves

Score/ Rank/ Score/ Rank/ Score/ Rank/ Score/ Rank/Note Position Note Position Note Position Note Position

100 74 566 49 4258 24 881199 1 73 624 48 4508 23 889998 72 717 47 4721 22 899397 2 71 771 46 4947 21 904696 70 867 45 5194 20 910995 69 967 44 5417 19 917294 3 68 1056 43 5652 18 922693 67 1187 42 5888 17 927092 66 1307 41 6132 16 930491 4 65 1416 40 6359 15 934190 6 64 1556 39 6581 14 937689 13 63 1671 38 6796 13 939688 21 62 1806 37 7012 12 941787 24 61 1963 36 7210 11 943186 35 60 2101 35 7397 10 944085 50 59 2267 34 7567 9 944584 72 58 2425 33 7738 8 945583 106 57 2599 32 7912 7 945982 142 56 2777 31 8046 6 946581 174 55 2962 30 8183 5 946880 214 54 3169 29 8281 4 947179 255 53 3367 28 8415 3 947278 315 52 3587 27 8525 2 947377 366 51 3791 26 8638 1 947476 423 50 4025 25 8723 075 485

N.B. These rankings pertain to official contestants only. /N.B. Ces rangs ne s’appliquent qu’aux concurrents officiels.

Distribution of Marks / Distribution des pointsThis chart pertains to official contestants only. / Le graphique s’appliquent qu’aux concurrents officiels.

Number of competitors: 9474Average Mark: 48.04

Score/ Percentage of Students/ Cumulative Percentage/Note Pourcentage des etudiants Pourcentage accumule81-100 2.2 2.276-80 2.9 5.171-75 4.0 9.166-70 5.8 14.961-65 7.2 22.256-60 9.1 31.351-55 11.2 42.546-50 12.3 54.841-45 12.3 67.136-40 11.0 78.131-35 8.3 86.426-30 5.7 92.121-25 4.1 96.10-20 3.9 100.0

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Score/Score

City/Ville

Rank/Rang

School/École

271Calgary1 Western Canada H.S.

269Richmond Hill2 Bayview S.S.

266Scarborough3 Sir John A. Macdonald C.I.

265Scarborough4 Dr. Norman Bethune C.I.

262North York5 A.Y. Jackson S.S.

262Toronto5 University of Toronto Schools

261Windsor7 Vincent Massey S.S.

260North York8 Don Mills C.I.

257Burnaby9 Burnaby North S.S.

257North York9 Earl Haig S.S.

257Saskatoon9 Walter Murray C.I.

257West Vancouver9 West Vancouver S.S.

256Markham13 Markham District H.S.

253Nepean14 Bell H.S.

253Markham14 Pierre Elliott Trudeau H.S.

252Coquitlam16 Pinetree S.S.

252North York16 York Mills C.I.

251Scarborough18 Agincourt C.I.

251Richmond18 Richmond S.S.

251Vancouver18 Sir Winston Churchill S.S.

251Vancouver18 St. George's School

250Ottawa22 Lisgar C.I.

249Burnaby23 Moscrop S.S.

249Mississauga23 St. Francis Xavier S.S.

248Gloucester25 Colonel By S.S.

248North York25 Georges Vanier S.S.

248Calgary25 Henry Wise Wood Sr. H.S

248Vancouver25 Lord Byng S.S.

248North York25 Marc Garneau C.I.

248Westmount25 Marianopolis College

248Victoria25 Mount Douglas S.S.

248Thornhill25 St. Robert C.H.S.

248Thornhill25 Thornhill S.S.

246Vancouver34 Eric Hamber S.S.

246Ottawa34 Glebe Collegiate Institute

246Mississauga34 Glenforest S.S.

246Richmond Hill34 Richmond Hill H.S.

246Mississauga34 The Woodlands School

246Hamilton34 Westdale S.S.

245Vancouver40 Magee S.S.

245Toronto40 Northern S.S.

244Toronto42 North Toronto C.I.

244Vancouver42 Point Grey S.S.

243Waterloo44 Waterloo C.I.

241London45 A.B. Lucas S.S.

241Newmarket45 Sir William Mulock S.S.

239Mississauga47 Bronte College Of Canada

239Surrey47 Semiahmoo S.S.

239Vancouver47 University Transition Program

239North York47 Victoria Park C.I.

238Belleville51 Moira S.S.

238Victoria51 St. Michael's Univ. School

2011Euclid Contest/Concours Euclide

Team List/Palmarès d'équipes

Grade/Niveau

Location/Endroit

Name/Nom

School/École

Group I/Groupe I Scores/Notes 99 - 91CHIN JONAS 12MarkhamPierre Elliott Trudeau H.S.

RICKARDS JAMES 11GloucesterColonel By S.S.

SARDARLI MARIYA 11EdmontonStrathcona H.S.

SPINK HUNTER 12CalgaryWestern Canada H.S.

SPIVAK DANIEL 10Richmond HillBayview S.S.

Group II/Groupe II Scores/Notes 90 - 89CHEN YUZHOU 12ScarboroughSir John A. Macdonald C.I.

DONG ANQI 11SaskatoonWalter Murray C.I.

JIANG HEINRICH 12WindsorVincent Massey S.S.

KANG DONG WON 10TorontoNorth Toronto C.I.

LIU VICTOR 12ScarboroughDr. Norman Bethune C.I.

SU CHANG 12CalgaryWestern Canada H.S.

SUN SUSAN 11West VancouverWest Vancouver S.S.

TANG HENRY HENG 11Richmond HillBayview S.S.

WANG CHAO 12ScarboroughSir John A. Macdonald C.I.

WANG JASON 12NanaimoDover Bay S.S.

WANG ZEXUA 12North YorkA.Y. Jackson S.S.

XU HANTIAN 12VancouverPoint Grey S.S.

YANG FRANKLIN 12North YorkDon Mills C.I.

ZHAN ERIC 11TorontoUniversity of Toronto Schools

ZHAO HAN CHAO 12ScarboroughDr. Norman Bethune C.I.

Group III/Groupe III Scores/Notes 88 - 85BABICH YAROSLAV 12CalgarySir Winston Churchill H.S.

BOOKATZ GIDON 12BrandonVincent Massey H.S.

CHAN MICHAEL 11ThornhillThornhill S.S.

CHEN JEFFERY 11NewmarketSir William Mulock S.S.

DAY DYLAN 12HalifaxJ.L. Ilsley H.S.

DING PETER 11VancouverSt. George's School

DU RICHARD 9North York

GUO LINGQING 11TorontoUniversity of Toronto Schools

HAN TONY 11SurreySemiahmoo S.S.

HAN ZE HUA 12ScarboroughAgincourt C.I.

HE JIMMY 12TorontoUniversity of Toronto Schools

HUANG FAN 12NepeanBell H.S.

JIANG BOWEN 12WindsorVincent Massey S.S.

KAN BRYAN 12MarkhamMarkham District H.S.

KHAN SUFYAN 12North YorkEarl Haig S.S.

LIAO ELIZABETH 12HamiltonWestdale S.S.

LIM URSULAANN 10BurnabyBurnaby North S.S.

LIN XU 12LondonH.B. Beal S.S.

LIU SHUO 12OttawaGlebe Collegiate Institute

LUO KEVIN 11VancouverEric Hamber S.S.

LYNCH JASON 11CalgaryBishop Carroll H.S.

MAO CHENYI 12North YorkDon Mills C.I.

PARK WON HYUK 12RichmondRichmond S.S.

PARK C CHANG SUN 12VancouverMagee S.S.

QIN HUNTER 11WindsorVincent Massey S.S.

RAMKUMAR RITVIK 12MississaugaGlenforest S.S.

SHEN CHARLIE 12CoquitlamPinetree S.S.

SHIN JUNGSUB 11SurreyHoly Cross Reg. H.S.


Student Honour Roll/Liste d'honneur d'étudiants

Group III/Groupe III Scores/Notes 88 - 85SONG PAGE 12North YorkYork Mills C.I.

SUKMADJI ALVIN Y 11North YorkEarl Haig S.S.

SUN YUE RU 12WestmountMarianopolis College

TANG JOHNNY 9MarkhamMarkham District H.S.

WANG HONGYI 12VictoriaMount Douglas S.S.

WANG ZICHENG 10BurnabyBurnaby North S.S.

WANG ZIHAO 11VancouverLord Byng S.S.

WEAVER IAN 12HalifaxHalifax West H.S.

WEN YANG 12ScarboroughSir John A. Macdonald C.I.

WU KAIYU 12MississaugaMeadowvale S.S.

WU RUIWEN 12TorontoUniversity of Toronto Schools

XIE YUKUAN 10North YorkDon Mills C.I.

YAO BOWEI 12WindsorVincent Massey S.S.

YI YEJIN 12VancouverUniversity Transition Program

YOUNAN SIMON 12MississaugaSt. Francis Xavier S.S.

YU ELISHA 11BurnabyMoscrop S.S.

ZENG JOE 12North YorkDon Mills C.I.

ZHANG AMY 11MarkhamMarkham District H.S.

ZHANG JUSTIN 11ScarboroughDr. Norman Bethune C.I.

ZHAO BILL 11North YorkA.Y. Jackson S.S.

ZHENG ALBERT 11North YorkA.Y. Jackson S.S.

ZHOU KAIVEN 12EdmontonStrathcona H.S.

ZHOU YEXINHAO 9North YorkMarc Garneau C.I.

Group IV/Groupe IV Scores/Notes 84 - 83ADAMS SCOTT 12SaskatoonWalter Murray C.I.

BANERJEE NEIL 11MississaugaGlenforest S.S.

BEIGI ARSHIA 11West VancouverWest Vancouver S.S.

CAI XUESI 12WestmountMarianopolis College

CHAN HARRIS 12ThornhillSt. Robert C.H.S.

CHEUNG MATTHEW 12MarkhamBrother Andre C.H.S.

CHO RAYMOND 11West VancouverWest Vancouver S.S.

CHOI WILLIAM 12OakvilleIroquois Ridge H.S.

CHU WEILIAN 10EdmontonOld Scona Academic H.S.

CUI BOLUN 12North YorkGeorges Vanier S.S.

CUI DAVID 12VancouverSir Winston Churchill S.S.

CURELEA ANDREI 12WindsorVincent Massey S.S.

DING FREDERICK 12Richmond HillRichmond Hill H.S.

DING LIQING 12TorontoBranksome Hall

FANG JIMMY 12ThornhillSt. Robert C.H.S.

FU ZIHAO 12Vancouver

GAO JINGYI 12St CatharinesRidley College

GATEA ALEXANDRU 10WaterlooWaterloo C.I.

GO HARRY 11LangleyR.E. Mountain S.S.

GONG SHUYANG 12BurnabyBurnaby North S.S.

GU BAILEY 10OttawaLisgar C.I.

HAN SEUNGWOOK 12West VancouverMulgrave School

HE STEVEN 12North YorkDon Mills C.I.

HE TIM 12CalgaryHenry Wise Wood Sr. H.S

JI ZEXI 12North YorkMarc Garneau C.I.

KANG JEEHUN 12North VancouverBodwell H.S.

KIM KYUNGJIN 12SaskatoonWalter Murray C.I.

LAI LEO 10VancouverSir Winston Churchill S.S.

LAN TIAN 12TorontoNorthern S.S.

LEE DARRICK 12RichmondRichmond S.S.

LEE JOSHUA 12MississaugaSt. Francis Xavier S.S.



Group IV/Groupe IV Scores/Notes 84 - 83LEE WOOJUNG 11VictoriaSt. Michael's Univ. School

LI HUI 12VictoriaMount Douglas S.S.

LI MICHAEL 12North YorkEarl Haig S.S.

LI SIMON 11NepeanBell H.S.

LI SIMON ANG 11North York

LI VICK 12ThornhillThornhill S.S.

LIAO CHRISTINA 12HamiltonWestdale S.S.

LIN BORIS 11SurreyElgin Park S.S.

LIU DORIS YAN 11VancouverDavid Thompson S.S.

LIU XINYAO 12OttawaGlebe Collegiate Institute

LU WANXIN 12North YorkDon Mills C.I.

MADRAS DAVID 12North YorkEarl Haig S.S.

MATTHEWS KEVIN 12VancouverKitsilano S.S. (English)

MICHAEL TANG 11MarkhamPierre Elliott Trudeau H.S.

QIU XIN 12ScarboroughAgincourt C.I.

SALAZAR JULIAN 11CalgaryHenry Wise Wood Sr. H.S

SCHIEFER NICHOLAS 11Richmond HillHoly Trinity School

SHAO JASON 11OttawaLisgar C.I.

SHEN SIRUI 12WindsorVincent Massey S.S.

SHI ROBERT 13ScarboroughR.H. King Academy

SUO SHUNDA 10North York

WANG CODY 11CalgaryWestern Canada H.S.

WANG HAIYI 12BellevilleBayside S.S.

WANG JESSE K 10OttawaLisgar C.I.

XI PEIQI 11DuncanCowichan Sr. S.S.

XIA QING XIAO 11VancouverSt. George's School

XUE CHUQI 12North YorkYork Mills C.I.

YOO JEANNIE 12LangleyWalnut Grove S.S.

YOO YOUNGHO 12North YorkEarl Haig S.S.

YOUNG BILLY 12WindsorVincent Massey S.S.

YU STEVEN 11CoquitlamPinetree S.S.

YUAN TAO 12North YorkA.Y. Jackson S.S.

ZHANG GAVIN 9VancouverSir Winston Churchill S.S.

ZHANG XIAN RONG 12VancouverDavid Thompson S.S.

ZHAO JONATHAN 11North York

ZHOU HUI XUAN 12North YorkGeorges Vanier S.S.

ZHOU HUITING 12MississaugaBronte College Of Canada

ZHOU JOSEPH 10WindsorVincent Massey S.S.

ZHOU KEVIN 11ScarboroughWoburn C.I

Group V/Groupe V Scores/Notes 82 - 80BAEK WONJAE 12GloucesterColonel By S.S.

BAI JOHNNY WE 12WindsorVincent Massey S.S.

BAXTER THOMAS 12HamiltonHillfield-Strathallan Coll. H.S.

BEIGI BARDIA 12West VancouverWest Vancouver S.S.

BI SIFAN 12WaterlooSir John A. Macdonald S.S.

BI ZIDA 12North YorkRoyal Crown Academic School

CAMPBELL RUTGER 12OttawaLisgar C.I.

CHANG CHEN 9WindsorVincent Massey S.S.

CHAU BRIAN 12VancouverPrince of Wales S.S.

CHEUNG ANNIE 12TorontoUniversity of Toronto Schools

CHOI CYUCHUL 12North YorkYork Mills C.I.

CHOI KEVIN 12Richmond HillRichmond Hill H.S.

CHONG DANIEL 12LondonA.B. Lucas S.S.

CHU KEVIN 12BurnabyMoscrop S.S.

DUAN JUNRAN 10ScarboroughSir John A. Macdonald C.I.



Group V/Groupe V Scores/Notes 82 - 80ESPIRITU SHADRIELL 12DrydenDryden H.S.

FALLAHI FARZAD 11West VancouverWest Vancouver S.S.

FAN KEVIN 12BurnabyMoscrop S.S.

FEHR LUKAS 11SaskatoonWalter Murray C.I.

FREEMAN MARK 12MapleTanenbaum CHAT

FUNG U ALEXANDER 11TorontoUniversity of Toronto Schools

GAO LANXIN 12North YorkA.Y. Jackson S.S.

GAO YINXIN 12ScarboroughL'Amoreaux C.I.

GONG GRACY 12VancouverMagee S.S.

GUAN ERIC 12ScarboroughDr. Norman Bethune C.I.

GUO JOHNSON 12ScarboroughDavid & Mary Thomson C.I.

HA JIHYEN 12RothesayKennebecasis Valley H.S.

HAN XU 11WaterlooWaterloo C.I.

HE NICOLE 12New WestminsterNew Westminster S.S.

HUANG QIN RAN 12EtobicokeMartingrove C.I.

JACOB JOHN VARUN 12ThornhillSt. Robert C.H.S.

KANESHWARAN KIRUSANTH 11North YorkVictoria Park C.I.

KANG ANDREW 9VictoriaSt. Michael's Univ. School

KGUYEN IHANH NAM 12TorontoGreat Lakes Col. of Toronto

KONG NATHAN 11TorontoUpper Can Col-Upper School

KUO PATRIC 12DeltaSeaquam S.S.

LAI JOHN 11TorontoUniversity of Toronto Schools

LAU KEVIN 12Richmond HillRichmond Hill H.S.

LE THE QUOC NAM 12KanataA.Y. Jackson S.S.

LEE ALEX 10WaterlooWaterloo C.I.

LEE JAE JOON 10Shawnigan LakeShawnigan Lake School

LEE JAE MIN 11Richmond HillBayview S.S.

LEE MIN HYUK 12SurreyNorth Surrey S.S.

LI BAI 11CalgaryHenry Wise Wood Sr. H.S

LI JIMING 10VancouverSt. George's School

LI QINYI 12CharlottetownCharlottetown Rural H.S.

LI SHIDA 12WestmountMarianopolis College

LI SHUOZHE 12North YorkEarl Haig S.S.

LI ZIYAN 10VancouverLord Byng S.S.

LIN YUAN 12CoquitlamPinetree S.S.

LIU DAVID SIQ 12WindsorVincent Massey S.S.

LIU SHAWN 10WindsorVincent Massey S.S.

LIU YV YANG 12WestmountMarianopolis College

LIU ZIHUI 12North YorkDon Mills C.I.

LU LIWEN 11BrandonVincent Massey H.S.

MA XIAOQI 12ScarboroughAgincourt C.I.

MAK LAUREN 12CoquitlamPinetree S.S.

NAM HEEJOO 10CalgaryWestern Canada H.S.

NG MATTHEW 11MississaugaSt. Francis Xavier S.S.

NGUYEN THANH NAM 12TorontoGreat Lakes Col. of Toronto

NI LIANG 12North YorkVictoria Park C.I.

NING XIN 12North YorkA.Y. Jackson S.S.

OH HENRY 12Richmond HillRichmond Green S.S.

PANG ARTHUR 12AuroraSt. Andrew's College

PARK JIHO 12Port CoquitlamRiverside S.S.

PARK SUNGWHAN 12FrederictonFredericton H.S.

PU XINYI 12CharlottetownCharlottetown Rural H.S.

RIDOUT SEAN 12TorontoNorthern S.S.

SHIN DAVID 10VancouverEric Hamber S.S.

SHIN JAHYUN 12North YorkLoretto Abbey C.S.S.

SONG GEOFFRY 11OttawaLisgar C.I.

SONG NAM 12CalgarySir Winston Churchill H.S.



Group V/Groupe V Scores/Notes 82 - 80SUN NAN 12ThornhillWestmount C.I.

SUN YI FAN 12VancouverPoint Grey S.S.

TANG DAVID 11CalgaryWestern Canada H.S.

TANG DI 12North YorkGeorges Vanier S.S.

TANG MU 10VancouverLord Byng S.S.

TING RALPH RYA 12RichmondRichmond S.S.

TONG FREID 11MississaugaThe Woodlands School

TSUI ROGER 11BurnabyBurnaby Central S.S.

WANG YUTONG 12SurreyJohnston Heights Jr. S.S.

WANG ZHENG 12RichmondHugh Boyd S.S.

WEI LU 12ScarboroughAgincourt C.I.

WHITE PATRICK 11North YorkCrescent School

WILSON NATHAN 12St. John'sHoly Heart of Mary Reg. H.S.

WINQUIST CAINAN 12LondonA.B. Lucas S.S.

WONG DAVIN 12Richmond HillRichmond Hill H.S.

WOO JAY YOUNG 11LondonLondon Central S.S.

WU GAVIN 10VancouverSir Winston Churchill S.S.

WU HENRY 9TorontoUniversity of Toronto Schools

WU KAI YI 11WindsorVincent Massey S.S.

WU TONY 10ScarboroughDr. Norman Bethune C.I.

WU XINRUI 12NepeanBell H.S.

WU YU 12ScarboroughAgincourt C.I.

XIAO RUI 12VancouverSir Winston Churchill S.S.

XIE JIAHUI 12BurnabyMoscrop S.S.

XIE ZUOQI 12MississaugaBronte College Of Canada

XU FAN 12VancouverLord Byng S.S.

XU JOSHUA 11TorontoNorthern S.S.

XU YUWEI 9WindsorVincent Massey S.S.

XUE JENNY 11BellevilleMoira S.S.

YAN D JERRY 11Richmond HillRichmond Hill H.S.

YANG JIAYU 12TorontoBranksome Hall

YAO XIAO KUN 12MississaugaThe Woodlands School

YI JASON 12TorontoNorth Toronto C.I.

YU DAVID 11WindsorVincent Massey S.S.

YU MICHAEL 11NepeanBell H.S.

YUAN TOM 12MarkhamMarkham District H.S.

ZENG CHENG 12MississaugaThe Woodlands School

ZHANG CYRIL 12North YorkDon Mills C.I.

ZHANG LILY 12KitchenerCameron Heights C.I.

ZHANG YIPEI 12ScarboroughAgincourt C.I.

ZHAO TIAN LE 12MississaugaLorne Park S.S.



International/Unofficial Results Resultats internationaux/non-officiels

UNOFFICIAL STUDENTS / ELEVES NON-OFFICIEL

Name/Nom School/Ecole Location/EndroitGROUP I / GROUPE I SCORES / NOTES 100 - 91CHEN GONG Hwa Chong Institution SingaporeSHIYU HUANG Hwa Chong Institution SingaporeALEX SONG ICAE Troy, MIRUN XIAN TAN Hwa Chong Institution SingaporeKAIDI YAN Hwa Chong Institution Singapore

GROUP II / GROUPE II SCORES / NOTES 90 - 87ZHIQI BU Shenzhen College of International Education Shenzhen, ChinaZEQIN CHEN Hangzhou Foreign Language School Hangzhou, ChinaZHIMING CHEN Evan Hardy C.I. Saskatoon, SKZHIKANG CHENANG Shanghai, ChinaJIAYING GAO Wuxi No1 H.S Wuxi, ChinaGRACE GENG West Vancouver S.S. West Vancouver, BCXUEPENG HUA H.S. Affiliated to Nanjing Normal University Nanjing, ChinaYAN JIN H.S. Affiliated to Nanjing Normal University Nanjing, ChinaYIMING KANG Cameron Heights C.I. Kitchener, ONSHI JIE KHOR Hwa Chong Institution SingaporeTRUNG HIE LE Anglo-Chinese School SingaporeYUCHEN LI Qingdao Hongguang Foreign Language College Qingdao, ChinaCHERN YUE LIM Hwa Chong Institution SingaporeYI LIU York Mills C.I. North York, ONSHIMENG MA Shanghai, ChinaYULIN MAO Hwa Chong Institution SingaporeMIAO MING Shanghai, ChinaANUPA MURALI Bishop Brady H.S. Concord, NHAKHIL NISTALA ICAE Troy, MIBOHDAN PETRIVSKYY Lviv Physics and Math Lyceum LvivVIKRAM PRASAD ICAE Troy, MIJOSEPH RENZI ICAE Troy, MIQIFAN SHEN Suzhou High School Suzhou, ChinaYIRANYIRA SHI H.S. Affiliated to Nanjing Normal University Nanjing, ChinaZHAN SONG H.S. Affiliated to Nanjing Normal University Nanjing, ChinaLIU TIANQI Meicun Senior High School Wuxi, ChinaZIQUAN WANG Suzhou High School Suzhou, ChinaBRIAN XU ICAE Troy, MIYANGXINYE YANG Shenzhen College of International Education Shenzhen, ChinaTING JING YUAN Help University College Kuala Lumpur, MalaysiaJUSTINE ZHANG Sir Winston Churchill H.S. Calgary, ABYINING ZHANG Vanier College Saint-Laurent, QCTIANCHEN ZHAO Point Grey S.S. Vancouver, BCTIANYU ZHOU Mount Douglas S.S. Victoria, BCZIHAN ZHOU H.S. Affiliated to Nanjing Normal University Nanjing, ChinaHAN ZHU Hwa Chong Institution SingaporeWEITAO ZHU Suzhou High School Suzhou, ChinaZHIGUANG ZHU H.S. Affiliated to Nanjing Normal University Nanjing, China

2011 Results Euclid Contest 2011 Résultats Concours Euclide

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