2010 results fryer contest galois contest hypatia contest 2010

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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 2010 Results Fryer Contest (Grade 9) Galois Contest (Grade 10) Hypatia Contest (Grade 11) 2010 esultats Concours Fryer (9 e ann´ ee – Sec. III) Concours Galois (10 e ann´ ee – Sec. IV) Concours Hypatie (11 e ann´ ee – Sec. V) c 2010 Centre for Education in Mathematics and Computing

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Page 1: 2010 Results Fryer Contest Galois Contest Hypatia Contest 2010

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

2010Results

Fryer Contest(Grade 9)

Galois Contest(Grade 10)

Hypatia Contest(Grade 11)

2010Resultats

Concours Fryer(9e annee – Sec. III)

Concours Galois(10e annee – Sec. IV)

Concours Hypatie(11e annee – Sec. V)

c©2010 Centre for Education in Mathematics and Computing

Page 2: 2010 Results Fryer Contest Galois Contest Hypatia Contest 2010

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 BaeJanet BakerErsal CahitKaren ColeJennifer CoutureSerge D’AlessioFrank DeMaioFiona DunbarMike EdenBarry FergusonJudy FoxSteve FurinoSandy GrahamAngie HildebrandJudith KoellerJoanne KursikowskiAngie MurphyDean MurrayJen NissenJ.P. PrettiLinda SchmidtKim SchnarrJim SchurterCarolyn SedoreIan VanderBurghTroy Vasiga

Problems Committee / Comite des problemes

Judith Koeller (Chair / president), University of Waterloo, Waterloo, ONLino Demasi, Simon Fraser University, Burnaby, BCRad dePeiza, Toronto, ONSandy Emms Jones, Forest Heights C.I., Kitchener, ONJohn Galbraith, Sir John A. Macdonald S.S., Waterloo, ONShawn Godin, Cairine Wilson S.S., Orleans, ONAndre Ladouceur, Gloucester, ONPeter O’Hara, Glendale H.S., Tilsonburg, ONPaul Ottaway, University of British Columbia, Vancouver, BCJudy Shanks, Pickering H.S., Ajax, ON

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Page 3: 2010 Results Fryer Contest Galois Contest Hypatia Contest 2010

Comments on the Papers Commentaires sur les epreuves

Overall CommentsThe year 2010 marked the eighth writings of the Fryer, Galois and Hypatia Contests. The FGH Contests aredesigned to give students in Grades 9, 10 and 11 an additional mathematical challenge during the school year,and one that requires full written solutions. Being able to do mathematics is an important skill; being able tocommunicate one’s findings (in mathematics or in any other field) is also very important.

We were very pleased this year to see another healthy increase in the number of participants in these Contests.In general, many students writing these Contests are doing a better job each year of writing clear solutions to theproblems. That being said, there is always work that can be done to help them improve these skills. Some studentsreduced their scores because they gave answers rather than solutions or presented untidy or illegible solutions.

The averages on the Fryer, Galois and Hypatia Contests this year were 23.3, 23.6 and 23.7, respectively. Wewill continue to try to keep the averages on these papers in this range. Here are some specific comments on theproblems.

Fryer Contest

1. Average: 8.9This problem was very well done. A handful of students presented answers only with no explanations.

2. Average: 6.5Parts (a) and (b)(i) were well done. In part (b)(ii), many students assumed that n was odd and attemptedto explain why the average was odd, which is the converse of the required statement. Also in parts (b)(ii)and (c), some students attempted to explain why the general statements were true by trying a small numberof numerical examples.

3. Average: 6.0Parts (a) and (b) were well done. In part (c), many students determined that Train 1 travelled 210 km beforeTrain 2 started moving. Also in part (c), some students tried to explain too much rather than developinga distance-speed-time chart or converting to an algebraic solution. Many students incorrectly assumed thateach train travelled half the distance between Amville and Batton.

4. Average: 1.9Part (a) was generally well done, though a number of students believed that 0 is a positive integer. A key ideathat led many quickly to a solution in (b) was the realization that seven-digit palindromes are completelydetermined by their first four digits. A few students had very simple solutions to (c). Part (d) was a majorchallenge for most students, though we did see a handful of very nice complete solutions.

Galois Contest

1. Average: 8.5This question was very well done, as there were many different ways of combining the rates to solve theproblems. After correctly determined that Emily saves 6 cents during a 15 minute shower in part (c), manystudents inadvertently converted this rate to a savings of 6 cents per minute, not 6 cents in 15 minutes.

2. Average: 7.1Part (a) was very well done. In parts (b) and (c), many students obtained correct expressions for the areas,though a good number of these did not simplify their answers. In part (d), a common error was to assumethat 4ACB is right-angled, and use the lengths of AC and CB as calculated in parts (b) and (c). Thisincorrect assumption led many students to an equation that they were not able to solve.

3. Average: 5.1Part (a) was very well done by the majority of students. In part (b), there were some well-crafted arguments.Some students considered the parity of x and y, drawing conclusions about the parity of p and q. Other

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Comments on the Papers Commentaires sur les epreuves

students started with p even and q odd and reasoned that x and y would not then be integers. Some studentstried to describe an even integer as p = 2k and an odd integer as q = 2k + 1 for some integer k, not realizingthat this assumes that p and q are consecutive. In part (c), a number of students applied their work in parts(a) and (b). Many spotted that x2 − y2 = (x − y)(x + y), and listed all the pairs of factors of 420. Someused the insight from part (b) to then discard those pairs of factors which did not match in parity.

4. Average: 2.9In part (a), many students noticed the fact that the two triangles share a height, and reduced the ratioof 6 : 10. In part (b), many students were able to determine the area of 4ABC. In (c), many studentssuccessfully computed the area of 4PV Y . Further progress was made by students who found other ratiosof area in pairs of triangles with a shared height.

Hypatia Contest

1. Average: 9.6This question was very well done. Many solutions were well presented. It was nice to see solutions thatinvolved computing the distance (2000 km) where flying and riding the bus cost the same amount.

2. Average: 6.1The largest hurdle in this problem for many students was understanding the functional notation. Studentscomfortable with functional notation were generally successful in solving all three parts. Part (c) was solvedin several different ways and sometimes answered first which then quickly gave answers to parts (a) and (b).

3. Average: 5.6Most students tried all parts of this problem. Very few had trouble computing the measures of the angles inpart (a). The majority of students provided one of the many possible correct solutions in part (b). The tworemaining parts were approached in a variety of different ways. The Sine Law was the most commonly usedtool. This sometimes resulted in decimal approximations instead of the exact answers shown in the modelsolutions.

4. Average 2.4Part (a) was reasonable well done, but students sometimes missed the negative or irrational roots. Whilenot many students attempted parts (b) and (c), there were a number of beautiful arguments among thosethat were marked.

Please visit our website at www.cemc.uwaterloo.ca to download the 2010 Fryer, Galois and HypatiaContests, plus full solutions.

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Comments on the Papers Commentaires sur les epreuves

Commentaires generauxL’annee 2010 est la huitieme edition des concours Fryer, Galois et Hypatie. Les concours de FGH ont ete creespour donner aux etudiants de 9e, 10e et 11e annee (sec. III, IV et V) un defi mathematique supplementairependant l’annee scolaire qui exige des solutions ecrites completes. Etre capable de faire des mathematiques estune aptitude importante. Pouvoir communiquer ses conclusions (en mathematiques ou autres domaines) est aussitres important.

Nous sommes ravis cette annee de constater une croissance du nombre de participants a ces concours. Engeneral, plusieurs des etudiants participant a ces concours s’ameliorent d’annee en annee en ce qui concerneecrire des solutions claires. Cependant, il y a toujours du travail a faire pour les aider a developper leurs aptitudes.Certains des etudiants ont eu des notes plus basses car ils presentaient uniquement des reponses au lieu de solutionsou des solutions non soignees ou illisibles.

Cette annee, les moyennes des concours Fryer, Galois et Hypatie etaient de 23,3, 23,6 et 23,7 respectivement.Nous tenterons de continuer a conserver cette gamme pour les moyennes de ces examens. Voici quelques commen-taires specifiques sur les problemes de ces examens.

Concours Fryer

1. Moyenne: 8,9Ce probleme a ete tres bien reussi. Quelques eleves ont presente des reponses seulement, sans explications.

2. Moyenne: 6,5Les parties (a) et (b)(i) ont ete bien reussies. Dans la partie (b)(ii), beaucoup d’eleves ont suppose que netait impair et ont tente de demontrer que la moyenne etait impaire, ce qui est la reciproque de ce qu’ilfallait demontrer. Dans les parties (b)(ii) et (c), certains eleves ont tente d’expliquer pourquoi les enoncesgeneraux etaient vrais en montrant qu’ils etaient vrais dans quelques cas numeriques particuliers.

3. Moyenne: 6,0Les parties (a) et (b) ont ete bien reussies. Dans la partie (c), bon nombre d’eleves ont determine que letrain 1 avait parcouru 210 km avant le depart du train 2. Dans la partie (c), certains eleves ont tente de toutexpliquer au lieu de developper un tableau distance-vitesse-temps ou d’utilser un modele algebrique. Bonnombre d’eleves ont suppose, a tort, que chaque train avait parcouru la moitie de la distance entre Amvilleet Batton.

4. Moyenne: 1,9La partie (a) a ete assez bien reussie, bien que quelques eleves croyaient que 0 etait un entier strictementpositif. Dans la partie (b), beaucoup d’eleves ont utilise une idee-cle, a savoir que les palindromes de 7chiffres sont completement determines par leurs quatre premiers chiffres. Quelques eleves ont utilise unesolution tres simple dans la partie (c). La partie (d) presentait un defi de taille pour la plupart des eleves,mais quelques eleves ont tout de meme presente de belles solutions completes.

Concours Galois

1. Moyenne: 8,5Cette question a ete tres bien reussie. Dans la partie (c), apres avoir determine qu’Emilie epargnait 6 centspendant une douche de 15 minutes, beaucoup d’eleves ont conclu qu’elle epargnait 6 cents par minute aulieu de 6 cents par 15 minutes.

2. Moyenne: 7,1La partie (a) a ete tres bien reussie. Dans les parties (b) et (c), beaucoup d’eleves ont obtenu de bonnesexpressions pour l’aire, sans toutefois les simplifier. Dans la partie (d), bon nombre d’eleves ont suppose,a tort, que le triangle ACB etait rectangle. Ils ont ensuite utilise les longueurs de AC et de CB obtenuesdans les parties (b) et (c). Cela leur a donne une equation qu’ils n’ont pas reussi a resoudre.

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Comments on the Papers Commentaires sur les epreuves

3. Moyenne: 5,1La partie (a) a ete tres bien reussie par la majorite des eleves. Dans la partie (b), certains eleves ont presentedes arguments astucieux. Certains ont considere la parite de x et de y pour tirer des conclusions sur la paritede p et de q. D’autres ont suppose que p etait pair et que q etait impair pour conclure que x et y ne seraientpas des entiers. Quelques eleves ont utilise p = 2k (k etant un entier quelconque) pour exprimer un nombrepair et q = 2k + 1 pour exprimer un nombre impair, sans realiser qu’ils supposaient ainsi que p et q etaientdes entiers consecutifs. Dans la partie (c), certains eleves ont utilise leurs resultats des parties (a) et (b).Beaucoup d’entre eux ont utilise l’identite x2 − y2 = (x− y)(x + y), ce qui leur a permis d’ecrire toutes lespaires de facteurs de 420. Certains ont eu la perspicacite d’utiliser les resultats de la partie (b) pour rejeterles paires de facteurs qui ne presentaient pas la bonne parite.

4. Moyenne: 2,9Dans la partie (a), beaucoup d’eleves ont vu que les triangles partageaient la meme hauteur et ils ont ensuitereduit le rapport 6 : 10. Dans la partie (b), beaucoup d’eleves ont reussi a determiner l’aire du triangleABC. Dans la partie (c), bon nombre d’eleves ont reussi a determiner l’aire du triangle PV Y . D’autresont pu progresser davantage en trouvant des rapports d’aires de triangles qui partageaient une meme hauteur.

Concours Hypatie

1. Moyenne: 9,6Cette question a ete tres bien reussie. Les eleves ont utilise une variete de solutions. Il etait agreable devoir des solutions dans lesquelles on a determine la distance (2000 km) pour laquelle le cout etait le memeen autocar et en avion.

2. Moyenne: 6,1L’obstacle principal a franchir, pour certains eleves, etait la comprehension de la notation fonctionnelle.Ceux qui la comprenaient ont generalement reussi les trois parties. La partie (c) pouvait etre resolue deplusieurs facons et si on la resolvait en premier, elle donnait les reponses des parties (a) et (b).

3. Moyenne: 5,6La plupart des eleves ont tente de resoudre toutes les parties du probleme. Tres peu d’entre eux n’ont pasreussi a determiner les mesures de la partie (a). La partie (b) pouvait etre resolue de plusieurs facons et lamajorite des eleves l’ont reussie. Les eleves ont utilise une variete d’approches pour resoudre les deux autresparties. La loi des sinus semble avoir ete l’outil le plus populaire. A quelques occasions, cela a donne desreponses approximatives au lieu des nombres exacts que l’on peut voir dans les exemples de solutions.

4. Moyenne 2,4La partie (a) a ete assez bien reussie, bien que certains eleves n’aient pas traite des racines negatives ou irra-tionnelles. Peu d’eleves ont essaye de resoudre les parties (b) ou (c), mais certains d’entre eux ont presentede beaux arguments.

Veuillez visiter notre site Web a www.cemc.uwaterloo.ca pour telecharger les concours Fryer, Galoiset Hypatie 2010, avec solutions completes.

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Enrollment Inscription

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

Enrollment/Inscription

NL 45NS 165NB 196PE 20QC 354ON 7572MB 309SK 65AB 624BC 1490International 2155

Total 12995

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Page 8: 2010 Results Fryer Contest Galois Contest Hypatia Contest 2010

Student Rankings Classements des eleves

Hypatia/Fryer Galois Hypatie

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

40 1 1 139 8 21 4338 29 42 8937 41 73 15436 77 149 20235 120 225 26234 190 303 33533 259 390 41432 327 497 51031 437 608 63930 537 714 77129 676 837 88428 790 955 101127 940 1082 111426 1130 1199 123925 1298 1336 136224 1513 1494 149123 1725 1676 160622 1924 1866 171021 2117 2019 181920 2309 2173 192719 2512 2347 202518 2683 2487 212717 2848 2620 224316 3002 2732 232915 3132 2827 243714 3243 2932 253913 3314 3007 266112 3382 3084 276611 3435 3133 287810 3464 3180 29559 3493 3224 30068 3507 3262 30247 3535 3286 30386 3545 3299 30455 3554 3313 30554 3558 3323 30613 3560 3331 30632 3561 3335 30691 3338 30790 3564 3340

N.B. These rankings pertain to ALL contestants /N.B. Ces rangs se rapportent a TOUS concurrents

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Fryer – Gold Standard Palmares individuel – Fryer

The top 25% of the competitors in each of the three Contests were divided into three categories: Gold Standard, SilverStandard and Bronze Standard, in the ratio 1 : 2 : 3. The names of the those students achieving the Gold Standard (that is,scoring in roughly the top 4%) are listed alphabetically below for each Contest.

Les candidats qui se classent dans le premier quart de classement dans chacun des trois concours ont ete repartis en troiscategories: le niveau or, le niveau argent et le niveau bronze, selon le ratio 1 : 2 : 3. Le nom des etudiants qui ont obtenu leniveau or (c’est-a-dire ceux qui se classent parmi les premiers 4 p. 100) est donne par ordre alphatbetique ci-dessous pourchaque concours.

Name/Nom School/Ecole Location/EndroitSAM ABERNETHY Cornwallis Sr. and Jr. H.S. Halifax, NSDUCKSUNG AHN The Anglo-American School of Moscow Moscow, Russian FederationRIZKY APRILIANTI GCN International Pamekasan, IndonesiaADITHYA BALASUBRAMANIA ICAE Troy, MIROHIT BHADANGE ICAE Troy, MISAHIT BOLLINENI ICAE Troy, MICASEY BOROSKI Vincent Massey S.S. Windsor, ONMICHAEL BRODETH Math Trainers Guild of Philippines Zamboanga City, PhilippinesTANNYA CAI Elmwood School Rockcliffe, ONVICTORIA CAO John Campbell P.S. Windsor, ONPATRICK CELON Math Trainers Guild of Philippines Zamboanga City, PhilippinesANGELA CHAO Glenforest S.S. Mississauga, ONCLAIRE CHEN University of Toronto Schools Toronto, ONCRYSTAL CHEN North York, ONJENNIFER CHEN Havergal College North York, ONMICHAEL CHEN Vincent Massey S.S. Windsor, ONSTEVEN CHEN Vincent Massey S.S. Windsor, ONGEORGE CHENG University of Toronto Schools Toronto, ONVANICE CHEUNG Branksome Hall Toronto, ONKEVIN CHO Sentinel S.S. West Vancouver , BCSALLY CHOI Prince of Wales S.S. Vancouver, BCWIRIAWAN CHRISTOPHER Surya Institute Tangerang, IndonesiaWEILIAN CHU Grandview Heights Jr. H.S. Edmonton, ABNATASHA CONSUL ICAE Troy, MIWENCHE CUI Bayview S.S. Richmond Hill, ONGRACIA DONG Bayview S.S. Richmond Hill, ONSACHIN DOSHI The Woodlands School Mississauga, ONWILDY FACHRIZAL GCN International Pamekasan, IndonesiaHOWARD FENG Bayview S.S. Richmond Hill, ONSAMANTHA FOSADO SOLIS E.S. St. Luc Montreal, QCSTUART FOWLER Waterloo C.I. Waterloo, ONQIAOYU GAO North York, ONSHUBHAM GARG Tom Baines School Calgary, ABSABRINA GE University of Toronto Schools Toronto, ONBAILEY GU Lisgar C.I. Ottawa, ONMITCHELL GUNN London, ONSHANNON GUO Parkside H.S. Dundas, ONXU HAICHUAN Port Credit S.S. Mississauga, ONERIN HEMM Frontenac S.S. Kingston, ONJORDAN HO Marc Garneau C.I. North York, ONLEWIS HO Chinese Int’l School Braemar Hill, Hong KongANGIE HSU West Vancouver S.S. West Vancouver, BCDANCHENG HU Acadia Jr. H.S. Winnipeg, MBTIGER HUANG Upper Canada College Toronto, ONTOM HUANG Richmond Hill H.S. Richmond Hill, ONDANIEL HUI Woburn C.I. Scarborough, ONDHARINI ILANGOMARAN Marc Garneau C.I. North York, ON

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Fryer – Gold Standard Palmares individuel – Fryer

Name/Nom School/Ecole Location/EndroitMAYURESH IYER ICAE Troy, MIHIRSH JAIN ICAE Troy, MIALYF JANMOHAMED Upper Canada College Toronto, ONKURTIS JANTZEN Queen Elizabeth H.S. Calgary, ABDEREK JEDRAL University of Toronto Schools Toronto, ONHAOCHEN JI The Woodlands School Mississauga, ONXIN JIANG North York, ONJEEVITESH JUNEJA Port Credit S.S. Mississauga, ONSEUNGYEON JUNG Fudan Int’l School Shanghai, ChinaANDREW KANG Victoria, BCSHERRY KAO Bishop Strachan School Toronto, ONTAYLPR KEATING Crescent School North York, ONYOUNGSANG KIM Pinetree S.S. Coquitlam, BCANGUS KONG Vincent Massey S.S. Windsor, ONSACHIN KOTECHA Frontenac S.S. Kingston, ONNITIN KUMAR ICAE Troy, MIJAE YOUNG KWON E.S. St. Luc Montreal, QCALEX LABACH Waterloo C.I. Waterloo, ONELBERT LAI Waterloo C.I. Waterloo, ONLEO LAI Prince of Wales S.S. Vancouver, BCFREDRIC LAM Centennial Reg’l H.S. Greenfield Park, QCJAEYOUNG LEE The Anglo-American School of Moscow Moscow, Russian FederationJONGSEO LEE Prince of Wales S.S. Vancouver, BCDAVID YE LI North York, ONFRANK LI Markham D.H.S. Markham, ONSCOTT LI Northern S.S. Toronto, ONTHOMAS LI Chinese Int’l School Braemar Hill, Hong KongYUN LIN Pinetree S.S. Coquitlam, BCHSIN-YEN LIU William Lyon Mackenzie C.I. North York, ONSHAWN LIU Vincent Massey S.S. Windsor, ONTIAN JING LIU College St. Louis Lasalle, QCWINSTON LIU Lorne Park S.S. Mississauga, ONJOSHUA LO Richmond Hill H.S. Richmond Hill, ONEDWARD LU Sir John A. Macdonald S.S. Waterloo, ONKAI LU Waterloo C.I. Waterloo, ONMICHELLE LU Earl Haig S.S. North York, ONGARY LUOO ICAE Troy, MICHANUKYA MALLA ICAE Troy, MIHIMIG MARCOS Math Trainers Guild of Philippines Zamboanga City, PhilippinesDHRUV MEDARAMETLA ICAE Troy, MINICOLAES MIN Walter Murray C.I. Saskatoon, SKGARY MOK David Thompson S.S. Vancouver, BCANTONIO MOLINA Ste. Anne Fredericton, NBPRIYA MURALI St. Francis Xavier S.S. Mississauga, ONPATRICK MURPHY St. Thomas Aquinas S.S. London, ONROSEMARY NAM University of Toronto Schools Toronto, ONMOHAMMAD NASIRUDDIN GCN International Pamekasan, IndonesiaSEANNE NG Math Trainers Guild of Philippines Zamboanga City, PhilippinesRAENELLE NGO Math Trainers Guild of Philippines Zamboanga City, PhilippinesAKHIL NISTALA ICAE Troy, MIJAEWON OH Waterloo C.I. Waterloo, ONMARIO ONGKIKO Math Trainers Guild of Philippines Zamboanga City, PhilippinesSKANDA PALANI ICAE Troy, MILUCAS PALMER Vincent Massey S.S. Windsor, ONERIC PAN London, ONMICHAEL PANG Acadia Jr. H.S. Winnipeg, MB

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Fryer – Gold Standard Palmares individuel – Fryer

Name/Nom School/Ecole Location/EndroitSACHIN PASRICHA Upper Canada College Toronto, ONJOSHEN PATEL ICAE Troy, MIBO YUAN PENG Academie Ste. Cecile Int’l Windsor, ONCAMERON PORTEOUS Forest Heights C.I. Kitchener, ONRAGHAV PRABHU ICAE Troy, MIYUSUF QADEER ICAE Troy, MIALVIN QIU Richmond Hill H.S. Richmond Hill, ONBOBBY QIU Don Mills C.I. North York, ONBRYAN QIU Richmond Hill H.S. Richmond Hill, ONMENGTING QIU University of Toronto Schools Toronto, ONARIFIN RAHMAN Marc Garneau C.I. North York, ONRAJ RAINA ICAE Troy, MIHONGRU REN Acadia Jr. H.S. Winnipeg, MBJOSEPH RENZI ICAE Troy, MICHRISTIAN RICHARD Ste. Anne Fredericton, NBALEX RODRIGUES John Ware Jr. H.S. Calgary, ABVALENTINA SAMOYLENKO E.S. St. Luc Montreal, QCSTEPHEN SANJAYA Surya Institute Tangerang, IndonesiaPARTH SHAH ICAE Troy, MIPRIYANKA SHANMUGASUNDAR ICAE Troy, MIYEJI SHIN The Anglo-American School of Moscow Moscow, Russian FederationAPURVA SHRIVASTAVA ICAE Troy, MIDESMOND SISSON Queen Elizabeth H.S. Calgary, ABRUI SONG Walter Murray C.I. Saskatoon, SKDANIEL SPIVAK Bayview S.S. Richmond Hill, ONCUTHBERT SUN ICAE Troy, MIJASON SUN Marc Garneau C.I. North York, ONSIMONN SUO North York, ONKEITH TAM Bayview S.S. Richmond Hill, ONJOHNNY TANG Scarborough, ONDIELLE TIO Math Trainers Guild of Philippines Zamboanga City, PhilippinesALEXANDER TOY Lower Canada College Montreal, QCMIKAELA UY Math Trainers Guild of Philippines Zamboanga City, PhilippinesJORDY VERASAMY Iroquois Ridge H.S. Oakville, ONCHRIS WAN Chinese Int’l School Braemar Hill, Hong KongHANCHEN WANG Sir Winston Churchill S.S. Vancouver, BCMIKE WANG Moscrop S.S. Burnaby, BCJANSEN WANGSAWIDJAJA Surya Institute Tangerang, IndonesiaYUANHAO WEI Earl of March S.S. Kanata, ONLUCAS WEN Waterloo C.I. Waterloo, ONJOSHUA WIJAYA Surya Institute Tangerang, IndonesiaSANDY WONG John Campbell P.S. Windsor, ONSHANNON WONG Richmond Hill H.S. Richmond Hill, ONANGELA WU John F. Ross C.V.I. Guelph, ONHENRY WU University of Toronto Schools Toronto, ONJENNY WU Marc Garneau C.I. North York, ONKENNY WU West Vancouver S.S. West Vancouver, BCKEVIN WU North York, ONSHUYI WU Acadia Jr. H.S. Winnipeg, MBTONY WU North York, ONXIAOZE WU North York, ONYUKUAN XIE Don Mills C.I. North York, ONALAN XU ICAE Troy, MIBRIAN XU ICAE Troy, MIDENNIS XU Abbey Park H.S. Oakville, ONZEN YAN Scarborough, ON

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Fryer – Gold Standard Palmares individuel – Fryer

Name/Nom School/Ecole Location/EndroitBOB YANG Sir Winston Churchill S.S. Vancouver, BCBYRON YANG Moscrop S.S. Burnaby, BCCARLA YANG Seaquam S.S. Delta, BCISABELLE YANG Don Mills C.I. North York, ONSIQI YANG Pinetree S.S. Coquitlam, BCYI YANG Moscrop S.S. Burnaby, BCDENNIS YE Sir John A. Macdonald C.I. Scarborough, ONCYNTHIA YEUNG Holy Trinity School Richmond Hill, ONMEHMET YILDIZ Tevitol H.S. Gebze, TurkeyTONY YIN Agincourt C.I. Scarborough, ONTED YING The Woodlands School Mississauga, ONJUSTIN YTURZAETA Math Trainers Guild of Philippines Zamboanga City, PhilippinesALLEN YU Marc Garneau C.I. North York, ONLUCY YU Sir John A. Macdonald C.I. Scarborough, ONRAYMOND YU University of Toronto Schools Toronto, ONREENA ZHAN University of Toronto Schools Toronto, ONBOHAN ZHANG Marc Garneau C.I. North York, ONCHARLENE ZHANG Gleneagle S.S. Coquitlam, BCJASON ZHANG Pleasant View Jr. H.S. North York, ONZHUOWEI ZHANG West Point Grey Academy Vancouver, BCKAI XI ZHAO E.S. St. Luc Montreal, QCRAY ZHAO Dr. Norman Bethune C.I. Scarborough, ONDAVID ZHENG New Westminster S.S. New Westminster, BCJOSEPH ZHOU Vincent Massey S.S. Windsor, ONWILLIAM ZHOU Britannia S.S. Vancouver, BCXINYANG ZHOU London Central S.S. London, ONYEXINHAO ZHOU North York, ONANTONIA ZHU St. John’s-Ravenscourt School Winnipeg, MBHENRY ZHU Waterloo C.I. Waterloo, ONROBERT ZHU Iroquois Ridge H.S. Oakville, ON

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Galois – Gold Standard Palmares individuel – Galois

The top 25% of the competitors in each of the three Contests were divided into three categories: Gold Standard, SilverStandard and Bronze Standard, in the ratio 1 : 2 : 3. The names of the those students achieving the Gold Standard (that is,scoring in roughly the top 4%) are listed alphabetically below for each Contest.

Les candidats qui se classent dans le premier quart de classement dans chacun des trois concours ont ete repartis en troiscategories: le niveau or, le niveau argent et le niveau bronze, selon le ratio 1 : 2 : 3. Le nom des etudiants qui ont obtenu leniveau or (c’est-a-dire ceux qui se classent parmi les premiers 4 p. 100) est donne par ordre alphatbetique ci-dessous pourchaque concours.

Name/Nom School/Ecole Location/EndroitYONG JIN AHN Chinese Int’l School Braemar Hill, Hong KongHYOJI AN Esquimalt Community School Victoria, BCSEUNGJIN AN St. Andrew’s College Aurora, ONHARRY BANG Vincent Massey S.S. Windsor, ONARSHIA BEIGI West Vancouver S.S. West Vancouver, BCMEHMET BESIKCI Tevitol H.S. Gebze, TurkeyUJWAL BHARATH ICAE Troy, MIMATTHEW BRENNAN Upper Canada College Toronto, ONXIANGE CAI Shenzhen College of Int’l Education Shenzhen, ChinaHAZAL CAN Tevitol H.S. Gebze, TurkeyYIQI CAO Bayview S.S. Richmond Hill, ONBENJAMIN CHASNOV Chinese Int’l School Braemar Hill, Hong KongALLEN CHEN Ridley College St Catharines, ONBENJAMIN CHEN Unionville H.S. Markham, ONEDREA CHEN Britannia S.S. Vancouver, BCGREGORY CHEN Thornhill S.S. Thornhill, ONYANG CHEN Fuyuan School Shenzhen, ChinaCHARLIE CHENG Western Canada H.S. Calgary, ABJI CHENG Concord College of Sino-Canada Shenzhen, ChinaSEAN CHENG Math Trainers Guild of Philippines Zamboanga City, PhilippinesRAYMOND CHO West Vancouver S.S. West Vancouver, BCKENNETH CO Math Trainers Guild of Philippines Zamboanga City, PhilippinesXIAOYU DENG North York, ONRICHARD DU North York, ONXIAOHAN DU Vaughan Road Academy York, ONJIAYAO FAN E.S. St. Luc Montreal, QCZHIHAO FAN Henan Experimental H.S. Zhengzhou, ChinaLUKAS FEHR Walter Murray C.I. Saskatoon, SKYIHUI FENG E.S. St. Luc Montreal, QCTAL FRIEDMAN Thornhill S.S. Thornhill, ONHARRY GO R.E. Mountain S.S. Langley, BCMALAN GOONEWARDENA Lincoln Community School Accra, GhanaCHENGKAI GU Beijing Concord College of Sino-Canada Beijing, ChinaLUCY GU Grand Canadian Academy Nanjing, ChinaJEREMIAH GUNAWAN Surya Institute Tangerang, IndonesiaMIN SOO HAN Hillfield-Strathallan College Hamilton, ONMOHAMMAD HEFDI GCN International Pamekasan, IndonesiaNURUL HIDAYATI GCN International Pamekasan, IndonesiaLUIS HONG SANCHEZ Teda Int’l School Tianjin, ChinaJINGCHAN HU Sir Winston Churchill S.S. Vancouver, BCKEVIN HWANG Seaquam S.S. Delta, BCSANASI JAYAWARDENA Bluevale C.I. Waterloo, ONDANIEL JIANG Western Canada H.S. Calgary, ABDONG JIANG Scarborough, ONGU JOLIN Don Mills C.I. North York, ONCEM KALKANLI Tevitol H.S. Gebze, TurkeyDONG WON KANG North Toronto C.I. Toronto, ON

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Galois – Gold Standard Palmares individuel – Galois

Name/Nom School/Ecole Location/EndroitCHRISTINA KIM St. Michael’s Univ. School Victoria, BCJAE WON KIM Southridge School Surrey, BCJINSOO KIM Sir Frederick Banting S.S. London, ONNATHAN KONG Upper Canada College Toronto, ONBJORN KWOK Crescent School North York, ONSITE L Concord College of Sino-Canada Shenzhen, ChinaNICHOLAS LAI Chinese Int’l School Braemar Hill, Hong KongALEX LEE Waterloo C.I. Waterloo, ONJAE MIN LEE Bayview S.S. Richmond Hill, ONJOSHUA LEE Crescent School North York, ONSEUNGWON LEE Southridge School Surrey, BCWILLIAM LEE St. Michael’s Univ. School Victoria, BCANDREW LEUNG Crescent School North York, ONBAI LI Henry Wise Wood Sr. H.S Calgary, ABGEORGE LI The Woodlands School Mississauga, ONHAO NAN LI Henan Experimental H.S. Zhengzhou, ChinaJASON LI Bayview S.S. Richmond Hill, ONLORITA LI Moira S.S. Belleville, ONSIMON ANG LI North York, ONMEGAN LIANG Western Canada H.S. Calgary, ABQI RAN KEN LIAO Albert Campbell C.I. Scarborough, ONASHLEY LIM Toronto District Christian H.S. Woodbridge, ONHYUN SUK LIM Fieldstone Day School North York, ONHENG YU LIN E.S. St. Luc Montreal, QCJACOB LIN Washington H.S TaiwanJAMES LIN Western Canada H.S. Calgary, ABMANDY LIN Prince of Wales S.S. Vancouver, BCXI LIN Henan Experimental H.S. Zhengzhou, ChinaHENRY LIU Sir Winston Churchill S.S. Vancouver, BCJOHNSON LIU L’Amoreaux C.I. Scarborough, ONYI LIU York Mills C.I. North York, ONYUE LIU Fort Richmond C.I. Winnipeg, MBDAVID LU ICAE Troy, MIFEIYU LU Bayview S.S. Richmond Hill, ONSEAN LU Vincent Massey S.S. Windsor, ONANGELA MA University of Toronto Schools Toronto, ONHENRY MORCO Math Trainers Guild of Philippines Zamboanga City, PhilippinesABDUL MUNIF GCN International Pamekasan, IndonesiaMATTHEW NG St. Francis Xavier S.S. Mississauga, ONLIAM PAKINGAN Francis Libermann C.H.S. Scarborough, ONGREGORY PARK ICAE Troy, MIJAY PARK West Vancouver S.S. West Vancouver, BCJOHN PARK Pinetree S.S. Coquitlam, BCKEUNHYUNG PARK White Oaks S.S. Oakville, ONSANGMIN PARK Tashkent Int’l School Tashkent, UzbekistanVIKRAM PRASAD ICAE Troy, MIMICHAEL PRYSIAZNY E.L. Crossley S.S. Fonthill, ONTERRY PYUN Richmond Hill H.S. Richmond Hill, ONHUNTER QIN Vincent Massey S.S. Windsor, ONYEJI RHA Burnaby Central S.S. Burnaby, BCKEVIN SHEN Sir Winston Churchill S.S. Vancouver, BCSIRUI SHEN Vincent Massey S.S. Windsor, ONTON NU SHUY ANH Vincent Massey S.S. Windsor, ONJOE SU Lisgar C.I. Ottawa, ONDAWEI SUN Beijing Concord College of Sino-Canada Beijing, ChinaZHEWEI SUN Vincent Massey S.S. Windsor, ON

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Galois – Gold Standard Palmares individuel – Galois

Name/Nom School/Ecole Location/EndroitJULIUS SY Math Trainers Guild of Philippines Zamboanga City, PhilippinesJANE TAN Burnaby South S.S. Burnaby, BCKEEFE TAN Math Trainers Guild of Philippines Zamboanga City, PhilippinesDAVID TANG Western Canada H.S. Calgary, ABHENRY TANG Bayview S.S. Richmond Hill, ONJORDAN TEITELBAUM Tanenbaum CHAT Maple, ONMONICA VANYA SANTOSO Surya Institute Tangerang, IndonesiaEMILIO VERDUGO PAREDE Resurrection C.S.S. Kitchener, ONELLEN WANG Marc Garneau C.I. North York, ONHAN WANG Beijing Concord College of Sino-Canada Beijing, ChinaOSCAR WANG Chinese Int’l School Braemar Hill, Hong KongYIDING WANG Fraser Heights S.S. Surrey, BCYIJIE WANG Henan Experimental H.S. Zhengzhou, ChinaYIQIAO WANG Beijing Concord College of Sino-Canada Beijing, ChinaYUNQING WANG University of Toronto Schools Toronto, ONZOE WANG Harry Ainlay H.S. Edmonton, ABERWIN WIBOWO Surya Institute Tangerang, IndonesiaJAY YOUNG WOO London Central S.S. London, ONGONGHAO WU York Mills C.I. North York, ONMICHAEL WU St. John’s-Ravenscourt School Winnipeg, MBNEIL WU Marc Garneau C.I. North York, ONQINGXIAO XIA St. George’s School Vancouver, BCCINDY XIONG Burnaby Central S.S. Burnaby, BCDAVID XUE Earl Haig S.S. North York, ONBILLY YAO Grand Canadian Academy Nanjing, ChinaALLEN YIEH Seaquam S.S. Delta, BCLI YIN William Lyon Mackenzie C.I. North York, ONJASON YOO Upper Canada College Toronto, ONHYUH SEUNG YOU West Vancouver S.S. West Vancouver, BCELISHA YU Moscrop S.S. Burnaby, BCHAOZHI ZHANG Shenzhen College of Int’l Education Shenzhen, ChinaJUNCHEN ZHANG Pierre Elliott Trudeau H.S. Markham, ONKEXIN ZHANG Prince of Wales S.S. Vancouver, BCMINHAO ZHANG Henan Experimental H.S. Zhengzhou, ChinaSTEVEN ZHANG West Vancouver S.S. West Vancouver, BCJONATHAN ZHAO North Toronto C.I. Toronto, ONEREAL ZHONG Grand Canadian Academy Nanjing, ChinaHENRONG ZHOU Shenzhen College of Int’l Education Shenzhen, ChinaJACKY ZHOU Lord Byng S.S. Vancouver, BCKEVIN ZHOU Woburn Scarborough, ONSHIJIE ZHOU Hillfield-Strathallan College Hamilton, ONYI CHEN ZHOU Thornhill S.S. Thornhill, ONJIALIN ZHU Unionville H.S. Markham, ONRUNXING ZHU Jarvis C.I. Toronto, ONYIFU ZHU Shenzhen College of Int’l Education Shenzhen, China

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Page 16: 2010 Results Fryer Contest Galois Contest Hypatia Contest 2010

Hypatia – Gold Standard Palmares individuel – Hypatie

The top 25% of the competitors in each of the three Contests were divided into three categories: Gold Standard, SilverStandard and Bronze Standard, in the ratio 1 : 2 : 3. The names of the those students achieving the Gold Standard (that is,scoring in roughly the top 4%) are listed alphabetically below for each Contest.

Les candidats qui se classent dans le premier quart de classement dans chacun des trois concours ont ete repartis en troiscategories: le niveau or, le niveau argent et le niveau bronze, selon le ratio 1 : 2 : 3. Le nom des etudiants qui ont obtenu leniveau or (c’est-a-dire ceux qui se classent parmi les premiers 4 p. 100) est donne par ordre alphatbetique ci-dessous pourchaque concours.

Name/Nom School/Ecole Location/EndroitSCOTT ADAMS Walter Murray C.I. Saskatoon, SKBARDIA BEIGI West Vancouver S.S. West Vancouver, BCANDREA BOOTSMA St. Mary’s H.S. Kitchener, ONVITALIK BUTERIN The Abelard School Toronto, ONWENDY CAI Richmond Green S.S. Richmond Hill, ONXUESI CAI E.S. St. Luc Montreal, QCHARRIS CHAN St. Robert C.H.S. Thornhill, ONBRIAN CHAU Prince of Wales S.S. Vancouver, BCYIDUO CHEN Wuxi Guanghua Private School Wuxi, ChinaZHOU BO CHEN St. George’s School Vancouver, BCJUN CHO Resurrection C.S.S. Kitchener, ONCHARLIE CHOI York Mills C.I. North York, ONWILLIAM CHOI Iroquois Ridge H.S. Oakville, ONWONJOHN CHOI St. Francis Xavier S.S. Mississauga, ONDANIEL CHONG A.B. Lucas S.S. London, ONNEIL CHUA GOY Math Trainers Guild of Philippines Zamboanga City, PhilippinesAMALIA CONG London Central S.S. London, ONSARAH JANE CUA Math Trainers Guild of Philippines Zamboanga City, PhilippinesDYLAN DAY J.L. Ilsley H.S. Halifax, NSFREDERICK DING Richmond Hill H.S. Richmond Hill, ONJACK DING Don Mills C.I. North York, ONJASMINE DING William Lyon Mackenzie C.I. North York, ONJUNLI DING Sentinel S.S. West Vancouver, BCLIQING DING Branksome Hall Toronto, ONALEX FAN A.Y. Jackson S.S. North York, ONJIMMY FANG St. Robert C.H.S. Thornhill, ONJIAYUE GAO Sir Winston Churchill S.S. Vancouver, BCJINGYI GAO Ridley College St Catharines, ONLANXIN GAO A.Y. Jackson S.S. North York, ONZHENYUAN GAO Wuxi Guanghua Private School Wuxi, ChinaMELODY GUAN University of Toronto Schools Toronto, ONLINCOLN GUO University of Toronto Schools Toronto, ONSHUYANG GUO Pinetree S.S. Coquitlam, BCSIYAN GUO Beijing Concord College of Sino-Canada Beijing, ChinaJIMMY HE University of Toronto Schools Toronto, ONNICOLE HE New Westminster S.S. New Westminster, BCJIAYING HOU Beijing Concord College of Sino-Canada Beijing, ChinaALICE HU West Vancouver S.S. West Vancouver, BCFAN HUANG Bell H.S. Nepean, ONBOWEN JIANG Vincent Massey S.S. Windsor, ONHEINRICH JIANG Vincent Massey S.S. Windsor, ONMIN KANG The Anglo-American School of Moscow Moscow, Russian FederationCAI KEVIN Carver C.H.S. Burnaby, BCSUFYAN KHAN Earl Haig S.S. North York, ONGENESIS KIM Grand Canadian Academy Nanjing, ChinaPAUL KIM St. George’s School Vancouver, BCTIAN LAN Northern S.S. Toronto, ON

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Hypatia – Gold Standard Palmares individuel – Hypatie

Name/Nom School/Ecole Location/EndroitKEVIN LAU Richmond Hill H.S. Richmond Hill, ONLEILA LEE Riverside S.S. Port Coquitlam, BCSEUNGHWAN LEE Universal American School Dubai, UAEALAN LI Westdale S.S. Hamilton, ONSHIDA LI E.S. St. Luc Montreal, QCSIMON LI Bayview S.S. Richmond Hill, ONSIYA LI Concord College of Sino-Canada Shenzhen, ChinaTONG LI Guangdong Country Garden School Foshan City, ChinaZHUO LI Shenzhen College of Int’l Education Shenzhen, ChinaELIZABETH LIAO Westdale S.S. Hamilton, ONZIJING LIN Bronte College Of Canada Mississauga, ONDAVID SIQI LIU Vincent Massey S.S. Windsor, ONRICHARD LIU University of Toronto Schools Toronto, ONSHUOLI LIU Glebe C.I. Ottawa, ONVICTOR LIU Dr. Norman Bethune C.I. Scarborough, ONVIVIAN LIU Dover Bay S.S. Nanaimo, BCYUHAO LIU Shenzhen College of Int’l Education Shenzhen, ChinaJANENE LOKEY Chinese Int’l School Braemar Hill, Hong KongMANNING LU Glebe C.I. Ottawa, ONKEN LUO Shenzhen College of Int’l Education Shenzhen, ChinaMIAN MA West Vancouver S.S. West Vancouver, BCZHIHAO MAI Vincent Massey S.S. Windsor, ONCHENYI MAO Don Mills C.I. North York, ONPOURYA MASOUDIAN Earl Haig S.S. North York, ONGENYI MENG Shenzhen College of Int’l Education Shenzhen, ChinaLINGYAO MENG Henan Experimental H.S. Zhengzhou, ChinaKARTHIK NATARAJAN Sir Winston Churchill C.V.I. Thunder Bay, ONJUNHO OH Meadowridge School Maple Ridge, BCMICHAEL OLIVER O’Neill C.V.I. Oshawa, ONEDDIE PARK Western Canada H.S. Calgary, ABVICTOR POPE University of Toronto Schools Toronto, ONGINNY QIU Agincourt C.I. Scarborough, ONHAOLIAN QUAN Nancy Campbell C.I London, ONRITVIK RAMKUMAR Glenforest S.S. Mississauga, ONMENGYE REN Lord Byng S.S. Vancouver, BCJAMES RICKARDS Colonel By S.S. Gloucester, ONDA YUN RONG Boren Sino-Canadian School Jiangmen, ChinaCHARLIE SHEN Pinetree S.S. Coquitlam, BCSUNNY SHEN Steveston London S.S. Richmond, BCCHARLIE SHI Grand Canadian Academy Nanjing, ChinaJAHYUN SHIN Loretto Abbey C.S.S. North York, ONALEX SONG Windsor, ONSURAJ SRINIVASAN Fort Richmond C.I. Winnipeg, MBCHANG SU Western Canada H.S. Calgary, ABLINAN SU Shenzhen College of Int’l Education Shenzhen, ChinaMIRINAE SUN Ernest Manning H.S. Calgary, ABSUSAN SUN West Vancouver S.S. West Vancouver, BCZIJUN TAN Richmond Green S.S. Richmond Hill, ONDA TANG Vaughan S.S. Thornhill, ONSKY TANG Georges Vanier S.S. North York, ONNUTTAWUT TARAPHAN Lord Byng S.S. Vancouver, BCMING KAN TO Town Centre Montessori Private School Markham, ONSHELDON TUNG University of Toronto Schools Toronto, ONJACOB JOHN VARUN St. Robert C.H.S. Thornhill, ONJASON WANG Dover Bay S.S. Nanaimo, BCWEIKE WANG E.S. St. Luc Montreal, QC

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Hypatia – Gold Standard Palmares individuel – Hypatie

Name/Nom School/Ecole Location/EndroitXIAO FAN WANG Dr. Norman Bethune C.I. Scarborough, ONYAOU WANG St. Michael’s University School Victoria, BCZEYI WANG Concord College of Sino-Canada Shenzhen, ChinaMUAN WEI Beijing Concord College of Sino-Canada Beijing, ChinaYANG WEN Sir John A. Macdonald C.I. Scarborough, ONKRISJANIS WHITTAKER LEE University of Toronto Schools Toronto, ONSHERWIN WONG University of Toronto Schools Toronto, ONADRIAN WU University of Toronto Schools Toronto, ONLIYU WU Henan Experimental H.S. Zhengzhou, ChinaZHENG RONG WU Math Trainers Guild of Philippines Zamboanga City, PhilippinesDI XIAO Lisgar C.I. Ottawa, ONRUI PHILIP XIAO Sir Winston Churchill S.S. Vancouver, BCSELINA XIE Moscrop S.S. Burnaby, BCZUOQI XIE Nancy Campbell C.I London, ONJEFF XIONG Moscrop S.S. Burnaby, BCFAN XU Lord Byng S.S. Vancouver, BCFANG XU Sentinel S.S. West Vancouver, BCZEPENG XU Beijing Concord College of Sino-Canada Beijing, ChinaYIXUAN YAN Prince of Wales S.S. Vancouver, BCFRANKLIN YANG Don Mills C.I. North York, ONLUCY YANG Sir William Mulock S.S. Newmarket, ONYUNG LIN YANG Northern S.S. Toronto, ONFAN YIN Vincent Massey S.S. Windsor, ONKEVIN YU Sentinel S.S. West Vancouver, BCOULIN YU E.S. St. Luc Montreal, QCSTEVEN YU Pinetree S.S. Coquitlam, BCCHENG ZENG The Woodlands School Mississauga, ONRAYMOND ZENG Heritage Woods Secondary Port Moody, BCERIC ZHAN University of Toronto Schools Toronto, ONHANGTIAN ZHAN Concord College of Sino-Canada Shenzhen, ChinaCHENYU ZHANG Beijing Concord College of Sino-Canada Beijing, ChinaJACK ZHANG St. Andrew’s College Aurora, ONLILY ZHANG Cameron Heights C.I. Kitchener, ONQINGYUAN ZHANG Shenzhen College of Int’l Education Shenzhen, ChinaTAYLOR ZHANG David Thompson S.S. Vancouver, BCTOM ZHANG York Mills C.I. North York, ONXIANGYU ZHANG Shenzhen College of Int’l Education Shenzhen, ChinaMENG ZHAO Western Canada H.S. Calgary, ABZHIHENG ZHENG Beijing Concord College of Sino-Canada Beijing, ChinaALLEN ZHOU Moscrop S.S. Burnaby, BCCONGYUN ZHOU Sentinel S.S. West Vancouver, BCXUEHAN ZHOU Shenzhen College of Int’l Education Shenzhen, ChinaYIFANG ZHU Appleby College Oakville, ONZHENBO ZHU Sentinel S.S. West Vancouver, BCJESSICA ZOU Centennial C.V.I. Guelph, ON

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