The CENTRE for EDUCATION in MATHEMATICS …

1 The CENTRE for EDUCATIONin MATHEMATICS and COMPUTINGLe CENTRE d EDUCATIONen MATH EMATIQUES et en Contest(Grade 9)Cayley Contest(Grade 10)Fermat Contest(Grade 11)2015R esultatsConcours Pascal(9eann ee Sec. III)Concours Cayley(10eann ee Sec. IV)Concours Fermat(11eann ee Sec. V)c 2015 CENTRE for EDUCATION in MATHEMATICS and ComputingCompetition OrganizationOrganisation du ConcoursCentre for EDUCATION in MATHEMATICS and computing Faculty and Staff /Personnel du Concours canadien de math ematiquesEd AndersonJeff AndersonTerry BaeSteve BrownErsal CahitHeather CulhamSerge D AlessioFrank DeMaioJanine DietrichJennifer DoucetFiona DunbarMike EdenBarry FergusonJudy FoxSteve FurinoJohn GalbraithSandy GrahamConrad HewittAngie HildebrandCarrie KnollJudith KoellerBev MarshmanMike MiniouDean MurrayJen PrettiKim SchnarrCarolyn SedoreIan VanderBurghTroy VasigaJoAnn VincentTim Zhou2 Competition OrganizationOrganisation du ConcoursProblems Committees / Comit es des probl`emesPascal Contest / Concours PascalWally Webster (Chair / pr esident), Dashwood, ONLloyd Auckland, St.

2 Thomas, ONJanet Christ, Walter Murray , Saskatoon, SKMike Miniou, University of Waterloo, Waterloo, Pretti, University of Waterloo, Waterloo, ONJim Schurter, Listowel, ONTyler Somer, Kitchener, ONAnna Spanik, Halifax West , Halifax, NSAaron Warner, St. Mildred s-Lightbourn School, Oakville, ONCayley Contest / Concours CayleyJen Nelson (Chair / pr esidente), University of Waterloo, Waterloo, ONKirsten Boucher, Ajax, ONBarry Ferguson, University of Waterloo, Waterloo, ONJordan Grant, St. John s-Kilmarnock School, Breslau, ONChristopher Ing, Vincent Massey , Windsor, ONChristine Ruza, Elmira , Elmira, ONMichelle Vidberg, Galt , Cambridge, ONFermat Contest / Concours FermatPaul Fennell (Chair / pr esident), London, ONSandra DellaMaestra, University of Toronto Schools, Toronto, ONConrad Hewitt, University of Waterloo, Waterloo, ONSteve Lau, John Diefenbaker , Hanover, ONCarol Miron, Albert Campbell , Toronto, ONMichael Regep, Mentor College, Mississauga, ONDavid Shepherd, Ravenna, ONMartin Tuchtie, Fenelon Falls , Fenelon Falls, ON3 ForewordAvant-ProposOur congratulations go to all who participated in this year s Pascal, Cayley and Fermat Contests.

3 This year sContests were resounding successes, with averages of , and across the three Contests. The numberof eligible contestants with perfect papers on the three Contests were 30, 6 and always, we would like to thank the hard-working Problems Committees. Most of the members of these Com-mittees are active secondary school teachers from across Canada who volunteers their time and contribute dozensof hours of expertise. Without their intriguing and sometimes amusing problems, these Contests would not 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 support! Please con-tinue to encourage your colleagues and fellow students to become involved in our f elicitations vont `a tous les participants du Concours Pascal, Cayley et Fermat de cette ann ee.

4 Les Con-cours de cette ann ee retentissaient de succ`es, avec des moyennes de 100,8, 92,4 et 96,3 `a travers les trois nombre de candidats eligibles poss edant un concours parfait etait de 30, 6 et aimerions surtout remercier les Comit es de probl`emes pour leur dur travail. La plupart des membres de cesComit es sont des enseignant(e)s d ecole secondaire actifs d un bout `a l autre du Canada qui offre leur temps etcontribuent des douzaines d heures d expertise. Sans leurs probl`emes perspicaces et amusants, ces Concours neseraient pas aimerions remercier aussi tous les participants incluant les enseignants et les etudiants. Nous esp eronsque les concours vous ont offert des math ematiques int eressantes qui vous ont amus ees et port ees `a r efl pour votre soutien continu e!

5 4 EnrollmentInscriptionNumber of schools registered by province /Nombre d ecoles inscrit par provincePascal Cayley FermatAB1126052BC198194191MB565246NB3334 32NL504036NS423831NT222ON746699697PE976Q C959797SK313232YT111 International166173163 Total154114291386 Number of students registered by province /Nombre d etudiants inscrit par provincePascal Cayley FermatAB29241046902BC483839713162MB13038 64842NB593554368NL756542459NS910699491NT 141414ON13101105659067PE18810064QC231821 961948SK692450401YT243 International402735822917 Total316662458720638 Total number of students enrolled / Nombre d inscriptions individuelles:768915 Champions 2015 Champions 20152015 STUDENT CHAMPIONS AND CHAMPIONSHIP TEAMSPALMAR`ES INDIVIDUEL ET PALMAR`ES PAR EQUIPE 2015 PASCAL CONTEST / CONCOURS PASCALSTUDENTS / EL`EVESS tudents are listed in alphabetical order / Les el`eves sont nomm es en ordre alphabetiqueSchoolLocationGrade EcoleEndroitNiveauCOCO CHENP inetree CHENN orth York8 ZHIYANG CHENS carborough8 STEVEN CHOWA lbert Campbell DUWilliam Lyon Mackenzie York9 HOWARD HALIMU niversity of Toronto SchoolsToronto8 JIASHU HANSir Winston Churchill Myer Falls9 ALEXANDER KITAEVW aterloo MUHAMMAD MITHANIG ordon Graydon Memorial Mississauga9 VAISHNAVAN SOMASEKARAM King s-Edgehill SchoolWindsor9 NICHOLAS SULLIVANA shbury CollegeRockcliffe9 KYLE TREBINSKIEW hite Pines C.

6 And Ste Marie9 QINGYU WANGE cole Int l de MontrealWestmount9 MARK WILKINSC entennial Reg l Park9 JIANG WUNew Westminster Westminster 9 LUCY YANF raser Heights YANGB urnaby South YANGW hite Oaks ZHANGS carborough9 RUICHEN ZHANGL isgar / EQUIPESS choolLocationScore EcoleEndroitNoteChampion / Premi`ere University of Toronto Schools Toronto438 Second / Deuxi`emeSir Winston Churchill / Troisi`emeLisgar 434 Fifth / Cinqui`emeWhite Oaks 2015 Champions 20152015 STUDENT CHAMPIONS AND CHAMPIONSHIP TEAMSPALMAR`ES INDIVIDUEL ET PALMAR`ES PAR EQUIPE 2015 CAYLEY CONTEST / CONCOURS CAYLEYSTUDENTS / EL`EVESS tudents are listed in alphabetical order / Les el`eves sont nomm es en ordre alphabetiqueSchoolLocationGrade EcoleEndroitNiveauBRYAN DINGU pper Can CollegeToronto10 EDWARD JIANGM oscrop KWANSir Winston Churchill Calgary10 JASON LIPinetree PANG Marc Garneau York 10 TEAMS / EQUIPESS choolLocationScore EcoleEndroitNoteChampion / Premi`ere Pinetree / Deuxi`emeSir Winston Churchill Calgary430 Third / Troisi`emeMarc Garneau York427 Fourth / Quatri`emeNew Westminster Westminster 424 Fifth / Cinqui`emeMoscrop 2015 Champions 20152015 STUDENT CHAMPIONS AND CHAMPIONSHIP TEAMSPALMAR`ES INDIVIDUEL ET PALMAR`ES PAR EQUIPE 2015 FERMAT CONTEST / CONCOURS FERMATSTUDENTS / EL`EVESS tudents are listed in alphabetical order / Les el`eves sont nomm es en ordre alphabetiqueGold MedalsSchoolLocationGradeM edailles d or EcoleEndroitNiveauRUIZHE CHENG Prince of Wales OFieldstone King s College Schol Toronto11 KYNE SANTOSSt.

7 Mary s Lucas XUUniversity Hill ZHANGNew Westminster Westminster 11 RUIZHI ZHAOT ommy Douglas CollegiateSaskatoon11 TEAMS / EQUIPESS choolLocationScore EcoleEndroitNoteChampion / Premi`ere Jackson York412 Bur Oak / Troisi` Lucas Hill 410 University Transition Program Vancouver4208 Champions 2015 Champions 20152015 FERMAT CONTEST REGIONAL CHAMPIONSCHAMPIONS R EGIONAUX AU CONCOURS FERMAT 2015 Each student below will receive a$200 prize / Chaque etudiant ci-dessous recevrait un prix de 200$ProvinceStudentSchoolLocationProvinc e Etudiant EcoleEndroitABALEXANDRE BOUFERGUENEOld Scona Academic KANGC entennial XIONGW estern Canada XUUniversity Hill HO MANGK elvin MANSOURISt. John s-Ravenscourt SchoolWinnipegNBLANFENG SUNR othesay Netherwood SchoolRothesayNLDANIEL HEALEYG ander CollegiateGanderNTABIGALE COADE cole Sir John Franklin BOWENDr.

8 John Hugh Gillis SchoolAntigonishNSPAUL DIAMONDC obequid Educational CentreTruroNSBAILEY FERGUSONC obequid Educational CentreTruroNSRYAN HEBBPark View EDUCATION CentreBridgewaterNSVICTOR LAMOUREUXH alifax West ROBINSONC obequid Educational CentreTruroNSJIANRONG YUKing s-Edgehill SchoolWindsorON Central FAITH GUOBur Oak Central JIACHENG ZHANGBur Oak Central TIANWEI ZHANGB ayview HillON EstKEVIN LIUBell NordLORNA LANP retty River AcademyCollingwoodON MetroSEEUN OFieldstone King s College School TorontoON OuestKYNE SANTOSSt. Mary s OuestKAI Lucas MACDONALDE cole Francois BuoteCharlottetownQCANTHONY ANASTASOPOULOS West Island CollegeDollard-Des-OrmeauxSKRUIZHI ZHAOT ommy Douglas CollegiateSaskatoonYTASHLEY Collins SchoolWhitehorse9 Correct AnswersBonnes Rponses#PascalCayleyFermat1 DAE2 ADA3 CCD4 CDB5 BBB6 ABE7 ECD8 EDB9 ACB10 CAA11 BEE12 DED13 EBC14 EDB15 CBA16 ACC17 ABD18 CAE19 BAE20 AEC21 DDA22 EDA23 BEE24 BAC25 DBE10 Pascal ContestConcours PascalNumber of Contestants / Nombre de concurrents:25273 Average mark / Note of contestants selecting each option / Pourcentage de concurrents par choix:Correct% not% correctAnswer/attempted/of attemptedBonne% sans% tentativesR eponser eponser eussies# ContestConcours CayleyNumber of Contestants / Nombre de concurrents.

9 19071 Average mark / Note of contestants selecting each option / Pourcentage de concurrents par choix:Correct% not% correctAnswer/attempted/of attemptedBonne% sans% tentativesR eponser eponser eussies# ContestConcours FermatNumber of Contestants / Nombre de concurrents:15796 Average mark / Note of contestants selecting each option / Pourcentage de concurrents par choix:Correct% not% correctAnswer/attempted/of attemptedBonne% sans% tentativesR eponser eponser eussies# RankingsClassements des el`evesScore/PascalCayleyFermatNoteRank/ Rank/Rank/Position Position Position15011114914814714614531714434921 4314299374141140282551392845613829358151 3740010736136418110381356191631346231646 7133975206116132100321311913112312891921 3012872981961291624406242128170341624312 7223750530512622965273071252838669543124 2951697549123340285967912235798886891214 1771065826120437311218621195108135912381 1852831412125411758141689158211660801763 1599115667720271897114705721221958113780 3247024111128064256424771118695296430151 1090693085308810996803478358110810169364 9369310710747412643091061115243214444105 1175647955080104121875003522310312719546 2577810213193573359671011370062026502100 1415664866741

10 Score/PascalCayleyFermatNoteRank/Rank/Ra nk/Position Position Position99146737022731198150887337754797 1556478028089961603181668338951642885968 7729416878897291099317276945295519217639 9830984691180211024910236901837410624104 8789187141097110824881910911417111428719 4471185411423861975312203116868520070125 4211999842036112868122148320691132301245 5822098413648126928121201139531290980214 4514258131277921683145211331078219201478 1135037722164150881367676223631537513833 7522563156111397974227511583814107732293 9160621424072231171627214377712328016510 1450770234341670214619692357816863147086 8237161700314804672384317152148826623980 1731414980652410117460150526424195176021 5097632430817700151586224411178221521861 2449917932152636024605180501531259246771 8152153505824762182331538457248371831715 4185624899183801545055249651845015485542 5017185171552253250671854815545522512818 5961557151251901864415596502523718678156 164925272187221563114 Student RankingsClassements des el`evesScore/PascalCayleyFermatNoteRank/ Rank/Rank/Position Position These rankings pertain to eligible contestantsonly Ces rangs se rapportent seulement aux concur-rents admissibles15 Team ScoresNotes des equipesScores/PascalCayleyFermatNotes# of Schools/ # of Schools/ # of Schools/Nod ecolesNod ecolesNod ecoles440 - 450100430 - 439820420 - 4293441410 - 41950108400 - 409742114390 - 399932313380 - 3891205331370 - 3791084560360 - 3691037167350 - 3591057088340 - 3498710597330 - 339598398320 - 3296393110310 - 3193790104300 - 309257873 Number of three student teams / Nombre d equipes de trois el`evesPascal Contest / Concours Pascal: 1040 Cayley Contest / Concours Cayley: 950 Fermat Contest / Concours Fermat: 91716 The CENTRE for EDUCATIONin MATHEMATICS and COMPUTINGLe CENTRE d EDUCATIONen MATH EMATIQUES et en Contest(Grade 9)Cayley Contest(Grade 10)Fermat Contest(Grade 11)2015R esultatsConcours Pascal(9eann ee Sec.)