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1、TheCENTREfEDUCATIONinMATHEMATICSCOMPUTINGcemc.uwaterloo.caEuclidContestThursdayApril62017(inNthAmericaSouthAmerica)FridayApril72017(outsideofNthAmericaSouthAmerica)Time:212hoursc?2017UniversityofWaterlooDonotopenthisbook
2、letuntilinstructedtodoso.Numberofquestions:10Eachquestioniswth10marksCalculatsareallowedwiththefollowingrestriction:youmaynotuseadevicethathasinteraccessthatcancommunicatewithotherdevicesthatcontainspreviouslystedinfmati
3、on.Fexampleyoumaynotuseasmartphoneatablet.Partsofeachquestioncanbeoftwotypes:1.SHTANSWERpartsindicatedby?wth3markseach?fullmarksgivenfacrectanswerwhichisplacedinthebox?partmarksawardedonlyifrelevantwkisshowninthespacepro
4、vided2.FULLSOLUTIONpartsindicatedby?wththeremainderofthe10marksfthequestion?mustbewrittenintheappropriatelocationintheanswerbooklet?marksawardedfcompletenessclaritystyleofpresentation?acrectsolutionpolypresentedwillnotea
5、rnfullmarksWRITEALLANSWERSINTHEANSWERBOOKLETPROVIDED.?Extrapaperfyourfinishedsolutionssuppliedbyyoursupervisingteachermustbeedintoyouranswerbooklet.Writeyournameschoolnamequestionnumberonanyedpages.?Expressanswersassimpl
6、ifiedexactnumbersexceptwhereotherwiseindicated.Fexampleπ11?√2aresimplifiedexactnumbers.Donotdiscusstheproblemssolutionsfromthiscontestonlinefthenext48hours.Thenamegradeschoollocationscerangeofsometopscingstudentswillbepu
7、blishedonourwebsitecemc.uwaterloo.ca.Inadditionthenamegradeschoollocationsceofsometopscingstudentsmaybesharedwithothermathematicalganizationsfotherrecognitionopptunities.3.(a)Inthediagram?ABCisrightangledatB?ACDisrightan
8、gledatA.AlsoAB=3BC=4CD=13.WhatistheareaofquadrilateralABCDBACD3413(b)ThreeidenticalrectanglesPQRSWTUVXWVYarearrangedasshownsothatRSliesalongTX.Theperimeterofeachofthethreerectanglesis21cm.Whatistheperimeterofthewholeshap
9、eQPYVUTXWSR(c)Oneofthefacesofarectangularprismhasarea27cm2.Anotherfacehasarea32cm2.Ifthevolumeoftheprismis144cm3determinethesurfaceareaoftheprismincm2.4.(a)Theequationsy=a(x?2)(x4)y=2(x?h)2krepresentthesameparabola.Whata
10、rethevaluesofahk(b)Inanarithmeticsequencewith5termsthesumofthesquaresofthefirst3termsequalsthesumofthesquaresofthelast2terms.Ifthefirsttermis5determineallpossiblevaluesofthefifthterm.(Anarithmeticsequenceisasequenceinwhi
11、cheachtermafterthefirstisobtainedfromtheprevioustermbyaddingaconstant.Fexample357911isanarithmeticsequencewithfiveterms.)5.(a)Danwasbninayearbetween13001400.Stevewasbninayearbetween14001500.EachwasbnonApril6inayearthatis
12、aperfectsquare.Eachlivedf110years.InwhatyearwhiletheywerebothaliveweretheiragesbothperfectsquaresonApril7(b)DetermineallvaluesofkfwhichthepointsA(12)B(112)C(k6)fmarightangledtriangle.6.(a)Thediagramshowstwohillsthatmeeta
13、tO.Onehillmakesa30?anglewiththehizontaltheotherhillmakesa45?anglewiththehizontal.PointsABareonthehillssothatOA=OB=20m.VerticalpolesBDACareconnectedbyastraightcableCD.IfAC=6mwhatisthelengthofBDfwhichCDisasshtaspossibleCDO
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