Gauss滑铁卢高斯初中数学竞赛(Grade 8).docx

Gauss滑铁卢高斯初中数学竞赛(Grade8)Scoring:Thereisnopenaltyforanincorrectanswer.Eachunansweredquestionisworth2,toamaximumof10unansweredquestions.PartA:Eachcorrectanswerisworth5.1.Thecostof1melonis$3.Whatisthecostof6melons?(A)$12(B)$15(C)$18(D)$21(E)$242.Inthediagram,thenumberlineisdividedinto10equalparts.Thenumbers0,1andParemarkedontheline.WhatisthevalueofP?(A)0.2(B)0.6(C)0.7(D)0.8(E)0.93.Thevalueof(2+3)2?(22+32)is(A)50(B)12(C)15(D)?15(E)?12:/doczj/doc/b53132966e1aff00bed5b9f3f90f76c661374c21.htmlkshmiistravellingat50km/h.Howmanykilometresdoesshetravelin30minutes?(A)30km(B)50km(C)25km(D)150km(E)100km5.Evgenyhas3roses,2tulips,4daisies,and6lilies.Ifherandomlychoosesoneofthese?owers,whatistheprobabilitythatitisatulip?(A)315(B)1215(C)615(D)415(E)2156.Theheightsof?vestudentsatGleesonMiddleSchoolareshowninthegraph.Therangeoftheheightsisclosestto(A)75cm(B)0cm(C)25cm(D)100cm(E)50cmKinleyEmmaCamNyahSanjayStudents7.Thecirclehasadiameterof1cm,asshown.Thecircumferenceofthecircleisbetween(A)2cmand3cm(B)3cmand4cm(C)4cmand5cm(D)5cmand6cm(E)6cmand8cm1cm8.RichandBenateanentirechocolatecake.TheratiooftheamounteatenbyRichtotheamounteatenbyBenis3:1.WhatpercentageofthecakedidBeneat?(A)66%(B)50%(C)75%(D)25%(E)10%9.The26lettersofthealphabetarewritteninorder,clockwisearoundacircle.Theciphertextofamessageiscreatedbyreplacingeachletterofthemessagebytheletterthatis4lettersclockwisefromtheoriginalletter.(ThisiscalledaCaesarcipher.)Forexample,themessageZAPhasciphertextDET.WhatistheciphertextofthemessageWIN?(A)ALN(B)ZLN(C)AMR(D)AMQ(E)ZMQ10.Thesumof3consecutiveevennumbersis312.Whatisthelargestofthese3numbers?(A)54(B)106(C)86(D)108(E)102PartB:Eachcorrectanswerisworth6.11.If4x+12=48,thevalueofxis(A)12(B)32(C)15(D)6(E)912.Thereisa3hourtimedi?erencebetweenVancouverandToronto.Forexample,whenitis1:00p.m.inVancouver,itis4:00p.m.inToronto.WhattimeisitinVancouverwhenitis6:30p.m.inToronto?(A)9:30p.m(B)2:30p.m.(C)3:30p.m.(D)8:30p.m.(E)4:30p.m.13.MateoandSydneywinacontest.Ashisprize,Mateoreceives$20everyhourforoneweek.Asherprize,Sydneyreceives$400everydayforoneweek.Whatisthedi?erenceinthetotalamountsofmoneythattheyreceiveovertheoneweekperiod?(A)$560(B)$80(C)$1120(D)$380(E)$78414.Thenumber2018hasexactlytwodivisorsthatareprimenumbers.Thesumofthesetwoprimenumbersis(A)793(B)1011(C)38(D)209(E)50715.Fiveclassmates,Barry,Hwan,Daya,Cindy,andEdwillcompeteinacontest.Therearenotiesallowed.Inhowmanywayscan?rst,secondandthirdplaceawardsbegivenout?(A)6(B)60(C)125(D)3(E)2716.Thereareseveralgroupsofsixintegerswhoseproductis1.Whichofthefollowingcannotbethesumofsuchagroupofsixintegers?(A)?6(B)?2(C)0(D)2(E)617.AtranslationmovespointA(?3,2)totheright5unitsandup3units.Thistranslationisdoneatotalof6times.Afterthesetranslations,thepointisat(x,y).Whatisthevalueofx+y?(A)34(B)49(C)53(D)47(E)4318.Thevolumeofarectangularprismis30cm3.Thelengthoftheprismisdoubled,thewidthistripled,andtheheightisdividedbyfour.Thevolumeofthenewprismis(A)31cm3(B)120cm3(C)60cm3(D)90cm3(E)45cm319.Themean(average)heightofagroupofchildrenwouldbeincreasedby6cmif12ofthechildreninthegroupwereeach8cmtaller.Howmanychildrenareinthegroup?(A)16(B)14(C)21(D)26(E)920.LinesegmentsPQandRSareparallel.PointsT,U,VareplacedsothatQTV=30?,SUV=40?,andTVU=x?,asshown.Whatisthevalueofx?(A)80(B)85(C)65(D)70(E)75PQRS30?40?x?TUVPartC:Eachcorrectanswerisworth8.21.Abagcontainsmarblesof?vedi?erentcolours.Onemarbleischosenatrandom.Theprobabilityofchoosingabrownmarbleis0.3.Choosingabrownmarbleisthreetimesaslikelyaschoosingapurplemarble.Choosingagreenmarbleisequallylikelyaschoosingapurplemarble.Choosingaredmarbleisequallylikelyaschoosingayellowmarble.Theprobabilityofchoosingamarblethatiseitherredorgreenis(A)0.2(B)0.25(C)0.35(D)0.4(E)0.5522.SquarePQRShassidelength30,asshown.Thesquareisdividedinto5regionsofequalarea:SPT,STU,SVW,SWR,andquadrilateralSUQV.ThevalueofSUSTisclosestto(A)1.17(B)1.19(C)1.21(D)1.23(E)1.25PQRSTUVW303023.Thesmallestpositiveintegernforwhichn(n+1)(n+2)isamultipleof5isn=3.Allpositiveintegers,n,forwhichn(n+1)(n+2)isamultipleof5arelistedinincreasingorder.Whatisthe2018thintegerinthelist?(A)3362(B)3360(C)3363(D)3361(E)336424.Lynnechoosesfourdistinctdigitsfrom1to9andarrangesthemtoformthe24possiblefour-digitnumbers.These24numbersareaddedtogethergivingtheresultN.Forallpossiblechoicesofthefourdistinctdigits,whatisthelargestsumofthedistinctprimefactorsofN?(A)157(B)148(C)127(D)146(E)12425.Inthe2×12gridshown,AshleydrawspathsfromAtoFalongthegridlines.Ineverypath,?therearetwoormorearrowsarrangedheadtotail,?thetailofthe?rstarrowstartsatAandtheheadofthelastarrowendsatF,?twoconsecutivearrowsmustbeperpendiculartooneanother,?notwoarrowscanintersectatmorethanonepoint,and?allarrowshavedi?erentlengths.ThepathfromAtoFshownconsistsofarrowsofthreedi?erentlengths:left2,up1,right11.Howmanydi?erentpathsaretherefromAtoF?(A)54(B)55(C)56(D)57(E)58