Gauss滑铁卢高斯初中数学竞赛(Grade 8)-数学Mathematics-2018-试题 exam

TheCENTREforEDUCATION

inMATHEMATICSandCOMPUTING

cemc.uwaterloo.ca

GaussContest

Grade8

(TheGrade7Contestisonthereverseside)

Wednesday,May16,2018

(inNorthAmericaandSouthAmerica)

Thursday,May17,2018

(outsideofNorthAmericaandSouthAmerica)

Time:1hour©2017UniversityofWaterloo

Calculatingdevicesareallowed,providedthattheydonothaveanyofthefollowingfeatures:(i)internetaccess,(ii)theabilitytocommunicatewithotherdevices,(iii)previouslystoredinformationsuchasformulas,programs,notes,etc.,(iv)acomputeralgebrasystem,(v)dynamicgeometrysoftware.

Instructions

1.Donotopenthecontestbookletuntilyouaretoldtodoso.

2.Youmayuserulers,compassesandpaperforroughwork.

3.Besurethatyouunderstandthecodingsystemforyouranswersheet.Ifyouarenotsure,askyourteachertoexplainit.

4.Thisisamultiple-choicetest.EachquestionisfollowedbyfivepossibleanswersmarkedA,B,C,D,andE.Onlyoneoftheseiscorrect.Whenyouhavemadeyourchoice,entertheappropriateletterforthatquestiononyouranswersheet.

5.Scoring:Eachcorrectanswerisworth5inPartA,6inPartB,and8inPartC.Thereisnopenaltyforanincorrectanswer.Eachunansweredquestionisworth2,toamaximumof10unansweredquestions.

6.Diagramsarenotdrawntoscale.Theyareintendedasaidsonly.

7.Whenyoursupervisorinstructsyoutostart,youwillhavesixtyminutesofworkingtime.

Thename,schoolandlocationofsometop-scoringstudentswillbepublishedontheWebsite,

cemc.uwaterloo.ca.YouwillalsobeabletofindcopiesofpastContestsandexcellentresources

forenrichment,problemsolvingandcontestpreparation.Grade8Scoring:Thereisnopenaltyforanincorrectanswer.

Eachunansweredquestionisworth2,toamaximumof10unansweredquestions.

PartA:Eachcorrectanswerisworth5.

1.Thecostof1melonis$3.Whatisthecostof6melons?

(A)$12(B)$15(C)$18(D)$21(E)$24

2.Inthediagram,thenumberlineisdividedinto10equal

parts.Thenumbers0,1andParemarkedontheline.

WhatisthevalueofP?

(A)0.2(B)0.6(C)0.7

(D)0

.8(E)0.901P

3.Thevalueof(2+3)2−(22+32)is

(A)50(B)12(C)15(D)−15(E)−12

4.Lakshmiistravellingat50km/h.Howmanykilometresdoesshetravelin30minutes?

(A)30km(B)50km(C)25km(D)150km(E)100km

5.Evgenyhas3roses,2tulips,4daisies,and6lilies.Ifherandomlychoosesoneof

theseflowers,whatistheprobabilitythatitisatulip?

(A)315(B)1215(C)615(D)415(E)215

6.TheheightsoffivestudentsatGleesonMiddleSchoolare

showninthegraph.Therangeoftheheightsisclosest

to

(A)75cm(B)0cm(C)25cm

(D)100cm(E)50

cmHeights of Students

KinleyEmmaCamNyahSanjay

Students7.Thecirclehasadiameterof1cm,asshown.The

circumferenceofthecircleisbetween

(A)2cmand3cm

(B)3

cmand4cm

(C)4cmand5cm

(D)5cmand6cm

(E)6cmand8cm1 cm

8.RichandBenateanentirechocolatecake.TheratiooftheamounteatenbyRichto

theamounteatenbyBenis3:1.WhatpercentageofthecakedidBeneat?

(A)66%(B)50%(C)75%(D)25%(E)10%

9.The26lettersofthealphabetarewritteninorder,clockwisearoundacircle.The

ciphertextofamessageiscreatedbyreplacingeachletterofthemessagebytheletter

thatis4lettersclockwisefromtheoriginalletter.(ThisiscalledaCaesarcipher.)

Forexample,themessageZAPhasciphertextDET.Whatistheciphertextofthe

messageWIN?

(A)ALN(B)ZLN(C)AMR(D)AMQ(E)ZMQGrade8

10.Thesumof3consecutiveevennumbersis312.Whatisthelargestofthese3numbers?

(A)54(B)106(C)86(D)108(E)102

PartB:Eachcorrectanswerisworth6.

11.If4x+12=48,thevalueofxis

(A)12(B)32(C)15(D)6(E)9

12.Thereisa3hourtimedifferencebetweenVancouverandToronto.Forexample,when

itis1:00p.m.inVancouver,itis4:00p.m.inToronto.WhattimeisitinVancouver

whenitis6:30p.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$20everyhourfor

oneweek.Asherprize,Sydneyreceives$400everydayforoneweek.Whatisthe

differenceinthetotalamountsofmoneythattheyreceiveovertheoneweekperiod?

(A)$560(B)$80(C)$1120(D)$380(E)$784

14.Thenumber2018hasexactlytwodivisorsthatareprimenumbers.Thesumofthese

twoprimenumbersis

(A)793(B)1011(C)38(D)209(E)507

15.Fiveclassmates,Barry,Hwan,Daya,Cindy,andEdwillcompeteinacontest.There

arenotiesallowed.Inhowmanywayscanfirst,secondandthirdplaceawardsbe

givenout?

(A)6(B)60(C)125(D)3(E)27

16.Thereareseveralgroupsofsixintegerswhoseproductis1.Whichofthefollowing

cannotbethesumofsuchagroupofsixintegers?

(A)−6(B)−2(C)0(D)2(E)6

17.AtranslationmovespointA(−3,2)totheright5units

andup3units.Thistranslationisdoneatotalof6times.

Afterthesetranslations,thepointisat(x,y).Whatis

thevalueofx+y?

(A)34(B)49(C)53

(D)47(E)43y

xA (– 3, 2)

18.Thevolumeofarectangularprismis30cm3.Thelengthoftheprismisdoubled,the

widthistripled,andtheheightisdividedbyfour.Thevolumeofthenewprismis

(A)31cm3(B)120cm3(C)60cm3(D)90cm3(E)45cm3

19.Themean(average)heightofagroupofchildrenwouldbeincreasedby6cmif12of

thechildreninthegroupwereeach8cmtaller.Howmanychildrenareinthegroup?

(A)16(B)14(C)21(D)26(E)9

20.LinesegmentsPQandRSareparallel.PointsT,U,V

areplacedsothat∠QTV=30◦,∠SUV=40◦,and

∠TVU=x◦,asshown.Whatisthevalueofx?

(A)80(B)85(C)65

(D)70(E)75PQ

RS30˚

40˚x˚T

UV