2024年3月13日发(作者：广州教师招聘数学试卷)

TheCENTREforEDUCATION

inMATHEMATICSandCOMPUTING

FryerContest

(Grade9)

Thursday,April12,2012

(inNorthAmericaandSouthAmerica)

Friday,April13,2012

(outsideofNorthAmericaandSouthAmerica)

©2012UniversityofWaterloo

Donotopenthisbookletuntilinstructedtodoso.

Time:75minutesNumberofquestions:4

CalculatorsarepermittedEachquestionisworth10marks

Partsofeachquestioncanbeoftwotypes:

NSWERpartsindicatedby

•worth2or3markseach

•fullmarksgivenforacorrectanswerwhichisplacedinthebox

•partmarksawardedonlyifrelevantworkisshowninthespaceprovided

LUTIONpartsindicatedby

•worththeremainderofthe10marksforthequestion

•mustbewrittenintheappropriatelocationintheanswerbooklet

•marksawardedforcompleteness,clarity,andstyleofpresentation

•acorrectsolutionpoorlypresentedwillnotearnfullmarks

WRITEALLANSWERSINTHEANSWERBOOKLETPROVIDED.

•Extrapaperforyourfinishedsolutionssuppliedbyyoursupervisingteachermustbe

ourname,schoolname,andquestionnumber

onanyinsertedpages.

•Expresscalculationsandanswersasexactnumberssuchasπ+1and

√

2,etc.,rather

,exceptwhereotherwiseindicated.

Donotdiscusstheproblemsorsolutionsfromthiscontestonlineforthenext48hours.

Thename,grade,schoolandlocationofsometop-scoringstudentswillbepublishedinthe

FGHResultsonourWebsite,.

TIPS:readtheinstructionsonthefrontcoverofthisbooklet.

llanswersintheanswerbookletprovided.

stionsmarked,placeyouranswerintheappropriateboxinthe

answerbookletandshowyourwork.

stionsmarked,provideawell-organizedsolutionintheanswer

hematicalstatementsandwordstoexplainallofthesteps

tsomedetailsinroughonaseparatepieceofpaper

beforewritingyourfinishedsolution.

eintendedasaidsonly.

1.(a)InCarrotford,candidateAranformayorandreceived1008votesoutofatotal

rcentageofallvotesdidcandidateAreceive?

(b)InBeetland,exactlythreecandidates,B,CandD,ateB

wontheelectionbyreceiving

3

5

ofallvotes,whilecandidatesCandDtiedwith

thesamenumberofpercentageofallvotesdidcandidateCreceive?

(c)InCabbagetown,exactlytwocandidates,EandF,ranformayorand6000

,only90%ofthesevoteshadbeencounted.

CandidateEreceived53%ymorevoteshadbeencounted

?

(d)InPeaville,exactlythreecandidates,G,HandJ,lofthe

voteswerecounted,Ghadreceived2000votes,Hhadreceived40%ofthevotes,

andJhadreceived35%yvotesdidcandidateHreceive?

mefactorizationof144is2×2×2×2×3×3or2

4

×3

2

.Therefore,144isa

perfectsquarebecauseitcanbewrittenintheform(2

2

×3)×(2

2

×3).

Theprimefactorizationof45is3

2

×ore,45isnotaperfectsquare,but45×5

isaperfectsquare,because45×5=3

2

×5

2

=(3×5)×(3×5).

(a)Determinetheprimefactorizationof112.

(b)Theproduct112×positiveinteger,whatisthe

smallestpossiblevalueofu?

(c)Theproduct5632×positiveinteger,whatisthe

smallestpossiblevalueofv?

(d)Aperfectcubeisanintegerthatcanbewrittenintheformn

3

,wherenisan

mple,8isaperfectcubesince8=2

3

.Theproduct112×wisa

positiveinteger,whatisthesmallestpossiblevalueofw?


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