第一章第六章 AMC.docx
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第一章第六章 AMC.docx
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第一章第六章AMC
第一章AMC81985Problems
1.1985AJHSMEProblems/Problem1
A.1B.0C.49D.
E.50
2.1985AJHSMEProblems/Problem2
90+91+92+93+94+95+96+97+98+99=
A.845B.945C.1005D.1025E.1045
3.1985AJHSMEProblems/Problem3
A.0.002B.0.2C.20D.200E.1988
4.1985AJHSMEProblems/Problem4
TheareaofpolygonABCDEF,insquareunits,is
A.24B.30C.46D.66E.74
5.1985AJHSMEProblems/Problem5
Thebargraphshowsthegradesinamathematicclassforthelastgradingperiod.IfA,B,CandDaresatisfactorygrades,whatfractionofthegradesshowninthegrapharesatisfactory?
A.
B.
C.
D.
E.
6.1985AJHSMEProblems/Problem6
Areamofpapercontaining500sheetsis5cmthick.Approximatelyhowmanysheetsofthistypeofpaperwouldtherebe7.5cmhigh?
A.250B.550C.667D.750E.1250
7.1985AJHSMEProblems/Problem7
A“stair-step”figureismadeofalternatingblackandwhitesquaresineachrow.Rows1through4areshown.Allrowsbeginandendwithwhitesquare.Thenumberofblacksquaresinthe37throwis
A.34B.35C.36D.37E.38
8.1985AJHSMEProblems/Problem8
Ifa=-2,thelargestnumberintheset{-3a,4a,
a2,1}is
A.-3aB.4aC.
D.a2E.1
9.1985AJHSMEProblems/Problem9
Theproductofthe9factors(1-
)(1-
)(1-
)…(1-
)=
A.
B.
C.
D.
E.
10.1985AJHSMEProblems/Problem10
Thefractionhalfwaybetween
and
(onthenumberline)is
A.
B.
C.
D.
E.
11.1985AJHSMEProblems/Problem11
Apieceofpapercontainingsixjoinedsquareslabeledasshowninthediagramisfoldedalongtheedgesofthesquarestoformacube.ThelabelofthefaceoppositethefacelabeledXis
A.ZB.UC.VD.WE.Y
12.1985AJHSMEProblems/Problem12
Asquareandatrianglehaveequalperimeters.Thelengthsofthethreesidesofthetriangleare6.2cm,8.3cmand9.5cm.Theareaofthesquareis
A.24cm2B.36cm2C.48cm2D.64cm2E.144cm2
13.1985AJHSMEProblems/Problem13
Ifyouwalkfor45minutesatarateof4mphandtherunfor30minutesatarateof10mph,howmanymileswillyouhavegoneattheendofonehourand15minutes?
A.3.5milesB.8milesC.9milesD.25
milesE.480miles
14.1985AJHSMEProblems/Problem14
Thedifferencebetweena6.5%salestaxanda6%salestaxonanitempricedat$20beforetaxis
A.$0.01B.$0.10C.$0.50D.$1E.$10
15.1985AJHSMEProblems/Problem15
Howmanywholenumbersbetween100and400containthedegit2?
A.100B.120C.138D.140E.148
16.1985AJHSMEProblems/Problem16
TheratioofboystogirlsinMr.Brown’smathclassis2:
3.Ifthereare30studentsintheclass,howmanymoregirlsthanboysareintheclass?
A.1B.3C.5D.6E.10
17.1985AJHSMEProblems/Problem17
Ifyouraveragescoreonyourfirstsixmathematicstestswas84andyouraveragescoreonyourfirstsevenmathematicstestswas85,thenyourscoreontheseventhtestwas
A,86B.88C.90D.91E.92
18.1985AJHSMEProblems/Problem18
Ninecopiesofacertainpamphletcostlessthan$10.00whiletencopiesofthesamepamphlet(atthesameprice)costmorethan$11.00.Howmuchdoesonecopyofthispamphletcost?
A.$1.07B.$1.08C.$1.09D.$1.10E.$1.11
19.1985AJHSMEProblems/Problem19
Ifthelengthandwidthofarectangleareeachincreasedby10%,thentheperimeteroftherectangleisincreasedby
A.1%B.10%C.20%D.21%E.40%
20.1985AJHSMEProblems/Problem20
Incertainyear,JanuaryhadexactlyfourTuesdaysandfourSaturdays.OnwhatdaydidJanuary1fallthatyear?
A.MondayB.TuesdayC.WednesdayD.FridayE.Saturday
21.1985AJHSMEProblems/Problem21
Mr.Greenreceivesa10%raiseeveryyear.Hissalaryafterfoursuchraiseshasgoneupbywhatpercent?
A.lessthan40%B.40%C.44%D.45%E.morethan45%
22.1985AJHSMEProblems/Problem22
Assumeevery7-digitwholenumberisapossibletelephonenumberexceptthosethatbeginwith0or1.Whatfractionoftelephonenumbersbeginwith9andendwith0?
A.
B.
C.
D.
E.
23.1985AJHSMEProblems/Problem23
KingMiddleSchoolhas1200students.Eachsudenttakes5classesaday.Eachteacherteaches4classes.Eachclasshas30studentsand1teacher.HowmanyteachersarethereatKingMiddleSchool?
A.30B.32C.40D.45E.50
24.1985AJHSMEProblems/Problem24
Inamagictriangle,eachofthesixwholenumber10-15isplacedinoneofthecirclessothatthesum,S,ofthethreenumbersoneachsideofthetriangleisthesame.ThelargestpossiblevalueforSis
A.36B.37C.38D.39E.40
25.1985AJHSMEProblems/Problem25PQ
Fivecardsarelyingonatableasshown.346
Eachcardhasaletterontheonesideandawholenumberontheotherside.Janesaid,“Ifavowelisononesideofanycard,thenanevennumberisontheotherside.”MaryshowedJanewaswrongbyturningoveronecard.WhichcarddidMaryturnover?
A.3B.4C.6D.PE.Q
第二章AMC81986Problems
26.1986AJHSMEProblems/Problem1
InJuly1861,366inchesofrainfellinCherrapunji,India.Whatwastheaveragerainfallininchesperhourduringthatmonth?
A.
B.
C.
D.
E.
27.1986AJHSMEProblems/Problem2
Whichofthefollowingnumbershasthelargestreciprocal?
A.
B.
C.1D.5E.1986
28.1986AJHSMEProblems/Problem3
Thesmallestsumonecouldgetbyaddingthreedifferentnumbersfromtheset{7,25,-1,12,-3}is
A.-3B.-1C.3D.5E.21
29.1986AJHSMEProblems/Problem4
Theproduct(1.8)(40.3+0.07)isclosestto
A.7B.42C.74D.84E.737
30.1986AJHSMEProblems/Problem5
Acontestbeganatnoononedayandended1000minuteslater.Atwhattimedidthecontestend?
A.10:
00p.m.B.midnightC.2:
30p.m.D.4:
40p.m.E.6:
40a.m.
31.1986AJHSMEProblems/Problem6
=
A.-3B.-
C.
D.2E.6
32.1986AJHSMEProblems/Problem7
Howmanywholenumbersarebetween
and
A.5B.6C.7D.
E.
33.1986AJHSMEProblems/Problem8
Intheproductshown,Bisadigit.ThevalueofBis
A.3B.5C.6D.7E.8
34.1986AJHSMEProblems/Problem9
Usingonlythepathsandthedirectionsshown,howmanydifferentroutesaretherefromMtoN?
A.2B.3C.4D.5E.6
35.1986AJHSMEProblems/Problem10
Apicture3feetacrossishunginthecenterofawallthatis19feetwide.Howmanyfeetfromtheendofthewallisthenearestedgeofthepicture?
A.
B.8C.
D.16E.22
36.1986AJHSMEProblems/Problem11
IfA*Bmeans
then(3*5)*8is
A.6B.8C.12D.16E.30
37.1986AJHSMEProblems/Problem12
Thetablebelowdisplaysthegradedistributionofthe30studentsinamathematicsclassonthelasttwotests.Forexample,exactlyonestudentreceiveda‘D’onTest1anda‘C’onTest2(seecircledentry).Whatpercentofthestudentsreceivedthesamegradeonbothtests?
A.12%B.25%C.
D.40%E.50%
38.1986AJHSMEProblems/Problem13
Theperimeterofthepolygonshownis
A.14B.20C.28D.48
E.cannotbedeterminedfromtheinformationgiven
39.1986AJHSMEProblems/Problem14
If200≤a≤400and600≤b≤1200,thenthelargestvalueofthequotient
is
A.
B.3C.6D.300E.600
40.1986AJHSMEProblems/Problem15
SalepricesattheAjaxOutletStoreare50%beloworiginalprices.OnSaturdaysanadditionaldistountof20%offthesalepriceisgiven.WhatistheSaturdaypriceofacoatwhoseoriginalpriceis$180?
A.$54B.$72C.$90D.$108E.$110
41.1986AJHSMEProblems/Problem16
Abargraphshowsthenumberofhamburgerssoldbyafastfoodchaineachseason.However,thebarindicatingthenumbersoldduringthewinteriscoveredbyasmudge.Ifexactly25%ofthechain’shamburgersaresoldinthefall,howmanymillionhamburgersaresoldinwinter?
A.2.5B.3C.3.5D.4E.4.5
42.1986AJHSMEProblems/Problem17
Letоbeanoddwholenumberandletпbeanywholenumber.Whichofthefollowingstatementsaboutthewholenumber(о2+по)isalwaystrue?
A.itisalwaysoddB.itisalwaysevenC.itisevenonlyifпiseven
D.itisoddonlyifпisoddE.itisoddonlyifпiseven
43.1986AJHSMEProblems/Problem18
Arectangulargrazingareaistobefencedoffonthreesidesusingpartofa100meterrockwallasthefourthside.Fencepostsaretobeplacedevery12metersalongthefenceincludingthetwopostswherethefencemeetstherockwall.Whatisthefewestnumberofpostsrequiredtofenceanarea36mby60m?
A.11B.12C.13D.14E.16
44.1986AJHSMEProblems/Problem19
Atthebeginningofatrip,themileageodometerread56,200miles.Thedriverfilledthegastankwith6gallonsofgasoline.Duringthetrip,thedriverfilledhistankagainwith12gallonsofgasolinewhentheodometerread56,560.Attheendofthetrip,thedriverfilledhistankagainwith20gallonsofgasoline.Theodometerread57,060.Tothenearesttenth,whatwasthecar’saveragemiles-per-gallonfortheentiretrip?
A.22.5B.22.6C.24.0D.26.9E.27.5
45.1986AJHSMEProblems/Problem20
Thevalueoftheexpression
isclosestto
A.0.003B.0.03C.0.3D.3E.30
46.1986AJHSMEProblems/Problem21
SupposeoneoftheeightletteredidenticalsquaresisincludedwiththefoursquaresintheT-shapedfigureoutlined.Howmanyoftheresultingfigurescanbefoldedintoatoplesscubicalbox?
A.2B.3C.4D.5E.6
47.1986AJHSMEProblems/Problem22
Alan,Beth,CarlosandDianawerediscussingtheirpossiblegradesinmathematicsclassthisgradingperiod.Alansaid,“IfIgetanA,thenBethwillgetanA.”Bethsaid,“IfIgetanA,thenCarloswillgetanA.”Carlossaid,“IfIgetanA,thenDianawillgetanA.”Allofthesestatementsweretrue,butonlytwoofthestudentsreceivedanA.WhichtworeceivedA?
A.Alan,BethB.Beth,CarlosC.CarlosandDiana
D.Alan,DianaE.Beth,Diana
48.1986AJHSMEProblems/Problem23
ThelargecirclehasdiameterAC.ThetwosmallcircleshavetheircentersonACand
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