AMC10美国数学竞赛真题 xx年Word格式.docx

AMC10美国数学竞赛真题 xx年Word格式.docx

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.Whatis

Problem2

Anumberismorethantheproductofitsreciprocalanditsadditiveinverse.Inwhichintervaldoesthenumberlie?

Problem3

Thesumoftwonumbersis.Supposeisaddedtoeachnumberandtheneachoftheresultingnumbersisdoubled.Whatisthesumofthefinaltwonumbers?

Problem4

Whatisthemaximumnumberforthepossiblepointsofintersectionofacircleandatriangle?

Problem5

Howmanyofthetwelvepentominoespicturedbelowhaveatleastonelineofsymmetry?

Problem6

Let

and

denotetheproductandthesum,respectively,ofthedigitsof

.Suppose

isa

?

theinteger.Forexample,

two-digitnumbersuchthat.Whatistheunitsdigitof

Problem7

Whenthedecimalpointofacertainpositivedecimalnumberismovedfourplacestotheright,thenewnumberisfourtimesthereciprocaloftheoriginalnumber.Whatistheoriginalnumber?

Problem8

Wanda,Darren,Beatrice,andChiaretutorsintheschoolmathlab.Their

scheduleisasfollows:

Darrenworkseverythirdschoolday,Wandaworkseveryfourthschoolday,Beatriceworkseverysixthschoolday,andChiworkseveryseventhschoolday.Todaytheyareallworkinginthemathlab.Inhowmanyschooldaysfromtodaywilltheynextbetogethertutoringinthelab?

Problem9

ThestateincometaxwhereKristinlivesisleviedattherateof

ofannualincomeplus

ofanyamountabove

ofthefirst

.Kristinofher

noticedthatthestateincometaxshepaidamountedtoannualincome.Whatwasherannualincome?

Problem10

If,

andarepositivewith

and

then

Problem11

Considerthedarksquareinanarrayofunitsquares,partofwhichisshown.The?

rstringofsquaresaroundthiscentersquarecontainsunitsquares.Thesecondringcontainsunitsquares.Ifwecontinuethisprocess,thenumberofunitsquaresintheringis

Problem12

Supposethatistheproductofthreeconsecutiveintegersandthatby.Whichofthefollowingisnotnecessarilyadivisorof?

isdivisible

Problem13

Atelephonenumberhastheform,whereeachletterrepresentsadifferentdigit.Thedigitsineachpartofthenumbersareindecreasingorder;

thatis,,,and.Furthermore,,,andareconsecutiveevendigits;

,,andareconsecutiveodddigits;

and.Find.

Problem14

Acharitysellsbenefitticketsforatotalof.Someticketssellforfullprice（awholedollaramount）,andtherestsellsforhalfprice.Howmuchmoneyisraisedbythefull-pricetickets?

Problem15

Astreethasparallelcurbsfeetapart.Acrosswalkboundedbytwoparallelstripescrossesthestreetatanangle.Thelengthofthecurbbetweenthestripesisfeetandeachstripeisfeetlong.Findthedistance,infeet,betweenthestripes?

Problem16

Themeanofthreenumbersismorethantheleastofthenumbersandlessthanthegreatest.Themedianofthethreenumbersis.Whatistheirsum?

Problem17

Whichoftheconeslistedbelowcanbeformedfromaradiusbyaligningthetwostraightsides?

sectorofacircleof

Problem18

Theplaneistiledbycongruentsquaresandcongruentpentagonsasindicated.Thepercentoftheplanethatisenclosedbythepentagonsisclosestto

Problem19

Patwantstobuyfourdonutsfromanamplesupplyofthreetypesofdonuts:

glazed,chocolate,andpowdered.Howmanydifferentselectionsarepossible?

Problem20

Aregularoctagonisformedbycuttinganisoscelesrighttrianglefromeachofthecornersofasquarewithsidesoflength.Whatisthelengthofeachsideoftheoctagon?

Problem21

Arightcircularcylinderwithitsdiameterequaltoitsheightisinscribedinarightcircularcone.Theconehasdiameterandaltitude,andtheaxesofthecylinderandconecoincide.Findtheradiusofthecylinder.

Problem22

Inthemagicsquareshown,thesumsofthenumbersineachrow,column,anddiagonalarethesame.Fiveofthesenumbersarerepresentedby,,,,and.Find.

Problem23

Aboxcontainsexactlyfivechips,threeredandtwowhite.Chipsarerandomlyremovedoneatatimewithoutreplacementuntilalltheredchipsaredrawnorallthewhitechipsaredrawn.Whatistheprobabilitythatthelastchipdrawniswhite?

Problem24

Intrapezoid

,

areperpendicularto,and.Whatis

with

Problem25

Howmanypositiveintegersnotexceeding?

aremultiplesoforbutnot