AMC 10A 试题及答案解析Word文档格式.docx

AMC 10A 试题及答案解析Word文档格式.docx

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=theamountPamspent=theamountSusanspent

▪

Pampays10moredollarsthanSusan

2、Defineand.Whatis?

3、Anaquariumhasarectangularbasethatmeasures100cmby40cmandhasaheightof50cm.Itisfilledwithwatertoaheightof40cm.Abrickwitharectangularbasethatmeasures40cmby20cmandaheightof10cmisplacedintheaquarium.Byhowmanycentimetersdoesthewaterrise?

Thevolumeofthebrickis.Thusthewatervolumerose.

4、Thelargeroftwoconsecutiveoddintegersisthreetimesthesmaller.Whatistheirsum?

Letthetwoconsecutiveoddintegersbe,.Then,soandtheirsumis.

5、Aschoolstoresells7pencilsand8notebooksfor.Italsosells5pencilsand3notebooksfor.Howmuchdo16pencilsand10notebookscost?

Weletcostofpencilsincents,numberofnotebooksincents.Then

Subtractingtheseequationsyields.Backwardssolvinggives.Thustheansweris.

6、AtEuclidHighSchool,thenumberofstudentstakingtheAMC10was60in2002,66in2003,70in2004,76in2005,78and2006,andis85in2007.Betweenwhattwoconsecutiveyearswastherethelargestpercentageincrease?

Wecomputethepercentageincreases:

1.

2.

3.

4.

5.

Theansweris.

Infact,theanswerfollowsdirectlyfromexaminingthedifferencesbetweeneachyear.Thelargestdifferencesare,anditiseasytoseethatduetothedecreasedstartingnumberofstudentsin2002thatthatwillbeouranswer.

7、LastyearMr.JohnQ.Publicreceivedaninheritance.Hepaid20%infederaltaxesontheinheritance,andpaid10%ofwhathehasleftinstatetaxes.Hepaidatotalofforbothtaxes.Howmanydollarswastheinheritance?

Afterpayinghistaxes,hehasoftheinheritanceleft.Sinceisoftheinheritance,thewholeinheritanceis.

8、Trianglesandareisosceleswithand.PointDisinside.,and.Whatisthedegreemeasureof?

Weanglechase,andfindoutthat:

9、Realnumbersandsatisfytheequationsand.Whatis?

And

Substitutiongives,andsolvingforyields.Thus.

10、TheDunbarfamilyconsistsofamother,afather,andsomechildren.Theaverageageofthemembersofthefamilyis,thefatherisyearsold,andtheaverageageofthemotherandchildrenis.Howmanychildrenareinthefamily?

Letbethenumberofchildren.Thenthetotalagesofthefamilyis,andthetotalnumberofpeopleinthefamilyis.So

11、Thenumbersfromtoareplacedattheverticesofacubeinsuchamannerthatthesumofthefournumbersoneachfaceisthesame.Whatisthiscommonsum?

Thesumofthenumbersonthetopfaceofacubeisequaltothesumofthenumbersonthebottomfaceofthecube;

thesenumbersrepresentalloftheverticesofthecube.Thustheansweris.

12、Twotourguidesareleadingsixtourists.Theguidesdecidetosplitup.Eachtouristmustchooseoneoftheguides,butwiththestipulationthateachguidemusttakeatleastonetourist.Howmanydifferentgroupingsofguidesandtouristsarepossible?

Eachtouristhastopickinbetweentheguides,sofortouriststherearepossiblegroupings.However,sinceeachguidemusttakeatleastonetourist,wesubtractthecaseswhereaguidehasnotourist.Thustheansweris.

13、Yanissomewherebetweenhishomeandthestadium.Togettothestadiumhecanwalkdirectlytothestadium,orelsehecanwalkhomeandthenridehisbicycletothestadium.Heridestimesasfastashewalks,andbothchoicesrequirethesameamountoftime.WhatistheratioofYan'

sdistancefromhishometohisdistancefromthestadium?

LetthedistancefromYan'

sinitialpositiontothestadiumbeandthedistancefromYan'

sinitialpositiontohomebe.Wearetryingtofind,andwehavethefollowingidentitygivenbytheproblem:

Thusandtheansweris

14、Atrianglewithsidelengthsintheratioisinscribedinacircleofradius.Whatistheareaofthetriangle?

Since3-4-5isaPythagoreantriple,thetriangleisarighttriangle.Sincethehypotenuseisadiameterofthecircumcircle,thehypotenuseis.Thentheotherlegsareand.Theareais

15、Fourcirclesofradiusareeachtangenttotwosidesofasquareandexternallytangenttoacircleofradius,asshown.Whatistheareaofthesquare?

Thediagonalhaslength.Thereforethesideshavelength,andtheareais

AlternateSolution

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