SAT数学难题-hard-math-problem

1.Inthefigurebelow,thegraphofy=kx2intersectstriangleABCatB.IfAB=BCandtheareaoftrian-gleABCis6,whatisthevalueofk?(3,0)BACy=kx2(–1,0)2.Foralln,letnbedefinedasn=n2n2.Ifaandbarepositiveintegersanda,b,whichofthefollowingcouldbetrue?I.(a+b)iseven.II.(a+b)isodd.III.(ab)isnegative.3.Thegraphsoftwolinearfunctions,fandg,areper-pendicular.Iff(2)=4andf(4)=1,whichofthefollowingcoulddefineg?(A)g(x)=12x+4(B)g(x)=x+1(C)g(x)=2x+4(D)g(x)=2x3(E)g(x)=x+54.If(xh)(x+k)=x216,whatisthevalueofh+k?(A)8(B)4(C)0(D)4(E)8-3-2-11234567-2-112345675.Aportionofthegraphofthefunctionhisshowninthexy-planeabove.Ifh(4)h(s)=4,whichofthefollowingcouldbethevalueofs?(A)2(B)0(C)1(D)4(E)71OPQ6.Inthefigureabove,threeidenticalcirclesofradius8withcentersO,PandQaretangenttoeachother.Whatistheareaoftheshadedregionboundbythecircles?7.TheparticipantsinacertaincommunityserviceclubcomefromallfourgradelevelsinSmithvilleHighSchool.Thereareequalnumbersofsophomoresandjuniors.Thenumberofseniorsistwentymorethantwicethenumberofsophomoresandjuniorscombined,andthereare20freshmen.Ifthenumberofsophomores,juniorsandseniorscombinedaccountsfor80percentoftheclub’sparticipants,howmanyseniorsarethereintheclub?8.Forintegersaandbwherea0andb0,lettheoperationbedefinedasab=aba.Whichofthefollowingcouldbethevalueofab?I.ab
a1II.0III.19.Thevalueofaninvestmentincreasedby20percentto$800bytheendofthefirstweek.Tothenearestdollar,whatwasthevalueoftheinvestmentatthebeginningoftheweek?-3-2-11234567-2-11234567y=f(x)y=g(x)10.Thefigureaboveshowsthegraphsofthefunctionsfandg.Ifgisdefinedintermsofatransformationoffsuchthatg(x)=f(x+h)+k,whatisthevalueofhk?11.Forallxandy,lettheoperationx_ybeequaltothewholenumberremainderobtainedwhenfinding2xy.Ifsisanevenintegerandthevalueof7_s=2,whatisapossiblevalueofs?2OPQRS30º12.Inthefigureabove,OPQRisasquare,andPSisthearcofacirclewithcenterO.IfthelengthofarcPSis,theareaoftheshadedsectoriswhatfractionoftheareaofOPQR?(A)2(B)4(C)8(D)12(E)1513.Jackdrovetoworkinthemorningatanaveragespeedof45milesperhour.Hereturnedhomeintheeveningalongthesamerouteandaveraged30milesperhour.IfJackspentatotalofonehourcommutingtoandfromwork,howmanymilesdidhedrivetoworkinthemorning?14.Astudentisweighinglargeandsmallmarbles.Whileweighingonelargemarblewith8smallmar-bles,thestudentdiscoversthatthelargemarble’sweightis5timestheaverage(arithmeticmean)oftheweightofthesmallmarbles.Thelargemarble’sweightiswhatfractionofthetotalweightofthe9marbles?(–1,0)ABCDE15.Inthefigureabove,rectangleABCDliesonthecoordinateplanewithpointDlocatedattheorigin.IfAB=AE=ED,whatistheareaofquadrilateralBCDE?105º150ºABCDEFNote:Figurenotdrawntoscale.16.Inthefigureabove,triangleABCandparallelogramCDEFareconstructedwithB,C,andFalongthesameline.IftheratioofCF:BC=1:2andDE=2p3,whatistheareaoftriangleABC?(A)3p2(B)6(C)6p33p2(D)6p3(E)6p3+6317.Thefunctionfisdefinedasf(x)=(xn)(x+m)forallvaluesofx.Ifthefunctiongisdefinedasg(x)=f(x)+3,whatisthey-interceptofthegraphofgintermsofnandm?(A)3n+3m(B)3n3m(C)3nm(D)3nm(E)nm3a;b;ba;a;:::18.Inthesequenceabove,eachtermafterthefirsttwoisobtainedbyfindingthedierencebetweenthetwopreviousterms.Ifa=3andb=4,whatisthesumofthefirst200termsofthissequence?g(x)=x2+ch(x)=g(x5)+319.Theequationsoftwofunctions,gandh,areshownabove,wherecisaconstantinteger.Ifthegraphofhhastwosolutions,whatisthemaximumpossiblevalueofc?(A)5(B)4(C)3(D)1(E)320.TriangleABChassidelengths3,8,anda.TriangleDEFhassidelengths7,10,andd.Ifaanddarebothintegers,whatisthesmallestpossiblevalueof(da)?(A)10(B)8(C)6(D)0(E)521.Anantiquecoincollectorhasanumberofcoinsandseveraldisplaycases.Ifheputsonecoinineachcase,therearefourcoinsleftoutofthecases.Ifinsteadheputsthreecoinsineachcase,allcoinsareplaced,andtherearesixemptycasesleftover.Howmanycoinsdoesthecollectorhave?xºABStartStop22.Asmallcircle,A,isrolledaroundthecircumferenceofalargercircle,B,asshowninthefigureabove.CircleAstartsatthepositionindicated“Start”andmakestwocompleterotations,comingtorestatthepositionmarked“Stop”.IftheratiooftheareasofAtoBis1to25,whatisthevalueofx?423.Whenthepositiveintegerwisdividedby6,theremainderis3.Whenthepositiveintegerxisdividedby7,theremainderis5.Howmanypossiblevaluesofwxaretheresuchthatwx500?24.Fortheirseniorclasstrip,allseniorsatSmithvilleHighSchoolchosebetweengoingtoanamusementparkandseeingatheaterperformance.If20morethan40percentoftheseniorschosetogototheamusementparkandtheremaining160studentschosetogotothethemepark,howmanytotalseniorswentontheseniorclasstrip?25.Mr.Halyardhasforgottentwoofthenumbersinthe5-digitzipcodeofhisson’smailingaddress.Heremembersthatthedigits3-8-7appeartogether,inthatorder,somewherewithinthezipcode,andthatazerodoesnotappearintheremainingdigits.Ifheguessesatrandom,whatistheprobabilitythatMr.Halyardwillwritethecorrectzipcodeonapackageheismailingtohisson?26.Lettheoperationjkbedefinedas“good”ifthesetofallprimefactorsofjincludesallnumbersinthesetofprimefactorsofk.WhichofthefollowingisNOTgood?(A)80100(B)6015(C)124(D)1121(E)102027.Inastore,thelistpriceofoneitemisxdollars,andthelistpriceofanotherisydollars.Ifadiscou