小站教育SAT数学难题汇总及答案.docx

小站教育SAT数学难题汇总及答案.docx

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小站教育SAT数学难题汇总及答案

SAT数学难题汇总及答案

x^2表示x的平方，=！

表示不等于。

pi表示圆周率

类型1：

20.Theleastintegerofasetofconsecutiveintegersis-25.Ifthesumoftheseintegersis26,howmanyintegersareinthisset

（A）25（B）26（C）50（D）51（E）52

14.Exactly4actorstryoutforthe4partsinaplay.Ifeachactorcanperformanyonepartandnoonewillperformmorethanonepart,howmanydifferentassignmentsofactorsarepossible

16.SetXhasxmembersandsetYhasymembers.SetZconsistsofallmembersthatareineithersetXorsetYwiththeexceptionofthekcommonmembers（k>0）.WhichofthefollowingrepresentsthenumberofmembersinsetZ

（A）x+y+k（B）x+y-k（C）x+y+2k（D）x+y-2k

（E）2x+2y-2k

20.Thereare75morewomenthanmenenrolledinLindenCollege.Iftherearenmenenrolled,then,intermsofn,whatpercentofthoseenrolledaremen

17.Amerchantsellsthreetypesofclocksthatchimeasindicatedbythecheckmarksinthetableabove.Whatisthetotalnumberofchimesoftheinventoryofclocksinthe90-minuteperiodfrom7:

15to

8:

45

18.Ifthe5cardsshownaboveareplacedinarowso

isneverateitheend,howmanydifferentarrangementsarepossible

20.When15isdividedbythepositiveintegerk,theremainderis3.Forhowmanydifferentvaluesofkisthistrue

（A）One（B）Two（C）Three（D）Four（E）Five

17.Onthenumberlineabove,thereare9equalintervalsbetween0and1.Whatisthevalueofx

19.Ifa,b.c,andfarefournonzeronumbers,thenallofthefollowingproportionsareequivalent

EXCEPT（A）a/f=b/c（B）f/c=b/a（C）c/a=f/b（D）a/c=b/f（E）af/bc=1/1

8.Ifaandbarepositiveintegersand

whatisthevalueofab

（A）6（B）12（C）18（D）24（E）36

16.Afterthefirstterm,eachterminasequenceis3greaterthan1/3oftheprecedingterm.Iftisthefirsttermofthesequenceandt=!

0.whatistheratioofthesecondtermtothefirstterm

15.TheAcmePlumbingCompanywillsendateamof3plumberstoworkonacertainjob.Thecompanyhas4experiencedplumbersand4trainees.Ifateamconsistsof1experiencedplumberand2trainees,howmanydifferentsuchteamsarepossible

p.r.andsarethreedifferentprimenumbersgreaterthan2,andn=p*r*s,howmanypositivefactors,including1andn.doesnhave

18.Ifthesumoftheconsecutiveintegersfrom-22tox,inclusive,is72,whatisthevalueofx（A）23

（B）25（C）50（D）75（E）94

17.Forallpositiveintegersjandk.letj\R\kbedefinedasthewholenumberremainderwhenjisdividedbyk.If13\R\k=2,whatisthevalueofk

19,Inasetofelevendifferentnumbers,whichofthefollowingCANNOTaffectthevalueofthemedian

（A）Doublingeachnumber

（B）Increasingeachnumberby10

（C）Increasingthesmallestnumberonly（D）Decreasingthelargestnumberonly（E）Increasingthelargestnumberonly

15.Astorecharges$28foracertaintypeofsweater.Thispriceis40percentmorethantheamountitcoststhestoretobuyoneofthesesweaters.Atanend-of-seasonsale,storeemployeescanpurchaseanyremainingsweatersat30percentoffthestore'scostHowmuchwoulditcostanemployeeto

purchaseasweaterofthistypeatthissale（A）$

（B）$（C）$（D）$（E）$

andCorinnestandback-to-back.Theyeachtake10stepsinoppositedirectionsawayfromeachotherandstop.Alicethenturnsaround,walkstowardCorinne.andreachesherin17steps.ThelengthofoneofAlice'sstepsishowmanytimesthelengthofoneofCorinne'ssteps（AllofAlice'sstepsarethesamelengthandallofCorinne'sstepsarethesamelength.）

14.Ifnandpareintegersgreaterthan1andifpisafactorofbothn+3andn+10.whatisthevalueofp

（A）3（B）7（C）10（D）13（E）30

16.Inamixtureofpeanutsandcashews,theratiobyweightofpeanutstocashewsis5to2.Howmanypoundsofcashewswilltherebein4poundsofthismixture

14.Howmanyintegersgreaterthan20andlessthan30areeachtheproductofexactlytwodifferentnumbers,bothofwhichareprime

（A）Zero（B）One（C）Two（D）Three（E）Four

20.Ifkisapositiveinteger,whichofthefollowingmustrepresentanevenintegerthatistwicethevalueofanoddinteger

（A）2k

（B）2k+3（C）2k+4（D）4k+1（E）4k+2

类型2：

18.Theshadedregioninthefigureaboveisboundedbythex‐axis,thelinex=4,andthegraphofy=f（x）.Ifthepoint（a,b）liesintheshadedregion,whichofthefollowingmustbetrue

I.a<4II.b

（B）IIIonly

（C）IandIIonly（D）IandIIIonly（E）I.II,andIII

19.Atabottlingcompany,machineAfills,abottlewithspringwaterandmachineBacceptsthebottle

onlyifthenumberoffluidouncesisbetween

117

8

and

121

8

IfmachineBacceptsabottle

containingnfluidounces,whichofthefollowingdescribesallpossiblevaluesofn

7.Dwaynehasanewspaperrouteforwhichhecollectskdollarseachday.Fromthisamounthepaysoutk/3dollarsperdayforthecostofthepapers,andhesavestherestofthemoney.Intermsofk,howmanydayswillittakeDwaynetosave$1,000

17.Inthexy-coordinateplane,thegraphofx=y*y-4intersectslinelat（0,p）and（5,t）.Whatisthegreatestpossiblevalueoftheslopeofl

18.Estherdrovetoworkinthemorningatanaveragespeedof45milesperhour.Shereturnedhomeintheeveningalongthesamerouteandaveraged30milesperhour.IfEstherspentatotalofonehourcommutingtoandfromwork,howmanymilesdidEstherdrivetoworkinthemorning

14.If（a+b）^=（a-b）^,whichofthefollowingmustbetrue（A）b=0

（B）a+b=1（C）a-b=1

（D）a^2+b^2=1（E）a^2-b^2=1

15.Thefigureaboveshowsthegraphsofy=x*xandy=a-x*xforsomeconstanta.Ifthelengthof

PQisequalto6,whatisthevalueofa（A）6

（B）9（C）12（D）15

18.Duringasale,acustomercanbuyoneshirtforxdollars.Eachadditionalshirtthecustomerbuyscostszdollarslessthanthefirstshirt.Forexample,thecostofthesecondshirtisx-zdollars.Whichofthefollowingrepresentsthecustomer'scost,indollars,fornshirtsboughtduringthissale

16.Letthefunctionhbedefinedbyh（x）=14+x^2/4.Ifh（2m）=9m,whatisonepossiblevalueofm

16.Ifxisanintegergreaterthan1andify=x+1/x,whichofthefollowingmustbetrueI.y=!

xII.yisaninteger.III.xy>x^2

（A）Ionly

（B）IIIonly

（C）IandIIonly（D）IandIIIonly（E）I,II,andIII

6.Ifmandkarepositiveand10（m^2）*k^-1=100m,whatism^-1!

intermsofk（A）k/10

（B）k/90

（C）k^10（D）1/10k

（E）1/90k

8.Thefigureaboveshowsthegraphofaquadraticfunctionfthathasaminimumatthepoint（1,1）.Iff（b）=f（3）,whichofthefollowingcouldbethevalueofb

（A）-3（B）-2（C）-1（D）1（E）5

16.Ifa+2bisequalto125percentof4b,whatisthevalueofa/b

'sbiologyexperimentinvolvedtiming12hamstersinamaze.Eachhamsterreceivedatleastonepracticebeforebeingtimed.Thescatterplotaboveshowsthetimeeachhamstertooktocompletethemazeandthecorrespondingnumberofpracticesthateachhamsterreceived.Basedonthedata,whichofthefollowingfunctionsbestmodelstherelationshipbetweent,thenumberofsecondstocompletethemaze,andp,thenumberofpractices

（A）t（p）=44（B）t（p）=p（C）t（p）=44p

（D）t（p）=p/44（E）t（p）=p+44

20.Forallnumbers.tandv.lettheoperation□bedefinedbyx□v=xy-yIfaandbrepositiveintegers,whichofthefollowingcanbeequaltozero

I.a□b

II.（a+b）□bIIl.a□（a+b）（A）Ionly

（B）IIonly（C）IIlonly（D）Iandll（E）IandIIl

18.Inthefigureabove,ABCDisarectangle.PointsAandClieonthegraphofy=p*x^3,wherepisaconstant.IftheareaofABCDis4,whatisthevalueofp

19.Ifk,n,x,andyarepositivenumberssatisfyingx^（-4/3）=k^-2andy^（4/3）=n^2,whatis

（xy）^（-2/3intermsofnandk

（A）1（B）1/2（C）3/2

（D）6/5（E）3

8.Thepriceofgroundcoffeebeansisddollarsfor8ouncesandeachouncemakesccupsofbrewedcoffee.Intermsofcandd.whatisthedollarcostofthegroundcoffeebeansrequiredtomake1cupofbrewedcoffee

15.Ifx^2-y^2=10andx+y=5.whatisthevalueofx-y

18.Theaverage（arithmeticmean）ofthetestscoresofaclassofpstudentsis70.andtheaverageofthetestscoresofaclassofnstudentsis92.Whenthescoresofbothclassesarecombined,theaveragescoreis86.

Whatisthevalueofp/n

14.Whichofthefollowingisequivalenttoh（m+1）（A）g（m）

（B）g（m）+l（C）g（m）-1（D）h（m）+1（E）h（m）-1

hascontainersoftwodifferentsizes.Thetotalcapacityof16containersof-onesizeisxgallons,andthetotalcapacityof8containersoftheothersizeisalsoxgallons,andx>0.Intermsofx,whatisthecapacity,ingallons,ofeachofthelargercontainers

（A）4x（B）2x（C）x/2（D）x/8（E）x/16

18.Letthefunctionfbedefinedbyf（x）=x^2+18.Ifmisapositivenumbersuchthatf（2m）=2f（m）,whatisthevalueofm

19.Thecostofmaintenanceonanautomobileincreaseseachyearby10percent,andAndrewpaidS300thisyearformaintenanceonhisautomobile.IfthecostcformaintenanceonAndrew'sautomobilenyearsfromnowisgivenbythefunctionc（n）=300x^n,whatisthevalueofx

（A）（B）（C）（D）（E）30

xy=7andx-y=5.thenx^2*y-xy^2=（A）2

（B）12（C）24（D）35（E）70

17.Linem（notshown）passesthroughOandintersectsABbetweenAandB.Whatisonepossiblevalueoftheslopeoflinem

17.Ifkandhareconstantsandx^2+kx+7isequivalentto（x+1）（x+h）.whatist