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【小站教育】SAT数学难题汇总及答案

【小站教育】SAT数学难题汇总及答案

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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:

stintegerofatofconcutiveintegersis—umofthe

integersis26,howmanyintegersareinthist?

(A)25（B)26（C）

50(D）51（E)52

14。actorcanperform

anyonepartandnoonewillperformmorethanonepart,howmanydifferent

assignmentsofactorsarepossible？

sxmembersandtYhasymembers。SetZconsistsofallmembers

thatareineithertXortYwiththeexceptionofthekcommonmembers(k>

0）。WhichofthefollowingreprentsthenumberofmembersintZ?

(A）x+y+k(B)x+

y—k（C)x+y+2k

(D）x+y-2k

（E）2x+2y—2k

re75morewomenthanmenenrolledinLindenCollege。Iftherearen

menenrolled，then,intermsofn,whatpercentofthoenrolledaremen?

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【小站教育】SAT数学难题汇总及答案

17。Amerchantllsthreetypesofclocksthatchimeasindicatedbythecheck

thetotalnumberofchimesoftheinventoryof

clocksinthe90-minuteperiodfrom7:15to

8：45？

5cardsshownaboveareplacedinarowsoisneverateitheend,

howmanydifferentarrangementsarepossible？

15isdividedbythepositiveintegerk,theremainderis3。Forhowmany

differentvaluesofkisthistrue?

（A)One(B）Two(C）

Three(D)Four（E）

Five

umberlineabove，

thevalueofx？

19。Ifa，b。c，andfarefournonzeronumbers，thenallofthefollowing

proportionsareequivalent

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

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【小站教育】SAT数学难题汇总及答案

barepositiveintegersandwhatisthevalueofab？

4/18

【小站教育】SAT数学难题汇总及答案

(A)6(B)12（C)

18（D)24（E）

36

hefirstterm，eachterminaquenceis3greaterthan1/3ofthe

hefirsttermofthequenceandt=！the

ratioofthecondtermtothefirstterm？

ePlumbingCompanywillndateamof3plumberstoworkonacertain

panyhas4experiencedplumbersand4trainees。Ifateamconsistsof

1experiencedplumberand2trainees,howmanydifferentsuchteamsarepossible？

。r。andsarethreedifferentprimenumbersgreaterthan2，andn=p*

r＊s，howmanypositivefactors，including1andn。doesnhave?

18。Ifthesumoftheconcutiveintegersfrom—22tox,inclusive,is

72,whatisthevalueofx?（A)23

(B)25（C）50(D）

75（E）94

bedefinedasthewholenumber

remainderwhenjisdividedbyk。If13Rk=2，whatisthevalueofk？

19，Inatofelevendifferentnumbers,whichofthefollowingCANNOTaffectthe

valueofthemedian?

(A）Doublingeachnumber

(B）Increasingeachnumberby10

（C）Increasingthesmallestnumberonly

（D)Decreasingthelargestnumberonly

(E）Increasingthelargestnumberonly

5/18

【小站教育】SAT数学难题汇总及答案

charges$28foracertaintypeofsweater。Thispriceis40percent

morethantheamountitcoststhestoretobuyoneofthesweaters。Atanend-

of-asonsale,storeemployeescanpurchaanyremainingsweatersat30percent

offthestore'scostHowmuchwoulditcostanemployeeto

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【小站教育】SAT数学难题汇总及答案

purchaasweaterofthistypeatthis

sale？(A）＄8。40

（B)$14。00(C）

＄19。60（D)＄20。

00(E)＄25.20

17。AliceandCorinnestandback-to—chtake10stepsinopposite

directionsawayfromeachotherandstop。Alicethenturnsaround,walkstoward

Corinne。andreachesherin17steps。ThelengthofoneofAlice’sstepsishow

manytimesthelengthofoneofCorinne'ssteps？（AllofAlice’sstepsarethe

samelengthandallofCorinne’sstepsarethesamelength.)

14。Ifnandpareintegersgreaterthan1andifpisafactorofbothn+3and

n+10。whatisthevalueofp？

(A）3(B)7(C)10

（D)13(E）30

tureofpeanutsandcashews,theratiobyweightofpeanutstocashews

ypoundsofcashewswilltherebein4poundsofthismixture？

14。Howmanyintegersgreaterthan20andlessthan30areeachtheproductof

exactlytwodifferentnumbers，bothofwhichareprime？

（A）Zero（B)One

（C)Two(D)Three

(E)Four

positiveinteger，whichofthefollowingmustreprentaneven

integerthatistwicethevalueofanoddinteger?

（A）2k

(B)2k+3（C）2k+

4（D)4k+1（E）4k+

2

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【小站教育】SAT数学难题汇总及答案

类型2：

dedregioninthefigureaboveisboundedbythex‐axis，thelinex

=4，andthegraphofy=f（x）.Ifthepoint(a,b）liesintheshadedregion,

whichofthefollowingmustbetrue?

I。a〈4II.b

（a）(A）Ionly

(B）IIIonly

（C）IandIIonly(D）

IandIIIonly(E）I。

II，andIII

tlingcompany，machineAfills，abottlewithspringwaterandmachine

Bacceptsthebottle

onlyifthenumberoffluid

ouncesisbetween

11

7

8

and

12

1

8

IfmachineBaccepts

abottle

containingnfluidounces,whichofthefollowingdescribesall

possiblevaluesofn?

8/18

【小站教育】SAT数学难题汇总及答案

hasanewspaperrouteforwhichhecollectskdollarachday。From

thisamounthepaysoutk/3dollarsperdayforthecostofthepapers，andhe

sofk，howmanydayswillittakeDwayneto

save$1,000?

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【小站教育】SAT数学难题汇总及答案

17。Inthexy-coordinateplane，thegraphofx=y＊y-4interctslinelat（0,

p)and（5,t).Whatisthegreatestpossiblevalueoftheslopeofl?

18。Estherdrovetoworkinthemorningatanaveragespeedof45milesperhour.

Shereturnedhomeintheeveningalongthesamerouteandaveraged30milesper

hour。IfEstherspentatotalofonehourcommutingtoandfromwork，howmany

milesdidEstherdrivetoworkinthemorning?

14。If（a+b)^0.5=(a—b)^—0.5，whichofthe

followingmustbetrue？（A）b=0

(B)a+b=1(C)a-

b=1

（D）a^2+b^2=1(E)

a^2-b^2=1

ureaboveshowsthegraphsofy=x＊xandy=a—x*xforsome

engthof

PQiqualto6,whatisthevalueofa?

(A）6

（B）9（C）12

（D)15

18。Duringasale，ditional

shirtthecustomerbuyscostszdollarslessthanthefirstshirt。Forexample，

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【小站教育】SAT数学难题汇总及答案

thecostofthecondshirtisx-zdollars。Whichofthefollowingreprents

thecustomer’scost,indollars，fornshirtsboughtduringthissale？

11/18

【小站教育】SAT数学难题汇总及答案

16。Letthefunctionhbedefinedbyh(x)=14+x^2/(2m)=9m，whatisone

possiblevalueofm?

16。Ifxisanintegergreaterthan1andify=x+1/x，whichofthe

followingmustbetrue?I.y=！。xy〉x^2

(A）Ionly

(B)IIIonly

（C）IandIIonly（D)

IandIIIonly(E)I，II,

andIII

karepositiveand10(m^2)*k^—1=100m,whatism^-1！in

termsofk?（A)k/10

（B）k/90

(C)k^0.5/10(D)1/10k

（E)1/90k

8。Thefigureaboveshowsthegraphofaquadraticfunctionfthathasaminimum

atthepoint(1，1).Iff(b)=f(3),whichofthefollowingcouldbethevalueof

b？

（A）-3(B)—2

(C)-1(D)1（E)

5

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【小站教育】SAT数学难题汇总及答案

16。Ifa+2biqualto125percentof4b，whatisthevalueofa/b？

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【小站教育】SAT数学难题汇总及答案

15。Doug'mster

tterplotaboveshowsthe

timeeachhamstertooktocompletethemazeandthecorrespondingnumberof

nthedata,whichofthefollowing

functionsbestmodelstherelationshipbetweent,thenumberofcondstocomplete

themaze，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。operation□bedefinedbyx□v=xy-y

Ifaandbrepositiveintegers,whichofthefollowingcanbeequaltozero?

I.a□b

II.(a+b）□bIIl.a

□（a+b）（A)Ionly

（B)IIonly（C)IIl

only（D)Iandll(E)

IandIIl

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【小站教育】SAT数学难题汇总及答案

15/18

【小站教育】SAT数学难题汇总及答案

18。Inthefigureabove,ABCDisarectangle。PointsAandClieonthegraphof

y=p*x^3？,reaofABCDis4,whatisthevalueof

p?

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

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【小站教育】SAT数学难题汇总及答案

(D)6/5(E)3

8。Thepriceofgroundcoffeebeansisddollarsfor8ouncesandeachouncemakes

ccupsofbrewedcoffee。Intermsofcandd。whatisthedollarcostofthe

groundcoffeebeansrequiredtomake1cupofbrewedcoffee？

^2-y^2=10andx+y=5。whatisthevalueof

x-y？

18。Theaverage(arithmeticmean)ofthetestscoresofaclassofpstudentsis

averageofthetestscoresofaclassofnstudentsis92。Whenthe

scoresofbothclassarecombined,theaveragescoreis86.

Whatisthevalueofp/n？

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【小站教育】SAT数学难题汇总及答案

fthefollowingiquivalenttoh（m+

1)？（A)g(m)

（B）g(m）+l(C)g

（m）-1（D)h(m）+1

(E)h（m）—1

7。alcapacityof16containers

of—onesizeisxgallons，andthetotalcapacityof8containersoftheother

sizeisalsoxgallons,andx〉0。Intermsofx，whatisthecapacity，in

gallons,ofeachofthelargercontainers?

(A)4x(B)2x(C）

x/2(D)x/8(E)x/16

18。Letthefunctionfbedefinedbyf（x）=x^2+18。Ifmisapositivenumber

suchthatf(2m)=2f（m），whatisthevalueofm？

19。Thecostofmaintenanceonanautomobileincreaachyearby10percent，

andAndrewpaidS300thisyearformaintenanceonhisautomobile。Ifthe

costcformaintenanceonAndrew’sautomobilenyearsfromnowisgivenby

thefunctionc（n)=300x^n，whatisthevalueofx?

（A)0。1(B)0.3

（C)1。1(D)1。3

（E)30

=7andx-y=5。thenx^2＊y—

xy^2=(A）2

(B）12（C）24

(D)35(E）70

（notshown)passthroughOandinterctsABbetweenAandB。What

isonepossiblevalueoftheslopeoflinem？

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【小站教育】SAT数学难题汇总及答案

hareconstantsandx^2+kx+7iquivalentto(x+1）(x+h)。

whatisthevalueofk？(A)0

(B)1（C）7(D）

8

（E）Itcannotbedeterminedfromtheinformation

given。

(A）1(B）5（C）

24（D）25（E)

26

16。Tocelebrateacolleague'sgraduation，themcoworkersinanofficeagreedto

he

coworkersfailtocontribute,whichofthefollowingreprentstheadditional

amount，indollars，thateachoftheremainingcoworkersmustcontributetopay

forthelunch?

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【小站教育】SAT数学难题汇总及答案

类型3

y—coordinateplane,thedistancebetweenpointB（10，18）andpoint

A（x，3）is17。Whatisonepossiblevalueofx?

tternisud

repeatedlytocompletelycoverarectangularregion12Lunitslongand10Lunits

yrectanglesofdimensionLbyWareneeded？

(A）30（B）36(C）

100（D)150（E）

180

igureabove,AB=BCandDE=EF=DFIfthemeasureof/.ABCis30°

andthemeasureof

/。BDEis50°,whatisthemeasureof

/DFA?（A）30°

(B）35°（C）40°

(D)45°(E)50°

gmentsaretobedrawnconnectingvertexVwitheachoftheother11verticesin

thefigure。Howmanyofthegmentswillnotlieonanedgeofthefigure？

20/18

【小站教育】SAT数学难题汇总及答案

igureabove，sofn,ofthedegreemeasuresof

thefouranglesmarkedwitharrows？

(A)n

（B)2n

（O180—n(D)360-

n（E)360—2n

16。

shadedareais64pisquareinchesandthesmallercirclehasaradiusof6inches,

whatistheradius,ininches,ofthelargercircle？

20。ctionf

isdefinedbyf（x）=x^3—ctiongisdefinedbyg(x)=f(x+h)+k，

wherehandkitareconstants。Whatisthevalueofhk?

（A)-6(B）—3

(C)-2（D)3（E）

6

21/18

【小站教育】SAT数学难题汇总及答案

15。Thecubeshownabovehadgesoflength2，andAand8aremidpointsoftwo

oftheedges。WhatisthelengthofAB(notshown）?

20。Inthefigureabove,arcSBTisonequarterofacirclewithcenterRand

eperimeter

oftheshadedregionis

(A)8-3pi(B）

10+3pi（C）14+3pi

（D)1+6pi(E)

12+6pi

angleABCD,pointEisthemidpointofBC。Iftheareaofquadrilateral

ABEDis2/3，whatistheareaofrectangleABCD？

(A)1/2（B）3/4(C）

8/9（D)1(E)8/3

8。RectangleABCDliesinthexy—coordinateplanesothatitssidesarenot

paralleltotheaxes。Whatistheproductoftheslopesofallfoursidesof

rectangleABCD？

(A)—2（B)—1

（C）0(D)1（E）

2

22/18

【小站教育】SAT数学难题汇总及答案

igureabove,y+z=?(A）

180

（B)195（C)215

(D)230

（E)245

ureaboveshowspartofacirclewhocircumferenceis45。Ifarcsof

length2andlengthbcontinuetoalternatearoundtheensurecirclesothatthere

are18arcsofeachlength,whatisthedegreemeasureofeachofthearcsof

lengthb?

（A)4°（B）6°

（C）10°(D)16°

(E）20°

ivelinegmentsinthefigureaboveareallcongruent,whatisthe

ratioofthelengthofAC（notshown）tothelengthofBD？

(A)2^0.5to1（B)

3^0.5to1(C)2^0。5

to2(D）3^0。5to2

（E）3^0.5to2^0.。5

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【小站教育】SAT数学难题汇总及答案

15。Inthefigureabove，EBCDisasquareandAE=8WhatistheareaofEBCD?

igureabove,ifthelegsoftriangleABCareparalleltotheaxes，

whichofthefollowingcouldbethelengthsofthesidesoftriangleABC?

（A)2。29^0.5(B）

2。5，and7

（C)3，3，and3*2^0.5（D)

3，4，and5

（E）4，5，and41^0。5

类型4:

verage(arithmeticmean)ofxandyisk,whichofthefollowingisthe

averageofx，y，andz?

（A)（2k+z)/3(B)

（2k+z)/2（C)

（k+z)/3（D)（k+z）

/2

（E)2(k+z）/3

INAPRESCHOOLCLASS

Number

ofSiblings

Number

ofStudents

03

16

22

31

8。Thetableaboveshowshowmanystudentsinaclassof12preschoolershad0,1，

2,or3siblings。Later,anewstudentjoinedtheclass，andtheaverage

（arithmeticmean）numberofsiblingsperstudentbecameequaltothemedian

ysiblingsdidthenewstudenthave?

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【小站教育】SAT数学难题汇总及答案

(A）0（B)1(C）

2(D)3（E)4

leaboveshowsstudentenrollmentatWestonHighSchoolfrom1992through

edianenrollmentforthefiveyearswas1351，andnotwoyearshadthe

sameenrollmentwhatisthegreatestpossiblevalueforx？

【答案】

类型1题

号

答案类型2题

号

答案类型3题

号

答案类型4题

号

答案

20E18A20E18A

14246D18B8A

16D16316E181350

1714920E8E

187219A182,18

20E15C15B

174/9，.44416D20B

20C18D18A

8B17116C

19A15E8D

16C162,719C

15248C16E

17815A178

18B181615192

19E187019A

171114A1610

15B18320B

14B170〈X<0。

375

18A

171。4317D15D

25/18

【小站教育】SAT数学难题汇总及答案

14D152

20E16D

161.1417B

14E

16C

7D

1818

8A

183/8。375

7D

19C

16E

19C

14E

8A