sat数学试题.docx
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sat数学试题
SAT数学题分成了选择题和计算题,相对于SAT数学选择题,答案还有一些提示的作用,SAT数学计算题就需要大家自己进行解答了。
下面为大家推荐的这道SAT数学计算题是非常典型的代数方程类的题目,大家一起来看看吧。
Whatvalueof
satisfiesbothoftheequationsabove?
Thecorrectansweris1/2or.5
Explanation
Difficulty:
Medium
Since
thevalueof
iseither
or
.
OR
Thetwovaluesof
thatsatisfythefirstequationare
and
.
Since
thevalueof
iseither
or
.
OR
Thetwovaluesof
thatsatisfythesecondequationare
and
.
Youareaskedtofindthevalueof
thatsatisfiesbothequations.Thatvalueis
.Theanswercanbeenteredinthegridas
or
.
下面是两道SAT数学练习题,都是选择题,后面附有答案及其解析。
SAT数学练习题可以让大家更快更好的了解SAT数学考试的出题方式以及应对方式。
下面是详细内容,我们一起来看一下这些SAT数学练习题的吧。
1、ConeAhasvolume24.Whenitsradiusandheightaremultipliedbythesamefactor,thecone’ssurfaceareadoubles.WhatisConeA’snewvolume?
(A)
(B)48
(C)
(D)96
(E)Notenoughinformationtotell
2、A
rectanglestandssothatits6inchsideliesflatagainsttheground.Iftherectangleisrotatedaroundtheaxisofoneofitstwo4inchsides,whatisthevolumeoftheresultingcylinder?
(A)24Ï€
(B)36Ï€
(C)64Ï€
(D)96Ï€
(D)144Ï€
Answers
1、C
Theformulaforacone’ssurfaceareaisπr2+πrl.Acone’svolumeis1/3πr2h.Soifthedimensionsofaconearemultipliedbythesamefactor,a,
thenitssurfaceareamultipliesbythesquareofthatfactor.Ifthedimensionsofaconearemultipliedbythesamefactor,thevolumebecomesmultipliedbythecubeofthatfactor:
Ingeneral,forsolids,ifeachdimensionofaconeismultipliedbythesamefactor,thesolid’ssurfaceareaismultipliedbythesquareofthatfactor,anditsvolumeincreasesbythecubeofthatfactor.IfthesurfaceareaofConeAdoubles,itsdimensionsaremultipliedbyafactorof
Thus,thecone’svolumeismultipliedbyafactorof
ConeA’snewvolumeis
2、E
Iftherectangleisrotatedaboutasideoflength4,thentheheightofthecylinderwillbe4andtheradiuswillbe6.
Onceyouvisualizethecylinder,youcanpluginthevaluesforthevolumeofacylinder:
一道SAT数学题(抛物线)
天道留学 时间:
2011-08-26
点击:
26次
下面是一道关于抛物线的SAT数学题及其解法的内容,非常详细。
SAT题中,抛物线是必考的一类,虽然中学课程都有所涉及,还是相对比较抽象,尤其是在理解SAT数学题的表达方式上。
下面我们来看看这道关于抛物线的SAT数学题吧。
ReadthefollowingSATtestquestionandthenclickonabuttontoselectyouranswer.
Thequadraticfunction
isgraphedinthe
-planeabove.If
forallvaluesof
whichofthefollowingcouldbethecoordinatesofpoint
?
AnswerChoices
(A)
(B)
(C)
(D)
(E)
ThecorrectanswerisC
Explanation
Thefactthat
forallvaluesof
meansthatthepoint
isthemaximumofthequadraticfunction
so
mustbethevertexoftheparabola.Theparabolaintersectsthe
-axisatthepoints
and
so
mustbehalfwaybetween
and
.Therefore,
.Ofthechoices,theonlyonewith
-coordinateequalto
is
.Therefore,
couldbethecoordinatesofpoint
.
1.Whatisthelengthofthelinesegmentinthex-yplanewithendpointsat(-2,-2)and(2,3)?
A.3
B.√31
C.√41
D.7
E.9
CorrectAnswer:
C
解析:
Sketchadiagramandcalculatethedistance(hypotenuseofarighttriangle)usingPythagorastheorem.
Verticalheightoftriangle=5;horizontalside=4;hypotenuse=√(25+16)=√41
2.nisanintegerchosenatrandomfromtheset{5,7,9,11}
pischosenatrandomfromtheset{2,6,10,14,18}
Whatistheprobabilitythatn+p=23?
A.0.1
B.0.2
C.0.25
D.0.3
E.0.4
CorrectAnswer:
A
解析:
Eachoftheintegersinthefirstsetcouldbecombinedwithanyfromthesecondset,givingatotalof4x5=20possiblepairs.Ofthesethecombinationsthatcouldgiveasumof23are(5+18),and(9+14).Thismeansthattheprobabilityofgettingasumof23is2/20=1/10
3.Adressonsaleinashopismarkedat$D.Duringthediscountsaleitspriceisreducedby15%.Staffareallowedafurther10%reductiononthediscountedprice.IfastaffmemberbuysthedresswhatwillshehavetopayintermsofD?
A.0.75D
B.0.76D
C.0.765D
D.0.775D
E.0.805D
CorrectAnswer:
C
解析:
Ifthepriceisreducedby15%,thenthenewpricewillbe0.85D.Ifthisnewpriceisfurtherreducedby10%,thediscountedpricewillbe0.9x0.85D=0.765D
4.Allthedotsinthearrayare2unitsapartverticallyandhorizontally.Whatisthelengthofthelongestlinesegmentthatcanbedrawnjoininganytwopointsinthearraywithoutpassingthroughanyotherpoint?
A.2
B.2√2
C.3
D.√10
E.√20
CorrectAnswer:
E
解析:
Thelongestlinesegmentthatcanbedrawnwithoutpassingthroughanydotsotherthanthoseatthebeginningandendofthesegment,suchalinecouldgofromthemiddledotinthetoprowtoeitherthebottomleftorrightdot.Inanycasethesegmentwillbethehypotenuseofarighttrianglewithsides2and4.UsingPythagorastheoremthehypotenusewillbe√(2²+4²)=√20
5.IftheradiusofthecirclewithcentreOis7andthemeasureofangleAOBis100,whatisthebestapproximationtothelengthofarcAB?
A.9
B.10
C.11
D.12
E.13
CorrectAnswer:
D
解析:
Iftheradiusis7,thecircumference=14π.Thelengthofthearcis100/360ofthecircumference.Takingπas22/7weget.(100x14x22)/(360x7)whichreducesto440/36=12.22(i.e.approx.12)
1、AtCentralHighSchool,themathclubhas
membersandthechessclubhas
members.Ifatotalof
studentsbelongtoonlyoneofthetwoclubs,howmanystudentsbelongtobothclubs?
AnswerChoices
(A)
(B)
(C)
(D)
(E)
ThecorrectanswerisC
Explanation
Let
standforthenumberofstudentswhobelongtobothclubs.The
membersofthemathclubcanbebrokendownintotwogroups:
thosewhoareinbothclubs(thereare
studentsinthiscategory)andthosewhoareinthemathclubonly(thereare
studentsinthiscategory).
The
membersofthechessclubcanalsobebrokendownintotwogroups:
studentswhoareinbothclubsand
studentswhoareinthechessclubonly.
Sinceatotalof
studentsbelongtoonlyoneofthetwoclubs,youknowthat
.Solvingthisequationgives
so
studentsbelongtobothclubs。
2、If
isdivisibleby
and
whichofthefollowingisalsodivisiblebythesenumbers?
AnswerChoices
(A)
(B)
(C)
(D)
(E)
ThecorrectanswerisD
Explanation
Since
isdivisibleby
and
mustbeamultipleof
as
istheleastcommonmultipleof
and
.Somemultiplesof
are
and
.
Ifyouaddtwomultiplesof
thesumwillalsobeamultipleof
.Forexample,
and
aremultiplesof
andtheirsum,
isalsoamultipleof
.
Ifyouaddamultipleof
toanumberthatisnotamultipleof
thesumwillnotbeamultipleof
.Forexample,
isamultipleof
and
isnot.Theirsum,
isnotamultipleof
.
Thequestionaskswhichanswerchoiceisdivisibleby
and
;thatis,whichanswerchoiceisamultipleof
.Alltheanswerchoicesareintheformof"
plusanumber."Onlychoice(D),
has
addedtoamultipleof
.Thesumof
and
isalsoamultipleof
sothecorrectanswerischoice(D).
3、Inan
solutionofwaterandalcohol,theratiobymassofwatertoalcoholis
to
.If
gramsofasolutionconsistingof
gramswaterforeachgramofalcoholisaddedtothe
solution,whatfractionbymassofthenewsolutionisalcohol?
AnswerChoices
(A)
(B)
(C)
(D)
(E)
ThecorrectanswerisB
Explanation
Tofindwhatfractionbymassofthenewsolutionisalcohol,youcanfindhowmanygramsofalcoholareinthefinalsolutionof
grams.Sincethe
solutionis
partalcoholto
partswater,itis
alcohol.Soitcontains
gramsofalcohol.Similarly,the
solutionis
alcoholbymass,soitcontains
gramsofalcohol.Thus,thefinal20-gramsolutioncontains
gramsofalcohol,so
or
ofitisalcohol.
1.Ofthefollowing,whichisgreaterthan?
A.2/5
B.4/7
C.4/9
D.5/11
E.6/13
2.Ifanobjecttravelsatfivefeetpersecond,howmanyfeetdoesittravelinonehour?
A.30
B.300
C.720
D.1800
E.18000
3.Whatistheaverage(arithmeticmean)ofallthemultiplesoftenfrom10to190inclusive?
A.90
B.95
C.100
D.105
E.110
4.Acubicalblockofmetalweighs6pounds.Howmuchwillanothercubeofthesamemetalweighifitssidesaretwiceaslong?
A.48
B.32
C.24
D.18
E.12
5.Inaclassof78students41aretakingFrench,22aretakingGermanand9studentsaretakingbothFrenchandGerman.Howmanystudentsarenotenrolledineithercourse?
A.6
B.15
C.24
D.33
E.54
1.CorrectAnswer:
B
Explanation:
Onewaytodealwithfractionsistoconvertthemalltodecimals.(Usingyourcalculator,dividethenumeratorbythedenominator).
Inthiscaseallyouwouldneedtodoistoseewhichisgreaterthan0.5.
Otherwisetoseewhichisgreaterthan?
doublethenumeratorandseeiftheresultisgreaterthanthedenominator.InB,thecorrectanswer,doublingthenumeratorgivesus8,whichisbiggerthan7.
2.CorrectAnswer:
E
Explanation:
Ifanobjecttravelsat5feetperseconditcovers5x60feetinoneminute,and5x60x60feetinonehour.Answer=18000(E)
3.CorrectAnswer:
C
Explanation:
Youcouldaddupallthemultiplesof10(10+20