SAT1数学知识点总结.docx
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SAT1数学知识点总结.docx
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SAT1数学知识点总结
SATI数学
I.解题技巧训练
1Theunitsdigitof23333ishowmuchlessthanthehundredthsdigitof
(A)1(B)2(C)3(D)4(E)5
2.Whatistheunitsdigitof1597365?
3.Bobhasapileofpokerchipsthathewantstoarrangeinevenstacks.Ifhestackstheminpilesof10,hehas4chipsleftover.Ifhestackstheminpilesof8,hehas2chipsleftover.IfBobfinallydecidestostackthechipsinonly2stacks,howmanychipscouldbeineachstack?
A.14B.17C.18D.24E.34
4.Ifxandyaretwodifferentintegersandtheproduct35xyisthesquareofaninteger,whichofthefollowingcouldbeequaltoxy?
A.5B.70C.105D.140E.350
5.Ifx2=y3and(x-y)2=2x,thenycouldequal(A)64(B)16(C)8(D)4(E)2
6.Forpositiveintegersp,t,xandy,ifpx=tyandx-y=3,whichofthefollowingCANNOTequalt?
A.1B.2C.4D.9E.25
7.If3t-3>6s+9andt-5s<12,andsisapositiveintegerlessthan4,thentcouldbeanyofthefollowingEXCEPTA.6B.8C.10D.12E.23
8.Ifnandpareintegersgreaterthan1andifpisafactorofbothn+3andn+10,whatisthevalueofp?
A.3B.7C.10D.13E.30
9.Ifxisapositiveintegergreaterthan1,andx3-4xisodd,thenxmustbe
(A)even(B)odd(C)prime(D)afactorof8(E)divisibleby8
10.
Ifthegraphaboveisthatoff(x),whichofthefollowingcouldbef(x)
A.f(x)=
B.f(x)=
C.f(x)=/x/+3D.f(x)=|x+3|E.f(x)=|3x|
11.xy=x+y.Ify>2,whatareallpossiblevaluesofxthatsatisfytheequationabove?
A.x<0,B.0
II.算术――对应知识点训练
1.代数题
(1).Karlboughtxbagsofredmarblesforydollarsperbag,andzbagofbluemarblesfor3ydollarsperbag.Ifheboughttwiceasmanybagsofbluemarblesasredmarbles,thenintermsofy,whatwastheaveragecost,indollars,perbagofmarbles?
(A)
(B)
(C)3x-y(D)2y(E)6y
(2)Atthisbakesale,Mr.Rightsold30%ofhispiestoonefriend.Mr.Rightthensold60%oftheremainingpiestoanotherfriend.WhatpercentofhisoriginalnumberofpiesdidMr.Righthaveleft?
(A)10%(B)18%(C)28%(D)36%(E)40%
(3)Atatrackmeet,2/5ofthefirst-placefinishersattendedSouthportHighSchool,and1/2ofthemweregirls.If2/9ofthefirst-placefinisherswhodidNOTattendSouthportHighSchoolweregirls,whatfractionalpartofthetotalnumberoffirst-placefinisherswereboys?
(A)1/9(B)2/15(C)7/18(D)3/5(E)2/3
2.中位数
(4)Numberofsiblingsperstudentinapreschoolclass
Numberofsiblings
NumberofStudents
0
3
1
6
2
2
3
1
Thetableaboveshowshowmanystudentsinaclassof12preschoolershad0,1,2,or3siblings.Later,anewstudentjoinedtheclass,andtheaverage(arithmeticmean)numberofsiblingsperstudentbecameequaltothemediannumberofsiblingsperstudent.Howmanysiblingsdidthenewstudenthave?
A.0B.1C.2D.3E.4
(5)Inasetofelevendifferentnumbers,whichofthefollowingCANNOTaffectthevalueofthemedian?
A.Doublingeachnumber
B.Increasingeachnumberby10
C.Increasingthesmallestnumberonly
D.Decreasingthelargestnumberonly
E.Increasingthelargestnumberonly
(6).Theleastandgreatestnumbersinalistof7realnumbersare2and20,respectively.Themedianofthelistis6,andthenumber3occursmostofteninthelist.Whichofthefollowingcouldbetheaverage(arithmeticmean)ofthenumbersinthelist?
I.7II.8.5III.10
A.IonlyB.IandIIonlyC.IandIIIonlyD.IIandIIIonlyE.I,IIandIII
3.集合部分
(6)SetFconsistofalloftheprimenumbersfrom1to20inclusive,andsetGconsistofalloftheoddnumbersfrom1to20inclusive.IffisthenumberofvaluesinsetF,gisthenumberofvaluesofinSetG,andjisthenumberofvaluesinF∪G,whichofthefollowinggivesthecorrectvalueoff(j-g)?
A.4B.8C.10D.11E.18
(7)SetXhasxmembersandsetYhasymembers.SetZconsistsofallmembersthatareineitherSetXorSetYwiththeexceptionofthekcommonmembers(k>0).WhichofthefollowingrepresentsthenumberofmembersinsetZ?
A.x+y+kB.x+y-kC.x+y+2kD.x+y-2kE.2x+2y-2k
(8)Ofthe240campersatasummercamp,5/6couldswim,if1/3ofthecamperstookclimbinglessons,whatwastheleastpossiblenumberofcamperstakingclimbinglessonswhocouldswim?
A.20B.40C.80D.120E.200
(9)SetFconsistofalloftheprimenumbersfrom1to20inclusive,andsetGconsistofalloftheoddnumbersfrom1to20inclusive.IffisthenumberofvaluesinsetF,gisthenumberofvaluesofinSetG,andjisthenumberofvaluesinF∪G,whichofthefollowinggivesthecorrectvalueoff(j-g)?
A.4B.8C.10D.11E.18
4.排列组合题
(10)Mr.Jonesmustchoose4ofthefollowing5flavorsofjellybean:
apple,berry,coconut,kumquat,andlemon,HowmanydifferentcombinationsofflavorscanMr.Joneschoose?
(11)
Ifthe5cardsshownaboveareplacedinarowsothat
isneverateitherend,howmanydifferentarrangementsarepossible?
(12)
Asshownabove,acertaindesignistobepaintedusing2differentcolors.If5differentcolorsareavailableforthedesign,howmanydifferentlypainteddesignsarepossible?
A.10B.20C.25D.60E.120
(13)Intheinteger3589thedigitsarealldifferentandincreasefromlefttoright.Howmanyintegersbetween4000and5000havedigitsthatarealldifferentandthatincreasedfromlefttoright?
(14).
Onthemapabove,Xrepresentsatheater,YrepresentsChris’shouse,andZrepresentsPeter’shouse.ChriswalksfromhishousetoPeter’shousewithoutpassingthetheaterandthenwalkswithPetertothetheaterandthenwalkswithoutwalkingbyhisownhouseagain.HowmanydifferentroutscanChristake?
(15)Inacertaingame,8cardsarerandomlyplacedface-downonatable.Thecardsarenumberedfrom1to4withexactly2cardshavingeachnumber.Ifaplayerturnsovertwoofthecards,whatistheprobabilitythatthecardswillhavethesamenumber?
(16)TheAcmePlumbingCompanywillsendateamof3plumberstoworkonacertainjob.Thecompanyhas4experiencedplumbersand4trainees.Ifateamconsistsof1experiencedplumberand2trainees,howmanydifferentsuchteamsarepossible?
(17)Ifp,r,m,n,tandsaresixdifferentprimenumbersgreaterthan2,andn=p*r*s*m*n*t,howmanypositivefactors,including1andn,doesnhave?
5.数列部分
(14)Theleastintegerofasetofconsecutiveintegersis-25.Ifthesumoftheseintegersis26,howmanyintegersareinthisset?
A.25B.26C.50D.51E.52
(15)1,2,2,3,3,3,4,4,4,4….
Allpositiveintegersappearinthesequenceabove,andeachpositiveintegerkappearsinthesequencektimes.Inthesequence,eachtermafterthefirstisgreaterthanorequaltoeachofthetermsbeforeit.Iftheinteger12firstappearsinthesequenceasthenthterm,whatisthevalueofn?
(16)Thefirsttermofasequenceofnumbersis2.Subsequently,everyeventerminthesequenceisfoundbysubtracting3fromthepreviousterm,andeveryoddterminthesequenceisfoundbyadding7tothepreviousterm.Whatisthedifferencebetween77thand79thtermsofthissequence?
A.11B.7C.4D.3E.2
6.应用题
(16)Apositiveintegerissaidtobe“tri-factorable”ifitistheproductofthreeconsecutiveintegers.Howmanypositiveintegerslessthan1000aretri-factorable?
(17)TomandAlisonarebothsalespeople.Tom’sweeklycompensationconsistsof$300plus20percentofhissale.Alison’sweeklycompensationconsistsof$200plus25percentofhersales.Iftheybothhadthesameamountofsalesandthesamecompensationforaparticularweek,whatwasthatcompensation,indollars?
(Disregarddollarsignwhengriddingyouranswer)
(18)Tocelebrateacolleague’sgraduation,themcoworkersinanofficeagreedtocontributeequallytoacateredlunchthatcostsatotalofydollars.Ifpofthecoworkersfailtocontribute,whichofthefollowingrepresentstheadditionalamount,indollars,thateachoftheremainingcoworkersmustcontributetopayforthelunch?
A.
B.
C.
D.
E.
(19)Inacertainstore,theregularpriceofarefrigeratoris$600.Howmuchmoneyissavedbybuyingthisrefrigeratorat20percentofftheregularpriceratherthanbuyingitonsaleat10percentofftheregularpricewithanadditionaldiscountof10percentoffthesaleprice?
(A)$6(B)$12(C)$24(D)$54(E)$60
7.整除,最小公倍数,余数问题
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