GMAT數(shù)學講義教案課件

GMAT數(shù)學講義GMAT數(shù)學講義有關(guān)數(shù)學的運算Add,plusSubtractDifferenceMultiply,timesProductdivide加減差乘積除第1頁/共151頁有關(guān)數(shù)學的運算Add,plus加第1頁/共151頁有關(guān)數(shù)學的運算DivisibleDividedevenlyDividentDivisorQuotientRemainder第2頁/共151頁有關(guān)數(shù)學的運算Divisible第2頁/共151頁有關(guān)數(shù)學的運算DivisibleDividedevenlyDividentDivisorQuotientRemainder可被整除的被整除被除數(shù)，紅利因子，除數(shù)商余數(shù)第3頁/共151頁有關(guān)數(shù)學的運算Divisible可被整除的第3頁/共151頁Whichofthefollowingcouldbetheremainderwhenfourconsecutivepositiveintegersareeachdividedby3?A.1,2,3,1B.1,2,3,4C.0,1,2,3D.0,1,2,0E.0,2,3,0第4頁/共151頁WhichofthefollowingcouldbPowerRadicalsign,rootsignfactorial第5頁/共151頁Power第5頁/共151頁乘方方根階乘N!=1*2*3*(N-2)*(N-1)*N

且規(guī)定0!=1

例如

8!=1*2*3*4*5*6*7*8PowerRadicalsign,rootsignfactorial第6頁/共151頁乘方階乘Power第6頁/共151頁1、根號8除以2倍根號2第7頁/共151頁1、根號8除以2倍根號2第7頁/共151頁IfUnitedStatesimportsincreased20percentandexportdecreased10percentduringacertainyear,theratioofimportstoexportsattheendoftheyearwashowmanytimestheratioatthebeginningoftheyear?A.12/11B.4/3C.11/8D.3/2E.2第8頁/共151頁IfUnitedStatesimportsincre有關(guān)數(shù)學的運算RoundoffRoundto熟悉：sqrt(2)=1.414

sqrt(3)=1.732

sqrt(5)=2.236

第9頁/共151頁有關(guān)數(shù)學的運算Roundoff熟悉：第9頁/共151頁有關(guān)數(shù)學的運算RoundoffRoundto四舍五入四舍五入熟悉：sqrt(2)=1.414

sqrt(3)=1.732

sqrt(5)=2.236

第10頁/共151頁有關(guān)數(shù)學的運算Roundoff四舍五入熟悉：第10頁/共1有關(guān)集合SetSubsetPropersubsetSolutionsetComplementarysetintersection第11頁/共151頁有關(guān)集合Set第11頁/共151頁有關(guān)集合SetSubsetPropersubsetSolutionsetComplementarysetintersection集合子集真子集解集補集交集第12頁/共151頁有關(guān)集合Set集合第12頁/共151頁最近演了3部電影。調(diào)查了100個人，其中20人看了所有3部，10人什么都沒看?？戳嗣坎侩娪暗娜藬?shù)分別為：47，48，55。問：只看了2部的人數(shù)？

A20，

B30，

C40，

D70，

E90。

第13頁/共151頁最近演了3部電影。調(diào)查了100個人，其中20人看了所有3部，代數(shù)式方程不等式AlgebraicLiketerms,similartermsInequalityTriangleinequality第14頁/共151頁代數(shù)式方程不等式Algebraic第14頁/共151頁代數(shù)式方程不等式AlgebraicLiketerms,similartermsInequalityTriangleinequality代數(shù)項同類項不等式三角不等式第15頁/共151頁代數(shù)式方程不等式Algebraic代數(shù)項第15頁/共15OriginalequationEquivalentequationLinearequationQuadraticequation第16頁/共151頁Originalequation第16頁/共151頁OriginalequationEquivalentequationLinearequationQuadraticequation原方程同解方程，等價方程一次方程二次方程第17頁/共151頁Originalequation原方程第17頁/共151頁1.00001*0.99999+1.00002*0.99998=?第18頁/共151頁1.00001*0.99999+1.00002*0.999分數(shù)fractionimproper

fractionproper

fraction

denominator

numerator

Mixednumber第19頁/共151頁分數(shù)fraction第19頁/共151頁分數(shù)分數(shù)假分數(shù)真分數(shù)分母分子帶分數(shù)fractionimproper

fractionproper

fraction

denominator

numerator

Mixednumber第20頁/共151頁分數(shù)分數(shù)fraction第20頁/共151頁小數(shù)DecimalInfinitedecimalRecurringdecimaltenths’

digit

tenth

units’

digit

3-digit

number

第21頁/共151頁小數(shù)Decimal第21頁/共151頁小數(shù)DecimalInfinitedecimalRecurringdecimaltenths’

digit

tenth

units’

digit

3-digit

number

小數(shù)無窮小數(shù)循環(huán)小數(shù)十位十分位個位三位數(shù)第22頁/共151頁小數(shù)Decimal小數(shù)第22頁/共151頁基本數(shù)論integer

IrrationalRealnumber,rationalnumber

multiplier

multiple

natural

number

reciprocal第23頁/共151頁基本數(shù)論integer

第23頁/共151頁基本數(shù)論整數(shù)無理數(shù)有理數(shù)乘數(shù)倍數(shù)自然數(shù)倒數(shù)integer

IrrationalRealnumber,rationalnumber

multiplier

multiple

natural

number

reciprocal第24頁/共151頁基本數(shù)論整數(shù)integer

第24頁/共151頁PositivenumberNegativenumberOddnumberEvennumberCompositenumberPrimenumber第25頁/共151頁Positivenumber第25頁/共151頁PositivenumberNegativenumberOddnumberEvennumberCompositenumberPrimenumber正數(shù)負數(shù)奇數(shù)偶數(shù)合數(shù)質(zhì)數(shù)第26頁/共151頁Positivenumber正數(shù)第26頁/共151頁MultipleFactorGreatestcommonfactorLeastcommonmultiple第27頁/共151頁Multiple第27頁/共151頁MultipleFactorGreatestcommonfactorLeastcommonmultiple倍數(shù)約數(shù)最大公約數(shù)最小公倍數(shù)第28頁/共151頁Multiple倍數(shù)第28頁/共151頁Domainrange

第29頁/共151頁Domain第29頁/共151頁定義域值域Domainrange

第30頁/共151頁定義域Domain第30頁/共151頁mean

arithmatic

mean

geometric

mean

第31頁/共151頁mean

第31頁/共151頁平均數(shù)算術(shù)平均數(shù)幾何平均數(shù)（幾何平均數(shù)）

n個數(shù)之積的n次方根

mean

arithmatic

mean

geometric

mean

第32頁/共151頁平均數(shù)mean

第32頁/共151頁median第33頁/共151頁median第33頁/共151頁median（中數(shù)）

將一堆數(shù)排序之后，正中間的一個數(shù)（奇數(shù)個數(shù)字），

或者中間兩個數(shù)的平均數(shù)（偶數(shù)個數(shù)字）

e.g.

median

of

1,7,4,9,2,2,2,2,2,5,8

is

2

median

of

1,7,4,9,2,5

is

(5+7)/2=6

第34頁/共151頁median（中數(shù)）

將一堆數(shù)排序之后，正中間的一個數(shù)（mode第35頁/共151頁mode第35頁/共151頁mode眾數(shù)一堆數(shù)中出現(xiàn)次數(shù)最多的數(shù)Eg.1、2、3、2、4、21、1、2、3、3第36頁/共151頁mode眾數(shù)第36頁/共151頁三角形

余玄定理兩線垂直的條件為K1K2=(-1)

三的倍數(shù)的特點：所有位數(shù)之和可被3整除

第37頁/共151頁三角形

余玄定理第37頁/共151頁Inthexy-plane,pointR(2,3)andpointS(5,6)aretwoverticesoftriangleRST.ifthesumoftheslopesofthesidesofthetriangleis1,whichofthefollowinganglescouldbearightangle?1.R2.S3.TA.noneB.1onlyC.3onlyD.1and3onlyE.1,2and3第38頁/共151頁Inthexy-plane,pointR(2,3)a...2/3

as

many

A

as

B...twice

as

many...

A

as

B

A=2/3*B

A=2*B第39頁/共151頁...2/3

as

many

A

as

B

A=2/3*B第Sequencearithmetic

progressiongeometric

progression第40頁/共151頁Sequence第40頁/共151頁Sequencearithmetic

progressiongeometric

progression數(shù)列等差數(shù)列等比數(shù)列第41頁/共151頁Sequence數(shù)列第41頁/共151頁一個電影院，第一排有16個位置，每后一排多兩個，最后一排64，問總共多少？

第42頁/共151頁一個電影院，第一排有16個位置，每后一排多兩個，最后一排64

一個球落下彈回原高度75%，到第三次落地共旅程為2146CM，問最初高度？第43頁/共151頁一個球落下彈回原高度75%，到第三次落地共旅程為2146CFunctionInversefunctionExponentLogarithmComplementaryfunctionLinearfunctionQuadraticfunction第44頁/共151頁Function第44頁/共151頁FunctionInversefunctionExponentLogarithmComplementaryfunctionLinearfunctionQuadraticfunction函數(shù)反函數(shù)指數(shù)對數(shù)余函數(shù)一次函數(shù)二次函數(shù)第45頁/共151頁Function函數(shù)第45頁/共151頁Forallpositivevaluesofx,thefunctionfisdefinedby.ofthefollowing,whichisthebestapproximationoff(x)forvalueofxgreaterthan1000?第46頁/共151頁Forallpositivevaluesofx,第47頁/共151頁第47頁/共151頁第48頁/共151頁第48頁/共151頁Abscissaordinate

QuadrantCoordinateSlopeintercede

第49頁/共151頁Abscissa第49頁/共151頁Abscissaordinate

QuadrantCoordinateSlopeintercede

橫坐標縱坐標象限坐標斜率

截距第50頁/共151頁Abscissa橫坐標第50頁/共151頁

排列(permutation)組合(combination)

第51頁/共151頁

排列(permutation)第51頁/共151頁有兩個老師三個學生排隊，老師只能在最前或最后，有多少種排法？第52頁/共151頁有兩個老師三個學生排隊，老師只能在最前或最后，有多少種排法？6本書其中paperbook4本,hardbook2本.求取3本至少1本hardbook,有多少種取法(2次)第53頁/共151頁6本書其中paperbook4本,hardboow概率(probability)第54頁/共151頁w概率(probability)第54頁/共151頁tOnMonday,AndersonHighSchool’sbasketballteamwillplaytheteamfromBakerHighSchool.OnWednesday,Baker’steamwillplaytheteamfromColeHighSchool.OnFriday,ColewillplayAnderson.ineachgame,eitherteamhasa50percentchanceofwinning.(a)whatistheprobabilitythatAndersonwillwinbothitsgame?(b)whatistheprobabilitythatBakerwilllosebothitsgame?(c)whatistheprobabilitythatAndersonwillwinbothitsgameandBakerwilllosebothitsgame?第55頁/共151頁tOnMonday,AndersonHighSchoo

拋三次硬幣，相同的面朝上的概率第56頁/共151頁拋三次硬幣，相同的面朝上的概率第56頁/共151頁onthedeskshowabove,aplayerspinsthearrowtwice.thefractionisformed,whereaisthenumberofthesectorwherethearrowstopsafterthefirstspinandbisthenumberisthesectorwherethearrowstopsafterthesecondspin.oneveryspin,eachofthenumberedsectorshasanequalprobabilityofbeingthesectoronwhichthearrowstops.whatistheprobabilitythatthefractionisgreaterthan1?A.B.C.D.E.第57頁/共151頁onthedeskshowabove,aplayeIncludedangleInteriorangleExteriorangleAjacentangle第58頁/共151頁Includedangle第58頁/共151頁IncludedangleInteriorangleExteriorangleAjacentangle夾角內(nèi)角外角鄰角第59頁/共151頁Includedangle夾角第59頁/共151頁StraightangleSupplementaryanglescomplementary

angles第60頁/共151頁Straightangle第60頁/共151頁StraightangleSupplementaryanglescomplementary

angles平角補角余角第61頁/共151頁Straightangle平角第61頁/共151頁AcuteangleObtuseangleRightangle第62頁/共151頁Acuteangle第62頁/共151頁AcuteangleObtuseangleRightangle銳角鈍角直角第63頁/共151頁Acuteangle銳角第63頁/共151頁CentralangleRoundangle第64頁/共151頁Centralangle第64頁/共151頁CentralangleRoundangle圓心角圓周角第65頁/共151頁Centralangle圓心角第65頁/共151頁TriangleEquilateraltrianglesIsoscelestrianglesPythagoreantheorem第66頁/共151頁Triangle第66頁/共151頁TriangleEquilateraltrianglesIsoscelestrianglesPythagoreantheorem三角形等邊三角形等腰三角形畢達哥拉斯定理第67頁/共151頁Triangle三角形第67頁/共151頁CongruenttrianglesSimilartriangles第68頁/共151頁Congruenttriangles第68頁/共151頁CongruenttrianglesSimilartriangles全等三角形相似三角形第69頁/共151頁Congruenttriangles全等三角形第69頁/共

一個三角形，一個角60度，另一個45度，45度角對應的邊長10，問60度對應的邊長。第70頁/共151頁一個三角形，一個角60度，另一個45度，45度角對應的邊長In△PQRabove,and.whatisthevalueofthefraction

第71頁/共151頁In△PQRabove,第71頁/Inthefigureabove,arcSBTisonequarterofacirclewithcenterRandradius6.ifthelengthplusthewidthofrectangleABCRis8,thentheperimeteroftheshadedregionisA.B.C.D.E.第72頁/共151頁Inthefigureabove,arcSBTiQuadrilateralsParallelogramsRectanglesSquaresTrapezoidrhombus第73頁/共151頁Quadrilaterals第73頁/共151頁QuadrilateralsParallelogramsRectanglesSquaresTrapezoidrhombus四邊形平行四邊形矩形正方形梯形菱形第74頁/共151頁Quadrilaterals四邊形第74頁/共151頁Inthefigureshowabove,lengthsAB,BD,andCDareallunits.anglesAandCareboth.whatistheperimeterofABCD?WhatistheareaofABCD?第75頁/共151頁Inthefigureshowabove,lengtdiagonal

segment

length

width

perimeter

area

第76頁/共151頁diagonal

segment

length

diagonal

segment

length

width

perimeter

area

對角線線段長寬周長面積第77頁/共151頁diagonal

segment

length

PolygonPentagonHexagonheptagon

第78頁/共151頁Polygon第78頁/共151頁PolygonPentagonHexagonheptagon

多邊形五邊形六邊形七邊形第79頁/共151頁Polygon多邊形第79頁/共151頁Octagonenneagon=nonagondecagon第80頁/共151頁Octagon第80頁/共151頁Octagonenneagon=nonagondecagon八邊形九邊形十邊形第81頁/共151頁Octagon八邊形第81頁/共151頁CirclesDiameterRadiusArcchord第82頁/共151頁Circles第82頁/共151頁CirclesDiameterRadiusArcchord圓直徑半徑弧弦第83頁/共151頁Circles圓第83頁/共151頁Tangentcircumference第84頁/共151頁Tangent第84頁/共151頁Tangentcircumference切線周長第85頁/共151頁Tangent切線第85頁/共151頁Inthefigureshowabove,Aiscenterofacirclewhoseareais25.BandCarepointsonthecircle.themeasureofangleABCis.whatisthelengthoflinesegmentBC?第86頁/共151頁Inthefigureshowabove,AisCubesRectangularsolidsPrismsCylindersConeSpherespyramids第87頁/共151頁Cubes第87頁/共151頁CubesRectangularsolidsPrismsCylindersConeSpherespyramids立方體長方體棱柱圓柱圓錐球棱錐第88頁/共151頁Cubes立方體第88頁/共151頁increase

by

increase

to

in

terms

of

..第89頁/共151頁increase

by

increase

to

inincrease

by

increase

to

in

terms

of

..增加了

增加到用…表達

第90頁/共151頁increase

by

increase

to

inInthexy-planeabove,pointQandSarethecentersoftheciecles,whicharetangenttothex-axis.whatistheslopoflineQS?A.1/8B.1/4C.1/2D.7/8E.1第91頁/共151頁Inthexy-planeabove,pointQAwheelhasanouterdiameterof11inchs,asshownabove.therimis1inchwideandthediameterofthehubis2inches.ifeachspokeextend?inchintothehuband?inchintotherim,whatisthesumofthelengthofthe5spokes,ininches?第92頁/共151頁AwheelhasanouterdiameterThefigureaboveshowstheremainingpiecesofapaperchainfromwhichasectionhasbeenremoved.thefirstlinkoftheoriginalchainwasredandthecolorsofthelinksformedtherepeatingpatternofred(R),yellow(Y),green(G),white(W)andblue(B)fromlefttoright.whichofthefollowingcouldbethenumberoflinksinthesectionthatwasremoved?A.60B.61C.62D.63E.64第93頁/共151頁ThefigureaboveshowstheremInaplane,tworegions,SandT,arecalled“unlinked”if(1)ShasnopointsincommonwithT.(2)anylinesegmentthatcanbedrawnwithbothendpointsinShasnopointsincommonwithanylinesegmentthatcanbedrawwithbothendpointsinT.Whichofthefollowingshowsapairofregionsthatareunlinked?第94頁/共151頁Inaplane,tworegions,SandT3,5,-5,…Thefirstterminthesequenceofnumbersshowaboveis3.eacheven-numberedtermis2morethantheprevioustermandeachodd-numberedterm,afterthefirst,is-1timesthepreviousterm.forexample,thesecondtermis3+2,andthethirdtermis.whatisthe55thtermofthesequence?A.-5B.-3C.-1D.3E.5第95頁/共151頁3,5,-5,…第95頁/共5.101001000100001…Thedecimalnumberaboveconsistsofonly1’sand0’stotherightofthedecimalpoint.thefirst1isfollowedbyone0,thesecond1isfollowedbytwo0’s,thethird1isfollowedbythree0’s,andsoon.whatisthetotalnumberof0’sbetween98thandthe101st1inthisdecimalnumber?A.288B.291C.294D.297E.300第96頁/共151頁5.101001000100001…第96頁/共151頁◎☆◆㊣⊙Ifthe5cardsshowaboveareplacedinarowsothat◆isneverateitherend,howmanydifferentarrangementsarepossible?第97頁/共151頁◎☆◆㊣⊙第9◎☆◆㊣⊙Ifthe5cardsshowaboveareplacedinarowsothat◆isneverateitherend,howmanydifferentarrangementsarepossible?79第98頁/共151頁◎☆◆㊣⊙第9Ellipsehyperbolaparabola第99頁/共151頁EllipsehyperbolaEllipsehyperbolaparabola

橢圓雙曲線拋物線第100頁/共151頁EllipsehyperbolaThefigureaboveshowsthegraphsofy=x^2andy=a-x^2forsomeconstanta.ifthelengthofPQisequalto6,whatisthevalueofa?A.6B.9C.12D.15E.18第101頁/共151頁ThefigureaboveshowsthegraThequadraticfunctiongisgivenby,whereaandcarenegativeconstants.whichofthefollowingcouldbethegraphofg?第102頁/共151頁ThequadraticfunctiongisgiThefigureaboveshowsthegraphofaquadraticfunctionfthathasaminimumatthepoint(1,1).iff(b)=f(3),whichofthefollowingcouldbethevalueofb?A.-3B.-2C.-1D.1E.5第103頁/共151頁ThefigureaboveshowsthegraInthefigureabove,ABCDisarectangle.pointsAandClieonthegraphof,wherepisaconstant..iftheareaofABCDis4,whatisthevalueofp?第104頁/共151頁Inthefigureabove,ABCDisaPointOhascoordinates(0,0),pointPliesonthegraphof,andpointBhascoordinates.ifOP=BP,theareaoftriangleOPBisA.1.7B.3.0C.3.5D.4.7E.5.2第105頁/共151頁PointOhascoordinates(0,0),Lily’slockcombinationconsistsof3two-digitnumber.thecombinationsatisfiesthethreeconditionsbelow.Onenumberisodd.Onenumberisamultipleof5.Onenumberisthedayofthemonthoflily’sbirthday.Ifeachnumbersatisfiesexactlyoneoftheconditions,whichofthefollowingcouldbethecombinationtothelock?A.14-20-13B.14-25-13C.15-18-16D.20-15-20E.34-30-21第106頁/共151頁Lily’slockcombinationconsisN,__,2n,__Thefirstnumberinthesequenceaboveisn,ermsofp,whatisthesixthnumberinthesequenceA.3pB.4pC.5pD.6pE.7p第107頁/共151頁N,__,2n,1/x=0.0N1/y=0.00PThefractions1/xand1/ycanbewrittenasdecimalsasshowabove,whereNandPrepresentdifferentdigits.whichofthefollowingisequalto1/xyisSequalsNtimesPandSisadigit?A.0.0000SB.0.000SC.0.00SD.0.0SE.0.S第108頁/共151頁1/x=0.0N1/y=0.00P第108頁/共Thefigureaboveshowsacylinderwithradius2andhight5.ifpointsAandBlieonthecircumferenceorthetopandbottomofthecylinder,respectively,whatisthegreatestpossiblestraight-linedistancebetweenAandB?A.3B.5C.7D.E.第109頁/共151頁Thefigureaboveshowsacylind1,234,…1,920,21…,484,490Theintegeraboveisformedbywritingtheintegersfrom1to50,inolder,nexttoeachother.iftheintegerisreadfromlefttoright,whatisthe50thdigitfromtheleft?A.0B.1C.2D.3E.9第110頁/共151頁1,234,…1,920,21…,484,490第110頁/Ahestartingposition,pointAonthecircletouchesthelineforthefirsttimeatpoint0ontheline.AtwhatpointonthelinewillpointAtouchthelineforthefourthtime?A.12B.10C.8D.6E.4第111頁/共151頁AcircleofradiusrollsWhichofthefollowinghasthesamevolumeasthecylindershownabovewithradiusxandheight2x?A.acylinderwithradius2xandheightxB.AcylinderwithradiusandheightxC.Acubewithedge2xD.AcubewithedgeE.Arectangularsolidwithdimensionsx,2x,第112頁/共151頁WhichofthefollowinghastheInthescheduleabove,eachsessionistobe1.5hourslong,eachbreakistobe?hourlong,andlunchistobe1hourlong.ifsession4istoendat4:30P.M,atwhattimeshouldsession1begin?

A.8:15A.M

B.8:30A.M

C.8:45A.M

D.9:00A.M

E.9:15A.MEventBeginningTimeEndingTimeSession1BreakSession2LunchSession3BreakSession44:30P.M第113頁/共151頁Inthescheduleabove,eachsesAmerchantsellsthreetypesofclocksthatchimeasindicatedbythecheckmarksinthetableabove.whatisthetotalnumberofchimesoftheinventoryofclocksinthe90-minuteperiodfrom7:15to8:45?Number0fclocksChimesntimesonthenthHourChimesonceonthehourChimesonceonthehalfhourTypeA10√√TypeB5√TypeC3√√第114頁/共151頁Amerchantsellsthreetypeso

a,3a,…Thefirstterminthesequenceaboveisa,andeachtermafterthefirstis3timestheprecedingterm.ifthesumofthefirst5termis605.whatisthevalueofa?第115頁/共151頁a,3a,Inthefigureabove,ABCDisarectanglewithBC=4andAB=6PointsP,Q,andRaredifferentpointsonaline(notshown)thatisparalleltoAD.pointsPandQaresymmetricaboutlineABandpointsQandRaresymmetricaboutlineCD.whatisthelengthofPR?A.6B.8C.10D.12E.20第116頁/共151頁Inthefigureabove,ABCDisaNumberofsiblingsperstudentinapreschoolclassThetableaboveshowshowmanystudentsinaclassof12preschoolershad0,1,2,or3siblings.later,anewstudentjoinedtheclass,andtheaverage(arithmeticmean)numberofsiblingsperstudentsbecameequaltothemediannumberofsiblingsperstudent.howmanysiblingsdidthenewstudentshave?A.0B.1C.2D.3E.4NumberofSiblingsNumberofStudents03162231第117頁/共151頁NumberofsiblingsperstudentIfp,r,andsarethreedifferentprimenumbersgreaterthan2,andn=p×r×s,howmanypositivefactors,including1andn,doesnhave?第118頁/共151頁Ifp,r,andsarethreediffereHowmanyintegersgreaterthan20andlessthan30areeachthepreductofexactlytwodifferentnumbers,bothofwhichareprime?A.zeroB.oneC.twoD.threeE.four第119頁/共151頁HowmanyintegersgreaterthanIfi=,forwhichofthefolloeingvaluesofndoeshaveapositivevalue?A.23B.24C.25D.26E.27第120頁/共151頁Ifi=,forwhichofthefTwoidenticalspheresofradius6intersectsothatthedistancebetweentheircentersis10.thepointsofintersectionofthetwospheresfromacircle.whatistheareaofthiscircle?A.B.C.D.E.第121頁/共151頁TwoidenticalspheresofradiuEachofthe3circlesistangenttotheother2,andeachsideoftheequilateraltriangleistangentto2ofthecircles.ifthelengthofonesideofthetriangleisx,whatistheradius,intermsofx,ofoneofthecircles?A.B.C.D.E.第122頁/共151頁Eachofthe3circlesistangeInaremainderof4isobtainedwhenisdividedbyx-2,whatisthevalueofk?A.4B.6C.10D.12E.14第123頁/共151頁Inaremainderof4isobtaineInthestopsignshowninthefigureabove,allsideshaveequallengthandallangleshaveequalmeasure.ifthefigurecouldberotated225degreesinaclockwisedirection,pointGwouldbeinthepositionofpointA.IB.JC.KD.LE.M第124頁/共151頁InthestopsignshownintheAschoolbushas10doubleseatsineachof2rows.twostudentscansitineachdoubleseat.ifanemptybusstartsoutandmakestwostops,pickingupthreetimesthenumberofstudentsatthesecondstopasatthefirststop,andifthebusisthenfilledtoseatingcapacity,howmanystudentsgotonthebusatthesecondstop?A.5B.10C.15D.20E.30第125頁/共151頁Aschoolbushas10doubleseaKNKNKNKN+_______232IfKandNaredigitsinthetwodigitnumbersinthesumabove,thenK+N=第126頁/共151頁KNIfKandNaredigitsInthefigureabove,thecircleinscribedinPQRShasradius3.whatistheperimeterofsquarePQRS?A.9B.24C.36D.54E.81第127頁/共151頁Inthefigureabove,thecircleInalistofnumbers,thefirstnumberis3.thesecondis4.andeachsubsequentnumberisthesumofalltheproceedingnumbersinthelist.ifthe20thnumberinthelistisx.whatisthe25thnumberinthelist?A.7XB.16XC.32XD.35XE.161X第128頁/共151頁Inalistofnumbers,thefirstInthefigureaboveiftheareaoftheinscribedrectangularregionis32,thenthecircumferenceofthecircleisA.B.C.D.E.第129頁/共151頁InthefigureaboveiftheareAcertainintegernisamultipleofboth5and9.whichofthefollowingmustbetrue?Ⅰ.nisanoddintegerⅡ.nisequalto45Ⅲ.nisamultipleof15A.ⅢonlyB.ⅠandⅡonlyC.ⅠandⅢonlyD.ⅡandⅢonlyE.Ⅰ,ⅡandⅢ第130頁/共151頁AcertainintegernisamultiInthefigureabove,thecircleisinscribedinthesquare.ifthesquarehassideoflength100,thentheperimeterofthesquareisapproximatelyhowmuchgreaterthanthecircumferenceofthecircle?A.9686B.2150C.243D.100E.86第131頁/共151頁Inthefigureabove,thecircleAsecretarytyped6letters,eachofwhichhadeither1or2pages.ifthesecretarytyped10pagesinall,howmanyofthelettershad2pages?A.1B.2C.3D.4E.5第132頁/共151頁Asecretarytyped6letters,eaAt9:00a.m.trainTleftthetrainstationandtwohourslatertrainSleftthesamestationonaparalleltrack.iftrainTaveraged60kilometersperhourandtrainSaveraged75kilometersperhouruntilSpassedT,atwhattimedidSpassT?A.2:00p.mB.5:00p.mC.6:00p.mD.7:00p.mE.9:00p.m第133頁/共151頁At9:00a.m.trainTleftthetThevolumeofthecubeinthefigureaboveis64.iftheverticesof△PQRaremidpointsofthecube’sedges,whatistheperimeterof△PQR?A.6B.C.D.12E.第134頁/共151頁ThevolumeofthecubeintheThefigureaboveshowsthepathtracedbytheendofapendulumasitmovesfrompointXtopointY.howmanycentimetersdoestheendofthependulumtravelalongthearcfromXtoY?A.B.C.D.E.第135頁/共151頁ThefigureaboveshowsthepatThreeindividualscontributed$800eachtowardthepurchaseofacomputer.iftheyboughtthecomputeronsalefor$1950plus10percentsalestax,howmuchmoneyshouldberefundedtoeachindividual?A.$65B.$85C.$150D.$195E.$255第136頁/共151頁ThreeindividualscontributedInthefigureabove,arcsPRandQSaresemicircleswithcentersatQandRrespectively.ifPQ=5,whatistheperimeteroftheshadedregion?A.B.C.D.E.第137頁/共151頁Inthefigureabove,arcsPRanWhichofthefollowingstatementsmustbetrueaboutthecubeabove?Ⅰ.planeFEHisparalleltoplaneGDCⅡ.BGisperpendiculartoplaneFEDⅢ.FEisparalleltoBC.A.ⅠonlyB.ⅡomlyC.ⅢonlyD.ⅠandⅡE.Ⅰ,ⅡandⅢ第138頁/共151頁WhichofthefollowingstatemeIf△PQRand△PRSaboveareequilateral,whatfractionofPQRSisshaded?A.1/3B.1/4C.1/6D.1/9E.1/12第139頁/共151頁If△PQRand△PRSaboveareequInthefigureabove,OisthecenterofthecircleandarcSRThaslength,ifthecircumferenceofthecircleis,whatisthevalueofx+y?A.60B.90C.120D.150E.itcannotbedeterminedfromtheinformationgiven.第140頁/共151頁Inthefigureabove,OisthecIfBandDarecentersofthecirclesshowninthefigureaboveandifBD=12,BC=2,andDE=3,thenAB=A.12B.14C.21D.22E.24第141頁/共151頁IfBandDarecentersoftheIntherectangularcoordinatesystemabove,theareaoftheshadedregionisA.1.5B.2C.2.5D.3E.4第142頁/共151頁IntherectangularcoordinateInthefigureabove,theproductofanytwonumbersinadjacentcirclesisequaltotheproductofthetwonumbersthatareoppositethosecircles.forexample.3×f=4×6.whatisthevalueofj?A.3B.4C.6D.12E.20第143頁/共151頁Inthefigureabove,theproduThefigureaboveshowsthelengthsofthesidesofanequiangularpolygon,whatistheareaofthepolygon?

A.7B.8C.9D.

E.itcannotbedeterminedfromtheinformationgiven.第144頁/共151頁ThefigureaboveshowsthelenWhatistheperimeterofthepentagonabove?A.21B.26C.28D.31E.41第145頁/共151頁WhatistheperimeteroftheWhatistheareaofthehexagonalregionshowninthefigureabove?A.B.108C.D.216E.itcannotbedeterminedfromtheinformationgiven第146頁/共151頁WhatistheareaofthehexagoTherectangularsolidaboveismadeupofeightcubesofthesamesize,eachofwhichhasexactlyonefacepaintedblue.whatisthegreatestfractionofthetotalsurfaceareaofthesolidthatcouldbeblue?A.1/6B.3/14C.1/4D.2/7E.1/3第147頁/共151頁TherectangularsolidaboveisInthefigureabove,eachofthefoursquareshassidesoflengthx.if△PQRisformedbyjoiningthecentersofthreeofthesquares,whatistheperimeterof△PQRintermsofx?A.B.C.D.E.第148頁/共151頁Inthefigureabove,eachoftInthefigureabove,OandParethecentersoftwocircles.ifeachcirclehasradiusr,whatistheareaoftheshadedregion?A.B.C.D.E.第149頁/共151頁Inthefigureabove,OandParInthefigureabove,threewiresarebraided.thatis,bystartingintheorderA,B,C,theouterleftwireAisbroughtoverwireBtothemiddleposition.formingtheordersho