GMAT数学1.docx
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GMAT数学1.docx
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GMAT数学1
GMAT数学
第一部分数学基础知识
一、代数Algebra
例1比较大小:
.
Thenumberofdistinctpositivefactorsofn14比较大小
例2:
252因子的个数是多少?
例3比较大小:
Aprinternumberedconsecutivelythepagesofabook,beginningwith1onthefirstpage.Innumberingthepage,heprintedatotalof204digits.
Thenumberofpagesinthebook105
例4比较大小:
Inacertaintwo-digitnumber,
theunits'digitistwicethetens'digit.5
Thetens'digit
例5比较大小:
二、描述统计descriptivestatistics
例6比较大小:
某长方形的周长为40,该长方形的最大面积100
例7比较大小:
空间5个点能够构成的直线数目10
例8:
求3,13,17的标准方差。
三、排列组合combination、概率probability
1.排列组合排列计算公式:
,组合计算公式:
。
2.概率
例9:
假如世界杯比赛共有32支球队,分成8个组,每组4个队,每组前两名出线,然后成对进行淘汰赛,直至决赛决出冠军,并且淘汰队不参加比赛,从中间任选出一场比赛观看是半决赛的机会有多大?
例10:
有4对男女,每对中有1男1女,从每对中选出1人,选出2男2女的概率是多少?
例11:
有3个打字员为4家公司服务,如果4家公司各有1份文件要录入,他们只能找到这3个打字员录入,且各公司对打字员的要求是随机的。
问每个打字员都收到文件的概率是多少?
例12:
两个骰子,六面的值分别为1,2,3,4,5,6,投掷这两个骰子,问其中一个骰子的值比另一个的值大2的概率为多大?
四、几何(Geometry)
例13比较大小:
RisapointintherectangularcoordinatesystemandOR=5.
Thex-coordinateofpointR54.9
例14比较大小:
(RS)2+(ST)2(RT)2
例15:
Accordingtothegraphabove,whenx=3,yismostnearly:
(A)-1(B)-1/2(C)0(D)1/2(E)1
五、文字题(WordProblem)
1.利息问题(interest)
单利simpleinterest复利compoundinterest
例16:
If$8000isinvestedat6percentsimpleannualinterest,howmuchinterestisearnedafter3months?
例17:
If$10,000isinvestedat10percentsimpleannualinterest,compoundsemiannually,whatisthebalanceafter1year?
2.折扣问题(discount)
例18:
Thepriceofanitemisdiscountedby20percentandthenthisreducedpriceisdiscountedbyanadditional30percent.Thesetwodiscountsareequaltoanoveralldiscountofwhatpercent?
3.英美常识问题
GRE难题解析
例1:
Onacertainnumberline,if-7isadistanceof4fromnand7isadistanceof18fromn,thenn=?
(A)25(B)11(C)-3(D)11(E)-11
例2:
Thediagramrepresentsarectangulargarden.Theshadedregionsareplantedinflowers,andtheunshadedregionisawalk2feetwide.Allanglesarerightangles.
Thesumoftheareasofthe2,800squarefeet
shadedregions
例3:
Themapshowstheonlyroadsthatconnectthefourtownsandshowsthedistancealongeachroad.
TheroaddistancebetweenAustenandSeburg
TheroaddistancebetweenCoaltownandWoodland
例4:
Howmanypositiveintegerslessthan20areequaltothesumofapositivemultipleof3andapositivemultipleof4?
(A)Two(B)Five(C)Seven(D)Ten(E)Nineteen
例5:
Whichofthefollowingsymbolsshouldbesubstitutedfor
tomakebothofthestatementstrueforallintegersnsuchthat-2 (A)≤(B)<(C)=(D)>(E)≥ 4-n 6 4-n 5 例6: Inasoccerleague,Iftherewere10teamsandeachteamplayedeachoftheotherteams16times,howmanygamesdideachteamplay? (A)144(B)140(C)134(D)125(E)106 例7: (NOTE: DRAWNTOSCALE) POPULATIONOFTHEU.S.AGE55ANDOVER 1984ANDPROJECTIONSFOR1995 INCOMEDISTRIBUTIONFORPOPULATION OFTHEU.S.AGE55ANDOVER,1984 In1984medianincomeforapersoninthe55~64agecategorywasinwhichofthefollowingintervals? (A)lessthan$10,000(B)$10,000~$19,999(C)$20,000~$24,999(D)$25,000~$34,999(E)$35,000~$49,999 例8: Asampleofemployeesweretastedondata-entryskillsforonehour,andthenumberoferrors(x)theymadeandthepercentofemployees(p)makingxerrorswererecordedasfollows. Numberoferrorx 0 1 2 3 4 5 6ormore PercentofemployeesP 2% 5% 10% 24% 14% 20% 22% whatwasthemediannumberoferrorsinthesample? (A)3(B)3.5(C)4(D)4.5 (E)Itcannotbedeterminedfromtheinformationgiven. 例9: d=7.56872andDisthedecimalexpressionfordroundedtothenearestthousandth. ThenumberofdecimalplacewheredandDdiffer 4 例10: Inacertaincountry,apersonisbornevery3secondsandapersondiesevery10seconds.Therefore,thebirthanddeathratesaccountforapopulationgrowthrateofonepersonevery 例11: Ofthepositiveintegersthataremultiplesof30andarelessthanorequalto360,whatfractionaremultiplesof12? (A)1/6(B)1/5(C)1/3(D)2/5(E)1/2 8inches 例12: ThefigureshowsalargesquareformedbyfittingthreeL-shapedtilesandonesmallsquaretiletogether.Ifarectangularfloor10feetby12feetistobetiledinlargesquaresofthisdesign,howmanyL-shapedtileswillbeneeded? (A)810(B)405(C)270(D)135(E)45 8inches 例13: Thedailyrateforahotelroomthatsleeps4peopleis$39foronepersonandxdollarsforeachadditionalperson.If3peopletaketheroomforonedayandeachpays$21fortheroom,whatisthevalueofx? (A)6(B)8(C)12(D)13(E)24 例14: Apositiveintegerwithexactlytwodifferentdivisorsgreaterthan1mustbe (A)aprime(B)aneveninteger(C)amultipleof3 (D)thesquareofaprime(E)thesquareofanoddinteger 例15: x>z,y>zx+yz 例16: x>yandxy≠0(x+y)/x(x+y)/y 例17: 2AF=AB=BD=DE=AE ThesumoftheareaoftriangularregionABFandareaoftriangularregionCDE TheareaofrectangularregionBCEF 例18: Eachofthefollowingnumbershastwodigitsblottedout.Whichofthenumberscouldbethenumberofhoursinxdays,wherexisaninteger? (A)25 06(B)50 26(C)56 02(D)62 50(E)65 20 例19: Thereare1200representstoapoll,eachfavoringtheirpreferenceforcandidatesA,B,andC.54%favoredA,48%favoredB,and42%favoredC,andthereis30%favoredbothAandB.What’sthelargestpossiblenumberofrepresentsfavoringc,butnotC&B,norC&A? (A)25%(B)30%(C)28%(D)38%(E)40% 例20: Outof100ladiesattendingthechurchfete,85hadawhitehandbag;75hadblackshoes;60carriedanumbrella;90worearing,Howmanyladiesmusthavehadallfouritems? (A)15(B)35(C)5(D)10(E)25 例21: Inaninsurancecompany,eachpolicyhasapaperrecordandanelectricrecord.Forthosepolicieshavingincorrectpaperrecord,60%alsohavingincorrectelectricrecord;Forthosepolicieshavingincorrectelectricrecord,75%alsohavingincorrectpaperrecord.3%ofallpolicieshavebothincorrectpaperandincorrectelectricrecord.Ifwerandomlypickoutonepolicy,what’stheprobabilitythattheonehavingbothcorrectpaperandcorrectelectricrecord? (A)0.80(B)0.94(C)0.75(D)0.88(E)0.92 ak 100 200 300 400 500 pk 0.10 0.25 0.20 0.25 0.20 例22: Ifinanexperimenttheprobabilitiesofobtainingthevaluesa1,a2,a3,a4,a5arep1,p2,p3,p4,p5,respectively,thentheexpectedvalueisdefinedasa1p1+a2p2+a3p3+a4p4+a5p5.Forthevaluesandtheircorrespondingprobabilitiesinthetableabove,whatistheexpectedvalue? (A)350(B)320(C)300(D)270(E)250 例23: Thestandarddeviationofthesamplemeasurements0,2,4,6,and8 Thestandarddeviationofthesamplemeasurements1,3,5,7,and9 例24: Whatisthetotalnumberofdifferent5-digitnumbersthatcontainallofthedigits2,3,4,7and9andinwhichnoneoftheevendigitsoccurnexttoeachother? (A)72(B)100(C)120(D)60(E)48 例25: Wateristobepouredatarateof2.5gallonsperminuteintoa500-gallontankthatinitiallycontains50gallonsofwater. Thepercentofthetank'scapacitythatwillbe filled1hourafterwaterbeginstobepouredin 60percent 例26: Inthefigure,ifx,y,andzareintegerssuchthatx (A)59and91(B)69and135(C)91and178(D)120and135(E)120and178 例27: Thefigureshowsthedimensionsofrectangularboxthatistobecompletelywrappedwithpaper.Ifasinglesheetofpaperistobeusedwithoutpatching,thenthedimensionsofthepapercouldbe (A)17inby25in(B)21inby24in(C)24inby12in (D)24inby14in(E)26inby14in 例28: Inthetable,whatistheleastnumberoftableentriesthatareneededtoshowthemileagebetweeneachcityandeachoftheotherfivecities? (A)15(B)21(C)25(D)30(E)36 例29: Astorecurrentlychargesthesamepriceforeachtowelthatitsells.Ifthecurrentpriceofeachtowelwastobeincreasedby$1,10fewerofthetowelscouldbeboughtfor$120,excludingsalestax.Whatisthecurrentpriceofeachtowel? (A)$1(B)$2(C)$3(D)$4(E)$12 GRE数学常用符号及术语 一.数学中常用符号 +: plus X: multiply -: subtract ÷: divide V~: square root |...|: absolute value =: is equal to =/=: is not equal to >: is greater than <: is less than //: is parallel to _|_: is perpendicular to >=: is greater than or equal to (或 no less than) <=: is less than or equal to (或no more than) 二.表达相应数目的前缀 1: uni-,mono- 2: bi-,du-,di- 3: tri-,ter-, 4: tetra-,quad-, 5: penta-,quint, 6: hex-,sex-, 7: sept-,hapta-, 8: oct, 9: enn-, 10: dec-,deka-, 三.数学中常用单词术语 abscissa 横坐标 absolutevalue 绝对值 acuteangle 锐角 adjacentangle 邻角 addition 加 algebra 代数 altitude 高 anglebisector 角平分线 arc 弧 area 面积 arithmeticmean 算术平均值(总和除以总数) arithmeticprogression 等差数列(等差级数) arm 直角三角形的股 at 总计(乘法) average 平均值 base 底 becontainedin 位于...上 bisect 平分 center 圆心 chord 弦 circle 圆形 circumference 圆周长 circumscribe 外切,外接 clockwise 顺时针方向 closestapproximation 最相近似的 combination 组合 commondivisor 公约数,公因子 commonfactor 公因子 complementaryangles 余角(二角和为90度) Compositenumber 合数(可被除1及本身以外其它的数整除) concentriccircle 同心圆 cone 圆锥(体积=1/3*∏*r*r*h) congruent 全等的 consecutiveinteger 连续的整数 coordinate 坐标的 cost 成本 counterclockwise 逆时针方向 cube 1.立方数 2.立方体(体积=a*a*a 表面积=6*a*a) cylinder 圆柱体 decagon 十边形 decimal 小数 decimalpoint 小数点 decreased 减少 decreaseto 减少到 decreaseby 减少了 degree 角度 define 1.定义2.化简 denominator 分母 de
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