2025年GRE数学真题试卷

2025年GRE数学真题试卷考试时间：______分钟总分：______分姓名：______Section1:QuantitativeReasoningDirections:ForeachQuantitativeReasoningquestion,indicatethebestanswer,usingthedirectionsprovided.Allnumbersusedarerealnumbers.Question1:Ifarectanglehasaperimeterof30inchesandawidthof5inches,whatisitsareainsquareinches?A.75B.100C.150D.200E.250Question2:Thesumoffourconsecutiveevenintegersis184.Whatisthelargestoftheseintegers?A.44B.46C.48D.50E.52Question3:If$x=-3$,whatisthevalueof$x^2-6x+9$?A.0B.6C.9D.18E.27Question4:Astoreoffersadiscountof20%onallitems.Ifashirtoriginallycosts$d$dollars,howmuchwillacustomerpayfortheshirt?A.$0.2d$B.$0.8d$C.$d-0.2$D.$d+0.2d$E.$1.2d$Question5:Inatriangle,thelengthsoftwosidesare8cmand15cm.Whichofthefollowingcouldbethelengthofthethirdside?I.5cmII.23cmIII.28cmA.IonlyB.IIonlyC.IandIIonlyD.IandIIIonlyE.IIandIIIonlyQuestion6:If$a=\frac{3}{4}$and$b=\frac{2}{5}$,whatisthevalueof$a-b$?A.$\frac{7}{20}$B.$\frac{3}{10}$C.$\frac{1}{2}$D.$\frac{7}{10}$E.$\frac{17}{20}$Question7:Abagcontains5redmarbles,8bluemarbles,and7greenmarbles.Ifamarbleisrandomlyselectedfromthebag,whatistheprobabilityofselectingabluemarble?A.$\frac{8}{20}$B.$\frac{8}{21}$C.$\frac{7}{20}$D.$\frac{3}{7}$E.$\frac{13}{20}$Question8:Iftheaverage(arithmeticmean)offivenumbersis10,whatisthesumofthefivenumbers?A.5B.10C.50D.100E.500Question9:Atraintravelsataconstantspeedof60milesperhour.Howfarwillittravelin3.5hours?A.20milesB.60milesC.140milesD.210milesE.420milesQuestion10:If$y=3x^2-2x+5$,whatisthevalueof$y$when$x=-2$?A.-1B.11C.21D.25E.27Question11:Whichofthefollowingisafactorof$x^2-4x-5$?A.xB.-xC.1D.-1E.5Question12:Acirclehasaradiusof7cm.Whatistheapproximatecircumferenceofthecircleincentimeters?(Use$\pi\approx\frac{22}{7}$)A.44B.56C.77D.88E.154Question13:If$|x-5|=3$,whatisthevalueof$x$?A.2B.8C.-2D.-8E.2or8Question14:Aboxcontains12lightbulbs,ofwhich3aredefective.Iftwobulbsarerandomlyselectedfromtheboxwithoutreplacement,whatistheprobabilitythatbothbulbsaredefective?A.$\frac{1}{11}$B.$\frac{3}{22}$C.$\frac{1}{4}$D.$\frac{5}{12}$E.$\frac{9}{44}$Question15:Iftheslopeofalineis$\frac{3}{4}$andthelinepassesthroughthepoint(2,5),whatistheequationofthelineinslope-interceptform($y=mx+b$)?A.$y=\frac{3}{4}x+\frac{11}{2}$B.$y=\frac{3}{4}x+2$C.$y=\frac{3}{4}x-1$D.$y=\frac{4}{3}x+2$E.$y=\frac{4}{3}x-1$Question16:If$a>0$and$b<0$,whichofthefollowingmustbetrue?I.$a+b>0$II.$ab>0$III.$\frac{a}{b}<0$A.IonlyB.IIonlyC.IandIIIonlyD.IIandIIIonlyE.I,II,andIIIQuestion17:Thenumber0.0001234iswhatpercentof0.01234?A.0.1%B.1%C.10%D.100%E.1000%Question18:Ifaspherehasavolumeof36$\pi$cubicinches,whatisitsradiusininches?A.3B.4C.6D.9E.12Question19:Inacertainsequence,thefirsttermis2,andeachsubsequenttermisobtainedbymultiplyingtheprevioustermby3andthensubtracting1.Whatisthefifthtermofthesequence?A.55B.58C.59D.60E.62Question20:AcartravelsfromCityAtoCityBatanaveragespeedof50milesperhourandreturnsfromCityBtoCityAatanaveragespeedof60milesperhour.Whatistheaveragespeedfortheentireroundtrip,inmilesperhour?A.55B.55.5C.56D.57.5E.58Section2:QuantitativeReasoningDirections:ForeachQuantitativeReasoningquestion,indicatethebestanswer,usingthedirectionsprovided.Allnumbersusedarerealnumbers.Question21:Iftheratioofcatstodogsinapetstoreis3:5,andthereare24cats,howmanydogsarethereinthestore?A.30B.32C.40D.48E.80Question22:ThecoordinatesofpointPare(4,-3).WhatisthedistancefrompointPtotheorigin(0,0)?A.3B.4C.5D.7E.9Question23:If$3x-7=11$,whatisthevalueof$2x+5$?A.10B.12C.13D.14E.15Question24:Acubehasasurfaceareaof54squareinches.Whatisthevolumeofthecubeincubicinches?A.27B.36C.42D.64E.81Question25:If$x^2-9=0$,whatisthesumofthesolutionsfor$x$?A.0B.3C.6D.-9E.-18Question26:Agrocerystoresold15applesfor$d$dollars.Atthisrate,howmanydollarswouldthestorechargefor25apples?A.$\frac{15}{25}d$B.$\frac{25}{15}d$C.$\frac{15d}{25}$D.$15\times25d$E.$d\times\frac{15}{25}$Question27:Inarighttriangle,thetwolegsare6inchesand8incheslong.Whatisthelengthofthehypotenuseininches?A.10B.12C.14D.28E.48Question28:If$a=\frac{1}{3}$and$b=\frac{1}{4}$,whatisthevalueof$a^2+b^2$?A.$\frac{1}{7}$B.$\frac{5}{12}$C.$\frac{25}{49}$D.$\frac{5}{18}$E.$\frac{25}{48}$Question29:Abagcontains10whiteballsand6blackballs.Ifaballisrandomlyselectedandnotreplaced,whatistheprobabilityofselectingawhiteballontheseconddraw?A.$\frac{10}{16}$B.$\frac{6}{16}$C.$\frac{10}{15}$D.$\frac{6}{15}$E.$\frac{1}{3}$Question30:Theaverage(arithmeticmean)scoreof5studentsis80.Ifonestudent'sscoreisremoved,theaveragescoreoftheremainingstudentsis78.Whatwasthescoreoftheremovedstudent?A.60B.65C.70D.75E.80Question31:IfthecoordinatesofpointAare(3,2)andthecoordinatesofpointBare(7,8),whatistheslopeofthelinepassingthroughpointsAandB?A.$\frac{3}{4}$B.$\frac{4}{3}$C.1D.-1E.-$\frac{4}{3}$Question32:Arectangularsolidhasalengthof6cm,awidthof4cm,andaheightof5cm.Whatisthetotalsurfaceareaofthesolidinsquarecentimeters?A.76B.84C.90D.96E.100Question33:If$x^2-7x+10=0$,whichofthefollowingisasolutionfor$x$?A.2B.3C.5D.7E.10Question34:Thediameterofacircleis12cm.Whatistheareaofthecircleinsquarecentimeters?(Use$\pi\approx\frac{22}{7}$)A.36$\pi$B.44$\pi$C.48$\pi$D.72$\pi$E.96$\pi$Question35:If$|2x-5|=1$,whatisthevalueof$x$?A.2B.3C.4D.3or4E.2or3Question36:Ateamwon60%ofitsgames.Iftheteamplayed40games,howmanygamesdidtheteamwin?A.16B.20C.24D.30E.34Question37:Iftheslopeofalineis-2andthelinepassesthroughthepoint(1,4),whatistheequationofthelineinpoint-slopeform($y-y_1=m(x-x_1)$)?A.$y-4=-2(x-1)$B.$y-4=2(x-1)$C.$y-1=-2(x-4)$D.$y-1=2(x-4)$E.$y-4=-2(x+1)$Question38:If$a$and$b$arepositiveintegersand$a^2+b^2=25$,whichofthefollowingcouldbethevalueof$a+b$?A.5B.7C.9D.10E.11Question39:Amixturecontains20%acidand80%water.If30litersofwaterareaddedtothemixture,theresultingmixturecontains15%acid.Howmanylitersoftheoriginalmixturewerethere?A.20B.30C.40D.50E.60Question40:If$f(x)=2x^3-3x^2+4$,whatisthevalueof$f(-1)$?A.3B.5C.-1D.-5E.-3试卷答案Section1:Question1:C解析：矩形周长=2*(长+宽)，所以长=(30/2)-5=10inches。面积=长*宽=10*5=50squareinches。选项C150是错误的，可能是计算错误。Question2:E解析：设四个连续偶数为x,x+2,x+4,x+6。和为x+(x+2)+(x+4)+(x+6)=4x+12=184。解方程4x=172，得x=43。所以这四个数是43,45,47,49。最大的数是49。选项E52是错误的，可能是计算错误。Question3:C解析：代入x=-3，计算(-3)^2-6*(-3)+9=9+18+9=36。选项C9是错误的，可能是计算错误。Question4:B解析：折扣后价格=原价*(1-折扣率)=d*(1-0.2)=0.8d。Question5:C解析：三角形两边之和大于第三边，两边之差小于第三边。8+15=23>第三边，15-8=7<第三边。所以第三边长度范围是(7,23)。选项I5不在此范围内，选项II23在范围内，选项III28不在此范围内。只有I和II可能。Question6:E解析：a-b=3/4-2/5=(15-8)/20=7/20。选项E17/20是错误的，可能是计算错误。Question7:B解析：蓝球概率=蓝球数/总球数=8/(5+8+7)=8/21。Question8:C解析：平均数=总和/数量，所以总和=平均数*数量=10*5=50。Question9:D解析：距离=速度*时间=60miles/hour*3.5hours=210miles。Question10:E解析：代入x=-2，计算3*(-2)^2-2*(-2)+5=3*4+4+5=12+4+5=21。选项E27是错误的，可能是计算错误。Question11:E解析：因式分解x^2-4x-5=(x-5)(x+1)。所以因子是5。Question12:C解析：圆周长=2*π*半径=2*(22/7)*7=44cm。选项C77是错误的，可能是计算错误。Question13:E解析：|x-5|=3表示x-5=3或x-5=-3。解得x=8或x=2。Question14:A解析：第一次抽到defect的概率=3/12。第二次抽到defect且第一次抽到defect的概率=(3/12)*(2/11)=6/132=1/11。Question15:A解析：点斜式方程为y-y1=m(x-x1)。代入m=3/4,(x1,y1)=(2,5)，得y-5=(3/4)(x-2)。整理得y-5=(3/4)x-(3/2)，即y=(3/4)x-(3/2)+5=(3/4)x+(10/2-3/2)=(3/4)x+7/2=(3/4)x+11/2。选项A(11/2)是正确的。Question16:D解析：I.a+b>0。因为a>0,b<0，但|a|可能大于|b|，所以a+b可能小于0。此选项不必须为真。II.ab>0。a>0,b<0，所以ab<0。此选项不必须为真。III.a/b<0。a>0,b<0，所以a/b>0。此选项不必须为真。因此，没有选项必须为真。Question17:B解析：0.0001234/0.01234=1234/12340=1/10=0.1。所以百分比是0.1*100%=10%。Question18:B解析：球体积=(4/3)*π*r^3。36π=(4/3)*π*r^3。消去π，得36=(4/3)*r^3。乘以3/4，得27=r^3。所以r=3inches。Question19:C解析：第一项a1=2。第二项a2=2*3-1=5。第三项a3=5*3-1=14。第四项a4=14*3-1=41。第五项a5=41*3-1=123-1=122。选项C59是错误的，可能是计算错误。Question20:C解析：总距离=2*(50*60)/(50+60)=2*3000/110=6000/110=600/11≈54.545...milesperhour。最接近的选项是C56。Section2:Question21:C解析：猫狗比例3:5，表示猫数/狗数=3/5。猫数=24，所以24/狗数=3/5。狗数=(24*5)/3=80/3=40。Question22:C解析：距离=√((x2-x1)^2+(y2-y1)^2)=√((7-4)^2+(8-(-3))^2)=√(3^2+11^2)=√(9+121)=√130。√130≈11.4。选项C5是错误的，可能是计算错误。Question23:D解析：3x-7=11。3x=18。x=6。2x+5=2*6+5=12+5=17。选项D14是错误的，可能是计算错误。Question24:A解析：立方体表面积=6*(6^2)=6*36=216squareinches。选项A27是错误的，可能是计算错误。Question25:C解析：因式分解x^2-7x+10=(x-2)(x-5)=0。解得x=2或x=5。和为2+5=7。Question26:B解析：15applescostddollars，所以1applecostsd/15dollars。25applescost25*(d/15)=(25/15)d=(5/3)d。选项B(25/15)d是正确的。Question27:A解析：勾股定理a^2+b^2=c^2。6^2+8^2=c^2。36+64=c^2。100=c^2。c=10inches。Question28:D解析：a^2+b^2=(1/3)^2+(1/4)^2=1/9+1/16=(16+9)/144=25/144。选项D5/18是错误的，可能是计算错误。Question29:C解析：方法一：总球数=10+6=16。第一次选到白球的概率=10/16。如果第一次选到白球，剩下15个球（9白6黑），第二次选到白球的概率=9/15。如果第一次选到黑球，剩下15个球（10白5黑），第二次选到白球的概率=10/15。总概率=(10/16)*(9/15)+(6/16)*(10/15)=(90+60)/240=150/240=5/8。方法二：第二次选到白球，考虑两种情况：第一次选到白球或第一次选到黑球。总概率=第一次白*(第二次白)+第一次黑*(第二次白)=(10/16)*(9/15)+(6/16)*(10/15)=5/8。选项C5/15是错误的，可能是计算错误。Question30:B解析：5学生的总分数=80*5=400。剩下4学生的总分数=78*4=312。被移除的学生的分数=400-312=88。选项B65是错误的，可能是计算错误。Question31:B解析：斜率m=(y2-y1)/(x2-x1)=(8-2)/(7-3)=6/4=3/2=1.5。选项B