2026年GRE考試數(shù)學部分專項試題及答案考試時長：120分鐘滿分：100分班級：__________姓名：__________學號：__________得分：__________試卷名稱：2026年GRE考試數(shù)學部分專項試題及答案考核對象：準備參加GRE考試的考生題型分值分布：-判斷題（總共10題，每題2分）總分20分-單選題（總共10題，每題2分）總分20分-多選題（總共10題，每題2分）總分20分-案例分析（總共3題，每題6分）總分18分-論述題（總共2題，每題11分）總分22分總分：100分---一、判斷題（每題2分，共20分）1.Thesetofintegersisclosedunderdivision.2.Ifafunctioniscontinuousonaclosedinterval,itmustattainitsmaximumandminimumvaluesonthatinterval.3.Theequation\(x^2+y^2=1\)representsacirclecenteredattheoriginwithradius1.4.Thederivativeof\(f(x)=x^3\)is\(f'(x)=3x^2\).5.Thesumoftheinterioranglesofatriangleisalways180degrees.6.Asquarematrixwithalleigenvaluesequalto1istheidentitymatrix.7.Theprobabilityofrollingasumof7withtwofairsix-sideddiceis\(\frac{1}{6}\).8.Theareaofatrapezoidcanbecalculatedusingtheformula\(\frac{1}{2}(b_1+b_2)h\),where\(b_1\)and\(b_2\)arethelengthsoftheparallelsides.9.Themedianofadatasetisalwaysequaltoitsmean.10.Thegraphof\(y=\ln(x)\)isconcavedownforall\(x>0\).二、單選題（每題2分，共20分）1.Whatisthevalueof\(\frac{3}{4}+\frac{2}{3}\)?A.\(\frac{17}{12}\)B.\(\frac{5}{7}\)C.\(\frac{11}{12}\)D.\(\frac{7}{12}\)2.If\(f(x)=2x-5\),whatis\(f(3)\)?A.1B.4C.6D.73.Theslopeofthelinepassingthroughthepoints\((1,2)\)and\((4,8)\)is:A.2B.3C.4D.54.Whatisthevalueof\(\sqrt{49}\)?A.7B.-7C.49D.\(-49\)5.Theequation\(2x+3y=6\)canberewritteninslope-interceptformas:A.\(y=\frac{2}{3}x+2\)B.\(y=-\frac{2}{3}x+2\)C.\(y=3x+2\)D.\(y=-3x+2\)6.Theproductof\(3i\)and\(-2i\)is:A.6B.-6C.6iD.-6i7.Thevolumeofacubewithsidelength4is:A.16B.24C.64D.968.Thesolutiontotheinequality\(x-3>5\)is:A.\(x>8\)B.\(x<8\)C.\(x>2\)D.\(x<2\)9.Themidpointofthesegmentjoining\((2,3)\)and\((6,7)\)is:A.\((4,5)\)B.\((3,5)\)C.\((5,4)\)D.\((2,6)\)10.Theset\(\{1,2,3,4\}\)hashowmanysubsets?A.4B.8C.16D.32三、多選題（每題2分，共20分）1.Whichofthefollowingareprimenumbers?A.2B.3C.4D.52.Thegraphof\(y=x^2\)is:A.Symmetricaboutthey-axisB.Symmetricaboutthex-axisC.ConvexupwardD.Convexdownward3.Thesolutionstotheequation\(x^2-4=0\)are:A.2B.-2C.4D.-44.Whichofthefollowingfunctionsarecontinuouseverywhere?A.\(f(x)=x^3\)B.\(f(x)=\frac{1}{x}\)C.\(f(x)=\sqrt{x}\)D.\(f(x)=\sin(x)\)5.Thepropertiesofaparallelograminclude:A.OppositesidesareparallelB.OppositesidesareequalinlengthC.OppositeanglesareequalD.Diagonalsbisecteachother6.Thefollowingareexamplesoflinearequations:A.\(y=2x+1\)B.\(3x-4y=7\)C.\(x^2+y=5\)D.\(y=\frac{1}{2}x-3\)7.Thefollowingarepropertiesoflogarithms:A.\(\log(a\cdotb)=\log(a)+\log(b)\)B.\(\log(a^b)=b\log(a)\)C.\(\log(a)-\log(b)=\log\left(\frac{a}\right)\)D.\(\log(1)=0\)8.Thefollowingaretypesoftrianglesbasedonangles:A.AcutetriangleB.RighttriangleC.ObtusetriangleD.Equilateraltriangle9.Thefollowingarepropertiesofmatrices:A.TheproductoftwomatricesiscommutativeB.ThedeterminantofatriangularmatrixistheproductofitsdiagonalentriesC.Theinverseofamatrixexistsifandonlyifitsdeterminantisnon-zeroD.Thetransposeofamatrixisobtainedbyswappingitsrowsandcolumns10.Thefollowingaremeasuresofcentraltendency:A.MeanB.MedianC.ModeD.Variance四、案例分析（每題6分，共18分）1.Aboxcontains5redballs,3blueballs,and2greenballs.Iftwoballsaredrawnatrandomwithoutreplacement,whatistheprobabilitythatbothballsarered?2.Theaveragescoreofaclassof30studentsis75.Iftheaveragescoreof10studentswhoscored70is72,whatistheaveragescoreoftheremaining20students?3.Acompanyproduces1000unitsofaproductatacostof$50,000.Ifthesellingpriceperunitis$100,whatistheprofitifthecompanysells800units?五、論述題（每題11分，共22分）1.Explaintheconceptofafunctionandprovideanexampleofareal-worldscenariowhereafunctioncanbeusedtomodelarelationship.2.Discusstheimportanceofstatisticalmeasuressuchasmean,median,andmodeindataanalysis.Provideanexampleofhowthesemeasurescanbeusedtointerpretadataset.---標準答案及解析一、判斷題1.False.Thesetofintegersisnotclosedunderdivisionbecausedividingtwointegersmayresultinanon-integer.2.True.BytheExtremeValueTheorem,acontinuousfunctiononaclosedintervalattainsitsmaximumandminimumvalues.3.True.Theequation\(x^2+y^2=1\)representsacirclecenteredattheoriginwithradius1.4.True.Thederivativeof\(f(x)=x^3\)is\(f'(x)=3x^2\).5.True.Thesumoftheinterioranglesofatriangleisalways180degrees.6.False.Asquarematrixwithalleigenvaluesequalto1isnotnecessarilytheidentitymatrix;itcouldbeanyscalarmultipleoftheidentitymatrix.7.False.Theprobabilityofrollingasumof7withtwofairsix-sideddiceis\(\frac{6}{36}=\frac{1}{6}\).8.True.Theareaofatrapezoidcanbecalculatedusingtheformula\(\frac{1}{2}(b_1+b_2)h\).9.False.Themedianisnotalwaysequaltothemean;theyareequalonlyinsymmetricdistributions.10.False.Thegraphof\(y=\ln(x)\)isconcavedownwardforall\(x>0\).二、單選題1.A.\(\frac{3}{4}+\frac{2}{3}=\frac{9}{12}+\frac{8}{12}=\frac{17}{12}\)2.D.\(f(3)=2(3)-5=6-5=7\)3.B.Theslopeis\(\frac{8-2}{4-1}=\frac{6}{3}=2\)4.A.\(\sqrt{49}=7\)5.A.\(2x+3y=6\implies3y=-2x+6\impliesy=\frac{-2}{3}x+2\)6.A.\(3i\cdot(-2i)=-6i^2=-6(-1)=6\)7.C.Thevolumeis\(4^3=64\)8.A.\(x-3>5\impliesx>8\)9.A.Themidpointis\(\left(\frac{2+6}{2},\frac{3+7}{2}\right)=(4,5)\)10.C.Thesethas\(2^4=16\)subsets.三、多選題1.A,B,D.2,3,and5areprimenumbers.2.A,C.Thegraphissymmetricaboutthey-axisandconvexupward.3.A,B.Thesolutionsare\(x=2\)and\(x=-2\).4.A,C,D.\(f(x)=x^3\),\(f(x)=\sqrt{x}\),and\(f(x)=\sin(x)\)arecontinuouseverywhere.5.A,B,C,D.Allpropertiesaretrueforaparallelogram.6.A,B,D.\(y=2x+1\),\(3x-4y=7\),and\(y=\frac{1}{2}x-3\)arelinearequations.7.A,B,C,D.Allpropertiesaretrueforlogarithms.8.A,B,C.Acute,right,andobtusetrianglesarebasedonangles.9.B,C,D.Thedeterminantofatriangularmatrixistheproductofitsdiagonalentries,theinverseexistsifthedeterminantisnon-zero,andthetransposeswapsrowsandcolumns.10.A,B,C.Mean,median,andmodearemeasuresofcentraltendency.四、案例分析1.Theprobabilityofdrawingtworedballsis\(\frac{5}{10}\cdot\frac{4}{9}=\frac{20}{90}=\frac{2}{9}\).2.Thetotalscoreoftheclassis\(30\cdot75=2250\).Thetotalscoreofthe10studentsis\(10\cdot72=720\).Thetotalscoreoftheremaining20studentsis\(2250-720=1530\).Theaveragescoreoftheremainingstudentsis\(\frac{1530}{20}=76.5\).3.Therevenuefromselling800unitsis\(800\cdot100=80,000\).Theprofitis\(80,000-50,000=30,000\).五、論述題1.Afunctionisarelationbetweenasetof