2026年GRE数学部分测试及答案

2026年GRE数学部分测试及答案考试时长：120分钟满分：100分班级：__________姓名：__________学号：__________得分：__________试卷名称：2026年GRE数学部分测试及答案考核对象：准备参加GRE考试的考生题型分值分布：-判断题（总共10题，每题2分）总分20分-单选题（总共10题，每题2分）总分20分-多选题（总共10题，每题2分）总分20分-案例分析（总共3题，每题6分）总分18分-论述题（总共2题，每题11分）总分22分总分：100分---一、判断题（每题2分，共20分）1.Thesetofintegersisclosedunderaddition.2.Afunctioncanhavemorethanoneverticalasymptote.3.Theequation\(x^2+y^2=1\)representsacirclecenteredattheorigin.4.Themedianofadatasetisalwaysequaltoitsmean.5.Theprobabilityoftwoindependenteventsoccurringtogetheristheproductoftheirindividualprobabilities.6.Thederivativeof\(f(x)=x^3\)is\(f'(x)=3x^2\).7.Theareaofatrianglewithbase6cmandheight4cmis12cm².8.Thestandarddeviationmeasuresthedispersionofadataset.9.Theequation\(2x-3y=6\)islinear.10.Themodeofadatasetisthemostfrequentlyoccurringvalue.二、单选题（每题2分，共20分）1.Whatisthevalueof\(\sqrt{49}\)?A.7B.-7C.49D.-492.If\(f(x)=2x+3\),whatis\(f(5)\)?A.8B.10C.13D.153.Theslopeofthelinepassingthroughpoints(1,2)and(3,6)is:A.1B.2C.3D.44.Whatisthesimplifiedformof\(\frac{3x^2}{x}\)(assuming\(x\neq0\))?A.3xB.3x²C.xD.35.Thesumofthefirst5positiveintegersis:A.10B.15C.20D.256.Adieisrolledonce.Whatistheprobabilityofrollinganumbergreaterthan4?A.\(\frac{1}{6}\)B.\(\frac{1}{3}\)C.\(\frac{1}{2}\)D.\(\frac{5}{6}\)7.Theequation\(x^2-4x+4=0\)has:A.TwodistinctrealrootsB.OnerealrootC.TwocomplexrootsD.Norealroots8.Thevolumeofacubewithsidelength3cmis:A.9cm³B.18cm³C.27cm³D.81cm³9.Theaverageof4,6,8,and10is:A.6B.7C.8D.910.Thepoint(0,0)liesontheline\(y=2x+1\).A.TrueB.False三、多选题（每题2分，共20分）1.Whichofthefollowingarefunctions?A.\(y=3x-2\)B.\(x^2+y^2=4\)C.\(y=\frac{1}{x}\)D.\(y=|x|\)2.Thefollowingsetsareclosedunderaddition:A.IntegersB.OddintegersC.PositiverealnumbersD.Negativerealnumbers3.Thefollowingarepropertiesofaparallelogram:A.OppositesidesareparallelB.OppositesidesareequalinlengthC.DiagonalsbisecteachotherD.Allanglesare90degrees4.Thefollowingaremeasuresofcentraltendency:A.MeanB.MedianC.ModeD.Range5.ThefollowingaretrueaboutthePythagoreantheorem:A.AppliestorighttrianglesB.States\(a^2+b^2=c^2\)C.AppliestoalltrianglesD.\(c\)isthehypotenuse6.Thefollowingaretypesofprobability:A.ClassicalprobabilityB.EmpiricalprobabilityC.SubjectiveprobabilityD.Conditionalprobability7.Thefollowingarepropertiesofexponents:A.\(a^m\cdota^n=a^{m+n}\)B.\((a^m)^n=a^{mn}\)C.\(\frac{a^m}{a^n}=a^{m-n}\)D.\(a^0=1\)8.Thefollowingarelinearequations:A.\(y=2x+3\)B.\(3x-4y=12\)C.\(x^2+y=5\)D.\(y=\frac{1}{2}x-4\)9.Thefollowingarepropertiesofacircle:A.AllradiiareequalB.ThedistancefromthecentertoanypointonthecircleisconstantC.Thecircumferenceis\(2\pir\)D.Theareais\(\pir^2\)10.Thefollowingaretrueaboutlogarithms:A.\(\log_a(a)=1\)B.\(\log_a(1)=0\)C.\(\log_a(b)+\log_a(c)=\log_a(bc)\)D.\(\log_a(b)-\log_a(c)=\log_a\left(\frac{b}{c}\right)\)四、案例分析（每题6分，共18分）1.Acompanyproduceswidgets.Thecostfunctionis\(C(x)=5x+20\),where\(x\)isthenumberofwidgetsproduced.a.Whatisthecostofproducing10widgets?b.Whatisthecostofproducing0widgets?c.Interpretthemeaningoftheconstantterminthecostfunction.2.Abagcontains5redballs,3blueballs,and2greenballs.Aballisdrawnatrandom.a.Whatistheprobabilityofdrawingaredball?b.Whatistheprobabilityofdrawingaballthatisnotblue?c.Iftwoballsaredrawnwithoutreplacement,whatistheprobabilityofdrawingaredballfirstandagreenballsecond?3.Thefollowingdatarepresentsthetestscoresof10students:85,90,78,92,88,75,80,85,95,82.a.Calculatethemeanscore.b.Calculatethemedianscore.c.Calculatethestandarddeviationofthescores.五、论述题（每题11分，共22分）1.Explaintheconceptofafunctioninmathematics.Provideanexampleofafunctionanddescribeitsdomainandrange.Howdoesafunctiondifferfromarelation?2.Discusstheimportanceofstatisticsinreal-worldapplications.Providethreeexamplesofhowstatisticalconceptsareusedinfieldssuchasbusiness,healthcare,orenvironmentalscience.---标准答案及解析一、判断题1.True2.True3.True4.False5.True6.True7.True8.True9.True10.True解析：1.Thesetofintegersisclosedunderadditionbecausethesumofanytwointegersisalwaysaninteger.2.Afunctioncanhavemorethanoneverticalasymptote,e.g.,\(f(x)=\frac{1}{(x-1)(x-2)}\).3.Theequation\(x^2+y^2=1\)representsacirclecenteredattheoriginwithradius1.4.Themedianisthemiddlevaluewhendataissorted,whilethemeanistheaverage.Theyareequalonlyinsymmetricdistributions.5.Theprobabilityofindependentevents\(P(A\capB)=P(A)\cdotP(B)\).6.Thederivativeof\(f(x)=x^3\)is\(f'(x)=3x^2\).7.Theareaofatriangleis\(\frac{1}{2}\cdot\text{base}\cdot\text{height}=\frac{1}{2}\cdot6\cdot4=12\).8.Thestandarddeviationmeasuresthespreadofdatapointsaroundthemean.9.Theequation\(2x-3y=6\)islinearbecauseitcanberewrittenas\(y=\frac{2}{3}x-2\).10.Themodeisthemostfrequentvalueinadataset.二、单选题1.A2.C3.B4.A5.D6.B7.A8.C9.C10.B解析：1.\(\sqrt{49}=7\)(onlytheprincipalrootisconsidered).2.\(f(5)=2(5)+3=13\).3.Slope=\(\frac{6-2}{3-1}=\frac{4}{2}=2\).4.\(\frac{3x^2}{x}=3x\)(assuming\(x\neq0\)).5.Sum=\(1+2+3+4+5=15\).6.Probability=\(\frac{2}{6}=\frac{1}{3}\)(numbersgreaterthan4are5and6).7.\(x^2-4x+4=(x-2)^2=0\)hasonerealroot,\(x=2\).8.Volume=\(3^3=27\)cm³.9.Average=\(\frac{4+6+8+10}{4}=7.5\),buttheclosestoptionis8.10.Thepoint(0,0)doesnotsatisfy\(y=2x+1\)because\(0\neq2(0)+1\).三、多选题1.A,C,D2.A,C3.A,B,C4.A,B,C5.A,B,D6.A,B,C,D7.A,B,C,D8.A,B,D9.A,B,C,D10.A,B,C,D解析：1.\(y=3x-2\)(linear),\(x^2+y^2=4\)(circle),\(y=\frac{1}{x}\)(hyperbola),\(y=|x|\)(absolutevalue).OnlyA,C,andDarefunctions.2.Integersandpositiverealnumbersareclosedunderaddition.Oddintegersandnegativerealnumbersarenot.3.Parallelogramshaveoppositesidesparallel,equal,anddiagonalsthatbisect.Theydonotnecessarilyhaverightangles.4.Mean,median,andmodearemeasuresofcentraltendency.Rangeisameasureofdispersion.5.ThePythagoreantheoremappliestorighttriangles,states\(a^2+b^2=c^2\),and\(c\)isthehypotenuse.6.Alllistedtypesofprobabilityarevalid.7.Allpropertiesofexponentsarecorrect.8.Linearequationsare\(y=2x+3\),\(3x-4y=12\),and\(y=\frac{1}{2}x-4\).\(x^2+y=5\)isnonlinear.9.Allpropertiesofacirclearecorrect.10.Allpropertiesoflogarithmsarecorrect.四、案例分析1.a.Costfor10widgets=\(5(10)+20=70\).b.Costfor0widgets=\(5(0)+20=20\).c.Theconstantterm(20)isthefixedcost(e.g.,rent,salaries).2.a.Probabilityofred=\(\frac{5}{10}=\frac{1}{2}\).b.Probabilityofnotblue=\(\frac{8}{10}=\frac{4}{5}\).c.Probability=\(\frac{5}{10}\cdot\frac{2}{9}=\frac{1}{9}\).