近10年广西GRE单元测试难题及答案

近10年广西GRE单元测试难题及答案

一、单项选择题（每题2分，共20分）1.Whichofthefollowingistheclosestapproximationtothevalueof√17+√19?A.7B.8C.9D.10E.112.Ifxandyarepositiveintegerssuchthatx=8y+12,whatisthegreatestcommondivisorofxandy?(1)x=12u,whereuisaninteger.(2)y=12v,wherevisaninteger.A.Statement(1)ALONEissufficient,butstatement(2)aloneisnotsufficient.B.Statement(2)ALONEissufficient,butstatement(1)aloneisnotsufficient.C.BOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEissufficient.D.EACHstatementALONEissufficient.E.Statements(1)and(2)TOGETHERareNOTsufficient.3.Inacertainsequence,thefirsttermis1,andeachtermafterthefirstis1morethanthereciprocaloftheprecedingterm.Whatisthefifthtermofthesequence?A.3/5B.5/8C.8/5D.5/3E.13/84.Ifaandbarepositiveintegersand(2^a)(3^b)=2,592,whatisthevalueofa+b?A.6B.7C.8D.9E.105.Arectangularfloorthatmeasures8metersby10metersistobecoveredwithcarpetsquaresthateachmeasure2metersby2meters.Ifthecarpetsquarescost$12apiece,whatisthetotalcostforthenumberofcarpetsquaresneededtocoverthefloor?A.$200B.$240C.$480D.$960E.$1,9206.If\(x\neq0\),whichofthefollowingisequivalentto\(\frac{x(x^{2})^{3}}{x^{2}}\)?A.\(x^{2}\)B.\(x^{3}\)C.\(x^{4}\)D.\(x^{5}\)E.\(x^{6}\)7.Theaverage(arithmeticmean)of6numbersis8.5.Whenonenumberisdiscarded,theaverageoftheremainingnumbersbecomes7.2.Whatisthediscardednumber?A.7.8B.9.8C.10.0D.12.4E.15.08.Iftheratiooftheareasoftwosquaresis2:1,thentheratiooftheperimetersofthesquaresisA.1:√2B.√2:1C.2:1D.4:1E.8:19.If\(x=\frac{1}{2}\),whichofthefollowinghasthegreatestvalue?A.\(x^{2}\)B.\(2x\)C.\(2-x\)D.\(\frac{2}{x}\)E.\(\frac{1}{x}\)10.Inaclassof30students,12areboys.If6moregirlsjointheclass,whatfractionoftheclasswillbeboys?A.\(\frac{1}{3}\)B.\(\frac{2}{5}\)C.\(\frac{1}{2}\)D.\(\frac{3}{5}\)E.\(\frac{2}{3}\)二、多项选择题（每题2分，共20分）1.Whichofthefollowingareprimenumbers?(Selectallthatapply)A.2B.9C.11D.15E.172.If\(x>0\)and\(y>0\),whichofthefollowingexpressionsarepositive?(Selectallthatapply)A.\(x+y\)B.\(x-y\)C.\(xy\)D.\(\frac{x}{y}\)E.\(x^{2}-y^{2}\)3.Theset\(S=\{2,4,6,8,10\}\).Whichofthefollowingsubsetsof\(S\)haveanaverage(arithmeticmean)greaterthan5?(Selectallthatapply)A.\(\{2,4,6\}\)B.\(\{4,6,8\}\)C.\(\{6,8,10\}\)D.\(\{2,8,10\}\)E.\(\{4,8,10\}\)4.Whichofthefollowingequationsrepresentalinethatpassesthroughthepoint\((2,3)\)?(Selectallthatapply)A.\(y=x+1\)B.\(y=2x-1\)C.\(y=3\)D.\(x=2\)E.\(y=-x+5\)5.If\(a\)and\(b\)areintegers,and\(ab=24\),whichofthefollowingcouldbethevalueof\(a+b\)?(Selectallthatapply)A.10B.11C.13D.25E.-106.Thefollowingarethescoresofastudentinfivetests:70,80,90,100,\(x\).Whichofthefollowingvaluesof\(x\)wouldmakethemedianofthescoresequalto85?(Selectallthatapply)A.82B.85C.88D.90E.927.Whichofthefollowingaresolutionstotheinequality\(|x-3|<2\)?(Selectallthatapply)A.\(x=1\)B.\(x=2\)C.\(x=3\)D.\(x=4\)E.\(x=5\)8.Foraright-trianglewithlegsoflengths\(a\)and\(b\)andhypotenuseoflength\(c\),whichofthefollowingrelationshipshold?(Selectallthatapply)A.\(a^{2}+b^{2}=c^{2}\)B.\(a+b>c\)C.\(a^{2}+c^{2}=b^{2}\)(when\(b\)isthehypotenuse)D.\(c-a<b\)E.\(c^{2}-b^{2}=a^{2}\)9.Ifafunction\(f(x)=x^{2}+2x-3\),whichofthefollowingvaluesof\(x\)satisfy\(f(x)=0\)?(Selectallthatapply)A.\(x=-3\)B.\(x=-1\)C.\(x=1\)D.\(x=3\)E.\(x=0\)10.Whichofthefollowingstatementsaboutacirclearetrue?(Selectallthatapply)A.Thediameteristwicetheradius.B.Thecircumferenceofacircleis\(2\pir\).C.Theareaofacircleis\(\pir^{2}\).D.Achordisalinesegmentthatpassesthroughthecenterofthecircle.E.Anarcisapartofthecircumferenceofthecircle.三、判断题（每题2分，共20分）1.Thesumoftwooddnumbersisalwaysanoddnumber.(True/False)2.If\(x>y\),then\(x^{2}>y^{2}\).(True/False)3.Atrianglewithsidelengths3,4,and5isaright-triangle.(True/False)4.Thefunction\(y=2x+1\)isalinearfunction.(True/False)5.Thesetofallintegersisasubsetofthesetofallrationalnumbers.(True/False)6.Ifanumberisdivisibleby6,itmustbedivisibleby3.(True/False)7.Theareaofasquarewithsidelength\(s\)is\(4s\).(True/False)8.Theequation\(x^{2}+1=0\)hasrealsolutions.(True/False)9.Iftwolinesareparallel,theirslopesareequal.(True/False)10.Themedianofasetofdataisalwaysoneofthedatapointsintheset.(True/False)四、简答题（每题5分，共20分）1.Explainhowtofindthegreatestcommondivisor(GCD)oftwopositiveintegersusingtheEuclideanalgorithm.Answer:TheEuclideanalgorithmfindstheGCDoftwopositiveintegers\(a\)and\(b\)(\(a>b\))byrepeatedlyapplyingthedivisionalgorithm.Divide\(a\)by\(b\)togetaquotient\(q\)andanon-negativeremainder\(r\)(\(a=bq+r\),\(0\leqr<b\)).Thenreplace\(a\)with\(b\)and\(b\)with\(r\)andrepeatuntil\(r=0\).Thenon-zeroremainderinthelastnon-zerostepistheGCD.2.Whatisthedifferencebetweenapermutationandacombination?Answer:Apermutationisanarrangementofobjectswheretheordermatters.Forexample,arranging3lettersA,B,Cindifferentordersgivesdifferentpermutations.Acombinationisaselectionofobjectswheretheorderdoesnotmatter.Choosing2lettersoutofA,B,Cisacombination,andABisthesameasBAincombinations.3.Howdoyoudetermineifafunctionisone-to-one?Answer:Afunction\(y=f(x)\)isone-to-oneifforevery\(y\)valueintherange,thereisexactlyone\(x\)valueinthedomainthatmapstoit.Algebraically,if\(f(x_1)=f(x_2)\)implies\(x_1=x_2\)forall\(x_1,x_2\)inthedomain.Graphically,itpassesthehorizontallinetest.4.WhatisthePythagoreantheoremanditsconverse?Answer:ThePythagoreantheoremstatesthatinaright-trianglewithlegs\(a\)and\(b\)andhypotenuse\(c\),\(a^{2}+b^{2}=c^{2}\).Itsconversesaysthatif\(a,b,c\)arethesidelengthsofatriangleand\(a^{2}+b^{2}=c^{2}\),thenthetriangleisaright-trianglewiththeright-angleoppositethesideoflength\(c\).五、讨论题（每题5分，共20分）1.Discusstheimportanceofunderstandingprobabilityinreal-lifesituations.Answer:Probabilityhelpsindecision-making.Ininsurance,itassessesriskstosetpremiums.Inweatherforecasting,itpredictsthelikelihoodofevents.Insports,itcanbeusedtoanalyzeteamperformance.Understandingprobabilityallowsustomakemoreinformedchoicesbasedonthelikelihoodofdifferentoutcomes.2.Howcanyouusefunctionstomodelreal-worldphenomena?Answer:Functionscanrepresentrelationshipsbetweenvariablesinreal-worldscenarios.Forexample,alinearfunctioncanmodeltherelationshipbetweendistanceandtimeinaconstant-speedmotion.Aquadraticfunctioncandescribethepathofaprojectile.Byidentifyingvariablesandtheirrelationships,wecancreatefunctionstopredictandanalyzereal-worldsituations.3.Whataretheadvantagesanddisadvantagesofusingstatisticstodrawconclusions?Answer:Advantages:Statisticscansummarizelargeamountsofdata,identifytrends,andmake