ETS官方GRE数学样题.docx
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ETS官方GRE数学样题
【ETS官方】GRE考试改革最新数学样题及解析
GRE®RevisedGeneralTest:
QuantitativeReasoningSampleQuestions
Figures
Thisdocumentincludesfigures,whichappearonscreen.Followingeachfigureonscreenistextdescribingthatfigure.Readersusingvisualpresentationsofthefiguresmaychoosetoskippartsofthetextdescribingthefigurethatbeginwith“Beginskippablefiguredescription”andendwith“Endskippablefiguredescription.”
MathematicalEquationsandExpressions
Thisdocumentincludesmathematicalequationsandexpressions.Someofthemathematicalequationsandexpressionsarepresentedasgraphics.Incaseswhereamathematicalequationorexpressionispresentedasagraphic,averbalpresentationisalsogivenandtheverbalpresentationcomesdirectlyafterthegraphicpresentation.Theverbalpresentationisingreenfonttoassistreadersintellingthetwopresentation-modesapart. Readersusingaudioalonecansafelyignorethegraphicalpresentations,andreadersusingvisualpresentationsmayignoretheverbalpresentations.
Introduction
TherevisedQuantitativeReasoningsectioncontainsfourtypesofquestions:
Multiple-choiceQuestions—SelectOneAnswerChoice
Multiple-choiceQuestions—SelectOneorMoreAnswerChoices
NumericEntryQuestions
QuantitativeComparisonQuestions
EachquestionappearseitherindependentlyasadiscretequestionoraspartofasetofquestionscalledaDataInterpretationset.AllofthequestionsinaDataInterpretationsetarebasedonthesamedatapresentedintables,graphs,orotherdisplaysofdata.Belowaredescriptions,directions,andsamplesofeachtypeofquestion.
Multiple-ChoiceQuestions—SelectOneAnswerChoice
Thesequestionsaremultiple-choicequestionsthataskyoutoselectonlyoneanswerchoicefromalistoffivechoices.
SampleQuestions
Directions:
Selectasingleanswerchoice.
Samplequestion1belowisbasedonfigure1.
Figure1
Beginskippablefiguredescription.
Figure1isacirclewithcenterC.Twodiametersofthecirclearedrawn,dividingthecircleinto4sectors.Twononadjacentsectorsareshaded,andthecentralangleofoneoftheunshadedsectorsmeasures160degrees.
Endskippablefiguredescription.
1. Figure1aboveshowsacirclewithcenterCandradius6.Whatisthesumoftheareasofthetwoshadedregions?
A.
7.5pi
B.
6pi
C.
4.5pi
D.
4pi
E.
3pi
Answer:
D(
4pi)
Samplequestion2belowisbasedonfigure2.
Figure2
Beginskippablefiguredescription.
Figure2showsthegraphinthexyplaneofthefunctionfofx=theabsolutevalueof2x,endabsolutevalue,+4. Thereareequallyspacedtickmarksalongthexaxisandalongtheyaxis. Thefirsttickmarktotherightoftheorigin,andthefirsttickmarkabovetheorigin,arebothlabeled1.
ThegraphofthefunctionfisintheshapeoftheletterV. Itisabovethexaxisandissymmetricwithrespecttotheyaxis.
Thelowestpointonthegraphoffisthepoint0comma4ontheyaxis.
Goingleftwardfromthepoint0comma4thegraphoffisalinethatslantsupward,passingthroughthepointnegative2comma8.
Goingrightwardfromthepoint0comma4thegraphoffisalinethatslantsupward,passingthroughthepoint2comma8.
Endskippablefiguredescription.
2. Figure2aboveshowsthegraphofafunctionf,definedby
fofx=theabsolutevalueof2x,endabsolutevalue,+4forallnumbersx.Forwhichofthefollowingfunctionsgdefinedforallnumbersxdoesthegraphofgintersectthegraphoff?
A.
gofx=xminus2
B.
gofx=x+3
C.
gofx=2xminus2
D.
gofx=2x+3
E.
gofx=3xminus2
Answer:
E(
gofx=3xminus2)
Multiple-ChoiceQuestions—SelectOneorMoreAnswerChoices
Thesequestionsaremultiple-choicequestionsthataskyoutoselectoneormoreanswerchoicesfromalistofchoices.Aquestionmayormaynotspecifythenumberofchoicestoselect.
SampleQuestions
Directions:
Selectoneormoreanswerchoicesaccordingtothespecificquestiondirections.
Ifthequestiondoesnotspecifyhowmanyanswerchoicestoselect,selectallthatapply.
Thecorrectanswermaybejustoneofthechoicesormaybeasmanyasallofthechoices,dependingonthequestion.
Nocreditisgivenunlessyouselectallofthecorrectchoicesandnoothers.
Ifthequestionspecifieshowmanyanswerchoicestoselect,selectexactlythatnumberofchoices.
1. EachemployeeofacertaincompanyisineitherDepartmentXorDepartmentY,andtherearemorethantwiceasmanyemployeesinDepartmentXasinDepartmentY.Theaverage(arithmeticmean)salaryis$25,000fortheemployeesinDepartmentXandis$35,000fortheemployeesinDepartmentY.Whichofthefollowingamountscouldbetheaveragesalaryforalloftheemployeesinthecompany?
Indicateallsuchamounts.
A. $26,000
B. $28,000
C. $29,000
D. $30,000
E. $31,000
F. $32,000
G. $34,000
Answer:
A($26,000)andB($28,000)
2. Iff,g,andharepositiveintegers,fisafactorofg,andgisafactorofh,whichofthefollowingstatementsmustbetrue?
Indicateallsuchstatements.
A. fisafactorof
gsquared.
B. fisafactorofgh.
C. fisafactorof
hminusg.
Answer:
A(fisafactorof
gsquared),B (fisafactorofgh.),andC(fisafactorof
hminusg)
NumericEntryQuestions
Questionsofthistypeaskyoueithertoentertheanswerasanintegeroradecimalinasingleanswerboxortoenteritasafractionintwoseparateboxes—oneforthenumeratorandoneforthedenominator.Inthecomputer-administeredtest,thecomputermouseandkeyboardareusedtoentertheanswer.
SampleQuestions
Directions:
Enteryouranswerintheanswerbox(es)belowthequestion.
Equivalentformsofthecorrectanswer,suchas2.5and2.50,areallcorrect.Fractionsdonotneedtobereducedtolowestterms.
Entertheexactanswerunlessthequestionasksyoutoroundyouranswer.
1. If
x=10tothepowernegative1,whatisthevalueof
openparenthesis,x+thefraction1overx,closeparenthesis,times,openparenthesis,1overx,closeparenthesis?
AnswerBox
Answer:
101
2. Auniversityadmitted100studentswhotransferredfromotherinstitutions.Ofthesestudents,34transferredfromtwo-yearcommunitycolleges,25transferredfromprivatefour-yearinstitutions,andtheresttransferredfrompublicfour-yearinstitutions.Iftwodifferentstudentsaretobeselectedatrandomfromthe100students,whatistheprobabilitythatbothstudentsselectedwillbestudentswhotransferredfromtwo-yearcommunitycolleges?
Giveyouranswerasafraction.
Fractionanswerboxes
Answer:
17over150(oranyequivalentfraction).
QuantitativeComparisonQuestions
Questionsofthistypeasktheexamineetocomparetwoquantities—QuantityAandQuantityB—andthendeterminewhichoffourstatementsdescribesthecomparison.
SampleQuestions
Directions:
CompareQuantityAandQuantityB,usingtheadditionalinformationgiven,ifany. Selectoneofthefollowingfouranswerchoices.
A. QuantityAisgreater.
B. QuantityBisgreater.
C. Thetwoquantitiesareequal.
D. Therelationshipcannotbedeterminedfromtheinformationgiven.
Asymbolthatappearsmorethanonceinaquestionhasthesamemeaningthroughoutthequestion.
1.
QuantityA:
xsquared+1
QuantityB:
2x,minus1
A. QuantityAisgreater.
B. QuantityBisgreater.
C. Thetwoquantitiesareequal.
D. Therelationshipcannotbedeterminedfromtheinformationgiven.
Answer:
A(QuantityAisgreater.)
Samplequestion2belowisbasedonfigure3.
Figure3
Beginskippablefiguredescription.
Figure3showsparallelogramRSTU.SidesR UandS Tarehorizontal,withS Tabove,andslightlytotheleftofsideR U.DiagonalS U,whichextendsfromvertexSattheupperleftoftheparallelogramtovertexUatthelowerrightoftheparallelogram,dividestheparallelogramintotwotriangles,R S UandU S T;andtheangleatvertexSinto2adjacentanglesR S UandU S T.ThemeasureofangleR S Uisxdegrees,andthemeasureofangleU S Tisydegrees.
Endskippablefiguredescription.
2.
ItisgiventhatRSTUisaparallelogram.
QuantityA:
x
QuantityB:
y
A. QuantityAisgreater.
B. QuantityBisgreater.
C. Thetwoquantitiesareequal.
D. Therelationshipcannotbedeterminedfromtheinformationgiven.
Answer:
D(Therelationshipcannotbedeterminedfromtheinformationgiven.)
DataInterpretationSets
DataInterpretationquestionsaregroupedtogetherandrefertothesametable,graph,orotherdatapresentation.Thesequestionsaskyoutointerpretoranalyzethegivendata.ThetypesofquestionsmaybeMultiple-choice(bothtypes)orNumericEntry.
SampleQuestions
Directions:
Questions1to3arebasedonthedatainthefollowingtable.
ThetableshowsthepercentchangeinmonthlyvalueofinventoryatsixbusinessesfromApriltoJune.
Business
PercentChangefromApriltoMay
PercentChangefromMaytoJune
G
+6
+8
K
+5
minus5
M
+2
+12
R
+8
minus5
V
+14
0
Z
+2
minus10
Note:
Inventoryvaluesaredeterminedattheendofeachmonth.
1. IfthevalueofinventoryatBusinessKwas$30,000forApril,whatwasthevalueofinventoryatBusinessKforJune?
A. $22,500
B. $29,925
C. $30,000
D. $33,000
E. $33,075
Answer:
B($29,925)
2. AtBusinessM,thevalueofinventoryforMaywaswhatpercentofthevalueofinventoryforJune?
Giveyouranswertothenearest0