ETS官方GRE数学样题.docx

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