Quantitative Reasoning Measure.docx
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Quantitative Reasoning Measure.docx
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QuantitativeReasoningMeasure
IntroductiontotheQuantitativeReasoningMeasure
TheQuantitativeReasoningmeasureoftheGRE®revisedGeneralTestassessesyour:
∙basicmathematicalskills
∙understandingofelementarymathematicalconcepts
∙abilitytoreasonquantitativelyandtomodelandsolveproblemswithquantitativemethods
Someofthequestionsinthemeasureareposedinreal-lifesettings,whileothersareposedinpurelymathematicalsettings.Theskills,conceptsandabilitiesaretestedinthefourcontentareasbelow:
∙Arithmetictopicsincludepropertiesandtypesofintegers,suchasdivisibility,factorization,primenumbers,remaindersandoddandevenintegers;arithmeticoperations,exponentsandradicals;andconceptssuchasestimation,percent,ratio,rate,absolutevalue,thenumberline,decimalrepresentationandsequencesofnumbers.
∙Algebratopicsincludeoperationswithexponents;factoringandsimplifyingalgebraicexpressions;relations,functions,equationsandinequalities;solvinglinearandquadraticequationsandinequalities;solvingsimultaneousequationsandinequalities;settingupequationstosolvewordproblems;andcoordinategeometry,includingslopesandinterceptsoflinesandgraphsoffunctions,equationsandinequalities.
∙Geometrytopicsincludeparallelandperpendicularlines,circles,triangles—includingisosceles,equilateraland30°-60°-90°triangles—quadrilaterals,otherpolygons,congruentandsimilarfigures,three-dimensionalfigures,area,perimeter,volume,thePythagoreantheoremandanglemeasurementindegrees.Theabilitytoconstructproofsisnottested.
∙Dataanalysistopicsincludebasicdescriptivestatistics,suchasmean,median,mode,range,standarddeviation,interquartilerange,quartilesandpercentiles;interpretationofdataintablesandgraphs,suchaslinegraphs,bargraphs,circlegraphs,boxplots,scatterplotsandfrequencydistributions;elementaryprobability,suchasprobabilitiesofcompoundeventsandindependentevents;randomvariablesandprobabilitydistributions,includingnormaldistributions;andcountingmethods,suchascombinations,permutationsandVenndiagrams.Thesetopicsaretypicallytaughtinhighschoolalgebracoursesorintroductorystatisticscourses.Inferentialstatisticsisnottested.
Thecontentintheseareasincludeshighschoolmathematicsandstatisticsatalevelthatisgenerallynohigherthanasecondcourseinalgebra;itdoesnotincludetrigonometry,calculusorotherhigher-levelmathematics.TheMathReviewprovidesdetailedinformationaboutthecontentoftheQuantitativeReasoningmeasure.
Themathematicalsymbols,terminologyandconventionsusedintheQuantitativeReasoningmeasurearethosethatarestandardatthehighschoollevel.Forexample,thepositivedirectionofanumberlineistotheright,distancesarenonnegativeandprimenumbersaregreaterthan1.Whenevernonstandardnotationisusedinaquestion,itisexplicitlyintroducedinthequestion.
Inadditiontoconventions,therearesomeassumptionsaboutnumbersandgeometricfiguresthatareusedintheQuantitativeReasoningmeasure.Twooftheseassumptionsare(i)allnumbersusedarerealnumbersand(ii)geometricfiguresarenotnecessarilydrawntoscale.MoreaboutconventionsandassumptionsappearsinMathematicalConventions.
QuantitativeReasoningQuestionTypes
TheQuantitativeReasoningmeasurehasfourtypesofquestions:
∙QuantitativeComparison
∙Multiple-choiceQuestions—SelectOneAnswerChoice
∙Multiple-choiceQuestions—SelectOneorMoreAnswerChoices
∙NumericEntry
EachquestionappearseitherindependentlyasadiscretequestionoraspartofasetofquestionscalledaDataInterpretationset.AllofthequestionsinaDataInterpretationsetarebasedonthesamedatapresentedintables,graphsorotherdisplaysofdata.
Inthecomputer-basedtest,youareallowedtouseabasiccalculator—providedon-screen—ontheQuantitativeReasoningmeasure.Readmoreaboutusingthecalculator.
QuantitativeComparisonQuestions
Description
Questionsofthistypeaskyoutocomparetwoquantities–QuantityAandQuantityB–andthendeterminewhichofthefollowingstatementsdescribesthecomparison:
∙QuantityAisgreater.
∙QuantityBisgreater.
∙Thetwoquantitiesareequal.
∙Therelationshipcannotbedeterminedfromtheinformationgiven.
TipsforAnswering
1.Becomefamiliarwiththeanswerchoices.QuantitativeComparisonquestionsalwayshavethesameanswerchoices,sogettoknowthem,especiallythelastanswerchoice,"Therelationshipcannotbedeterminedfromtheinformationgiven."Neverselectthislastchoiceifitisclearthatthevaluesofthetwoquantitiescanbedeterminedbycomputation.Also,ifyoudeterminethatonequantityisgreaterthantheother,makesureyoucarefullyselectthecorrespondinganswerchoicesoasnottoreversethefirsttwoanswerchoices.
2.Avoidunnecessarycomputations.Don'twastetimeperformingneedlesscomputationsinordertocomparethetwoquantities.Simplify,transformorestimateoneorbothofthegivenquantitiesonlyasmuchasisnecessarytocomparethem.
3.Rememberthatgeometricfiguresarenotnecessarilydrawntoscale.Ifanyaspectofagivengeometricfigureisnotfullydetermined,trytoredrawthefigure,keepingthoseaspectsthatarecompletelydeterminedbythegiveninformationfixedbutchangingtheaspectsofthefigurethatarenotdetermined.Examinetheresults.Whatvariationsarepossibleintherelativelengthsoflinesegmentsormeasuresofangles?
4.Pluginnumbers.Ifoneorbothofthequantitiesarealgebraicexpressions,youcansubstituteeasynumbersforthevariablesandcomparetheresultingquantitiesinyouranalysis.Considerallkindsofappropriatenumbersbeforeyougiveananswer:
e.g.,zero,positiveandnegativenumbers,smallandlargenumbers,fractionsanddecimals.IfyouseethatQuantityAisgreaterthanQuantityBinonecaseandQuantityBisgreaterthanQuantityAinanothercase,choose"Therelationshipcannotbedeterminedfromtheinformationgiven."
5.Simplifythecomparison.Ifbothquantitiesarealgebraicorarithmeticexpressionsandyoucannoteasilyseearelationshipbetweenthem,youcantrytosimplifythecomparison.Tryastep-by-stepsimplificationthatissimilartothestepsinvolvedwhenyousolvetheequation
forx,orthatissimilartothestepsinvolvedwhenyoudeterminethattheinequality
isequivalenttothesimplerinequality
Beginbysettingupacomparisoninvolvingthetwoquantities,asfollows:
where
isa"placeholder"thatcouldrepresenttherelationshipgreaterthan(>),lessthan(<)orequalto(=)orcouldrepresentthefactthattherelationshipcannotbedeterminedfromtheinformationgiven.Thentrytosimplifythecomparison,step-by-step,untilyoucandeterminearelationshipbetweensimplifiedquantities.Forexample,youmayconcludeafterthelaststepthat
representsequalto(=).Basedonthisconclusion,youmaybeabletocompareQuantitiesAandB.Tounderstandthisstrategymorefully,seesamplequestions6–9.
SamplequestionsH:
\powerprep2\docs\quantitative-reasoning\questions-comparison-samples.html
Multiple-choiceQuestions—SelectOneAnswerChoice
Description
Thesequestionsaremultiple-choicequestionsthataskyoutoselectonlyoneanswerchoicefromalistoffivechoices.
TipsforAnswering
1.Usethefactthattheansweristhere.Ifyouranswerisnotoneofthefiveanswerchoicesgiven,youshouldassumethatyouranswerisincorrectanddothefollowing:
oRereadthequestioncarefully–youmayhavemissedanimportantdetailormisinterpretedsomeinformation.
oCheckyourcomputations–youmayhavemadeamistake,suchasmis-keyinganumberonthecalculator.
oReevaluateyoursolutionmethod–youmayhaveaflawinyourreasoning.
∙Examinetheanswerchoices.Insomequestionsyouareaskedexplicitlywhichofthechoiceshasacertainproperty.Youmayhavetoconsidereachchoiceseparatelyoryoumaybeabletoseearelationshipbetweenthechoicesthatwillhelpyoufindtheanswermorequickly.Inotherquestions,itmaybehelpfultoworkbackwardfromthechoices,say,bysubstitutingthechoicesinanequationorinequalitytoseewhichoneworks.However,becareful,asthatmethodmaytakemoretimethanusingreasoning.
∙Forquestionsthatrequireapproximations,scantheanswerchoicestoseehowcloseanapproximationisneeded.Inotherquestions,too,itmaybehelpfultoscanthechoicesbrieflybeforesolvingtheproblemtogetabettersenseofwhatthequestionisasking.Ifcomputationsareinvolvedinthesolution,itmaybenecessarytocarryoutallcomputationsexactlyandroundonlyyourfinalanswerinordertogettherequireddegreeofaccuracy.Inotherquestions,youmayfindthatestimationissufficientandwillhelpyouavoidspendingtimeonlongcomputations.
SampleQuestions
Directions:
Selectasingleanswerchoice.
1.If
whatisthevalueofx?
(A)
(B)
(C)4
(D)7
(E)12
Explanation
Solvingtheequationforx,youget
andso
ThecorrectanswerischoiceA,
2.Whichofthefollowingnumbersisfarthestfromthenumber1onthenumberline?
(A)
(B)
(C)0
(D)5
(E)10
Explanation
Circlingeachoftheanswerchoicesinasketchofthenumberline(Figure4)showsthatofthegivennumbers,
isthegreatestdistancefrom1.
Figure4
Anotherwaytoanswerthequestionistorememberthatthedistancebetweentwonumbersonthenumberlineisequaltotheabsolutevalueofthedifferenceofthetwonumbers.Forexample,thedistancebetween
and1is
andthedistancebetween10and1is
Thecorrectanswerischoice
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- 关 键 词:
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