GREMathConventions.docx
- 文档编号:23258618
- 上传时间:2023-05-15
- 格式:DOCX
- 页数:27
- 大小:145.07KB
GREMathConventions.docx
《GREMathConventions.docx》由会员分享,可在线阅读,更多相关《GREMathConventions.docx(27页珍藏版)》请在冰豆网上搜索。
GREMathConventions
GRADUATERECORDEXAMINATIONS®
MathematicalConventions
Copyright©2010byEducationalTestingService.Allrightsreserved.ETS,theETSlogo,GRADUATERECORDEXAMINATIONS,andGREareregisteredtrademarksofEducationalTestingService(ETS)intheUnitedStatesandothercountries.
Thisistheaccessibleelectronicformat(Word)editionofMathematicalConventions.Adownloadablelargeprint(PDF)version,aswellasaLargePrintFiguresupplementisavailablefromtheGRE®website.Otherdownloadablepracticeandtestfamiliarizationmaterialsinlargeprintandaccessibleelectronicformatsarealsoavailable.AtactilefiguresupplementforMathematicalConventions,alongwithadditionalaccessiblepracticeandtestfamiliarizationmaterialsinotherformats,isavailablefromE T SDisabilityServicesMondaytoFriday8:
30amto5pmNewYorktime,at16 0 9-7 7 17 7 8 0,or18 6 6-3 8 78 6 0 2(tollfreefortesttakersintheUnitedStates,U STerritoriesandCanada),orviaemailatstassd@ets.org.
ThemathematicalcontentcoveredinthiseditionofMathematicalConventionsisthesameasthecontentcoveredinthestandardeditionofMathematicalConventions.However,therearedifferencesinthepresentationofsomeofthematerial.Thesedifferencesaretheresultofadaptationsmadeforpresentationofthematerialinaccessibleformats.Therearealsoslightdifferencesbetweenthevariousaccessibleformats,alsoasaresultofspecificadaptationsmadeforeachformat.
Informationforscreenreaderusers:
Thisdocumenthasbeencreatedtobeaccessibletoindividualswhousescreenreaders.Youmaywishtoconsultthemanualorhelpsystemforyourscreenreadertolearnhowbesttotakeadvantageofthefeaturesimplementedinthisdocument.Pleaseconsulttheseparatedocument,GREScreenReaderInstructions.doc,forimportantdetails.
Figures
Thisdocumentincludesfigures.Inaccessibleelectronicformat(Word)editions,figuresappearonscreen.Followingeachfigureonscreenistextdescribingthatfigure.Readersusingvisualpresentationsofthefiguresmaychoosetoskippartsofthetextdescribingthefigurethatbeginwith“Beginskippabledescriptionof…”andendwith“End…”
MathematicalEquationsandExpressions
Thisdocumentincludesmathematicalequationsandexpressions.Someofthemathematicalequationsandexpressionsarepresentedasgraphics.Incaseswhereamathematicalequationorexpressionispresentedasagraphic,averbalpresentationisalsogivenandtheverbalpresentationcomesdirectlyafterthegraphicpresentation.Theverbalpresentationisingreenfonttoassistreadersintellingthetwopresentationmodesapart.Readersusingaudioalonecansafelyignorethegraphicalpresentations,andreadersusingvisualpresentationsmayignoretheverbalpresentations.
Overview
Note:
Someofthemathematicalconventionsdiscussedinthisdocumentareconventionsusedinprinteditionsoftestsandpracticematerial.BrailleeditionsusetheNemethCodeofMathematicsandScienceNotation.
ThemathematicalsymbolsandterminologyusedintheQuantitativeReasoningmeasureofthetestareconventionalatthehighschoollevel,andmostoftheseappearintheMathReview.Whenevernonstandardorspecialnotationorterminologyisusedinatestquestion,itisexplicitlyintroducedinthequestion.However,therearesomeassumptionsaboutnumbersandgeometricfiguresthatareparticulartothetest.TheseassumptionsappearinthetestatthebeginningoftheQuantitativeReasoningsections,andtheyareelaboratedbelow.
Also,somenotationandterminology,whilestandardatthehighschoollevelinmanycountries,maybedifferentfromthoseusedinothercountriesorfromthoseusedathigherorlowerlevelsofmathematics.Suchnotationandterminologyareclarifiedbelow.Becauseitisimpossibletoascertainwhichnotationandterminologyshouldbeclarifiedforanindividualtesttaker,morematerialthannecessarymaybeincluded.
Finally,therearesomeguidelinesforhowcertaininformationgivenintestquestionsshouldbeinterpretedandusedinthecontextofansweringthequestions—informationsuchascertainwords,phrases,quantities,mathematicalexpressions,anddisplaysofdata.Theseguidelinesappearattheend.
Numbersandquantities
1.Allnumbersusedinthetestquestionsarerealnumbers.Inparticular,integersandbothrationalandirrationalnumbersaretobeconsidered,butimaginarynumbersarenot.Thisisthemainassumptionregardingnumbers.Also,allquantitiesarerealnumbers,althoughquantitiesmayinvolveunitsofmeasurement.
2.Numbersareexpressedinbase10unlessotherwisenoted,usingthe10digits0through9andaperiodtotherightoftheonesdigit,orunitsdigit,forthedecimalpoint.Also,innumbersthatare1,000orgreater,commasareusedtoseparategroupsofthreedigitstotheleftofthedecimalpoint.
3.Whenapositiveintegerisdescribedbythenumberofitsdigits,forexample,atwodigitinteger,thedigitsthatarecountedincludetheonesdigitandallthedigitsfurthertotheleft,wheretheleftmostdigitisnot0.Forexample,5,000isafourdigitinteger,whereas031isnotconsideredtobeathreedigitinteger.
4.Someotherconventionsinvolvingnumbers:
onebillionmeans1 , 0 0 0 , 0 0 0 , 0 0 0,or
10totheninthpower(not
10tothetwelfthpower,asinsomecountries);
onedozenmeans12;
theGreekletter
pirepresentstheratioofthecircumferenceofacircletoitsdiameterandisapproximately3.14.
5.Whenapositivenumberistoberoundedtoacertaindecimalplaceandthenumberishalfwaybetweenthetwonearestpossibilities,thenumbershouldberoundedtothegreaterpossibility.
Example:
23.5roundedtothenearestintegeris24,and123.985roundedtothenearest0.01is123.99.
Whenthenumbertoberoundedisnegative,thenumbershouldberoundedtothelesserpossibility.
Example:
negative36.5roundedtothenearestintegeris
negative37.
6.Repeatingdecimalsaresometimeswrittenwithabaroverthedigitsthatrepeat,asin
25over12=thedecimal2.083,withabaroverthedigit3and
1seventh=thedecimal0.142857,withabaroverthedigits1,4,2,8,5,and7.
7.Ifr,s,andtareintegersandrs=t,thenrandsarefactors,ordivisors,oft;also,tisamultipleofr(andofs)andtisdivisiblebyr(andbys).Thefactorsofanintegerincludepositiveandnegativeintegers.
Example1:
negative7isafactorof35.
Example2:
8isafactorof
negative40.
Example3:
Theinteger4hassixfactors:
negative4,negative2,negative1,1,2,and4.
Thetermsfactor,divisor,anddivisibleareusedonlywhenr,s,andtareintegers.However,thetermmultiplecanbeusedwithanyrealnumberssandtprovidedrisaninteger.
Example1:
1.2isamultipleof0.4.
Example2:
negative2piisamultipleof
pi.
8.Theleastcommonmultipleoftwononzerointegersaandbistheleastpositiveintegerthatisamultipleofbothaandb.Thegreatestcommondivisor(orgreatestcommonfactor)ofaandbisthegreatestpositiveintegerthatisadivisorofbothaandb.
9.Whenanintegernisdividedbyanonzerointegerdresultinginaquotientqwithremainderr,thenn = qd + r,where
0islessthanorequaltor,whichislessthantheabsolutevalueofd.Furthermore,r=0ifandonlyifnisamultipleofd.
Example1:
When20isdividedby7,thequotientis2andtheremainderis6.
Example2:
When21isdividedby7,thequotientis3andtheremainderis0.
Example3:
When
negative17isdividedby7,thequotientis
negative3andtheremainderis4.
10.Aprimenumberisanintegergreaterthan1thathasonlytwopositivedivisors:
1anditself.Thefirstfiveprimenumbersare2,3,5,7,and11.Acompositenumberisanintegergreaterthan1thatisnotaprimenumber.Thefirstfivecompositenumbersare4,6,8,9,and10.
11.Oddandevenintegersarenotnecessarilypositive.
Example1:
negative7isodd,
Example2:
negative18and0areeven.
12.Theinteger0isneitherpositivenornegative.
Mathematicalexpressions,symbols,andvariables
1.Asiscommoninalgebra,italicletterslikexareusedtodenotenumbers,constants,andvariables.Lettersarealsousedtolabelvariousobjects,suchasline
l,pointP,functionf,setS,listT,eventE,randomvariableX,BrandX,CityY,andCompanyZ.Themeaningofaletterisdeterminedbythecontext.
2.Whennumbers,constants,orvariablesaregiven,theirpossiblevaluesareallrealnumbersunlessotherwiserestricted.Itiscommontorestrictthepossiblevaluesinvariousways.Herearethreeexamples.
Example1:
nisanonzerointeger.
Example2:
1islessthanorequaltox,whichislessthanpi
Example3:
Tisthetensdigitsofatwodigitpositiveinteger,soTisanintegerfrom1to9.
3.Standardmathematicalsymbolsatthehighschoollevelareused.Theseincludethestandardsymbolsforthearithmeticoperationsofaddition,subtraction,multiplicationanddivision,
thoughmultiplicationisusuallydenotedbyjuxtaposition,oftenwithparentheses,forexample,2yand
openparenthesis,3,closeparenthesis,openparenthesis,4.5,closeparenthesis,anddivisionisusuallydenotedwithahorizontalfractionbar,forexample,
theexpressionwover3,writtenwithahorizontalfractionbar.Sometimesmixednumbers,ormixedfractions,areused,like
4and3 eighthsandnegative10andonehalf.(Themixednumber
4and3eighthsisequaltothefraction
35over8andthemixednumber
negative10andonehalfisequaltothefraction
negative21over2).Exponentsarealsoused
- 配套讲稿:
如PPT文件的首页显示word图标,表示该PPT已包含配套word讲稿。双击word图标可打开word文档。
- 特殊限制:
部分文档作品中含有的国旗、国徽等图片,仅作为作品整体效果示例展示,禁止商用。设计者仅对作品中独创性部分享有著作权。
- 关 键 词:
- GREMathConventions