gmatmathreview

MATHREVIEWforPracticingtoTaketheGeneralTestPublishedfortheGraduateRecordExaminationsBoardbyEducationalTestingServiceCopyright2002byEducationalTestingService.Allrightsreserved.EDUCATIONALTESTINGSERVICE,ETS,theETSlogos,GRADUATERECORDEXAMINATIONS,andGREareregisteredtrademarksofEducationalTestingService.®MATHREVIEWTheMathReviewisdesignedtofamiliarizeyouwiththemathematicalskillsandconceptslikelytobetestedontheGraduateRecordExaminationsGeneralTest.Thismaterial,whichisdividedintothefourbasiccontentareasofarithmetic,algebra,geometry,anddataanalysis,includesmanydefinitionsandexampleswithsolutions,andthereisasetofexercises(withanswers)attheendofeachofthesefoursections.Note,however,thisreviewisnotintendedtobecompre-hensive.Itisassumedthatcertainbasicconceptsarecommonknowledgetoallexaminees.Emphasisis,therefore,placedonthemoreimportantskills,concepts,anddefinitions,andonthoseparticularareasthatarefrequentlyconfusedormisunderstood.Ifanyofthetopicsseemespeciallyunfamiliar,weencourageyoutoconsultappropriatemathematicstextsforamoredetailedtreatmentofthosetopics.TABLEOFCONTENTS1.ARITHMETIC1.1Integers....................................................................................................61.2Fractions..................................................................................................71.3Decimals..................................................................................................81.4ExponentsandSquareRoots.................................................................101.5OrderingandtheRealNumberLine.....................................................111.6Percent...................................................................................................121.7Ratio......................................................................................................131.8AbsoluteValue......................................................................................13ARITHMETICEXERCISES......................................................................14ANSWERSTOARITHMETICEXERCISES............................................172.ALGEBRA2.1TranslatingWordsintoAlgebraicExpressions.....................................192.2OperationswithAlgebraicExpressions................................................202.3RulesofExponents...............................................................................212.4SolvingLinearEquations......................................................................212.5SolvingQuadraticEquationsinOneVariable......................................232.6Inequalities............................................................................................242.7Applications..........................................................................................252.8CoordinateGeometry............................................................................28ALGEBRAEXERCISES............................................................................31ANSWERSTOALGEBRAEXERCISES..................................................343.GEOMETRY3.1LinesandAngles...................................................................................363.2Polygons................................................................................................373.3Triangles................................................................................................383.4Quadrilaterals........................................................................................403.5Circles...................................................................................................423.6Three-DimensionalFigures...................................................................45GEOMETRYEXERCISES.........................................................................47ANSWERSTOGEOMETRYEXERCISES..............................................504.DATAANALYSIS4.1MeasuresofCentralLocation...............................................................514.2MeasuresofDispersion.........................................................................514.3FrequencyDistributions........................................................................524.4Counting................................................................................................534.5Probability.............................................................................................544.6DataRepresentationandInterpretation.................................................55DATAANALYSISEXERCISES...............................................................62ANSWERSTODATAANALYSISEXERCISES.....................................696ARITHMETIC1.1IntegersThesetofintegers,I,iscomposedofallthecountingnumbers(i.e.,1,2,3,...),zero,andthenegativeofeachcountingnumber;thatis,I
...,,,,,,,,....3210123
Therefore,someintegersarepositive,somearenegative,andtheinteger0isneitherpositivenornegative.Integersthataremultiplesof2arecalledevenintegers,namely...,,,,,,,,....6420246
Allotherintegersarecalledoddintegers;therefo