美国加州数学考试

CALIFORNIASTANDARDSTESTReleasedTestQuestionsAlgebraIIIntroduction-AlgebraIIThefollowingreleasedtestquestionsaretakenfromtheAlgebraIIStandardsTest.ThistestisoneoftheCaliforniaStandardsTestsadministeredaspartoftheStandardizedTestingandReporting(STAR)ProgramunderpoliciessetbytheStateBoardofEducation.AllquestionsontheCaliforniaStandardsTestsareevaluatedbycommitteesofcontentexperts,includingteachersandadministrators,toensuretheirappropriatenessformeasuringtheCaliforniaacademiccontentstandardsinAlgebraII.Inadditiontocontent,allitemsarereviewedandapprovedtoensuretheiradherencetotheprinciplesoffairnessandtoensurenobiasexistswithrespecttocharacteristicssuchasgender,ethnicity,andlanguage.ThisdocumentcontainsreleasedtestquestionsfromtheCaliforniaStandardsTestformsin2003,2004,2005,2006,2007,and2008.FirstonthepagesthatfollowarelistsofthestandardsassessedontheAlgebraIITest.Nextarereleasedtestquestions.Followingthequestionsisatablethatgivesthecorrectanswerforeachquestion,thecontentstandardthateachquestionismeasuring,andtheyeareachquestionlastappearedonthetest.Thefollowingtablelistseachreportingcluster,thenumberofitemsthatappearontheexam,andthenumberofreleasedtestquestionsthatappearinthisdocument.SomeofthereleasedtestquestionsforAlgebraIIarethesametestquestionsfoundindifferentcombinationsontheIntegratedMathematics2and3CaliforniaStandardsTestsandtheSummativeHighSchoolMathematicsCaliforniaStandardsTest.NUMBEROFNUMBEROFREPORTINGQUESTIONSONRELEASEDTESTCLUSTEREXAMQUESTIONSPolynomialsandRationalExpressions1928Quadratics,Conics,andComplexNumbers1724ExponentsandLogarithms1524Series,Combinatorics,andProbabilityandStatistics1420TOTAL6596Inselectingtestquestionsforrelease,threecriteriaareused:(1)thequestionsadequatelycoveraselectionoftheacademiccontentstandardsassessedontheAlgebraIITest;(2)thequestionsdemonstratearangeofdifficulty;and(3)thequestionspresentavarietyofwaysstandardscanbeassessed.Thesereleasedtestquestionsdonotreflectallofthewaysthestandardsmaybeassessed.Releasedtestquestionswillnotappearonfuturetests.FormoreinformationabouttheCaliforniaStandardsTests,visittheCaliforniaDepartmentofEducation’sWebsiteat—1—ThisisasampleofCaliforniaStandardsTestquestions.ThisisNOTanoperationaltestform.Testscorescannotbeprojectedbasedonperformanceonreleasedtestquestions.Copyright©2009CaliforniaDepartmentofEducation.CALIFORNIASTANDARDSTESTReleasedTestQuestionsAlgebraIITHEPOLYNOMIALSANDRATIONALEXPRESSIONSREPORTINGCLUSTERThefollowingfiveCaliforniacontentstandardsareincludedinthePolynomialsandRationalExpressionsreportingclusterandarerepresentedinthisbookletby28testquestions.ThesequestionsrepresentonlysomewaysinwhichthesestandardsmaybeassessedontheAlgebraIICaliforniaMathematicsStandardsTest.CALIFORNIACONTENTSTANDARDSINTHISREPORTINGCLUSTERAlgebraII1.0*Studentssolveequationsandinequalitiesinvolvingabsolutevalue.2.0*Studentssolvesystemsoflinearequationsandinequalities(intwoorthreevariables)bysubstitution,withgraphs,orwithmatrices.3.0*Studentsareadeptatoperationsonpolynomials,includinglongdivision.4.0*Studentsfactorpolynomialsrepresentingthedifferenceofsquares,perfectsquaretrinomials,andthesumanddifferenceoftwocubes.7.0* Studentsadd,subtract,multiply,divide,reduce,andevaluaterationalexpressionswithmonomialandpolynomialdenominatorsandsimplifycomplicatedrationalexpressions,includingthosewithnegativeexponentsinthedenominator.*Denoteskeystandards—2—ThisisasampleofCaliforniaStandardsTestquestions.ThisisNOTanoperationaltestform.Testscorescannotbeprojectedbasedonperformanceonreleasedtestquestions.Copyright©2009CaliforniaDepartmentofEducation.CALIFORNIASTANDARDSTESTReleasedTestQuestionsAlgebraIITHEQUADRATICS,CONICS,ANDCOMPLEXNUMBERSREPORTINGCLUSTERThefollowingsevenCaliforniacontentstandardsareincludedintheQuadratics,Conics,andComplexNumbersreportingclusterandarerepresentedinthisbookletby24testquestions.ThesequestionsrepresentonlysomewaysinwhichthesestandardsmaybeassessedontheAlgebraIICaliforniaMathematicsStandardsTest.CALIFORNIACONTENTSTANDARDSINTHISREPORTINGCLUSTERAlgebraII5.0*Studentsdemonstrateknowledgeofhowrealandcomplexnumbersarerelatedbotharithmeticallyandgraphically.Inparticular,theycanplotcomplexnumbersaspointsintheplane.6.0*Studentsadd,subtract,multiply,anddividecomplexnumbers.8.0*Studentssolveandgraphquadraticequationsbyfactoring,completingthesquare,orusingthequadraticformula.Studentsapplythesetechniquesinsolvingwordproblems.Theyalsosolvequadraticequationsinthecomplexnumbersystem.9.0*Studentsdemonstrateandexplaintheeffectthatchangingacoefficienthasonthegraphofquadraticfunctions;thatis,studentscandeterminehowthegraphofaparabolachangesasa,b,andcvaryintheequationy=a(x–b)2+c.10.0*Studentsgraphquadraticfunctionsanddeterminethemaxima,minima,andzerosofthefunction.16.0Studentsdemonstrateandexplainhowthegeometryofthegraphofaconicsection(e.g.,asymptotes,foci,eccentricity)dependsonthecoefficientsofthequadraticequationrepresentingit.17.0Givenaquadraticequationoftheformax2+by2+cx+dy+e=0,studentscanusethemethodforcomple