MATHADVISEMENTGUIDE

Recommendationsformathcoursesarebasedonyourplacementresults,degreeprogramandcareerinterests

MathPlacement:MAT001orMAT003orMAT013• IfyouplantotakeMAT109(CollegeAlgebra&Trigonometry),youmustregisterforMAT003• IfyourmajordoesNOTrequireMAT109,youcanregisterforMAT013orMAT003• IfyouplantoregisterforMAT013ANDhaveaRDG001placement,RDG001mustbecompletedbefore

orbetakenwhiletakingMAT013MathPlacement:MAT002orMAT012

• IfyouplantotakeMAT109(CollegeAlgebra&Trigonometry),youmustregisterforMAT002• IfyourmajordoesNOTrequireMAT109,youcanregisterforMAT012orMAT002• IfyouplantoregisterforMAT012ANDhaveaRDG001placement,RDG001mustbecompletedbefore

orbetakenwhiletakingMAT012MathPlacement:MAT100ORsuccessfulcompletionofMAT002/MAT003/MAT012/MAT013

• Youmayenrollinanyofthefollowingcreditmathcoursesandthesecoursescanbetakeninanyorder:• MAT100-ATopicalApproachtoMathematics(4credits)• MAT101-ConceptsofMathematics(3credits)• MAT102-IntroductiontoStatistics(3credits)• MAT118-FiniteMathematics:QuantitativeAnalysis(3credits)

Forstudentsinselectedteachereducationtransferprograms:• MAT114-FoundationsofMathematicsforEducators(3credits)

(YoumaynotreceivecreditforbothMAT100andMAT114)• IfyouhaveaplacementforENG001orRDG001,youmustsuccessfullycompletethesecoursesbefore

takingacreditmathcourseMathPlacement:MAT109ORsuccessfulcompletionofMAT002/MAT003

• Youmaytakeanyofthecourseslistedaboveaswellasthefollowingandthesecoursescanbetakeninanyorder:

• MAT109–CollegeAlgebra&Trigonometry(4credits)or

• MAT116–EngineeringTechnicalMathI(4credits)(YoumaynotreceivecreditforbothMAT109andMAT116)

• IfyouhaveaplacementforENG001orRDG001,youmustsuccessfullycompletethesecoursesbeforetakingacreditmathcourse

• IfyouwanttoregisterforPre-CalculusorCalculusI,youmaygotothePlacementTestingCentertotaketheAdvancedAlgebraandFunctionsTesttodetermineyourhighestmathplacement

MathPlacement:MAT111ORagradeofCorhigherinMAT109• Youmaytakeanyofthecourseslistedaboveaswellasthefollowingandthesecoursescanbetakenin

anyorder:• MAT111–Pre-Calculus(4credits)

or• MAT117–EngineeringTechnicalMathII(4credits)

(YoumaynotreceivecreditforbothMAT111andMAT117)MathPlacement:MAT112ORagradeofCorhigherinMAT111orMAT117

• Youmaytakeanyofthecourseslistedaboveaswellasthefollowingandthesecoursescanbetakeninanyorder:

• MAT112-CalculuswithApplicationsinBusinessandSocialSciences(4credits)or

• MAT122-CalculusI(4credits)(YoumaynotreceivecreditforbothMAT112andMAT122)

Lookinsidefordetaileddescriptionsofallcourses

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Studentsshouldcarefullyconsiderthedescriptionsbelowtodecidewhichcoursesaremostappropriateforthem.Somedescriptionsincludeinformationthatsupplementsthecollegecatalog.

DEVELOPMENTALMATHCOURSESForfrequentlyaskedquestions,visithttp://matcmp.ncc.edu/index.php?loc=mathpath

MAT003-IntegratedArithmeticandBasicAlgebra(0credits-6contacthours)MathPlacement:MAT001/MAT003/MAT013.CourseDescription:Arithmeticandalgebrawillbeintegratedthroughoutthesemester.Emphasiswillbeplacedonthefundamentaloperationsofintegersandrationalnumbers,ratioandproportion,percentage,factoring,linearandfractionalequations,exponents,radicals,quadraticequations,andrighttriangles.Variousrelationshipswillbeexploredbothgraphicallyandanalytically.Hand-heldcalculatorswillbeused.ThiscoursesatisfiestheprerequisiteforMAT109(CollegeAlgebra&Trigonometry).Thiscoursecombinesthebasicsofarithmeticwiththeessentialsofalgebratopreparestudentsforcreditmathcourses.Topicsinclude:

• arithmeticoperationsincludingapplicationsinvolvingproportions,ratios,andpercent• solvinglinearequations• graphinglinearequations• solvingsystemsoflinearequations• operationsonpolynomials• factoringpolynomials• solvingpolynomialequations

MAT013-IntegratedArithmeticandQuantitativeReasoning1(0credits-6contacthours)

MathPlacement:MAT001/MAT013/MAT003.Prerequisite:RDG001,maybetakenconcurrently.CourseDescription:Thiscourseintegratesarithmeticandquantitativeliteracywithmathematicalconceptssuchasfluencywithnumbers,proportionalreasoning,datainterpretation,algebraicreasoning,graphinglines,andmodeling.Groupworkandclassdiscussionswillbeusedtoinvestigatemathematicalconceptsbasedonreal-lifeexamples.Someexamplesinclude:socialjustice,homerepair,populationgrowthanddensity,andcongressionalstructure.Studentswhointendtomajorinscience,technology,engineeringormathematicsmusttakeMAT003.Hand-heldcalculatorswillbeused.ThiscoursedoesnotsatisfytheprerequisiteforMAT109(CollegeAlgebra&Trigonometry).IfyouneedMAT109asadegreerequirement,youmustsuccessfullycompleteMAT003beforeregisteringforMAT109.Thiscoursecombinesthebasicsofarithmeticwiththeessentialsofquantitativereasoningtopreparestudentsforcreditmathcourses.Topicsinclude:

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• arithmeticoperationsincludingapplicationsinvolvingproportions,ratios,andpercent• estimationandsolvingapplicationsinvolvinglargenumbers• estimationusingfractions,percentandratios• unitconversions• analyzingmeasuresofcentraltendency• reading,interpreting,andanalyzingquantitativedatafromgraphs• usingformulasandalgebraicexpressionsinrealisticapplications• creatingandsolvingequationsthatrelatetoquantitativereasoningapplications• graphingandanalyzinglinearmodelsbyfocusingonrateofchangeofparameters

MAT002-IntroductoryAlgebra(0credits–4.5contacthours)MathPlacement:MAT002/MAT012.CourseDescription:Topicsinclude:fundamentalprocessesofarithmeticandalgebra,factoring,linearandfractionalequations,exponents,radicals,quadraticequationsandrighttriangletrigonometry.Hand-heldcalculatorswillbeused.ThiscoursesatisfiestheprerequisiteforMAT109(CollegeAlgebra&Trigonometry).Thiscoursepreparesstudentsforalgebraintensivecreditmathcoursesbyteachingtheessentialsofalgebra.Topicsinclude:

• solvinglinearequations• graphinglinearequations• solvingsystemsoflinearequations• operationsonpolynomials• factoringpolynomials• solvingpolynomialequations

MAT012-QuantitativeReasoning1(0credits–4.5contacthours)MathPlacement:MAT012/MAT002.Prerequisite:RDG001,maybetakenconcurrently.CourseDescription:Thiscourseintegratesquantitativeliteracywithmathematicalconceptssuchasfluencywithnumbers,proportionalreasoning,datainterpretation,algebraicreasoning,graphinglines,andmodeling.Groupworkandclassdiscussionswillbeusedtoinvestigatemathematicalconceptsbasedonreal-lifeexamples.Someexamplesinclude:socialjustice,homerepair,populationgrowthanddensity,andcongressionalstructure.Studentswhointendtomajorinscience,technology,engineeringormathematicsmusttakeMAT002.Hand-heldcalculatorswillbeused.ThiscoursedoesnotsatisfytheprerequisiteforMAT109(CollegeAlgebra&Trigonometry).IfyouneedMAT109asadegreerequirement,youmustsuccessfullycompleteMAT002beforeregisteringforMAT109.Thiscoursefocusesonreal-worldcontextualizedapplicationsofquantitativereasoningtopreparestudentsforcreditmathcourses.Topicsinclude:

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• estimationandsolvingapplicationsinvolvinglargenumbers• estimationusingfractions,percentandratios• unitconversions• analyzingmeasuresofcentraltendency• reading,interpreting,andanalyzingquantitativedatafromgraphs• usingformulasandalgebraicexpressionsinrealisticapplications• creatingandsolvingequationsthatrelatetoquantitativereasoningapplications• graphingandanalyzinglinearmodelsbyfocusingonrateofchangeofparameters

CREDITMATHCOURSES

MAT100-ATopicalApproachtoMathematics(4credits)MathPlacement:MAT100.Prerequisite:SuccessfulcompletionofMAT,ENG001andRDG001developmentalcourserequirementspriortostartingthecourse.CourseDescription:Fundamentalmathematicstopicsandtheirapplications.Topicsincludeproblemsolving,numbersystems,geometry,consumermathematics,mathematicalmodeling,managementscience,andsocialchoiceanddecisionmaking.StudentswillNOTreceivecreditforbothMAT100andMAT114.MAT100satisfiesSUNYGENED-GMAT;NCCGENED-MATH.Thiscourseincludesavarietyofdifferentmathematicaltopicsandtheirapplications.Someofthetopicsare:

• criticalthinkingskills:masteringtheskillsofreasoning,estimatingandproblemsolving• numbertheoryandrealnumbersystem:arithmetic,geometricandFibonaccisequences• algebra,graphs,andfunctions:usingsystemsoflinearinequalitiestofindoptimalsolutions

ofbusinessapplicationswithlimitedresources• metricsystem:conversionsto/frommetricsysteminreal-lifeexamples• consumermathematics:simpleandcompoundinterestinapplicationssuchascreditcard

debt,mortgagesandsavingsplans• graphtheory:solvingEulerandHamiltoniancircuits,spanningtreesinreal-world

applications,suchasthetravelingsalesmanproblem,bybruteforce,nearestneighborandKruskal’sAlgorithmmethods

• votingmethods:plurality,majority,BordaCount,PairwisewithEliminationandArrow’sImpossibilityTheorem,andimportanceofdecidingonvotingmethodanditsflawsbeforeballotsarecast

Thiscoursemaybeofparticularinteresttostudentsinterestedinbanking,informationtechnology,businessorgovernment.

MAT101-ConceptsofMathematics(3credits)MathPlacement:MAT100.Prerequisite:SuccessfulcompletionofMAT,ENG001andRDG001developmentalcourserequirementspriortostartingthecourse.CourseDescription:Topicsincludeformalsymboliclogic,arguments,methodsofproof,basicconceptsofsets,andsetoperations.MAT101satisfiesSUNYGENED-GMAT;NCCGENED-MATH.

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Thisisalogiccourse,soitmayseemverydifferentfromothermathcourses.Thiscourselooksatthelanguageofargumentsandproofs,ratherthanfocusingonnumbersandcalculations.Topicsinclude:• formalsymboliclogic:symboliclogicrules• validityofarguments:usewritteninformationtodrawvalidconclusions• formalproof• settheory

Otherpossibletopicsinclude:• circuitstheory• strategiesforsimplegames(liketic-tac-toe)• basicdecisiontheory

Thiscoursemaybeofparticularinteresttostudentsinterestedinjournalism,informationtechnology,education,English,philosophyorlaw.MAT102-IntroductiontoStatistics(3credits)MathPlacement:MAT100.Prerequisite:SuccessfulcompletionofMAT,ENG001andRDG001developmentalcourserequirementspriortostartingthecourse.CourseDescription:Topicsincludeappropriateandinappropriateusesofstatistics,measuresofcentraltendencyandvariability,basicconceptsofprobability,thebinomial,normaland‘t’distributions,testinghypotheses,estimation,chi-square,linearregression,andcorrelation.MAT102satisfiesSUNYGENED-GMAT;NCCGENED-MATH.MAT102servesasaperquisiteforMAT103(AppliedStatistics)andMAT119(DataScience/Analytics).Innewspapers,television,magazinesandontheInternet,weseegraphsandfiguresthatarepresentedtousasfacts.Itisusefultoknowhowthisinformationisgatheredandorganized,andtodeterminewhethertheseclaimsseemaccurateormisleading.Introductorystatisticsisanimportantcourseforunderstandingsuchdataandachievingsuccessinmanyprofessionalcareers.Inthiscourse,topicsinclude:

• appropriateandinappropriateusesofstatistics• theorganizationandpresentationofdata• descriptivestatistics• linearcorrelationandregression• probabilityapplications• discreteandcontinuousprobabilitydistributions• samplingdistributions• estimation• hypothesistesting• thechi-squaredistribution

Thiscoursemaybeofparticularinteresttostudentsinterestedincriminaljustice,datascience,government,leadershipcareers,business,psychology,sociology,educationornursing.

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MAT109-CollegeAlgebra&Trigonometry(4credits)MathPlacement:MAT109.Prerequisite:SuccessfulcompletionofMAT002orMAT003,ENG001andRDG001developmentalcourserequirementspriortostartingthecourse.CourseDescription:Thiscourseconsidersfundamentalideasfromalgebra,trigonometryandfunctionsincludingexponentialsandlogarithms.Aproblem-solvingapproachisused.MAT109satisfiesSUNYGENED-GMAT;NCCGENED-MATH.ThiscourseisintendedtopreparestudentsforMAT111(Pre-Calculus)andmaybeofparticularinteresttostudentsinterestedinscience,technology,engineeringormathematicscareers.

ItfurtherdevelopsthealgebrafromMAT002(IntroductoryAlgebra)orMAT003(IntegratedArithmeticandBasicAlgebra).

IfyouplantotakeMAT109,someoftheskillsyouareexpectedtoknowbeforeenteringtheclassarelistedbelow.Ifthismaterialisunfamiliartoyou,thenyoushouldconsidertakingMAT002beforeregisteringforMAT109.

• Express 0 18 3−− + asasinglefraction.

Answer: 23

−

• Findtheproductof ( )( )2 4 3 5 .x x− +

Answer: 26 2 20x x− − • Solveforr: 2 .r cπ =

Answer: 2crπ

=

• Solveforx: 14 3 .6 2x

=

Answer: 149

x =

• 2 2Factor completely: 25 36 .x y−

Answer: ( )( )5 6 5 6x y x y+ − • If 3 2,y x− = − findtheslopeandthey-intercept.

Answer:slope:3andy-intercept: ( )0, 2− • Simplify : 32 Answer: 4 2

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• 1 1Add: x y+

Answer:x yxy+

• Solveforx: 2 5 6x x+ = − Answer: { 2, 3}x = − −

• Simplify7 8

5 9

124x yx y

andexpresstheanswerwithpositiveexponents.

Answer:23xy

MAT111-Pre-Calculus(4credits)MathPlacement:MAT111.Prerequisite:agradeofCorhigherinMAT109orMAT116.CourseDescription:Thisisapreparatorycourseforthestudyofcalculus.Thefunctionconceptplaysaunifyingroleinthestudyofpolynomial,rational,exponential,logarithmic,andtrigonometricfunctions.Modeling,usingelementaryfunctions,isstressedthroughoutthecourse.MAT111satisfiesSUNYGENED-GMAT;NCCGENED-MATH.Thiscoursemaybeofparticularinteresttostudentsinterestedinscience,technology,engineeringormathematicscareers.IfyouplantotakeMAT111,thenyouwillbeexpectedtohaveastrongfoundationinintermediatealgebra,withsomeknowledgeoffunctions,graphingandtrigonometry.Belowaresomeconceptsyourinstructorwillexpectyoutobefamiliarwithbeforeyouenterthecourse.Ifthismaterialisunfamiliartoyou,thenyoushouldconsidertakingMAT109beforeregisteringforMAT111.

• Express 5 32x x

−−

asasinglefraction.

Answer: 2

2 102

xx x−

−

• Findanequationofthelinepassingthroughthepoints ( )2, 6 and (5, 12).− − Answer: 2 2y x= − −

• Simplytheexpression2

4

x xx⋅ andexpresstheanswerwithpositiveexponents.

Answer: 32

1x

• Whatistheexactvalueofsin 60 ?o

Answer: 32

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• Solve 23 5 1 0x x− + = forx.

Answer: 5 136

x ±=

• Solve for : 5x ax xy= +

Answer:5xa y

=+

• If 2( )f x x= thenwhatis ( )?f x h+

Answer: 2 2( ) 2f x h x xh h+ = + +

• Removetheparenthesesandsimplifytheexpression 2 2 29 7 12 ( 3 ) .a a a a a⎡ ⎤− − − −⎣ ⎦

Answer: 23 9a a+ • Factorcompletely:

3 23 27 156 .x x x+ − Answer: ( )( )3 13 4x x x+ − • Factorcompletely:

4 2 22 .x bx b− +

Answer: ( )22x b−

MAT112-CalculuswithApplicationsinBusinessandSocialSciences(4credits)Thiscourseisintendedforstudentsenrolledinnon-scienceprograms.MathPlacement:MAT112.Prerequisite:agradeofCorhigherinMAT111orMAT117.CourseDescription:ThiscourseisNOTrecommendedforMath,Engineering,ScienceorComputerSciencestudentsand itdoesnotsatisfy theprerequisite forMAT123(Calculus II).Thiscourse isintended to introduce the fundamental concepts and techniques of calculus to the non-sciencestudents.Specialemphasis isgiventoapplicationsinBusinessandSocialSciences.Topics includefunctionsandgraphs, thederivativeanddifferentiation techniquesofalgebraic,exponentialandlogarithmicfunctionsofasinglevariable,theconceptofmarginineconomics,elasticityofdemand,differentials,relatedratesandoptimizationproblems,growthanddecayapplications,integralsandintegrationtechniques,applicationofintegrals,includingproducerandconsumersurplus,incomestreams,probability.StudentswillNOTreceivecreditforbothMAT112andMAT122.MAT112satisfiesSUNYGENED-GMAT;NCCGENED-MATH.IfyouplantotakeMAT112,youwillbeexpectedtohaveastrongfoundationinpre-calculus.Belowaresomeconceptsyourinstructorwillexpectyoutobefamiliarwithbeforeyouenterthecourse.

Ifthismaterialisunfamiliartoyou,thenyoushouldconsidertakingMAT111beforeregisteringforMAT112.

• Findthesolutionsetfortheinequality 2 2 8 0x x− − < .Answer: 2 4x− < <

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• Simplifytheexpression 4 42 5 .x x⋅ Answer:100x

• Simplifytheexpression( )22 1xx+

andexpresstheanswerwithoutadenominator.

Answer: 3 12x x x−+ +

• If ( )32( ) 2 1 and ( ) ( ( )),h x x h x f g x= + = find ( ).f x

Answer: 3( )f x x=

• If 2

3( )4xh x

x−

=−

,findtheequationsofallhorizontalandverticalasymptotestothegraphof

)(xh .Answer:Verticalasymptotesare 2 and 2x x= = −

Horizontalasymptoteis 0y =

• If 3( ) 5,f x x= + findtheaveragerateofchangeof ( )f x withrespecttoxontheinterval1 3.x≤ ≤

Answer:13• Solve 3 27xe = forx.

Answer: ln 27 which can be simplified to ln 33

x x= =

• If 2)( xxf = and 0≠h expressh

xfhxf )()( −+ insimplestform.

Answer: 2x h+

• If ln and lnx a y b= = express 3 2ln a b intermsofxandy.

Answer: ( )13

22 or3 3x yx y+ +

• If 2( ) 4 2f x x x= + ,find ( )12 .f

Answer:2

MAT114-FoundationsofMathematicsforEducators(3credits)Thiscourseisonlyforstudentsenrolledinselectedteachereducationtransferprograms.

MathPlacement:MAT100.Prerequisite:SuccessfulcompletionofMAT,ENG001andRDG001developmentalcourserequirementspriortostartingthecourse.CourseDescription:Thiscourseisintendedforstudentswhoareinterestedinteachingattheelementaryschoollevel.Topicsincludeadevelopmentofbinaryalgorithms,therealnumbers,

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fieldpropertiesoftherealnumbersystemasappliedtoabstractmathematicalsystems,numerationssystems,functionsandequivalencerelations,solvingsystemsofalgebraicequationsandnumbertheory,includingsomealgebraicproofs.Applications,historicalperspectives,problemsolvinganduseoftechnologywillbeemphasizedinalltopics.StudentswillNOTreceivecreditforbothMAT100andMAT114.MAT114satisfiesSUNYGENED-n/a;NCCGENED-MATH.MAT116–EngineeringTechnicalMathI(4credits)Thiscourseisonlyforstudentsenrolledinselectedengineeringtechnologyprograms.MathPlacement:MAT109.Prerequisite:SuccessfulcompletionofMAT002orMAT003,ENG001andRDG001developmentalcourserequirementspriortostartingthecourse.CourseDescription:Designedforstudentsinengineeringtechnologyprograms.Topicsincludeoperationswithrealnumbers,exponentsandscientificnotation,equationsandinequalities,functionsandgraphs,systemofequationsanddeterminants,triangletrigonometryandintroductiontogeneraltrigdefinitions,algebraicproductsandfactoring,solvingequationsbyfactoringandquadraticformula,fractionalequationsandoperationswithalgebraicfractions.Applicationsareconsideredfromvariousscientific,technical,andpracticalareas.StudentswillNOTreceivecreditforbothMAT109andMAT116.MAT116satisfiesSUNYGENED-GMAT;NCCGENED-MATH.ThiscourseisintendedtopreparestudentsforMAT117(EngineeringTechnicalMathII)orMAT111(Pre-Calculus).ItfurtherdevelopsthealgebrafromMAT002(IntroductoryAlgebra)orMAT003(IntegratedArithmeticandBasicAlgebra).

StudentsshouldonlyregisterforMAT116underthefollowingconditions:

a.TheyneedtotakeMAT116fortheirmajor

b.TheyneedtotakeMAT117fortheirmajor,butdon’tyetfulfilltheprerequisiteIfyouplantotakeMAT116,someoftheskillsyouareexpectedtoknowbeforeenteringtheclassarelistedbelow.Ifthismaterialisunfamiliartoyou,thenyoushouldconsidertakingMAT002beforeregisteringforMAT116.

• Express 0 18 3−− + asasinglefraction.

Answer: 23

−

• Findtheproductof ( )( )2 4 3 5 .x x− + Answer: 26 2 20x x− − • Solveforr: 2 .r cπ =

Answer: 2crπ

=

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• Solveforx: 14 3 .6 2x

=

Answer: 149

x =

• 2 2Factor completely: 25 36 .x y−

Answer: ( )( )5 6 5 6x y x y+ − • If 3 2,y x− = − findtheslopeandthey-intercept.

Answer:slope:3andy-intercept: ( )0, 2− • Simplify : 32 Answer: 4 2

• 1 1Add: x y+

Answer:x yxy+

• Solveforx: 2 5 6x x+ = − Answer: { 2, 3}x = − −

• Simplify7 8

5 9

124x yx y

andexpresstheanswerwithpositiveexponents.

Answer:23xy

MAT117–EngineeringTechnicalMathII(4credits)Thiscourseisonlyforstudentsenrolledinselectedengineeringtechnologyprograms.MathPlacement:MAT111.Prerequisite:agradeofCorhigherinMAT109orMAT116.CourseDescription:Designedforstudentsinengineeringtechnologyprograms.Topicsincluderationalexponentsandradicals,functionsandtheirgraphs,polynomials,exponential,logarithmicandtrigonometricfunctions,conicsections,introductionderivativesandintegrals.Applicationsareconsideredfromvariousscientific,technical,andpracticalareas.StudentswillNOTreceivecreditforbothMAT111andMAT117.MAT117satisfiesSUNYGENED-GMAT;NCCGENED-MATH.IfyouplantotakeMAT117,thenyouwillbeexpectedtohaveastrongfoundationinintermediatealgebra,withsomeknowledgeoffunctions,graphingandtrigonometry.Belowaresomeconceptsyourinstructorwillexpectyoutobefamiliarwithbeforeyouenterthecourse.Ifthismaterialisunfamiliartoyou,thenyoushouldconsidertakingMAT116beforeregisteringforMAT117.

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• Express 5 32x x

−−

asasinglefraction.

Answer: 2

2 102

xx x−

−

• Findanequationofthelinepassingthroughthepoints ( )2, 6 and (5, 12).− − Answer: 2 2y x= − −

• Simplytheexpression2

4

x xx⋅ andexpresstheanswerwithpositiveexponents.

Answer: 32

1x

• Whatistheexactvalueofsin 60 ?o

Answer: 32

• Solve 23 5 1 0x x− + = forx.

Answer: 5 136

x ±=

• Solve for : 5x ax xy= +

Answer:5xa y

=+

• If 2( )f x x= thenwhatis ( )?f x h+

Answer: 2 2( ) 2f x h x xh h+ = + + • Removetheparenthesesandsimplifytheexpression 2 2 29 7 12 ( 3 ) .a a a a a⎡ ⎤− − − −⎣ ⎦

Answer: 23 9a a+

• Factorcompletely:3 23 27 156 .x x x+ −

Answer: ( )( )3 13 4x x x+ −

• Factorcompletely:4 2 22 .x bx b− +

Answer: ( )22x b−

MAT118-FiniteMathematics:QuantitativeAnalysis(3credits)MathPlacement:MAT100.Prerequisite:SuccessfulcompletionofMAT,ENG001andRDG001developmentalcourserequirementspriortostartingthecourse.CourseDescription:Topicsincludeapplicationsoffinitemathematicalmodels,primarilytoproblemsinbusinessandmanagement.Matrixoperations,Markovanalysis,linearprogrammingandthesimplexmethod,gameanddecisiontheory.MAT118satisfiesSUNYGENED-GMAT;NCCGENED-MATH.

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MAT118tiesavarietyofinterconnectedmathtopicstogetherwithapplicationstobusiness,socialscienceandotherfields.Sometopicsincludedinthiscourseare:

• probability• linearprogramming• gametheory(gambling/competingbusinesses)• matrixoperations• Markovchains

Thiscoursemaybeofparticularinteresttostudentsfocusingonbusinessorforstudentswhoneedaneasilytransferableliberalartsmathcourse.MAT122-CalculusI(4credits)MathPlacement:MAT112.Prerequisite:agradeofCorhigherinMAT111orMAT117.CourseDescription:Topicsincludedefinitionsoflimit,continuityandderivative,ratesofchange,tangenttoacurve,derivativesofelementaryfunctions,products,quotients,chainrule,higherorder,implicitandinversedifferentiation,meanvaluetheorem,maximaandminima,differentials,definitionofdefiniteintegral,FundamentalTheoremofIntegralCalculus,applications,integrationofelementaryfunctions.StudentswillNOTreceivecreditforbothMAT112andMAT122.MAT122satisfiesSUNYGENED-GMAT;NCCGENED-MATH.Thiscoursemaybeofparticularinteresttostudentsinterestedinscience,technology,engineeringormathematicscareers.IfyouplantotakeMAT122,youwillbeexpectedtohaveastrongfoundationinpre-calculus.Belowaresomeconceptsyourinstructorwillexpectyoutobefamiliarwithbeforeyouenterthecourse.Ifthismaterialisunfamiliartoyou,thenyoushouldconsidertakingMAT111beforeregisteringforMAT122

• Findthesolutionsetfortheinequality 2 2 8 0x x− − < .Answer: 2 4x− < <

• Simplifytheexpression 4 42 5 .x x⋅ Answer:100x

• Simplifytheexpression( )22 1xx+

andexpresstheanswerwithoutadenominator.

Answer: 3 12x x x−+ +

• If ( )32( ) 2 1 and ( ) ( ( )),h x x h x f g x= + = find ( ).f x

Answer: 3( )f x x=

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• Findtheexactvalueof 3tan sin .4 2π π−

Answer:2

• If 2

3( )4xh x

x−

=−

,findtheequationsofallhorizontalandverticalasymptotestothegraphof

)(xh . Answer:Verticalasymptotesare 2 and 2x x= = −

Horizontalasymptoteis 0y =

• If 3( ) 5,f x x= + findtheaveragerateofchangeof ( )f x withrespecttoxontheinterval1 3.x≤ ≤

Answer:13• Solve 3 27xe = forx.

Answer: ln 27 which can be simplified to ln 33

x x= =

• If 2)( xxf = and 0≠h expressh

xfhxf )()( −+ insimplestform.

Answer: 2x h+

• If ln and lnx a y b= = express 3 2ln a b intermsofxandy.

Answer: ( )13

22 or3 3x yx y+ +

• If 2( ) 4 2f x x x= + ,find ( )12 .f

Answer:2