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Published by the Caribbean Examinations Council ncerelatedtothesyllabusshouldbeaddressedto:ThePro- 876)630- ‐5200FacsimileNumber:(876)967- ‐4972E- pyright ichaelBB14038,BarbadosCXC 37/G/SYLL 10
ContentsRATIONALE.1AIMS.1PRE- BUS .2SUGGESTIONSFORTEACHINGTHESYLLABUS .2CERTIFICATIONANDDEFINITIONOFPROFILES .3FORMATOFTHEEXAMINATIONS .3REGULATIONSFORRESITCANDIDATES .5REGULATIONSFORPRIVATECANDIDATES .6MISCELLANEOUSSYMBOLS .6LISTOFFORMULAE .8USEOFELECTRONICCALCULATORS .9SECTION1:ALGEBRAANDFUNCTIONS TRY ATHEMATICALAPPLICATIONS .24GUIDELINESFORTHESCHOOLBASEDASSESSMENT .29ASSESSMENTCRITERIA .31RESOURCES .47GLOSSARY .48CXC37/G/SYLL 10
CXC 37/G/SYLL 10
AdditionalMathematicsSyllabus rideditselfinbeingaknowledge- eself- onofalgebraicknowledgeandmathematicalreasoning.On completing this course students will be able to make a smooth transition to higher levels of study inMathematics, or move on to career choices where a deeper knowledge of the general concepts ofMathematics is required. This course of study, which includes fundamentals of Pure and AppliedMathematics, caters to diverse interests enabling students to develop critical-thinking skills applicable toother subject udentstheconfidenceandabilitytoapproachproblem- sofsolvingcomplexreal- ematicalsituationwithconfidence.This syllabus will contribute to the development of the Ideal Caribbean Person as articulated by theCARICOM Heads of Government in the following areas: “demonstrate multiple literacies, independent andcritical thinking and innovative application of science and technology to problem solving. Such a personshould also demonstrate a positive work attitude and value and display creative imagination andentrepreneurship”. In keeping with the UNESCO Pillars of Learning, on completion of this course the study,students will learn to do, learn to be and learn to transform themselves and society. Mathematics;CXC 37/G/SYLL 101
onlogically;6.developskillsinformulatingreal- hasScience,BusinessandtheArts. PRE- balandwrittencommunicationskills. foursectionsasfollows:Section1- ‐AlgebraandFunctionsSection2- ‐CoordinateGeometryandTrigonometrySection3- ‐IntroductoryCalculusSection4- ‐BasicMathematicalApplications taneouslywithCAPEUnit1intheSixthForm.CXC 37/G/SYLL 102
threecognitivelevels.Conceptualknowledge- hmicknowledge- caldeductionandinferences.Reasoning- ntermsofagivenreal- ‐worldproblem,andtoengageproblem- ‐solving. nessayorproblem- s)Section123ThisPaperwillconsistof45multiple- s,IndicesandLogarithmsSeriesCo- ionIntegrationTotalCXC 37/G/SYLL 10No.ofitems232454338563Total20141145
of6compulsorystructuredandproblem- roblem- ationofdifferentsectionsofthesyllabus.CXC 37/G/SYLL 104
ER0230%50%PAPER0320%200100% whichtheyre- repeatthiscomponent,providedtheyre- olorotherapprovededucationalinstitution.CXC 37/G/SYLL 105
institutionsrecognizedbytheCouncil. MISCELLANEOUSSYMBOLS ltoisproportionaltoinfinity derivativeofywithrespecttoxthenthderivativeofyw ithrespecttoxthefirst,second, definiteintegralofywithrespecttoxbetweenthelimitsx aandx bCXC 37/G/SYLL 106
ProbabilityandStatisticsA BA BSP(A)P(A )P(A inesegmentABthemagnitudeofâ a onoftheCartesiancoordinateaxes,xandyrespectivelyxi yjMechanicsxv,a,,gCXC 37/G/SYLL ogravity7
LISTOF ectorswherev xi yjTrigonometryDifferentiationCXC 37/G/SYLL 108
StatisticsProbabilityKinematics aveanelectronicnon- tronichand- g- inoroutsideoftheexaminationroomareprohibited.CXC 37/G/SYLL 109
theabilitytouseconceptstomodelandsolvereal- raticfunctionintheformCXC 37/G/SYLL 10Quadraticequationsinoneunknown.10
cientsofax2 bx c nequalitieswithlinearfactors.CXC 37/G/SYLL 1011
functions;Arrowdiagrams.Function,domain,co- edinterval,one- ‐to- ‐onefunction,ontofunction,one- ‐to- qualto3.3.determinewhetheragivenfunctionismany- ‐to- ‐oneorone- ‐to- y f(x)anditsinverse;f- ‐1(x)asthereflectionoff(x)intheliney at,ifgistheinverseoff,thenf[g(x)] nsCXC 37/G/SYLL onalizationofdenominatorsofsurds.12and
factthatlogab cac sbyusingthelaws:(i)5.(PQ) P (ii) (iii) x sequence;CXC 37/G/SYLL 1013
atgeometricseriesareconvergentonlyif- ‐1 r raandFunctions.CXC 37/G/SYLL 1014
Functions(one- ‐to- ‐one,onto,one- ‐to- which:(i)will,orwillnot,beone- ‐to- o- ifbothone- ‐to- unctionf:A herealline,ortheset{x R x 1},andtheco- ‐domainBisRortheset{y R y eticandgeometricseriestosolvereal- ‐worldproblemssuchasinvestments.CXC 37/G/SYLL 1015
litytouseconceptstomodelandsolvereal- ,g,c,r line.CXC 37/G/SYLL 10Tangentsandnormalstothecircle.16
tsshouldbeableto:1.expressavectorintheformTwo- ons.orxi yj;x,y ormulaeforarclengthl rqandsectorareaA ½r2q;CXC 37/G/SYLL 10Applicationsofarclengthandsectorarea.17
exactvaluesofsine,cosineandtangentforq heidentity;8.usetheformulaeforsin(A B),cos(A B)andtan(A B);Compound- sforsin2x,cos2x,tan2x;Double- seinvolvingtheuseofcos2q sin2q learningactivitieslistedbelow.CXC 37/G/SYLL 1018
lowingtrigonometricformulae:sin(A B),cos(A B),tan(A XC 37/G/SYLL 1019
ytouseconceptstomodelandsolvereal- hederivativeatapointx casthegradientofthetangenttothegraphatx usexn ederivativesofsinxandcosx.sinx cosxcosx - ‐sinx;CXC 37/G/SYLL 1020
constant(ii)f(x) g(x) f(x) rmalstocurves.CXC 37/G/SYLL 10Stationarypoints.21
ntiation;Anti- 5.integratefunctionsoftheformwherea,b,narerealandn - tions;Integrationofasinx grals;Thedefiniteintegral: F(b)- andthelinesparalleltothey- ‐axis;CXC 37/G/SYLL 1022
esofrevolutionaboutthex- fy x,y 0andx ntvaluesofn,forexamplen eaofthegivenregion.CXC 37/G/SYLL 1023
ata.2.representnumericaldatadiagrammatically;Stem- ‐and- ‐leafdiagramsandbox- ‐and- isadvantagesofstem- ‐and- ‐leafdiagramsandbox- ‐and- ‐whiskerplotsindataanalyses;4.interpretstem- ‐and- ‐leafdiagramsandbox- ‐and- sfromrawdata,groupeddata,stem- ‐and- ‐leafdiagrams,box- ‐and- ,interquartilerange,semi- ‐inter- ionmeasuresthespreadofasetofdata.CXC 37/G/SYLL 1024
sinasamplespaceisequaltoone;(ii)0 P(A) 1foranyeventA;(iii)P(A') otoccur;4.useP(AÈB) P(A) P(B)- ÇB) lprobabilityConditionalprobability.P(A B)whereP(A B) B) P(A) P(B)orP(A B) ramstosolveproblemsinvolvingprobability.CXC 37/G/SYLL ediagramsandVenndiagrams.
weendistanceanddisplacement,andspeedandv
Mathematics, or move on to career choices where a deeper knowledge of the general concepts of Mathematics is required. This course of study, which includes fundamentals of Pure and Applied Mathematics, caters to diverse interests enabling students to develop cr
