Mathematics Analysis And Approaches - Alignment JS
Mapping ofInternational Baccalaureate Diploma Programme Mathematics:Analysis and Approaches syllabuswith Cambridge University Press Coursebooks:(Published in 2012)Mathematics Higher Level for the IB Diploma,Mathematics Standard Level for the IB Diploma,and Mathematical Studies Standard Level for the IB Diploma
The new syllabus is categorised into Mathematics Analysis and Approaches SL and HL and Mathematics Applications and Interpretation SLand HL. Having looked at the content of both categories, it is clear that each consists of the blend of topics from previous syllabuses:Mathematical Studies SL, Mathematics SL, Mathematics HL, and Further Mathematics HL, and some additional topics not listed in theprevious syllabus.Consequently, teachers who previously used the IB Mathematics coursebooks by Cambridge University Press* can still use these books forteaching the new syllabus. The purpose of this document is to align the content of the Mathematics Analysis and Approaches syllabus withthe content of the Cambridge University Press coursebooks that published in 2012.The alignment itself is structured into four columns: Mathematics Analysis and Approaches (Number and Algebra, Functions, Geometry andTrigonometry, Statistics and Probability, and Calculus), Mathematics HL, Mathematics SL, and Mathematical Studies SL contents. For ease ofreference, the numbering in this document follows the exact format that is printed in the syllabus and the coursebooks.Please use this document as a guide as it may not cater for all the details.Best wishes,Carolus SadsoeitoeboenACS Jakarta School, Indonesia* Mathematical Studies Standard Level for IB Diploma, Mathematics Standard Level for IB Diploma, Mathematics Higher Level for IB Diploma, and 4 Optionbooks: Mathematics Higher Level Topic 7 Statistics and Probability, Topic 8 Set, Relations and Groups, Topic 9 Calculus, and Topic 10 DiscreteMathematics
Topic 1 : Number and algebraMathematics: analysis andapproachesFirst assessment 2021Mathematics Higher Level for theIB Diploma CoursebookMathematics Standard Level forthe IB Diploma CoursebookMathematical Studies StandardLevel for the IB DiplomaCoursebookStandard LevelSL. 1.1Operations withnumbers in the form๐ 10& where 1 ๐ 10 and k is an integerArithmetic sequencesand seriesSL 1.2Use of the formulae forthe nth term and thesum of the first n termsof the sequence.Use of sigma notationfor sums of arithmeticsequences.ApplicationsAnalysis, interpretationand prediction where amodel is not perfectlyarithmetic in real life.1.37C7DArithmetic sequencesArithmetic series6C6DArithmetic sequencesArithmetic series3.13.27DArithmetic series6DArithmetic series3.13.27BGeneral series andsigma notation6BGeneral series andsigma notation7HMixed questions6HMixed question onsequences and series3.27C7DArithmetic SequenceArithmetic Series6C6DArithmetic sequencesArithmetic series3.13.2Expressing very largeand very smallnumbers in standardformArithmetic sequenceArithmetic series:the sum of anarithmetic sequenceArithmetic sequenceArithmetic series:the sum of anarithmetic sequenceArithmetic series:the sum of anarithmetic sequenceArithmetic sequenceArithmetic series:the sum of anarithmetic sequenceMathematics: Analysis and approaches 2
Mathematics: analysis andapproachesFirst assessment 2021SL 1.3SL 1.5Mathematics Standard Level forthe IB Diploma CoursebookMathematical Studies StandardLevel for the IB DiplomaCoursebookGeometric sequencesand series.7E7FGeometric sequenceGeometric series6E6FGeometric sequencesGeometric series3.33.4Use of the formulae forthe nth term and thesum of the first n termsof the sequence.Use of sigma notationfor sums of geometricsequences.7FGeometric series6FGeometric series3.47BGeneral series andsigma notation6BGeneral series andsigma notation7HMixed questions6HMixed questions onsequences and series7HMixed questions6HMixed questions onsequences and series2ALaws of exponents2ALaws of exponents2C2DThe value eIntroducing logarithms2C2DThe number eIntroduction tologarithmsApplications.SL 1.4Mathematics Higher Level for theIB Diploma CoursebookFinancial applications ofgeometric sequencesand series: compound interest annual depreciationLaws of exponents withinteger exponents.Introduction tologarithms with base 10and e.GeometricsequencesGeometric series:the sum of ageometric sequenceGeometric series:the sum of ageometric sequence3.4Geometric series:the sum of ageometric sequence4.2Compound interestMathematics: Analysis and approaches 3
Mathematics: analysis andapproachesFirst assessment 2021Numerical evaluation oflogarithms usingtechnologySimple deductive proof,numerical and algebraic;how to lay out a lefthand side to right-handSL 1.6side (LHS to RHS) proof.The symbols andnotation for equalityand identity.Laws of exponents withrational exponents.Mathematics Higher Level for theIB Diploma Coursebook2C2DThe value eIntroducing logarithms25AThe principle ofmathematical induction25FInduction and inequality2AMathematics Standard Level forthe IB Diploma Coursebook2C2DThe number eIntroduction tologarithmsLaws of exponents2ALaws of exponents2ELaws of logarithms2ELaw of logarithms2ELaws of logarithms2ELaw of logarithmsMathematical Studies StandardLevel for the IB DiplomaCoursebookLaws of logarithms.Log , ๐ฅ๐ฆ log , ๐ฅ log , ๐ฆSL 1.7log ,๐ฅ log , ๐ฅ log , ๐ฆ๐ฆlog , ๐ฅ 3 ๐ log , ๐ฅFor ๐, ๐ฅ, ๐ฆ 0Change of base of alogarithm.Mathematics: Analysis and approaches 4
Mathematics: analysis andapproachesFirst assessment 2021Mathematics Higher Level for theIB Diploma CoursebookMathematics Standard Level forthe IB Diploma CoursebookMathematical Studies StandardLevel for the IB DiplomaCoursebooklog 7 ๐ฅ,log 7 ๐for ๐, ๐, ๐ฅ 0log , ๐ฅ Solving exponentialequations, includingusing logarithmsSL 1.8SL 1.9Sum of infiniteconvergent geometricsequencesThe binomial theorem:Expansion of๐ ๐ ; , ๐ โ.2GSolving exponentialequations2GSolving exponentialequations7GInfinite geometric series6GInfinite geometric series8AIntroducing the binomial7AtheoremApplying the binomial7BtheoremProducts of binomial7CexpansionsBinomial expansions asapproximationsIntroducing the binomial7AtheoremHigher LevelThe product principleand the additionprincipleCounting arrangementsAlgebra of factorials8B8C8DUse of Pascalโs triangleand nCr .AHL 1.10Counting principles,including permutationsand combinations8A1A1B1CIntroduction to thebinomial theoremBinomial coefficientsApplying the binomialtheoremIntroduction to thebinomial theoremMathematics: Analysis and approaches 5
Mathematics: analysis andapproachesFirst assessment 2021Mathematics Higher Level for theIB Diploma Coursebook1D1E1F1GExtension of thebinomial theorem tofractional and negativeindices, i.e. ๐ ๐ ; ,8CCounting selectionExclusion principleCounting orderedselectionsKeeping objectstogether or separatedProducts of binomialexpansionsMathematics Standard Level forthe IB Diploma Coursebook7CMathematical Studies StandardLevel for the IB DiplomaCoursebookApplying the binomialtheorem๐ โ.AHL 1.11AHL 1.12AHL 1.13Partial fractionsComplex numbers: thenumber i, where i2 1.Cartesian form ๐ง ๐ ๐i; the terms real part,imaginary part,conjugate, modulus andargument.15AThe complex plane15BModulus-argument(polar) Norm๐ง ๐ cos ๐ i sin ๐ ๐cis๐15B15CDefinition and basicarithmetic of perties of complexconjugatesMathematics: Analysis and approaches 6
Mathematics: analysis andapproachesFirst assessment 2021Euler form:๐ง ๐eHIAHL 1.14Sums, products andquotients in Cartesian,polar or Euler forms andtheir geometricinterpretation.Complex conjugateroots of quadratic andpolynomial equationswith real coefficientsDe Moivreโs theoremand its extension torational exponentsPower and roots ofcomplex numbersProof by mathematicalinductionAHL 1.15Proof by contradiction.Mathematics Higher Level for theIB Diploma Coursebook15GComplex exponents15CProperties of complexconjugates15DComplex solutions topolynomial equationsSums and products ofroots of polynomialsOperations in polar form15E15F15G15H25A25B25C25D25E25FMathematics Standard Level forthe IB Diploma CoursebookMathematical Studies StandardLevel for the IB DiplomaCoursebookComplex exponentsRoots of complexnumbersThe principle ofmathematical inductionInduction and seriesInduction andsequencesInduction anddifferentiationInduction and divisibilityMathematics: Analysis and approaches 7
Mathematics: analysis andapproachesFirst assessment 2021Use of acounterexample toshow that a statement isnot always true.AHL 1.16Solutions of systems oflinear equations (amaximum of threeequations in threeunknowns), includingcases where there is aunique solution, aninfinite number ofsolutions or no solution.Mathematics Higher Level for theIB Diploma Coursebook25B25C25D25E25F4FInduction andinequalitiesInduction and seriesInduction andsequencesInduction anddifferentiationInduction and divisibilityInduction andinequalitiesSystems of linearequationsMathematics Standard Level forthe IB Diploma CoursebookMathematical Studies StandardLevel for the IB DiplomaCoursebook2.1Linear equations2.2Pairs of linearequationsMathematics: Analysis and approaches 8
Topic 2 : FunctionsMathematics: analysis andapproachesFirst assessment 2021Mathematics Higher Level for theIB Diploma CoursebookMathematics Standard Level forthe IB Diploma CoursebookMathematical Studies StandardLevel for the IB DiplomaCoursebookStandard LevelDifferent forms of theequation of a straight line.14.4The equation of astraight line14.1The gradient of alineThe gradient of aline(Prior Learning Topics : CoordinateGeometry, Mathematics HLSyllabus)SL 2.1Gradient; intercepts.Lines with gradients mand m .14.1The gradient of aline12Parallel line m m .12Perpendicular lines๐J ๐K 1SL 2.2Concept of a function,domain, range and graph5A5CRelations, functions andgraphsDomain and range4BDomain and range17.117.2What is a function?Functions in moredetailMathematics: Analysis and approaches 9
Mathematics: analysis andapproachesFirst assessment 2021SL 2.3Mathematics Higher Level for theIB Diploma CoursebookMathematics Standard Level forthe IB Diploma CoursebookFunction notation, forexample, f(x), v(t), C(n).5BFunction notation4AFunction notationThe concept of a functionas a mathematical model5BFunction notation2BExponential functionInformal concept that aninverse function reversesor undoes the effect of afunction.Inverse function as areflection in the line y x,and the notation ๐ MJ ๐ฅ .5EInverse functions4DInverse functions5EInverse functions4DInverse functionsThe graph of a function ;its equation ๐ฆ ๐ ๐ฅ .5ARelations, functions andgraphs4BDomain and rangeCreating a sketch frominformation given or acontext, includingtransferring a graph fromscreen to paper.Using technology to graphfunctions including theirsums and differences.Mathematical Studies StandardLevel for the IB DiplomaCoursebook17.2Function in moredetail17.4Drawing graphs anddiagrams17.4Drawing graphs anddiagramsMathematics: Analysis and approaches 10
Mathematics: analysis andapproachesFirst assessment 2021Determine key feature ofSL 2.4graphsFinding the point ofintersection of two curvesor lines using technology.Composite functions.SL 2.5Identity function. Findingthe inverse functionf-1Mathematics Higher Level for theIB Diploma Coursebook4CFeatures of graphs3CFeatures of graphs5DComposite functions4CComposite functions5EInverse functions4DInverse functions3DThe quadratic formulaand discriminant1AThe quadratic form2f ( x) ax bx c : itsgraph, y โ intercept(0 , c). Axis of symmetry.The form off ( x) a( x - p)( x - q) ,x โ intercepts (p , 0),(q , 0).The form2f ( x) a( x - h) k ,SL 2.7Mathematical Studies StandardLevel for the IB DiplomaCoursebook17.4Drawing graphs anddiagrams17.4Drawing graphs anddiagrams(x).The quadratic functionSL 2.6Mathematics Standard Level forthe IB Diploma Coursebookvertex (h , k)Solution of quadraticequations andinequalities.The quadratic formula.2.3Quadratic equations18.2Quadratic functionsand their graphs2y ax bx c1CThe factorised formy a( x - p)( x - q)(Prior Learning Topics : Algebra,Mathematics HL Syllabus)(Prior Learning Topics : Algebra,Mathematics HL Syllabus)4GSolving inequalities3BSolving equations bysubstitution3DThe quadratic formulaand discriminant1DThe quadratic formulaand the discriminantMathematics: Analysis and approaches 11
Mathematics: analysis andapproachesFirst assessment 2021The discriminantMathematics Higher Level for theIB Diploma CoursebookMathematics Standard Level forthe IB Diploma CoursebookMathematical Studies StandardLevel for the IB DiplomaCoursebook2D b - 4ac and thenature of the roots, thatis, two distinct real roots,two equal real roots, noreal roots.The reciprocal function1f ( x) , x ยน 0 : its graphxand self-inverse natureSL 2.8form f ( x) 5F4ERational functionsax bandcx dtheir graphs.Rational functions of theEquations of vertical andhorizontal asymptotes.Exponential functions andtheir graphs:xf ( x) a , a 0, f ( x) eSL 2.9Rational functionsLogarithmic functions andtheir graphs:f ( x) log a x, x 0,2B16FExponential functionsThe exponential andnatural logarithmfunctions2BExponential functions16FThe exponential andnatural logarithmfunctions2FGraphs of logarithmsx17.317.3Rational functionsRational functions19.1Exponentialfunctions and theirgraphsf ( x) ln x, x 0.Mathematics: Analysis and approaches 12
Mathematics: analysis andapproachesFirst assessment 2021Solving equations, bothgraphically andanalyticallySL 2.10Mathematics Higher Level for theIB Diploma Coursebook4ASolving equations byfactorising4BSolving equations bysubstitutionUsing a graphicalcalculator to solveequationsUse of technology tosolve a variety ofequations, including thosewhere there is noappropriate analyticapproach.4DApplications of graphingskills and solvingequations that relate toreal-life situations.4DMathematics Standard Level forthe IB Diploma Coursebook3ASolving equations byfactorising3DUsing a graphicalcalculator to solveequationsUsing a graphicalcalculator to solveequations8FModelling usingtrigonometric functionsMathematical Studies StandardLevel for the IB DiplomaCoursebook2.1Linear equations2.2Pairs of linearequations2.3Quadratic equations2.12.22.3Linear equationsPairs of linearequationsQuadratic equationsTransformation of graphsSL 2.11Translations:y f ( x) b; y f ( x - a)6ATranslations5ATranslationsReflections (in both axes):y - f ( x); y f (- x).Vertical stretch with scalefactor p : y pf ( sMathematics: Analysis and approaches 13
Mathematics: analysis andapproachesFirst assessment 2021Horizontal stretch with1scale factor : y f (qx )qCompositetransformations.Mathematics Higher Level for theIB Diploma CoursebookMathematics Standard Level forthe IB Diploma formation5DConsecutivetransformation3AWorking withpolynomial3BRemainder and factortheoremsSums and products ofroots of polynomialsMathematical Studies StandardLevel for the IB DiplomaCoursebookHigher LevelPolynomial functions,their graphs andequations; zeros, rootsand factorsAHL 2.12 The factor and remaindertheorems.Sums and product of theroots of polynomialequations.Rational functions of theformax b,f ( x) 2AHL 2.13cx dx e15E2AHL 2.14ax bx cand f ( x) dx eOdd and even functions6GSymmetries of graphsand functionsMathematics: Analysis and approaches 14
Mathematics: analysis andapproachesFirst assessment 2021Finding the inverseMathematics Higher Level for theIB Diploma CoursebookMathematics Standard Level forthe IB Diploma Coursebook5EInverse functions4DInverse functions5EInverse functions4DInverse functions4GSolving Inequalities6DModulus transformationMathematical Studies StandardLevel for the IB DiplomaCoursebook-1functions, f ( x) ,Including domainrestriction.Self-inverse functions.Solution of g ( x) ยณ f ( x),AHL 2.15 both graphically andanalytically.The graphs of thefunctions, y f (x) andy f ( x ), y AHL 2.161,f ( x)y f (ax b) , y [ f ( x)]2Solution of modulusequations andinequalities.Mathematics: Analysis and approaches 15
Topic 3: Geometry and trigonometryMathematics: analysis andapproachesFirst assessment 2021The distance betweentwo points in threedimensional space, andtheir midpoint.SL 3.1SL 3.2Volume and surfacearea of threedimensional solidsincluding right-pyramid,right cone, sphere,hemisphere andcombinations of thesesolids.The size of an anglebetween twointersecting lines orbetween a line and aplane.Mathematics Higher Level for theIB Diploma Coursebook9A9BMathematics Standard Level forthe IB Diploma CoursebookStandard LevelRadian measure8ADefinitions and graphs8Bof sine and cosinefunctionsMeasuring anglesDefinitions and graphsof the sine and cosinefunction(Prior Learning Topics :Geometry, HL Syllabus)11ETrigonometry in threedimensions14EUse of sine, cosine andtangent ratios to findthe sides and angles ofright-angled triangles.11AAngles and intersectionsbetween lines andplanesRight-angled trianglesThe sine rule:11BThe sine ruleMathematical Studies StandardLevel for the IB DiplomaCoursebook16.1Finding the length ofa line within a threedimensional solid16.3Calculating volumesand surface areas ofthree-dimensionalsolids10ETrigonometry in threedimensions16.2Finding the size of anangle in a threedimensional solid10ARight-angled triangles15.1Trigonometric ratios10BThe sine rule15.4The sine ruleMathematics: Analysis and approaches 16
Mathematics: analysis andapproachesFirst assessment 2021๐๐๐ sin ๐ด sin ๐ต sin ๐ถThe cosine rule:Mathematical Studies StandardLevel for the IB DiplomaCoursebookThe cosine rule10CThe cosine rule15.5The cosine ruleArea of a triangle as1๐๐sin ๐ถ.211DArea of a triangle10DArea of a triangle15.6Area of a triangleApplications of right andnon-right angledtrigonometry, includingPythagorasโ theorem.Angles of elevation anddepression.Construction of labeleddiagrams from writtenstatements.The circle: radianmeasure of angles;length of an arc; area ofa sector.11ETrigonometry in threedimensions10ETrigonometry in threedimensions15.1Trigonometric ratios11ARight-angled triangles10ARight-angled triangles15.2Angles of elevationand depressionConstructing labeleddiagramscos ๐ถ SL 3.4Mathematics Standard Level forthe IB Diploma Coursebook11C๐ K ๐ K ๐ K 2๐๐cos ๐ถSL 3.3Mathematics Higher Level for theIB Diploma Coursebook๐K ๐K ๐ K;2๐๐15.79A11F11GRadian measureLength of an arcArea of a sector8A10F10GMeasuring anglesLength of an arcArea of a sectorMathematics: Analysis and approaches 17
Mathematics: analysis andapproachesFirst assessment 2021Definition of cos ๐, sin ๐In terms of the unitSL 3.5circle.Definition oftan ๐ SL 3.6Mathematics Higher Level for theIB Diploma Coursebook9BDefinitions and graphsof sine and cosinefunctions8BDefinitions and graphsof the sine and cosinefunctions9CDefinition and graph ofthe tangent function8CDefinition and graph ofthe tangent function9DExact values oftrigonometric functions8DExact values oftrigonometric functions11BThe sine rule10BThe sine rule10CTrigonometric identities9CTrigonometric identities12ADouble angle identities9EDouble angle identities10DUsing identities to solveequations9DUsing identities to solveequationssin ๐cos ๐Exact values oftrigonometric ratios ofW W W W0, , , , and theirX Y Z Kmultiples.Extension of the sinerule to the ambiguouscase.The PythagoreanidentitysinK ๐ cos K ๐ 1.Double angle identitiesfor sine and cosine.The relationshipbetween trigonometricratios.Mathematics Standard Level forthe IB Diploma CoursebookMathematical Studies StandardLevel for the IB DiplomaCoursebook15.1Trigonometric ratiosMathematics: Analysis and approaches 18
Mathematics: analysis andapproachesFirst assessment 2021The circular functionssin ๐ฅ, cos ๐ฅ, and tan ๐ฅ;Amplitude, theirperiodic nature, andtheir graphsComposite functions ofSL 3.7the form๐ ๐ฅ ๐ sin ๐ ๐ฅ ๐Real-life contexts.AHL 3.9Mathematics Standard Level forthe IB Diploma Coursebook9BDefinitions and graphsof sine and cosinefunctions8BDefinitions and graphsof the sine and cosinefunctions9ETransformations oftrigonometric graphs8ETransformations oftrigonometric graphs9ETransformations oftrigonometric graphsModeling usingtrigonometric functionsIntroducingtrigonometric equations8FModeling usingtrigonometric functions9AIntroducingtrigonometric equations9BHarder trigonometricequations9CTrigonometric identitiesMathematical Studies StandardLevel for the IB DiplomaCoursebook ๐Transformations.SL 3.8Mathematics Higher Level for theIB Diploma Coursebook9FSolving trigonometricequations in a finiteinterval, both graphicallyand analyticallyEquations leading toquadratic equations insin ๐ฅ , cos ๐ฅ, or tan ๐ฅ .10ADefinition of thereciprocal trigonometricratios sec ๐, cosec ๐,and cot ๐.Pythagorean identities:1 tanK ๐ sec K ๐12D10B12DHarder trigonometricequationsHigher LevelReciprocal trigonometricfunctionsReciprocal trigonometricfunctionsMathematics: Analysis and approaches 19
Mathematics: analysis andapproachesFirst assessment 20211 cot K ๐ cosec K ๐The inverse functions๐ ๐ฅ arcsin ๐ฅ,๐ ๐ฅ arccos ๐ฅ๐ ๐ฅ arctan ๐ฅ , theirdomain and ranges;their graphs.Compound angleidentitiesAHL 3.10Double angle identityfor tan.Relationships betweentrigonometric functionsAHL 3.11 and the symmetryproperties of theirgraphs.AHL 3.12 Concepts of a vector;position vectors;displacement vectors.Representation ofvectors using directedline segments.Base vectors i, j, k.Components of a vector:Mathematics Higher Level for theIB Diploma CoursebookMathematics Standard Level forthe IB Diploma Coursebook9GInverse trigonometricfunctions12DReciprocal trigonometricfunctionsDouble angle identities9EDouble angle identities9EDouble angle identities9BDefinitions and graphsof sine and cosinefunctions8BDefinitions and graphsof the sine and cosinefunctions13APositions anddisplacements11APositions anddisplacements13APositions anddisplacements11APositions anddisplacements13APositions anddisplacementsPositions anddisplacements11APositions anddisplacementsPositions anddisplacements12A13A11AMathematical Studies StandardLevel for the IB DiplomaCoursebookMathematics: Analysis and approaches 20
Mathematics: analysis andapproachesFirst assessment 2021๐ฃJ๐ ๐ฃK๐ฃZ ๐ฃJ ๐ ๐ฃK ๐ ๐ฃZ ๐.Mathematics Higher Level for theIB Diploma CoursebookMathematics Standard Level forthe IB Diploma CoursebookAlgebraic and geometricapproaches to thefollowing: the sum anddifference of twovectors the zero vector O,the vector โ ๐13BVector Algebra11BVector algebra13BVector Algebra11BVector algebra multiplication by ascalar, ๐๐,parallelvectorsmagnitude of avector , ๐ ; unit๐vector,13BVector Algebra11BVector algebra13CDistances11CDistances position vectorsOA a, OB b13APositions anddisplacements11APositions anddisplacements displacement vectorAB b โ a13APositions anddisplacements11APositions anddisplacements Mathematical Studies StandardLevel for the IB DiplomaCoursebook๐Mathematics: Analysis and approaches 21
Mathematics: analysis andapproachesFirst assessment 2021Proofs of geometricalproperties usingvectors.The definition of thescalar product of twovectors.AHL 3.13 The angle between twovectors.Perpendicular vectors;parallel vectors.Vector equation of a linein two and threedimensions: ๐ ๐ ๐๐The angle between twoAHL 3.14 lines.Simple applications tokinematics.Coincident, parallel,intersecting and skewlines, distinguishingAHL 3.15between these cases.Mathematics Higher Level for theIB Diploma CoursebookMathematics Standard Level forthe IB Diploma Coursebook13EProperties of the scalarproduct11EProperties of the scalarproduct13DAngles11DAngles13EProperties of the scalarproductVector equation of a line11G11FSolving problemsinvolving linesVector equation of a lineAngles and intersectionsbetween lines andplanesSolving problems withlines11DAngles11GSolving problemsinvolving lines11GSolving problemsinvolving lines14A14E14B14BSolving problems withlinesMathematical Studies StandardLevel for the IB DiplomaCoursebookPoint of intersection.Mathematics: Analysis and approaches 22
Mathematics: analysis andapproachesFirst assessment 2021The definition of thevector product of twovectors.AHL 3.16 Properties of the vectorproduct.Geometricinterpretation of ๐ ๐Vector equations of aplane:๐ ๐ ๐๐ ๐๐, whereb and c are non-parallelvectors within the plane.๐ ๐ ๐ ๐, where n isAHL 3.17a normal to the planeand a is the positionvector on a point on theplane.Cartesian equation of aplane ๐๐ฅ ๐๐ฆ ๐๐ง ๐Intersections of : a linewith a plane; twoplanes; three planes.AHL 3.18Angle between: a lineand a plane; two planes.Mathematics Higher Level for theIB Diploma Coursebook13GProperties of the vectorproduct13G14DProperties of the vectorproductProperties of the vectorproductEquations of a plane14DEquations of a plane14DEquations of a plane14EAngles and intersectionsbetween lines andplanesAngles and intersectionsbetween lines andplanes13G14EMathematics Standard Level forthe IB Diploma Coursebook11GMathematical Studies StandardLevel for the IB DiplomaCoursebookSolving problemsinvolving linesMathematics: Analysis and approaches 23
Topic 4 : Statistics and probabilityMathematics: analysis andapproachesFirst assessment 2021Mathematics Higher Level for theIB Diploma CoursebookMathematics Standard Level forthe IB Diploma CoursebookMathematical Studies StandardLevel for the IB DiplomaCoursebookStandard LevelSL 4.1SL 4.2Concepts of population,sample, random sample,discrete and continuousdata.Reliability of datasources and bias insampling.Interpretation ofoutliers.21ASome importantconcepts in statistics5.1Classifying data21ASome importantconcepts in statistics5.1Classifying data21ASome importantconcepts in statistics5.8Box and whiskerdiagramsSampling techniquesand their effectiveness.Presentation of data(discrete andcontinuous): frequencydistributions (tables).Histograms.21ASome importantconcepts in statisticsFrequency tables andgroup data7.1Range andinterquartile rangSimple discrete dataCumulative frequency;cumulative frequencygraphs; use to findmedian, quartiles,percentiles, range and21C21B21BMeasures of spreadMeasures of spread16.CFrequency tables andgrouped data5.216E16DHistogramsCumulative frequency5.65.7Frequency histogramCumulativefrequency16BMeasures of spread7.1Range andinterquartile rangeMathematics: Analysis and approaches 24
Mathematics: analysis andapproachesFirst assessment 2021interquartile range(IQR).Production andunderstanding of boxand whisker diagrams.Measures of centraltendency (mean,median and mode).SL 4.3SL 4.4Mathematics Higher Level for theIB Diploma Coursebook21CMathematics Standard Level forthe IB Diploma CoursebookMathematical Studies StandardLevel for the IB DiplomaCoursebook16DCumulative frequency5.8Box and whiskerdiagramsFrequency tables andgroup data16AMeasures of the centreof data6.1Finding the medianfor simple dataFinding the mean fordiscrete andcontinuous dataIdentifying the modeor modal class6.2Estimation of meanfrom grouped data.Modal class.21CFrequency tables andgroup data16CFrequency tables andgrouped data6.3Measures of dispersion(interquartile range,standard deviation andvariance)Effect of constantchanges on the originaldata.Quartiles of discretedata.21BMeasures of spread16BMeasures of spread7.1Range andinterquartile range7.2Standard deviationLinear correlation ofbivariate data.21BMeasures of spread(Prior Learning: Statistics andprobability, Mathematics HLSyllabus)16FConstant changes todata16BMeasures of spread7.1Range andinterquartile range16GCorrelation12.1The concept ofcorrelationMathematics: Analysis and approaches 25
Mathematics: analysis andapproachesFirst assessment 2021Pearsonโs productmoment correlationcoefficient, r.Scatter diagrams; linesof best fit, by eye,passing through themean point.Equation of theregression line of y on x.Use of the equation ofthe regression line forprediction purposes.Interpret the meaning ofthe parameters, a and b,in a linear regression๐ฆ ๐๐ฅ ๐Concepts of trial,outcome, equally likelyoutcomes, relativefrequency, sample space(U) and event.SL 4.5The probability of an;(q)event A is P(A) ;(s)Mathematics Higher Level for theIB Diploma CoursebookMathematics Standard Level forthe IB Diploma Coursebook16GCorrelation16GCorrelation16HLinear regression12.516HLinear regression12.616HLinear regression12.6Using the equationof the regression line10.2Sample spacediagrams10.3Calculatingprobability and theexpected value22AIntroduction toprobability17AEmpirical probability22BCombined events andVenn diagrams17BTheoretical probability22CTree diagrams andfinding the intersectionIntroduction toprobability17AEmpirical probability22AMathematical Studies StandardLevel for the IB DiplomaCoursebook12.4Pearsonโs productmoment correlationcoefficient, r12.2Scatter diagrams12.3Line of best fitRegression line of yon xUsing the equationof the regression lineMathematics: Analysis and approaches 26
Mathematics: analysis andapproachesFirst assessment 2021The complementaryevents A and Aโ (not A).Expected number ofoccurrences.Use of Venn diagrams,tree diagrams, samplespace diagrams andtables of outcomes tocalculate probabilities.Combined events:SL 4.6Mathematics Higher Level for theIB Diploma Coursebook22AIntroduction toprobabilityMathematics Standard Level forthe IB Diploma Coursebook17AEmpirical probability18BExpectation of a discreterandom variable22CTree diagrams andfinding the intersection17CCombined events andVenn diagrams22BCombined events andVenn diagrams17CCombined events andVenn diagrams10.5Tree diagrams andVenn diagramsMutually exclusiveevents:๐ ๐ด ๐ต 0.Conditional probability:w(q x)P(A B) .22BCombined events andVenn diagrams17CCombined events andVenn diagrams10.4Mutually exclusiveevents22FConditional probability17DTree diagrams andfinding intersections10.8ConditionalprobabilityIndependent events:22DIndependent events17EIndependent events
3.2 Arithmetic series: the sum of an arithmetic sequence Analysis, interpretation and prediction where a model is not perfectly arithmetic in real life. 7C 7D Arithmetic Sequence Arithmetic Series 6C 6D Arithmetic sequences Arithmetic series 3.1 3.2 Arithmetic sequence Arithmetic s
Mathematics: analysis and approaches standard level . paper 1 markscheme . Mathematics: analysis and approaches standard level . paper 2 specimen paper . Mathematics: analysis and approaches standard level . paper 2 markscheme . Candidate session number Mathematics: analysis and approaches Higher level Paper 1 13 pages Specimen paper 2 hours 16EP01 nstructions to candidates Write your session .
IBDP MATHEMATICS: ANALYSIS AND APPROACHES SYLLABUS SL 1.1 11 General SL 1.2 11 Mathematics SL 1.3 11 Mathematics SL 1.4 11 General 11 Mathematics 12 General SL 1.5 11 Mathematics SL 1.6 11 Mathematic12 Specialist SL 1.7 11 Mathematic* Not change of base SL 1.8 11 Mathematics SL 1.9 11 Mathematics AHL 1.10 11 Mathematic* only partially AHL 1.11 Not covered AHL 1.12 11 Mathematics AHL 1.13 12 .
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Practice Test Answer and Alignment Document Mathematics: Geometry Performance Based Assessment - Online PARCC PBA Online Assessment: Geometry Mathematics Practice Test - Answer and Alignment Document 2 Item Number Answer Key Evidence Statement Keys Integrated Math Alignment Part 1: Non-Calculator 1 B, D, E G-CO.1 1 2 G-GPE.6 3
as HSC Year courses: (in increasing order of difficulty) Mathematics General 1 (CEC), Mathematics General 2, Mathematics (โ2 Unitโ), Mathematics Extension 1, and Mathematics Extension 2. Students of the two Mathematics General pathways study the preliminary course, Preliminary Mathematics General, followed by either the HSC Mathematics .
2. 3-4 Philosophy of Mathematics 1. Ontology of mathematics 2. Epistemology of mathematics 3. Axiology of mathematics 3. 5-6 The Foundation of Mathematics 1. Ontological foundation of mathematics 2. Epistemological foundation of mathematics 4. 7-8 Ideology of Mathematics Education 1. Industrial Trainer 2. Technological Pragmatics 3.
for each alignment (1). Estimates of phylogeny and inferences of pos-itive selection were sensitive to alignment treat-ment. Confirming previous studies showing that alignment method has a considerable effect on tree topology (12โ14), we found that 46.2% of the 1502 ORFs had one or more differing trees depending on the alignment procedure used.
Approaches to Web Application Development CSCI3110 Department of Computing, ETSU Jeff Roach . Web Application Approaches and Frameworks Scripting (or Programmatic) Approaches Template Approaches Hybrid Approaches Frameworks . Programmatic Approaches The page is generated primarily from code
