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Comparison of South AustraliaMathematics and the new IBMathematics CoursesBy Carolyn Farr, Matthew Durant, Naomi Belgrade,Vanessa Gorman, Catherine Quinn and Deb Woodard-Knight

Topic 1 - Number and 1.141.1511 General11 Mathematics11 Mathematics11 Mathematic12 General11 General11 Mathematics11 General12 General11 Mathematic12 Specialist11 Mathematics11 Mathematics11 Mathematics11 Mathematics12 Specialist 11 Mathematics11 Mathematic11 GeneralNot coveredTopic 2 - 62.72.82.92.1011 General11 Mathematics11 Mathematic12 Specialist11 Mathematics11 Mathematics11 Mathematic11 GeneralNot covered12 Specialist11 Mathematics11 Mathematic12 Methods12 Methods * only 153.1611 Mathematic11 General11 Mathematic11 General11 Mathematic11 General11 Mathematic11 General11 MathematicsNot covered11 Mathematics11 Mathematics11 Mathematics11 Mathematic* 2-dimensional12 Specialist12 Specialist11 Mathematic12 Specialist11 General* only partially* only partially11 General11 General* only .54.64.74.84.94.104.114.124.1311 General11 General11 General12 GeneralYear 10-10AYear 10-10A12 Methods12 Methods12 MethodsNot coveredNot coveredNot coveredNot covered4 - Statistics and pic 3 - Geometry and TrigonometryIBDP MATHEMATICS: APPLICATIONS AND INTERPRETATION SYLLABUS11 Mathematics* only partially11 Mathematics11 Mathematics11 Mathematics12 General

TopicTopic 5 - Not covered12 Methods12 MethodsNot coveredNot covered12 5.155.165.175.1811 Mathematic12 Methods11 Mathematic12 Methods11 Mathematic12 Methods11 Mathematic12 Methods12 Methods11 Mathematic12 Methods11 Mathematic12 Methods12 Methods12 Methods12 Methods12 Methods 12 Specialist12 Methods 12 Specialist12 Methods 11 Mathematics12 Specialist12 SpecialistNot coveredNot coveredNot covered* only partially

Topic 1 - Number and 1.141.151.1611 General11 Mathematics11 Mathematics11 General11 Mathematics 12 General11 Mathematics11 Mathematic12 Specialist11 Mathematic* Not change of base11 Mathematics11 Mathematics11 Mathematic* only partiallyNot covered11 Mathematics12 Specialist 11 Mathematics * Not Euler's form11 Mathematic12 Specialist12 Specialist 11 Mathematics12 SpecialistTopic 2 - 611 General11 Mathematics11 Mathematic12 Specialist11 Mathematics11 Mathematics12 Methods 12 Specialist11 Mathematics11 Mathematics11 Mathematic12 Specialist11 Mathematic12 Methods11 Mathematics11 Mathematics12 Specialist 11 Mathematics12 Specialist12 Specialist * only partiallyNot covered12 Specialist * only 143.153.163.173.1811 Mathematic11 General11 Mathematic11 General11 Mathematic11 General11 Mathematic11 General11 Mathematics11 Mathematics11 Mathematics11 Mathematics11 Mathematic12 Specialist11 Mathematics11 Mathematics12 Specialist 11 Methods (2D)11 Mathematic12 Specialist12 Specialist12 Specialist12 Specialist12 Specialist * only partially12 SpecialistSLSLSLSL4.14.24.34.411 General11 Mathematics11 General11 Mathematic* only partially12 LAHLTopic 3 - Geometry and TrigonometryIBDP MATHEMATICS: ANALYSIS AND APPROACHES SYLLABUS

Topic 4 - Statistics and ProTopic 5 - .114.124.134.14Year 10-10AYear 10-10A12 Methods12 Methods12 Methods12 GeneralNot covered12 MethodsNot covered12 5.155.165.175.185.1911 Mathematic12 Methods11 Mathematic12 Methods11 Mathematic12 Methods11 Mathematic12 Methods12 Methods12 Methods12 Methods12 Methods 11 Mathematics12 Methods 11 Mathematics12 Methods * only partially12 Methods 12 Specialist12 Methods 11 MathematicsNot covered12 Specialist12 Specialist * only partially12 Specialist * only partially12 Methods 12 Specialist12 Specialist * only partiallyNot covered11 Mathematics11 Mathematics11 Mathematics12 General* only partially* only partially

Stage 1 GeneralMathematicsUnit (Topic)Topic 1 Investing andBorrowingSubtopic 1.1 Investing forInterestContentIncluded in IncludedIncluded inIncludedIncluded inin AppsCommentsPriorAnalysisin Apps HLAnalysis SLSLlearningHLNot specifically mentioned in SL1.4 SL 1.4 common content SL 1.4 common content SL 1.4 common content * * Annualised rates are notspecifically mentioned in SL 1.4 SL 1.4 common content

SL 1.4 common contentSubtopic 1.2: Investingin sharesShares not mentioned in the IBGuideSubtopic 1.3: Return oninvestmentShares not mentioned in the IBGuide *Subtopic 1.4: Costs ofborrowing * Inflation mentioned in SL 1.4,but not taxLoans only mentioned in "Othercontexts" below SL 1.4 in theguide.

Loans only mentioned in "Othercontexts" below SL 1.4 in theguide.Topic 2: MeasurementSubtopic 2.1:Application ofmeasuring devices andunits of measurement Subtopic 2.2: Perimeterand area of planeshapes prior knowledge? AISL 1.6 SL 1.1 common content SL 3.3 common content prior knowledge? And SL 3.4common content

Not specifically mentioned.Not specifically mentioned.Subtopic 2.3: Volumeand surface area ofsolids SL 3.1Prior knowledge?not specifically mentioned SL 3.1 common contentSubtopic 2.4: Scale andratesPrior knowledge?Prior knowledge?

* * SL 5.1 common content "ratesof change" density notmentioned explicitly.?assume this is included in IBTopic 3: StatisticalinvestigationSubtopic 3.1: Thestatistical investigationprocess SL 4.1 common content?assume this is included in IBSubtopic 3.2: Samplingand collecting dataSubtopic 3.3:Classifying andorganising data SL 4.1 common content SL 4.1 common content SL 4.1 common contentnot specifically mentioned

SL 4.2 common content SL 4.1 common contentSubtopic 3.4: Theshape, location, andspread of distributionsof numerical data?assume this is included in IB SL 4.3 common content SL 4.3 common content SL 4.1 - 4.4 common content

?assume this is included in IBSubtopic 3.5: Formingand supportingconjectures across twoor more groups *Topic 4: Applications of Subtopic 4.1: Similaritytrigonometry * Categorical data is notspecifically mentioned

Subtopic 4.2: Righttriangle geometry SL 3.2 common content SL 3.2 common contentSubtopic 4.3: Area oftrianglesnot specifically mentionedSubtopic 4.4: Solvingproblems with non-righttriangles SL 3.2 common content SL 3.2 common content SL 3.2 common content

SL 3.2 common content SL 3.2 common content SL 2.1 common content SL 2.1 common content AISL2.5also "linear models" SL 2.1 common content SL 2.1 common content Topic 5: Linear andexponential functionsand their graphsSubtopic 5.1: Linearfunctions and graphs

SL 2.1 common content * AI SL 2.5, AASL 2.9 * AI SL 2.5, AASL 2.9 AI SL 2.5, AASL 2.9 Subtopic 5.2:Exponential functionsand graphs SL 1.4 common content andfurther technology use in AISL1.7 also *SL 2.5 common content AIHL2.9 "half-life"included?

Topic 6: Matrices andnetworksSubtopic 6.1: Matrixarithmetic and costingapplications AIHL 1.14 AIHL 1.14 AIHL 1.14 AIHL 1.14 AIHL 1.14 AIHL 1.14 AIHL 1.14?assume this is in IB?assume this is in IBSubtopic 6.2: Networks AIHL 3.14 AIHL 3.14 AIHL 3.14 AIHL 3.14

?Topic 7: Open topic * Schools may choose to develop a topic that isrelevant to their local context.partially includedincluded AIHL 3.14 AIHL 3.15 AIHL 3.15 AIHL 3.16 ?possibly a low-level example ofnetwork problems in AIHL?possibly related to low-levelVoronoi diagram problems?

Stage 2 GeneralMathematicsUnit (Topic)ContentTopic 1: Modellingwith linearrelationshipsSubtopic 1.1:Simultaneouslinear equationsConsider the different ways a linear function can berepresented and the links between them: Contextual description Numerical sequence Graph Algebraic formulaFor a problem with two independent variables,consider how much information is required todetermine a unique solution.Consider how contextual problems involvingsimultaneous linear equations can be solved efficiently.Using electronic technology for: graphing, using theequation solver functionality.Non-unique solutionsHow can linear functions be used to optimise asituation where we have control of two variables?Setting up the constraints (with inequalities) and anobjective function. Graphing the feasible region.Finding the optimal solution.Considering wastageSubtopic 1.2:LinearprogrammingTopic 2: Modellingwith matricesSubtopic 2.1:Application ofmatrices tonetworkproblemsIncluded IncludedIncluded IncludedIncludedininin Apps in Appsin PriorAnalysis AnalysisSLHLlearningSLHLComments No linear programming in IBNo linear programming in IBHow do we deal with an optimal solution that is notachievable because only discrete values are allowed?No linear programming in IBWhat happens to the optimal solution if the originalparameters change?No linear programming in IBConsider how can a matrix be used to show theconnections in a network. AIHL 3.14 Graph theory focusConnectivity matrices AIHL 3.15 Graph theory focusConsider how matrix operations help to find thenumber of indirect connections in a network. AIHL 3.15 Graph theory focusPowers of matrices and multi-stage connections AIHL 3.15 Graph theory focus

No specific Dominance matrixapplication mentioned in the IBguide.No specific Dominance matrixapplication mentioned in the IBguide.No specific Dominance matrixapplication mentioned in the IBguide.No specific Dominance matrixapplication mentioned in the IBguide.No specific Dominance matrixapplication mentioned in the IBguide.Limitations of using higher powersConsider of what use weighted sums of the powers ofconnectivity matrices are.· Measures of efficiency or redundancyPrediction in dominance relationshipsReasonableness of weightings and limitations of themodelSubtopic 2.2:Application ofmatrices totransitionproblemsTransition matrices and its properties.2 by 2 systemsConsider how can future trends be predicted.Consider what happens in the long run in a transitionmodel. The steady state.Consider the effect changes to the initial conditionshave on the steady state.3 by 3 or higher order systems AIHL 4.19 (AIHL goes further,considering eigenvectors andeigenvalues) AIHL 4.19 (AIHL goes further,considering eigenvectors andeigenvalues) AIHL 4.19 (AIHL goes further,considering eigenvectors andeigenvalues) AIHL 4.19 (AIHL goes further,considering eigenvectors andeigenvalues) AIHL 4.19 (AIHL goes further,considering eigenvectors andeigenvalues) AIHL 4.19 (AIHL goes further,considering eigenvectors andeigenvalues)

Consider the limitations of the transition matrix model.Topic 3: StatisticalmodelsSubtopic 3.1:BivariatestatisticsAIHL 4.19 (AIHL goes further,considering eigenvectors andeigenvalues)Consider how bivariate data be modelled when therelationship appears linear but is not perfect. SL 4.4 common content· The statistical investigation process· Independent and dependent variables· Scatter plotsCorrelation coefficients SL 4.4 common contentSL 4.4 common contentSL 4.4 common contentSL 4.4 common contentSL 4.1 and SL 4.4 commoncontentSL 4.4 common contentSL 4.4 common content SL 4.4 common contentThe effects of outliersCausalityLinear regressionidentification and interpretation of the slope andintercept of the graph of the linear equation in thecontext of the model Not mentioned in the IB GuideResidual plotsExponential regression y a*(b x) interpretation of the values of ‘a ’ and ‘b ’ Interpolation and extrapolation, reliability, andinterpretation of predicted results Subtopic 3.2: TheParameters μ (mean) and σ (standard deviation), Bellnormalshape and symmetry about the meandistribution AIHL 2.9 Exponential modelsand AIHL 4.13 (AIHL 4.13 goesfurther and includes quadratic,cubic, exponential, power andsine regression)AIHL 4.13 (AIHL goes further andincludes quadratic, cubic,exponential, power and sineregression)AIHL 4.13 (AIHL goes further andincludes quadratic, cubic,exponential, power and sineregression)SL 4.9 common content

Topic 4: FinancialmodelsConsider why so many observed sets of data appearnormally distributed. Quantities that arise as the sum ofa large number of independent random variables canbe modelled as normal distributions. SL 4.9 common contentConsider why normal distributions are important. Thevariation in many quantities occurs in an approximatelynormal manner. Normal distributions may be used tomake predictions and answer questions that relate tosuch quantities SL 4.9 common content SL 4.9 common content SL 4.9 common content SL 4.9 common contentConsider how the characteristics of the normaldistribution can be used for prediction. 68:95:99.7%rule.Calculation of area under the curve, looking at theposition of one, two, and three standard deviationsfrom the meanCalculation of non-standard proportionsCalculation of values on the distribution, given the areaunder the curveSubtopic 4.1:The compound interest model is used to plan for theModels for savingfuture. * On GDC using Financial Mode · Finding FV , PV , n, and I Consider how the compound interest model can beimproved to make it more realistic and flexible. Future valued annuities Calculation of: Future value, The regular deposit,number of periods, interest rate, the value of theaccumulated savings after a given period. Total interest earned SL 4.9 common contentSL 1.4 common content andfurther technology use in AISL1.7 alsoSL 1.4 common content andfurther technology use in AISL1.7 alsoSL 1.4 common content andfurther technology use in AISL1.7 alsoSL 1.4 common content andfurther technology use in AISL1.7 alsoSL 1.4 common content andfurther technology use in AISL1.7 alsoSL 1.4 common content andfurther technology use in AISL1.7 also

Consider what factors should be considered whenselecting an investment. Interest as part of taxable income, including calculationsThe effects of inflation, including calculationsInstitution and government chargesComparison of two or more investments involvingnominal and/or flat interest by conversion to anequivalent annualised rate (effective rate)Subtopic 4.2:Models forborrowingNot specifically mentioned in SL1.4Consider how can a regular income be provided fromsavings? Annuities. Superannuation.Consider if money must be borrowed, how much will itcost? Reducing-balance loans, finding the repayment for agiven loan, calculating total interest paid, the size of anoutstanding debt after a given time. Consider how could the amount of interest paid on aloan can be reduced. Interest-only loans and sinking fundsFinding the effect of: increasing the frequency ofpayments, increasing the value of the payments,reducing the term of the loan, paying a lump sum offthe principal owing, changing interest rates, usingoffset accounts Consider: Is the nominal rate of interest quoted by abank what is really being paid on a loan? Loan interest rates, including variable rate, fixed rate,and others. Interest paid. Calculation of the comparisonrates for two or more loans to determine the mostappropriate option.SL 1.4 common content andfurther technology use in AISL1.7 alsoNot specifically mentioned in SL1.4SL 1.4 common contentNot specifically mentioned in SL1.4 Not specifically mentioned in SL1.4Loans only mentioned in "Othercontexts" below SL 1.4 in theguide.Loans only mentioned in "Othercontexts" below SL 1.4 in theguide.Loans only mentioned in "Othercontexts" below SL 1.4 in theguide.Loans only mentioned in "Othercontexts" below SL 1.4 in theguide. Loans only mentioned in "Othercontexts" below SL 1.4 in theguide. Loans only mentioned in "Othercontexts" below SL 1.4 in theguide. Loans only mentioned in "Othercontexts" below SL 1.4 in theguide.

Topic 5: DiscretemodelsSubtopic 5.1:Critical pathanalysisSubtopic 5.2:AssignmentproblemsTopic 6: Open topicFor a job requires the completion of a series of taskswith set precedence, what is the minimum time inwhich this job can be finished?Although a precedence networkis a graph, this particularapplication is possibly notcovered in the IB Graph Theorycontent in AIHL 3.16Precedence tables. Drawing directed networks. Dummy links.Although a precedence networkis a graph, this particularapplication is possibly notcovered in the IB Graph Theorycontent in AIHL 3.16Critical tasks. Forward and backward scans. Minimumcompletion time. Critical path.Although a precedence networkis a graph, this particularapplication is possibly notcovered in the IB Graph Theorycontent in AIHL 3.16Earliest and latest starting times for individual tasks. Slack time.Although a precedence networkis a graph, this particularapplication is possibly notcovered in the IB Graph Theorycontent in AIHL 3.16Assignment problems deal with allocating tasks in away that minimises ‘costs’ (note that ‘costs’ can bemeasurements such as time or distance, as well asmoney). For example, if the times in which fourswimmers each do 50 metres of each of the fourdifferent strokes are known, how should they be placedin a medley relay to minimise the total time for them tocomplete the race?Not mentioned in the IB Guide.The Hungarian algorithm for finding the optimum solution.Not mentioned in the IB Guide.Finding minimum cost. Finding maximum profit. Non-square arrays.Not mentioned in the IB Guide.Schools may choose to develop a topic that is relevantto their own local context. When this option isundertaken, the open topic developed replaces Topic 2:Modelling with matrices.

* Shares topic *partially included includedNot mentioned in the IB Guide.

Stage 1MathematicsUnit (topics)Includedin PriorlearningContentTopic 1: Functions Subtopic 1.1: Lines andand graphslinear relationshipsIncluded IncludedIncluded Includedin Analysis in Analysisin Apps SL in Apps HLSLHL SL 2.1 common content SL 2.1 common content *Intersections found using technology in SL 2.4common content. AASL 2.10 - solvingequations both graphically and analytically. *AASL 2.8.SL 2.4 common content mentions"determine key features of graphs .verticaland horizontal asymptotes using technology." Subtopic 1.2: Inverseproportion𝑦𝑦 Features of the graph of1𝑥𝑥 Featuresof horizontal and verticalasymptotes includng translations.Subtopic 1.3: Relations Equations of circles in both centre/radiusand expanded formSubtopic 1.4: FunctionsTopic 2:Polynomials * * * *AASL 2.8, AASL 2.11.SL 2.4 commoncontent mentions "determine key features ofgraphs .vertical and horizontal asymptotesusing technology." SL 2.2 common content Recognise the distinction betweenfunctions and relations.Subtopic 2.1: QuadraticQuadratic relationships in everydayrelationshipssituationsFeatures of the graph of y x 2 and therelationships between y a(x-b) 2 c and y (x-a)(x-b).Commentsnot explicitly mentioned but suspect includedin SL 2.2. AISL2.5, AASL2.6 (as examples). * *AISL2.5(technology use focus for finding roots),AASL2.6.

*? * *AASL 2.7 (presume technology approachtaught in AA also) AISL2.5 * *AAHL2.12. AISL2.5(cubics only). * *AISL2.5 (modelling with cubics) * *Subtopic 2.2: Cubic andquartic polynomialsGraphs of the cubic function in differentforms. Extending from the quadratic and cubicfunctions — behaviour can be expectedfrom the graphs of quartic functions. * *AASL 2.7 (?presume technology approachtaught also) AISL2.5(only us

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 .