VCE Further Mathematics Units 3 and 4 – All Topics

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Description

1. Data Analysis
2. Recursion and Financial Mathematics
3. Matrices
4. Network and Decision Mathematics
5. Geometry and Measurement
6. Graphs and Relations




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Outcome 1

Unit 3
On completion of this unit, the student should be able to select and apply the mathematical concepts, models and techniques as specified in Area of Study 1 in a range of contexts of increasing complexity.

Key knowledge
• the facts, concepts and techniques associated with data analysis and recursion and financial modelling
• standard models studied in data analysis and recursion and financial modelling and their area of application
• general formulation of the concepts, techniques and models studied in data analysis and recursion and financial modelling
• assumptions and conditions underlying the use of the concepts, techniques, and models associated with data analysis and recursion and financial modelling.

Key skills
• identify, recall and select facts, concepts, models and techniques needed to investigate and analyse statistical features of a data set with several variables that can include time series data
• select and implement standard financial models to investigate and analyse a financial or mathematically equivalent non-financial situation that requires the use of increasingly sophisticated models to complete the analysis
• interpret and report the results of a statistical investigation or of completing a modelling or problem-solving task in terms of the context under consideration, including discussing the assumptions in application of these models.

Unit 4
On completion of this unit, the student should be able to select and apply the mathematical concepts, models and techniques from the two selected modules in a range of contexts of increasing complexity.

Key knowledge
• the facts, concepts and techniques associated with the modules studied
• the standard models studied and their area of application
• the general formulation of the concepts, techniques and models introduced in the applications modules studied
• assumptions and conditions underlying the use of the facts, concepts, techniques, and models introduced in the modules studied.

Key skills
• identify, recall and select the mathematical concepts, models and techniques needed to solve an extended problem or conduct an investigation in a variety of contexts
• solve and analyse an extended investigation or practical problem in an unfamiliar context
• implement standard models to analyse a practical context that requires the use of increasingly sophisticated variations of the original model to answer the questions posed
• interpret and report the results of modelling or problem-solving activities in terms of the context of the situation being analysed, including discussing assumptions made.

Outcome 2

Unit 3
On completion of this unit, the student should be able to select and appropriately use numerical, graphical, symbolic and statistical functionalities of technology to develop mathematical ideas, produce results and carry out analysis in situations requiring problem-solving, modelling or investigative techniques or approaches.

Key knowledge
• the difference between exact numerical and approximate numerical answers when using technology to perform computation, and rounding to a given number of decimal places or significant figures
• domain and range requirements for specification of graphs of models and relations, when using technology
• the role of parameters in specifying general forms of models and equations
• the relation between numerical, graphical and symbolic forms of information about models and equations and the corresponding features of those functions and equations
• similarities and differences between formal mathematical expressions and their representation by technology
• the selection of an appropriate functionality of technology in a variety of mathematical contexts.

Key skills
• distinguish between exact and approximate presentations of mathematical results produced by technology, and interpret these results to a specified degree of accuracy in terms of a given number of decimal places or significant figures
• use technology to carry out numerical, graphical and symbolic computation as applicable
• produce results using a technology that identify examples or counter-examples for propositions
• produce tables of values, families of graphs and collections of other results using technology, which support general analysis in problem-solving, investigative and modelling contexts
• use appropriate domain and range specifications to illustrate key features of graphs
• identify the relation between numerical, graphical and symbolic forms of information about models and equations and the corresponding features of those models and equations
• specify the similarities and differences between formal mathematical expressions and their representation by technology
• select an appropriate functionality of technology in a variety of mathematical contexts, related to data analysis, recurrence relations and financial modelling, and provide a rationale for these selections
• apply suitable constraints and conditions, as applicable, to carry out required computations
• relate the results from a particular technology application to the nature of a particular mathematical task (investigative, problem solving or modelling) and verify these results
• specify the process used to develop a solution to a problem using technology, and communicate the key stages of mathematical reasoning (formulation, solution, interpretation) used in this process.

Unit 4
On completion of this unit, the student should be able to select and appropriately use numerical, graphical, symbolic and statistical functionalities of technology to develop mathematical ideas, produce results and carry out analysis in situations requiring problem-solving, modelling or investigative techniques or approaches.

Key knowledge
• the difference between exact numerical and approximate numerical answers when using technology to perform computation, and rounding to a given number of decimal places or significant figures
• domain requirements for specification of graphs of models and relations, when using technology
• the role of parameters in specifying general forms of models, relations and equations
• the relation between numerical, graphical and symbolic forms of information about models, relations and equations and the corresponding features of those models, relations and equations
• the selection of an appropriate functionality of technology in a variety of mathematical contexts.

Key skills
• distinguish between exact and approximate presentations of mathematical results produced by technology, and interpret these results to a specified degree of accuracy
• use technology to carry out numerical, graphical and symbolic computation as applicable
• produce results using a technology that identifies examples or counter-examples for propositions
• produce tables of values, families of graphs and collections of other results using technology that supports general analysis in problem-solving, investigative and modelling contexts
• use appropriate domain and range specifications to illustrate key features of graphs of models and relations
• identify the relation between numerical, graphical and symbolic forms of information about functions and equations and the corresponding features of those models and equations
• specify the similarities and differences between formal mathematical expressions and their representation by technology
• select an appropriate functionality of technology in a variety of mathematical contexts related to matrices, networks, geometry and measurement, and graphs and relations as applicable, and provide a rationale for these selections
• apply suitable constraints and conditions, as applicable, to carry out required computations related to matrices, networks, geometry and measurement, and graphs and relations as applicable
• relate the results from a particular technology application to the nature of a particular mathematical task (investigative, problem solving or modelling) and verify these results
• specify the process used to develop a solution to a problem using technology, and communicate the key stages of mathematical reasoning (formulation, solution, interpretation) used in this process.

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