On completion of each unit the student should be able to select and apply mathematical facts, concepts, models and techniques from the topics covered in the unit to investigate and analyse extended application problems in a range of contexts.
To achieve this outcome the student will draw on knowledge and skills outlined in the areas of study.
• the facts, concepts, and techniques associated with the topics studied
• the standard mathematical models used in the topics studied
• the facts, concepts, techniques and/or models suitable to solve extended application problems or to conduct a structured investigation in context
• assumptions and conditions underlying the facts, concepts, techniques, and models used when solving a problem or conducting an investigation.
• identify, recall and select the mathematical facts, concepts and techniques needed to solve an extended problem or conduct an investigation in a variety of contexts
• recall, select and use standard mathematical models to represent practical situations
• use specific models to comment on particular situations being analysed and to make predictions
• interpret and report the results of applying these models in terms of the context of the problem being solved, including discussing the assumptions applying to the application of such models.
On completion of this unit the student should be able to select and 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.
To achieve this outcome the student will draw on knowledge and skills outlined in all the areas of study.
• 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, and 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 functions, relations 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.
• 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, which support 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 connection between numerical, graphical and symbolic forms of information about functions, relations and equations and the corresponding features of those models, relations 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 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.