On completion of each unit the student should be able to apply mathematical processes in non-routine contexts, including situations requiring problem-solving, modelling or investigative techniques or approaches, and analyse and discuss these applications of mathematics.

To achieve this outcome the student will draw on knowledge and skills outlined in one or more areas of study.

Key knowledge
• the key mathematical content from one or more areas of study related to a given context
• specific and general formulations of concepts used to derive results for analysis within a given context
• the role of examples, counter-examples and general cases in working mathematically
• inferences from analysis and their use to draw valid conclusions related to a given context.

Key skills
• specify the relevance of key mathematical content from one or more areas of study to the investigation of various questions in a given context
• develop mathematical formulations of specific and general cases used to derive results for analysis within a given context
• use a variety of techniques to verify results
• make inferences from analysis and use these to draw valid conclusions related to a given context
• communicate conclusions using both mathematical expression and everyday language, in particular, the interpretation of mathematics with respect to the context.

On completion of each 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.

To achieve this outcome the student will draw on knowledge and related skills outlined in all the areas of study.
Key knowledge

• the exact and approximate specification of mathematical information such as numerical data, graphical forms and general or specific forms of solutions to equations produced by the use of technology
• domain and range requirements for specification of graphs of functions and relations, when using technology
• the role of parameters in specifying general forms of functions and equations
• the relation between numerical, graphical and symbolic forms of information about functions 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
• use technology to carry out numerical, graphical and symbolic computation as applicable
• produce results using a technology which 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 functions and relations
• identify the relation between numerical, graphical and symbolic forms of information about functions and equations and the corresponding features of those functions and equations
• specify the similarities and differences between formal mathematical expressions and their representation by technology, in particular, equivalent forms of symbolic expressions
• 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.