On completion of each unit, the student should be able to apply mathematical processes in non-routine contexts and analyse and discuss these applications of mathematics in at least three areas of study.

To achieve this outcome the student will draw on knowledge and skills outlined in at least three areas of study.

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

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 for the investigation
• make inferences from analysis and use these to draw valid conclusions related to a given context for the investigation
• construct mathematical proofs
• communicate conclusions using both mathematical expression and everyday language; in particular, the interpretation of mathematics with respect to the context for the investigation.

On completion of this unit the student should be able to use technology to produce results and carry out analysis in situations requiring problem-solving, modelling or investigative techniques or approaches in at least three areas of study.

To achieve this outcome the student will draw on knowledge and related skills outlined in at least three areas of study.

Key knowledge
• exact and approximate technological specification of mathematical information such as numerical data, graphical forms and the solutions of equations
• domain and range requirements for the technological specification of graphs of functions and relations
• 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 in various technology applications
• the selection of an appropriate technology application in a variety of mathematical contexts.

Key skills
• distinguish between exact and approximate presentations of mathematical results, 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 technology that identifies examples or counter-examples for propositions
• produce tables of values, families of graphs and collections of other results which support general analysis in problem-solving, investigative or modelling contexts
• apply analysis in problem-solving, investigative or modelling contexts
• use an appropriate domain and range of technological specifications which 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 in various technology applications
• make appropriate selections for technology applications in a variety of mathematical contexts, and provide a rationale for these selections
• relate the results from a particular application to a mathematical task (investigative, problem solving or modelling).