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Advice for teachers -
Mathematical Methods

Units 3 and 4

Performance criteria

The following performance criteria have been developed to assist teachers in the assessment of School Assessed Coursework for Mathematical Methods Units 3 and 4. The performance criteria for the Application task and for the two modelling or problem-solving tasks relate the mark weightings for the outcomes to these assessment tasks and provide a basis for decision about level of achievement.


Application task performance criteria

 

Unit 3

Outcome 1

Define and explain key concepts as specified in the content from the areas of study, and apply a range of related mathematical routines and procedures.
Mark range Criterion
0 - 3 Appropriate use of mathematical conventions, symbols and terminology

Application of mathematical conventions in diagrams, tables and graphs, such as axes labels and conventions for asymptotes. Appropriate and accurate use of symbolic notation in defining mathematical terms or expressions, such as formulas, equations and transformations. Use of correct expressions in symbolic manipulation or computation in mathematical work. Use of correct terminology, including set notation, to specify relations and functions, such as domain, co-domain, range and rule. Description of key features of relations and functions, such as asymptotes, coordinates for axial intercepts and stationary points.

0 - 6 Definition and explanation of key concepts

Definition of mathematical concepts using appropriate terminology, phrases and symbolic expressions. Provision of examples which illustrate key concepts and explain their role in the development of related mathematics. Statement of conditions or restrictions which apply to the definition of a concept. Identification of key concepts in relation to each area of study and explanation of the use of these concepts in applying mathematics in different practical or theoretical contexts.

0 - 6 Accurate use of mathematical skills and techniques

Use of algebra and numerical values to evaluate expressions, substitute into formulas, construct lists and tables, produce graphs and solve equations. Use of mathematical routines and procedures involving algebra, functions, coordinate geometry, calculus to obtain results and solve problems. Identification of domain and range of a function or relation and other key features using numerical, graphical and algebraic techniques, including approximate or exact specification of values.


 

Unit 3

Outcome 2

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.

Mark range Criterion
0 - 4 Identification of important information, variables and constraints

 

Identification of key characteristics of a problem, task or issue and statement of any assumptions underlying the use of relevant mathematics in the given context. Choice of suitable variables, parameters and constants for the development of mathematics related to various aspects of a given context. Specifications of constraints, such as domain and range constraints, related to aspects of a context.

0 - 8 Application of mathematical ideas and content from the specified areas of study

Demonstration of understanding of key mathematical content from one or more areas of study in relation to a given context. Use of specific and general formulations of concepts and mathematical content drawn from the areas of study to derive results for analysis in this context. Appropriate use of examples to illustrate the application of a mathematical process, or use of a counter-example to disprove a proposition or conjecture. Use of a variety of approaches to develop functions as models for data presented in tabular, diagrammatic or graphical form. Use of algebra, coordinate geometry, derivatives, gradients, anti-derivatives and integrals, to set up and solve problems.

0 - 8 Analysis and interpretation of results

Analysis and interpretation of results obtained from examples or counter-examples to establish or refute general case propositions or conjectures related to a context for investigation. Generation of inferences from analysis to draw conclusions related to the context for investigation, and to verify or modify conjectures. Discussion of the validity and limitations of any models.

 

Unit 3

Outcome 3

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.
Mark range Criterion
0 - 6 Appropriate selection and effective use of technology

Relevant and appropriate selection and use of technology, or a functionality of the selected technology for the mathematical context being considered. Distinction between exact and approximate results produced by technology, and interpretation of these results to a required accuracy. Use of appropriate range and domain and other specifications which illustrate key features of the mathematics under consideration.

0 - 9 Application of technology

Use and interpretation of the relationship between numerical, graphical and symbolic forms of information produced by technology about relations, functions and equations and the corresponding features of those relations, functions or equations.

Analysis of the relationship of the results from an application of technology to the nature of a particular mathematical question, problem or task. Use of tables of values, families of graphs or collections of other results produced using technology to support analysis in problem-solving, investigative or modelling contexts. Production of results efficiently and systematically which identify examples or counter-examples which are clearly relevant to the task.

A sample record sheet for the application task (doc - 73.5kb) can be used to record student level of achievement with respect to the available marks for the performance criteria relating to each outcome, and to indicate pointers corresponding to relevant aspects of the task.


Modelling or problem-solving task performance criteria

 

Unit 4

Outcome 1

Define and explain key terms and concepts as specified in the content from the areas of study, and apply a range of related mathematical routines and procedures.
Mark range Criterion
Task 1
0 - 2
Appropriate use of mathematical conventions, symbols and terminology

Application of mathematical conventions in diagrams, tables and graphs, such as axes labels and conventions for asymptotes. Appropriate and accurate use of symbolic notation in defining mathematical terms or expressions, such as equations and transformations. Use of correct expressions in symbolic manipulation or computation in mathematical work. Use of correct terminology, including set notation, to specify relations and functions, such as domain, co-domain, range and rule. Description of key features of relations and functions, including probability mass and density functions, such as asymptotes, coordinates for axial intercepts and stationary points.

Task 2
0 - 2
Task 1
0 - 3
Definition and explanation of key concepts

Definition of mathematical concepts using appropriate terminology, phrases and symbolic expressions. Provision of examples which illustrate key concepts and explain their role in the development of related mathematics. Statement of conditions or restrictions which apply to the definition of a concept. Identification of key concepts in relation to each area of study and explanation of the use of these concepts in applying mathematics in different practical or theoretical contexts.

 

Task 2
0 - 2
Task 1
0 - 3
Accurate use of mathematical skills and techniques

Use of algebra and numerical values to evaluate expressions, substitute into formulas, construct tables, produce graphs and solve equations. Use of mathematical routines and procedures involving algebra, functions, coordinate geometry, calculus, probability and statistics to obtain results and solve problems. Identification of domain and range of a function or relation and other key features using numerical, graphical and algebraic techniques, including approximate or exact specification of values.

 

Task 2
0 - 3

 

Unit 4

Outcome 2

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.
Mark range Criterion
Task 1
0 - 2
Identification of important information, variables and constraints

Identification of key characteristics of a problem, task or issue and statement of any assumptions underlying the use of relevant mathematics in the given context. Choice of suitable variables, including random variables, parameters and constants for the development of mathematics related to various aspects of a given context. Specifications of constraints, such as domain and range constraints, related to aspects of a context.

Task 2
0 - 2
Task 1
0 - 4
Identification of important information, variables and constraints

Identification of key characteristics of a problem, task or issue and statement of any assumptions underlying the use of relevant mathematics in the given context. Choice of suitable variables, parameters and constants for the development of mathematics related to various aspects of a given context. Specifications of constraints, such as domain and range constraints, related to aspects of a context.

Task 2
0 - 4
Task 1
0 - 4
Analysis and interpretation of results

Analysis and interpretation of results obtained from examples or counter-examples to establish or refute general case propositions or conjectures related to a context for investigation. Generation of inferences from analysis to draw conclusions related to the context for investigation, and to verify or modify conjectures. Discussion of the validity and limitations of any models.

 

Task 2
0 - 4

 

Unit 4

Outcome 3

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.
Mark range Criterion
Task 1
0 - 3
Appropriate selection and effective use of technology

Relevant and appropriate selection and use of technology, or a function of the selected technology for the mathematical context being considered. Distinction between exact and approximate results produced by technology, and interpretation of these results to a required accuracy. Use of appropriate range and domain and other specifications which illustrate key features of the mathematics under consideration.

Task 2
0 - 3
Task 1
0 - 4
Application of technology

Use and interpretation of the relation between numerical, graphical and symbolic forms of information produced by technology about functions and equations and the corresponding features of those functions or equations.

Analysis of the relationship of the results from an application of technology to the nature of a particular mathematical question, problem or task. Use of tables of values, families of graphs or collections of other results produced using technology to support analysis in problem solving, investigative or modelling contexts. Production of results efficiently and systematically which identify key features, examples or counter-examples which are clearly relevant to the task.

Task 2
0 - 5

A sample record sheet for modelling or problem-solving task 1 (doc - 69kb) and A sample record sheets for modelling or problem-solving task 2 (doc - 69kb) can be used to record student level of achievement with respect to the available marks for the performance criteria relating to each outcome, and to indicate pointers corresponding to relevant aspects of the task.

 

These performance criteria may be used in several ways:

  • directly in conjunction with the sample record sheets and teacher annotations for pointers with respect to key aspects of the task related to each criterion for the outcomes
  • directly with the descriptive text for each criterion modified to incorporate task specific elements as applicable
  • as a template for teachers to develop their own criteria and descriptive text for each criterion, including their own allocation of marks for the criteria with the total mark allocation for each outcome as specified in the study design.