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Advice for teachers -
Specialist Mathematics

Units 3 and 4

Performance criteria

The following performance criteria have been developed to assist teachers in the assessment of School Assessed Coursework for Specialist Mathematics 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 complex numbers, vectors, derivatives, anti-derivatives and integrals. Use of correct expressions in symbolic manipulation or computation in mathematical work. Use of correct terminology to specify relations and functions, such as domain, range and rule.

0 - 6 Definition and explanation of key concepts

Definition of mathematical concepts using appropriate phrases and symbolic expressions. Provision of examples which illustrate key concepts and explain their role in the development of related mathematics. Identification of key concepts in relation to each area of study and explanation of the use of these concepts in applying mathematics in different contexts. Construction of mathematical expressions involving concepts such as complex numbers, vectors, derivatives, anti-derivatives and integrals.

0 - 6 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 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, with an emphasis on general cases, in non-routine contexts, 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 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 algebra, coordinate geometry, calculus, vectors and complex numbers 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 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.

0 - 9 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 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.


SPECIALIST MATHEMATICS SCHOOL - ASSESSED COURSEWORK
Modelling or Problem-Solving Tasks

Unit 4

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
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 complex numbers, vectors, derivatives, anti-derivatives and integrals, random variables, parameters, statistics and distributions. Use of correct expressions in symbolic manipulation or computation in mathematical work. Use of correct terminology to specify relations and functions, such as domain, range and rule and confidence intervals.

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

Definition of mathematical concepts using appropriate phrases and symbolic expressions. Provision of examples which illustrate key concepts and explain their role in the development of related mathematics. Identification of key concepts in relation to each area of study and explanation of the use of these concepts in applying mathematics in different contexts. Construction of mathematical expressions involving concepts such as complex numbers, vectors, derivatives, anti-derivatives and integrals, random variables, parameters, distributions, estimators, hypotheses, tests and errors.

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 and statistical techniques, including approximate or exact specification of values.

Task 2
0 - 3

Unit 4

Outcome 2

Apply mathematical processes, with an emphasis on general cases, in non-routine contexts, 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, constants parameters and statistics 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

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, conjecture or hypothesis. Use of algebra, coordinate geometry, functions, calculus, vectors, complex numbers probability and statistics to set up and solve problems.

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 and hypotheses. Discussion of the validity and limitations of any models or inferences, and the structure and correctness of proofs.

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, statistical and symbolic forms of information produced by technology about functions and relations, equations and data and the corresponding features of those functions, relations, equations or data. 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, distributions 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.

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.