# Achievement standards

## Concepts and Techniques

A B C D E
• demonstrates knowledge and understanding of concepts of functions, calculus, vectors and statistics in routine and non-routine problems in a variety of contexts
• synthesises information to select and apply techniques in mathematics to solve routine and non-routine problems in a variety of contexts
• develops, selects and applies mathematical models to routine and non-routine problems in a variety of contexts
• constructs mathematical proofs in a variety of contexts using a range of techniques
• uses digital technologies effectively to graph, display and organise mathematical information to solve a range of routine and non-routine problems in a variety of contexts
• demonstrates knowledge of concepts of functions, calculus, vectors and statistics in routine and non-routine problems
• synthesises information to select and apply techniques in mathematics to solve routine and non-routine problems
• selects and applies mathematical models to routine and non-routine problems
• constructs mathematical proofs in a variety of contexts and adapts previously seen mathematical proofs
• uses digital technologies appropriately to graph, display and organise mathematical information to solve a range of routine and non-routine problems
• demonstrates knowledge of concepts of functions, calculus, vectors and statistics that apply to routine problems
• selects and applies techniques in mathematics to solve routine problems
• applies mathematical models to routine problems
• constructs simple mathematical proofs and adapts previously seen mathematical proofs
• uses digital technologies to graph, display and organise mathematical information to solve routine problems
• demonstrates knowledge of concepts of functions, calculus, vectors and statistics
• uses simple techniques in mathematics in routine problems
• demonstrates familiarity with mathematical models
• reproduces previously seen mathematical proofs
• uses digital technologies to display some mathematical information in routine problems
• demonstrates limited familiarity with simple concepts of functions, calculus, vectors and statistics
• uses simple techniques in a structured context
• demonstrates limited familiarity with mathematical models
• reproduces previously seen simple mathematical proofs
• uses digital technologies for arithmetic calculations and to display limited mathematical information

## Reasoning and Communication

A B C D E
• represents mathematical and statistical information in numerical, graphical and symbolic form in routine and non-routine problems in a variety of contexts
• communicates succinct and reasoned mathematical and statistical judgments and arguments, including proofs, using appropriate language
• interprets the solutions to routine and non-routine problems in a variety of contexts
• explains the reasonableness of the results and solutions to routine and non-routine problems in a variety of contexts
• identifies and explains the validity and limitations of models used when developing solutions to routine and non-routine problems
• represents mathematical and statistical information in numerical, graphical and symbolic form in routine and non-routine problems
• communicates clear and reasoned mathematical and statistical judgments and arguments, including proofs, using appropriate language
• interpret the solutions to routine and non-routine problems
• explains the reasonableness of the results and solutions to routine and non-routine problems
• identifies and explains limitations of models used when developing solutions to routine problems
• represents mathematical and statistical information in numerical, graphical or symbolic form in routine problems
• communicates mathematical and statistical arguments, including previously seen proofs, using appropriate language
• describes solutions to routine problems
• describes the appropriateness of the results of calculations
• identifies limitations of simple models
• represents simple mathematical and statistical information in a structured context
• communicates simple mathematical and statistical information using appropriate language
• identifies solutions to routine problems
• demonstrates limited familiarity with the appropriateness of the results of calculations
• identifies simple models