Mathematics
Areas for Assessment
Knowledge, skills and understanding
Students:
Working Mathematically – develop understanding and fluency in mathematics through inquiry, exploring and connecting mathematical concepts, choosing and applying problem-solving skills and mathematical techniques, communication and reasoning
Number and Algebra – develop efficient strategies for numerical calculation, recognise patterns, describe relationships and apply algebraic techniques and generalisation
Measurement and Geometry – identify, visualise and quantify measures and the attributes of shapes and objects, and explore measurement concepts and geometric relationships, applying formulas, strategies and geometric reasoning in the solution of problems
Statistics and Probability – collect, represent, analyse, interpret and evaluate data, assign and use probabilities, and make sound judgements.
Grade A10
A student performing at this grade uses and interprets formal definitions and generalisations when explaining solutions; generalises mathematical ideas and techniques and selects and uses efficient strategies consistently and accurately to solve unfamiliar multi-step problems; uses deductive reasoning in presenting clear and concise mathematical arguments and formal proofs; synthesises mathematical techniques, results and ideas across the course.
A student at this grade typically:
- uses graphical techniques and a variety of analytical methods to solve problems involving quadratic equations and simultaneous equations; manipulates algebraic expressions and equations with consideration given to restrictions on the values of variables
- solves problems involving surface area and volume of right pyramids, right cones, spheres, and related composite solids, and applies similarity relationships for area and volume; applies deductive reasoning to prove properties of isosceles and equilateral triangles, and special quadrilaterals
- uses and interprets the mean and standard deviation to make comparisons between data sets; critically evaluates the processes of planning, collecting, analysing and reporting studies in the media and elsewhere.
Grade A9
A student performing at this grade uses formal definitions and generalisations when explaining solutions; generalises mathematical ideas and techniques and selects and uses efficient strategies to solve unfamiliar multi-step problems; uses deductive reasoning in presenting mathematical arguments and formal proofs.
A student at this grade typically:
- performs operations with surds and indices in numerical and algebraic contexts; analyses and describes graphs of physical phenomena; uses analytical methods to solve complex linear, quadratic, simple cubic, and simultaneous equations, including simultaneous equations where one equation is non-linear
- uses trigonometry to solve practical problems involving non-right-angled triangles; constructs geometrical arguments and formal proofs of geometrical relationships
- uses the mean and standard deviation to make comparisons between data sets; evaluates the use of data to inform decision-making processes.
Grade B8
A student performing at this grade uses formal definitions when explaining solutions; selects and uses efficient strategies to solve familiar and some unfamiliar multi-step problems; uses some deductive reasoning in presenting mathematical arguments; may require some guidance to determine the most efficient methods.
A student at this grade typically:
- applies special products to expand binomial products and factorises a variety of quadratic expressions; draws and interprets a variety of graphs, and applies coordinate geometry techniques to solve problems
- calculates the surface area and volume of right pyramids, right cones, spheres, and related composite solids; constructs geometrical arguments to prove a general geometrical result, giving reasons
- calculates and uses standard deviation to analyse data; interprets the relationship between numerical variables using lines of best fit.
Grade B7
A student performing at this grade selects and uses appropriate mathematical language, notations and conventions to communicate mathematical ideas and solutions; systematically applies appropriate strategies to solve familiar multi-step problems; constructs appropriate mathematical arguments to prove and justify results; often requires guidance to determine the most efficient methods.
A student at this grade typically:
- applies the compound interest formula to solve financial mathematics problems, including those involving depreciation; solves simultaneous linear equations using an algebraic or graphical method; draws and interprets graphs of simple parabolas, circles and exponentials
- calculates the surface area and volume of simple composite solids; solves trigonometry problems involving bearings, angles of elevation and depression, and angles measured in degrees and minutes
- determines and uses quartiles and the interquartile range to compare sets of data; evaluates sources of data in media reports and elsewhere; evaluates conditional statements in chance situations.
Grade C6
A student performing at this grade uses appropriate mathematical language, notations and diagrams to communicate mathematical ideas and solutions; applies appropriate strategies to solve familiar multi-step problems; constructs some appropriate mathematical arguments to obtain and justify results.
A student at this grade typically:
- expands and factorises simple algebraic expressions and simplifies algebraic expressions involving fractions and positive, negative and zero indices; solves simple quadratic equations
- uses formulae to calculate the surface area and volume of right prisms and cylinders; uses simple deductive reasoning in solving numerical problems in different geometrical contexts, and applies tests for proving that triangles are congruent
- determines the quartiles and interquartile range for a set of data; constructs and interprets displays of bivariate numerical data; calculates probabilities and interprets the results for multi-step chance experiments.
Grade C5
A student performing at this grade uses mathematical language, notations and diagrams to communicate mathematical ideas; applies appropriate strategies, often with the assistance of given diagrams and formulae, to solve simple familiar problems; constructs some mathematical arguments to obtain results.
A student at this grade typically:
- uses conversion graphs to convert from one unit to another and given graphs to solve simple linear simultaneous equations; finds and graphs the equations of straight lines given the gradient and y-intercept
- solves simple word problems in trigonometry; applies results related to the angle sum for polygons to solve simple numerical problems
- identifies simple relationships between two statistical variables; calculates probabilities for multi-step chance experiments.
Grade D4
A student performing at this grade uses appropriate mathematical terminology, diagrams and symbols in mathematical contexts; selects and uses appropriate standard strategies to solve simple familiar problems; provides some reasoning to support conclusions that are appropriate to the context.
A student at this grade typically:
- graphs simple linear and non-linear relationships by constructing a table of values; uses diagrams to solve simple coordinate geometry problems
- finds the area of simple composite figures; given diagrams, uses trigonometry to find sides and angles in right-angled triangles
- interprets back-to-back stem-and-leaf plots, and statistical claims made in the media; calculates relative frequencies to estimate probabilities of simple and compound events.
Grade D3
A student performing at this grade uses mathematical terminology, diagrams and symbols in mathematical contexts; uses appropriate standard strategies to solve simple familiar problems; provides some reasoning to support conclusions.
A student at this grade typically:
- solves simple financial mathematics problems involving earning and spending money and, given the formula, calculates simple interest; completes a table of values to graph simple linear relationships
- expresses trigonometric ratios for angles in right-angled triangles in terms of an unknown side; uses the scale factor to find unknown sides in similar triangles
- calculates the mean, median and range to compare two sets of numerical data; uses data from Venn diagrams and two-way tables to calculate simple probabilities.
Grade E2
A student performing at this grade uses some mathematical terminology in mathematical contexts; uses, with guidance, standard strategies to solve simple familiar problems; provides some reasoning in identifying a simple mathematical relationship.
A student at this grade typically:
- solves simple financial mathematics problems involving earning money; simplifies simple algebraic expressions involving positive integral indices
- uses given diagrams and formulae to solve simple problems involving area and surface area; uses a calculator to find approximations of trigonometric ratios of given angles measured in degrees; constructs simple scale drawings
- determines the mean and range for a set of data.