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• Mathematics Version 2.0: Level 10 achievement standards

  By the end of Level 10, students recognise the effect of approximations of real numbers in repeated calculations.

  Students use mathematical modelling to solve problems involving growth and decay in financial and other applied situations, applying linear, quadratic and exponential...

  Level description | Mathematics | Mathematics Version 2.0 | Level 10

• VC2M10M01

  solve problems involving the surface area and volume of composite objects using appropriate units

  Elaborations

  • determining the volumes and surface areas of composite solids, formed from a range of right prisms and cylinders, by considering the individual solids from which they are constructed
  • estimating the surface area and volume of composite objects in practical contexts
  • using mathematical modelling to provide solutions to problems involving surface area and volume; for example, ascertaining the rainfall that can be saved from a rooftop and the optimal shape and dimensions for rainwater storage based on where it will be located on a property, or determining whether to hire extra freezer space for the amount of ice cream required at a fundraising event for the school or community

  VC2M10M01 | Mathematics | Mathematics Version 2.0 | Level 10 | Measurement

• Mathematics Version 2.0: Level 10 description

  In Level 10, learning in Mathematics builds on each student’s prior learning and experiences and provides the basis for a sound background in number, algebra, function, geometry and statistics. Students engage in a range of approaches to the learning and doing of mathematics that...

  Level description | Mathematics | Mathematics Version 2.0

• VC2M10M02

  interpret and use logarithmic scales in applied contexts involving small and large quantities and change 

  Elaborations

  • understanding that the logarithmic scale is calibrated in terms of order of magnitude, for example, doubling or powers of 10
  • identifying and interpreting data representations (charts and graphs) that use logarithmic scales (for example, graphs representing percentage change, a wide range of values or exponential growth) and discussing when it is appropriate to use this type of scale and when it is not appropriate
  • investigating and interpreting logarithmic scales used in real-world contexts (for example, Richter, decibel and sensitivity scales or growth in investments, timescales and the spread of microorganisms and disease) and describing reasons for choosing to use a logarithmic scale rather than a linear scale
  • investigating dating methods of geological sites to provide evidence of Aboriginal and Torres Strait Islander Peoples’ presence in Australia, including the Madjedbebe dig in the Northern Territory, that use logarithmic scales, scientific notation and measurement accuracy in the dating

  VC2M10M02 | Mathematics | Mathematics Version 2.0 | Level 10 | Measurement

• VC2M10P02

  describe the results of two- and three-step chance experiments, both with and without replacements, assign probabilities to outcomes and determine probabilities of events; investigate the concept of independence

  Elaborations

  • recognising that a subsequent event can be dependent, and that this will affect the way its probability is calculated, for example, cards chosen from a standard deck without replacement, conditional selection problems from a fixed sample size, or the Bertrand’s box paradox

  VC2M10P02 | Mathematics | Mathematics Version 2.0 | Level 10 | Probability

• VCMMG343

  Solve problems involving surface area and volume for a range of prisms, cylinders and composite solids

  Elaborations

  • investigating and determining the volumes and surface areas of composite solids by considering the individual solids from which they are constructed

  VCMMG343 | Mathematics | Level 10 | Measurement and Geometry | Using units of measurement

• Mathematics: Level 10 description

  In Level 10, students extend their use of mathematical models to a wide range of familiar and unfamiliar contexts, involving the use of all types of real numbers. They recognise the role of logical argument and proof in establishing mathematical propositions. Students apply mental, written or...

  Level description | Mathematics

• VC2M10P01

  use the language of ‘if … then …’, ‘given’, ‘of’ and ‘knowing that’ to investigate conditional statements and identify common mistakes in interpreting such language, and describe and interpret situations involving conditional probability; design and conduct simulations using digital tools to model...

  Elaborations

  • using two-way tables and Venn diagrams to understand conditional statements using the language of ‘if … then …’, ‘given’, ‘of’ and ‘knowing that’ and identifying common mistakes in interpreting such language
  • using arrays and tree diagrams to represent, interpret and compare probabilities of dependent and independent events 
  • using samples of different sizes with and without replacement from a population to identify when the difference in methods becomes negligible
  • using simulations to gather data on frequencies for situations involving chance that appear to be counterintuitive, such as the three-door problem or the birthday problem
  • identifying situations in real life where probability simulations are used for decision-making, such as supply and demand of product, insurance risk and queueing 
  • using simulation to predict the number of people likely to be infected with a strain of flu or virus

  VC2M10P01 | Mathematics | Mathematics Version 2.0 | Level 10 | Probability

• VCMSP348

  Use the language of ‘if ....then, ‘given’, ‘of’, ‘knowing that’ to investigate conditional statements and identify common mistakes in interpreting such language

  Elaborations

  • using two-way tables and Venn diagrams to understand conditional statements
  • using arrays and tree diagrams to determine probabilities

  VCMSP348 | Mathematics | Level 10 | Statistics and Probability | Chance

• VCMSP347

  Describe the results of two- and three-step chance experiments, both with and without replacements, assign probabilities to outcomes and determine probabilities of events. Investigate the concept of independence

  Elaborations

  • recognising that an event can be dependent on another event and that this will affect the way its probability is calculated

  VCMSP347 | Mathematics | Level 10 | Statistics and Probability | Chance

• Mathematics: Level 10 achievement standards

  Number and Algebra

  Students recognise the connection between simple and compound interest. They solve problems involving linear equations and inequalities, quadratic equations and pairs of simultaneous linear equations and related graphs, with and without the use of digital technology. Students...

  Level description | Mathematics | Level 10

• VC2M10M04

  use mathematical modelling to solve practical problems involving direct and inverse proportion and scaling of objects; formulate problems and interpret solutions in terms of the situation, including the impact of measurement errors on the accuracy of results; evaluate and modify models as necessary...

  Elaborations

  • exploring contexts where measurement errors may impact research results and how measurement data impacted by error can result in biased findings
  • using plans and elevation drawings to investigate making changes to building designs, employing appropriate scales and converting to actual measurements within the context to make decisions about changes
  • analysing and applying scale and ratios in situations such as production prototypes and 3D printing; for example, using a 3D printer to produce scaled versions of actual objects
  • estimating the scale of an object by measuring a linear dimension and using typical life-size dimensions to determine the scale factor; for example, measuring the dimensions of a toy car to determine a scale that can be used to estimate the dimensions of a life-size car
  • investigating compliance with building codes and standards in design and construction, such as for escalators in shopping centres

  VC2M10M04 | Mathematics | Mathematics Version 2.0 | Level 10 | Measurement

• VC2M10N01

  recognise the effect of using approximations of real numbers in repeated calculations and compare the results when using exact representations

  Elaborations

  • comparing and contrasting the effect of truncation or rounding on the final result of calculations when using approximations of real numbers rather than exact representations
  • investigating the impact of approximation on multiple calculations in contexts that involve the area of compound shapes involving circles, the surface area and volume of compound objects, and repeated calculations of simple interest where the solutions are not exact cents

  VC2M10N01 | Mathematics | Mathematics Version 2.0 | Level 10 | Number

• VC2M10A13

  solve simple quadratic equations using a range of strategies, including null factor law

  Elaborations

  • using techniques to solve quadratic equations, including grouping like terms, completing the square, the quadratic formula and null factor law, and choosing 2 integers with the required product and sum
  • using digital tools to explore the conditions for solutions to exist
  • using digital tools to explore both graphically and algebraically the link between the value of the discriminant and the number of real solutions to a quadratic equation

  VC2M10A13 | Mathematics | Mathematics Version 2.0 | Level 10 | Algebra

• VC2M10ST03

  construct two-way tables and discuss possible relationship between categorical variables

  Elaborations

  • using two-way tables to investigate and comparing the survey responses to questions involving five-point Likert scale against 2 different categories of respondents, for example, junior students’ responses compared to senior students’ responses to a survey question
  • recording data in two-way tables and using percentages and proportions to identify patterns and associations in the data
  • conducting a litter survey around the school, considering the relationship between different categorical variables such as the day of the week (as canteen specials might lead to different types of litter) or the weather (due to hot days leading to more icy poles and cold drinks being sold)

  VC2M10ST03 | Mathematics | Mathematics Version 2.0 | Level 10 | Statistics

• VCMSP353

  Investigate and describe bivariate numerical data, including where the independent variable is time

  Elaborations

  • investigating biodiversity changes in Australia since European occupation
  • constructing and interpreting data displays representing bivariate data over time
  • constructing scatter-plots for two numerical variables and investigate trends such as water storage levels over time or weight and height distributions

  VCMSP353 | Mathematics | Level 10 | Statistics and Probability | Data representation and interpretation

• VCMSP350

  Construct and interpret box plots and use them to compare data sets

  Elaborations

  • understanding that box plots are an efficient and common way of representing and summarising data and can facilitate comparisons between data sets
  • using parallel box plots to compare data about the age distribution of Aboriginal and Torres Strait Islander people with that of the Australian population as a whole

  VCMSP350 | Mathematics | Level 10 | Statistics and Probability | Data representation and interpretation

• VC2M10ST01

  compare data distributions for continuous numerical variables using quartiles and interquartile range and appropriate data displays including boxplots, histograms and dot plots; discuss the shapes of these distributions in terms of centre, spread, shape and outliers in the context of the data

  Elaborations

  • finding the five-number summary (minimum and maximum values, median and upper and lower quartiles) and using its graphical representation, the boxplot, as tools for both numerically and visually comparing the centre and spread of data sets
  • exploring the effect of varying data values, including outliers, on the interquartile range for different sets of data
  • constructing and interpreting boxplots and using them to compare data sets, understanding that boxplots are an efficient and common way of representing and summarising data and can facilitate comparisons between data sets
  • comparing shapes of distributions using boxplots, histograms, cumulative frequency graphs and dot plots, discussing symmetry, skew and modality
  • using digital tools to compare boxplots and histograms as displays of the same data in the light of the statistical questions being addressed and the effectiveness of the display in helping to answer the question
  • comparing the information that can be extracted and the stories that can be told about continuous and discrete numerical data sets that have been displayed in different ways, including histograms, dot plots, boxplots and cumulative frequency graphs

  VC2M10ST01 | Mathematics | Mathematics Version 2.0 | Level 10 | Statistics

• VC2M10ST05

  plan and conduct statistical investigations of situations that involve bivariate data, including where the independent variable is time; evaluate and report findings with consideration of limitations of any inferences

  Elaborations

  • designing statistical investigations that collect bivariate data over time through observation, experiment or measurement; graphing, interpreting and analysing data; and reporting within the context of the statistical investigation question
  • investigating and comparing anecdotal claims with data collected from well-constructed surveys, including those concerning climate, housing affordability and natural resources, with consideration of data validity and limitations of interpolation or extrapolation
  • using a statistical investigation to address the question ‘Is there a relationship between vaccines and immunity from a virus?’
  • investigating biodiversity changes in Australia before and after colonisation by comparing related bivariate numerical data, discussing and reporting on associations

  VC2M10ST05 | Mathematics | Mathematics Version 2.0 | Level 10 | Statistics

• VC2M10ST02

  construct scatterplots and consider a line of good fit; comment on the association between the 2 numerical variables in terms of strength, direction and linearity

  Elaborations

  • discussing the difference between association and cause and effect, and relating this to situations such as health, diversity of species and climate
  • using statistical evidence to make, justify and critique claims about association between variables, such as in contexts of climate change, migration, online shopping and social media 
  • informally using a line of good fit by eye and using digital tools to compare and discuss the reliability of any predictions
  • investigating the relationship between 2 variables of spearthrowers used by Aboriginal and Torres Strait Islander Peoples by using data to construct scatterplots, make comparisons and draw conclusions 

  VC2M10ST02 | Mathematics | Mathematics Version 2.0 | Level 10 | Statistics