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• 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

• VC2M10M03

  solve practical problems by applying Pythagoras’ theorem and trigonometry to right-angled triangles, including problems involving direction and angles of elevation and depression

  Elaborations

  • applying right-angled trigonometry to solve navigation problems involving bearings; for example, determining the bearing and estimating the distance of the final leg of an orienteering course
  • applying Pythagoras’ theorem and trigonometry to problems in surveying and design, where three-dimensional problems are decomposed into two-dimensional problems; for example, investigating the dimensions of the smallest box needed to package an object of a particular length
  • using a clinometer to measure angles of inclination, and applying trigonometry and proportional reasoning to determine the height of buildings in practical contexts
  • applying Pythagoras’ theorem and trigonometry and using dynamic geometry software to design three-dimensional models of practical situations involving angles of elevation and depression; for example, modelling a crime scene
  • exploring navigation, design of technologies or surveying by Aboriginal and Torres Strait Islander Peoples, investigating geometric and spatial reasoning and how these connect to trigonometry 

  VC2M10M03 | Mathematics | Mathematics Version 2.0 | Level 10 | Measurement

• VC2M10SP01

  apply deductive reasoning to formulate proofs involving shapes in the plane and use theorems to solve spatial problems

  Elaborations

  • distinguishing between a practical demonstration and a proof; for example, demonstrating that triangles are congruent by placing them on top of each other, as compared to using congruence tests to establish that triangles are congruent
  • developing proofs involving congruent triangles and angle properties, communicating the proof using a sequence of logically connected statements
  • applying an understanding of relationships to deduce properties of geometric figures; for example, the base angles of an isosceles triangle are equal
  • investigating proofs of geometric theorems and using them to solve spatial problems, for example, applying logical reasoning and similarity to proofs and numerical exercises involving plane shapes, and using visual proofs to justify solutions
  • using dynamic geometry software to find the quadrilateral that has a vertex on each side of a rectangle and has the shortest possible path, and proving that the path forms a parallelogram

  VC2M10SP01 | Mathematics | Mathematics Version 2.0 | Level 10 | Space

• VC2M10A01

  factorise algebraic expressions by taking out a common algebraic factor

  Elaborations

  • using the distributive law and the exponent laws to factorise algebraic expressions
  • understanding the relationship between factorisation and expansion

  VC2M10A01 | Mathematics | Mathematics Version 2.0 | Level 10 | Algebra

• 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

• 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