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• VC2M10AA06

  apply understanding of polynomials to sketch a range of curves and describe the features of these curves from their equation

  Elaborations

  • investigating the features of graphs of polynomials including axes intercepts and the effect of repeated factors

  VC2M10AA06 | Mathematics | Mathematics Version 2.0 | Level 10A | Algebra

• VCMNA361

  Apply understanding of polynomials to sketch a range of curves and describe the features of these curves from their equation

  Elaborations

  • investigating the features of graphs of polynomials including axes intercepts and the effect of repeated factors

  VCMNA361 | Mathematics | Level 10A | Number and Algebra | Linear and non-linear relationships

• VCMNA337

  Solve simultaneous linear equations, using algebraic and graphical techniques including using digital technology

  Elaborations

  • associating the solution of simultaneous equations with the coordinates of the intersection of their corresponding graphs

  VCMNA337 | Mathematics | Level 10 | Number and Algebra | Linear and non-linear relationships

• VCMNA364

  Solve simultaneous equations using systematic guess-check-and-refine with digital technology

  Elaborations

  • using graphs to determine a convergent set of intervals which contain a point of intersection of the graphs of two functions
  • using cobweb diagram to solve simultaneous equations numerically

  VCMNA364 | Mathematics | Level 10A | Number and Algebra | Linear and non-linear relationships

• Mathematics Version 2.0: Level 10A description

  Level 10A provides optional, additional content to extend students in their mathematical studies in number, algebra, function, geometry, probability and statistics.

  Level 10A does not include an achievement standard and does not require reporting.

  Students may extend...

  Level description | Mathematics | Mathematics Version 2.0

• VC2M10SP02

  interpret networks and network diagrams used to represent relationships in practical situations and describe connectedness

  Elaborations

  • investigating how networks and network diagrams can be used to model authentic situations, recognising what real-world quantity is represented by the nodes (vertices), and what real-world quantity is represented by the links between them (edges)
  • investigating the use of graphs to represent a network, for example, investigating the Seven Bridges of Königsberg problem
  • investigating how polyhedrons may be represented as a network using edges, vertices, and interior and exterior faces; and representing the number of edges, vertices and faces in a table, exploring and demonstrating how Euler’s formula F + V = E + 2 applies
  • investigating how a social network, intranet, local area network (LAN), electrical wiring or wireless network of a home can be represented as a network diagram to specify relationships; for example, using network diagrams to investigate practical problems involving connections, power overload or the need for routers
  • investigating the use of networks to represent authentic situations, for example, rail or air travel between or within London, Paris and Hong Kong; a food web representing a simple ecosystem; metabolic networks and other chemical or biological structures
  • representing Aboriginal and Torres Strait Islander Peoples’ kinship systems using network diagrams and exploring the significance of relationships to Country/Place

  VC2M10SP02 | Mathematics | Mathematics Version 2.0 | Level 10 | Space

• VC2M9A06

  use mathematical modelling to solve applied problems involving change, including financial contexts involving simple interest; formulate problems, choosing to use either linear or quadratic functions or other simple variations; interpret solutions in terms of the context; evaluate the model and...

  Elaborations

  • modelling practical contexts using linear functions such as cooking times that include resting or cooling times, or water leakage from water tanks, using tables and graphs or digital tools and algebraically
  • modelling measurement situations and determining the perimeter and areas of rectangles where the length, l, of the rectangle is a linear function of its width, w; for example, l=w,  l=w+5,  l=3w,  l=2w+7
  • modelling practical contexts (for example, area, paths of projectiles, parabolic mirrors, satellite dishes) using simple quadratic functions, tables and graphs (hand drawn or using digital tools) and, algebraically, interpreting features of the graphs such as the turning point and intercepts in context; for example, area, paths of projectiles, parabolic mirrors, satellite dishes
  • modelling and solving problems involving financial contexts using linear functions, for example, combinations of purchases of different items when they have a set amount of money to spend, profit/loss situations and trade quotes involving call-out fees
  • modelling situations involving change, for example, change in daily temperature during the ski season, fluctuation of speed above and below the speed limit, and acceleration and deceleration of a car coming to and moving off from a set of traffic lights
  • modelling the hunting techniques of Aboriginal and Torres Strait Islander Peoples using quadratic functions and exploring the effect of increasing the number of hunters to catch more prey 

  VC2M9A06 | Mathematics | Mathematics Version 2.0 | Level 9 | Algebra

• Mathematics | Mathematics: Structure

  The curriculum is organised by the three strands of Number and Algebra, Measurement and Geometry, and Statistics and Probability.

  Each strand is organised by sub-­strands. Sub-strands group content descriptions under an appropriate concept, to provide both a focus and a clear sequence for the...

  Overview material | Mathematics

• VC2M5A02

  find unknown values in numerical equations involving multiplication and division using the properties of numbers and operations

  Elaborations

  • using knowledge of equivalent number sentences to form and find unknown values in numerical equations; for example, given that 3 × 5 = 15 and 30 ÷ 2 = 15, then 3 × 5 = 30 ÷ 2, and therefore the solution to 3 × 5 = 30 ÷ □ is 2
  • using relational thinking, and an understanding of equivalence and number properties to determine and reason about numerical equations; for example, explaining whether an equation involving equivalent multiplication number sentences is true, such as 15 ÷ 3 = 30 ÷ 6
  • using materials, diagrams and arrays to demonstrate that multiplication is associative and commutative but division is not – for example, using arrays to demonstrate that 2 × 3 = 3 × 2 but 6 ÷ 3 does not equal 3 ÷ 6; demonstrating that 2 × 2 × 3 = 12 and 2 × 3 × 2 = 12 and 3 × 2 × 2 = 12; and understanding that 8 ÷ 2 ÷ 2 = (8 ÷ 2) ÷ 2 = 2 but 8 ÷ (2 ÷ 2) = 8 ÷ 1 = 8
  • using materials, diagrams or arrays to recognise and explain the distributive property, for example, where 4 × 13 = 4 × 10 + 4 × 3
  • constructing equivalent number sentences involving multiplication to form a numerical equation, and applying knowledge of factors, multiples and the associative property to find unknown values in numerical equations; for example, considering 3 × 4 = 12 and knowing 2 × 2 = 4, then 3 × 4 can be written as 3 × (2 × 2) and, using the associative property, (3 × 2) × 2 so 3 × 4 = 6 × 2 and so 6 is the solution to 3 × 4 = □ × 2

  VC2M5A02 | Mathematics | Mathematics Version 2.0 | Level 5 | Algebra

• VC2M10AA08

  use function notation to describe the relationship between dependent and independent variables in modelling contexts

  Elaborations

  • identifying independent and dependent variables in modelling contexts and representing the relation between them using tables, graphs and rules
  • using technology to draw graphs of functions defined using function notation with consideration of domain and range

  VC2M10AA08 | Mathematics | Mathematics Version 2.0 | Level 10A | Algebra

• VC2M10AP02

  investigate reports of studies in digital media and elsewhere for information on their planning and implementation

  Elaborations

  • evaluating the appropriateness of sampling methods in reports where statements about a population are based on a sample
  • evaluating whether graphs in a report could mislead, and whether graphs and numerical information support the claims made

  VC2M10AP02 | Mathematics | Mathematics Version 2.0 | Level 10A | Probability

• VCMNA363

  Use function notation to describe the relationship between dependent and independent variables in modelling contexts

  Elaborations

  • identify independent and dependent variables in modelling contexts and represent the relation between them using tables, graphs and rules
  • using technology to draw graphs of functions defined using function notation with consideration of domain and range

  VCMNA363 | Mathematics | Level 10A | Number and Algebra | Linear and non-linear relationships

• VCMSP371

  Investigate reports of studies in digital media and elsewhere for information on their planning and implementation

  Elaborations

  • evaluating the appropriateness of sampling methods in reports where statements about a population are based on a sample
  • evaluating whether graphs in a report could mislead, and whether graphs and numerical information support the claims

  VCMSP371 | Mathematics | Level 10A | Statistics and Probability | Chance

• VC2M10AA05

  describe, interpret, and sketch parabolas, hyperbolas, circles and exponential functions and their transformations

  Elaborations

  • applying transformations, including translations, reflections in the axes and stretches to help graph parabolas, rectangular hyperbolas, circles and exponential functions

  VC2M10AA05 | Mathematics | Mathematics Version 2.0 | Level 10A | Algebra

• VCMNA359

  Describe, interpret and sketch parabolas, hyperbolas, circles and exponential functions and their transformations

  Elaborations

  • applying transformations, including translations, reflections in the axes and stretches to help graph parabolas, rectangular hyperbolas, circles and exponential functions

  VCMNA359 | Mathematics | Level 10A | Number and Algebra | Linear and non-linear relationships

• VCMNA342

  Solve equations using systematic guess-check-and-refine with digital technology

  Elaborations

  • refining intervals on graphs and/or in tables of values to determine with increasing accuracy when the values of two functions are approximately equal

  VCMNA342 | Mathematics | Level 10 | Number and Algebra | Linear and non-linear relationships

• VC2M3ST02

  create and compare different graphical representations of data sets, including using software where appropriate; interpret the data in terms of the context

  Elaborations

  • comparing various student-generated data representations and describing their similarities and differences
  • using digital tools and graphing software to construct graphs of data acquired through experiments or observation and interpreting the data and making inferences; for example, graphing data from a science experiment and interpreting the results
  • selecting appropriate formats or layout styles to present data as information, depending on the type of data and the audience; for example, lists, tables, graphs and infographics
  • using newspapers or magazines to find examples of different displays of data, interpreting and describing the information they present

  VC2M3ST02 | Mathematics | Mathematics Version 2.0 | Level 3 | Statistics

• VC2M4A01

  find unknown values in numerical equations involving addition and subtraction, using the properties of numbers and operations

  Elaborations

  • demonstrating the commutative properties of addition using materials, diagrams and number lines; for example, using number lines to demonstrate that 5 + 2 = 2 + 5, and demonstrating that 2 + 2 + 3 = 7 and 2 + 3 + 2 = 7 and 3 + 2 + 2 = 7
  • using balance scales and informal uniform units to create addition or subtraction number sentences showing equivalence, such as 7 + 8 = 6 + 9, and to find unknowns in equivalent number sentences, such as 6 + 8 = □ + 10
  • using relational thinking and knowledge of equivalent number sentences to explain whether equations involving addition or subtraction are true; for example, explaining that 27 − 14 = 17 − 4 is true and using a number line to show the common difference is 13

  VC2M4A01 | Mathematics | Mathematics Version 2.0 | Level 4 | Algebra

• Mathematics Version 2.0: Foundation Level description

  In Foundation, learning in Mathematics builds on each student’s prior learning and experiences, including the learning opportunities acquired through the implementation of the Victorian Early Years Learning and Development Framework (VEYLDF). Students engage in a range of approaches to the...

  Level description | Mathematics | Mathematics Version 2.0

• VCMMG286

  Choose appropriate units of measurement for area and volume and convert from one unit to another

  Elaborations

  • choosing units for area including mm², cm², m², hectares, km², and units for volume including mm³, cm³, m³
  • recognising that the conversion factors for area units are the squares of those for the corresponding linear units
  • recognising that the conversion factors for volume units are the cubes of those for the corresponding linear units

  VCMMG286 | Mathematics | Level 8 | Measurement and Geometry | Using units of measurement