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• VC2M9M02

  solve problems involving very small and very large measurements, timescales and intervals expressed in scientific notation

  Elaborations

  • representing very large and very small real numbers in scientific notation, converting real numbers expressed in scientific notation into decimal form; for example, the approximate geological age of Earth is 4.6 × 10⁹ years, and the mass of a glucose molecule is 2.99 × 10⁻²² grams
  • using knowledge of place value and applying exponent laws to operate with numbers expressed in scientific notation in applied contexts; for example, performing calculations involving extremely small numbers in scientific and other contexts
  • examining the degree of accuracy that different measurement instruments provide in a science laboratory, such as a measuring cylinder compared with a pipette, and recording data values to the correct degree of accuracy using appropriate scientific notation

  VC2M9M02 | Mathematics | Mathematics Version 2.0 | Level 9 | Measurement

• VC2M9M01

  solve problems involving the volume and surface area of right prisms, cylinders and composite objects using appropriate units

  Elaborations

  • analysing nets of objects to generate short cuts and establish formulas for surface area 
  • determining the amount of material needed to make can-coolers for a class fundraising project and working out the most cost-efficient way to cut out the pieces
  • finding different prisms that have the same volume but different surface areas, making conjectures as to what type of prism would have the smallest or largest surface area
  • investigating objects and technologies of Aboriginal and Torres Strait Islander Peoples, analysing and connecting surface area and volume, and exploring their relationship to their capacity

  VC2M9M01 | Mathematics | Mathematics Version 2.0 | Level 9 | Measurement

• VC2M9ST05

  plan and conduct statistical investigations involving the collection and analysis of different kinds of data; report findings and discuss the strength of evidence to support any conclusions

  Elaborations

  • planning and conducting an investigation using questions together with analysis of a secondary data set collected from online databases such as the Australian Bureau of Statistics
  • planning and conducting an investigation relating to consumer spending habits; and modelling market research on what teenagers are prepared to spend on technology compared to clothing, with consideration of sample techniques and potential sources of bias
  • investigating where would be the best location for a tropical fruit plantation, by conducting a statistical investigation comparing different variables such as the annual rainfall in various parts of Australia, Indonesia, New Guinea and Malaysia, land prices and associated farming costs
  • posing statistical questions; collecting, representing and interpreting data from different sources in relation to reconciliation between Aboriginal and Torres Strait Islander Peoples and non-Indigenous Australians; and considering the relationships between variables

  VC2M9ST05 | Mathematics | Mathematics Version 2.0 | Level 9 | Statistics

• VC2M9SP03

  design, test and refine algorithms involving a sequence of steps and decisions based on geometric constructions and theorems; discuss and evaluate refinements 

  Elaborations

  • creating an algorithm using pseudocode or flow charts to apply the triangle inequality, or an algorithm to generate Pythagorean triples
  • creating and testing algorithms designed to construct or bisect angles, using pseudocode or flow charts
  • developing an algorithm for an animation of a geometric construction, or a visual proof, evaluating the algorithm using test cases

  VC2M9SP03 | Mathematics | Mathematics Version 2.0 | Level 9 | Space

• VC2M9P02

  calculate relative frequencies from given or collected data to estimate probabilities of events involving ‘and’, inclusive ‘or’ and exclusive ‘or’

  Elaborations

  • understanding that relative frequencies from large data sets or long-run experiments can provide reliable measures of probability and can be used to make predictions of decisions 
  • using Venn diagrams or two-way tables to estimate frequencies of events involving ‘and’ and ‘or’ questions

  VC2M9P02 | Mathematics | Mathematics Version 2.0 | Level 9 | Probability

• VC2M9SP01

  recognise the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles using properties of similarity

  Elaborations

  • understanding the terms ‘base’, ‘altitude’, ‘hypotenuse’, and ‘adjacent’ and ‘opposite’ sides to an angle, in a right-angled triangle, and identifying these for a given right-angled triangle
  • investigating patterns to reason about nested similar triangles that are aligned on a coordinate plane, connecting ideas of parallel sides and identifying the constancy of ratios of corresponding sides for a given angle
  • establishing an understanding that the sine of an angle can be considered as the length of the altitude of a right-angled triangle with a hypotenuse of length one unit and similarly the cosine as the length of the base of the same triangle, and relating this to enlargement and similar triangles
  • relating the tangent of an angle to the altitude and base of nested similar right-angled triangles, and connecting the tangent of the angle at which the graph of a straight line meets the positive direction of the horizontal coordinate axis to the gradient of the straight line

  VC2M9SP01 | Mathematics | Mathematics Version 2.0 | Level 9 | Space

• VC2M9M03

  solve spatial problems, applying angle properties, scale, similarity, ratio, Pythagoras’ theorem and trigonometry in right-angled triangles

  Elaborations

  • investigating the applications of Pythagoras’ theorem in authentic problems, including applying Pythagoras’ theorem and trigonometry to problems in surveying and design
  • applying the formula for calculation of distances between points on the Cartesian plane from their coordinates, emphasising the connection to vertical and horizontal displacements between the points 
  • understanding the relationship between the corresponding sides of similar right-angled triangles and establishing the relationship between areas of similar figures and the ratio of corresponding sides, the scale factor
  • using images of proportional relationships to estimate actual measurements (for example, taking a photograph of a person standing in front of a tree and using the image and scale to estimate the height of the tree), discussing the findings and ways to improve the estimates
  • investigating theorems and conjectures involving triangles, for example, the triangle inequality and generalising links between the Pythagorean rule for right-angled triangles, and related inequalities for acute and obtuse triangles, determining the minimal sets of information for a triangle from which other measures can all be determined
  • using knowledge of similar triangles, Pythagoras’ theorem, rates and algebra to design and construct a Biltmore stick, used to measure the diameter and height of a tree, and calculating the density and dry mass to predict how much paper could be manufactured from the tree

  VC2M9M03 | Mathematics | Mathematics Version 2.0 | Level 9 | Measurement

• VC2M9N01

  recognise that the real number system includes the rational numbers and the irrational numbers, and solve problems involving real numbers with and without using digital tools

  Elaborations

  • investigating the real number system by representing the relationships between irrational numbers, rational numbers, integers and natural numbers and discussing the difference between exact representations and approximate decimal representations of irrational numbers
  • using a real number line to indicate the solution interval for inequalities of the form ax+b <c ,
    for example, 2x+7<0 ; or of the form ax+b>c , for example, 1.2x-5.4>10.8
  • using positive and negative rational numbers to solve problems, for example, for financial planning such as budgeting
  • solving problems involving the substitution of real numbers into formulas, understanding that solutions can be represented in exact form or as a decimal approximation, such as calculating the area of a circle using the formula A=πr2 and specifying the answer in terms of π as an exact real number; for example, the circumference of a circle with diameter 5 units is 5π units, and the exact area is π(52)2=254π square units, which rounds to 19.63 square units, correct to 2 decimal places
  • investigating the position of rational and irrational numbers on the real number line, using geometric constructions to locate rational numbers and square roots on a number line; for example, 2 is located at the intersection of an arc and the number line, where the radius of the arc is the length of the diagonal of a one-unit square

  VC2M9N01 | Mathematics | Mathematics Version 2.0 | Level 9 | Number

• VC2M9A05

  identify and graph quadratic functions, solve quadratic equations graphically and numerically, and use null factor law to solve monic quadratic equations with integer roots algebraically, using graphing software and digital tools as appropriate

  Elaborations

  • recognising that in a table of values, if the second difference between consecutive values of the dependent variable is constant, then it is a quadratic
  • graphing quadratic functions using digital tools and comparing what is the same and what is different between these different functions and their respective graphs; interpreting features of the graphs such as symmetry, turning point, maximum and minimum values; and determining when values of the quadratic function lie within a given range
  • solving quadratic equations algebraically and comparing these to graphical solutions
  • using graphs to determine the solutions of quadratic equations; recognising that the roots of a quadratic function correspond to the x-intercepts of its graph and that if the graph has no x-intercepts, then the corresponding equation has no real solutions
  • relating horizontal axis intercepts of the graph of a quadratic function to the factorised form of its rule using the null factor law; for example, the graph of the function y=x2-5x+6 can be represented as y=x-2x-3 with x-axis intercepts where either x-2=0 or x-3=0
  • recognising that the equation x2=a, where a>0, has 2 solutions, x=a and x=-a (for example, if x2=39 then x=39=6.245 correct to 3 decimal places, or x=-39=-6.245 correct to 3 decimal places) and representing these graphically
  • graphing percentages of illumination of moon phases in relation to Aboriginal and Torres Strait Islander Peoples’ understandings that describe the different phases of the moon

  VC2M9A05 | Mathematics | Mathematics Version 2.0 | Level 9 | Algebra