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• VC2M10AM02

  explore the effect of increasingly small changes in the value of variables on the average rate of change and in relation to limiting values

  Elaborations

  • using the gradient of the line segment between 2 distinct points as a measure of rate of change to obtain numerical approximations to instantaneous speed and interpreting ‘tell me a story’ piecewise linear position-time graphs

  VC2M10AM02 | Mathematics | Mathematics Version 2.0 | Level 10A | Measurement

• 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

• VC2M10AST01

  calculate and interpret the mean and standard deviation of data and use these to compare data sets; investigate the effect of individual data values, including outliers, on the standard deviation

  Elaborations

  • using the standard deviation to describe the spread of a set of data
  • using the mean and standard deviation to compare numerical data sets
  • constructing distributions for the mean and standard deviation of simple random samples from a population

  VC2M10AST01 | Mathematics | Mathematics Version 2.0 | Level 10A | Statistics

• VCMSP372

  Calculate and interpret the mean and standard deviation of data and use these to compare data sets. Investigate the effect of individual data values including outliers, on the standard deviation

  Elaborations

  • using the standard deviation to describe the spread of a set of data
  • using the mean and standard deviation to compare numerical data sets
  • constructing distributions for the mean and standard deviation of simple random samples from a population

  VCMSP372 | Mathematics | Level 10A | Statistics and Probability | Data representation and interpretation

• VCMMG368

  Use the unit circle to define trigonometric functions as functions of a real variable, and graph them with and without the use of digital technologies

  Elaborations

  • establishing the symmetrical properties of trigonometric functions
  • investigating angles of any magnitude
  • understanding that trigonometric functions are periodic and that this can be used to describe motion
  • identifying points on the unit circle via arc lengths in radians, which correspond to specified values of the circular functions sine, cosine and tangent

  VCMMG368 | Mathematics | Level 10A | Measurement and Geometry | Pythagoras and trigonometry

• VC2M10AA02

  devise and use algorithms and simulations to solve mathematical problems

  Elaborations

  • applying a systematic guess-check-and-refine algorithm to identify an approximate value for the root of an equation in an interval
  • developing simulations for counterintuitive problems in probability such as the Monty Hall problem or derangements

  VC2M10AA02 | Mathematics | Mathematics Version 2.0 | Level 10A | Algebra

• VC2M10AST03

  use digital tools to investigate bivariate numerical data sets; where appropriate use a straight line to describe the relationship allowing for variation, make predictions based on this straight line and discuss limitations

  Elaborations

  • investigating different techniques for finding a ‘line of best fit’
  • using a fitted line to data to make predictions between and beyond existing data values and discussing limitations of these predictions

  VC2M10AST03 | Mathematics | Mathematics Version 2.0 | Level 10A | Statistics

• VCMNA358

  Devise and use algorithms and simulations to solve mathematical problems

  Elaborations

  • applying a systematic guess-check-and-refine algorithm to identify an approximate value for the root of an equation in an interval
  • developing simulations for counter-intuitive problems in probability such as the Monty Hall problem or derangements

  VCMNA358 | Mathematics | Level 10A | Number and Algebra | Patterns and algebra

• VCMSP373

  Use digital technology to investigate bivariate numerical data sets. Where appropriate use a straight line to describe the relationship allowing for variation, make predictions based on this straight line and discuss limitations

  Elaborations

  • investigating different techniques for finding a ‘line of best fit’
  • using a fitted line to data to make predictions between and beyond existing data value sand discuss limitations of these predictions

  VCMSP373 | Mathematics | Level 10A | Statistics and Probability | Data representation and interpretation

• Mathematics: Level 10A description

  Level 10A provides optional, additional content for students to be extended in their mathematical studies.

  Students could extend work in number and algebra to investigate the structure and properties of number systems, with further analysis of order relations and inequalities. They could extend...

  Level description | Mathematics

• VC2M10AA10

  experiment with functions and relations using digital tools, making and testing conjectures and generalising emerging patterns

  Elaborations

  • applying a bisection algorithm to determine the approximate location of the horizontal axis intercepts of the graph of a quadratic function such as fx=2x2-3x-7
  • applying transformations to the graph of x2+y2=1
  • identifying the coordinates of any points of intersection of the graph of a linear function with the graph of a quadratic function or a circle
  • identifying intervals on the real number line over which a given quadratic function is positive or negative
  • using a table of values to determine when an exponential growth or decay function exceeds or falls below a given value, such as monitoring the trend in value of a share price in a context of exponential growth or decay

  VC2M10AA10 | Mathematics | Mathematics Version 2.0 | Level 10A | Algebra

• VC2M10AA04

  explore the inverse relationship between exponential functions and logarithmic functions and the solution of related equations

  Elaborations

  • using the definition of a logarithm and the exponent laws to establish the logarithm laws
  • evaluating 10x for decimal values of x and relating this to a logarithm base 10 scale; solving exponential equations algebraically using logarithms with base 10, for example, 5000×1.01x=10 000⇒x= log10(2)log10(1.01)≈69.66 ; and connecting to the graph of the corresponding function

  VC2M10AA04 | Mathematics | Mathematics Version 2.0 | Level 10A | Algebra

• VC2M10AP01

  explore counting principles, and factorial notation as a representation that provides efficient counting in multiplicative contexts, including calculations of probabilities

  Elaborations

  • applying the multiplication principle to problems involving combinations including probabilities relating to sampling with and without replacement, and representing these using tree diagrams
  • understanding that a set with n elements has 2ⁿ different subsets formed by considering each element for inclusion or not in combination, and that these can be systematically listed using a tree diagram or a table; for example, the set {a, b, c} has 2³ = 8 subsets which are { ∅, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}}
  • using the definition of n! to represent and calculate in contexts that involve choices from a set; for example, how many different combinations of 3 playing cards from a pack? How many if the suits are ignored? How many with and without replacement?
  • performing calculations on numbers expressed in factorial form, such as n!r! to evaluate the number of possible arrangements of n objects in a row, r of which are identical; for example, 5 objects, 3 of which are identical, can be arranged in a row in
    5!3!=5×4×3×2×13×2×1= 20 different ways

  VC2M10AP01 | Mathematics | Mathematics Version 2.0 | Level 10A | Probability