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• VC2M10AA09

  solve linear and non-linear simultaneous equations using graphing or systematic guess-check-and-refine with digital tools

  Elaborations

  • using graphs to determine a convergent set of intervals that contain a point of intersection of the graphs of 2 functions
  • using a cobweb diagram to solve simultaneous equations numerically

  VC2M10AA09 | Mathematics | Mathematics Version 2.0 | Level 10A | Algebra

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• VC2M10AN02

  perform operations on numbers involving fractional exponents and surds

  Elaborations

  • exploring the notion that amn= a1nm= anm= amn=am1n , where m is a non-zero integer and n is a natural number, and evaluating corresponding expressions; for example, 823=832= 22=4  and 823= 823=643=4

  VC2M10AN02 | Mathematics | Mathematics Version 2.0 | Level 10A | Number

• 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

• VC2M10AA03

  simplify combinations of linear expressions with rational coefficients and the solution of related equations

  Elaborations

  • simplifying sums and differences of linear expressions of the form ax+bc where
    a and b are integers, and c is a non-zero integer, for example, 6x-112-7x4+9-5x3=-5x-3012
  • solving equations involving sums and differences of linear expressions with rational coefficients, for example, -2x3+49= 1157x-1 ⇒-30x+20=693x-99 ⇒x=119723 , and verifying the solution

  VC2M10AA03 | Mathematics | Mathematics Version 2.0 | Level 10A | Algebra