Numbers and Algebra

Outcomes

Ratios and Rates
- MA5.3-4NA
  Draws, interprets and analyses graphs of physical phenomena
  - Solve problems involving direct proportion; explore the relationship between graphs and equations corresponding to simple rate problems (ACMNA208)
    - Interpret distance/time graphs when the speed is variable
      
      Play Activities 26
      
      Examples
    - Describe qualitatively the rate of change of a graph using terms such as 'increasing at a decreasing rate'
      
      Play Activities 5
      
      Examples
Linear Relationships
- MA5.3-8NA
  Uses formulas to find midpoint, gradient and distance on the Cartesian plane, and applies standard forms of the equation of a straight line
  - Find the midpoint and gradient of a line segment (interval) on the Cartesian plane (ACMNA294)
    - Use the concept of an average to establish the formula for the midpoint, M, of the interval joining two points (x1,y1) and (x2,y2) on the Cartesian plane: M(x,y) = (x1 + x2 / 2, y1 + y2 / 2)
      
      Play Activities 2
      
      Examples
  - Solve problems using various standard forms of the equation of a straight line
    - Find the equation of a line passing through two points
      
      Play Activities 6
      
      Examples
Non-Linear Relationships
- MA5.3-9NA
  Sketches and interprets a variety of non-linear relationships
  - Describe, interpret and sketch parabolas, hyperbolas, circles and exponential functions and their transformations (ACMNA267)
    - Find x- and y-intercepts, where appropriate, for the graph of y = ax squared + bx + c, given a, b and c
      
      Play Activities 4
      
      Examples
    - Determine the equation of the axis of symmetry of a parabola using: CCT the midpoint of the interval joining the points at which the parabola cuts the x-axis the formula x = -b/2a
      
      Play Activities 3
      
      Examples