unit three math review

• Hiking trip taken by the Oakville Hiking Club


  1. Began hiking 8km in 4 hours

  2. Stopped and rested for 6 hours

  3. Began hiking back 8km in 8 hours
• Linear relation


  Relation where the graph is a straight line

  
• Non-linear relation


  Relation where the graph is not a straight line
• Finding slope of a graph


  Determine the rise and run between any two points on the line
• Direct variation


  Straight line passing through the origin(zero)
• Partial variation


  Straight line that does not pass through the origin(zero)
• Determining if a linear relation is direct or partial variation


  Look at the graph(going through origin or no), table of values(first differences), or equation(initial value)
• Finding cost per person


  Use slope formula: (total cost2 - total cost1) / (number of guests2 - number of guests1) first answer and second answer divided = answer
• Calculating rate of change from a table of values

  Use slope formula: (y2 - y1) / (x2 - x1)
• Rate of change


  The slope of the line, represents the change in y per unit change in x
• Initial value


  The y-intercept, represents the starting value
• Direct variation


  Linear relation where y = mx, the rate of change is the constant of proportionality
• Partial variation


  Linear relation where y = mx + b, the rate of change is the slope and the initial value is the y-intercept
• Determining cost for a given number of guests


  Substitute the number of guests into the equation y = mx + b
• Writing an equation to represent a scenario


  Define variables, then write the equation in the form y = mx + b
• Slope


  Represents the cost per unit, e.g. cost per hour for parking
• 1. intercept


  Represents the fixed/initial cost, e.g. cost of concert ticket
• Graphing multiple linear equations


  Plot each equation on the same coordinate plane

  
• Fixed cost


  Initial/flat fee to rent the jet ski
• Cost per minute


  Rate of change, represents the cost per unit time for using the jet ski
• Writing linear equations to represent situations


  Define variables, then write the equation in the form y = mx + b
• Determining point of intersection


  Find the x and y values where the two lines cross
• Climate


  Long-term weather patterns in a region
• Canada has such different climate areas
• Factors that affect climate


  • ACRONYM to remember them
  • Explanation of each factor
• Reading a climate graph


  1. Calculate temperature range

  2. Determine seasonal distribution of precipitation
• Climate


  Connections to populations
• Components of soil


  • List of components
• Layers of soil


  • List of layers
  • What is humus
• Soil profiles and processes


  1. Leaching vs calcification

  2. Wet-climate vs dry-climate soil
• Vegetation regions


  • Characteristics of each region
• Cordilleran Region


  • What makes it unique
• Causes of climate change


  • List of causes
  • Who is responsible
• Solutions to climate change


  • List of solutions
  • What groups must take action