3.3.2 Understanding interpreting rate of change

• What do rates of change measure?

  Change in one quantity relation to another
• The instantaneous rate of change can be calculated using the average rate of change formula.

  False
• Which mathematical technique is used to find the instantaneous rate of change?

  Calculus
• The slope of the tangent line on a curve represents the instantaneous rate of change.
• The instantaneous rate of change is represented by the slope of the tangent
• Speed is calculated using the formula distance divided by time
• The formula for the average rate of change is (Change in Quantity) / (Change in Time
• The instantaneous rate of change is derived using calculus
• The slope of the tangent line on a curve represents the instantaneous rate of change
• The instantaneous rate of change requires the use of calculus to find the derivative
• The formula for calculating speed is distance divided by time.
• What is the average speed of a cyclist who covers 25 kilometers in 2 hours?

  12.5 km/h
• Match the graph type with the corresponding rate of change:

  Increasing Line ↔️ Positive Rate of Change

  Decreasing Line ↔️ Negative Rate of Change

  Horizontal Line ↔️ Zero Rate of Change
• What are common examples of rates of change?

  Speed and temperature change
• The slope of a straight line in a distance-time graph represents the average speed.


  True
• The rate of temperature change per hour measures how temperature varies over time.


  True
• If a cyclist covers 25 km in 2 hours, their average speed is 12.5 km/h.


  True
• The instantaneous rate of change might be higher or lower than the average rate of change at a specific point.

  True
• The slope of the tangent line at a point on a graph gives the instantaneous speed at that moment.


  True
• The slope of a tangent line on a graph represents the instantaneous rate of change at that point.


  True
• How is the average rate of change calculated?

  (Change in Quantity)/(Change in Time)
• The instantaneous rate of change is the rate of change at a specific point in time.
• The slope of a straight line on a graph represents the average rate of change.


  True
• What does the average rate of change measure?

  Change over a time interval
• What is a common example of a rate of change?

  Speed
• How is the average rate of change calculated?

  (Change in Quantity) / (Change in Time)
• What does the instantaneous rate of change measure?

  Change at a specific point
• What does the slope of a straight line on a graph represent?

  Average rate of change
• What is the formula for the average rate of change in general terms?

  (Change in Quantity) / (Change in Time)