Rate of Change Mastery
A Grade 11 Math worksheet focusing on understanding and calculating the rate of change from various representations including graphs, tables, and equations.
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Rate of Change Mastery
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Read each question carefully and show all your work. Calculate the rate of change as indicated for each problem.
1. The graph below shows the distance a car travels over time. Calculate the average rate of change (speed) of the car between t = 1 hour and t = 3 hours.
2. Complete the following statements based on the table below, which shows the population of a town over several years.
Year | Population ---|--- 2000 | 10,000 2005 | 12,500 2010 | 14,000 2015 | 16,500
a) The average rate of change in population between 2000 and 2005 is people per year.
b) The average rate of change in population between 2010 and 2015 is people per year.
3. Which of the following linear equations has the greatest rate of change?
y = 2x + 5
y = -3x + 10
y = (1/2)x - 1
y = 4x - 7
4. Determine if the following statements are True or False.
a) The instantaneous rate of change can be found by calculating the slope of the tangent line to a curve at a specific point.
True
False
b) For a linear function, the average rate of change between any two points is always the same as the instantaneous rate of change.
True
False
5. A ball is dropped from a height. Its height (h) in meters after t seconds is given by the function h(t) = 50 - 4.9t². Calculate the average rate of change of the ball's height between t = 1 second and t = 2 seconds. What does this value represent?