Prior to working with rates of change, one should have an understanding of basic algebra, a variety of constants and non-constants ways in which a dependent variable can change with respect to changes in a second independent variable. It is also recommended that one has experience calculating slope and slope intercepts. The rate of change is a measure of how much one variable changes for a given change of a second variable, which is, how much one variable grows (or shrinks) in relation to another variable.
The following questions require you to calculate the rate of change. Solutions are provided in the PDF. The speed at which a variable changes over a specific amount of time is considered the rate of change. Real life problems as those presented below require an understanding of calculating the rate of change. Graphs and formulas are used to calculate rates of change. Finding the average rate of change is similar to a slope of the secant line that passes through two points.
Here are 10 practice questions below to test your understanding of rates of change. You will find PDF solutions here and at the end of the questions.
The distance a race car travels around a track during a race is measured by the equation:
Where t is the time in seconds and s is the distance in meters.
Determine the car's average speed:
- During the first 5 seconds
- Between 10 and 20 seconds.
- 25 m from the start
Determine the instantaneous speed of the car:
- At 1 second
- At 10 seconds
- At 75 m
The amount of medicine in a milliliter of a patient's blood is given by the equation:
Where M is the amount of medicine in mg, and t is the number of hours passed since administration.
Determine the average change in medicine:
- In the first hour.
- Between 2 and 3 hours.
- 1 hour after administration.
- 3 hours after administration.
Examples of rates of change are used daily in life and include but are not limited to: temperature and time of day, rate of growth over time, rate of decay over time, size and weight, increases and decreases of stock over time, cancer rates of growth, in sports rates of change are calculated about players and their statistics.
Learning about rates of change usually begins in high school and the concept is then re-visited in calculus. There are often questions about the rate of change on SATs and other college entry assessments in mathematics. Graphing calculators and online calculators also have the ability to calculate a variety of problems involving the rate of change.