Average rate of change worksheet for Algebra 1
In Algebra 1 average rate of change is slope with a new name: take two points from a table or a function, and divide the change in output by the change in input. Some questions find the rate over several intervals in a row and ask whether it stays the same, which is how a line differs from a curve.
Also taught in Precalculus, Calculus and Algebra 2, each at its own level and with its own examples.
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Sigma Prep · sigmaprep.io/worksheets Name Average Rate of Change Date Period Find each rate of change, and answer what is asked. Leave answers exact.
Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep |
Sigma Prep · sigmaprep.io/worksheets Name Average Rate of ChangeAnswer keyVersion 4 Date Period Find each rate of change, and answer what is asked. Leave answers exact.
Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep |
How to do these
Find the average rate of change from to .
- The outputs go from 4 to 19, a change of 15.
- The inputs go from 1 to 6, a change of 5.
- 15 ÷ 5 = 3.
The answer is .
Where students go wrong
Using the two columns next to each other instead of the endpoints asked for. From x = 1 to x = 6 means the first and last columns here, even with a column in between.
Also called average rate of change over an interval, difference quotient or slope of a secant line.
What you can put on this worksheet
- Average rate of change over an interval
- Average rate of change of on →
- The difference quotient
- Simplify for →
- The equation of the secant line
- Write the equation of the secant line of from to →
- The general difference quotient
- Simplify for →
- From a table
- Find the average rate of change from to . →
- Are the rates increasing or decreasing?
- Find the average rate of change over each interval. Are the rates increasing,
decreasing or the same, and what does that show?
→ ; the same, so the graph is a line - Average speed and the speed limit
- A car passes mile marker 32, and 30 minutes later it passes mile marker 67. The speed limit is 55 mph. Must it have gone faster than the limit at some moment? → Average speed mph; yes: by the mean value theorem it went exactly 70 mph at some moment
- From a graph, fractional endpoints
- The graph of is shown. Find its average rate of change on →