Worksheets · Algebra 1

Algebra 1 average rate of change worksheet

The average rate of change is the slope between two points on the graph, so it is rise over run with the function doing the work. The difference quotient is the same thing with the second point written as h away from the first.

Select your difficulty

Pick more than one for a sheet that mixes them.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Average Rate of Change

Date Period

Find each rate of change. Leave answers exact.

  1. Average rate of change of f(x)=−2x2+8x+9 on [−2,0]
  2. Average rate of change of f(x)=−3x2−x on [−4,−2]
  3. Average rate of change of f(x)=−2x−2 on [3,4]
  4. Average rate of change of f(x)=−2x+6 on [−2,−1]
  5. Average rate of change of f(x)=3x2−5x+4 on [−1,2]
  6. Average rate of change of f(x)=−3x2−6x−3 on [−1,0]
  7. Average rate of change of f(x)=2x−4 on [−5,−3]
  8. Average rate of change of f(x)=−3x2+4x−2 on [−2,1]
  9. Average rate of change of f(x)=3x2+7x+6 on [5,6]
  10. Average rate of change of f(x)=x on [5,8]
  11. Average rate of change of f(x)=3x+9 on [−4,−2]
  12. Average rate of change of f(x)=−x on [0,1]
  13. Average rate of change of f(x)=x2−6x−4 on [4,5]
  14. Average rate of change of f(x)=2x−7 on [−4,−3]
  15. Average rate of change of f(x)=2x on [0,1]
  16. Average rate of change of f(x)=−3x2+8x+7 on [−5,−4]
  17. Average rate of change of f(x)=x+7 on [−4,−3]
  18. Average rate of change of f(x)=3x2−5x−8 on [−4,−2]
  19. Average rate of change of f(x)=−3x2−3x+8 on [4,6]
  20. Average rate of change of f(x)=−2x2−3x−6 on [−3,0]

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Average Rate of ChangeAnswer keyVersion 1

Date Period

Find each rate of change. Leave answers exact.

  1. Average rate of change of f(x)=−2x2+8x+9 on [−2,0]12
  2. Average rate of change of f(x)=−3x2−x on [−4,−2]17
  3. Average rate of change of f(x)=−2x−2 on [3,4]−2
  4. Average rate of change of f(x)=−2x+6 on [−2,−1]−2
  5. Average rate of change of f(x)=3x2−5x+4 on [−1,2]−2
  6. Average rate of change of f(x)=−3x2−6x−3 on [−1,0]−3
  7. Average rate of change of f(x)=2x−4 on [−5,−3]2
  8. Average rate of change of f(x)=−3x2+4x−2 on [−2,1]7
  9. Average rate of change of f(x)=3x2+7x+6 on [5,6]40
  10. Average rate of change of f(x)=x on [5,8]1
  11. Average rate of change of f(x)=3x+9 on [−4,−2]3
  12. Average rate of change of f(x)=−x on [0,1]−1
  13. Average rate of change of f(x)=x2−6x−4 on [4,5]3
  14. Average rate of change of f(x)=2x−7 on [−4,−3]2
  15. Average rate of change of f(x)=2x on [0,1]2
  16. Average rate of change of f(x)=−3x2+8x+7 on [−5,−4]35
  17. Average rate of change of f(x)=x+7 on [−4,−3]1
  18. Average rate of change of f(x)=3x2−5x−8 on [−4,−2]−23
  19. Average rate of change of f(x)=−3x2−3x+8 on [4,6]−33
  20. Average rate of change of f(x)=−2x2−3x−6 on [−3,0]3

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

Average rate of change of f(x)=x2−3x on [1,4]

  1. f(4) is 16 minus 12, which is 4.
  2. f(1) is 1 minus 3, which is -2.
  3. The rise is 6 and the run is 3.

The answer is 2.

Where students go wrong

Dividing by the wrong run, or subtracting the outputs in one order and the inputs in the other. Keep the same endpoint on top and bottom: f(b) minus f(a) over b minus a, in that order both times.

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 f(x)=3x2−7x on [1,2] → 2
The difference quotient
Simplify f(0+h)−f(0)h for f(x)=2x2+3x−8 → 2h+3

Questions about these worksheets

Yes. Every average rate of change sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Algebra 1 is usually taken around 8th or 9th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the average rate of change questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 2: average rate of change over an interval and the difference quotient. Tick as many as you want and set how many of each, or let it spread them evenly.

Dividing by the wrong run, or subtracting the outputs in one order and the inputs in the other. Keep the same endpoint on top and bottom: f(b) minus f(a) over b minus a, in that order both times.