Worksheets · Calculus

Newton's method worksheet

Guess a root, draw the tangent there, and see where it crosses the axis. That crossing is a better guess, and repeating it closes in fast.

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

Newton's Method

Date Period

Answer each question. Give exact values.

  1. Use Newton's method on f(x)=x2−3x−20 from x0=3. Find x2 exactly.
  2. Use Newton's method on f(x)=x2+3x−30 from x0=2. Find x2 exactly.
  3. Use Newton's method on f(x)=x2+2x−19 from x0=2. Find x2 exactly.
  4. Use Newton's method on f(x)=x2−30 from x0=2. Find x2 exactly.
  5. Use Newton's method on f(x)=x2−x−6 from x0=1. Find x2 exactly.
  6. Use Newton's method on f(x)=x2−6 from x0=1. Find x2 exactly.
  7. Use Newton's method on f(x)=x2+2x−13 from x0=2. Find x2 exactly.
  8. Use Newton's method on f(x)=x2−3x−7 from x0=2. Find x2 exactly.
  9. Use Newton's method on f(x)=x2+x−7 from x0=3. Find x2 exactly.
  10. Use Newton's method on f(x)=x2−2x−23 from x0=3. Find x2 exactly.
  11. Use Newton's method on f(x)=x2+2x−15 from x0=4. Find x2 exactly.
  12. Use Newton's method on f(x)=x2+2x−8 from x0=1. Find x2 exactly.
  13. Use Newton's method on f(x)=x2−x−11 from x0=1. Find x2 exactly.
  14. Use Newton's method on f(x)=x2+2x−6 from x0=3. Find x2 exactly.
  15. Use Newton's method on f(x)=x2+3x−20 from x0=1. Find x2 exactly.
  16. Use Newton's method on f(x)=x2+2x−30 from x0=2. Find x2 exactly.
  17. Use Newton's method on f(x)=x2+x−10 from x0=4. Find x2 exactly.
  18. Use Newton's method on f(x)=x2+x−28 from x0=4. Find x2 exactly.
  19. Use Newton's method on f(x)=x2+3x−26 from x0=1. Find x2 exactly.
  20. Use Newton's method on f(x)=x2+3x−3 from x0=2. Find x2 exactly.

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

Sigma Prep · sigmaprep.io/worksheets

Name

Newton's MethodAnswer keyVersion 1

Date Period

Answer each question. Give exact values.

  1. Use Newton's method on f(x)=x2−3x−20 from x0=3. Find x2 exactly.1021147
  2. Use Newton's method on f(x)=x2+3x−30 from x0=2. Find x2 exactly.2626623
  3. Use Newton's method on f(x)=x2+2x−19 from x0=2. Find x2 exactly.1213348
  4. Use Newton's method on f(x)=x2−30 from x0=2. Find x2 exactly.40968
  5. Use Newton's method on f(x)=x2−x−6 from x0=1. Find x2 exactly.5513
  6. Use Newton's method on f(x)=x2−6 from x0=1. Find x2 exactly.7328
  7. Use Newton's method on f(x)=x2+2x−13 from x0=2. Find x2 exactly.757276
  8. Use Newton's method on f(x)=x2−3x−7 from x0=2. Find x2 exactly.12819
  9. Use Newton's method on f(x)=x2+x−7 from x0=3. Find x2 exactly.599273
  10. Use Newton's method on f(x)=x2−2x−23 from x0=3. Find x2 exactly.8714
  11. Use Newton's method on f(x)=x2+2x−15 from x0=4. Find x2 exactly.2461820
  12. Use Newton's method on f(x)=x2+2x−8 from x0=1. Find x2 exactly.209104
  13. Use Newton's method on f(x)=x2−x−11 from x0=1. Find x2 exactly.15523
  14. Use Newton's method on f(x)=x2+2x−6 from x0=3. Find x2 exactly.609368
  15. Use Newton's method on f(x)=x2+3x−20 from x0=1. Find x2 exactly.941285
  16. Use Newton's method on f(x)=x2+2x−30 from x0=2. Find x2 exactly.559120
  17. Use Newton's method on f(x)=x2+x−10 from x0=4. Find x2 exactly.1486549
  18. Use Newton's method on f(x)=x2+x−28 from x0=4. Find x2 exactly.4204873
  19. Use Newton's method on f(x)=x2+3x−26 from x0=1. Find x2 exactly.1379345
  20. Use Newton's method on f(x)=x2+3x−3 from x0=2. Find x2 exactly.45

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

How to do these

Use Newton's method on f(x)=x2−2 from x0=1. Find x1.

  1. f of 1 is minus 1, and the derivative there is 2.
  2. So x1 is 1 minus minus one over two.
  3. That is three halves.

The answer is 32.

Where students go wrong

Subtracting the derivative instead of dividing by it. The formula is x minus f over f prime; the division is what turns a height into a horizontal step.

Also called Newton Raphson, root finding or iteration formula.

Questions about these worksheets

Yes. Every newton's method 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.

Calculus is usually taken around 12th grade or a first college course, 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 newton's method 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.

Subtracting the derivative instead of dividing by it. The formula is x minus f over f prime; the division is what turns a height into a horizontal step.