Small practice
brighter futures.
Checking sign-in status
Menu

Calculus practice

Newton's Method worksheets

Approximate a real zero of polynomial and trigonometric functions through repeated Newton updates.

Ready-made English PDF · fixed settings

Worksheet · LetterWorksheet · A4
Customize worksheet ↓
With answer key

Customization below makes a separate PDF.

First page of the newton's method worksheets printable worksheetOpen full-size sample (first page)

Fixed English ready-made files. Custom settings below apply only to the configured PDF.

Ready to print

Start with a ready-made worksheet

Find f'(x), apply x next = x - f(x)/f'(x), and report the requested iterate.

Download the practice pages alone, or include a separate answer key or teacher model. Longer activities may use more than one page.

US Letter

Student worksheetWorksheet with answers

A4

Student worksheetWorksheet with answers
Customize this worksheet

Paper sizes and printing help · More calculus activities

Follow every iterate

Each worksheet keeps the original function, derivative, correction, and next value visible so students can audit the recurrence.

Learning objective

What this activity builds

Compute successive Newton iterates from an initial guess while carrying full precision.

Worked example

How is x1 found from x0?

x1=x0-f(x0)/f'(x0).

Evaluate the function and derivative at the same current iterate before subtracting the correction.

Teaching notes

Make the practice count

  • Carry unrounded values between iterations.
  • A starting guess targets one zero rather than every zero.
  • Use radians for trigonometric functions.

Make it yours

Customize the practice

Choose your options, update the preview, then download the exact same pages.

Choose the function or root families, problem count, and number of Newton iterations. Carry full precision between rows.

Worksheet settings

Function types
Page note and reproducible seed

The same settings and seed make the same questions. Shared links include your page note; leave personal information out.

Configured PDF · Newton's Method · US Letter

Preview ready. Download includes these exact pages.

4 student pages
Enlarged pages scroll. PDF size stays the same.
Math SheetNameScoreTeacherDateNewton's MethodUse the stated starting value and Newton update to approximate one real zero. Trigonometric arguments are in radians; carry full precision betweeniterations.1. degree 3f(x)=-16+14·x-6·x2+x3Start x0 = 4.000000. Complete 2 Newton iterations using full precision.Derivative f'(x):ix_if(x_i)f'(x_i)x_(i+1)01Nth iterate:2. degree 5f(x)=-1698+28·x+40·x2+32·x3+13·x4+2·x5Start x0 = 3.000000. Complete 2 Newton iterations using full precision.Derivative f'(x):ix_if(x_i)f'(x_i)x_(i+1)01Nth iterate:3. trigonometricf(x)=-8·sin4·x+1+5Start x0 = -0.100000. Complete 2 Newton iterations using full precision.Derivative f'(x):ix_if(x_i)f'(x_i)x_(i+1)01Nth iterate:math-sheet.comPage 1 of 4
Math SheetNameScoreTeacherDateNewton's MethodUse the stated starting value and Newton update to approximate one real zero. Trigonometric arguments are in radians; carry full precision betweeniterations.4. degree 4f(x)=194+304·x+136·x2+27·x3+2·x4Start x0 = -1.000000. Complete 2 Newton iterations using full precision.Derivative f'(x):ix_if(x_i)f'(x_i)x_(i+1)01Nth iterate:5. trigonometricf(x)=6·sin3·x+4-2Start x0 = -1.200000. Complete 2 Newton iterations using full precision.Derivative f'(x):ix_if(x_i)f'(x_i)x_(i+1)01Nth iterate:6. degree 4f(x)=-365+79·x+51·x2+16·x3+2·x4Start x0 = 2.000000. Complete 2 Newton iterations using full precision.Derivative f'(x):ix_if(x_i)f'(x_i)x_(i+1)01Nth iterate:math-sheet.comPage 2 of 4
Math SheetNameScoreTeacherDateNewton's MethodUse the stated starting value and Newton update to approximate one real zero. Trigonometric arguments are in radians; carry full precision betweeniterations.7. degree 3f(x)=-216+78·x-26·x2+3·x3Start x0 = 7.000000. Complete 2 Newton iterations using full precision.Derivative f'(x):ix_if(x_i)f'(x_i)x_(i+1)01Nth iterate:8. degree 5f(x)=-88+25·x+33·x2+26·x3+11·x4+2·x5Start x0 = 1.000000. Complete 2 Newton iterations using full precision.Derivative f'(x):ix_if(x_i)f'(x_i)x_(i+1)01Nth iterate:9. degree 5f(x)=-3525+373·x+327·x2+146·x3+33·x4+3·x5Start x0 = 2.000000. Complete 2 Newton iterations using full precision.Derivative f'(x):ix_if(x_i)f'(x_i)x_(i+1)01Nth iterate:math-sheet.comPage 3 of 4
Math SheetNameScoreTeacherDateNewton's MethodUse the stated starting value and Newton update to approximate one real zero. Trigonometric arguments are in radians; carry full precision betweeniterations.10. degree 3f(x)=-80+10·x+5·x2+x3Start x0 = 3.000000. Complete 2 Newton iterations using full precision.Derivative f'(x):ix_if(x_i)f'(x_i)x_(i+1)01Nth iterate:11. degree 4f(x)=-270-7·x+13·x2-10·x3+3·x4Start x0 = 4.000000. Complete 2 Newton iterations using full precision.Derivative f'(x):ix_if(x_i)f'(x_i)x_(i+1)01Nth iterate:12. trigonometricf(x)=-5·sin5·x-2+3Start x0 = 0.600000. Complete 2 Newton iterations using full precision.Derivative f'(x):ix_if(x_i)f'(x_i)x_(i+1)01Nth iterate:math-sheet.comPage 4 of 4

A useful next step

Related activities