Numerical methods worksheet with answers

Free printable Numerical methods worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
xyx₀ = 1.5

Apply Newton–Raphson to f(x) = x² − 2 with the starting value x₀ = 1.5. Find x2.

f(x) = x² − 2f′(x) = 2xx₀ = 1.5
x2 =
2.Easy
xya = 1b = 2

Use the bisection method on f(x) = x³ − x − 3 with the starting interval [1, 2]. Find the midpoint c4 of step 4.

f(x) = x³ − x − 3[a, b] = [1, 2]n = 4
c4 =
3.Medium
xy00.51

Approximate ∫01 eˣ dx with Simpson's rule, n = 2, and compare it with the exact value. Find the absolute error |E| = |S − I|.

f(x) = eˣ[a, b] = [0, 1]n = 2
|E| =
4.Medium
xy00.33330.666711.3331.6672

Approximate ∫02 1/(1 + x³) dx with Simpson's rule using n = 6 strips. Give S.

f(x) = 1/(1 + x³)[a, b] = [0, 2]n = 6
S =
5.Hard
00.511.50123ty(0, 0.5)

Use Euler's method with h = 0.5 for y′ = 1 + sin(ty), y(0) = 0.5 to estimate y3 ≈ y(1.5).

y′ = 1 + sin(ty)y(0) = 0.5h = 0.5
y3 =
6.Hard
00.20.40.60.823ty(0, 3)

Solve y′ = t − y, y(0) = 3 with Euler's method and step h = 0.2 up to t = 0.8. The exact solution is y = t − 1 + (y₀ + 1)e−t. Find the global error |E| = |y(0.8) − y4|.

y′ = t − yy(0) = 3h = 0.2
|E| =

Answer key

  1. 1. x2 = 1.414
  2. 2. c4 = 1.688
  3. 3. |E| = 0.0005793
  4. 4. S = 1.091
  5. 5. y3 = 2.733
  6. 6. |E| = 0.1589

Full step-by-step solutions: practise this topic on examproblems.com.