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 = 0

Apply Newton–Raphson to f(x) = x³ + 2x − 2 with the starting value x₀ = 0. Find x2.

f(x) = x³ + 2x − 2f′(x) = 3x² + 2x₀ = 0
x2 =
2.Easy
x22.22.42.62.83y1.38631.43511.48161.52611.56861.6094

Use linear interpolation in the table to estimate y at x = 2.72.

x = 2.72
y =
3.Medium
xy11.52

Approximate ∫12 1/x dx with Simpson's rule, n = 2, and compare it with the exact value. Find the absolute error |E| = |S − I|.

f(x) = 1/x[a, b] = [1, 2]n = 2
|E| =
4.Medium
xy12.54

Approximate ∫14 1/x dx with Simpson's rule, n = 2, and compare it with the exact value. Find the absolute error |E| = |S − I|.

f(x) = 1/x[a, b] = [1, 4]n = 2
|E| =
5.Hard
00.20.40.622.53ty(0, 3)

Solve y′ = −2ty, y(0) = 3 with Euler's method and step h = 0.2 up to t = 0.6. The exact solution is y = y₀e−t². Find the global error |E| = |y(0.6) − y3|.

y′ = −2tyy(0) = 3h = 0.2
|E| =
6.Hard
00.511.520.51ty(0, 1)

Use Euler's method with h = 0.5 for y′ = cos t − y, y(0) = 1 to estimate y4 ≈ y(2).

y′ = cos t − yy(0) = 1h = 0.5
y4 =

Answer key

  1. 1. x2 = 0.8
  2. 2. y = 1.552
  3. 3. |E| = 0.001297
  4. 4. |E| = 0.03871
  5. 5. |E| = 0.2254
  6. 6. y4 = 0.4051

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