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 = 2

Apply Newton–Raphson to f(x) = ln x + x − 2 with the starting value x₀ = 2. Find x1.

f(x) = ln x + x − 2f′(x) = 1/x + 1x₀ = 2
x1 =
2.Easy
x123456y1.41421.732122.23612.44952.6458

Use linear interpolation in the table to estimate y at x = 2.6.

x = 2.6
y =
3.Medium
xy00.30.60.91.21.5

Approximate ∫01.5 1/(1 + x³) dx with the trapezoid rule using n = 5 strips. Give T.

f(x) = 1/(1 + x³)[a, b] = [0, 1.5]n = 5
T =
4.Medium
xy00.51

Approximate ∫01 sin x dx with the trapezoid rule, n = 2, and compare it with the exact value. Find the absolute error |E| = |T − I|.

f(x) = sin x[a, b] = [0, 1]n = 2
|E| =
5.Hard
00.20.40.60.80.60.81ty(0, 1)

Use Euler's method with h = 0.2 for y′ = t − y, y(0) = 1 to estimate y4 ≈ y(0.8).

y′ = t − yy(0) = 1h = 0.2
y4 =
6.Hard
00.20.4345ty(0, 3)

Use Euler's method with h = 0.1 for y′ = t + y, y(0) = 3 to estimate y5 ≈ y(0.5).

y′ = t + yy(0) = 3h = 0.1
y5 =

Answer key

  1. 1. x1 = 1.538
  2. 2. y = 1.893
  3. 3. T = 1.007
  4. 4. |E| = 0.009617
  5. 5. y4 = 0.6192
  6. 6. y5 = 4.942

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