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
x11.21.41.61.82y1.34991.43331.5221.61611.7161.8221

Use linear interpolation in the table to estimate y at x = 1.92.

x = 1.92
y =
2.Easy

The bisection method starts on an interval of length 4. Every step halves the interval. How many steps n are needed at least before the interval is shorter than 0.005?

b − a = 4ε = 0.005
n =
3.Medium
t (s)0102030405060v (m/s)5111210162222

A vehicle's speed is measured every 10 s (table). Estimate the distance s travelled from t = 0 to t = 60 s with the trapezoid rule.

h = 10 sn = 6
s = m
4.Medium
xy00.33330.66671

Approximate ∫01 1/√(1 + x⁴) dx with the trapezoid rule using n = 3 strips. Give T.

f(x) = 1/√(1 + x⁴)[a, b] = [0, 1]n = 3
T =
5.Hard
00.511.52−10−50ty(0, −1)

Solve y′ = y − t², y(0) = −1 with Euler's method and step h = 0.5 up to t = 2. The exact solution is y = t² + 2t + 2 + (y₀ − 2)eᵗ. Find the global error |E| = |y(2) − y4|.

y′ = y − t²y(0) = −1h = 0.5
|E| =
6.Hard
00.511.520123ty(0, 0)

Use Euler's method with h = 0.5 for y′ = 1 + sin(ty), y(0) = 0 to estimate y4 ≈ y(2).

y′ = 1 + sin(ty)y(0) = 0h = 0.5
y4 =

Answer key

  1. 1. y = 1.78
  2. 2. n = 10
  3. 3. s = 845 m
  4. 4. T = 0.9204
  5. 5. |E| = 4.948
  6. 6. y4 = 2.589

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