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

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 0.001?

b − a = 4ε = 0.001
n =
2.Easy
xya = 0b = 1

Use the bisection method on f(x) = e−x − x with the starting interval [0, 1]. Find the midpoint c4 of step 4.

f(x) = e−x − x[a, b] = [0, 1]n = 4
c4 =
3.Medium
xy012

Approximate ∫02 1/√(1 + x⁴) dx with Simpson's rule using n = 2 strips. Give S.

f(x) = 1/√(1 + x⁴)[a, b] = [0, 2]n = 2
S =
4.Medium
t (s)01234v (m/s)1481311

A vehicle's speed is measured every 1 s (table). Estimate the distance s travelled from t = 0 to t = 4 s with Simpson's rule.

h = 1 sn = 4
s = m
5.Hard
00.050.10.50.510.520.53ty(0, 0.5)

Take one step of the classical Runge–Kutta method (RK4) with h = 0.1 for y′ = t² + y², y(0) = 0.5. Find y₁ ≈ y(0.1).

y′ = t² + y²y(0) = 0.5h = 0.1
y1 =
6.Hard
00.20.40.60.82468ty(0, 3)

Use Euler's method with h = 0.2 for y′ = t + y, y(0) = 3 to estimate y4 ≈ y(0.8).

y′ = t + yy(0) = 3h = 0.2
y4 =

Answer key

  1. 1. n = 12
  2. 2. c4 = 0.5625
  3. 3. S = 1.357
  4. 4. s = 32 m
  5. 5. y1 = 0.5267
  6. 6. y4 = 6.494

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