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

Apply Newton–Raphson to f(x) = cos x − x with the starting value x₀ = 1. Find x1.

f(x) = cos x − xf′(x) = −sin x − 1x₀ = 1
x1 =
2.Easy
xyx₀ = 1

Apply Newton–Raphson to f(x) = x³ − x − 1 with the starting value x₀ = 1. Find x2.

f(x) = x³ − x − 1f′(x) = 3x² − 1x₀ = 1
x2 =
3.Medium
xy00.250.50.7511.251.5

Approximate ∫01.5 1/√(1 + x⁴) dx with Simpson's rule using n = 6 strips. Give S.

f(x) = 1/√(1 + x⁴)[a, b] = [0, 1.5]n = 6
S =
4.Medium
t (s)0102030405060v (m/s)671013121010

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

h = 10 sn = 6
s = m
5.Hard
00.5112ty(0, 0.5)

Solve y′ = t + y, y(0) = 0.5 with Euler's method and step h = 0.25 up to t = 1. The exact solution is y = −t − 1 + (y₀ + 1)eᵗ. Find the global error |E| = |y(1) − y4|.

y′ = t + yy(0) = 0.5h = 0.25
|E| =
6.Hard
00.10.20.30.50.60.70.8ty(0, 0.5)

Use Heun's method (improved Euler) with h = 0.1 for y′ = y(2 − y), y(0) = 0.5 to estimate y3 ≈ y(0.3).

y′ = y(2 − y)y(0) = 0.5h = 0.1
y3 =

Answer key

  1. 1. x1 = 0.7504
  2. 2. x2 = 1.348
  3. 3. S = 1.2
  4. 4. s = 600 m
  5. 5. |E| = 0.4153
  6. 6. y3 = 0.7551

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