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.

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1.Easy
x00.20.40.60.81y0.69310.78850.87550.95551.02961.0986

Use linear interpolation in the table to estimate y at x = 0.55.

x = 0.55
y =
2.Easy

The bisection method starts on an interval of length 2. Every step halves the interval. How many steps n are needed at least before the interval is shorter than 0.001?

b − a = 2ε = 0.001
n =
3.Medium
t (s)012345v (m/s)0564712

A vehicle's speed is measured every 1 s (table). Estimate the distance s travelled from t = 0 to t = 5 s with the trapezoid rule.

h = 1 sn = 5
s = m
4.Medium
xy012

Approximate ∫02 x³ dx with the trapezoid rule, n = 2, and compare it with the exact value. Find the absolute error |E| = |T − I|.

f(x) = x³[a, b] = [0, 2]n = 2
|E| =
5.Hard
00.51123ty(0, 3)

Solve y′ = −2ty, y(0) = 3 with Euler's method and step h = 0.25 up to t = 1.25. The exact solution is y = y₀e−t². Find the global error |E| = |y(1.25) − y5|.

y′ = −2tyy(0) = 3h = 0.25
|E| =
6.Hard
012−50ty(0, 0.5)

Solve y′ = y − t², y(0) = 0.5 with Euler's method and step h = 0.5 up to t = 2.5. The exact solution is y = t² + 2t + 2 + (y₀ − 2)eᵗ. Find the global error |E| = |y(2.5) − y5|.

y′ = y − t²y(0) = 0.5h = 0.5
|E| =

Answer key

  1. 1. y = 0.9355
  2. 2. n = 11
  3. 3. s = 28 m
  4. 4. |E| = 1
  5. 5. |E| = 0.0136
  6. 6. |E| = 3.586

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