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

The bisection method starts on an interval of length 0.5. Every step halves the interval. How many steps n are needed at least before the interval is shorter than 0.0001?

b − a = 0.5ε = 0.0001
n =
2.Easy
x00.511.522.5y00.24740.47940.68160.84150.949

Use linear interpolation in the table to estimate the value x where y = 0.7536.

y = 0.7536
x =
3.Medium
t (s)01234v (m/s)48141715

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
4.Medium
xy012

Approximate ∫02 1/(1 + x³) dx with Simpson's rule using n = 2 strips. Give S.

f(x) = 1/(1 + x³)[a, b] = [0, 2]n = 2
S =
5.Hard
00.050.10.150.211.11.2ty(0, 1)

Use Heun's method (improved Euler) with h = 0.1 for y′ = e−ty, y(0) = 1 to estimate y2 ≈ y(0.2).

y′ = e−tyy(0) = 1h = 0.1
y2 =
6.Hard
00.050.10.150.20.960.981ty(0, 1)

Use Heun's method (improved Euler) with h = 0.1 for y′ = −2ty, y(0) = 1 to estimate y2 ≈ y(0.2).

y′ = −2tyy(0) = 1h = 0.1
y2 =

Answer key

  1. 1. n = 13
  2. 2. x = 1.725
  3. 3. s = 49 m
  4. 4. S = 1.037
  5. 5. y2 = 1.179
  6. 6. y2 = 0.9607

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