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 4. Every step halves the interval. How many steps n are needed at least before the interval is shorter than 0.01?

b − a = 4ε = 0.01
n =
2.Easy

The bisection method starts on an interval of length 3. Every step halves the interval. How many steps n are needed at least before the interval is shorter than 0.0002?

b − a = 3ε = 0.0002
n =
3.Medium
xy00.16670.33330.50.66670.83331

Approximate ∫01 1/(1 + x³) dx with Simpson's rule using n = 6 strips. Give S.

f(x) = 1/(1 + x³)[a, b] = [0, 1]n = 6
S =
4.Medium
xy11.752.53.254

Approximate ∫14 1/x dx with the trapezoid rule, n = 4, and compare it with the exact value. Find the absolute error |E| = |T − I|.

f(x) = 1/x[a, b] = [1, 4]n = 4
|E| =
5.Hard
00.20.40.60.51ty(0, 0.5)

Use Euler's method with h = 0.25 for y′ = y(2 − y), y(0) = 0.5 to estimate y3 ≈ y(0.75).

y′ = y(2 − y)y(0) = 0.5h = 0.25
y3 =
6.Hard
00.511.5200.51ty(0, 0)

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

y′ = e−tyy(0) = 0h = 0.5
y4 =

Answer key

  1. 1. n = 9
  2. 2. n = 14
  3. 3. S = 0.8357
  4. 4. |E| = 0.0418
  5. 5. y3 = 1.161
  6. 6. y4 = 1.192

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