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 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 =
2.Easy
x00.511.522.5y11.16181.34991.56831.82212.117

Use linear interpolation in the table to estimate the value x where y = 1.2464.

y = 1.2464
x =
3.Medium
xy00.51

Approximate ∫01 eˣ dx with the trapezoid rule, n = 2, and compare it with the exact value. Find the absolute error |E| = |T − I|.

f(x) = eˣ[a, b] = [0, 1]n = 2
|E| =
4.Medium
xy00.250.50.751

Approximate ∫01 sin(x²) dx with Simpson's rule using n = 4 strips. Give S.

f(x) = sin(x²)[a, b] = [0, 1]n = 4
S =
5.Hard
00.20.40.60.20.4ty(0, 0.5)

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

y′ = −yy(0) = 0.5h = 0.25
y3 =
6.Hard
00.20.4−1−0.8−0.6−0.4ty(0, −1)

Use Euler's method with h = 0.1 for y′ = t − y, y(0) = −1 to estimate y5 ≈ y(0.5).

y′ = t − yy(0) = −1h = 0.1
y5 =

Answer key

  1. 1. n = 14
  2. 2. x = 0.7249
  3. 3. |E| = 0.03565
  4. 4. S = 0.3099
  5. 5. y3 = 0.2109
  6. 6. y5 = −0.5

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