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
xya = 1b = 4

Use the bisection method on f(x) = ln x + x − 4 with the starting interval [1, 4]. Find the midpoint c3 of step 3.

f(x) = ln x + x − 4[a, b] = [1, 4]n = 3
c3 =
2.Easy
x00.20.40.60.81y11.09541.18321.26491.34161.4142

Use linear interpolation in the table to estimate y at x = 0.75.

x = 0.75
y =
3.Medium
t (s)024681012v (m/s)8101415172321

A vehicle's speed is measured every 2 s (table). Estimate the distance s travelled from t = 0 to t = 12 s with the trapezoid rule.

h = 2 sn = 6
s = m
4.Medium
xy123

Approximate ∫13 1/x dx with Simpson's rule, n = 2, and compare it with the exact value. Find the absolute error |E| = |S − I|.

f(x) = 1/x[a, b] = [1, 3]n = 2
|E| =
5.Hard
00.20.40.60.511.5ty(0, 0.5)

Use Euler's method with h = 0.25 for y′ = t + y, y(0) = 0.5 to estimate y3 ≈ y(0.75).

y′ = t + yy(0) = 0.5h = 0.25
y3 =
6.Hard
00.510.511.5ty(0, 0.5)

Use Euler's method with h = 0.25 for y′ = y(2 − y), y(0) = 0.5 to estimate y4 ≈ y(1).

y′ = y(2 − y)y(0) = 0.5h = 0.25
y4 =

Answer key

  1. 1. c3 = 2.875
  2. 2. y = 1.322
  3. 3. s = 187 m
  4. 4. |E| = 0.0125
  5. 5. y3 = 1.18
  6. 6. y4 = 1.405

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