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 1. Every step halves the interval. How many steps n are needed at least before the interval is shorter than 0.0001?

b − a = 1ε = 0.0001
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 0.0001?

b − a = 3ε = 0.0001
n =
3.Medium
t (s)010203040v (m/s)9761113

A vehicle's speed is measured every 10 s (table). Estimate the distance s travelled from t = 0 to t = 40 s with Simpson's rule.

h = 10 sn = 4
s = m
4.Medium
xy00.751.5

Approximate ∫01.5 e−x² dx with Simpson's rule using n = 2 strips. Give S.

f(x) = e−x²[a, b] = [0, 1.5]n = 2
S =
5.Hard
00.20.40.600.1ty(0, 0)

Use Heun's method (improved Euler) with h = 0.25 for y′ = t² + y², y(0) = 0 to estimate y3 ≈ y(0.75).

y′ = t² + y²y(0) = 0h = 0.25
y3 =
6.Hard
00.050.10.150.20.50.60.7ty(0, 0.5)

Use Heun's method (improved Euler) with h = 0.1 for y′ = 1 + sin(ty), y(0) = 0.5 to estimate y2 ≈ y(0.2).

y′ = 1 + sin(ty)y(0) = 0.5h = 0.1
y2 =

Answer key

  1. 1. n = 14
  2. 2. n = 15
  3. 3. s = 353.3 m
  4. 4. S = 0.8461
  5. 5. y3 = 0.1503
  6. 6. y2 = 0.7131

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