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 0.001?

b − a = 3ε = 0.001
n =
2.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 0.05?

b − a = 0.5ε = 0.05
n =
3.Medium
xy012

Approximate ∫02 sin(x²) dx with Simpson's rule using n = 2 strips. Give S.

f(x) = sin(x²)[a, b] = [0, 2]n = 2
S =
4.Medium
t (s)024681012v (m/s)1010811151922

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
5.Hard
00.050.111.051.1ty(0, 1)

Take one step of the classical Runge–Kutta method (RK4) with h = 0.1 for y′ = t² + y², y(0) = 1. Find y₁ ≈ y(0.1).

y′ = t² + y²y(0) = 1h = 0.1
y1 =
6.Hard
00.20.40.611.52ty(0, 1)

Use Heun's method (improved Euler) with h = 0.25 for y′ = 1 + sin(ty), y(0) = 1 to estimate y3 ≈ y(0.75).

y′ = 1 + sin(ty)y(0) = 1h = 0.25
y3 =

Answer key

  1. 1. n = 12
  2. 2. n = 4
  3. 3. S = 0.8697
  4. 4. s = 158 m
  5. 5. y1 = 1.111
  6. 6. y3 = 2.136

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