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 0.5. Every step halves the interval. How many steps n are needed at least before the interval is shorter than 0.001?

b − a = 0.5ε = 0.001
n =
2.Easy
xya = 3b = 4

Use the bisection method on f(x) = x² − 10 with the starting interval [3, 4]. Find the midpoint c4 of step 4.

f(x) = x² − 10[a, b] = [3, 4]n = 4
c4 =
3.Medium
xy00.33330.666711.3331.6672

Approximate ∫02 √x·e−x dx with the trapezoid rule using n = 6 strips. Give T.

f(x) = √x·e−x[a, b] = [0, 2]n = 6
T =
4.Medium
xy00.51

Approximate ∫01 √(1 + x³) dx with the trapezoid rule using n = 2 strips. Give T.

f(x) = √(1 + x³)[a, b] = [0, 1]n = 2
T =
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′ = e−ty, y(0) = 1. Find y₁ ≈ y(0.1).

y′ = e−tyy(0) = 1h = 0.1
y1 =
6.Hard
00.050.10.50.550.6ty(0, 0.5)

Take one step of the classical Runge–Kutta method (RK4) with h = 0.1 for y′ = e−ty, y(0) = 0.5. Find y₁ ≈ y(0.1).

y′ = e−tyy(0) = 0.5h = 0.1
y1 =

Answer key

  1. 1. n = 9
  2. 2. c4 = 3.188
  3. 3. T = 0.6149
  4. 4. T = 1.134
  5. 5. y1 = 1.095
  6. 6. y1 = 0.5972

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