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 = 4b = 5

Use the bisection method on f(x) = x² − 20 with the starting interval [4, 5]. Find the midpoint c3 of step 3.

f(x) = x² − 20[a, b] = [4, 5]n = 3
c3 =
2.Easy
xya = 0b = 1

Use the bisection method on f(x) = e−x − x with the starting interval [0, 1]. Find the midpoint c3 of step 3.

f(x) = e−x − x[a, b] = [0, 1]n = 3
c3 =
3.Medium
xy00.51

Approximate ∫01 x³ dx with the trapezoid rule, n = 2, and compare it with the exact value. Find the absolute error |E| = |T − I|.

f(x) = x³[a, b] = [0, 1]n = 2
|E| =
4.Medium
xy00.751.52.253

Approximate ∫03 √x·e−x dx with the trapezoid rule using n = 4 strips. Give T.

f(x) = √x·e−x[a, b] = [0, 3]n = 4
T =
5.Hard
00.20.40.40.60.81ty(0, 0.5)

Use Heun's method (improved Euler) with h = 0.25 for y′ = e−ty, y(0) = 0.5 to estimate y2 ≈ y(0.5).

y′ = e−tyy(0) = 0.5h = 0.25
y2 =
6.Hard
00.050.10.150.20.50.60.7ty(0, 0.5)

Take one step of the classical Runge–Kutta method (RK4) with h = 0.2 for y′ = 1 + sin(ty), y(0) = 0.5. Find y₁ ≈ y(0.2).

y′ = 1 + sin(ty)y(0) = 0.5h = 0.2
y1 =

Answer key

  1. 1. c3 = 4.375
  2. 2. c3 = 0.625
  3. 3. |E| = 0.0625
  4. 4. T = 0.6627
  5. 5. y2 = 0.9111
  6. 6. y1 = 0.7128

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