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
xyx₀ = 3

Apply Newton–Raphson to f(x) = x³ − x − 5 with the starting value x₀ = 3. Find x1.

f(x) = x³ − x − 5f′(x) = 3x² − 1x₀ = 3
x1 =
2.Easy
xyx₀ = 1

Apply Newton–Raphson to f(x) = x² − 3 with the starting value x₀ = 1. Find x2.

f(x) = x² − 3f′(x) = 2xx₀ = 1
x2 =
3.Medium
xy00.30.60.91.21.5

Approximate ∫01.5 √(1 + x³) dx with the trapezoid rule using n = 5 strips. Give T.

f(x) = √(1 + x³)[a, b] = [0, 1.5]n = 5
T =
4.Medium
xy123

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

f(x) = 1/x[a, b] = [1, 3]n = 2
|E| =
5.Hard
00.10.20.33456ty(0, 3)

Solve y′ = 2y, y(0) = 3 with Euler's method and step h = 0.1 up to t = 0.3. The exact solution is y = y₀e2t. Find the global error |E| = |y(0.3) − y3|.

y′ = 2yy(0) = 3h = 0.1
|E| =
6.Hard
00.511.5051015ty(0, 3)

Use Heun's method (improved Euler) with h = 0.5 for y′ = t + y, y(0) = 3 to estimate y3 ≈ y(1.5).

y′ = t + yy(0) = 3h = 0.5
y3 =

Answer key

  1. 1. x1 = 2.269
  2. 2. x2 = 1.75
  3. 3. T = 1.989
  4. 4. |E| = 0.06805
  5. 5. |E| = 0.2824
  6. 6. y3 = 14.66

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