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 = 1b = 3

Use the bisection method on f(x) = x³ − x − 5 with the starting interval [1, 3]. Find the midpoint c4 of step 4.

f(x) = x³ − x − 5[a, b] = [1, 3]n = 4
c4 =
2.Easy
xyx₀ = 3.5

Apply Newton–Raphson to f(x) = x² − 13 with the starting value x₀ = 3.5. Find x2.

f(x) = x² − 13f′(x) = 2xx₀ = 3.5
x2 =
3.Medium
xy00.511.52

Approximate ∫02 x³ dx with the trapezoid rule, n = 4, and compare it with the exact value. Find the absolute error |E| = |T − I|.

f(x) = x³[a, b] = [0, 2]n = 4
|E| =
4.Medium
xy012

Approximate ∫02 sin x dx with the trapezoid rule, n = 2, and compare it with the exact value. Find the absolute error |E| = |T − I|.

f(x) = sin x[a, b] = [0, 2]n = 2
|E| =
5.Hard
00.511.502040ty(0, 2)

Use Euler's method with h = 0.5 for y′ = 2y, y(0) = 2 to estimate y3 ≈ y(1.5).

y′ = 2yy(0) = 2h = 0.5
y3 =
6.Hard
00.20.40.612ty(0, 1)

Use Heun's method (improved Euler) with h = 0.2 for y′ = t² + y², y(0) = 1 to estimate y3 ≈ y(0.6).

y′ = t² + y²y(0) = 1h = 0.2
y3 =

Answer key

  1. 1. c4 = 1.875
  2. 2. x2 = 3.606
  3. 3. |E| = 0.25
  4. 4. |E| = 0.12
  5. 5. y3 = 16
  6. 6. y3 = 2.51

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