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 = 4.5

Apply Newton–Raphson to f(x) = x² − 20 with the starting value x₀ = 4.5. Find x1.

f(x) = x² − 20f′(x) = 2xx₀ = 4.5
x1 =
2.Easy
xyx₀ = 1

Apply Newton–Raphson to f(x) = x³ − x − 5 with the starting value x₀ = 1. Find x2.

f(x) = x³ − x − 5f′(x) = 3x² − 1x₀ = 1
x2 =
3.Medium
xy00.33330.666711.3331.6672

Approximate ∫02 sin(x²) dx with Simpson's rule using n = 6 strips. Give S.

f(x) = sin(x²)[a, b] = [0, 2]n = 6
S =
4.Medium
xy00.16670.33330.50.66670.83331

Approximate ∫01 √x·e−x dx with Simpson's rule using n = 6 strips. Give S.

f(x) = √x·e−x[a, b] = [0, 1]n = 6
S =
5.Hard
00.20.40.40.60.81ty(0, 0.5)

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

y′ = e−tyy(0) = 0.5h = 0.5
y1 =
6.Hard
00.050.10.150.211.11.21.3ty(0, 1)

Take one step of the classical Runge–Kutta method (RK4) with h = 0.2 for y′ = t² + y², y(0) = 1. Find y₁ ≈ y(0.2).

y′ = t² + y²y(0) = 1h = 0.2
y1 =

Answer key

  1. 1. x1 = 4.472
  2. 2. x2 = 2.538
  3. 3. S = 0.8104
  4. 4. S = 0.3732
  5. 5. y1 = 0.9138
  6. 6. y1 = 1.253

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