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 = 1.5

Apply Newton–Raphson to f(x) = x² − 2 with the starting value x₀ = 1.5. Find x2.

f(x) = x² − 2f′(x) = 2xx₀ = 1.5
x2 =
2.Easy
x11.21.41.61.82y1.09861.16321.22381.28091.3351.3863

Use linear interpolation in the table to estimate y at x = 1.25.

x = 1.25
y =
3.Medium
xy00.511.52

Approximate ∫02 e−x² dx with Simpson's rule using n = 4 strips. Give S.

f(x) = e−x²[a, b] = [0, 2]n = 4
S =
4.Medium
xy00.511.52

Approximate ∫02 1/√(1 + x⁴) dx with Simpson's rule using n = 4 strips. Give S.

f(x) = 1/√(1 + x⁴)[a, b] = [0, 2]n = 4
S =
5.Hard
012−20−100ty(0, −1)

Use Euler's method with h = 0.5 for y′ = y − t², y(0) = −1 to estimate y5 ≈ y(2.5).

y′ = y − t²y(0) = −1h = 0.5
y5 =
6.Hard
00.050.100.050.1ty(0, 0)

Take one step of the classical Runge–Kutta method (RK4) with h = 0.1 for y′ = 1 + sin(ty), y(0) = 0. Find y₁ ≈ y(0.1).

y′ = 1 + sin(ty)y(0) = 0h = 0.1
y1 =

Answer key

  1. 1. x2 = 1.414
  2. 2. y = 1.178
  3. 3. S = 0.8818
  4. 4. S = 1.36
  5. 5. y5 = −12.83
  6. 6. y1 = 0.1003

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