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

Apply Newton–Raphson to f(x) = x³ + 2x − 5 with the starting value x₀ = 1. Find x2.

f(x) = x³ + 2x − 5f′(x) = 3x² + 2x₀ = 1
x2 =
2.Easy
xya = 0b = 1

Use the bisection method on f(x) = e−x − x with the starting interval [0, 1]. Find the midpoint c4 of step 4.

f(x) = e−x − x[a, b] = [0, 1]n = 4
c4 =
3.Medium
xy00.16670.33330.50.66670.83331

Approximate ∫01 1/(1 + x³) dx with Simpson's rule using n = 6 strips. Give S.

f(x) = 1/(1 + x³)[a, b] = [0, 1]n = 6
S =
4.Medium
xy00.33330.66671

Approximate ∫01 √x·e−x dx with the trapezoid rule using n = 3 strips. Give T.

f(x) = √x·e−x[a, b] = [0, 1]n = 3
T =
5.Hard
00.20.40.60.8−1−0.5ty(0, −1)

Use Euler's method with h = 0.2 for y′ = −y, y(0) = −1 to estimate y4 ≈ y(0.8).

y′ = −yy(0) = −1h = 0.2
y4 =
6.Hard
00.10.20.30.40.50.6ty(0, 0.5)

Use Heun's method (improved Euler) with h = 0.2 for y′ = cos t − y, y(0) = 0.5 to estimate y2 ≈ y(0.4).

y′ = cos t − yy(0) = 0.5h = 0.2
y2 =

Answer key

  1. 1. x2 = 1.331
  2. 2. c4 = 0.5625
  3. 3. S = 0.8357
  4. 4. T = 0.3389
  5. 5. y4 = −0.4096
  6. 6. y2 = 0.6527

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