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 = 2

Apply Newton–Raphson to f(x) = x² − 3 with the starting value x₀ = 2. Find x1.

f(x) = x² − 3f′(x) = 2xx₀ = 2
x1 =
2.Easy
x11.522.533.5y1.34991.56831.82212.1172.45962.8577

Use linear interpolation in the table to estimate y at x = 3.15.

x = 3.15
y =
3.Medium
xy00.51

Approximate ∫01 sin(x²) dx with the trapezoid rule using n = 2 strips. Give T.

f(x) = sin(x²)[a, b] = [0, 1]n = 2
T =
4.Medium
xy00.51

Approximate ∫01 x³ dx with the trapezoid rule, n = 2, and compare it with the exact value. Find the absolute error |E| = |T − I|.

f(x) = x³[a, b] = [0, 1]n = 2
|E| =
5.Hard
0120.511.5ty(0, 0.5)

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

y′ = e−tyy(0) = 0.5h = 0.5
y5 =
6.Hard
00.20.40.60.40.450.5ty(0, 0.5)

Use Heun's method (improved Euler) with h = 0.25 for y′ = t − y, y(0) = 0.5 to estimate y3 ≈ y(0.75).

y′ = t − yy(0) = 0.5h = 0.25
y3 =

Answer key

  1. 1. x1 = 1.75
  2. 2. y = 2.579
  3. 3. T = 0.3341
  4. 4. |E| = 0.0625
  5. 5. y5 = 1.522
  6. 6. y3 = 0.4653

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