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 = 2

Use the bisection method on f(x) = x² − 3 with the starting interval [1, 2]. Find the midpoint c4 of step 4.

f(x) = x² − 3[a, b] = [1, 2]n = 4
c4 =
2.Easy
x11.21.41.61.82y0.47940.56460.64420.71740.78330.8415

Use linear interpolation in the table to estimate y at x = 1.08.

x = 1.08
y =
3.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| =
4.Medium
xy00.511.52

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

f(x) = sin x[a, b] = [0, 2]n = 4
|E| =
5.Hard
00.511.52050100ty(0, 2)

Use Euler's method with h = 0.5 for y′ = 2y, y(0) = 2 to estimate y4 ≈ y(2).

y′ = 2yy(0) = 2h = 0.5
y4 =
6.Hard
00.20.42.53ty(0, 3)

Use Euler's method with h = 0.1 for y′ = −2ty, y(0) = 3 to estimate y5 ≈ y(0.5).

y′ = −2tyy(0) = 3h = 0.1
y5 =

Answer key

  1. 1. c4 = 1.688
  2. 2. y = 0.5135
  3. 3. |E| = 0.0625
  4. 4. |E| = 0.02963
  5. 5. y4 = 32
  6. 6. y5 = 2.441

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