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
x11.21.41.61.82y1.09861.16321.22381.28091.3351.3863

Use linear interpolation in the table to estimate the value x where y = 1.2409.

y = 1.2409
x =
2.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 =
3.Medium
xy012

Approximate ∫02 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, 2]n = 2
|E| =
4.Medium
xy00.33330.666711.3331.6672

Approximate ∫02 √x·e−x dx with Simpson's rule using n = 6 strips. Give S.

f(x) = √x·e−x[a, b] = [0, 2]n = 6
S =
5.Hard
00.20.40.980.991ty(0, 1)

Take one step of the classical Runge–Kutta method (RK4) with h = 0.5 for y′ = cos t − y, y(0) = 1. Find y₁ ≈ y(0.5).

y′ = cos t − yy(0) = 1h = 0.5
y1 =
6.Hard
00.51123ty(0, 3)

Use Euler's method with h = 0.25 for y′ = t − y, y(0) = 3 to estimate y4 ≈ y(1).

y′ = t − yy(0) = 3h = 0.25
y4 =

Answer key

  1. 1. x = 1.46
  2. 2. c4 = 1.688
  3. 3. |E| = 1
  4. 4. S = 0.6378
  5. 5. y1 = 0.9817
  6. 6. y4 = 1.266

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