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
x11.21.41.61.82y1.41421.48321.54921.61251.67331.7321

Use linear interpolation in the table to estimate the value x where y = 1.5228.

y = 1.5228
x =
2.Easy
xyx₀ = 1

Apply Newton–Raphson to f(x) = x³ + 2x − 10 with the starting value x₀ = 1. Find x2.

f(x) = x³ + 2x − 10f′(x) = 3x² + 2x₀ = 1
x2 =
3.Medium

The trapezoid rule is used for ∫01 eˣ dx. The error is at most (b − a)³·M/(12n²) with M = max|f″| on [0, 1]. Find the smallest number of strips n that guarantees an error below 0.0005.

f(x) = eˣ[a, b] = [0, 1]ε = 0.0005
n =
4.Medium
xy00.250.50.751

Approximate ∫01 x³ dx with the trapezoid rule, n = 4, and compare it with the exact value. Find the absolute error |E| = |T − I|.

f(x) = x³[a, b] = [0, 1]n = 4
|E| =
5.Hard
00.050.10.150.211.11.2ty(0, 1)

Use Heun's method (improved Euler) with h = 0.1 for y′ = e−ty, y(0) = 1 to estimate y2 ≈ y(0.2).

y′ = e−tyy(0) = 1h = 0.1
y2 =
6.Hard
00.050.10.150.200.10.2ty(0, 0)

Use Heun's method (improved Euler) with h = 0.1 for y′ = 1 + sin(ty), y(0) = 0 to estimate y2 ≈ y(0.2).

y′ = 1 + sin(ty)y(0) = 0h = 0.1
y2 =

Answer key

  1. 1. x = 1.32
  2. 2. x2 = 1.953
  3. 3. n = 22
  4. 4. |E| = 0.01563
  5. 5. y2 = 1.179
  6. 6. y2 = 0.203

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