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
x22.22.42.62.83y1.38631.43511.48161.52611.56861.6094

Use linear interpolation in the table to estimate y at x = 2.12.

x = 2.12
y =
2.Easy
xyx₀ = 2

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

f(x) = ln x + x − 3f′(x) = 1/x + 1x₀ = 2
x2 =
3.Medium
t (s)02468v (m/s)341099

A vehicle's speed is measured every 2 s (table). Estimate the distance s travelled from t = 0 to t = 8 s with Simpson's rule.

h = 2 sn = 4
s = m
4.Medium

The trapezoid rule is used for ∫02 sin x dx. The error is at most (b − a)³·M/(12n²) with M = max|f″| on [0, 2]. Find the smallest number of strips n that guarantees an error below 1 × 10⁻⁵.

f(x) = sin x[a, b] = [0, 2]ε = 1 × 10⁻⁵
n =
5.Hard
00.10.20.322.22.4ty(0, 2)

Solve y′ = 0.5y, y(0) = 2 with Euler's method and step h = 0.1 up to t = 0.3. The exact solution is y = y₀e0.5t. Find the global error |E| = |y(0.3) − y3|.

y′ = 0.5yy(0) = 2h = 0.1
|E| =
6.Hard
00.511.50.511.52ty(0, 2)

Use Euler's method with h = 0.5 for y′ = t − y, y(0) = 2 to estimate y3 ≈ y(1.5).

y′ = t − yy(0) = 2h = 0.5
y3 =

Answer key

  1. 1. y = 1.416
  2. 2. x2 = 2.208
  3. 3. s = 56 m
  4. 4. n = 259
  5. 5. |E| = 0.008418
  6. 6. y3 = 0.875

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