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 = 1.5

Apply Newton–Raphson to f(x) = x³ + 2x − 5 with the starting value x₀ = 1.5. Find x2.

f(x) = x³ + 2x − 5f′(x) = 3x² + 2x₀ = 1.5
x2 =
2.Easy
xya = 1b = 2

Use the bisection method on f(x) = x³ − x − 1 with the starting interval [1, 2]. Find the midpoint c4 of step 4.

f(x) = x³ − x − 1[a, b] = [1, 2]n = 4
c4 =
3.Medium
xy00.511.5

Approximate ∫01.5 1/√(1 + x⁴) dx with the trapezoid rule using n = 3 strips. Give T.

f(x) = 1/√(1 + x⁴)[a, b] = [0, 1.5]n = 3
T =
4.Medium
t (s)02468v (m/s)68131719

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
5.Hard
00.511.50.5ty(0, 0.5)

Solve y′ = t − y, y(0) = 0.5 with Euler's method and step h = 0.5 up to t = 1.5. The exact solution is y = t − 1 + (y₀ + 1)e−t. Find the global error |E| = |y(1.5) − y3|.

y′ = t − yy(0) = 0.5h = 0.5
|E| =
6.Hard
00.510.40.60.81ty(0, 0.5)

Solve y′ = y − t², y(0) = 0.5 with Euler's method and step h = 0.25 up to t = 1.25. The exact solution is y = t² + 2t + 2 + (y₀ − 2)eᵗ. Find the global error |E| = |y(1.25) − y5|.

y′ = y − t²y(0) = 0.5h = 0.25
|E| =

Answer key

  1. 1. x2 = 1.328
  2. 2. c4 = 1.313
  3. 3. T = 1.19
  4. 4. s = 100.7 m
  5. 5. |E| = 0.1472
  6. 6. |E| = 0.1449

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