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 = 3

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

f(x) = ln x + x − 3[a, b] = [1, 3]n = 4
c4 =
2.Easy
xyx₀ = 1

Apply Newton–Raphson to f(x) = ln x + x − 3 with the starting value x₀ = 1. Find x2.

f(x) = ln x + x − 3f′(x) = 1/x + 1x₀ = 1
x2 =
3.Medium
t (s)01234v (m/s)06121616

A vehicle's speed is measured every 1 s (table). Estimate the distance s travelled from t = 0 to t = 4 s with Simpson's rule.

h = 1 sn = 4
s = m
4.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| =
5.Hard
01201020ty(0, 1)

Use Euler's method with h = 0.5 for y′ = t + y, y(0) = 1 to estimate y5 ≈ y(2.5).

y′ = t + yy(0) = 1h = 0.5
y5 =
6.Hard
00.10.20.30.411.21.4ty(0, 1)

Use Euler's method with h = 0.1 for y′ = 1 + sin(ty), y(0) = 1 to estimate y4 ≈ y(0.4).

y′ = 1 + sin(ty)y(0) = 1h = 0.1
y4 =

Answer key

  1. 1. c4 = 2.125
  2. 2. x2 = 2.205
  3. 3. s = 42.67 m
  4. 4. |E| = 1
  5. 5. y5 = 11.69
  6. 6. y4 = 1.474

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