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 = 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 =
2.Easy
x00.511.522.5y00.24740.47940.68160.84150.949

Use linear interpolation in the table to estimate y at x = 1.15.

x = 1.15
y =
3.Medium
t (s)051015202530v (m/s)43886510

A vehicle's speed is measured every 5 s (table). Estimate the distance s travelled from t = 0 to t = 30 s with Simpson's rule.

h = 5 sn = 6
s = m
4.Medium
xy00.51

Approximate ∫01 eˣ dx with the trapezoid rule, n = 2, and compare it with the exact value. Find the absolute error |E| = |T − I|.

f(x) = eˣ[a, b] = [0, 1]n = 2
|E| =
5.Hard
00.10.20.31.61.82ty(0, 2)

Use Heun's method (improved Euler) with h = 0.1 for y′ = t − y, y(0) = 2 to estimate y3 ≈ y(0.3).

y′ = t − yy(0) = 2h = 0.1
y3 =
6.Hard
00.511.520123ty(0, 0.5)

Use Euler's method with h = 0.5 for y′ = 1 + sin(ty), y(0) = 0.5 to estimate y4 ≈ y(2).

y′ = 1 + sin(ty)y(0) = 0.5h = 0.5
y4 =

Answer key

  1. 1. c4 = 1.313
  2. 2. y = 0.5401
  3. 3. s = 176.7 m
  4. 4. |E| = 0.03565
  5. 5. y3 = 1.524
  6. 6. y4 = 2.824

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