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

The bisection method starts on an interval of length 3. Every step halves the interval. How many steps n are needed at least before the interval is shorter than 0.01?

b − a = 3ε = 0.01
n =
2.Easy
x012345y0.69311.09861.38631.60941.79181.9459

Use linear interpolation in the table to estimate y at x = 4.6.

x = 4.6
y =
3.Medium
t (s)0246810v (m/s)4912171717

A vehicle's speed is measured every 2 s (table). Estimate the distance s travelled from t = 0 to t = 10 s with the trapezoid rule.

h = 2 sn = 5
s = m
4.Medium
xy11.52

Approximate ∫12 1/x dx with Simpson's rule, n = 2, and compare it with the exact value. Find the absolute error |E| = |S − I|.

f(x) = 1/x[a, b] = [1, 2]n = 2
|E| =
5.Hard
00.050.10.150.200.10.2ty(0, 0)

Take one step of the classical Runge–Kutta method (RK4) with h = 0.2 for y′ = 1 + sin(ty), y(0) = 0. Find y₁ ≈ y(0.2).

y′ = 1 + sin(ty)y(0) = 0h = 0.2
y1 =
6.Hard
00.10.20.30.400.20.4ty(0, 0)

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

y′ = 1 + sin(ty)y(0) = 0h = 0.1
y4 =

Answer key

  1. 1. n = 9
  2. 2. y = 1.884
  3. 3. s = 131 m
  4. 4. |E| = 0.001297
  5. 5. y1 = 0.2027
  6. 6. y4 = 0.4142

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