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 = 0b = 1

Use the bisection method on f(x) = cos x − x with the starting interval [0, 1]. Find the midpoint c4 of step 4.

f(x) = cos x − x[a, b] = [0, 1]n = 4
c4 =
2.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 0.0002?

b − a = 3ε = 0.0002
n =
3.Medium
t (s)01234v (m/s)1481218

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
xy00.40.81.21.62

Approximate ∫02 √(1 + x³) dx with the trapezoid rule using n = 5 strips. Give T.

f(x) = √(1 + x³)[a, b] = [0, 2]n = 5
T =
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′ = e−ty, y(0) = 0. Find y₁ ≈ y(0.2).

y′ = e−tyy(0) = 0h = 0.2
y1 =
6.Hard
00.20.40.991ty(0, 1)

Use Euler's method with h = 0.1 for y′ = cos t − y, y(0) = 1 to estimate y5 ≈ y(0.5).

y′ = cos t − yy(0) = 1h = 0.1
y5 =

Answer key

  1. 1. c4 = 0.6875
  2. 2. n = 14
  3. 3. s = 33 m
  4. 4. T = 3.268
  5. 5. y1 = 0.1974
  6. 6. y5 = 0.9861

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