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 c3 of step 3.

f(x) = ln x + x − 3[a, b] = [1, 3]n = 3
c3 =
2.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 =
3.Medium
t (s)0102030405060v (m/s)10131417222424

A vehicle's speed is measured every 10 s (table). Estimate the distance s travelled from t = 0 to t = 60 s with the trapezoid rule.

h = 10 sn = 6
s = m
4.Medium
xy00.250.50.7511.251.5

Approximate ∫01.5 1/√(1 + x⁴) dx with the trapezoid rule using n = 6 strips. Give T.

f(x) = 1/√(1 + x⁴)[a, b] = [0, 1.5]n = 6
T =
5.Hard
00.20.400.20.4ty(0, 0)

Take one step of the classical Runge–Kutta method (RK4) with h = 0.5 for y′ = e−ty, y(0) = 0. Find y₁ ≈ y(0.5).

y′ = e−tyy(0) = 0h = 0.5
y1 =
6.Hard
00.20.411.21.4ty(0, 1)

Take one step of the classical Runge–Kutta method (RK4) with h = 0.5 for y′ = e−ty, y(0) = 1. Find y₁ ≈ y(0.5).

y′ = e−tyy(0) = 1h = 0.5
y1 =

Answer key

  1. 1. c3 = 2.25
  2. 2. c4 = 0.6875
  3. 3. s = 1070 m
  4. 4. T = 1.197
  5. 5. y1 = 0.4629
  6. 6. y1 = 1.371

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