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
xyx₀ = 1

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

f(x) = cos x − xf′(x) = −sin x − 1x₀ = 1
x2 =
2.Easy
xyx₀ = 0

Apply Newton–Raphson to f(x) = e−x − x with the starting value x₀ = 0. Find x1.

f(x) = e−x − xf′(x) = −e−x − 1x₀ = 0
x1 =
3.Medium
t (s)01234v (m/s)109141820

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

h = 1 sn = 4
s = m
4.Medium
xy00.511.522.53

Approximate ∫03 √x·e−x dx with the trapezoid rule using n = 6 strips. Give T.

f(x) = √x·e−x[a, b] = [0, 3]n = 6
T =
5.Hard
00.050.10.99980.99991ty(0, 1)

Take one step of the classical Runge–Kutta method (RK4) with h = 0.1 for y′ = cos t − y, y(0) = 1. Find y₁ ≈ y(0.1).

y′ = cos t − yy(0) = 1h = 0.1
y1 =
6.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 =

Answer key

  1. 1. x2 = 0.7391
  2. 2. x1 = 0.5
  3. 3. s = 56 m
  4. 4. T = 0.7172
  5. 5. y1 = 0.9998
  6. 6. y1 = 0.4629

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