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) = x³ − x − 1 with the starting value x₀ = 1. Find x2.

f(x) = x³ − x − 1f′(x) = 3x² − 1x₀ = 1
x2 =
2.Easy
xyx₀ = 0

Apply Newton–Raphson to f(x) = x³ + 2x − 3 with the starting value x₀ = 0. Find x2.

f(x) = x³ + 2x − 3f′(x) = 3x² + 2x₀ = 0
x2 =
3.Medium
t (s)0102030405060v (m/s)1081015152020

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

h = 10 sn = 6
s = m
4.Medium
t (s)02468v (m/s)1013151723

A vehicle's speed is measured every 2 s (table). Estimate the distance s travelled from t = 0 to t = 8 s with Simpson's rule.

h = 2 sn = 4
s = m
5.Hard
00.050.10.50.550.6ty(0, 0.5)

Take one step of the classical Runge–Kutta method (RK4) with h = 0.1 for y′ = 1 + sin(ty), y(0) = 0.5. Find y₁ ≈ y(0.1).

y′ = 1 + sin(ty)y(0) = 0.5h = 0.1
y1 =
6.Hard
0120102030ty(0, 3)

Use Euler's method with h = 0.5 for y′ = y − t², y(0) = 3 to estimate y5 ≈ y(2.5).

y′ = y − t²y(0) = 3h = 0.5
y5 =

Answer key

  1. 1. x2 = 1.348
  2. 2. x2 = 1.114
  3. 3. s = 840 m
  4. 4. s = 122 m
  5. 5. y1 = 0.6028
  6. 6. y5 = 17.55

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