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 = 2

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

f(x) = ln x + x − 3f′(x) = 1/x + 1x₀ = 2
x2 =
2.Easy
xya = 1b = 2

Use the bisection method on f(x) = x³ + 2x − 5 with the starting interval [1, 2]. Find the midpoint c3 of step 3.

f(x) = x³ + 2x − 5[a, b] = [1, 2]n = 3
c3 =
3.Medium
t (s)01020304050v (m/s)3365108

A vehicle's speed is measured every 10 s (table). Estimate the distance s travelled from t = 0 to t = 50 s with the trapezoid rule.

h = 10 sn = 5
s = m
4.Medium
xy00.511.52

Approximate ∫02 sin x dx with the trapezoid rule, n = 4, and compare it with the exact value. Find the absolute error |E| = |T − I|.

f(x) = sin x[a, b] = [0, 2]n = 4
|E| =
5.Hard
00.20.411.52ty(0, 1)

Take one step of the classical Runge–Kutta method (RK4) with h = 0.5 for y′ = t² + y², y(0) = 1. Find y₁ ≈ y(0.5).

y′ = t² + y²y(0) = 1h = 0.5
y1 =
6.Hard
00.51123ty(0, 3)

Use Euler's method with h = 0.25 for y′ = cos t − y, y(0) = 3 to estimate y5 ≈ y(1.25).

y′ = cos t − yy(0) = 3h = 0.25
y5 =

Answer key

  1. 1. x2 = 2.208
  2. 2. c3 = 1.375
  3. 3. s = 295 m
  4. 4. |E| = 0.02963
  5. 5. y1 = 2.055
  6. 6. y5 = 1.289

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