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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
xyx₀ = 2

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

f(x) = x² − 3f′(x) = 2xx₀ = 2
x2 =
2.Easy
x22.533.544.5y1.38631.50411.60941.70471.79181.8718

Use linear interpolation in the table to estimate the value x where y = 1.4688.

y = 1.4688
x =
3.Medium
xy00.511.52

Approximate ∫02 1/(1 + x³) dx with the trapezoid rule using n = 4 strips. Give T.

f(x) = 1/(1 + x³)[a, b] = [0, 2]n = 4
T =
4.Medium
xy00.51

Approximate ∫01 eˣ dx with the trapezoid rule, n = 2, and compare it with the exact value. Find the absolute error |E| = |T − I|.

f(x) = eˣ[a, b] = [0, 1]n = 2
|E| =
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
00.20.40.646ty(0, 3)

Use Euler's method with h = 0.25 for y′ = y − t², y(0) = 3 to estimate y3 ≈ y(0.75).

y′ = y − t²y(0) = 3h = 0.25
y3 =

Answer key

  1. 1. x2 = 1.732
  2. 2. x = 2.35
  3. 3. T = 1.087
  4. 4. |E| = 0.03565
  5. 5. y1 = 0.4629
  6. 6. y3 = 5.777

Full step-by-step solutions: practise this topic on examproblems.com.