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 = 1

Apply Newton–Raphson to f(x) = x³ + 2x − 2 with the starting value x₀ = 1. Find x1.

f(x) = x³ + 2x − 2f′(x) = 3x² + 2x₀ = 1
x1 =
2.Easy
xyx₀ = 1.5

Apply Newton–Raphson to f(x) = x³ + 2x − 5 with the starting value x₀ = 1.5. Find x2.

f(x) = x³ + 2x − 5f′(x) = 3x² + 2x₀ = 1.5
x2 =
3.Medium
xy11.52

Approximate ∫12 1/x dx with Simpson's rule, n = 2, and compare it with the exact value. Find the absolute error |E| = |S − I|.

f(x) = 1/x[a, b] = [1, 2]n = 2
|E| =
4.Medium
xy012

Approximate ∫02 √(1 + x³) dx with Simpson's rule using n = 2 strips. Give S.

f(x) = √(1 + x³)[a, b] = [0, 2]n = 2
S =
5.Hard
00.050.10.50.520.54ty(0, 0.5)

Take one step of the classical Runge–Kutta method (RK4) with h = 0.1 for y′ = cos t − y, y(0) = 0.5. Find y₁ ≈ y(0.1).

y′ = cos t − yy(0) = 0.5h = 0.1
y1 =
6.Hard
00.510.511.52ty(0, 2)

Use Heun's method (improved Euler) with h = 0.5 for y′ = −2ty, y(0) = 2 to estimate y2 ≈ y(1).

y′ = −2tyy(0) = 2h = 0.5
y2 =

Answer key

  1. 1. x1 = 0.8
  2. 2. x2 = 1.328
  3. 3. |E| = 0.001297
  4. 4. S = 3.219
  5. 5. y1 = 0.5474
  6. 6. y2 = 0.75

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