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
x11.522.533.5y1.09861.25281.38631.50411.60941.7047

Use linear interpolation in the table to estimate y at x = 3.25.

x = 3.25
y =
2.Easy
xya = 0b = 1

Use the bisection method on f(x) = cos x − x with the starting interval [0, 1]. Find the midpoint c4 of step 4.

f(x) = cos x − x[a, b] = [0, 1]n = 4
c4 =
3.Medium

The trapezoid rule is used for ∫02 x³ dx. The error is at most (b − a)³·M/(12n²) with M = max|f″| on [0, 2]. Find the smallest number of strips n that guarantees an error below 0.001.

f(x) = x³[a, b] = [0, 2]ε = 0.001
n =
4.Medium
xy012

Approximate ∫02 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, 2]n = 2
|E| =
5.Hard
00.20.40.611.52ty(0, 1)

Use Euler's method with h = 0.25 for y′ = y − t², y(0) = 1 to estimate y3 ≈ y(0.75).

y′ = y − t²y(0) = 1h = 0.25
y3 =
6.Hard
00.050.11.91.952ty(0, 2)

Take one step of the classical Runge–Kutta method (RK4) with h = 0.1 for y′ = cos t − y, y(0) = 2. Find y₁ ≈ y(0.1).

y′ = cos t − yy(0) = 2h = 0.1
y1 =

Answer key

  1. 1. y = 1.657
  2. 2. c4 = 0.6875
  3. 3. n = 90
  4. 4. |E| = 0.5238
  5. 5. y3 = 1.871
  6. 6. y1 = 1.905

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