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 = 0.5

Apply Newton–Raphson to f(x) = e−x − x with the starting value x₀ = 0.5. Find x1.

f(x) = e−x − xf′(x) = −e−x − 1x₀ = 0.5
x1 =
2.Easy
xya = 1b = 2

Use the bisection method on f(x) = ln x + x − 2 with the starting interval [1, 2]. Find the midpoint c4 of step 4.

f(x) = ln x + x − 2[a, b] = [1, 2]n = 4
c4 =
3.Medium
xy00.751.5

Approximate ∫01.5 sin(x²) dx with the trapezoid rule using n = 2 strips. Give T.

f(x) = sin(x²)[a, b] = [0, 1.5]n = 2
T =
4.Medium
xy00.511.52

Approximate ∫02 √(1 + x³) dx with Simpson's rule using n = 4 strips. Give S.

f(x) = √(1 + x³)[a, b] = [0, 2]n = 4
S =
5.Hard
00.050.10.50.510.520.53ty(0, 0.5)

Take one step of the classical Runge–Kutta method (RK4) with h = 0.1 for y′ = t² + y², y(0) = 0.5. Find y₁ ≈ y(0.1).

y′ = t² + y²y(0) = 0.5h = 0.1
y1 =
6.Hard
00.511.511.52ty(0, 1)

Use Euler's method with h = 0.5 for y′ = e−ty, y(0) = 1 to estimate y3 ≈ y(1.5).

y′ = e−tyy(0) = 1h = 0.5
y3 =

Answer key

  1. 1. x1 = 0.5663
  2. 2. c4 = 1.563
  3. 3. T = 0.6918
  4. 4. S = 3.24
  5. 5. y1 = 0.5267
  6. 6. y3 = 1.824

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