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 worksheet Practise 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

The bisection method starts on an interval of length 4. Every step halves the interval. How many steps n are needed at least before the interval is shorter than 0.05?

b − a = 4ε = 0.05

n =

2.Easy

Use linear interpolation in the table to estimate y at x = 4.3.

x = 4.3

y =

3.Medium

Approximate ∫₀² 1/√(1 + x⁴) dx with Simpson's rule using n = 2 strips. Give S.

f(x) = 1/√(1 + x⁴)[a, b] = [0, 2]n = 2

S =

4.Medium

The trapezoid rule is used for ∫₀² sin x 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 1 × 10⁻⁵.

f(x) = sin x[a, b] = [0, 2]ε = 1 × 10⁻⁵

n =

5.Hard

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

Use Euler's method with h = 0.1 for y′ = y − t², y(0) = 3 to estimate y₅ ≈ y(0.5).

y′ = y − t²y(0) = 3h = 0.1

y₅ =

Answer key

1. n = 7
2. y = 2.3
3. S = 1.357
4. n = 259
5. y₁ = 0.4629
6. y₅ = 4.799

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