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.

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1.Easy

Use linear interpolation in the table to estimate y at x = 0.95.

x = 0.95

y =

2.Easy

Use linear interpolation in the table to estimate the value x where y = 4.9521.

y = 4.9521

x =

3.Medium

Approximate ∫₀³ √x·e^−x dx with the trapezoid rule using n = 4 strips. Give T.

f(x) = √x·e^−x[a, b] = [0, 3]n = 4

T =

4.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 1 × 10⁻⁵.

f(x) = x³[a, b] = [0, 2]ε = 1 × 10⁻⁵

n =

5.Hard

Use Heun's method (improved Euler) with h = 0.1 for y′ = e^−ty, y(0) = 1 to estimate y₂ ≈ y(0.2).

y′ = e^−tyy(0) = 1h = 0.1

y₂ =

6.Hard

Use Heun's method (improved Euler) with h = 0.2 for y′ = t² + y², y(0) = 1 to estimate y₂ ≈ y(0.4).

y′ = t² + y²y(0) = 1h = 0.2

y₂ =

Answer key

1. y = 0.4569
2. x = 5.3
3. T = 0.6627
4. n = 895
5. y₂ = 1.179
6. y₂ = 1.669

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