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
xyx₀ = 1

Apply Newton–Raphson to f(x) = ln x + x − 3 with the starting value x₀ = 1. Find x2.

f(x) = ln x + x − 3f′(x) = 1/x + 1x₀ = 1
x2 =
2.Easy

The bisection method starts on an interval of length 3. Every step halves the interval. How many steps n are needed at least before the interval is shorter than 0.005?

b − a = 3ε = 0.005
n =
3.Medium
xy00.33330.666711.3331.6672

Approximate ∫02 1/√(1 + x⁴) dx with Simpson's rule using n = 6 strips. Give S.

f(x) = 1/√(1 + x⁴)[a, b] = [0, 2]n = 6
S =
4.Medium
xy00.3750.751.1251.5

Approximate ∫01.5 e−x² dx with Simpson's rule using n = 4 strips. Give S.

f(x) = e−x²[a, b] = [0, 1.5]n = 4
S =
5.Hard
00.20.40.60.60.8ty(0, 0.5)

Use Euler's method with h = 0.25 for y′ = t² + y², y(0) = 0.5 to estimate y3 ≈ y(0.75).

y′ = t² + y²y(0) = 0.5h = 0.25
y3 =
6.Hard
00.20.411.2ty(0, 1)

Use Euler's method with h = 0.1 for y′ = 0.5y, y(0) = 1 to estimate y5 ≈ y(0.5).

y′ = 0.5yy(0) = 1h = 0.1
y5 =

Answer key

  1. 1. x2 = 2.205
  2. 2. n = 10
  3. 3. S = 1.357
  4. 4. S = 0.8561
  5. 5. y3 = 0.8277
  6. 6. y5 = 1.276

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