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
xya = 1b = 2

Use the bisection method on f(x) = x³ − x − 3 with the starting interval [1, 2]. Find the midpoint c3 of step 3.

f(x) = x³ − x − 3[a, b] = [1, 2]n = 3
c3 =
2.Easy
xyx₀ = 0

Apply Newton–Raphson to f(x) = cos x − x with the starting value x₀ = 0. Find x1.

f(x) = cos x − xf′(x) = −sin x − 1x₀ = 0
x1 =
3.Medium
xy00.30.60.91.21.5

Approximate ∫01.5 √(1 + x³) dx with the trapezoid rule using n = 5 strips. Give T.

f(x) = √(1 + x³)[a, b] = [0, 1.5]n = 5
T =
4.Medium
xy00.16670.33330.50.66670.83331

Approximate ∫01 sin(x²) dx with the trapezoid rule using n = 6 strips. Give T.

f(x) = sin(x²)[a, b] = [0, 1]n = 6
T =
5.Hard
00.050.10.150.20.9991ty(0, 1)

Use Heun's method (improved Euler) with h = 0.1 for y′ = cos t − y, y(0) = 1 to estimate y2 ≈ y(0.2).

y′ = cos t − yy(0) = 1h = 0.1
y2 =
6.Hard
00.511.512ty(0, 0.5)

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

y′ = 1 + sin(ty)y(0) = 0.5h = 0.5
y3 =

Answer key

  1. 1. c3 = 1.625
  2. 2. x1 = 1
  3. 3. T = 1.989
  4. 4. T = 0.3128
  5. 5. y2 = 0.9986
  6. 6. y3 = 2.479

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