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
x00.511.522.5y0.69310.91631.09861.25281.38631.5041

Use linear interpolation in the table to estimate y at x = 1.7.

x = 1.7
y =
2.Easy
xyx₀ = 2

Apply Newton–Raphson to f(x) = x³ − x − 3 with the starting value x₀ = 2. Find x2.

f(x) = x³ − x − 3f′(x) = 3x² − 1x₀ = 2
x2 =
3.Medium
t (s)010203040v (m/s)23486

A vehicle's speed is measured every 10 s (table). Estimate the distance s travelled from t = 0 to t = 40 s with Simpson's rule.

h = 10 sn = 4
s = m
4.Medium
xy00.751.5

Approximate ∫01.5 1/√(1 + x⁴) dx with the trapezoid rule using n = 2 strips. Give T.

f(x) = 1/√(1 + x⁴)[a, b] = [0, 1.5]n = 2
T =
5.Hard
00.20.40.624ty(0, 1)

Use Heun's method (improved Euler) with h = 0.25 for y′ = t² + y², y(0) = 1 to estimate y3 ≈ y(0.75).

y′ = t² + y²y(0) = 1h = 0.25
y3 =
6.Hard
00.20.40.40.60.81ty(0, 0.5)

Take one step of the classical Runge–Kutta method (RK4) with h = 0.5 for y′ = e−ty, y(0) = 0.5. Find y₁ ≈ y(0.5).

y′ = e−tyy(0) = 0.5h = 0.5
y1 =

Answer key

  1. 1. y = 1.306
  2. 2. x2 = 1.674
  3. 3. s = 200 m
  4. 4. T = 1.181
  5. 5. y3 = 3.731
  6. 6. y1 = 0.9138

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