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 = 0b = 2

Use the bisection method on f(x) = x³ + 2x − 2 with the starting interval [0, 2]. Find the midpoint c3 of step 3.

f(x) = x³ + 2x − 2[a, b] = [0, 2]n = 3
c3 =
2.Easy
x11.522.533.5y1.09861.25281.38631.50411.60941.7047

Use linear interpolation in the table to estimate the value x where y = 1.6761.

y = 1.6761
x =
3.Medium
xy01.53

Approximate ∫03 sin x dx with the trapezoid rule, n = 2, and compare it with the exact value. Find the absolute error |E| = |T − I|.

f(x) = sin x[a, b] = [0, 3]n = 2
|E| =
4.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 =
5.Hard
00.20.40.50.60.7ty(0, 0.5)

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

y′ = cos t − yy(0) = 0.5h = 0.5
y1 =
6.Hard
0120123ty(0, 0)

Use Euler's method with h = 0.5 for y′ = 1 + sin(ty), y(0) = 0 to estimate y5 ≈ y(2.5).

y′ = 1 + sin(ty)y(0) = 0h = 0.5
y5 =

Answer key

  1. 1. c3 = 0.75
  2. 2. x = 3.35
  3. 3. |E| = 0.3879
  4. 4. T = 1.989
  5. 5. y1 = 0.6783
  6. 6. y5 = 2.643

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