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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Name: ____________________   Date: ____________

1.Easy
x00.20.40.60.81y11.06181.12751.19721.27121.3499

Use linear interpolation in the table to estimate y at x = 0.12.

x = 0.12
y =
2.Easy

The bisection method starts on an interval of length 1. Every step halves the interval. How many steps n are needed at least before the interval is shorter than 0.005?

b − a = 1ε = 0.005
n =
3.Medium
xy00.33330.666711.3331.6672

Approximate ∫02 √(1 + x³) dx with Simpson's rule using n = 6 strips. Give S.

f(x) = √(1 + x³)[a, b] = [0, 2]n = 6
S =
4.Medium
t (s)0102030405060v (m/s)766681116

A vehicle's speed is measured every 10 s (table). Estimate the distance s travelled from t = 0 to t = 60 s with Simpson's rule.

h = 10 sn = 6
s = m
5.Hard
00.050.10.150.20.50.55ty(0, 0.5)

Take one step of the classical Runge–Kutta method (RK4) with h = 0.2 for y′ = t² + y², y(0) = 0.5. Find y₁ ≈ y(0.2).

y′ = t² + y²y(0) = 0.5h = 0.2
y1 =
6.Hard
00.20.40.30.40.5ty(0, 0.5)

Use Heun's method (improved Euler) with h = 0.25 for y′ = −y, y(0) = 0.5 to estimate y2 ≈ y(0.5).

y′ = −yy(0) = 0.5h = 0.25
y2 =

Answer key

  1. 1. y = 1.037
  2. 2. n = 8
  3. 3. S = 3.241
  4. 4. s = 476.7 m
  5. 5. y1 = 0.5584
  6. 6. y2 = 0.3052

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