Name
Date
Variation Practice Test
You may use your calculator on all parts. Please show work where possible.
For 1-2, write a math model for each statement.
1. V varies directly with the square of x and m.
2. Z varies jointly with j and k, and inversely with the 4th-root of m.
3. The variable y varies inversely with the cube of x, and we know there is a constant k such that k =
3. If x is a large value, what can we expect the value of y to be (large, small, 0)?
4. Suppose that y varies directly as the square of x, and that y = 4 when x = 54. What the general
equation, and what is y when x = 45? Round your answer to the nearest hundredth.
5. Suppose that z is jointly proportional to x and the cube of y. If z = 77 when x =5 and y = 4, find
the general equation, and what is z when x = 4 and y = 5. Round your answer to the nearest
hundredth.
6. Suppose that y varies inversely as the cube of x, and that y = 13 when x = 10. Find the general
equation and y when x = 16. Round your answer to the nearest hundredth.
7. The frequency of vibration, V, varies directly as the square root of the tension, T, on the string,
and inversely as the length of the string, L. If the vibration of a string is V = 9 when T is 225 and
the length L is 5 inches, find the vibration V if T is 25 and the length L is 10 inches.
8. The lifting force, F , exerted on an airplane wing varies jointly as the area, A , of the wing's
surface and the square of the plane's velocity, v. The lift of a wing with an area of 220 square
feet is 21,400 pounds when the plane is going at 150 miles per hour. Find the lifting force if the
speed is 190 miles per hour. Round off your answer to the nearest pound.
9. The intensity of light, I, varies inversely with the square of the distance, d, from the light source.
If the intensity of a light is 40 candela when the distance is 2 feet from the source, find the
intensity of the same light from a distance of 14 feet.
10. The ideal gas law is often expressed as V =
, where P is the pressure exhibited by a so-called
“ideal gas.” If V = 22.4 liters when P = 1atm , n is 1 mole, and the temperature T = 273.15 K,
find the volume of the gas if P = 1atm, n is 3.75 moles and the temperature is T = 273.15 K.
11. Two variables, a and b, vary directly. If k > 0, describe the domain and range of the direct
variation function.