1. The sales tax on an item varies directly with the cost of that item. The sales tax on a $24 shirt is $1.44. If the shirt is on sale for $19, what will the tax be?

2. As you know (or should know) from science class, force is directly proportional to acceleration. Sam exerts a force of 120 Newtons and causes a cart to accelerate at 3 meters per second squared. How much force must Johnny exert to cause 4 meters per second squared of acceleration?

3. According to Ohm’s Law, current is inversely proportional to resistance. If the current is 8 amperes when the resistance is 3 Ohms, what is the resistance if the current is 12 amperes?

4. According to the Universal Gas Law, pressure and volume are inversely proportional (as long as temperature is constant). Five liters of gas is stored at a pressure of 1.2 atmospheres. If the volume is decreased to 2 liters, what is the pressure?

5. The kinetic energy of an object is directly proportional to the square of the object’s velocity. When a certain ball travels at 7.0 meters per second, its energy is 120 Joules. If the velocity increases to 8.0 meters per second, what is the kinetic energy?

6. The number of sheep that fit in a pen varies directly with the square of one side of the pen and inversely with the weight of each sheep. A pen with 25 yard sides holds 50 sheep that weigh 75 pounds. How many 90 pound sheep will a pen with 30 yard sides hold?

7. The amount of time it takes a person to get to school varies directly with the distance from school and inversely with the square root of the traffic index. It takes Jed, who lives 100 miles away and has a traffic index of 4, 25 minutes to get to school. How long will it take James, who lives 0.25 miles away but has a traffic index of 64 to arrive?

8. The “stretch” of a spring varies directly with the weight attached to it. When a four pound weight is on the spring, the spring is 27 cm long. When a nine pound weight is on the spring, the length is 52 cm. How long is the unstretched spring?

9. The intensity of light is inversely proportional to the square of the distance from the source. If a certain bulb produces 18 lux at 4 meters, how intense is the light at 3 meters?

10. How many cubic inches are in 2 cubic yards?

11. The area of a square is proportional to the square of the length of its side. If the side of the square is tripled in length, what happens to the area?