# GACE Math: Applications of Derivatives Chapter Exam

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#### Question 1 1. A farmer has 2400ft of fencing and wants to fence off a rectangular field that borders a straight river. He doesn't need fencing along the river. What are the dimensions of the field that has the largest area?

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Question 2
2.
You are designing a cylindrical package. You can spend $4 on packaging, which costs $0.10 per square cm. You would like to determine the maximum volume that you can contain in a cylinder that costs less than $4.

What is the radius of the cylinder with the maximum volume?

#### Question 3 3. You have 150 ft of fencing to use to enclose part of a yard. You choose to enclose the yard with a rectangular pen 'w' feet in width and 'd' feet in depth. As a function of 'w' and 'd', what is the equation for the perimeter of the rectangle?

#### Question 4 4. You can enclose a rectangular yard with a fence. The length of the longest side of the fence is going to be 2 times the length of the shortest side of the fence. Write the equation for the perimeter of the fence.

#### Question 5 5. You have 100 ft of fencing to use to enclose part of a yard. You first choose to enclose the yard with a rectangular pen 'w' feet in width and 'd' feet in depth. As a function of 'w', what is the equation for the area that you can enclose using 100 ft of fence?

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#### Question 6 6. You are standing on a building 50m tall with a ball. You throw it up into the air at a velocity of 5 meters per second. It is accelerating downward at -9.8 meters per second squared. Which of the following equations describes the height of the ball as a function of time, t?

#### Question 7 7. You are standing on a building on Mars with a ball, and you have decided that the appropriate equation of motion for the height of the ball as a function of time (t) is below. Which graph represents this equation?

#### Question 8 8. You are standing on a building on Jupiter with a ball, and you have decided that the appropriate equation of motion for the height of the ball in miles as a function of (t) is shown below on the graph. What is the highest that the ball gets?

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Question 9
9.
You are designing a cylindrical package. You can spend $4 on packaging, which costs $0.10 per square cm. You would like to determine the maximum volume that you can contain in a cylinder that costs less than $4.

What is the maximum volume you can obtain in a cylinder that costs $4?

#### Question 10 10. Which of the following is NOT a step that is required in order to solve optimization problems?

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#### Question 11 11. What is the maximum area that you can enclose in a rectangular pen with 150 feet of fencing?

#### Question 12 12. What is the maximum area that you can enclose in a rectangular pen that is three times as wide as it is deep and has a perimeter 100 feet?

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Question 13
13.
You are designing a cylindrical package. You can spend $4 on packaging, which costs $0.10 per square cm. You would like to determine the maximum volume that you can contain in a cylinder that costs less than $4.

What is the equation for the volume as a function of only the cylinder radius?

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Question 14
14.
You are designing a cylindrical package. You can spend $4 on packaging, which costs $0.10 square cm. You would like to determine the maximum volume that you can contain in a cylinder that costs less than $4.

What are the equations for the surface area and volume of this cylinder?

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Question 15
15.
You are designing a cylindrical package. You can spend $4 on packaging, which costs $0.10 per square cm. You would like to determine the maximum volume that you can contain in a cylinder that costs less than $4.

What is the derivative of the equation for volume with respect to the cylinder radius?

#### GACE Math: Applications of Derivatives Chapter Exam Instructions

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!