Differential Equations in AP Calculus: Help and Review Chapter Exam

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!

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Question 1 1. Solve the following differential equation for y=f(x) (assume that y is always positive).

Question 2 2. Solve the following differential equation for c=f(a).

Question 3 3. You have a tank that is shaped like a prism that is on its side. The triangular base of the tank is a right triangle of height 10 m and width 10 m. See the image below. If the tank is being filled at a rate of 30 cubic meters per minute, how quickly is the height changing?

Question 4 4. Consider a balloon that you are inflating with a constant flow rate such that dV/dt is constant. It is a perfect sphere. How does dr/dt change as time moves forward?

Question 5 5. Solve the following differential equation for y=f(x).

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Question 6 6. What is the equation for L as a function of x?

Question 7 7. Consider a balloon that you are inflating. It is a perfect sphere. If you are inflating it at a rate of F liters per minute (dV/dt = F), what is the equation for the change in radius as a function of time?

Question 8 8. Which of the following is NOT a differential equation?

Question 9 9. Air is being pumped into a spherical balloon so that its volume increases at a rate of 100 cubic cm/min. How fast is the surface area of the balloon increasing when its radius is 16cm?

Question 10 10. The number of widgets in your stock inventory (N) changes over time. You sell 5 times your stock inventory of widgets an hour and generate widgets at a rate given by the equation g(t). Which equation below describes this relationship?

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Question 11 11. Given a population growth of 3%, how long will it take for the population to grow from 100 to 150?

Question 12 12. If h equals 3 m, and x is moving at a rate of 3 m / second, how fast is L changing when x equals 4m?

Question 13 13. Imagine you have a sheet cake with a width of 12 inches and a length of 12 inches. If you are smearing icing on it at a rate of 12 oz / minute, how quickly is the height of icing changing? One ounce is about 1 cubic inch of icing.

Question 14 14. Solve the differential equation for your bank balance given as follows.

Question 15 15. Which of the following represents an equation for your bank balance as a function of time given a starting balance of $147 and an interest rate of 3%

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Question 16 16. Which of the following might describe how the population (P) changes as a function of time (t)?

Question 17 17. Which of the following statements is TRUE?

Question 18 18. Which of the following might be a differential equation for how the velocity of a kite depends on its position and the time?

Question 19 19. What is the equation of how L changes as a function of how x changes if h=6?

Question 20 20. The red and blue cars are 10 miles apart, but headed toward one another. The red car is traveling at 45 mph, and the blue car is traveling at a speed v(t). What is the equation for how the distance between them changes as a function of time?

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Question 21 21. Solve the following differential equation for y=f(x).

Question 22 22. If the red car is traveling at 45 mph, and the blue is braking so that v(t) = 60 - 30t, then when will they pass each other, assuming that they are 10 miles apart at t = 0?

Question 23 23. Solve the following differential equation for y=f(x) (assume that y is always positive).

Question 24 24. The following differential equation represents the change in population as a function of time. What does the 0.03 represent in this equation?

Question 25 25. If the population of a city grows 25% in 3 years, what is the yearly growth rate?

Differential Equations in AP Calculus: Help and Review 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!

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