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Unit 8

8.13 Multiple Choice Questions

4 min read•december 21, 2021

AP Calculus AB/BC ♾️

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Multiple Choice Practice for Applications of Integration

Welcome to Unit 8 AP Calculus Multiple Choice Questions! Grab some paper and a pencil 📄 to record your answers as you go. You can see how you did on the Unit 8 Practice Questions Answers and Review sheet once you're done. Don't worry, we have tons of resources available if you get stumped 😕 on a question. And if solo study is not your thing, join a group in Hours!

Not ready to take a quiz yet? Start studying unit 8 here: Intro to Unit 8

Facts about the test: Both the AP Calculus AB and BC exams have 45 multiple-choice questions and you will be given 1 hour and 45 minutes to complete the section. This means it should take you about 35 minutes to complete 15 questions.

*The following questions were not written by CollegeBoard and although they cover information outlined in the AP Calculus AB/BC Course and Exam Description, the formatting on the exam may be different.

1. Let f be the function given by f(x) = 6sin(x)cos(2x). What is the average value of f on the closed interval [5,8]?

A. -0.8237

B. -2.471

C. 0.653

D. 0.825

2. For time t ≥ 0, the velocity of a particle moving along the x-axis is given by v(t) = x^4 - 6x^3 + 2x^2. The initial position of the particle at time t=0 is x=6. Which of the following gives the total distance the particle travels from time t=0 to time t=5?

3. A magical furnace in a home consumes heating oil during a particular month at a rate modeled by the function f(t) = 0.6t^5 - 18t^3 + 16t, where f(t) is measured in gallons per day and t is the number of days since the start of the month. How many gallons of oil does the furnace consume during the first 10 days of the month?

A. 5000 gallons

B. 24267.6 gallons

C. 3.6 gallons

D. 55800 gallons

4. Let h be the function defined by h(x) = √3x+1. Let R be the region in the first quadrant bounded above by the graph of h for 0≤x≤4. What is the area of this?

5. Let p be the function defined by -8x^4 - 10x + 9 = p(x). Let R be the region in the first and second quadrant bounded above by the graph of p for -0.679≤x≤0.704. What is the area of this?

A. 12.012

B. 13.987

C. 11.767

D. 11

6. Let h be the function defined by h(x) = √3x+1. Let R be the region in the first quadrant bounded above by the graph of h for 0≤x≤4. The region R is the base of the solid. For this solid, each cross-section perpendicular to the x-axis is a semicircle whose diameter lies in R. Find the volume of the solid

A. (33π)/4

B. (33π)/8

C. 14π

D. (7π)/2

7. Let h be the function defined by h(x) = √3x+1. Let R be the region in the first quadrant bounded above by the graph of h for 0≤x≤4. Let g be the antiderivative of h. Find the length of the graph of g from x=0 to x=4.

8. The base of a solid is the region in the first quadrant between the graph of y=x^5 and the x-axis for 0≤x≤1. For the solid, each cross-section perpendicular to the x-axis is a semicircle. What is the volume of the solid?

A. π/22

B. π/44

C. π/88

D. π/110

9. Let R be the region in the first quadrant bounded by the graph of y=x^5, the line x=6, and the x-axis. R is the base of the solid whose cross-sections perpendicular to the x-axis are equilateral triangles. What is the volume of the solid?

10. When finding the volume between curves, if there is only one function and it is revolved around the x-axis, which formula would you use?

11. When using the washer method you have ___ radii and you subtract the ___ radius from the ___ radius.

A. one; bigger; smaller

B. one; smaller; bigger

C. two; smaller; bigger

D. two; bigger; smaller

12. Determine the arc length of f(x) = (1/6)x^3 + (1/2)x^(-1) from x=1 to x=2:

A. 3

B. 2

C. 2.43

D. 1.43

13. Determine the area of the region enclosed by y = x^2 and y=√x between x=0 and x=1.

A. 0

B. 1/3

C. -1/3

D. 2/3

14. Determine the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis: y=x, y=0, x=3, x=6.

A. 42.412

B. 63

C. 197.92

D. 200

15. Set up the integral for the volume of the bounded region revolved about the line y=8 using the washer method. The function is y = 8/(x^2) and the bounds are y=0, x=2, and x=5.