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# 9.10 Multiple Choice Questions

Dalia Savy

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## Multiple Choice Practice for Parametric Equations, Polar Coordinates & Vector-Valued Functions

Welcome to Unit 9 AP Calculus Multiple Choice Questions! Grab some paper and a pencil π to record your answers as you go. You can see how you did on the Unit 9 Practice Questions Answers and Review sheet once you're done. Don't worry, we have tons of resources available if you get stumped π 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 9 here: Intro to Unit 9

Parametric graph created in Desmos.

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. Which of the following is the derivative formula for differentiating a parametric equation?

2. Given x = 2βt and y = 3t^2 -2t. Find dy/dx. Evaluate at t=1.
A. -4
B. -2
C. 4
D. 0

3. What is the second derivative formula for a parametric equation?

4. Find all the points of horizontal and vertical tangency given x = t^2 + t and y = t^3 - 3t + 5.
A. t = -1 and -1/2Β
B. t = 1 and -1/2
C. t = 1 and -1
D. t = 1, -1, and -1/2

5. What is the arc length formula for a parametric equation?

6. What is the distance traveled by the object from t=1 to t=7 if the functions are dx/dt = tsin(t) and dy/dt=cos(t^2)
A. 15
B. 14.802
C. 13.015
D. 16

7. To find the speed of the particle, you take the absolute value of theβ¦
A. position vector.Β
B. velocity vector.
C. acceleration vector.
D. displacement vector.

8. When converting between polar and rectangular coordinates, you can use the following formulas to help you find x and y:
A. x = rcosΞΈ and y = rsinΞΈ
B. y = rcosΞΈ and x = rsinΞΈ
C. y=cosΞΈ and x = sinΞΈ
D. x = cosΞΈ and y = sinΞΈ

9. The formula to find the derivative of a polar function is:

10. What is the area formula for one polar curve?

11. Find the area bounded by the graph of r = 3 + 3sinΞΈ.
A. 42
B. 42.412
C. 21
D. 21.206

12. What is the formula for the polar area between two curves?

13. Find the area inside the smaller loop of the limacon r = 2cosΞΈ + 1.
A. 1
B. 0.6
C. 0.544
D. 0.78

14. Determine the area that is inside r = 3 + 2sinΞΈ and outside r = 2.
A. 23
B. 24
C. 24.187
D. 25

15. What is the arc length formula of a polar curve?

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