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9.10 Multiple Choice Questions

3 min readโ€ขdecember 31, 2021

Dalia Savy

Dalia Savy


AP Calculus AB/BCย โ™พ๏ธ

279ย resources
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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 ๐Ÿ“„ 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 ๐Ÿ˜• 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
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-ILcbAWUKFVy1.PNG?alt=media&token=18803ae3-67e6-4690-ba75-759bd4dce28c

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?
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-gwMPvwyjKcsh.png?alt=media&token=edcbf427-bfdb-497e-968c-655a30b06730

2. Given x = 2โˆšt 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?
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-FuEBI1OeL7pF.png?alt=media&token=9a3bd5fe-f43a-4cd8-a85a-61f45360c8e7

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 -1/2ย 
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?
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-Mrfu2d76oHQx.png?alt=media&token=91d9c10b-4a61-4fa5-a2d8-f62b905d5e65

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 theโ€ฆ
A. position vector.ย 
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 = rcosฮธ and y = rsinฮธ
B. y = rcosฮธ and x = rsinฮธ
C. y=cosฮธ and x = sinฮธ
D. x = cosฮธ and y = sinฮธ

9. The formula to find the derivative of a polar function is:
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-nWs7T4iJROUP.png?alt=media&token=78f961a4-c6a4-4648-80a1-84a14a204f82

10. What is the area formula for one polar curve?
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-SdhkipIt42Uq.png?alt=media&token=20f93d5d-1776-4008-80f9-4a1dfb9086ee

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

12. What is the formula for the polar area between two curves?
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-HX7wXwMbM83N.png?alt=media&token=9176d54a-256f-4c8a-8fd3-53fe2600355c

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

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

15. What is the arc length formula of a polar curve?
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-rrzhPdncH4R0.png?alt=media&token=8a2a1cf8-7504-480a-8aed-d0e5131d1bcf

๐Ÿ™ŒTime to Check Your Answers on Unit 9 Practice Questions Answers and Review!ย 
๐ŸคConnect with other students studying AP Calculus with Hours
Browse Study Guides By Unit
๐Ÿ‘‘Unit 1 โ€“ Limits & Continuity
๐Ÿค“Unit 2 โ€“ Fundamentals of Differentiation
๐Ÿค™๐ŸฝUnit 3 โ€“ Composite, Implicit, & Inverse Functions
๐Ÿ‘€Unit 4 โ€“ Contextual Applications of Differentiation
โœจUnit 5 โ€“ Analytical Applications of Differentiation
๐Ÿ”ฅUnit 6 โ€“ Integration & Accumulation of Change
๐Ÿ’ŽUnit 7 โ€“ Differential Equations
๐ŸถUnit 8 โ€“ Applications of Integration
๐Ÿฆ–Unit 9 โ€“ Parametric Equations, Polar Coordinates, & Vector-Valued Functions (BC Only)
โ™พUnit 10 โ€“ Infinite Sequences & Series (BC Only)
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