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**Parametric graph created in** **__Desmos__.

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**STOP!**β Before you look at the answers make sure you gave this practice quiz a try so you can assess your understanding of the concepts covered in unit 9. Click here for the practice questions:

__AP Calculus Unit 9 Multiple Choice Questions__.

**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?**

**Answer**: The answer is B. The derivative formula for a parametric equation is when you differentiate y and x separately in terms of t.

**2. Given x = 2βt and y = 3t^2 -2t. Find dy/dx. Evaluate at t=1.**

A. -4

B. -2

**C. 4**

D. 0

**Answer**: Take the derivative of each function separately. Then plugin 1.

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

**Answer**: The answer is B. The numerator is the second derivative of the first derivative and the denominator is the first derivative of the x function.

**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**

**Answer**: Take the first derivative. Set the numerator equal to zero for the horizontal tangent. Set the denominator equal to zero for the vertical tangent.

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

**Answer**: The answer is A. You must remember to square each of the functions and take the square root.

**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

**Answer**: Plug into a graphing calculator!

**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.

**Answer**: This should be the absolute value of the velocity vector. The speed can also sometimes be referred to also as the magnitude 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

**Answer**: The equation will be A due to the connection to the unit circle of cosine being x and sine being represented by y.

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

**Answer**: The answer is D since you are using the product rule of x=rcostheta and y=rsintheta.

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

**Answer**: The answer is D as you need to square the radius and the function is in terms of theta.

**11. Find the area bounded by the graph of r = 3 + 3sinΞΈ.**

A. 42

**B. 42.412**

C. 21

D. 21.206

**Answer**: Remember to half the integral!

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

**Answer**: The answer is A. Remember to square each function when taking the integral.

**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

**Answer**: Find the points of intersection first which will be 4pi/3 and 2pi/3 then take the integral of this.

**14. Determine the area that is inside r = 3 + 2sinΞΈ and outside r = 2.**

A. 23

B. 24

**C. 24.187**

D. 25

**Answer**: Set the two functions equal to find the points of intersection. From there then find the integral.

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

**Answer**: The answer is B. Both the derivative and the radius must be squared. You are differentiating in terms of theta.

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