Unit 9 Progress Check: MCQ Part A

AP Calculus BC Scoring Guide

Unit 9 Progress Check: MCQ Part A

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1. A curve is defined by parametric functions and , where and . For

what positive value of is ?

A 1.079

B 1.149

C 1.202

D 1.525

2. The instantaneous rate of change of the vector-valued funct ion is given by

. If , what is the value of ?

A

B

C

D

3. A curve in the -plane is defined by , where and . Which of

the following is equivalent to ?





A

B

C

D

4. A curve in the -plane is defined by the parametric equations and . What is

the slope of the line tangent to the curve at the point where ?

A

B

C 4

D 48

5. A curve in the -plane is defined by the parametric equations and . Which of the

following is an expression for in terms of ?

A

B

C

D





6. A curve is defined by the parametric functions and . What is in terms

of ?

A

B

C

D

7. A curve is defined by the parametric equations and . What is in terms of ?

A

B

C

D

8. A curve is defined by the parametric equations and , where is a differentiable

function. Which of the following gives the length of curve from to ?





A ⅆ

B ⅆ

C ⅆ

D ⅆ

9.

A curve in the -plane is given by the parametric equations and . The graph of is shown

above on the left, and the graph of the derivative is shown above on the right. Which of the following

integral expressions gives the length of the portion of the curve described by the parametric equations for

?

A ⅆ

B ⅆ

C ⅆ

D ⅆ





10. Which of the following gives the length of the curve defined by the parametric equations

and from to ?

A ⅆ

B ⅆ

C ⅆ

D ⅆ

11. If is the vector-valued function defined by , then

A

B

C

D

12. Let be the vector-valued function defined by . Which of the following is ?





A

B

C

D

13. The vector-valued function is defined by . Which of the following is

?

A

B

C

D

14. For time , the position of a particle moving in the -plane is given by the vector-valued function . If

the velocity of the particle is given by , which of the following could be an

expression for ?



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participation in the program is prohibited. of 7

A

B

C

D

15. The velocity vector of a particle moving in the -plane has components given by and .

If the initial position of the particle at is , which of the following expressions gives the

particle’s position ?

A and

B and

C and

D and

Unit 9 Progress Check: MCQ Part A

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