Unit 2 Progress Check MCQs Part A – AP Calculus Answers

Syntax Error (146567): Unknown operator ‘n*’ Syntax Error (146567): Unknown operator ‘n*’ Syntax Error (146567): Unknown operator ‘n*’ Syntax Error (146567): Unknown operator ‘n*’ Syntax Error (146567): Unknown operator ‘n*’ Syntax Error (146567): Unknown operator ‘n*’ Syntax Error (146567): Unknown operator ‘n*’ AP Calculus AB Scoring Guide

Unit 2 Progress Check: MCQ Part A

1. The derivative of a function is given by . At what value of for does the line tangent to the graph of at have slope 2 ?

A 0.512

B 1.849

C 2.287

D 8.113

2.

Let be the function given by . Selected values of are given in the table above. If the values in the table are used to approximate , what is the difference between the approximation and the actual value of ?

A 0

B 0.433

C 0.567

D 1

3. Let be the function given by . Which of the following statements is true?

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AP Calculus AB Scoring Guide

Unit 2 Progress Check: MCQ Part A

A

B

C

D

4.

Selected values of a function are shown in the table above. What is the average rate of change of over the interval ?

A

B

C

D

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AP Calculus AB Scoring Guide

Unit 2 Progress Check: MCQ Part A

5.

The graph of the function , shown above, consists of three line segments. What is the average rate of change of over the interval ?

A

B 0

C

D 4

6. The function is given by . What is the average rate of change of over the interval ?

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AP Calculus AB Scoring Guide

Unit 2 Progress Check: MCQ Part A

A

B

C

D 1

7. The derivative of the function is given by for all , and . Which of the following is an equation of the line tangent to the graph of at ?

A

B

C

D

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AP Calculus AB Scoring Guide

Unit 2 Progress Check: MCQ Part A

8.

The graph of , the derivative of a function , is shown above. The points and are on the graph of . Which of the following is an equation of the line tangent to the graph of at ?

A

B

C

D

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AP Calculus AB Scoring Guide

Unit 2 Progress Check: MCQ Part A

9.

The graph of the trigonometric function is shown above for . At which of the following points on the graph of could the instantaneous rate of change of equal the average rate of change of on the interval ?

A

B

C

D

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AP Calculus AB Scoring Guide

Unit 2 Progress Check: MCQ Part A

10. Which of the following statements, if true, can be used to conclude that exists? 1. exists. 2. is continuous at . 3. is differentiable at .

A I only

B II only

C II and III only

D I, II, and III

11.

Let be the function defined above. Which of the following statements is true?

A is neither continuous nor differentiable at .

B is continuous but not differentiable at .

C is differentiable but not continuous at .

D is both continuous and differentiable at .

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AP Calculus AB Scoring Guide

Unit 2 Progress Check: MCQ Part A

12.

The graph of the function , shown above, has a vertical tangent at and horizontal tangents at and . Which of the following statements is false?

A is not differentiable at because the graph of has a vertical tangent at .

is not differentiable at and because is not continuous at and B .

is not differentiable at and Syntax Error (146567): Unknown operator ‘n*’ Syntax Error (146567): Unknown operator ‘n*’ because the graph of has sharp corners at C and .

is not differentiable at and because the graph of has horizontal D tangents at and .

13. If , then

A

B

C

D

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AP Calculus AB Scoring Guide

Unit 2 Progress Check: MCQ Part A

14. If , then

A

B

C

D

15. If is the function defined by , what is ?

A

B

C

D

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