AP Calculus Practice Exam and Solutions

[Pages:46]AP Calculus AB Practice Exam

Calculus AB

Section 1, Part A

Time - 55 minutes Number of questions - 28

A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAM

Directions: Solve all of the problems that follow. Available space on the page may be used for

scratch work.

In this exam:

(1)

The domain of a function in this exam is assumed to be all real numbers for which the function is defined, unless specified otherwise.

(2)

The inverse notation

or the prefix "arc" may be used to indicate an inverse function.

x x For example, the inverse tangent of

may be written as arcsin( ) or as

.

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Calculus AB

1. Using the substitution

A)

B) C) D) E)

, the integral

Section 1, Part A

is equivalent to

2.

A)

B) C) D) E)

. Find

.

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Calculus AB

Section 1, Part A

3. A line through the point (2, -2) is tangent to function f at the point (-2, 6). What is

?

A) -8

B) -2

C)

D) 6

E) Undefined

4. Grain is pouring out of an opening in the bottom of a grain silo. The rate at which the height,

h t , of the grain in the silo is changing with respect to time, , is proportional to the square root of

the height. Which of the following is a differential equation describing this situation?

A)

B)

C)

D) E)

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Calculus AB

5. Where is the graph of

A)

B)

concave up? C)

D)

Section 1, Part A

E)

f 6. Shown is a graph of function .

At which value of x f is continuous but not differentiable?

A) a

B) b

C) c

D) d

E) e

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Calculus AB

Section 1, Part A

7. The table shows values of

. Although f , the derivative of function

real numbers, only selected values of

are shown.

is continuous over all

x -2 -1 0 1 2 3 4

4.1

2.3

1.2

0

-0.6

-0.8

-2

56

0

1.5

If

f has exactly two real zeros, then

is increasing over which of the following intervals?

A)

B)

C)

only

D)

E)

8.

.

A)

B) C) D) E)

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Calculus AB

Section 1, Part A

9. At each point (x y f , ) on a graph of function , the graph has a slope equal to

f graph of

goes through the point (2, 3), then

A)

. If the

B)

C)

D) E)

g 10. The derivative of function is given by

A)

B) C) D) E)

g . When is increasing?

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Calculus AB

f 11. Function

is defined as

Which of the following statements is true:

f I.

is continuous at

.

II.

exists.

f III.

is differentiable at

A) None of the statements are true.

B) I only C) II only D) I and II only E) I, II, and III

Section 1, Part A

12.

A)

B)

C)

D)

E)

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