ExamView - Calculus Chapter 4 Practice Test

[Pages:5]Name: ________________________ Class: ___________________ Date: __________

ID: A

AP Calculus AB Chapter 4 Practice

Multiple Choice Identify the choice that best completes the statement or answers the question.

1. Find the indefinite integral ????-9t2 + 14t - 2^?~~dt .

a. -9t3 + 14t2 - 2t + C b. -3t3 + 14t2 - 2t + C c. -3t3 + 7t2 - 2t + C d. -18t2 + 14t + C e. -9t3 + 14t2 - 2 + C

2. Find the indefinite integral and check the result by differentiation.

3z2

+ 12z z4

-

9

dz

a.

-3 z

+

12 z2

+

9 z3

+C

b.

-3 - 6 + 3 z z2 z3

c.

3 z

-

6 z2

+

3 z3

+C

d.

-3 + 6 + 3 z z2 z3

e.

-3 z

-

6 z2

+

3 z3

+C

3. Find the indefinite integral

2secy???tany - secy ^?~dy.

4. An evergreen nursery usually sells a certain shrub

after 4 years of growth and shaping. The growth

rate during those 4 years is approximated by

dh dt

=

2.5t + 6,

where

t

is

the

time

in

years

and

h

is

the height in centimeters. The seedlings are 15

centimeters tall when planted (t = 0). Find the

height after t years.

a. h(t) = 1.25t2 + 21t b. h(t) = 1.25t2 + 6t + 15 c. h(t) = 1.25t + 15 d. h(t) = 2.5t2 + 6t + 15 e. h(t) = 2.5t + 21

5. Find the limit of s(n) as n .

s (n)

=

5 n3

?????????????

n

3

(n + 7

1)

2

?

a. 5/7 b. 5 c. 1/7 d. 10/7 e. unbounded

a. 2secy tany + C b. 2secy - 2tany + C c. 2secy + tany + C d. 2 + 2 secy + C e. 2secy tany - 2secy + C

1

Name: ________________________

6. The graph of f consists of line segments, as shown in the figure. Evaluate the definite integral

10

f (x)dx using geometric formulas.

4

a. ?3 b. ?1 c. ?2 d. 1 e. 0 7. Find the area of the region bounded by the graphs of the equations y = x3 + x, x = 4, y = 0. Round your answer to the nearest whole number. a. 768 b. 96 c. 49 d. 72 e. 16

ID: A

8.

Find the average value of

f (x)

=

5????x2 + 5 ^?~~ x2

on the

interval ????1,3?.

a.

40 3

b. 35

c.

25 3

d.

80 3

e. 40

9. Determine all values of x in the interval ????1,3? for

which the function

f (x)

=

2????x2 + 4 ^?~~ x2

equals its

average

value

14 3

.

a. x = 4 b. x = ? 2 c. x = 2 d. x = 3 e. x = ? 3

10. Find the indefinite integral 5z4 cos z5 dz.

a. cos z5 + C

b.

sin z6 6

+C

c. sin z4 + C

d. sin z5 + C

e.

sin z5 5

+C

2

Name: ________________________

11. Find the indefinite integral u3 4 + u 4 du.

2

a.

2?????4 + u 4 ^?~~~ 3 12

+C

3

b.

?????4 + u 4 ^?~~~ 2 8

+C

3

c.

?????4 + u 4 ^?~~~ 2 12

+C

5

d.

2?????4 + u 4 ^?~~~ 2 20

+C

3

e.

2?????4 + u 4 ^?~~~ 2 12

+C

12. Find the indefinite integral of the following function and check the result by differentiation.

4u3 du u4 +5

a. 2 u3 + 5 + C

b. u 4 + 5 + C

c.

1 2

u4 +5 +C

d.

1 2

u3 +5 +C

e. 2 u4 + 5 + C

ID: A

13. Solve the differential equation.

df dz = 8z +

9z 9 - z2

a.

f (z)

=

4z 2

-

9 2

9 - z2 + C

b. f (z) = 4z2 - 9 + C 9- z2

c. f (z) = 4z2 + 9 9 - z2 + C

d. f (z) = 4z2 - 9 9 - z2 + C

e. f (z) = 4z - 9 9 - z2 + C

14. Find the indefinite integral of the following function.

sin2x dx

a. -2cos2x + C

b. -cos2x + C

c.

-cos2x 3

+C

d.

-cos2x 2

+C

e. sin2x + C

15. Find the indefinite integral of the following function.

cos3s ds

a. 3sin3s + C

b.

cos3s 3

+

C

c.

sin3s 3

+

C

d.

sin3s 3

+

C

e.

sin3s 4

+

C

3

Name: ________________________

16. Find the indefinite integral of the following function.

sint cos 7 t

dt

a.

(cos t) -6 7

+C

b.

(cos t) -6 6

+C

c.

(cos t) -7 6

+C

d.

(sin t) -6 7

+C

e.

(sin t) -6 6

+C

Short Answer

18. Find F (x) given

3x

F(x) = t4 dt .

-3x

19. Find F (x) given

3x

F(x) = t5 dt .

-3x

20. Find F (x) given

x+3

F(x) = (10t + 1)dt .

x

ID: A

17. Find an equation for the function f (x) whose

derivative is f (x) = 7sin(49x) and whose graph

passes

through

the

point

???????

49

,-

6 7

^?~~~~~

.

a.

f (x)

=

-1 7

cos (49x)

-

1

b.

f (x)

=

1 14

cos (49x)

+

1

c.

f (x)

=

1 49

cos (98x)

+

14

d.

f (x)

=

-1 7

cos (49x)

-

49

e.

f (x)

=

-1 98

cos (7x)

+

2

4

AP Calculus AB Chapter 4 Practice Answer Section

MULTIPLE CHOICE

1. C 2. E 3. B 4. B 5. E 6. C 7. D 8. A 9. D 10. D 11. E 12. E 13. D 14. D 15. C 16. B 17. A

SHORT ANSWER

18. F (x) = 162x 4 19. F (x) = 0 20. F (x) = 30

ID: A

1

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download