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
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