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Duplicate of AP Calculus AB Review
Duplicate of AP Calculus AB Review
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AP Calculus AB Review #calculus #math #ap #derivatives #integrals
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Questions
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Answers
1
What does the mean value theorem state (for continuous, differentiable functions)?
Average slope < 0
average slope > 0
average slope = instantaneous slope
average slope ≠ instantaneous slope
2
Choose the correct answer: ∫cos(x)
dx
sin(x) + C
-sin(x) + C
cot2(x) + C
sec(x) + C
3
The first derivative of a function provides information about the _______ of that function.
concavity
speed
slope
acceleration
4
Choose the correct answer.
7/27
-25/27
25/27
-7/27
5
Choose the correct answer.
e(t/2) + C
2e(t/2) + C
e(-t/2) + C
e-t + C
6
To find velocity from position, you must...
integrate once
integrate twice
find the 2nd derivative
find the 1st derivative
7
Choose the correct answer: ∫sec
2
(x)
dx
sin(x)cos(x) + C
tan(x) + C
cot2(x) + C
sin(x) + C
8
Find the lim
x→0
(
sin
x
/ 2x)
1/2
-1
0
-2
9
How do you find the area between two functions of x?
∫(top - bottom)dx
π(top + bottom)
top - bottom
∫(bottom - top)dx
10
Choose the correct answer: ∫csc(x)cot(x)
dx
cot(x) + C
-cot2(x) + C
-csc(x) + C
sec(x) + C
11
Choose the correct answer: ∫(1/x)
dx
ln∣x∣ + C
2x-2 + C
x-2 + C
x<span style="font-size: 13.3333330154419px;">n+1 + C</span>
12
Choose the correct answer: (d/dx)[cot(u)] =
-csc2(u)·u'
-csc(u)tan(u)·u'
sec(u)tan(u)·u'
sec2(u)·u'
13
Choose the correct answer: (d/dx)[
ln(u)
] =
(1/u)·u'
ln(u)·u'
ueu·u'
(1/u)∙ln(u)·u'
14
Choose the correct answer.
6x2cos(x3)
-6x2sin(x3)cos(x3)
-6x2sin(x3)
6x2sin(x3)cos(x3)
15
For all related rates problems, you must derive each term with respect to
area
volume
time
x
16
Choose the correct answer.
36
6
4
2
17
Choose the correct answer: (d/dx)[sin(u)] =
csc(u)·u'
cos(u)·u'
tan(u)·u'
-cos(u)·u'
18
Choose the correct answer.
x < -1 and x > 3
-1 < x < 3
All values of x
-3 < x < 1
19
Choose the correct answer.
16π/3
4π/3
8π/3
32π/5
20
Choose the correct answer: ∫sin(x)
dx
cos2(x) + C
-cos(x) + C
sin(x)cos(x) + C
cos(x) + C
21
Choose the correct answer: (d/dx)[
e
u
] =
eu·u'
ueu·u'
ueu
eu + C
22
The second derivative of a function provides information about the _______ of that function.
acceleration
slope
concavity
speed
23
Choose the correct answer.
y -1= -2(x - π/4)
y = -2(x - π/4)
y = 2(x - π/4)
y-1 = 2(x - π/4)
24
Choose the correct answer: ∫csc
2
(x)
dx
-cot2(x) + C
-cot(x) + C
sec(x) + C
sin(x) + C
25
Choose the correct answer: (d/dx)[sec(u)] =
sec(u)tan(u)·u'
-csc(u)tan(u)·u'
-csc(u)cot(u)·u'
sec(u)cot(u)·u'
26
Choose the correct answer: (d/dx)[
u/v
] =
(uv') / (vu')
uv' + vu'
(vu' - uv')/(v2)
uv' - vu'
27
Choose the correct answer: (d/dx)[tan(u)] =
csc(u)·u'
sec(u)·u'
sec2(u)·u'
-csc2(u)·u'
28
Choose the correct answer.
e+1
1
0
e-1
29
Choose the correct answer: (d/dx)[cos(u)] =
csc(u)·u'
sin(u)·u'
-sin(u)·u'
cos2(u)·u'
30
Choose the correct answer: (d/dx)[
vu
] =
uv' - vu'
u'v'
(uv') / (vu')
uv' + vu'
31
Choose the correct answer: (d/dx)[csc(u)] =
-csc(u)tan(u)·u'
csc(u)cot(u)·u'
sec2(u)·u'
-csc(u)cot(u)·u'
32
Choose the correct answer.
11
8
14
13
33
Choose the correct answer.
1
-3
-1
3
34
Choose the correct answer: (d/dx)[sec(u)] =
sec(u)cot(u)·u'
-csc(u)cot(u)·u'
sec(u)tan(u)·u'
-csc(u)tan(u)·u'
35
To find position from acceleration, you must...
find the 1st derivative
integrate once
integrate twice
find the 2nd derivative
36
Choose the correct answer: ∫sec(x)tan(x)
dx
tan(x) + C
sec2(x) + C
sec(x) + C
cot2(x) + C
37
Choose the correct answer.
14/3
16/3
28/3
32/3
38
Choose the correct answer.
4
6
2
7
