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AP Calculus AB Formula Test Review Quarter 4 Flashcards | StudBud
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AP Calculus AB Formula Test Review Quarter 4
AP Calculus AB Formula Test Review Quarter 4
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AP Calculus Formulas to Know & Understand
Flashcards
45 cards
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Questions
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Answers
1
d/dx(e
x
)
ex
ex/lna
1/x
exlna
2
A particle changes direction when
v(t)=0
x(t)=0
a(t)=0
v(t) crosses the t-axis
3
The following formulas are used to represent the _________________.
change in position
average acceleration
average time
average rate of change or average velocity
4
The extreme value theorem says if a function is differential from [a,b] there will be an
absolute min
absolute min and an absolute max
none of the above
absolute max
5
A POI is when f ''(x)=0.
False
True
6
The theorem shown in the picture is the
FTC
extreme value theorem
mean value theorem
average value theorem
7
The following formula represents the...
definition of derivative
definition of the derivative at x=a
"easy" way to calculate a derivative
Fundamental Theorem of Calculus
8
Odd functions are symmetric to the x-axis.
False
True
9
Find the derivative:
cosx
cos2x
-sinx
-cosx
10
A derivative fails to exist when there is a
cusp
all of them
corner
vertical tangent
11
a(t)=
x(t)
v'(t)
v(t)
x'(t)
12
The following formula represents the...
average value
definition of derivate
average rate of change
slope field
13
Evaluate the limit. lim
x->0
(1-cosx)/x
0
1
∞
DNE
14
\int_{ }^{ }\tan xdx=\sec^2x+c
False
True
15
Find the derivative:
tan2x
secxtanx
cscxtanx
sec2x
16
Find the derivative:
-sinx
-cscxcosx
sinx
sin2x
17
d/dx(lnx)
1/(xlna)
x
ex
1/x
18
Find the derivative:
u'v-uv'
(u'v+v'u)/(v2)
(u'v-v'u)/(v2)
u'v+uv'
19
d/dx(a
x
)=
axlna
ax
ax/lna
1/x
20
v(t)=
a(t)
x(t)
a'(t)
x'(t)
21
\int_{ }^{ }\sin xdx=\cos x+c
True
False
22
Find the derivative:
-csc2x
-cosx
-sec2x
-cscxcotx
23
d/dx(arctanx)
1/(1+x2)
-1/(1+x2)
-1/(√(x2-1)
1/(√(x2-1)
24
The formula given represents
the displacement of a particle
average velocity of a particle
average acceleration of a particle
the total distance traveled of a particle
25
Even functions are symmetric to the origin.
False
True
26
\int_{ }^{ }\frac{du}{u}=
au/lna+C
1/ulna+C
ln|u|+C
aulna+C
27
All critical points are either a max or a min.
True
False
28
In order to solve a Differential Equation you need to first
integrate
differentiate
separate variables.
graph a slope field
29
Which method for finding volume is NOT on the AP exam?
disc
known cross section
shell
washer
30
A limit exists when there is a
jump
hole
oscillation
vertical asympotote
31
Find the derivative:
nxn-1
(n-1)xn-1
nx
nxn
32
The FTC does which of the following
connects position and acceleration
finds exact area under a curve
says derivatives and integrals undo each other
finds extrema
33
\int_{ }^{ }\csc u\cot udu=
cscx+C
-cotx+C
cotx+C
-cscx+C
34
d/dx(arccosx)
-1/(√(1-x2)
-1/(1+x2)
1/(√(1-x2)
1/(1+x2)
35
A particle slows down when v(t) and a(t) are
different signs
are the same sign
36
The formula given represents
the displacement of a particle
average acceleration of a particle
the total distance traveled of a particle
average velocity of a particle
37
A particle is moving away from the origin when the position is positive and the velocity is negative.
True
False
38
The MVT is where the slope of the secant line is equal to the
slope of the tangent line
acceleration
slope of the normal line
inverse
39
\int_{ }^{ }\frac{du}{^{u^2+a^2}}=
arcsin(u/a)+c
(1/a)arctan(u/a)+c
(1/a)arcsec(u/a)+c
40
What does the integral equal?\int_{ }^{ }a^udu=
1/ulna
au/lna
aulna
1/u
41
Evaluate the limit. lim
x->0
sinx/x
DNE
1
∞
0
42
Find the derivative:
-sec2x
secx
-csc2x
-cscxcotx
43
Complete:
slope
concavity
minimum
maximum
44
Find the derivative:
(uv)n-1
u'+v'
u'v-uv'
uv'+u'v
45
Find the derivative:
sec2x
secx
sinx/cosx
csc2x
