PRACTICE AP Calculus AB Pop Memorization Quiz

Tests the knowledge of students with major concepts from each section of Calculus AB. #math #Calculus #quiz #CalculusAB #theorems #derivatives #integrals #limits #studyguide

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Questions 31

Answers

1
For any real number n, d/dx xⁿ =
xn+1/n+1
xn-1
nxn-1
n
2
Second derivative of f(x) is written
y''
d2y/dx2
f''(x)
All of the above
3
∫ cosx dx =
sinx + c
-sinx + c
tanx + c
-cosx + c
4
ln(e^x) and e^lnx =
x
1
lnx
ex
5
The Extreme Value Theorem: If x is continuous on a closed interval [a,b] the f(x) has both:
Absolute max and min
f'(x) and f''(x)
Inflection point
Concave up and down
6
This is the graph of...
ex
|x|
ln x
√x
7
lim x→0 sinx/x =
1
cosx
0
-cosx
8
For x>0, d/dx ln x =
x
1/x
ex
ln|x|
9
This graph shows
cosx
-sinx
sinx
-cosx
10
Points of inflection: If (c,f(c)) is a point of inflection of the graph of f, then
f'(c) = 0 or f'(c) is und
f'(c) = 0
f(c) = 0 or f(c) is und
f''(c) = 0 or f''(c) is und
11
d/dx [arctan u] =
u'/ 1+u2
-u'/ 1+u2
-u'/|u|√u2-1
u'/ |u|√u2-1
12
lim x→0: 1/x =
DNE
∞
-∞
0
13
Limits at Infinity: lim x→±∞ c/x^r =
∞
x
0
1
14
d/dx arccos u =
u/1+u2
u/√1-u2
-u/√1-u2
-u/1+u2
15
d/dx cotx =
-csc2x
tan2x
csc2x
-cscx cotx
16
This is the graph of:
√x
lnx
1/x
ex
17
f'(c) = f(b) - f(a) / b - a; what theorem is this?
Squeeze Theorem
Mean Value Theorem
Integral Mean Value Theorem
Extreme Value Theorem
18
d/dx sec x =
secxtanx
tan2x
tanx
sec2x
19
∫ a^x dx =
1/lna +c
1/a + c
1/lna × ax + c
ax + c
20
Def of a critical number: Let f be defined at c. If __ or __, then c is a critical number of f.
f(c) = 0
f'(c) = 0 and f'(c) is und
f'(c) = 0
f(c) = 0 and f(c) is und
21
∫ sin x dx =
-cosx + c
-cosx
cosx + c
cscx + c
22
d/dx a^x =
ln|x| + c
1/lna ⋅ ax +c
xax
lna ⋅ ax
23
For any constant c, d/dx c =
k
x
0
1
24
Product Rule: If f(x) and g(x) are differential at x, then d/dx [f(x)g(x)] =
f''(x)g(x) + f(x)g''(x)
f'(x)g'(x) + f'(x)g'(x)
f(x)g(x) + f(x)g(x)
f'(x)g(x) + f(x)g'(x)
25
d/dx tan x =
secxtanx
tan2x
sec2x
secx
26
∫ k dx =
kx + c
k + c
k
1
27
Integration of sec² x dx =
secx + c
-cotx + c
secxtanx + c
tanx + c
28
This is the graph of...
-tanx
cotx
cscx
tanx
29
d/dx [lnu] =
eu
u'/u
lnu
1/u
30
Equation of a tangent line at (c, f(c))
y = c + f'(c) ⋅ (x-f(c))
y = f(x) + f'(x) ⋅ (x-c)
y = f(c) + f'(c) ⋅ (x-c)
y' = f'(c) + f(c) ⋅ (x-c)
31
∫ cscx cotx dx =
cotx + c
-cotx + c
-cscx + c
-cosx + c

PRACTICE AP Calculus AB Pop Memorization Quiz Flashcards | StudBud

PRACTICE AP Calculus AB Pop Memorization Quiz

31 termsStudBud Administration38 plays

Tests the knowledge of students with major concepts from each section of Calculus AB. #math #Calculus #quiz #CalculusAB #theorems #derivatives #integrals #limits #studyguide

Flashcards31 cardsFPractice quizPHost liveL

Questions 31

Answers

1
For any real number n, d/dx xⁿ =
xn+1/n+1
xn-1
nxn-1
n
2
Second derivative of f(x) is written
y''
d2y/dx2
f''(x)
All of the above
3
∫ cosx dx =
sinx + c
-sinx + c
tanx + c
-cosx + c
4
ln(e^x) and e^lnx =
x
1
lnx
ex
5
The Extreme Value Theorem: If x is continuous on a closed interval [a,b] the f(x) has both:
Absolute max and min
f'(x) and f''(x)
Inflection point
Concave up and down
6
This is the graph of...
ex
|x|
ln x
√x
7
lim x→0 sinx/x =
1
cosx
0
-cosx
8
For x>0, d/dx ln x =
x
1/x
ex
ln|x|
9
This graph shows
cosx
-sinx
sinx
-cosx
10
Points of inflection: If (c,f(c)) is a point of inflection of the graph of f, then
f'(c) = 0 or f'(c) is und
f'(c) = 0
f(c) = 0 or f(c) is und
f''(c) = 0 or f''(c) is und
11
d/dx [arctan u] =
u'/ 1+u2
-u'/ 1+u2
-u'/|u|√u2-1
u'/ |u|√u2-1
12
lim x→0: 1/x =
DNE
∞
-∞
0
13
Limits at Infinity: lim x→±∞ c/x^r =
∞
x
0
1
14
d/dx arccos u =
u/1+u2
u/√1-u2
-u/√1-u2
-u/1+u2
15
d/dx cotx =
-csc2x
tan2x
csc2x
-cscx cotx
16
This is the graph of:
√x
lnx
1/x
ex
17
f'(c) = f(b) - f(a) / b - a; what theorem is this?
Squeeze Theorem
Mean Value Theorem
Integral Mean Value Theorem
Extreme Value Theorem
18
d/dx sec x =
secxtanx
tan2x
tanx
sec2x
19
∫ a^x dx =
1/lna +c
1/a + c
1/lna × ax + c
ax + c
20
Def of a critical number: Let f be defined at c. If __ or __, then c is a critical number of f.
f(c) = 0
f'(c) = 0 and f'(c) is und
f'(c) = 0
f(c) = 0 and f(c) is und
21
∫ sin x dx =
-cosx + c
-cosx
cosx + c
cscx + c
22
d/dx a^x =
ln|x| + c
1/lna ⋅ ax +c
xax
lna ⋅ ax
23
For any constant c, d/dx c =
k
x
0
1
24
Product Rule: If f(x) and g(x) are differential at x, then d/dx [f(x)g(x)] =
f''(x)g(x) + f(x)g''(x)
f'(x)g'(x) + f'(x)g'(x)
f(x)g(x) + f(x)g(x)
f'(x)g(x) + f(x)g'(x)
25
d/dx tan x =
secxtanx
tan2x
sec2x
secx
26
∫ k dx =
kx + c
k + c
k
1
27
Integration of sec² x dx =
secx + c
-cotx + c
secxtanx + c
tanx + c
28
This is the graph of...
-tanx
cotx
cscx
tanx
29
d/dx [lnu] =
eu
u'/u
lnu
1/u
30
Equation of a tangent line at (c, f(c))
y = c + f'(c) ⋅ (x-f(c))
y = f(x) + f'(x) ⋅ (x-c)
y = f(c) + f'(c) ⋅ (x-c)
y' = f'(c) + f(c) ⋅ (x-c)
31
∫ cscx cotx dx =
cotx + c
-cotx + c
-cscx + c
-cosx + c