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AP Calculus AB Quick Concept Review Flashcards | StudBud
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AP Calculus AB Quick Concept Review
AP Calculus AB Quick Concept Review
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#abcalculus
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Questions
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Answers
1
Which of the following theorems establishes the EXISTENCE of a function value?
Intermediate Value Theorem
Mean Value Theorem
Derivative Theorem
Fundamental Theorem of Calculus
2
The expression shown below represents
f ' (x)
f (h)
f (x)
f ' (h)
3
The expression shown below, is equivalent to which of the following?
f '(g(x)) g'(x)
f '(g(x))
(f ' (x))(g ' (x))
f '(g'(x))
4
Find the derivative of the function below.
18x^2 - 9 + C
6x^2 - 9
18x^3 - 9x
18x^2 - 9
5
Increasing/Decreasing of a function is determined by
The signs of the second derivative
Limits of the function
The signs of the first derivatives
The mins and maxes of the function
6
Given a differentiable function, slope of the secant line equals slope of the tangent on (a,b) by
Fundamental Theorem of Calculus
Intermediate Value Theorem
Your mom
Mean Value Theorem
7
Right Reimann sum is an overestimate when f(x) is
Concave Down
Concave Up
Decreasing
Increasing
8
Let c be a real number. The expression shown below, is equivalent to which of the following?
f ' (u)
f ' (t)
f(u) * u'
f(u) - f(c)
9
The integral is an accumulation function of the "signed" area between a functiona and x-axis.
True
False
10
When f'(x) changes from ________ to _________ you have a relative max on f(x)
Decreasing, Increasing
Positive, Negative
Increasing, Decreasing
Negative, Positive
11
The expression shown below represents
Mean Value Theorem
Average Value of f on [a,b]
Average Rate of Change of f on [a,b]
Fundamental Theorem of Calculus
12
The expression shown below, is equivalent to which of the following?
f ' (a) - f ' (b)
f(b) - f(a)
f ' (b) - f ' (a)
f(a) - f(b)
13
If s(t) position, v(t) velocity, a(t) accleration, then a particle is at rest when
v(t)=0
s(t)=0
a(t)=0
v(t) and a(t) have opposite signs
14
Given s(t) a position function, v(t) a velocity function. What's the total distance traveled?
l ∫v(t)dt l
∫ lv(t)l dt
∫ v(t) dt
∫ ls(t)l dt
15
The expression shown below represents
average value of f on [a,b]
Intermediate Value Theorem
Slope of the tangen line
average rate of change of on [a,b]
16
The slope of the tangent lines along a curve is also known as?
The limit
Concavity
Average rate of change
The derivative
17
When given v(t) and asked to find the derivative, you're looking for
Position s(t)
v(t) at a certain point
The slope of the tangent line of s(t)
Acceleration a(t)
18
Proving continuity of f at x = a requires ALL BUT the following
Showing f(a) exist
f(a) = limitx→a f(x)
Showing limit x→a f(x) exists by left and right hand limits
Showing f is differentiable at x=1
19
The expression shown below represents
Volume by Semi-Circular Cross Section
Volume by Disk Method
Volume by Washer Method
Area Between Curves
20
How do you know a particle is speeding up or slowing down?
Acceleration's sign
Velocity's sign
Critically thinking with the information is the problem
Comparing velocity's and acceleration's signs
21
What is the
FIRST
and crucial step to solving a differential equation?
Find the anti-derivative
Use the initial condition
Add a C
Separate the variables
22
If a function is differentiable at x = b then it is _________________ continuous at x = b.
never
always
sometimes
23
Linearization (aka tangent line approximation) will be an UNDERESTIMATE when f(x) is
Increasing
Concave up
Concave Down
Positve
24
Find this anti-derivative.
1/3x^3 - 5/2x^2 + 6x + C
1/2x^2 - 5x + C
1/3x^3 - 5/2x^2 + 6x
2x - 5 + C
25
Find this derivative.
35x^4 - (1/2)x^(-1/2)
0
7 + C
7x^4 - x^(-1/2)
26
The expression shown below represents
Intermediate Value Theorem
Definition of a derivative
Fundamental Theorem of Calculus
Mean Value Theorem
27
What is the limit of f(x) as x→1?
1
The limit does not exist.
2
3
28
Speed at time t is expressed as
v(t)
The opposite of v(t)
a(t)
Absolute Value of v(t)
