AP Calculus BC Study Guide UPDATED Exam Questions and CORRECT Answers

AP Calculus BC Study Guide UPDATED
Exam Questions and CORRECT Answers
Water leaking onto a floor forms a circular pool. The radius of the pool increases at a rate of 4
cm/min. How fast is the area of the pool increasing when the radius is 5 cm?


Which of the following represents the notation of our final answer to this problem? - CORRECT
ANSWER - dA/dt = 40pi cm²/min


Which of the following are acceptable guidelines for solving Related Rates problems? -
CORRECT ANSWER - -Label all quantities that can change as variables.
-Draw a picture.
-Find an equation that relates the variables.
^All of these are acceptable


A bicycle path and a road cross at right angles. A police woman stands on the road 70 meters
south of the crossing and watches an eastbound cyclist traveling at 6 meters per second. At how
many meters per second is the cyclist moving away from the police woman 4 seconds after
passing the intersection? - CORRECT ANSWER - 1.95 m/sec.


The radius of a circle is increasing at a constant rate of 0.4 feet/sec. What is the rate of increase
in the area of the circle at the instant when the circumference of the circle is 40 pi feet -
CORRECT ANSWER - 16pi ft²/second


A water tank in the shape of a right circular cone has a height of 10 feet. The top rim of the tank
is a circle with a radius of 4 feet. If water is being pumped into the tank at the rate of 2 cubic feet
per minute, what is the rate of change of the water depth, in feet per minute, when the depth is 5
feet?
(The volume V of a right circular cone is V = 1/3 pi r2h, where r is its radius and h is its height.)
- CORRECT ANSWER - 1/(2pi) ft/min


The maximum value of

,f(x) = x³ + 3x² - 9x - 2

on the interval [0, 2] is - CORRECT ANSWER -0


Find the value of c guaranteed by the Mean Value Theorem for f(x) = 2/(x-1) on [3,5] -
CORRECT ANSWER - x= 1 + (2√2)



Is Rolle's Theorem applicable to f(x) = 2/(x-1) on [3,5]? - CORRECT ANSWER - No, f(a)
does not equal f(b)


Determine whether or not Rolle's Theorem applies. If it does, find all values of c in the open
interval (a,b) such that f'(c)=0

f(x)= (2)/(x+1)²; [-3,0] - CORRECT ANSWER - No the theorem does not apply



Which of the following statements is true: - CORRECT ANSWER - The derivative of a
function may be used to determine whether or not the function is increasing or decreasing on any
intervals in its domain.


Find the differential dy of y= 2x - cot²(x) - CORRECT ANSWER - (2 + 2 cot x csc² x)dx


Which of the following functions are differentiable for all values of x?
I. f(x)=|x|
II. f(x)=³√x

III. f(x)=x³ - CORRECT ANSWER - III. only



Find f"(x) when f(x) = csc(x). - CORRECT ANSWER - f"(x) = cscx(cot²x + csc² x)



Find f"(x) when f(x) = x * sin(x). - CORRECT ANSWER - f"(x) = 2cos(x) - x * sin(x)

,The position of a particle moving along the x-axis is given by x(t)=t³-5t²-8t+2 for t≥0. The
particle is at rest is at t= - CORRECT ANSWER - 4



If f(x) = (2x + 1)⁴, then the fourth derivative of f(x) at x = 0 is - CORRECT ANSWER - 384


Suppose that f(x) and g(x) are differentiable for all x with the values given in the table below.
https://files.catbox.moe/z8gol2.png

Let h(x) = f(g(x)). Find h'(2). - CORRECT ANSWER - 20



If f(x) = (x+1)² cos(x), then f'(0) = - CORRECT ANSWER -2



If dy/dx = 5xy, then (d²y)/(dx²) = - CORRECT ANSWER - 25x²y + 5y



If dy/dx = 2x + 2y, then (d²y)/(dx²) = - CORRECT ANSWER - 4x + 4y + 2



For the curve x + y = 3xy, which of the following is equal to dy/dx? - CORRECT ANSWER -
(3y-1)/(1-3x)


If x³ + x * sin(y) = 1, then at point (1,0), dy/dx = - CORRECT ANSWER - -3


A function that is not differentiable at x = c must not be continuous at x = c. - CORRECT
ANSWER - False



Find f"(x) when f(x) = x * cos(x). - CORRECT ANSWER - f"(x) = -2sin(x) - x * cos(x)



If f(a) exists, them limx→a f(x) exists. - CORRECT ANSWER - False



limx→0(((x+3)² - 9)/x) - CORRECT ANSWER -6

, Which of the following points of discontinuity of https://files.catbox.moe/hce39h.png

is not removable? - CORRECT ANSWER -x=1


The function f is continuous on the closed interval [0,2] and has values given in the table above.
The equation f(x) = 1/2 must have at least two solutions in the interval [0,2] if k =

https://files.catbox.moe/k04p63.png - CORRECT ANSWER -0


Use the graph of f(x) to evaluate the limit.
https://files.catbox.moe/doizcg.png

lim x→2 lim f(x) = - CORRECT ANSWER - undefined


Use the graph of f(x) to evaluate the limit.
https://files.catbox.moe/qiiosj.png

lim x→1⁺ f(x) = - CORRECT ANSWER -2


Find the limit of:

https://files.catbox.moe/k7t3lc.png - CORRECT ANSWER -0


The equation of the horizontal asymptote for the graph of y = (3-e¹/ˣ)/(3+e¹/ˣ) is - CORRECT
ANSWER - y = 1/2


Solve for x:

5x-2>3 or x-7<1 - CORRECT ANSWER - (−∞,∞)



|2x−8|<3 - CORRECT ANSWER - (5/2, 11/2)