Download calculus bc - Fort Bend ISD

AP CALCULUS BC - AP REVIEW 2
Work the following on notebook paper, showing all work. Use your calculator only on problems 14 and 19.
14. (Calc ) For 0  t  31, the rate of change of the number of mosquitoes on Tropical Island at time t days is
t
modeled by R  t   5 t cos   mosquitoes per day. There are 1000 mosquitoes on Tropical Island at
 5
time t = 0.
(a) Show that the number of mosquitoes is increasing at time t = 6.
(b) At time t = 6, is the number of mosquitoes increasing at an increasing rate, or is the number of mosquitoes
increasing at a decreasing rate? Give a reason for your answer.
(c) According to the model, how many mosquitoes will be on the island at time t = 31? Round your answer to
the nearest whole number.
(d) To the nearest whole number, what is the maximum number of mosquitoes for 0  t  31? Show the
analysis that leads to your conclusion.
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15. If y  xy  x 2  1, then when x   1,
(A)
1
2
(B) 
1
2
(C)  1
dy
is
dx
(D)  2
(E) nonexistent
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16. Let f be a function defined for all real numbers x. If f   x  
4  x2
x2
, then f is decreasing on
the interval
(A)   , 2 
(B)   ,  
(C)   2, 4 
(D)   2,  
(E)  2,  
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 x3 for x  0
17. Let f be the function defined by f  x   
. Which of the following statements
 x for x  0
about f is true?
(A) f is an odd function.
(D) f   0  0 .
(B) f is discontinuous at x = 0. (C) f has a relative maximum.
(E) f   x   0 for x  0.
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18.
The graph of f  , the derivative of f is shown in the figure above. Which of the following describes all
relative extrema of f on the open interval (a, b)?
(A) One relative maximum and two relative minima
(B) Two relative maxima and one relative minimum
(C) Three relative maxima and one relative minimum
(D) One relative maximum and three relative minima
(E) Three relative maxima and two relative minima
19. (Calc) A particle moves along the x-axis with velocity at time t  0 given by v  t   1  e1 t .
(a) Find the acceleration of the particle at time t = 3.
(b) Is the speed of the particle increasing at time t = 3? Give a reason for your answer.
(c) Find all values of t at which the particle changes direction. Justify your answer.
(d) Find the total distance traveled by the particle over the time interval 0  t  3 .
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1
20. An antiderivative for 2
is
x  2x  2
2
x2
(A)   x 2  2 x  2 
(B) ln  x 2  2 x  2 
(C) ln
x 1
(D) arcsec  x  1
(E) arctan  x 1
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21. The region enclosed by the x-axis, the line x = 3, and the curve y  x is rotated about the x-axis. What
is the volume of the solid generated?
(A) 3
(B) 3 3 
(C)
9

2
(D) 9
(E)
36 3

5
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22.
0
(A)

3
3
dx
4  x2

(B)

4
(C)

6
(D)
1
ln 2
2
(E)  ln 2
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dy
 2 y 2 and if y  1 when x  1, then when x = 2, y =
dx
2
1
1
(A) 
(B) 
(C) 0
(D)
3
3
3
23. If
(E)
2
3
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24. The top of a 25-foot ladder is sliding down a vertical wall at a constant rate of 3 feet per minute.
When the top of the ladder is 7 feet from the ground, what is the rate of change of the distance
between the bottom of the ladder and the wall?
(A) 
(D)
7
feet per minute
8
7
feet per minute
8
(B)  24 feet per minute
(E)
21
feet per minute
25
(C)
7
feet per minute
24