TO: 2013 AP Calculus BC Students
FROM: T. Ericson, AP Calculus BC Teacher
As you probably know, the students who take AP Calculus AB and pass the Advanced
Placement Test will place out of one semester of college Calculus;
those who take AP Calculus BC and pass the Advanced Placement Test will place
out of two semesters of college Calculus. Because Calculus BC covers two semesters,
you will be learning Calculus twice as fast as the students who take Calculus AB. In
order to have enough time to learn the material of two college-level courses, we will
start learning Calculus as soon as possible when school begins and will not be able to
spend time reviewing the material you learned in Algebra, Geometry, and Precalculus.
Attached is a summer homework packet, which will be due the first day of Calculus class
in August. The material in the packet should be material you learned in Algebra II and
Precalculus.
You will turn in the packet the first day of Calculus class, and it will count as a daily
grade. On the third day of class, you will take a test on the material in the packet.
My recommendation is that you look over the problems in the packet when you receive it
but that you wait until the week before school starts to work the problems so that you
will remember the material very well when school starts.
All of the AP Calculus AB and BC classes at Clements will be using the TI-89 graphing
calculator. The Calculus teachers feel that it is the best calculator available. You will
be expected to have a TI-89 the first week of school.
I am looking forward to seeing you in Calculus in August.
CALCULUS BC
SUMMER HOMEWORK
This homework packet is due the first day of school. It will be turned in the first day of
Calculus class and will count as a daily grade. You will take a test on the material in the
packet on the third day of school.
Work these problems on notebook paper. All work must be shown.
Use your graphing calculator only on problems 31 - 42 and 55 – 61.
Find the x- and y-intercepts and the domain and range, and sketch the graph.
1. y 
x 1
2. y  9  x 2
3. y 
x
6. y  tan x,  2  x  2
9. y  csc x,  2  x  2
5. y  cos x,  2  x  2
8. y  sec x,  2  x  2
4. y  sin x,  2  x  2
7. y  cot x,  2  x  2
x
11. y  ln x
10. y  e x
  1, if x  1
 x 2  1, if x  0

12. y  3x  2, if x  1
13. y  
2 x  2, if x  0
7  2 x, if x  1

______________________________________________________________________________
Find the asymptotes (horizontal, vertical, and slant), symmetry, and intercepts, and sketch the graph.
2 x2  9
1
1
x2  2x  4
14. y 
15. y 
16.
17.
y

y

2
x 1
x 1
x2  4
 x  2


_____________________________________________________________________________________
Solve.
18. x  x  12  0
2
19.
 x  2   x  1  x  5  0
2
3
20.
3x  2
x4
0
21.
 2 x  5  x  1
3
 x  2
2
0
_____________________________________________________________________________________
Solve. Give exact answers in radians, 0  x  2 .
22. 2 cos 2 x  3cos x  2  0
23. 2sin 2 x  cos x  1
24. sin  2 x   cos x
25. 2 cos  2 x   1  0
26. 2 csc2 x  3csc x  2  0
27. tan 2 x  sec x  1
x
28. 2 cos    3  0
29. tan  2 x    3
30. 2sin  3x   3  0
3
_____________________________________________________________________________________
Solve. Show all steps. Give decimal answers correct to three decimal places.
31. e2 x  3  37
32. e2 x  5e x  6  0
50
34.
35. log 4  x 2  3 x   1
 11
2x
4e
37. log 2 ( x  3)  log 2 ( x  1)  log 2 12
39. log6  log 4  log 2 x    0
33. e x  12e x  1  0
36. ln  5 x  1  3
38. log8  x  5   log8  x  2   1
40. log3 (log 2 (log5 25))  x
41. The number of students in a school infected with the flu t days after exposure is modeled by the
300
function P  t  
.
1  e4  t
(a) How many students were infected after three days?
(b) When will 100 students be infected?
Solve. Show all steps. Give decimal answers correct to three decimal places.
42. Exponential growth is modeled by the function n  n0ek t . A culture contains 500 bacteria when t = 0.
After an hour, the number of bacteria is 1200.
(a) How many bacteria are there after four hours?
(b) After how many hours will there be 8000 bacteria?
__________________________________________________________________________________________
Evaluate.


43. tan  Cos  1  




45. cos Sin
1
3 

2  
 2x  




44. sec  Arc sin  

2 

2  
46. sec  Arc tan  4x  
__________________________________________________________________________________________
47. Convert the equation 2 x  3 y  8 into polar form.
48. Convert the equation r 2  2r sin   0 into rectangular form.
__________________________________________________________________________________________
Make a table, and sketch the graph.
49. r  3sin 
50. r  2  2 cos 
51. r  1  2 sin 
52. r  3  2 cos 
53. r  4 cos  3 
54. r  3sin  2 
__________________________________________________________________________________________
Write a function for each problem, and use your graphing calculator to solve. Give decimal answers correct to
three decimal places. Be sure to sketch the graph you used, and label it with your answer.
55. A rancher has 200 feet of fencing with which to enclose two adjacent
rectangular corrals, as shown. What dimensions should be used so
that the enclosed area will be a maximum?
56. A rectangle is bounded by the x-axis and the semicircle y  25  x 2
as shown. What length and width should the rectangle have so that
its area is a maximum?
57. Four feet of wire is to be used to form a square and a circle. Find the length of the sides of the square
and the radius of the circle that will enclose the maximum total area?
58. The sum of the perimeters of an equilateral triangle and a square is 10. Find the dimensions of the
triangle and the square that produce a minimum total area.
59. Two posts, one 12 feet high and the other 28 feet high, stand 30 feet apart.
They are to be secured by two wires, attached to a single stake, running
from ground level to the top of each post. How far from the left post
should the stake be placed to use the least wire?
60. A manufacturer makes a metal can in the shape of a cylinder that holds 1000 cm3 of oil. What radius
and height will minimize the amount of metal in the can?
61. A cylindrical metal container, open at the top, is to have a capacity of 24 in 3 . The cost of
material used for the bottom of the container is $0.15 per sq. in., and the cost of the material
used for the curved part is $0.05 per sq. in. Find the dimensions that will minimize the cost
of the material, and find the minimum cost.
Use the figure to find the limit.
62. lim f  x 
63. lim f  x 
x 3
x 
64. lim f  x 
65. lim f  x 
66. lim f  x 
67.
x0
x 2
x  
lim f  x 
x  5
__________________________________________________________________________________
Find the limit.
68. lim
x2  x  6
x3
x6
x  3
71. lim
x  6
69. lim
 x  5
x 0
2
 25
70. lim
x 0
x
x 8
3
x 2  3 x  18
72. lim
x  2
x 1 1
73. lim
x2
x 
x
3x  5 x 2
4x2  1
_____________________________________________________________________________________
Find the slope of the line tangent to the curve at the point P by using the formula:
Slope of tangent line  lim
f  x  f c
x c
xc
.
(You must know this formula.)
74. f  x   x 2  5 x  4, P (2, 2)
75. f  x  
76. f  x   x  2 x  1, P (2,1)
77. f  x   2 x 2  7 x  3, P (c, f (c))
3
2
x  6, P(3,3)
78. Find an equation of a line that is tangent to the curve f  x   x 3 and is parallel to the line
12 x  y  10  0.
79. Find an equation of a line that is tangent to the curve g  x   24  x 2 and is
perpendicular to the line x  8 y  6  0.
_____________________________________________________________________________________
Use the definition of the derivative to find the derivative:
f   x   lim
h0
80. f  x   x 2  8 x
82. f  x  
3
x4
f  x  h  f  x
h
. (You must know this formula.)
81. f  x  
x9
83. f  x   x 3  2 x 2  x  4