3. What is the sum 4 + 1 + 1/4 + 1/16 + ...?
5
4. What is the sum S
k3
?
k=1
5. In the binomial
expansion, (x + 3x-1)5,
the third term is?
6. Find the domain
for log2(x2
- 1)
7. Solve
for x: (a) ln (x + 1) - ln (x - 2) =
ln x2
(b) ln x + ln (x - 2) =
1
(c) 2 ln x = 7
8. Solve
for x:
9. Find the domain for 
10. Find the domain for 
11. Find the domain for 
12. f(x)
= 3x4 - 6x2
(a)
increasing
intervals (b)
decreasing
intervals
(c)
even, odd, or
neither (d)
relative
minimum
(e)
relative
maximum
13. f(x) =
x2 + 1
and g(x) = 2x +
3
(a)
(f + g)(x) = (b) (f
/g)(x)
= (c)
f (g(x))
=
(d) g (f (x))
=
(e)
f -1(x)
=
(f) g-1(x)
=
(g)
f -1(g(x)) =
14. Is y =
x3 + 3x even, odd,
or
neither?
15. Find
the equation of the line through
(1, -4) with slope 2.
16. Find
the quadratic function that has a
minimum at (-1,-2) and passes through (0,4).
17. Graph:
y > -x2 + 3x + 4
18.
Find two coterminal angles
to (a)
p/3 (b) 112o
19. Change 2p/3
to degrees
20. Change 260o to
radians
21. Find trigonometric function values for all the special angles
22. sin A = 2/7; A is in
quadrant
II Find the other
trigonometric
functions.
23. Solve the right triangles:
(a) C
= 90o, a = 2, c = 4
(b) A
= 30o, b = 75, C = 90o
(c) C
= 90o, B = 45o, b = 20
24. Find the exact values of the
trigonometric functions
for an angle A whose terminal side passes
through
(-1,-10).
25. sin A = -1/2, tan A > 0; Find all trigonometric function values.
26. Without your calculator, find:
(a) tan 225o
(b) cos 2p/3
(c)
sin 5p/4 (d) sec 17p/3
(e) csc
-p/6 (f) cot - 405o
27. Use your calculator to find: (a) sin 40o (b) cot 142o (c) sec 67o (d) csc 215o
28. Graph: (a) y = 2 sin
[3(x
-p/4)] +
1 (b)
y = - cos (x - p/3)
(c) y = 2 sec x (d)
y = cot x - 1
29. Use your calculator to find: (a) cos-1(1/4) (b) csc-110 (c) tan-16 (d) sec-112
30. Graph: (a) y = arctan
x
(b) y = arctan x -
3 (c)
y = 2 arctan
x
(d) y = | arctan x |
(e)
y = arctan
|x|
(f) y = arctan (x - 3)
31. sin (Arctan 3/4)
32. cot (Arctan
5/8)
33. sec [Arcsin (x - 1)]
34. sin (Arccos
x)
35. Arccos (-1/2)
36. csc (Arctan
(-5/12)
37.
38. Write the
equation for the inverse of the
function 
40.
Find the value of 
a. a
+ b = c
b. a
+ b + f = g
c. e
- f = b
d. c
- b = a
45. Draw the vector expressions,
using
parallelogram
addition:
a. a
+ b = c
b. a
+ b + f = g
c. e
- f = b
d. c
- b = a
46. Write the component vector for the points (5,6) and (-3,4).
47. What is the magnitude of the
vector
<5,8>?
48. Find a vector perpendicular
to
<8,1>.
49. Prove by mathematical
induction
that
1 + 4 + 9 + 16 + ... + n2 = n(n + 1)(2n + 1)
6
50. The center of the ellipse
16x2
+ 4y2 + 32x - 8y - 5 = 0 is
51. Write 5(cos 45o + i sin 45o) in rectangular form and in exponential form.
52. Multiply:
5(cos 45o
+ i sin 45o) 4(cos 15o + i sin 15o)
Divide:
5(cos 45o
+ i sin 45o) /4(cos 15o + i sin 15o)
53. Use DeMoivre's Theorem to find [2(cos 30o+ i sin 30o)]4 .
54. What does the graph of r = 5 look like? (Use your calculator to check)55. How many points of intersection do y = x3 - 1 and y = -x2 + 2x - 1 have?
56. Find the point(s) of intersection
for
y = 3x - 1 and y = 2x2 + 5.
57. Find (1 + i)1/3
58. Graph: x = 6t
y = sin t
59. A 90N force and a 110N force act on the same object.
The angle between the forces measures 90o.
Find the magnitude of the
resulting force.
60. Find the polar
coordinates for (1,-1).
61. Jane observes a raft floating on the
water bobbing up and
down with an amplitude of 8 feet. Beginning at the top of the wave, if
the raft
completes a full cycle every 5 seconds, what is the height of the raft
relative
to the lowest point after 25 seconds?
?
Limits
63. What is 
?
Limits at
Infinity
64. What is 
?
Limits at
Infinity
65. What is 
?
Limits at
Infinity
Limits 67. If
,
what is 
?
Properties
of Limits
68. What is the equation of the line which is tangent to the graph of y = 2x2 + 1 at x = 3?
69. What is the derivative of f(x) = 5 when x = 7?70. In which interval is the graph of f(x) decreasing when f(x) = (x - 1)(x + 2)(x - 3)
71. For what x-values is
discontinuous? Find the acceleration
at t = 5
sec.
73. Find the derivative of f(x) = 2x2
- 3x + 5
74. An outfielder catches a fly
ball and then throws it to third
base to tag the runner.
79. Find the cross
product of
<2,5,6>
and <-1,3,2> .
80. Find the equation
of the circle
whose
center is (-1,5) and is tangent to the x-axis.
81. In how many different orders may a
person
select 8 socks from a drawer, considering
each of
the socks to be different? Counting Principles
82. A box contains 5 red and 3 white
balls.
How many ways can 3 red and 1 white ball be chosen?
Counting Principles
83. A box contains 5 red balls and 3
white
balls. A second box contains 4 red balls and 2 white balls.
If one ball
is drawn from each box, what is the probability
that they are of the
same
color?
84. A stack of 52 playing cards consists
of 13 clubs, 13 diamonds, 13 hearts, and 13 spades.
Three cards
are drawn in succession. What is the probability
that they will
be
1 club and
2 diamonds
disregarding order?
85. An ordinary nickel is tossed 5 times
in a row. What is the probability
that the same face comes
up 3 times?
86. A card is drawn from a standard deck
of cards. What is the probability
that it is a queen
or a red
card?
87. A card is drawn from a standard deck
of cards. What is the probability
that it is a red jack?
88. The eccentricity of an ellipse is __
89. The eccentricity of a parabola is __
90. The eccentricity of a hyperbola is __
91. (2 + 3i)2 + (4 - i)(5 + 2i) - 1 = ? Complex Numbers92. Graph 4 - 2i
93. Simplify:
9x -2y3
27xy-5
94. Solve for x:
(a)
log216 =
x
(b) 9x = 27
(c)
loga(1/a)
= x (d) log (4/5) = x
(e)
ln .75
=
x
(f) ln (-.75) = x
95. Graph:
(a) y = 2x
(b) y = -2x
(c) y = 2x -
4 (d) y = 2 x-2
(e) y = 2 |x|
(f) y = 2 x/3
96. Graph:
(a) y = log 2
x
(b) y = ln x
(c)
y = ln (x - 1) (d) y = |ln x|
(e)
y = ln |x|
(f)
y = -ln (-x)
97. Solve for x: log35
=
x
98. Expand:
logb x2__
y2z3
99. Write as one
logarithm:
ln x - 2[
ln (x + 2) + ln (x -
2)]
100. Solve
for
x: (a) 42x
- 7 = 64
(b) ln (x -1) = 3.8
(c) ex
= 10
(d) 10x =
570
(e) 3x = 7
101. Solve for x: x2 -
ln
x =
24
102. Simplify:
\/-16
\/-8
103. Find a logistic
equation y
=
500
1 + Ae-kt
when (3,
200)
and (10, 410) satisfy it.
104. 2 + i
=
Complex
Numbers
1 - 3i
105. Know the definition
of e
107. The probability of an event is
2/3. What are the odds against this event occurring.
108. Write the equation of
the parabola y
= x2 - 5x + 1 in standard form.
109. The data below give the number of
bacteria found in a certain culture.
| Time (hrs) |
0 |
1 |
2 |
3 |
4 |
| Bacteria |
6 |
7 |
12 |
20 |
32 |
