1. Draw the vector expressions,
using
triangular
addition:
a. a
+ b = c
b. a
+ b + f = g
c. e
- f = b
d. c
- b = a
2. Draw the vector expressions,
using
parallelogram
addition:
a. a
+ b = c
b. a
+ b + f = g
c. e
- f = b
d. c
- b = a
3. Write the component vector for the points (5,6) and (-3,4).
4. What is the magnitude of the vector <5,8>?
5. What is the distance
between
the
points (1,4,-2) and (5,1,2)? Find the midpoint of the segment.
6. Find a vector perpendicular to <8,1>.
7. Find a vector perpendicular to <3,2,-1>.
8. What is lim
2x2
+ 5x + 3 ?
Limits
x® -1
x + 1
9. Find the dot product of <2,5,6> and <-1,3,2> .
10. Find the cross product of <2,5,6> and <-1,3,2> .
11. What is the 89th term in the arithmetic series 1 + 5 + 9 + 13 + ....
12. What is lim
2x2
+ 5x + 3 ?
Limits at
Infinity
x® ¥
x2 + 1
13. What is lim
2x2
+ 5x + 3 ?
Limits at
Infinity
x® ¥
x + 2
14. What is
lim 2x2
+ 5x + 3 ?
Limits at
Infinity
x® ¥
x3 + 1
15. The nth term of the series 2/3 + 3/4 + 4/5 + 5/6 + ...
16. What is the sum 4 + 1 + 1/4 + 1/16 + ...?
5
17. What is the sum S
k3
?
k=1
18. In the binomial expansion, (x + 3x-1)5, the third term is?
19. Prove by mathematical
induction
that
1 + 4 + 9 + 16 + ... + n2 = n(n + 1)(2n + 1)
6
20. Find the equation of the circle whose center is (-1,5) and is tangent to the x-axis.
21. The center of the ellipse 16x2 + 4y2 + 32x - 8y - 5 = 0 is
22. In how many different orders may a
person
select 8 socks from a drawer, considering
each of
the socks to be different? Counting Principles
23. A box contains 5 red and 3 white
balls.
How many ways can 3 red and 1 white ball be chosen?
Counting Principles
24. 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?
25. 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?
26. An ordinary nickel is tossed 5 times
in a row. What is the probability
that the same face comes
up 3 times?
27. A card is drawn from a standard deck
of cards. What is the probability
that it is a queen
or a red
card?
28. A card is drawn from a standard deck of cards. What is the probability that it is a red jack?
29. Evaluate
lim
x + 2
Limits
x® 5
30. If
lim
g(x) = 7, what is 5
lim g(x) ?
Properties
of Limits
x® 3
x® 3
31. What is the equation of the line which is tangent to the graph of y = 2x2 + 1 at x = 3?
32. What is the derivative of f(x) = 5 when x = 7?33. In which interval is the graph of f(x) decreasing when f(x) = (x - 1)(x + 2)(x - 3)
34. Write 5(cos 45o + i sin 45o) in rectangular form and in exponential form.
35. 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)
36. Use DeMoivre's Theorem to find [2(cos 30o+ i sin 30o)]4 .
37. What does the graph of r = 5 look like? (Use your calculator)38. How many points of intersection do y = x3 - 1 and -x2 + 2x - 1 have?
39. Find the point(s) of intersection for y = 3x - 1 and y = 2x2 + 5.
40. The eccentricity of an ellipse is __
41. The eccentricity of a parabola is __
42. The eccentricity of a hyperbola is __
43. For what x-values is y = | x2 - 1 | discontinuous?| x2 - 2x - 3|
44. s(t) = (t - 1)(t + 1)(t - 4) represents the position of a particle on a number line. Find the acceleration
at t = 5
sec.
45. (2 + 3i)2 + (4 - i)(5
+ 2i) - 1 = ? Complex
Numbers
46. Graph 4 - 2i
47. Simplify:
9x -2y3
27xy-5
48. 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
49. 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
50. 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)
51. Solve for x: log35
=
x
52. Expand:
logb x2__
y2z3
53. Write as one
logarithm:
ln x - 2[
ln (x + 2) + ln (x -
2)]
54. Solve
for
x: (a) 42x
- 7 = 64
(b) ln (x -1) = 3.8
(c) ex
= 10
(d) 10x =
570
(e) 3x = 7
55. Solve for x: x2 -
ln
x =
24
56. Solve
for x: (a) ln (x + 1) - ln (x - 2) =
ln x2
(b) ln x + ln (x - 2) =
1
(c) 2 ln x = 7
57. Simplify:
\/-16
\/-8
58. Find a logistic
equation y
=
500
1 + Ae-kt
when (3,
200)
and (10, 410) satisfy it.
59. 2 + i
=
Complex
Numbers
1 - 3i
60. Know the definition
of e
61. y =
200
1 + 50e-.12t
What is t when y
= 100?
62. Find the domain
for log2(x2
- 1)
63. Graph r = 2 + cos q
64. Find the derivative of f(x) = 2x2
- 3x + 5
65. Find two geometric means between 2
and 54
66. The probability of an event is
2/3. What are the odds against this event occurring.
67. Write the equation of
the parabola y
= x2 - 5x + 1 in standard form.
68. 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 |