Math 060 Final Exam Review/Practice Jam
Fall 2015
In problems 1 – 20, perform the given operation. Make sure to simplify your answers.
Write your final answers with positive exponents.
1.
3 x  7 2
2

x2 y3   x6 y 7 
2.   3 1  

 2x y   2 
1 
3. (3x) (2 x)  x 4 
3 
2
2
4
 2

4.   s 2t 7   24 s 4 t 
3


5.
 2 a b 
3
4
6. 6xy 0
7.
4a 6b
12a 1b 3
 4a 6b 
8. 
1 3 
 12a b 
0
9. 31  52
4a 1
10. 3
b
11.
a9 a 8
a 0 a 5
12. (3 y  1)(4 y 2  5 y  3)
13. (7 y 2  4)(7 y 2  4)
14. (3x  5)2  (2 x  3)(2 x  3)
15. (1  4w2 )  (2w2  5  6w)  (5w2  7 w)
16. ( 4 x 2 y  10 x)  ( 5x 2 y  2 x  3xy 2 )
17.
28 y 3  14 y 2  21y  49
7 y3
18.
16m3  8m2  4
8m2
19.
x3  4 x  3
x2
20.
12 x 2  14 x  10
3x  5
In problems 21 - 26, simplify the given expression. Write the answer in scientific
notation.
21.
4 103
8 105
22.  9 1013  6 10 6 
23.
2  10 6
5  10 2
24.
(0.06)(220, 000)
11, 000  0.0003
25. The length of a DNA molecule can exceed 0.0025 inches in some organisms.
26. When an unmanned rover, Opportunity, landed on Mars, the distance from Earth to Mars
was 198,700,000 miles.
In problems 27 - 31, state if the given expression is either a monomial, binomial, trinomial,
or none of these.
27. 9 x3  6 x5
28. 12x 4
29. 9 x3  2 x 7  5
30. 5x3 y 6  7 x10
31.
7
x6
In problems 32 – 48, factor completely. If it cannot be factor, state that it’s prime.
(Note:

 will be given.)
a  b   a  b   a  ab  b 
a3  b3   a  b  a2  ab  b2
3
3
2
2
32. x 2  3x  108
33. 11x 2  44
34. 5 x 2  20
35. 27 x 3  64
36. 18 x 2  63x  10
37. x 3  4 x 2  60 x
38. 3 x 4  48
39. 2 x3  3x 2  8 x  12
40. 20 x 2  70 x  30
41. x 2  6 x  9
42. m3  27
43. 49 x 2  36 y 2
44. 27 p 3  8
45. x 2  25
46. x 4  81
47. ( x  4)2  25 y 2
48. 8 x 4 y  12 x3 y 2  20 x 2 y 3
2 1
49. Find the slope of a line passing through  ,   and
3 2
1

 4,  
3

50. Find the slope of a line passing through  3, 4 and  3, 0  .
51. Write the equation of the line in slope-intercept form that passes through the points
 2,3 and 2,5 .
52. Find the equation of the line passing through  2, 3 and  2,5 . Write your answer in
slope-intercept form if possible.
53. Find the equation of the line passing through  2,3 and  2, 3 . Write your answer in
slope-intercept form if possible.
54. Write the equation of the line in point-slope form that passes through  5,2 and is
perpendicular to the line 3x  4 y  9 .
55. Find the equation of the line that passes through the point
and is parallel to the
line 2 x  3 y  5 . Write your answer in slope-intercept form.
1

56. Find the equation of the line that passes through the point  , 3  and is perpendicular to
3

the line x  5 .
57. Graph the line 3 x  4 y  12 by using the x- and y-intercepts.
58. Graph the line y 
5
x  4 using the slope and y-intercept.
2
3
59. Graph the line with x-intercept – 2 and slope =  .
4
60. State the slope, -intercept, and -intercept of  x  4 y  4 . Then graph the line.
61. State the slope, -intercept, and -intercept of x  3  4 . Then graph the line.
62. State the slope, -intercept, and -intercept of y  4  0 . Then graph the line.
63. The cost to rent a car for a day is $53 plus $0.62 for each mile driven. The total cost, ,
is given by the equation C  53  0.62x , where represents the total number of miles
driven.
a) How much will it cost to drive the car 50 miles?
b) If you have $75.32 to spend on renting the car, how far will you be able to drive it?
In problems 64 – 69, solve the system of equations using the indicated method. Write
answers as an ordered-pair (x,y). If there are infinitely many solutions or no solution, state
this.
64. Solve by graphing.
2x  y  3
3x  2 y  8
65. Solve by graphing.
y  2 x
x y 6
66. Solve by using substitution.
x  2  3y
5x  7 y  4
67. Solve by using elimination.
2x  4 y  2
3x  6 y  3
1
3
x
68. Solve by either substitution or elimination.
2
4
x  2 y  3
y
69. Solve by either substitution or elimination.
2x  4 y  2
 x  2 y  1
In problems 70 – 77, solve the given equation. Remember to check your answers for
possible extraneous solutions, when necessary.
70.
3
3 5
 3x    x  3
2
2 6
71. 14 x 2  7 x  0
72. ( x  2)( x  3)  56
73. b 2  18  11b
74. 6 x 2  36 x
75. Solve for x : 13x  14 y  3x  y  3
76. 5  0.2( y  2)  3.6 y  1.6
77.
2x 1 x x
  1
4
6 3
78. Solve by using quadratic formula: x 2  4 x  6  0
79. Solve by using quadratic formula: 4 x 2  1  4 x
80. Solve by using quadratic formula: x 2  6 x  10  0
81. Solve by completing the square: y 2  8  2 y
82. Solve by completing the square: 4 x 2  20 x  7  0
83. Solve for x:
84. Solve for C:
85. Solve for y:
y  mx  b
1
h( B  C )
2
10 x  5 y  30
A
In problems 86 - 88, solve each inequality, graph it, and write the solution set using interval
notation.
86. 3  2( x  2)  3( x  2)  10 .
87.
4
2 4
3
x  x
3
3 5
5
88. 6 x  4  2( x  7)
89.
When 30 is subtracted from seven-eighths of a number, the result is equal to one-half of
the number. What is the number?
90.
Peanuts sell for $4.00 per pound. Almonds sell for $6.50 per pound. How many pounds
of each type should be mixed together to make a 5-pound mixture that sells for $5 per
pound?
91.
Two cars travel the same route, both leaving from the same point. The slower car
averages 40 miles per hour, and the faster car averages 50 miles per hour. If the faster car
leaves 2 hours after the slower car, in how many hours will the faster car overtake the
slower car?
92.
Two cities are 400 miles apart. A car leaves one of the cities traveling toward the second
city at 45 miles per hour. At the same time, a bus leaves the second city at 35 miles per
hour. How long will it take for them to meet?
93.
A passenger jet took three hours to fly 1800 miles in the direction of the jetstream. The
return trip against the jetstream took four hours. What was the jet's speed in still air and
the jetstream's speed?
94. How many liters of a 50% alcohol solution must be added with 80 liters of a 20% alcohol
solution to make a 40% alcohol solution?
95.
How many milliliters of pure water must be added to 100 ml of a 7% iodine solution to
make a 2% iodine solution?
96.
Find the measure of the three interior angles of a triangle if the second is 9 degrees more
than five times the first and the third is three times the measure of the first.
97.
The sum of twice one number plus second number is fourteen. The first number plus
three times the second number is twenty-two. Find these numbers.
98.
Find the measure of two supplementary angles such that the larger angle is 5 degrees
more than 4 times the smaller angle.
99.
The length of a rectangular garden is 5 feet longer than the width. The area of the
rectangle is 300 square feet. Find the length and the width.
100. Henry has $10,000 to invest. He invests the money in two different accounts, one
expected to return 5% and the other expected to return 8%. If he wants to earn $575 for
the year, how much should he invest at each rate?
101. The width of a rectangular carpet is 7 meters shorter than the length, and the diagonal is
1 meters longer than the length. What are the length and the width of the carpet?
102. The sum of squares of two consecutive integers is 61. Find these integers.
103.
Rational Expressions
Simplify each rational expression
a)
x2  2 x  3
x 2  3x  2
4 x3  9 x
b)
6 x2  7 x  3
Perform the indicated operations. Simplify the result, if possible.
c)
x 2  36 5

10
6 x
x 2  7 x  12 2 x3  4 x 2
d)
 2
x2  4
x 9
e)
2 y2  5 6 y  5

y 3
y 3
f)
y2  2 y  3
y2  4 y  5

y 2  7 y  12 y 2  7 y  12
g)
3 x  9
x3

2
x  x6 2 x
h)
6y
3

y 4 y2
i)
2
 x  y
x y
2

x 2  xy
2y

3x  3 y x  y
Solve
j)
4 y
y
4


3y  5 y  2 3y  2 y 1
k)
5
2
4


x  2 2  x x 1
2