Download Note: This review represents the topics covered by the final exam

Introductory Algebra Final Exam Review
Note: This review represents the topics covered by the final exam. It is in no way intended to
represent the quantity of any particular type of problem on the final exam. The answers and graph
paper are provided at the end of this packet.
Terminology: Be able to recognize, identify and use these terms.
Absolute value
Equation
Factor
Multiple
LCD
Reciprocal
Solution
All real numbers
Conditional
Contradiction
Identity
Set-builder notation
Inequality
Interval notation
Roster notation
x-intercept
y-intercept
Origin
Quadrant
Ordered pair
Slope
Slope-intercept form
Parallel lines
Perpendicular lines
Linear system
System of linear
inequalities
Consistent system
Inconsistent
system
Independent equations
Dependent equations
For problems 1–20, simplify the expression. You could use a calculator, but it’s best to have an understanding
of order of operations (and fraction operations) without a calculator.
1. 3 15   4   16 
2.
11.
 7  3  4  3
3 7   3  10 
12.  6   8  9 
15  5 16 
3. 12  7   3  6     2  3
3
4.
2 3 1
 
5 4 2
4  11 1 

 
3  12
9 
13. 7  7
9 12
12
3 10
14.     
20  5 9 
5.  3    5 
15.
3  5  122  52   32
6.  4     5     3 
 15   6   16 
16.
 3  5  12 2
2
52   3
5 3 7
7.   
6 5 10
17. 42  3 5   2  7  5
4
8.
 4
5 10

2 3
9. 9  3  2
4
10.
3
4 11 1


3 12
9
18. 4   9  3    3
6  2 4
6  3  2  4    8 
3
19.


3
4   7  8 6   4 

20. 2  3   4    4  
5
4

 
0
2
 5 
1
Introductory Algebra Final Exam Review
For problems 21 – 23, set up and solve a linear equation to determine the solution.
21. What number is 250% of 74?
24. Write 0.05% as a decimal.
22. What is 6 increased by 20%?
25. Write 10 as a percent.
23. What percent of 70 is 14?
3 as a percent.
26. Write 10
For problems 27 – 35, set up the linear equation to solve. Be sure to define the variable used
in your equation.
27. A pipe 24 feet long is cut into three pieces. The first piece is twice as long as the second piece
and the third piece is 6 feet longer than the second piece. What are the lengths of all 3 pieces?
28. One number is 4 times a second number and their sum is 120. Find the numbers.
29. A major league pitcher throws a ball upward with an initial rate of 130 feet per second. The
height h (in feet) of the ball after t seconds is given by the formula h  130t  16t 2 . Determine
the height of the ball after 4 seconds.
30. In a physics class of 36 students, 5 more students received B’s than A’s and twice as many
students received C’s as A’s. Seven people received a grade below C. How many students
received A’s, B’s and C’s?
31. Food for hummingbirds must contain four times as much water as sugar. How much sugar
and water are needed to make 20 cups of food?
32. An employer announced a 6 ½ % salary increase for full-time employees. What was the
employee’s previous salary if their salary increased to $28,195?
33. One angle of a triangle is 10 degrees less than another angle, and the third angle is 30 degrees
less than twice the first angle. Find the measures of the three angles.
34. Two teachers are team-teaching for the first time together at Null Elementary School.
They are planning on shopping together to purchase decorations for their new room. They
are told that they will teach in one large room with a perimeter of 228 ft and the length is
6 ft greater than twice its width. What are the dimensions of their classroom?
35. A plumbing company charges $35 for the service call plus $25 for each hour of work. The
owner of an apartment complex budgeted $200 to repair its oven. How many hours of
service can the owner afford so that she does not exceed her budget?
2
Introductory Algebra Final Exam Review
For problems 36 - 39, determine the slope of the line that passes through the given points. You may use the
graph paper provided if needed.
 2,3 and  1, 5
38.  1, 10  and  5,6 
37.  2, 5 and  1, 5
39.  2,3 and  2, 5
36.
40. Determine the slope of the lines in the graphs below.
a)
b)
For problems 41 - 44, use the given graph to answer the questions that follow.












41. Approximate the value of x when y  3 .
43. Write the x-intercept as an ordered pair.
42. Write the y-intercept as an ordered pair.
44. Write the equation of the line in slope-intercept form.
3
Introductory Algebra Final Exam Review
For problems 45 - 48, graph the line and determine the slope and intercepts. You may use the graph paper
provided.
45.
3
x y 3
4
47. 
3
x  5  1
4
48. 3 
46. 2 x  5 y  10
1
y  2
2
49. Find the equation of the line that passes through the points  4,3 and  4, 1
50. Find the equation of the line with slope
1
that passes through (0,3).
2
51. Find the equation of the line with slope
1
that passes through (4, 3).
2
52. Find the equation of the line that passes through 1,3 and  2,1 .
53. Find the equation of the line with slope 0 that passes through (4, 3).
 4
54. Find the equation of the line that is perpendicular to y = 3x – 5 and passes through  0,  .
 5
55. Find the equation of the line parallel to 4x + 2y = 2 that passes through  3, 4  .
56. Find the equation of the line perpendicular to x  3 and passes through  3, 7  .
For problems 57 - 60, sketch the solution on a number line, and write the solution in set-builder and interval
notation.
57. Illustrate the solution set of 2 x  6  0 .
58. Illustrate the solution set of 
1
x6
2
59. Illustrate the solution set of
2
x  10
3
60. Illustrate the solution set of 5  x  2  x  1
Solve the following inequalities. Write your answer in interval notation.
61. 24  8x  8 or 2x  5  7
62. 24  8x  8 and 2x  5  7
4
Introductory Algebra Final Exam Review
Solve the following systems of equations.
63. x  3 y  27
2 x  3 y  9
64. 2 y  3 x  2
4x  6 y  
7
3
What is the y-coordinate of the
solution?
65. 5 x  4 y  3
8 x  6 y  20
What is the y-coordinate
of the solution?
What is the x-coordinate of the
solution?
For problems 66 and 67, solve the system of equations graphically. You may use the graph paper provided.
66.
3 x  4 y  5
5 x  3 y  1
67.
3x  7 y  14
1.5 x  3.5 y  17.5
Graph the following system of inequalities. You may use the graph paper provided.
68.
x  2y  2
x y 0
70.
x y 4
x y 4
69.
x4
y  3
71.
x y 3
5 x  y  27
Set up and solve a linear system to determine the solution to the application problems. Be sure to
define your variables used in the linear system.
72. Jack has saved a total of $2.15 in nickels and dimes in his piggy bank. He has 10 more nickels
than dimes. How many of each denomination does he have in his piggy bank?
73. The perimeter of a desk is 28 feet. If the width is 2 feet less than the length, find the
dimensions of the desk.
74. Del Monte Bloom Energy Drink contains 50% fruit juice while Rockstar Juice, an energy/
juice hybrid, contains 70% fruit juice. How much of the Del Monte Bloom Energy Drink
should be mixed with the Rockstar Juice drink to make 12 ounces of a 65% fruit juice
blend?
75. Corey has just moved into his first apartment and is trying to decide between two different
calling plans so that he can use his phone. The Unlimited Plus Plan has a $32.99 monthly fee
with unlimited free long-distance calls. The One Rate® 10¢ Nationwide Direct Plan has a
monthly fee of only $2.99, but there is also a 10¢ charge for each call made. How many calls
would someone with the One Rate® 10¢ Nationwide Direct Plan have to make for the
monthly cost to be the same as the Unlimited Plus Plan?
5
Introductory Algebra Final Exam Review
76. Evaluate: 3 15  20  (4)
77. Replace ? with the correct symbol: > < =
 5 ? 5
78. The sum of two supplementary angles is 180 . If the larger angle is 20 more than 7 times the smaller angle,
find the measure of the larger angle.
79. Anita recently received a 7.8% pay cut. Her hourly wage is now $21.21. Find her hourly wage before the pay
cut.
80. Linda and Dave leave simultaneously from the same starting point biking in opposite directions. Linda bikes at
7 miles per hour and Dave bikes at 10 miles per hour. How long will it be until they are 27 miles apart from each
other?
81. Two trains leave a train station at the same time. One travels north at 9 miles per hour. The other train travels
south at 11 miles per hour. In how many hours will the two trains be 132 miles apart?
2
82. If a plane can cover 906 miles in 1 hours, how long will a 2016 mile trip take?
3
83. A plane can travel 1980 miles in 9 hours with a tailwind. On the return trip, the trip takes 11 hours. Find the
speed of the plane in still air.
84. A ski lift runs at a rate of 22 ft/sec. At that rate, how many minutes would it take to cover a mile? (hint: 1 mile
= 5280 feet)
85. The perimeter of an equilateral triangle is 17 inches longer than the length of one side. Find the length of one
side.
86. Find the measure of each angle of the triangle. The second angle is 2 more than twice the first angle and the
third angle is 2 less than 3 times the first angle.
6
Introductory Algebra Final Exam Review
ANSWERS
1. 3
17. 76
2. 3
18. 
3. 1
38.
56. y  7
127
39. undefined
45
19. 2
4.
40. a)
13
20
20. 9
89
41.
100
1
5.
6.
7.
55. y  2x  2
8
3
b) undefined
58.  x x  12 ; (, 12]
21. 185
42. (0, 4)
1
22. 7.2
43. (3, 0)
23. 20 %
44. y 
7
15
24. 0.0005
4
x4
3
Graphs for #45 – 48 are
attached.
25. 1000 %
3
26. 30 %
4
3
4
45. m  ; (4,0); (0, 3)
9. 
17
12
4
10. 
3
37
11. 
1
1
2
2
27. 4 ft, 9 ft, 10
ft
30. A: 6; B: 11; C: 12
27
4
12. 
9
2
5
31. 4 cups sugar; 16 cups
water
14.

7
36
9
10
15. 13
16.
50
17

60.  x x 

11 

 , 4 


62.  2,6
63. 7
47. m is undefined; (8,0) ;
no y-intercept
65. 2
48. m  0; (0, 2) ;
no x-intercept
11 
;
4
61. (, )
64.
5
3
Graphs for #66 and 67 are
attached.
66. (1,2)
49. x  4
67. no solution
32. $26,474.18
13.
59.  x x  15 ; (, 15]
46. m   ; (5, 0); (0, 2)
28. 24; 96
29. 264 ft
Number lines for #57 – 60
are attached.
57.  x x  3 ; (3, )
3
4
2
24
8.

4
3
33. 55º, 45º, 80º
34. 36 ft by 78 ft
50. y 
1
x3
2
51. y 
1
x 1
2
52. y 
2
7
x
3
3
Graphs for #68 – 71 are
attached.
72. 11 dimes, 21 nickels
35. 6.6 hours
36. 8
37. 0
53. y  3
73. 8 ft by 6 ft
74. 3 oz Del Monte; 9 oz
Rockstar
75. 300 calls
1
4
54. y   x 
3
5
7
Introductory Algebra Final Exam Review
ANSWERS
45.
48.
46.
57.
58.
47.
59.
60.
8
Introductory Algebra Final Exam Review
ANSWERS
66. Intersection at (1, 2)
69. Intersection at (4, 3)
Solution
67. The lines are parallel; no solution.
70. Intersection at (4,0)
68. Intersection (2, 2)
71. Intersection at (4,7)
9
Introductory Algebra Final Exam Review
76. 60
77. <
78. 160
79. $23
80. 1.6 hours
81. 6.6 hours
82. 3.7 hours
83. 200 mph
84. 4 min.
85. 8
1
2
86. 30; 62; 88
10
Introductory Algebra Final Exam Review
GRAPH PAPER
11