Download Final Review 1st semester

1st Semester Final Exam Review- ALGEBRA 2011
Due: Wednesday, Thursday, or Friday, December 14, 15 or 16, 2011 as you walk into the
classroom to take your final. PLEASE STAPLE YOUR PINK HALL PASS TO THE FRONT OF
THIS PACKET.
NAME______________________________________________________ Period___________
1. Evaluate the expression a  b for a = 54 and b = 6.
2. Tri scored a total of 17 points in the basketball game, and he scored y points in the second half of
the game. Write an expression to determine the number of points he scored in the first half of the
game Then, find the number of points he scored in the first half of the game if he scored 6 points
in the second half of the game.
3. Salvador reads 11 books from the library each month for p months in a row. Write an expression
to show how many books Salvador read in all. Then, find the number of books Salvador read if he
read for 7 months.
4. Evaluate the expression
for
and
.
5. Evaluate x + (–36) for x = 44.
6. Subtract.
2 – (–10)
7. Evaluate x – (–15) for x = –12.
8. The highest temperature recorded in the town of Westgate this summer was 94ºF. Last winter, the
lowest temperature recorded was –1ºF. Find the difference between these extremes.
9. The temperature on the ground during a plane’s takeoff was 15ºF. At 38,000 feet in the air, the
temperature outside the plane was –26ºF. Find the difference between these two temperatures.
10. The elevator in the a downtown skyscraper goes from the top floor down to the lowest level of the
underground parking garage. If the building is 340 feet tall and the elevator descends 390 feet
from top to bottom, how far underground does the parking garage go?
11. Evaluate –11p for p = 5.
12. Evaluate k
(–10) for k = 80.
13. Divide.
0  (–11.346)
14. Erica hiked at Rancho San Antonio Park for 4.5 hours. Her average speed was 2.25 mi/h. How
many miles did she hike?
15. Simplify
.
16. Simplify
.
17. Simplify
.
18. Simplify
.
19. If the population of an ant hill doubles every 10 days and there are currently 20 ants living in the
ant hill, what will the ant hill population be in 30 days?
20. Simplify
.
21. Simplify
.
22. Evaluate
for x = 5.
23. Evaluate 1 + c • 6 for c = 4.
2
24. Simplify the expression
.
25. Simplify by combining like terms.
26. Graph the point (–2, –1).
27. Name the quadrant where the point (4, 4) is located.
28. Name the quadrant where the point (3, 0) is located.
29. Solve
.
30. Solve
.
31. Solve –7 + x = 34.
32. A toy company's total payment for salaries for the first two months of 2005 is $22,894. Write and
solve an equation to find the salaries for the second month if the first month’s salaries are
$11,955.
33. The range of a set of scores is 24, and the lowest score is 32. Write and solve an equation to find
the highest score. (Hint: In a data set, the range is the difference between the highest and the
lowest values.)
34. Solve
35. Solve
36. If
.
.
, find the value of
37. Solve
38. Solve
39. Solve
.
.
.
.
40. Sara needs to take a taxi to get to the movies. The taxi charges $3.00 for the first mile, and then
$2.00 for each mile after that. If the total charge is $9.00, then how far was Sara’s taxi ride to the
movie?
41. If 2x – 6 = 24, find the value of 3x.
42. The formula
gives the profit p when a number of items n are each sold at a cost c and
expenses e are subtracted. If
,
, and
, what is the value of c?
43. Solve
44. Solve
.
.
45. Solve
solutions.
. Tell whether the equation has infinitely many solutions or no
46. A professional cyclist is training for the Tour de France. What was his average speed in
kilometers per hour if he rode the 194 kilometers from Laval to Blois in 4.3 hours? Use the
formula
, and round your answer to the nearest tenth.
47. The fuel for a chain saw is a mix of oil and gasoline. The ratio of ounces of oil to gallons of
gasoline is 9:11. There are 44 gallons of gasoline. How many ounces of oil are there?
48. The local school sponsored a mini-marathon and supplied 84 gallons of water per hour for the
runners. What is the amount of water in quarts per hour?
49. Solve the proportion
.
50. An architect built a scale model of a shopping mall. On the model, a circular fountain is 42 inches
tall and 35 inches in diameter. If the actual fountain is to be 12 feet tall, what is its diameter?
51. Find the value of MN if
ABCD LMNO
cm,
cm, and
cm.
52. On a sunny day, a 5-foot red kangaroo casts a shadow that is 9 feet long. The shadow of a nearby
eucalyptus tree is 45 feet long. Write and solve a proportion to find the height of the tree.
53. Find 25% of 120.
54. 191 is 56% of what number? If necessary, round your answer to the nearest hundredth.
55. A compound is made up of various elements totaling 120 ounces. If the total amount of calcium
in the compound weighs 9 ounces, what percent of the compound is made up of calcium? If
necessary, round your answer to the nearest hundredth of a percent.
56. Aaron works part time as a salesperson for an electronics store. He earns $7.25 per hour plus a
percent commission on all of his sales. Last week Aaron worked 16 hours and earned a gross
income of $314.00. Find Aaron’s percent commission if his total sales for the week were $3,600.
If necessary, round your answer to the nearest hundredth of a percent.
57. After 8 months the simple interest earned annually on an investment of $6000 was $449. Find the
interest rate to the nearest tenth of a percent.
58. Bryan is a waiter. He waits on a table of 4 whose bill comes to $99.74. If Bryan receives a 20%
tip, approximately how much will he receive?
59. Hannah had dinner at her favorite restaurant. If the sales tax rate is 4% and the sales tax on the
meal came to $1.75, what was the total cost of the meal, including sales tax and an 18% tip?
60. Find the result when 20 is increased by 80%.
61. The price of a train ticket from Phoenix to New York is normally $140.00. However, children
under the age of 16 receive a 70% discount. Find the sale price for someone under the age of 16.
62. A shoes store buys sneakers at a wholesale price of $15 each. It then marks up the price by 54%,
and sells the sneakers. What is the amount of the markup? What is the selling price?
63. Write the inequality shown by the graph.
–7
–6
–5
–4
–3
–2
–1
0
1
2
3
4
5
6
7
m
64. To join the school swim team, swimmers must be able to swim at least 500 yards without
stopping. Let n represent the number of yards a swimmer can swim without stopping. Write an
inequality describing which values of n will result in a swimmer making the team. Graph the
solution.
65. Sam earned $450 during winter vacation. He needs to save $180 for a camping trip over spring
break. He can spend the remainder of the money on music. Write an inequality to show how
much he can spend on music. Then, graph the inequality.
66. Solve the inequality t – 7  –0.5 and graph the solutions.
67. Carlotta subscribes to the HotBurn music service. She can download no more than 16 song files
per week. Carlotta has already downloaded 13 song files this week. Write, solve, and graph an
inequality to show how many more songs Carlotta can download.
68. Rhonda has $465 in her saving account. She wants to save at least $625. Write and solve an
inequality to determine how much more money Rhonda must save to reach her goal. Let d
represent the amount of money in dollars Rhonda must save to reach her goal.
69. Solve the inequality and graph the solution.
70. Solve the inequality
 5 and graph the solutions.
71. Solve the inequality 3n  24 and graph the solutions.
72. Solve the inequality
 –2 and graph the solutions.
73. Solve the inequality –2i  –10 and graph the solutions.
74. Salar’s Choir class is performing a concert. He wants to buy as many tickets as he can afford. If
tickets cost $3.25 each and he has $14.25 to spend, how many tickets can he buy?
75. What is the greatest possible integer solution of the inequality
?
76. Solve the inequality 8b – 12  4 and graph the solutions.
77. Solve the inequality z – 11  3z  3 and graph the solutions.
78. A family travels to Bryce Canyon for three days. On the first day, they drove 150 miles. On the
second day, they drove 190 miles. What is the least number of miles they drove on the third day if
their average number of miles per day was at least 180?
79. Solve and graph
.
80. Mrs. Williams is deciding between two field trips for her class. The Science Center charges $80
plus $4 per student. The Dino Discovery Museum simply charges $6 per student. For how many
students will the Science Center charge less than the Dino Discovery Museum?
81. Solve the inequality
.
82. Solve
.
83. Solve and graph the solutions of the compound inequality
.
84. Solve and graph the compound inequality.
OR
85. Write the compound inequality shown by the graph.
–10 –9
–8
–7
–6
–5
–4
–3
–2
–1
0
1
2
86. Which of the following is a solution of
3
4
5
AND
6
7
8
9
10
x
?
87. Express the relation for the math test scoring system {(1, 2), (2, 3), (3, 5), (4, 10), (5, 5)} as a
table and as a graph.
88. Give the domain and range of the relation. Tell whether the relation is a function.
x
y
0
–4
1
0
2
3
3
4
89. Give the domain and range of the relation. Tell whether the relation is a function.
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
–4
–5
90. Determine a relationship between the x- and y-values. Write an equation.
1
2
3
4
x
–2
–1
0
1
y
91. For
92. Graph
, find
when x = 4.
for the domain D: {2, 1, 0, –1, –2}.
93. Graph the function
.
94. Graph the function
.
95. Use the graph of the function
2x + 1 to find the value of y when
.
y
6
5
4
3
2
1
–6 –5 –4 –3 –2 –1
–1
1
2
3
4
5
6
x
–2
–3
–4
–5
–6
96. Lionel observes that traffic is getting worse and it’s taking him longer to get to work. He records
once a week the following data for several weeks. Graph a scatter plot using the given data.
1
5.4
Week
Time (min)
2
5.3
3
7.2
4
6.1
5
8
6
6.9
7
8.8
8
8.7
97. Describe the correlation illustrated by the scatter plot.
y
11
10
9
8
7
6
5
4
3
2
1
1
2
3
4
5
6
7
8
9 10 11
x
98. Data was collected on the average winter temperature and the number of days with snow of a
random group of cities in the United States. Identify the correlation you would expect to see
between the average winter temperature and the number of days with snow.
99. Identify each graph as being a non-linear function, linear function, or not a function.
y
y
y
3
5
3
2
4
2
1
3
1
2
–3
–2
–1
–1
1
3 x
2
–2
1
–1
–1
–2
–1
1
x
101. Tell whether the function
is linear. If so, graph the function.
y
10
8
6
4
2
–2
–2
2
4
6
8
10
x
–4
–6
–8
–10
103. Find the x- and y-intercepts of
.
104. Use intercepts to graph the line described by the equation
105. Find the slope of the line.
y
8
6
4
2
(5, 0)
–8
–6
–4
4 x
satisfies a linear
102. Find the x- and y-intercepts.
–4
3
–3
100. Tell whether the set of ordered pairs
function. Explain.
–6
2
–2
–1
–3
–10 –8
1
–2
2
4
–2
–4
–6
–8
(3, –5)
6
8
x
.
106. Find the slope of the line.
y
10
8
(–8, 6)
6
4
2
–10 –8
–6
–4
(–8, –6)
–2
–2
2
4
6
8
10
x
–4
–6
–8
–10
107. Tell whether the slope of the line is positive, negative, zero, or undefined.
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
–4
–5
108. Find the slope of the line that contains
and
.
109. Find the slope of the line described by –5x + 6y = –60.
110. Tell whether the equation
variation.
represents a direct variation. If so, identify the constant of
111. Tell whether the relation is a direct variation. Explain.
x
y
–3
9
6
–18
7
–21
112. Graph the line with the slope  2 and y-intercept 3.
3
113. Write the equation that describes the line with slope =  3 and y-intercept =  2 in slope-intercept
form.
1
9
114. Write the equation that describes the line in slope-intercept form.
slope = –2, point (–4, 3) is on the line
115. Write the equation
equation.
in slope-intercept form. Then graph the line described by the
116. Graph the line with a slope of 1 that contains the point (6, 3).
117. Write an equation in slope-intercept form for the line that passes through (2, 5) and (6, 2).
118. A linear function has the same y-intercept as
Find the y-intercept and slope of the linear function.
and its graph contains the point
.
119. The equations of four lines are given. Identify which lines are parallel.
Line 1: y = 4x – 2
1
Line 2:
y + 4 = 7 (x – 4)
Line 3:
Line 4:
y = 7x – 7
1
x – 4 y = –7
120. Identify the lines that are perpendicular:
;
;
;
121. Write an equation in slope-intercept form for the line perpendicular to y = 8x – 3 that passes
through the point (–1, –3).
122. Describe the transformation from the graph of
to the graph of
2
123. Describe the transformation from the graph of
124. Graph
. Then reflect the graph of
describe the new graph.
125. Tell whether (2, 7) is a solution of
to the graph of g(x) = 3 x.
across the x-axis. Write a function
.
126.Graph the system of linear inequalities
127.Graph the system of linear inequalities
.
.
128. Graph the linear inequality y < 3x + 2. List all the steps to graph.
129.Graph 3x + 2y ≥ 6. List all steps to graph.
130. Is (-2, 4) a solution to y < 2x + 1?
131.Is (3, 1) a solution of y > x – 4 ?
.
to