Name______Per______Date______
Final Review
____ 1. Which graph represents a function?
a. b. c. d.
____ 2. Which situation best describes a positive correlation?
a.The amount of gasoline in a car and how far the car has traveled b.The temperature on Tuesdays c.The size of a sundae and the amount of calories it contains d.The size of a snowball and how long it has been melting
3. Give two ways to write the algebraic expression m ¸ 27 in words.
4. Julia wrote 14 letters to friends each month for y months in a row. Write an expression to show how many total letters Julia wrote.
5. Evaluate the expression y + b for y = 5 and b = 2.
6. Evaluate the expression z – f for z = 4 and f = 1.
7. Evaluate the expression xy for x = 6 and y = 3.
8. Evaluate the expression a ¸ b for a = 24 and b = 8.
9. Evaluate the expression for and .
10. Add.
34 + (–21)
11. Evaluate x + (–9) for x = 35.
12. Subtract.
–5 – (–8)
13. Evaluate x – (–10) for x = 12.
14. The highest temperature recorded in the town of Westgate this summer was 101ºF. Last winter, the lowest temperature recorded was –9ºF. Find the difference between these extremes.
15. 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 470 feet tall and the elevator descends 530 feet from top to bottom, how far underground does the parking garage go?
16. Multiply.
–8 • 9
17. Evaluate –5u for u = –4.
18. Divide.
–48 8
19. Evaluate k (–11) for k = –33.
20. Divide.
21. Divide.
0 ¸ 5.928
22. Carina hiked at Yosemite National Park for 1.75 hours. Her average speed was 3.5 mi/h. How many miles did she hike?
23. Simplify .
24. Simplify .
25. Simplify .
26. Simplify .
27. Simplify .
28. Simplify .
29. Evaluate for x = 9.
30. Evaluate 1 + x2 • 6 for x = 4.
31. Simplify the expression .
32. Translate the word phrase, the product of 8.5 and the difference of –4 and –8, into a numerical expression.
33. Simplify the expression .
34. Simplify by combining like terms.
35. Graph the point (1, 4).
36. Name the quadrant where the point (–3, 2) is located.
37. Name the quadrant where the point (–1, 0) is located.
38. A phone company advertises a new plan in which the customer pays a fixed amount of $25 per month for unlimited calls in the country, and $0.10 per minute for international calls. Find a rule for the monthly payment a customer pays according to the new plan. Write ordered pairs for the monthly payment when the customer uses 90, 120, 145, and 150 international minutes in a month.
39. Solve .
40. Solve .
41. Solve –14 + s = 32.
42. A toy company's total payment for salaries for the first two months of 2005 is $21,894. Write and solve an equation to find the salaries for the second month if the first month’s salaries are $10,205.
43. Solve 3n = 42.
44. Solve .
45. If , find the value of .
46. Solve .
47. Solve .
48. Solve .
49. Sara needs to take a taxi to get to the movies. The taxi charges $4.00 for the first mile, and then $2.75 for each mile after that. If the total charge is $20.50, then how far was Sara’s taxi ride to the movie?
50. If 8y – 8 = 24, find the value of 2y.
51. 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?
52. Solve .
53. Solve .
54. Solve . Tell whether the equation has infinitely many solutions or no solutions.
55. A video store charges a monthly membership fee of $7.50, but the charge to rent each movie is only $1.00 per movie. Another store has no membership fee, but it costs $2.50 to rent each movie. How many movies need to be rented each month for the total fees to be the same from either company?
56. A professional cyclist is training for the Tour de France. What was his average speed in miles per hour if he rode the 120 miles from Laval to Blois in 4.7 hours? Use the formula , and round your answer to the nearest tenth.
57. The formula for the resistance of a conductor with voltage V and current I is . Solve for V.
58. Solve for x.
59. The fuel for a chain saw is a mix of oil and gasoline. The ratio of ounces of oil to gallons of gasoline is 7:19. There are 38 gallons of gasoline. How many ounces of oil are there?
60. Ramon drives his car 150 miles in 3 hours. Find the unit rate.
61. Solve the proportion .
62. An architect built a scale model of a shopping mall. On the model, a circular fountain is 20 inches tall and 22.5 inches in diameter. If the actual fountain is to be 8 feet tall, what is its diameter?
63. Find the value of MN if cm, cm, and cm.
ABCD LMNO
64. On a sunny day, a 5-foot red kangaroo casts a shadow that is 7 feet long. The shadow of a nearby eucalyptus tree is 35 feet long. Write and solve a proportion to find the height of the tree.
65. Find 55% of 125.
66. What percent of 74 is 481? If necessary, round your answer to the nearest tenth of a percent.
67. 66 is 56% of what number? If necessary, round your answer to the nearest hundredth.
68. After 6 months the simple interest earned annually on an investment of $8000 was $975. Find the interest rate to the nearest tenth of a percent.
69. Hidemi is a waiter. He waits on a table of 4 whose bill comes to $69.98. If Hidemi receives a 20% tip, approximately how much will he receive?
70. Find the percent change from 24 to 72. Tell whether it is a percent increase or decrease. If necessary, round your answer to the nearest percent.
71. Find the result when 28 is decreased by 25%.
72. The price of a train ticket from Atlanta to Oklahoma City is normally $117.00. However, children under the age of 16 receive a 70% discount. Find the sale price for someone under the age of 16.
73. Describe the solutions of in words.
74. Graph the inequality m –3.4.
75. Write the inequality shown by the graph.
76. 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.
77. 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.
78. Solve the inequality n + 6 –1.5 and graph the solutions.
79. Carlotta subscribes to the HotBurn music service. She can download no more than 11 song files per week. Carlotta has already downloaded 8 song files this week. Write, solve, and graph an inequality to show how many more songs Carlotta can download.
80. Denise has $365 in her saving account. She wants to save at least $635. Write and solve an inequality to determine how much more money Denise must save to reach her goal. Let d represent the amount of money in dollars Denise must save to reach her goal.
81. Solve the inequality and graph the solution.
82. Solve the inequality 3 and graph the solutions.
83. Solve the inequality 2m £ 18 and graph the solutions.
84. Solve the inequality £ 2 and graph the solutions.
85. Solve the inequality 2f ³ –8 and graph the solutions.
86. Marco’s Drama class is performing a play. He wants to buy as many tickets as he can afford. If tickets cost $2.50 each and he has $14.75 to spend, how many tickets can he buy?
87. Solve the inequality n – 4 3 and graph the solutions.
88. Solve the inequality z + 8 z £ –4 and graph the solutions.
89. Solve and graph .
90. Mrs. Williams is deciding between two field trips for her class. The Science Center charges $135 plus $3 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?
91. Solve the inequality and graph the solution.
92. Solve the inequality .
93. Jamie throws a ball up into the air. Sketch a graph for the situation that describes the distance of the ball from the ground at every second since it was thrown up. Tell whether the graph is continuous or discrete.
94. 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.
95. Give the domain and range of the relation.
x / y5 / 11
6 / 13
0 / 0
–8 / –15
96. Give the domain and range of the relation.
97. Give the domain and range of the relation.
98. Give the domain and range of the relation.
99. Give the domain and range of the relation. Tell whether the relation is a function.
x / y0 / –5
1 / –1
1 / 3
1 / 6
100. Give the domain and range of the relation. Tell whether the relation is a function.
101. Determine a relationship between the x- and y-values. Write an equation.
x / 1 / 2 / 3 / 4y / 4 / 5 / 6 / 7
102. Identify the independent and dependent variables in the situation.
The amount of electricity used for air conditioning in homes increases as the temperature increases.
103. Identify the independent and dependent variables in the situation.
As Kyoko works more hours, her total pay increases.
104. A video club costs $25 to join. Each video that is rented costs $2.50. Let v represent the number of videos. Identify the independent and dependent variables. Then, write a rule in function notation for the situation.
105. For , find when x = –1.
106. Graph the function .
107. Use the graph of the function 2x + 2 to find the value of y when .
108. The temperature of air in a room that began at F is increasing by F per hour. Write a function that describes the temperature of the air over time. Graph the function to show the temperatures over the first 10 hours.
109. Graph a scatter plot using the given data.
x / 3 / 6 / 5 / 2 / 7 / 4 / 8 / 1y / 5 / 7.5 / 5 / 2.5 / 8 / 5.5 / 10 / 1.5
110. Describe the correlation illustrated by the scatter plot.
111. Data was collected on the number of pets and the height of a random group of students. Identify the correlation you would expect to see between the number of pets and the height.
112. Identify each graph as being a non-linear function, linear function, or not a function.
Graph A Graph B Graph C
113. Tell whether the set of ordered pairs satisfies a linear function. Explain.
114. Tell whether the function is linear. If so, graph the function.
115. Find the x- and y-intercepts.
116. Find the x- and y-intercepts of .
117. Use intercepts to graph the line described by the equation .
118. This table shows the number of swimmers in the ocean at a given time. Find the rate of change for each time period. During which period did the number of swimmers increase at the fastest rate?
Time / 10:30 am / 12:30 pm / 1:30 pm / 3:30 pm / 5:30 pmNumber of swimmers / 41 / 55 / 64 / 70 / 80
119. Find the slope of the line.
120. Find the slope of the line.
121. Tell whether the slope of the line is positive, negative, zero, or undefined.
122. Find the slope of the line that contains and .
123. The graph shows a linear relationship. Find the slope.
124. Tara creates a budget for her weekly expenses. The graph shows how much money is in the account at different times. Find the slope of the line. Then tell what rate the slope represents.
125. Find the slope of the line described by x – 3y = –6.
126. Graph the line with the slope and y-intercept –2.
127. Write the equation that describes the line with slope = and y-intercept = in slope-intercept form.
128. Write the equation that describes the line in slope-intercept form.
slope = 4, point (3, –2) is on the line
129. Write the equation in slope-intercept form. Then graph the line described by the equation.
130. The water level of a river is 34 feet and it is receding at a rate of 0.5 foot per day. Write an equation that represents the water level, w, after d days. Identify the slope and y-intercept and describe their meanings. In how many days will the water level be 26 feet?
131. Graph the line with a slope of that contains the point (3, –7).
132. Write an equation in point-slope form for the line that has a slope of and contains the point (–8, –7).
133. Write an equation in slope-intercept form of the line with slope that contains the point (2, 3).
134. Write an equation in slope-intercept form for the line that passes through (3, 7) and (7, 4).
135. A linear function has the same y-intercept as and its graph contains the point . Find the y-intercept and slope of the linear function.
136. The equations of four lines are given. Identify which lines are parallel.
Line 1: / y = x + 6Line 2: / x + y = –6
Line 3: / y = x – 8
Line 4: / y + 7 = (x + 4)
137. Identify the lines that are perpendicular:
; ; ;
138. Write an equation in slope-intercept form for the line parallel to y = x – 2 that passes through the point (8, –2).
139. Describe the transformation from the graph of to the graph of .
140. Describe the transformation from the graph of to the graph of g(x) = x.
141. Graph . Then reflect the graph of across the x-axis. Write a function to describe the new graph.
142. Graph and . Then describe the transformation from the graph of to the graph of .
143. A music club charges an initial joining fee of $20.00. The cost per CD is $10.25. The graph shows the cost of belonging to the club as a function of CDs purchased. How will the graph change if the cost per CD goes up by $2.00? (The new function is shown by the dotted line.)