Final Review 1st semester
Short Answer
1.Evaluate the expression ab for a = 54and b = 6.
2. Evaluate the expression for and .
3. Evaluate x – (–15) for x = –12.
- The elevator in 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?
5.Divide.
0 (–11.346)
6. Simplify .
- Evaluate for x = 5.
8.Simplify by combining like terms.
9.Name the quadrant where the point (3, 0) is located.
10. Solve –7 + x = 34.
11. Solve .
12.Solve .
13.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?
14.Solve .
15.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.
16.Solve the proportion
17.Which equation does not represent the same linear function as the other 3?
y = 1/3 x – 7y = 3x – 7
-9x + 3y = -21y – 5 = 3(x – 4)
18. 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.
- 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.
20.Solve the inequality 5 and graph the solutions.
21.Solve the inequality –2i –10 and graph the solutions.
22. Solve the inequality b – 12 4 and graph the solutions.
23.Solve and graph .
24.Solve .
25.Give the domain and range of the relation. Tell whether the relation is a function.
x / y0 / –4
1 / 0
2 / 3
3 / 4
26.For , find when x = 4.
- Graph the function .
- Describe the correlation illustrated by the scatter plot.
29.Tell whether the set of ordered pairs satisfies a linear function. Explain.
30.Find the x- and y-intercepts of .
31. Find the slope of the line.
32.Find the slope of the line described by –5x + 6y =60.
33.Graph the line with the slope and y-intercept 3.
34.Write the equation in slope-intercept form. Then graph the line described by the equation.
35.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.
- Write an equation in slope-intercept form for the line perpendicular to y = x – 3 that passes through the point (–1, –3).
37.Graph . Then reflect the graph of across the y-axis. Write a function to describe the new graph.
38.Triscored 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.
- Evaluate x + (–36) for x = 44.
40.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.
41.Evaluate –11p for p = 5.
42. 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?
43.Simplify .
- Simplify .
45.Evaluate 1 + c2 • 6 for c = 4.
46.Graph the point (–2, –1).
- Solve .
48.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.
- Solve .
- Solve .
- If 2x – 6 = 24, find the value of 3x.
- Solve .
53.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?
54.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?
55. 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.
- 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.
61.Solve the inequality 3n 24 and graph the solutions.
62.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?
63.Solve the inequality z – 11 z 3 and graph the solutions.
- Mrs. Williams is deciding between two field trips for her class. The ScienceCenter charges$80 plus $4 per student. The DinoDiscoveryMuseum simply charges $6 per student. For how many students will the ScienceCenter charge less than the DinoDiscoveryMuseum?
65.Give the domain and range of the relation. Tell whether the relation is a function.
66.Graph for the domain D: {2, 1, 0, –1, –2}.
x / y67. Use the graph of the function 2x + 1 to find the value of y when x = -2.
68.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.
69.Tell whether the function is linear. If so, graph the function.
70.Use intercepts to graph the line described by the equation .
71.Tell whether the slope of the line is positive, negative, zero, or undefined.
72.Tell whether the equation represents a direct variation. If so, identify the constant of variation.
73. Write the equation that describes the line with slope = and y-intercept = in slope-intercept form.
74. Graph the line with a slope of that contains the point (6, 3).
75. The equations of four lines are given. Identify which lines are parallel.
Line 1: / y = x – 2Line 2: / y + 4 = x - 4
Line 3: / y = x – 7
Line 4: / x – y = –7
76. Describe the transformation from the graph of to the graph of .
77. Salvadorreads 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.
78.Subtract.
2 – (–10)
79. 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.
80. Evaluate k (–10) for k = 80.
81.Simplify .
82.Simplify .
83. Simplify .
84.Simplify the expression
85. Name the quadrant where the point (4, 4) is located.
86. Solve .
87.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.)
88. If , find the value of .
89. Solve .
90. 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?
- Solve . Tell whether the
equation has infinitely many solutions or no solutions.
92.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?
93.Find the value of MN if cm, cm, and cm.
ABCD LMNO
94.Write the inequality shown by the graph.
95.Solve the inequality t – 7 –0.5 and graph the solutions.
96. Solve the inequality and graph the solution.
97.Solve the inequality –2 and graph the solutions.
98. Solve the inequality .
99.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.
x / y100.Determine a relationship between the x- and y-values. Write an equation.
x / 1 / 2 / 3 / 4y / –2 / –1 / 0 / 1
101.Graph the function .
102. Identify eachgraph as being a non-linear function, linear function, or not a function
103.Find the x- and y-intercepts.
104.Find the slope of the line.
105.Find the slope of the line that contains and .
106.Tell whether the relation is a direct variation. Explain.
x / –3 / 6 / 7y / 9 / –18 / –21
107. Write the equation that describes the line in slope-intercept form.
slope = –2, point (–4, 3) is on the line
108. Write an equation in slope-intercept form for the line that passes through (2, 5) and (6, 2).
109. Identify the lines that are perpendicular:
; ; ;
110. Graph
111. The relation between the number of hours a student works, h and the amount of money the student earns, m, is given by the function m = 8.50h. In this relation, what is the dependent variable?
112. Write the equation of the function thatwould pass through the points (-2, 12) and (2, 12).
113. 113. Tell whether the ordered pair (–2, 4) is a solution of the system .
114.Solve the system by graphing
115.Solve by using substitution. Express your answer as an ordered pair.
116.Solve by using elimination. Express your answer as an ordered pair.
117.Tell whether (2, 11) is a solution of .
118.Graph the system of linear inequalities
119. Tell whether the ordered pair (2, 10) is a solution of the system.
120.Solve the system by graphing.
121. Solve by using substitution. Express your answer as an ordered pair.
122.
122. Solve by using elimination. Express your answer as an ordered pair.
113.
123. Tell whether (-3, 5) is a solution of.
124.Graph the system of linear inequalities .