Final Review 1St Semester

Final Review 1st semester 12. Solve .

Short Answer 13. Sara needs to take a taxi to get to the movies. The taxi charges $3.00 for the first mile, and then 1. Evaluate the expression a  b for a = 54 and b = 6. $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? 2. Evaluate the expression for and .

3. Evaluate x – (–15) for x = –12. 14. Solve . 4. 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 15. A professional cyclist is training for the Tour de top to bottom, how far underground does the France. What was his average speed in kilometers parking garage go? 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. 5. Divide. 0  (–11.346)

6. Simplify .

7. Evaluate for x = 5.

8. Simplify by combining like terms. 16. Solve the proportion

9. Name the quadrant where the point (3, 0) is 17. Which equation does not represent the same linear located. function as the other 3? y = 1/3 x – 7 y = 3x – 7

10. Solve –7 + x = 34. -9x + 3y = -21 y – 5 = 3(x – 4)

11. Solve . 18. To join the school swim team, swimmers must be 23. Solve and graph . 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.

24. Solve .

19. 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, 25. Give the domain and range of the relation. Tell solve, and graph an inequality to show how whether the relation is a function. many more songs Carlotta can download. x y 0 –4 1 0 2 3 3 4

26. For , find when x = 4.

20. Solve the inequality  5 and graph the y=2 x + 2 27. Graph the function . solutions.

21. Solve the inequality –2i  –10 and graph the solutions.

22. Solve the inequality 8b – 12  4 and graph the solutions. 28. Describe the correlation illustrated by the scatter 32.Find the slope of the line described by –5x + 6y =60. plot.

11 10 33. Graph the line with the slope  3 and y-intercept 3. 9 2 8 7 6 5 4 3 2 1

1 2 3 4 5 6 7 8 9 10 11 x 34. Write the equation in slope- intercept form. Then graph the line described by the equation. 29. Tell whether the set of ordered pairs

satisfies a linear function. Explain.

30. Find the x- and y-intercepts of . 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.

31. Find the slope of the line.

y 36. Write an equation in slope-intercept form for the 10 line perpendicular to y = 8x – 3 that passes

8 through the point (–1, –3). (–8, 6) 6

–10 –8 –6 –4 –2 2 4 6 8 10 x –2

–4 (–8, –6) 37. Graph . Then reflect the graph of –6 across the y-axis. Write a function to –8 describe the new graph. –10 45. Evaluate 1 + c2 • 6 for c = 4.

46. Graph the point (–2, –1). 38. 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.

47. Solve .

39. Evaluate x + (–36) for x = 44.

48. A toy company's total payment for salaries for the first two months of 2005 is $22,894. Write and 40. The highest temperature recorded in the town of solve an equation to find the salaries for the Westgate this summer was 94ºF. Last winter, the second month if the first month’s salaries are lowest temperature recorded was –1ºF. Find the $11,955. difference between these extremes.

41. Evaluate –11p for p = 5. 49. Solve . 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?

50. Solve .

43. Simplify .

44. Simplify . 51. If 2x – 6 = 24, find the value of 3x. 61. Solve the inequality 3n  24 and graph the solutions. 52. Solve . 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?

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? 63. Solve the inequality z – 11  3z  3 and graph the solutions.

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? 64. 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 55. Sam earned $450 during winter vacation. He Science Center charge less than the Dino needs to save $180 for a camping trip over spring Discovery Museum? 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.

65. Give the domain and range of the relation. Tell whether the relation is a function.

5 56. Rhonda has $465 in her saving account. She wants to save at least $625. Write and 4 solve an inequality to determine how 3 much more money Rhonda must save to 2 reach her goal. Let d represent the amount 1 of money in dollars Rhonda must save to –5 –4 –3 –2 –1 1 2 3 4 5 x reach her goal. –1

–5 66. Graph for the domain D: {2, 1, 0, –1, 70. Use intercepts to graph the line described by the –2}. equation .

67.Use the graph of the function 2x + 1 to find the value of y when x = -2.

y 6 71. Tell whether the slope of the line is positive, 5 negative, zero, or undefined. 4 y 3 2 5 1 4 3 –6 –5 –4 –3 –2 –1–1 1 2 3 4 5 6 x 2 –2 1 –3 –4 –5 –4 –3 –2 –1 1 2 3 4 5 x –5 –1 –6 –2

68. Data was collected on the average winter temperature and the number of days with snow of 72. Tell whether the equation represents a a random group of cities in the United States. direct variation. If so, identify the constant of Identify the correlation you would expect to see variation. between the average winter temperature and the number of days with snow.

73. Write the equation that describes the line with 69. Tell whether the function is linear. If 1 9 so, graph the function. slope =  3 and y-intercept =  2 in slope-intercept form. 74.Graph the line with a slope of 1 that contains the point 79. The temperature on the ground during a plane’s (6, 3). 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 .

75.The equations of four lines are given. Identify which 82. Simplify . lines are parallel. Line y = 4x – 2 1: 83. Simplify . Line 1 y + 4 = x - 4 2: 7 Line y = 7x – 7 3: Line 1 2 x – y = –7 6+ 2 4: 4 84. Simplify the expression +(2 - 18) 2

76. Describe the transformation from the graph of to the graph of .

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 77. Salvador reads 11 books from the library each score is 32. Write and solve an equation to find month for p months in a row. Write an expression the highest score. (Hint: In a data set, the range is to show how many books Salvador read in all. the difference between the highest and the lowest Then, find the number of books Salvador read if values.) he read for 7 months. 88. If , find the value of .

78. Subtract. 2 – (–10) 89. Solve . 96.Solve the inequality and graph the solution. 90. The formula gives the profit p -x + 3 1 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?

97. Solve the inequality  –2 and graph the solutions.

91. 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?

98. Solve the inequality .

93. Find the value of MN if cm, cm, and cm. 99. Express the relation for the math test scoring ABCD LMNO system {(1, 2), (2, 3), (3, 5), (4, 10), (5, 5)} as a table and as a graph.

94. Write the inequality shown by the graph.

–7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 m 100. Determine a relationship between the x- and y- values. Write an equation.

95. Solve the inequality t – 7  –0.5 and graph the x 1 2 3 4 solutions. y –2 –1 0 1

101. Graph the function . 103. Find the x- and y-intercepts.

–10 –8 –6 –4 –2 2 4 6 8 10 x –2

102. Identify each graph as being a non-linear 104. Find the slope of the line. function, linear function, or not a function y 8 y y 3 5 6

2 4 4 1 3 2 2 (5, 0) –3 –2 –1 1 2 3 x –1 1 –8 –6 –4 –2 2 4 6 8 x –2 –2 –1 1 x –3 –1 –4 y 3 –6 (3, –5) 2 –8 1

–2 –1 1 2 3 4 x –1 105. Find the slope of the line that contains –2 and . –3

106. Tell whether the relation is a direct variation. Explain.

x –3 6 7 y 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 y�3 x 5

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 that would pass through the points (-2, 12) and (2, 12).