MA27 Algebra - Mesa Public Schools each equation for the variable in italics in Questions 13–18. (3.7 ... and (3, 5) 31. (2, 3) and (6, 0) Please ... Solve each equation in Questions

MPS/Rev. Spring 2010

MA27 Algebra

2nd Semester Exam Review

Name:

�

x = 9

�

50

49

�

4x

6

Ê Ë

ˆ ¯

3

Please show all work, as modeled in class. (Chapter in McDougal Littell Algebra I)

MA27 Algebra • 2nd Semester Exam Review 1 MPS/Rev. Spring 2010

1. Simplify each expression. (1.2)

a) 24 = b) 70 = 2. Simplify each expression. (1.2)

a) 152 = b) “five cubed” = Evaluate each expression when x = –3 and y = 2 in Questions 3–4. (1.2) 3. 2x + 3y3 = 4. (3y)2 – (x + 5) = 5. Simplify each expression. (1.3)

a) 7 – 2(5 + 4) + 15

�

3 b)

�

14 ! 2 + 23

32

- (3 +1)

6. Which of these equations best describes the pattern in the table? (1.7) a) y = |5x|

b) y = x – 12

c) y = x2

d) y = 5x



Simplify each expression for Questions 7–12. (2.6) 7. a) –5(m – 3) b) 7x – x 8. 3(2x2 + 5x – 1) 9. 5y + 3x + 2y + 7x 10. 3 + 2x – 4y + 1 – 7x 11. 6(y – 2) + 3(y + 2) 12. 2(3x – 1) – (x + 1) Solve each equation for the variable in italics in Questions 13–18. (3.7) 13. d = rt 14. A = bh



15. P = a + b + c 16. P = 2L + 2w

17. A =

�

1

2bh

18.

�

x =a + b

2

19. Write the equation of the line. (4.2) Graph each equation for Questions 20–21. (4.6) 20. y = x – 3



21.

�

y =3

5x -1

Evaluate the function for the given value. (4.8) 22. 2( )f x x= find: ( 4), ( 1), (0), (7)f f f f- - 23. Which of the equations below matches this table? (4.8)

x 1 2 3 –1 –2 y 1 4 9 1 4

a) y = –x + 2 b) y = x2

c) y = 2x + 3 d) y = –x2

Write in slope-intercept form the equation of the line that passes through each point and has the given slope in Questions 24–25. (5.2)

24. (0, 4) slope =

�

1

2

25. (–2, –5) slope =

�

3

4



Write the equation of the line that passes through the given points in Questions 26–27. (5.3) 26. (0, 1) and (–2, 0) 27. (5, 4) and (–2, –4)

Write the equation of the line in point-slope form in Questions 28–29. (5.2–5.3)

28.

29. Write each equation in standard form using the information given in Questions 30-31. (5.6) 30. (–6, 2) and (3, 5) 31. (2, 3) and (6, 0)



State whether the two lines given are perpendicular, parallel, or intersecting in Questions 32-33. (5.3) 32. 5x + y = 9 y = –5x + 6 33. 3x + 2y = 6 4x + 3y = 12 Solve each inequality and graph for Questions 34–38. (6.1– 6.2)

34. 124

x£ -

35. 23 < –7 – 2y

36. –2(x + 5) > 4

37.

�

x

-2+11! 4



38. 2x + 7 < –9x + 7

Solve each equation in Questions 39–41. (6.4)

39. |x| = –16 40.

�

9x = 45

41.

�

x

4+ 6 = 7

42. A track meet had 9 people running the 200-meter race. How many different ways could

there be 1st, 2nd, and 3rd place winners?

a) 24 b) 81 c) 504 d) 84



Match the situation to a graph that might represent it in Questions 43–44.

43. You ride your bike to your friends house, but make 2 stops on the way. 44. You ride your bike in a race and when you reach your maximum speed you continue for the

remainder of the race at that speed. Solve each inequality and graph for Questions 45–46. (6.1–6.2)

45. –4z ≥ 32

46. 7y – 3 < –38



Solve each inequality and graph its solution for Questions 47–48. (6.3)

47. –4 < x + 11 < 3

48. 2x – 9 < 1 or x – 12 > 3

49. At Lunchies, the menu lists the following choices:

Lettuce: iceberg, spinach, romaine Toppings: cheese, peppers, olives, tomatoes Dressing: ranch, blue cheese, Italian

How many different outcomes for choosing a salad are there if one item is chosen from each group?

a) 12 b) 4

c) 10 d) 36 50. Use the graph to determine the solution to the system of linear equations. (7.1)

x + y = 1 2x – y = 2



51. Graph to determine the solution of the linear system of equations. (7.1)

x + 2y = 2 x – y = 2

52. Determine the solution of each linear system of equations. (7.2, 7.3, 7.5) a) x + 3y = 11 b) 2x – y = 2 –x + 3y = 7 4x + 3y = 9 Write a system of linear equations and solve for Questions 53–54. 53. The sum of two numbers is 154. The difference of the numbers is 38. Find the numbers. 54. A cash register contains $20.90 in dimes and quarters. If there are 119 coins in all, how

many of each coin are in the cash register?



Solve and graph each inequality for Questions 55–56. (6.1)

55. x > 15

56.

�

x

4£ -12

Simplify each expression for Questions 57–58. (8.1) 57. a) y • y b) z5 • z 58. a) 2a(3b)(5a) b) (2a3b)3 59. Simplify each expression. (8.2)

a) 80 b) 3–3 c) a–3b2


a)

�

y

y3

b)

�

3x4

9x




a)

�

9xy4

-18x b)

�

2x

3

Ê Ë

ˆ ¯

3

62. Multiply. Write your answer in scientific notation. (8.4)

(2.3 x 107) x (3.4 x 10–4)

63. Multiply. Write your answer in scientific notation. (8.4)

(5.8 x 105) x (9.1 x 1013)

64. Solve the inequality and graph. (6.1–6.2)

–2(x + 5) > 4

65. Determine whether the ordered pair is a solution to the system of linear equations.

x – y = –5 x + 2y = 4 (–2, 3)



66. Graph to determine the solution to the system of linear equation. (7.1) 2x + y = 4 –4x – 2y = –8

67. Determine the solution of the linear system of equations. (7.2–7.3, 7.5)

2x – 3y = –8 x + y = 1

Simplify each expression for Questions 68–69. (9.1–9.2) 68. a)

�

100 b)

�

45

69. a)

�

16

25 b)

�

50

49

Solve each equation. Write your answer in simplest radical form for Questions 70–71. (9.1) 70. a) x2 = 25 b) x2 = –9 71. a) 3x2 = 36 b) x2 – 24 = 0



Solve each equation. Write your answer in simplest radical form for Questions 72–73. (9.6) 72. x2 – 7x + 12 = 0 73. 2x2 – 5x – 1 = 0 Simplify each expression for Questions 74–75. (8.1–8.3)

74. a) m2 • m3 b) 2–3

75. a) 3

5

x

x b) 23

2

18

12

yx

xy

76. At Mesa Hot-Dog’s, the menu lists the following:

Dogs: regular, foot-long, bratwurst Buns: white, whole wheat Toppings: cheese, kraut, chili, onions, peppers

How many different outcomes for choosing a hot dog are there if one item is chosen from each group?

a) 15 b) 36 c) 24 d) 30



77. Simplify each expression by adding or subtracting. Write your answer in standard form. (10.1) a) (x2 – 4) + (2x2 + 6) b) (2x2 – x + 1) – (3x2 + x + 1)

Simplify each expression for Questions 78–81. (10.2) 78. –4(x2 + 1) 79. 5x(2x2 – 3x – 1) 80. (x + 7)(x + 3) 81. (3x + 1)(x – 4) Factor for Questions 82–84. (10.5–10.7)

82. a) x2 + 7x + 6 b) x2 + 10x + 21 83. a) x2 – 5x + 6 b) x2 + 3x – 10 84. a) x2 – 4x – 21 b) x2 – 25



85. Factor completely. (10.6) 3x2 – 18x + 27

Solve each inequality and graph the solution for Question 86–87. (6.1-6.3)

86. 4112

!+-

x

87. –3x ≥ 18 or 4x + 7 ≥ 15

88. Simplify each expression. (8.1, 8.3, 9.2)

a) 3x • 5y b) (4x2)3

c) ba

ba

3

22

20

8 d) 225



Solve each equation. Write your answer in simplest radical form for Questions 89–90. (9.1, 9.6) 89. x2 = 18 90. x2 + 7x + 10 = 0 91. At Chandler Bike Shop, the following choices are available for bikes:

Bike: 2 speed, 3 speed, 10 speed Colors: blue, red, black, silver, gold, green

How many different outcomes are there for choosing a bike?

a) 18 b) 15 c) 12 d) 24

Simplify the expression if possible for Questions 92–94. (11.4)

92. 48

12x

93. xx

x

5

6

2+

94. xx

x

93

124

2-

-



95. Graph to determine the solution to the system of linear equation. (7.1)

3x – y = –2 x – 3y = 2

Simplify the expression for Questions 96–98. (12.2)

96. 7875 + 97. 12233 - 98. )524(5 - Solve each equation for Questions 99–100. (12.3)

99. 9=x

100. 016 =-x

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MA27 Algebra - Mesa Public Schools each equation for the variable in italics in Questions 13–18. (3.7 ... and (3, 5) 31. (2, 3) and (6, 0) Please ... Solve each equation in Questions