Name: Class: Date: Finite Summer 2017
Write an algebraic expression to represent each verbal expression.
1. 2 more than the quotient of a number and 5
2. the sum of two consecutive integers
3. 5 times the sum of a number and 1
4. 1 less than twice the square of a number
Write a verbal sentence to represent each equation.
5. 5 – 2x = 4
6. 3y = 4y3
7. 3c = 2(c – 1)
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Name: Class: Date: Finite Summer 2017
Solve each equation.
9. 14 = 8 – 6r
10. 9 + 4n = –59
11. 12. 13. –1.6r + 5 = –7.8
14. 6x – 5 = 7 – 9x
15. 5(6 – 4v) = v + 21
16. 6y – 5 = –3(2y + 1)
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Name: Class: Date: Finite Summer 2017
Solve each equation or formula for the specified variable.
17. E = mc2, for m
18. , for d
19. h = vt – gt2, for v
20. , for I
21. GEOMETRY The length of a rectangle is twice the width. Find the width if the perimeter is 60 centimeters. Define
a variable, write an equation, and solve the problem.
22. GOLF Luis and three friends went golfing. Two of the friends rented clubs for $6 each. The total cost of the rented
clubs and the green fees for each person was $76. What was the cost of the green fees for each person? Define a
variable, write an equation, and solve the problem.
Write an equation in slope-intercept form for the line described.
23. slope 2, y-intercept at 0
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Name: Class: Date: Finite Summer 2017
24. parallel to y = 4x + 2, y-intercept at 4
25. perpendicular to , passes through (0, 0)
26. parallel to y = –3x + 4, x-intercept at 4
27. perpendicular to , passes through (2, 3)
28. slope , x-intercept at 3
Write an equation in slope-intercept form for each graph.
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Name: Class: Date: Finite Summer 2017
30. 31. Write an equation in slope-intercept form for the line that satisfies each set of conditions.
32. slope –5, passes through (–3, –8)
33. slope , passes through (10, –3)
34. slope 0, passes through (0, –10)
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Name: Class: Date: Finite Summer 2017
35. slope , passes through (6, –8)
36. parallel to y = 4x – 5, y-intercept at –6
37. slope , x-intercept at –1
38. perpendicular to y = 3x – 2, passes through (6, –1)
39. parallel to , x-intercept at 9
40. passes through (–8, –7), perpendicular to the graph of y = 4x – 3
41. RESERVOIRS The surface of Grand Lake is at an elevation of 648 feet. During the current drought, the water
level is dropping at a rate of 3 inches per day. If this trend continues, write an equation that gives the elevation in feet
of the surface of Grand Lake after x days.
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Name: Class: Date: Finite Summer 2017
Write a quadratic equation in standard form with the given root(s). Example: Given 1, -3 then (X-1)(X+3)
then multiplying it together you get . Think of X=1 and X= -3 then adding -1 to one and +3
to the other gives you your 2 terms. If you have a fractions then move the denominator over next to the
variable such as (
42. 7, 2
43. 0, 3
44. –5, 8
45. –7, –8
46. –6, –3
47. 3, –4
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Name: Class: Date: Finite Summer 2017
48. 1, 49. , 2
50. 0, Factor each polynomial.
51. r3 + 3r2 – 54r
52. 8a 2 + 2a – 6
53. c2 – 49
54. 16r2 – 169
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Name: Class: Date: Finite Summer 2017
55. b 4 – 81
Solve each equation by factoring or quadratic formula
56. x2 – 4x – 12 = 0
57. x2 – 16x + 64 = 0
58. x2 – 6x + 8 = 0
59. x2 + 3x + 2 = 0
60. x2 – 4x = 0
61. 7x2 = 4x
62. 10x2 = 9x
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Name: Class: Date: Finite Summer 2017
63. x2 = 2x + 99
64. x2 + 12x = –36
65. 5x2 – 35x + 60 = 0
66. 36x2 = 25
67. 2x2 – 8x – 90 = 0
68. NUMBER THEORY Find two consecutive even positive integers whose product is 624.
69. NUMBER THEORY Find two consecutive odd positive integers whose product is 323.
70. GEOMETRY The length of a rectangle is 2 feet more than its width. Find the dimensions of the rectangle if its area
is 63 square feet.
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Name: Class: Date: Finite Summer 2017
71. PHOTOGRAPHY The length and width of a 6-inch by 8-inch photograph are reduced by the same amount to
make a new photograph whose area is half that of the original. By how many inches will the dimensions of the
photograph have to be reduced?
Solve each equation by using the Quadratic Formula or factoring. If it does not factor, leave solutions in
radical form reduced.
72. 7x2 – 5x = 0
73. 4x2 – 9 = 0
74. 3x2 + 8x = 3
75. x2 – 21 = 4x
76. 3x2 – 13x + 4 = 0
77. 15x2 + 22x = –8
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Name: Class: Date: Finite Summer 2017
78. x2 – 6x + 3 = 0
79. x2 – 14x + 53 = 0
80. 3x2 = –54
81. 25x2 – 20x – 6 = 0
82. 4x2 – 4x + 17 = 0
83. 8x – 1 = 4x2
84. x2 = 4x – 15
85. 4x2 – 12x + 7 = 0
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Name: Class: Date: Finite Summer 2017
Complete parts a–c for each quadratic equation.
a. Find the value of the discriminant. Value = b. Describe the number and type of roots. IF value < 0 No real solutions. IF value = 0, 1 real solution, or
if value >0 then 2 real solutions.
86. x2 – 16x + 64 = 0
87. x2 = 3x
88. 9x2 – 24x + 16 = 0
89. x2 – 3x = 40
90. 3x2 + 9x – 2 = 0
91. 2x2 + 7x = 0
92. 5x2 – 2x + 4 = 0
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Name: Class: Date: Finite Summer 2017
93. 12x2 – x – 6 = 0
94. 7x2 + 6x + 2 = 0
95. 12x2 + 2x – 4 = 0
96. 6x2 – 2x – 1 = 0
97. x2 + 3x + 6 = 0
98. 4x2 – 3x – 6 = 0
99. 16x2 – 8x + 1 = 0
100. 2x2 – 5x – 6 = 0
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Name: Class: Date: Finite Summer 2017
101. GRAVITATION The height h(t) in feet of an object t seconds after it is propelled straight up from the ground with
an initial velocity of 60 feet per second is modeled by the equation h(t) = –16t2 + 60t. At what times will the object
be at a height of 56 feet?
102. STOPPING DISTANCE The formula d = 0.05s2 + 1.1s estimates the minimum stopping
distance d in feet for a car traveling s miles per hour. If a car stops in 200 feet, what is the
fastest it could have been traveling when the driver applied the brakes?
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Name: Class: Date: Finite Summer 2017
Answer Key
1. 2. n + (n + 1)
3. 5(m + 1)
4. 2y2 – 1
5. The difference of 5 and twice a number is 4.
6. Three times a number is 4 times the cube of the number.
7. Three times a number is twice the difference of the number and 1.
8. The quotient of a number and 5 is 3 times the sum of twice the number and 1.
9. –1
10. –17
11. 12. 13. 8
14. 15. 16. 17. 18. 19. 20. 21. w = width; 2(2w) + 2w = 60; 10 cm
22. g = green fees per person; 6(2) + 4g = 76; $16
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Name: Class: Date: Finite Summer 2017
23. y = 2x
24. y = 4x + 4
25. y = –4x
26. y = –3x + 12
27. y = 2x – 1
28. 29. y = 2
30. 31. 32. y = –5x – 23
33. 34. y = –10
35. 36. y = 4x – 6
37. 38. 39. 40. 41. y = –0.25x + 648
42. x2 – 9x + 14 = 0
43. x2 – 3x = 0
44. x2 – 3x – 40 = 0
45. x2 + 15x + 56 = 0
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Name: Class: Date: Finite Summer 2017
46. x2 + 9x + 18 = 0
47. x2 + x – 12 = 0
48. 2x2 – 3x + 1 = 0
49. 3x2 – 7x + 2 = 0
50. 2x2 + 7x = 0
51. r(r + 9)(r – 6)
52. 2(4a – 3)(a + 1)
53. (c – 7)(c + 7)
54. (4r + 13)(4r – 13)
55. (b 2 + 9)(b + 3)(b – 3)
56. {6, –2}
57. {8}
58. {2, 4}
59. {–2, –1}
60. {0, 4}
61. 62. 63. {–9, 11}
64. {–6}
65. {3, 4}
66. 67. {9, –5}
68. 24, 26
69. 17, 19
70. 7 ft by 9 ft
71. 2 in.
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Name: Class: Date: Finite Summer 2017
72. 73. 74. 75. –3, 7
76. 77. 78. 79. 7 ± 2i
80. 81. 82. 83. 84. 85. 86. 0; 1 rational; 8
87. 9; 2 rational; 0, 3
88. 0; 1 rational; 89. 169; 2 rational; –5, 8
90. 105; 2 irrational; 91. 49; 2 rational; 0, Powered by Cognero
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Name: Class: Date: Finite Summer 2017
92. −76; 2 complex; 93. 289; 2 rational; 94. ; 2 complex; 95. 196; 2 rational; 96. 28; 2 irrational; 97. −15; 2 complex; 98. 2 irrational; 99. 0; 1 rational; 100. 23; 2 irrational; 101. 1.75 s, 2 s
102. about 53.2 mi/h
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