Download TAKE HOME FINAL

Name: ________________________
Date: ____________ Spring 2013
Algebra CD Pre-Test Final
Write the answer in the answer column at the right. Be sure to show ALL your
work, every step, for each problem or you will receive NO credit.
ANSWERS:
Simplify. Assume that no denominator is equal to zero. (8.1, 8.2)
1. y5  y3
2. (9c3 d5 )(-2cd2 )
3. (2w5 y4 ) 3
p 6q 2
4. 3
pq
5. 16r3 s-5
4r-1 s2
6. (-8x2 y2 ) 2
(4x3 y) 3

1. ______________
2. ______________
3. _______________
4. _______________
5. _______________
6. _______________
Simplify. (8.5, 8.6)
7. (11m2 – 2mp + 8p2) + (8m2 + 4mp – 2p2 )
7. _______________
8. (x + 9) – (x + 6)
8. _______________
9. 3xy(2x2 + 5xy – 7y2 )
9. _______________
10. 4c2 (c + 6) – 3c(2c2 – 3c + 1)
10. ______________
Page 1
Take Home Final Algebra CD
Solve. (8.6)
11. m(m – 5) + 8m = m(m + 2) – 4
ANSWERS:
11. ______________
Find each product. (8.7, 8.8)
12. (2x – y)(3x + 4y)
13. (2m + 2)(m2 – 2m + 3)
12. ______________
13. ______________
14. (5c – 4)2
15. (3a – 4b)(3a + 4b)
14. ______________
15. ______________
Find the prime factorization of each integer. (9.1)
16. 531
17. 1160
16. ______________
17. ______________
18. Factor completely: 168pq2r
18. ______________
Find the GCF of the given monomials.
19. –24, 36
20. 30n6 y2 t, 12n3 t4
19. ______________
20. ______________
Factor each polynomial. (9.2)
21. 8rs2 + 16rs
21. ______________
22. 3x2 + 21x + 27
22. _____________
23. 12a2 – 15ab – 16a + 20b
Page 2 of 8
(look closely with this one!)
23. _____________
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Take Home Final Algebra CD
Factor each polynomial, if possible. If the polynomial
cannot be factored using integers, write prime. (9.3, 9.4)
24. x2 – 25
25. n2 – 7n – 18
ANSWERS:
25. ______________
26. ______________
26. 5t2 + 17t – 12
27. 2x2 – 16x + 32
28. 6m2 + 7m – 3
29. x2 + 12x + 5
27. ______________
28. ______________
29. _____________
Solve each equation. (9.4)
30. (x – 5) (2x – 1) = 0
30. ______________
2
31. y + 4y = 45
31. ______________
32. n3 – 3n2 – 10n = 0
32. ______________
33. Find two consecutive even integers whose product is 224.
33. ______________
34. The area of a rectangular room is 90 square feet.
The length of the room is 1 foot longer than the width.
Find the dimensions of the room.
34. ______________
Find the following information for each parabola. (10.1, 10.2)
35. y = x2 – 4
l.o.s. ________ vertex: _____
36. same equation
x-int: ______ y-int: ______
35. ___see problem____
36. ___see problem____
37. ___see problem____
37. y = x2 + 6x + 5
38. same equation
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l.o.s. ________ vertex: _____
x-int: ______ y-int: ______
38. ___see problem____
G. Kelly 2013
Take Home Final Algebra CD
Solve each equation by graphing.
39. c2 + 6c + 8 = 0
40. b2 – 4b + 5 = 0
ANSWERS:
39. ______________
40. ______________
Solve by completing the square. Leave answer as reduced
radicals if necessary. (10.3)
41. m2 – 10m + 6 = -7
42. c2 + 12c = 13
41. ______________
42. ______________
43. Find the value of c that will make x2 + 3x + c a perfect
square trinomial.
Solve … either factor or use the quadratic formula. (10.4)
44. x2 – 4x + 5 = 0
45. x2 + 4x – 6 = 0
43. ______________
44. ______________
45. ______________
State the value of the discriminant and then determine the
number of real roots. (10.4)
46. a2 + 8a + 16 = 0
47. w2 – 6w + 7 = 0
46. ______________
47. ______________
Page 4 of 8
G. Kelly 2013
Take Home Final Algebra CD
Simplify. (11.1)
48.
49. 3 84
12
50.
63 +
28
ANSWERS:
48. ______________



49. ______________
51.
32
75
52.
50. ______________
8
3 3
51. ______________
52. ______________

53. ______________
Solve. (11.3)
53.
5p = 10
54.

6p  8 = p
54. ______________

Find the length of each missing side. (11.4)
55.
a = ______
15
56. a = 16, b = 12, c = ?
55. ______________
57. a = 5, c = 74 , b = ?
56. ______________
39

Simplify each expression. State the excluded values of the
variable. (12.2)
2b 14
59. 2
b  9b 14
12a
58.
48a 2b

57. ______________
58. ______________
59. ______________

Find each product. (12.3)
x 2 16 x  2

61. 2
x 4 x4
18x 2 15y 3

60.
10y 2 24 x

Page 5 of 8

60. ______________
61. ______________
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Take Home Final Algebra CD
Find each quotient. (12.4, 12.5)
62.
4 y  20 y  5

y3
2y  6
y  3y 10 2y  4

y 2  9y  8
y 1
2
63.
ANSWERS:
62. ______________
63. ______________

64. (8r2 + 5r – 20)  4r

65. (a2 – 10a + 16)  (a – 2)
64. ______________
65. ______________


66. (b2 + 5b – 2)  (b + 6)
66. ______________

Solve each
inequality (6.1, 6.2 & 6.3)
67) m + 6 < 2
68) d – (- 4) < 8
67. ______________
69) 2x – 3 > x
68. ______________
69. ______________
70) -4 + 6n < 7n
70. ______________
71) Negative fives times a number is no more than the sum
of negative three times the number and twelve.
71. ______________
72. ______________
72) -8f < 48
73) - 32 > - 4n
73. ______________
74) -5m + 9 > 24
75) -2x + 1 < 16 – x
74. ______________
75. ______________
2m  5
 9
76)
3
76. ______________
77. ______________
Solve the inequality and then graph on a number line. (6.4)
77) -14 < 3x + 1 < 4
Page 6 of 8
78) 2y – 3 < 7 or - 3y < - 18
78. ______________
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Take Home Final Algebra CD
Solve each open sentence, then graph the solution set. (6.5)
79) | c – 2 | > 6
ANSWERS:
79. ____________
80) | 2m – 9 | < 1
80. ____________
81) | 3 – 2r | > 7
81. ____________
For each graph, write an open sentence involving absolute value.
82)
1
11
82. ____________
83. ____________
83)
-6
-2
(Chapter 4 and 5)
84. Graph the equation y = 3x – 4.
Graph the inequality. (6.6)
86. x + 2y < 4
Page 7 of 8
85. Graph the equation 3x + 4y = 12.
Graph the system of equations (7.1)
87. 2x + y = 3
x–y=3
G. Kelly 2013
Take Home Final Algebra CD
Substitution: Use substitution to solve each system of equations.
If the system does NOT have exactly one solution, state whether
It has no solution or infinitely many. (7.2)
88. y = 6x
89. x = 2y + 7
2x +3y = -20
x=y+4
Use elimination ( + or -) to solve the system of equations. (7.3)
90. –x + y = 1
91. 7x + 4y = 2
x + y = 11
7x + 2y = 8
ANSWERS:
88. ______________
89. ______________
90. ______________
91. ______________
Use elimination (using mult.) to solve the system of equations. (7.4)
92. 5x – 2y = -10
93. 3x + 2y = -9
92. ______________
3x + 6y = 66
5x – 3y = 4
93. ______________
94. 2x + 3y = 10
5x + 2y = -8
94. ______________
Graph the system of inequalities (7.5)
95. y > x + 2
y < -2x – 1
Good Luck …
and study
for the in
class final
Page 8 of 8
G. Kelly 2013