Period 1: Due June 10th
Period 2: Due June 11th
Name: _________________________
Period: _______________
Algebra 1: Spring Semester Final Exam Study Guide
Polynomials
1. (3x3y)(4x4y7)
2. (4x2y2)(6x3y2)
3. (2x3y5z0)2
4. (4x4y-2z0)2
5.
27 x 6 y 3 z
36 xy 3 z 5
6.
18 x 4 y 7 z 2
26 x5 y 3 z
7. a-5b3c
8. a2b-3
9. (2x2 – 3x + 3) – (-3x2 + 2x + 3)
10. (-4x2 + 5x – 7) – (5x2 – 2x – 13)
11.
1 2
x (3 x  6 y )  5 x(8 x  y )
3
12.
2
x(5 x  10 y )  3 x(2 x  5 y )
5
13. (x – 3)(3x + 5)
14. (2x + 7)(5x + 2)
15. (x – 9)2
16. (2x + 3)2
17. (x – 5)(x + 5)
18. (2x – 3)(2x + 3)
Period 1: Due June 10th
Period 2: Due June 11th
Name: _________________________
Period: _______________
Factoring
19. What is the prime factorization of 624?
20. What is the prime factorization of 580?
21. Find the GCF of 12xy2z4 & 42x2y3z
22. Find the GCF of 20x3y5z & 35x4y5z3
23. Factor 21x2y – 34xy2
24. Factor 12x3y2 + 18xy
25. Factor 6x2 + 11x + 3
26. Factor 10x2 – 9x – 7
27. Factor x2 + 11x + 24
28. Factor x2 – 2x – 35
29. Factor 6x3 – 6x
30. Factor x3 – 81x
31. Factor x2 + 10x = 25
32. Factor 4x2 – 28x + 49
33. Solve 2x(x + 6) = 0
34. Solve x(3x – 5) = 0
35. Solve x2 + 2x – 35 = 0
36. Solve 2x2 – 5x – 3 = 0
Period 1: Due June 10th
Period 2: Due June 11th
Name: _________________________
Period: _______________
Quadratics
37. Find the equation for the axis of
38. Find the equation for the axis of
symmetry for y = 2x2 – 6x + 5
symmetry for y = x2 – 8x + 12
39. Would the graph of -3x2 – 2x = 9 = 0
have a maximum or minimum value?
40. Would the graph of 2x2 + 5x – 10 = 0
have a maximum or minimum value?
41. Find the vertex of x2 – 4x + 5 = 0
42. Find the vertex of x2 + 6x - 5 = 0
43. Write the formula for the quadratic equation
44. Write the formula for the discriminant
45. Solve 4x2 – 5x – 6 = 0 using the
46. Solve 3x2 + 8x + 4 = 0 using the
quadratic formula
47. What is the value of the discriminant
for the equation x2 – 8x + 2 = 0?
quadratic formula
48. What is the value of the discriminant
for the equation 2x2 + 8x – 3 = 0?
Period 1: Due June 10th
Period 2: Due June 11th
Name: _________________________
Period: _______________
Rational Expressions
49. State the excluded value(s) for
51. Simplify
10 x
14 y
x 2  64
x 2  x  56
53. State the excluded value(s) for
(2 x  1)(3x  1)
(2 x  1)( x  9)
3 x3 y 2 3 xz
 2
55. Multiply
z3
9y
57. Multiply
( x  6) 2
24
 2
16
(x  36)
x2  9 y 2
2x  6 y

59. Divide 2
2
3x  3 y
x  4 xy  3 y
61. Find
5 x 5 x  10

10
10
50. State the excluded value(s) for
52. Simplify
x
x  10
2 x2  5x  3
4 x2  9
54. State the excluded value(s) for
( x  1)( x  1)
( x  10)(2 x  3)
56. Multiply
5x 2 y 6 12 z

2 z 2 9 x3 z 4
58. Multiply
x2  9
33
 2
27
(x  18 x  81)
5x  5 y
x 2  25 y 2

60. Divide
10 x  5 y 2 x 2  3 xy  5 y 2
62. Find
2 x 10 x  9

3
3
Period 1: Due June 10th
Period 2: Due June 11th
Name: _________________________
Period: _______________
63. Find
4x
16 y

x  4y 4y  x
64. Find
5y
5x

5y  x x  5y
65. Find
x 1 7

x 1 x
66. Find
2x
x 1

x2
x
67. Find
x  3 2x 1

6
8
68. Find
x  2 x 1

4
3
69. It takes Alfred 10 minutes to wash
70. It takes Deanna 4 hours to decorate her
the dishes and it takes Aundrea 15
house. It takes her husband 8 hours to
minutes to do the same job. How
decorate the house. How long would it
long would it take if they worked
take if they worked together?
together?
Radical Expressions
71. Simplify
44x2 y5
72. Simplify
56x6 y 4
73. Simplify
3
7
74. Simplify
2
10
Period 1: Due June 10th
Period 2: Due June 11th
75. Simplify
2
3 3
77. Simplify 3 7  7 7
Name: _________________________
Period: _______________
76. Simplify
6
2 5
78. Simplify 2 5  9 5
79. Simplify
98  2 7
80. Simplify 2 45  20
81. Simplify
2(3 3  2)
82. Simplify 2 5( 7  2 5)
83. Solve x2 – 6x – 10 = 2 by completing
the square.
84. Solve x2 + 10x – 4 = -6 by completing
the square.