Algebra 2 – Midterm Practice Problems (mixed)
Simplify.
1. 5(x3 – 7x) – 8x(x2 + 4)
2. 6x2y(3x + 4) + 2x(7xy – 8)
3. –(xy – y) – 2x(y – 3)
4. (x + 4)2
5. (3x – 7)2
6. (4x + 9y)2
7.
8.
9.
10.
11.
12.
13.
14.
15.
1
Factor each expression completely.
16. 5x3 – 35x
17. 12x3y + 3y
18. 6x2 – 12x + 15
19. x2 – 49y2
20. x4 – 36
21. x4 – 81
22. x3 + 8
23. 8x3 + 1
24. 8x3 – 27
25. 2x3 + 6x2 + 5x + 15
26. 10x3 – 2x2 + 35x – 7
27. 12x3 – 4x2 – 3x + 1
28. x2 – 13x – 48
29. 2x2 – 13x – 24
30. 8x2 – 13x – 6
Solve by factoring.
31. 3x2 + 16x + 16 = 0
32. x4 – 16x2 + 48 = 0
33. 3x4 – 8x2 = 16
2
Solve the equations. If it is an inequality, graph it on a number line!
34. 2(x + 4) = 3(x – 7) + 4
35. 7(x – 8) = 5 – 2(x – 1)
36. ½(12x – 10) = 1 – (x + 2)
37. |2b – 7| = 25
38. |5b + 3| = 18
39. |4 – b| = 8
40. |x + 3| > 8
41. |2x – 9| > 13
42. |3x + 4| < 22
43. x + 2y = 7
x – 2y = 23
44. 4x + y = 7
2x + 5y = -1
45. 2x – 3y = 3
-2x + y = -4
46. 3x2 + 54 = 0
47. 2(x – 4)2 + 18 = 0
48. 3(x + 2)2 + 24 = 0
3
Solve the quadratic by one of the 4 methods learned (factoring, inverse operations, completing
the square, or quadratic formula).
49. x2 + 6x – 8 = 0
50. x2 – 8x + 4 = 0
51. x2 – 10x + 2 = 0
52. x3 – 3x2 – 6x + 8 = 0
53. x3 – x2 – 11x + 3 = 0
54. x4 – 9x3 + 23x2 – 81x + 126 = 0
Graph.
55. x + 4y = -4
56. 3x – 4y = 12
57. 3x + 5y = 12
58. y < 5
59. x > 2
60. x < -3
4
Graph.
61. 5 – 2x < 3(x + 4)
62. 7 – 2x > -3(x – 4)
63. 5x + 4 < 7 – (x – 9)
-6 -4 -2 0 2
64. -2 < x + 3 < 9
4
6
-6 -4 -2 0 2
65. 2 < x – 1 < 5
4
6
-6 -4 -2 0 2
66. 5 < 2x + 3 < 11
4
6
-6 -4 -2 0 2
67. f(x) = |x + 4| – 1
4
6
-6 -4 -2 0 2 4
68. f(x) = -2|x – 3| – 5
6
-6 -4 -2 0 2
69. f(x) = ½ |x + 4|
4
6
70. g(x) = -(x – 3)2 + 1
71. g(x) = (x + 2)2
72. g(x) = -2(x – 1)2 + 5
5
Graph.
73. y = x2 + 4x + 3
74. y = x2 – 2x – 8
75. y = x2 – 4x + 4
76.
77.
78.
79.
80.
81.
6