COLLEGE ALGEBRA MIDTERM REVIEW
Name: _______________________________________________________________
1. Identify which of the following numbers are natural numbers.
5
4,  ,  3, 8 , 6, 0.9,
6
5, 
3
10
2. Use inequality notation to describe the set.
John earned $36 or more.
a. t < 36
b. t > 36
c. t > 36
d. t < 36
Graph each set of numbers on the number line provided.
2. -4 < x < 3
3. [2, ∞)
4. (-8, 12]
5. (-∞, 9)
Write each set of numbers in interval notation. Place you answer in the blank provided.
____________________6.
____________________7.
)
4
)
5
[
-3
____________________8.
[
7
Find the distance between these points on the number line.
10. -20 and -9
11. -14 and 26
Simplify each of the following.
 5 x 3 
 3 
 4x 
12.
13.
3

2
1
27
1
 2 3
14.     
5 8
2
15. 31  6 1
16. (3  6) 2
Simplify using the order of operations.
17. 7 + (24 ÷ 2)
19.
5[62 + (9 - 5)]
4(2 -3)
18. 125 ÷ 5 + 200 ÷ 4
20.
2[3  (4  7) 2 ]
5(2  32 )
Evaluate the following expressions for x = -2, y = 0, and z = 2.
21. x3
22. –x5
23. xzy
24. 4(x – z)2
Simplify.
25.
49
26.
28. 10 16 y 3
29.
3
48
27. 5 40
24
30.
4
a5b12c9
Simplify each expression.
31.
75  2 27
32. 5 45  80
33. 2 3 81  3 3 24
34.
35. 4 3  7
36. ( 5  x) 2
200 x2  98x2
Write all answers without using negative exponents.
37. 27
2/3
38. (125)
2/3
 36 
39.  
 49 
Rationalize the denominator.
40.
2
3
41.
6x2
3x
3
42.
3
4
9
3/ 2
Give the degree of each polynomial and tell whether the polynomial is a monomial, a
binomial, or a trinomial.
43. x2 – 4 __________________
45. x3 11 __________________
44. 8x2y2z __________________
46. 6x4 – 2x2 + 9 __________________
Simplify each expression.
47. (14x + 5) + (10x + 5)
48. (6x + 14) - (9x + 5)
49. (12x) (12x + 11)
50. (6x + 3) (-5x + 2)
51.
3
3 2
52.
2
3 1
Divide using long division.
53. (15x3 + 20x2 + 5x) ÷ 5
55.
x 2  15 x  36
x3
54. (72x4 + 81x2 + 9x) ÷ 9x
56.
15 x 2  x  6
5x  3
Factor completely.
57. 3x2 - 3x
58. 24x3 + 168x
59. -3(x - 9) + x(x - 9)
60. (3x - 4)x - 4(3x - 4)
61. x2 - 18x + 81
62. x2 – 49
63. 9x2 – 16
64. x3 + 125
65. x2 -8x – 20
66. 25b 2  20b  4
Simplify.
67.
13a 2  325
a 5
68.
4k 2  4
32k  32
69.
x 2  3x  10
x2  2x  8
Multiply or divide.
4 x3 y 6 x 2 y 2
70.

3xy 4 10 x 4
2x
x2  2x

71.
3x  12 x 2  6 x  8
72.
3x
 (2 x  5)
2
2 x  9 x  10
73.
x 2  y 2 ( x  y)2

2 x2  8x
2 xy
Add or subtract.
74.
5x  1 5  4 x

x4 x4
75.
1
2

2
6u
9u
76.
1
b  12
 2
b  6 b  17b  66
77.
h  10 2h

h 2  16 h  4
Simplify each complex fraction.
7
78. 8
21
16
k m
m
79.
km
3m
ax  ab
2
2
80. x  b
xb
xb