Download Algebra 1B, Pre-Final Problems

Algebra 1B, Pre-Final Problems
Simplify.
1. 32 ÷ 8 + 4 • 3
3.
3x
2y + 1
2. 62 + 12 • (1 + 2)3 – 16 ÷ (3 – 1)
for x = 7 and y = 3
4. Write an equivalent expression. Use 8 for 1.
8
5
6
Simplify. Write as a fraction.
5.
17c
51bc
6. 56
72
7. Write using exponential notation: 4 • y • y • y
Evaluate each expression:
8. x4 – 8 for x = -4
9. (5n)2 for n = 6
10. Use the distributive property to write an equivalent expression: (5x + 8 +3p)4
11. Simplify and collect like terms: 4(5x + 6y + 3) + 2(x + 2y)
12. Write as an algebraic equation:
a. 6 more than b
b. 9 less than c
c. the sum of r and s
13. Let n be the number of magazines Scotty sold. Sherry sold half as many magazines as Scotty. Write an
expression for the number of magazines that Sherry sold.
14. Write as an algebraic expression: a number that is 3 less than twice x
15. Find the distance (d) traveled by a truck moving at a rate (r) of 55 miles/hour for the time (t) of 8 hours
using the formula d = rt
16. Find the length of a rectangle (l) with area (A) 64 cm2 and width (w) 16 cm. Use the formula A = lw
17. The sum of two numbers is 33. Their product is 242. What are the numbers?
Show that each number can be written as the ratio of two integers.
18. 4.2
19. -0.68
20. Evaluate:
| 17 | + | -17 |
Add.
21. -17 + (-25)
22. -
5 2
+
6
3
Subtract.
23.
Simplify.
(- ) ( )
5
6
-

3
2
24. -5 - (-3x) + 3x + 4x - (-12)
Find the reciprocal. Recall that all variables represent nonzero rational numbers.
25. 15
7
26. -0.4
27. 2a
3b
Divide.
28.
10 I F 5 I
F
G
H9 J
K G
H 6J
K
29.
5I F
3I
F
 J GJ
G
H6KH4 K
Multiply.
2
30.
(3a – 6b + 9)
3
31. 
F
G
H
IJ
K
3 2
x  y 8
4 3
Simplify.
32. [7(x + 5) – 19] – [4(x – 6) +10]
33. [6(x+4) – 12] – [5(x-8) + 11]
34. What axiom or property guarantees the truth of each statement?
a. y + [x + (-x)] = y + 0
b. 6x – 3y = 3(2x – y)
c. (a • b)c = a(b • c)
d.
1
• (x + y) = 1
x+y
35. Solve.
36.
x - 3
8
= 1
4
The 1996 population of San Diego was estimated to be about 1,170,000. This was about 3/7 of the
estimate for Chicago. What was the approximate population of Chicago? Write an equation and solve.
37. In Churchill, Manitoba, the average daily low temperature in January is -35°C. This is 55° less than what
it is in Key West, Florida. What is the average daily temperature in Key West in January? Write an
equation and solve.
38. Solve.
39. Solve
4
x  16
5
3
27
 r
2
4
40. A case of a dozen videocassette tapes costs $23.40. Write an equation and solve to find the cost of a single
tape.
41. Solve.
-5a + 4(2 + 2a) = -1
42. Darrell sold 3 fewer subscriptions than 4 times the number Brenda sold. Let B = the number Brenda sold.
Write an expression for the number Darrell sold.
Solve.
43. 5r – (2r + 8) = 16
44.
1
1
(6 x  24)  20   (12 x  72)
2
4
45. Clear the fractions and solve.
5
3
1
y y  2 y
16
8
4
Solve.
47. -3│a│ - 5 = -17
46. Solve for f:
r  2h 
1
f
4
48. 4│x-2│ + 3 = 7
49.
5 y

3 42
50. Write as a decimal: 7%
52. 45 is 30% of what number?
53. 40 is what percent of 2?
51. Express as a percent:
24
25
54. Solve: 4 + 3x < 28
Solve and graph:
55. Solve: 6(z- 5) < 5(7 - 2z)
56. 7y ≥ -21
57. -18y ≥ -36
58. Solve for x:
59. Clear the fractions and solve for y:
3x
 15
5
0.2 y  2.1  12
. y  0.3
Solve:
60. │x│ ≥ 2
61. │x+2│ < 5
62. 2│x-3│+1 > 3
63. Your quiz grades are 73, 75, 89, and 91. What is the lowest grade you can obtain on the last quiz and still
achieve an average of at least 85?
64. Find the greatest possible pair of integers such that one integer is twice the other and their sum is less
than 30.
65. The length of a rectangle is 26cm. What width will make the perimeter greater than 80cm?
66. The sum of three consecutive even integers is less than or equal to 42. Find the largest set of these numbers.
67. Alicia weighs 60 lbs less than her father. Their combined weights total 300 lb at most. What is the most
Alicia could weigh?
.
Simplify.
68. 32 • 40 • 7
69. x4 • x3 • x
71. (-6t2)3
72.
70. (5s2t3)(5s2t)
24a6b9
-6a6b3
73. (4a4b8)2(2a4b2)3
74. Express using positive exponents: 4x-3
Express in scientific notation:
75. (7 • 104)(2 • 102)
76. 8.4 • 106
2.0 • 108
77. Evaluate the polynomial for a = -1 and b = 2:
-3a3 + 7a2 – 3b -2
78. Add. (5x4 – 6x3 – 7x2 + x -1) + (4x3 – 6x + 1)
79. Subtract. (3m4 + 6m2 + 8m – 1) – (4m5 – 6m4 – 8m - 7)
Multiply.
80. 4x2(3x + 6)
81. (4x2 + 3)(x - 3)
82. (2x - 1)2
83. (2x2 + 6x + 1)(2x + 1)
Factor. Remember to look for a common factor.
84. 3p2 – 3p
85. 6m3n3 + 3m3n2 + m2n2
86. x2 – 4
87. x2 + 16x + 64
88. x2 + 8x +15
89. z2 – 10z + 24
90. a2 + 2ab – 35b2
91. 3x2 – 5x – 2
92. 12x2 + 28x – 24
93. 3x2 + 4x +1
Factor by Grouping.
94. 2y3 + 6y2 + y + 3
95. 2x3 – 8x2 – 9x + 36
Solve for x.
96. (x + 12)(x – 11) = 0
97. x2 + 6x + 5 = 0
98. 2y2 + 12y = -10
Translate to an equation and solve:
99. Eight more than the square of a number is six times the number.
100. The length of a rectangle is 4 m greater than the width. The area of the rectangle is 96 m2. Find the
length and width.