Download Summary Exercises

Summary
1. y 5
3. 8a
5. 5mn
2. c 10
y
4. 3
Exercises
1
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This exercise set is provided to give you practice with each of the objectives of the
chapter. Each exercise is keyed to the appropriate chapter section. Your instructor will
give you guidelines on how to best use these exercises.
6. a(a 5)
7. 17x 3
[1.1] Write, using symbols.
a2
8. a2
9. (x 6)(x 6)
x
10. 9
x4
11. x2
1. 5 more than y
2. c decreased by 10
3. The product of 8 and a
4. The quotient when y is divided
by 3
5. 5 times the product of m and n
6. The product of a and 5 less than a
7. 3 more than the product of 17 and x
8. The quotient when a plus 2 is
divided by a minus 2
9. The product of 6 more than a number and 6 less than the same number
12. x(x 3)
10. The quotient of a number and 9
13. 3
14. 75
15. 80
16. 400
17. 41
18. 25
19. 20
20. 16
21. 324
22. 27
23. 11
24. 169
13. 18 3 5
14. (18 3) 5
15. 5 42
25. 7
26. 46
16. (5 4)2
17. 5 32 4
18. 5(32 4)
27. 15
28. 80
19. 5(4 2)2
20. 5 4 22
21. (5 4 2)2
29. 19
30. 81
22. 3(5 2)2
23. 3 5 22
24. (3 5 2)2
31. 25
32. 6
33. 1
34. 3
35. 3
36. 6
37. 48
38. 2313
11. The quotient when 4 less than a number is divided by 2 more than the same
number
12. The product of a number and 3 less than the same number
[1.2] Evaluate each of the following expressions.
[1.2] Evaluate the expressions if x 3, y 6, z 4, and w 2.
25. 3x w
26. 5y 4z
27. x y 3z
28. 5z2
29. 3x2 2w2
30. 3x3
31. 5(x2 w2)
6z
32. 2w
2x 4z
33. yz
3x y
34. wx
x(y2 z2)
35. (y z)(y z)
y(x w)2
36. x2 2xw w2
37. w2y2 z3x
38. x2 12xz3
93
94
Chapter 1
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From Arithmetic to Algebra
39. 4a3, 3a2
[1.3] List the terms of the expressions.
40. 5x2, 7x, 3
39. 4a3 3a2
40. 5x2 7x 3
41. 5m2, 4m2, m2
42. 4ab2, ab2, 3ab2
[1.3] Circle like terms.
43. 12c
41. 5m2, 3m, 4m2, 5m3, m2
44. 7x
42. 4ab2, 3b2, 5a, ab2, 7a2, 3ab2, 4a2b
45. 2a
[1.3] Combine like terms.
46. 3c
47. 3xy
48. 7ab2
49. 19a b
50. x 5y
51. 3x3 9x2
52. a3 2a2 3a
53. 10a3
54. 7x2
55. 23 x
56. 25 x
57. x 5
58. 2x 5
59. x 4
60. 6n 7
61. x, 25 x
62. 0.10x 0.25q
43. 5c 7c
44. 2x 5x
45. 4a 2a
46. 6c 3c
47. 9xy 6xy
48. 5ab2 2ab2
49. 7a 3b 12a 2b
50. 6x 2x 5y 3x
51. 5x3 17x2 2x3 8x2
52. 3a3 5a2 4a 2a3 3a2 a
53. Subtract 4a3 from the sum of 2a3 and 12a3.
54. Subtract the sum of 3x2 and 5x2 from 15x2.
[1.1–1.3] Write an expression for each of the following problems.
55. Carpentry. If x feet (ft) are cut off the end of a board that is 23 ft long, how much
is left?
56. Money. Sergei has 25 nickels and dimes in his pocket. If x of these are dimes,
how many of the coins are nickels?
57. Age. Sam is 5 years older than Angela. If Angela is x years old now, how old is
Sam?
58. Money. Margaret has $5 more than twice as much money as Pho. Write an expression for the amount of money that Margaret has.
59. Geometry. The length of a rectangle is 4 meters (m) more than the width. Write
an expression for the length of the rectangle.
60. Number problem. A number is 7 less than 6 times the number n. Write an expression for the number.
61. Carpentry. A 25-ft plank is cut into two pieces. Write expressions for the length
of each piece.
62. Money. Bernie has x dimes and q quarters in his pocket. Write an expression for
the amount of money that Bernie has in his pocket.
63. {1, 3}
64. {1, 2, 3, 4, 5, 6}
65. {1, 0, 1, 2, 3}
66. {4, 3, 2, 1, 0, 1,
2, 3}
67. {1, 3}
68. {1, 0, 1, 2}
69. {x x 5}
[1.4] Use the roster method to list the elements of each set.
63. The set of all factors of 3.
64. The set of all positive integers less than 7.
65. The set of integers greater than 2 and less than 4.
66. The set of integers between 4 and 3 inclusive.
67. The set of all odd whole numbers less than 4.
68. The set of all integers greater than 2 and less than 3.
70. {x 2 x 4}
[1.4] Use set-builder notation to represent each set described.
71. {x x 3}
69. The set of all real numbers greater than 5.
72. {x 4 x 3}
77. {x x 3}
78. {x x 4}
79. {x 3 x 2}
80. {x 4 x 2}
95
Summary Exercises
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70. The set of all real numbers greater than 2 and less than 4.
71. The set of all real numbers less than or equal to 3.
72. The set of all real numbers between 4 and 3 inclusive.
[1.4] Plot the elements of each set on the number line.
73. {x x 1}
74. {x x 2}
2
1
0
75. {x 2 x 3}
2
0
76. {x 7 x 1}
0
7
3
1
0
[1.4] Use set-builder notation to describe each set.
]
77.
79.
3
0
[
3
2
1
0
1
2
[
78.
4
80.
4
3
3
2
2
1
1
0
1
]
0
1
2