Download State whether each sentence is true or false . If false , replace the

expression.
8. h – 7
Study Guide and Review -Chapter 1
State whether each sentence is true or false . If
false , replace the underlined term to make a
true sentence.
1. An exponent indicates the number the base is to be
multiplied by.
ANSWER: True
2. A coordinate system is formed by the intersection of
two number lines.
ANSWER: true
3. An expression is in simplest form when it contains
like terms and parentheses.
ANSWER: false; not in simplest form
ANSWER: the difference between h and 7
9. 3x
2
ANSWER: the product of 3 and x squared
3
10. 5 + 6m
ANSWER: five more than the product of six and m cubed
Write an algebraic expression for each verbal
expression.
11. a number increased by 9
ANSWER: x +9
12. two thirds of a number d to the third power
ANSWER: 4. In an expression involving multiplication, the
quantities being multiplied are called factors.
ANSWER: true
5. In a function, there is exactly one output for each
input.
ANSWER: true
6. Order of operations tells us to always perform
multiplication before subtraction.
ANSWER: true
7. Since the product of any number and 1 is equal to the
number, 1 is called the multiplicative inverse.
ANSWER: false; multiplicative identity
Write a verbal expression for each algebraic
expression.
8. h – 7
ANSWER: the difference between h and 7
9. 3x
13. 5 less than four times a number
ANSWER: 4x – 5
Evaluate each expression.
5
14. 2
ANSWER: 32
3
15. 6
ANSWER: 216
4
16. 4
ANSWER: 256
17. BOWLING Fantastic Pins Bowling Alley charges
$2.50 for shoe rental plus $3.25 for each game.
Write an expression representing the cost to rent
shoes and bowl g games.
ANSWER: 2.50 + 3.25g
2
ANSWER: the product of 3 and x squared
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10. 5 + 6m
Evaluate each expression.
18. 24 – 4 ∙ 5
ANSWER: 4
Page 1
Write an expression representing the cost to rent
shoes and bowl g games.
2
26. (a + 2bc) ÷ 7
ANSWER: Study
Guide and Review -Chapter 1
2.50 + 3.25g
Evaluate each expression.
18. 24 – 4 ∙ 5
ANSWER: 4
ANSWER: 10
27. ICE CREAM The cost of a one-scoop sundae is
$2.75, and the cost of a two-scoop sundae is $4.25.
Write and evaluate an expression to find the total
cost of 3 one-scoop sundaes and 2 two-scoop
sundaes.
ANSWER: 2.75(3) + 4.25(2); $16.75
2
19. 15 + 3 – 6
ANSWER: 18
20. 7 + 2(9 – 3)
Evaluate each expression using properties of
numbers. Name the property used in each step.
28. 18 ∙ 3(1 ÷ 3)
ANSWER: 18 ∙ 3(1 ÷ 3)
ANSWER: 19
Substitution
= 18 ∙ (3)
21. 8 ∙ 4 – 6 ∙ 5
Multiplicative
Inverse
Multiplicative
Identity
= 18 ∙ 1
ANSWER: 2
= 18
5
22. [(2 – 5) ÷ 9]11
ANSWER: 33
29. ANSWER: 23. ANSWER: 3
Evaluate each expression if a = 4, b = 3, and c =
9.
24. c + 3a
Substitution
Substitution
Multiplicative Inverse
ANSWER: 21
2
30. (16 – 4 ) + 9
2
25. 5b ÷ c
ANSWER: 2
ANSWER: 5
2
26. (a + 2bc) ÷ 7
ANSWER: 10
27. ICE CREAM The cost of a one-scoop sundae is
$2.75, and the cost of a two-scoop sundae is $4.25.
Write and evaluate an expression to find the total
cost of 3 one-scoop sundaes and 2 two-scoop
sundaes.
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ANSWER: 2.75(3) + 4.25(2); $16.75
(16 – 4 ) + 9
= 16 – 16 + 9
=0 +9
=9
Substitution
Additive Inverse
Additive Identity
31. ANSWER: Substitution
Page 2
Substitution
Multiplicative Inverse
(16 – 4 ) + 9
Substitution
= 16 – 16 + 9
Additive Inverse
=0 +9
9
Additive
Identity
Study=Guide
and Review
-Chapter
1
= 8 ∙ 5 ∙ 0.5
= (8 ∙ 5) ∙ 0.5
= 40 ∙ 0.5
= 20
Commutative (×)
Associative (×)
Substitution
Substitution
31. 35. 5.3 + 2.8 + 3.7 + 6.2
ANSWER: ANSWER: Substitution
Commutative (+)
Associative (+)
Substitution
Substitution
Substitution
Multiplicative Inverse
Multiplicative Identity
Substitution
32. 18 + 41 + 32 + 9
ANSWER: 18 + 41 + 32 + 9
= 18 + 32 + 41 + 9
= (18 + 32) + (41 + 9)
= 50 + 50
= 100
Commutative (+)
Associative (+)
Substitution
Substitution
36. SCHOOL SUPPLIES Monica needs to purchase a
binder, a textbook, a calculator, and a workbook for
her algebra class. The binder costs $9.25, the
textbook $32.50, the calculator $18.75, and the
workbook $15.00.
Find the total cost for Monica’s algebra supplies.
ANSWER: $75.50
Use the Distributive Property to rewrite each
expression. Then evaluate.
37. (2 + 3)6
33. ANSWER: ANSWER: 2(6) + 3(6); 30
Commutative (+)
Associative (+)
Substitution
Substitution
38. 5(18 + 12)
ANSWER: 5(18) + 5(12); 150
39. 8(6 – 2)
ANSWER: 8(6) – 8(2); 32
34. 8 ∙ 0.5 ∙ 5
ANSWER: 8 ∙ 0.5 ∙ 5
= 8 ∙ 5 ∙ 0.5
= (8 ∙ 5) ∙ 0.5
= 40 ∙ 0.5
= 20
40. (11 – 4)3
ANSWER: 11(3) – 4(3); 21
Commutative (×)
Associative (×)
Substitution
Substitution
41. –2(5 – 3)
ANSWER: –2(5) – (–2)(3); –4
35. 5.3 + 2.8 + 3.7 + 6.2
42. (8 – 3)4
ANSWER: ANSWER: 8(4) – 3(4); 20
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Commutative (+)
Rewrite each expression using the Distributive
Property. Then simplify.
11(3) – 4(3); 21
41. –2(5 – 3)
ANSWER: Study
Guide and Review -Chapter 1
–2(5) – (–2)(3); –4
42. (8 – 3)4
ANSWER: 8(4) – 3(4); 20
ANSWER: 4(3 + 5 + 4); 48
Find the solution set of each equation if the
replacement sets are x: {1, 3, 5, 7, 9} and y: {6,
8, 10, 12, 14}
50. y – 9 = 3
ANSWER: {12}
Rewrite each expression using the Distributive
Property. Then simplify.
43. 3(x + 2)
ANSWER: 3(x) + 3(2); 3x + 6
51. 14 + x = 21
ANSWER: {7}
44. (m + 8)4
ANSWER: m(4) + 8(4); 4m + 32
45. 6(d − 3)
52. 4y = 32
ANSWER: {8}
53. 3x – 11 = 16
ANSWER: 6(d) – 6(3); 6d – 18
46. –4(5 – 2t)
ANSWER: –4(5) – (–4)(2t); –20 + 8t
47. (9y – 6)(–3)
ANSWER: (9y)(–3) – (6)(–3); –27y + 18
48. –6(4z + 3)
ANSWER: –6(4z) + (–6)(3); –24z – 18
49. TUTORING Write and evaluate an expression for
the number of tutoring lessons Mrs. Green gives in 4
weeks.
ANSWER: {9}
54. ANSWER: {6}
55. 2(x – 1) = 8
ANSWER: {5}
Solve each equation.
56. a = 24 – 7(3)
ANSWER: 3
2
57. z = 63 ÷ (3 – 2)
ANSWER: 9
58. AGE Shandra’s age is four more than three times
Sherita’s age. Write an equation for Shandra’s age.
Then solve the equation if Sherita’s is 3 years old.
ANSWER: 4(3 + 5 + 4); 48
Find the solution set of each equation if the
replacement
sets by
are
x: {1, 3, 5, 7, 9} and y: {6,
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8, 10, 12, 14}
50. y – 9 = 3
ANSWER: 3K + 4 = E; 13
Express each relation as a table, a graph, and a
mapping. Then determine the domain and
range.
Page 4
59. {(1, 3), (2, 4), (3, 5), (4, 6)}
ANSWER: Sherita’s age. Write an equation for Shandra’s age.
Then solve the equation if Sherita’s is 3 years old.
ANSWER: Study
Guide and Review -Chapter 1
3K + 4 = E; 13
Express each relation as a table, a graph, and a
mapping. Then determine the domain and
range.
59. {(1, 3), (2, 4), (3, 5), (4, 6)}
Express the relation shown in each table,
mapping, or graph as a set of ordered pairs.
ANSWER: 62. ANSWER: {(5, 3), (3, –1), (1, 2), (–1, 0)}
D = {1, 2, 3, 4} R = {3, 4, 5, 6}
60. {(–1, 1), (0, –2), (3, 1), (4, –1)}
ANSWER: 63. ANSWER: {(–2, –2), (0, –3), (2, –2), (2, 0), (4, –1)}
64. GARDENING On average, 7 plants grow for every
10 seeds of a certain type planted. Make a table to
show the relation between seeds planted and plants
growing for 50, 100, 150, and 200 seeds. Then state
the domain and range and graph the relation.
ANSWER: D = {–1, 0, 3, 4} R = {–2, –1, 1}
61. {(–2, 4), (–1, 3), (0, 2), (–1, 2)}
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Express
relation
shown
in each table,
mapping, or graph as a set of ordered pairs.
Page 5
Determine whether each relation is a function.
63. 66. ANSWER: Study
Guide and Review -Chapter 1
{(–2, –2), (0, –3), (2, –2), (2, 0), (4, –1)}
64. GARDENING On average, 7 plants grow for every
10 seeds of a certain type planted. Make a table to
show the relation between seeds planted and plants
growing for 50, 100, 150, and 200 seeds. Then state
the domain and range and graph the relation.
ANSWER: ANSWER: function
67. {(8, 4), (6, 3), (4, 2), (2, 1), (6, 0)}
ANSWER: not a function
2
If f (x) = 2x + 4 and g(x) = x – 3, find each
value.
68. f (–3)
ANSWER: –2
69. g(2)
ANSWER: 1
70. f (0)
ANSWER: 4
71. g(–4)
ANSWER: 13
72. f (m + 2)
Determine whether each relation is a function.
ANSWER: 2m + 8
73. g(3p )
ANSWER: 2
9p – 3
65. 74. GRADES A teacher claims that the relationship
between number of hours studied for a test and test
score can be described by g(x) = 45 + 9x, where x
represents the number of hours studied. Graph this
function.
ANSWER: function
ANSWER: 66. ANSWER: function
67. {(8, 4), (6, 3), (4, 2), (2, 1), (6, 0)}
ANSWER: not a function
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2
If f (x) = 2x + 4 and g(x) = x – 3, find each
73. g(3p )
ANSWER: Study Guide and Review -Chapter 1
2
9p – 3
74. GRADES A teacher claims that the relationship
between number of hours studied for a test and test
score can be described by g(x) = 45 + 9x, where x
represents the number of hours studied. Graph this
function.
ANSWER: 75. Identify the function graphed as linear or nonlinear.
Then estimate and interpret the intercepts of the
graph, any symmetry, where the function is positive,
negative, increasing, and decreasing, the x-coordinate
of any relative extrema, and the end behavior of the
graph.
ANSWER: Nonlinear; the graph intersects the y-axis at about (0,
56), so the y-intercept is about 56. This means that
about 56,000 U.S. patents
were granted in 1980. The graph has no symmetry.
The graph does not intersect the x-axis, so there is no
x-intercept. This means that in
no year were 0 patents granted. The function is positive for all values of x, so the
number of patents will always have a positive value.
The function is increasing for all values of x. The yintercept is a relative minimum, so the number of
patents granted was at its lowest in 1980. As x
increases, y increases. As x decreases, y decreases.
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