Name: 
 

Algebra 1 Chapter 1


Multiple Choice
Identify the choice that best completes the statement or answers the question.
 
 
Write an algebraic expression for the phrase.
 

 1. 
the sum of b and 11
a.
b – 11
b.
mc001-1.jpg
c.
b + 11
d.
11b
 

 2. 
the product of g and 4
a.
4g
b.
g + 4
c.
mc002-1.jpg
d.
g – 4
 

 3. 
4 times the sum of q and p
a.
4q + p
b.
4 + q + p
c.
4qp
d.
4(q + p)
 

 4. 
–2 times the quantity q minus 3
a.
–2q – 3
b.
q(–2 – 3)
c.
mc004-1.jpg
d.
–2(q – 3)
 
 
Define a variable and write an expression for the phrase.
 

 5. 
the quotient of 6 times a number and 16
a.
mc005-1.jpg
b.
mc005-2.jpg
c.
mc005-3.jpg
d.
mc005-4.jpg
 

 6. 
4 minus a number
a.
4 – n
b.
4n
c.
mc006-1.jpg
d.
mc006-2.jpg
 

 7. 
The total cost to rent a row boat is $18 times the number of hours the boat is used. Write an equation to model this situation if c = total cost and h = number of hours.
a.
c = 18h
b.
c – 18 = h
c.
h = 18c
d.
mc007-1.jpg
 

 8. 
What equation models the data in the table if d = number of days and c = cost?
Days
Cost
2
44
3
66
5
110
6
132
a.
d = 22c
b.
c = 22d
c.
c = d + 22d
d.
c = d + 22
 

 9. 
An equilateral triangle has three sides of equal length. What is the equation for the perimeter of an equilateral triangle if P = perimeter and s = length of a side?
a.
s = 3P
b.
P = 3s
c.
P = 3 + s
d.
P = 3(s + s + s)
 

 10. 
Evaluate u + xy, for u = 18, x = 10, and y = 8.
a.
188
b.
36
c.
98
d.
224
 

 11. 
A pair of shoes costs $52.99 and the state sales tax is 8%. Use the formula C = p + rp to find the total cost of the shoes, where C is the total cost, p is the price, and r is the sales tax rate.
a.
$95.38
b.
$60.99
c.
$57.23
d.
$78.19
 

 12. 
When simplifying an expression, you ____ perform operations inside grouping symbols first.
a.
always
b.
sometimes
c.
never
 

 13. 
Evaluate the expression mc013-1.jpg for a = 4 and b = 3.
a.
36
b.
24
c.
81
d.
144
 

 14. 
You can use the formula mc014-1.jpg to convert temperature in degrees Fahrenheit, F, to temperature in degrees Celsius, C. What is 62°F in degrees Celsius? Round your answer to the nearest tenth.
a.
30°C
b.
16.7°C
c.
52.2°C
d.
2.4°C
 

 15. 
A rational number is ____ a real number.
a.
always
b.
sometimes
c.
never
 

 16. 
Write the number 2.4 in the form mc016-1.jpg, using integers, to show that it is a rational number.
a.
mc016-2.jpg
b.
mc016-3.jpg
c.
mc016-4.jpg
d.
mc016-5.jpg
 

 17. 
Simplify each element in the matrix.
mc017-1.jpg
a.
mc017-2.jpg
b.
mc017-3.jpg
c.
mc017-4.jpg
d.
mc017-5.jpg
 

 18. 
Evaluate mc018-1.jpg for x = –2 and y = 3.
a.
4
b.
8
c.
–4
d.
–8
 
 
Simplify the expression.
 

 19. 
mc019-1.jpg
a.
108
b.
36
c.
18
d.
9
 

 20. 
mc020-1.jpg
a.
29
b.
80
c.
128
d.
92
 

 21. 
mc021-1.jpg
a.
297
b.
868
c.
437
d.
867
 

 22. 
–9 + 6
a.
15
b.
–3
c.
–15
d.
3
 

 23. 
–4.8 – (–4.9) + 5.7
a.
–4
b.
–5.8
c.
5.8
d.
–15.4
 

 24. 
mc024-1.jpg
a.
mc024-2.jpg
b.
mc024-3.jpg
c.
mc024-4.jpg
d.
mc024-5.jpg
 

 25. 
mc025-1.jpg
a.
mc025-2.jpg
b.
mc025-3.jpg
c.
mc025-4.jpg
d.
mc025-5.jpg
 

 26. 
mc026-1.jpg
a.
13
b.
–13
c.
12
d.
–12
 

 27. 
–6.5(–4.9)
a.
–16.25
b.
–31.85
c.
–12.25
d.
31.85
 

 28. 
mc028-1.jpg
a.
–32
b.
16
c.
–10
d.
32
 

 29. 
mc029-1.jpg
a.
20
b.
125
c.
–625
d.
625
 

 30. 
mc030-1.jpg(–12m + 38)
a.
mc030-2.jpgm + 38
c.
mc030-4.jpgm + 76
b.
–24m + mc030-3.jpg
d.
mc030-5.jpgm + mc030-6.jpg
 

 31. 
(–5 – c)(–1)
a.
–5 + c
b.
5 + c
c.
5 – c
d.
–5 – c
 

 32. 
mc032-1.jpg
a.
mc032-2.jpg
c.
mc032-4.jpg
b.
mc032-3.jpg
d.
mc032-5.jpg
 

 33. 
mc033-1.jpg
a.
585
b.
169
c.
26
d.
181
 

 34. 
3.7 – 1.8 – 3.67 + 4.4 – 1.34
a.
–7.51
b.
–1.29
c.
1.29
d.
8.63
 

 35. 
mc035-1.jpg
a.
36
b.
–72
c.
72
d.
–36
 

 36. 
mc036-1.jpg
a.
–18n + 81mn – 153np
c.
–2n + 9mn – 17np
b.
–2n + 9m – 17p
d.
–2n – 9mn + 17np
 

 37. 
Evaluate the formula mc037-1.jpg for B = 9 in.2 and h = 32 in.
a.
288 in.3
b.
9.6 in.3
c.
32 in.3
d.
96 in.3
 

 38. 
Name the set(s) of numbers to which 1.68 belongs.
a.
rational numbers
b.
natural numbers, whole numbers, integers, rational numbers
c.
rational numbers, irrational numbers
d.
none of the above
 

 39. 
Name the set(s) of numbers to which –5 belongs.
a.
whole numbers, natural numbers, integers
b.
rational numbers
c.
whole numbers, integers, rational numbers
d.
integers, rational numbers
 

 40. 
Which set of numbers is the most reasonable to describe the number of desks in a classroom?
a.
whole numbers
c.
rational numbers
b.
irrational numbers
d.
integers
 

 41. 
Order the numbers from least to greatest.
mc041-1.jpg, mc041-2.jpg, mc041-3.jpg
a.
mc041-4.jpg, mc041-5.jpg, mc041-6.jpg
c.
mc041-10.jpg, mc041-11.jpg, mc041-12.jpg
b.
mc041-7.jpg, mc041-8.jpg, mc041-9.jpg
d.
mc041-13.jpg, mc041-14.jpg, mc041-15.jpg
 

 42. 
The opposite of a negative number is ____ negative.
a.
always
b.
sometimes
c.
never
 

 43. 
Write mc043-1.jpg, mc043-2.jpg, mc043-3.jpg in order from least to greatest.
a.
mc043-4.jpg, mc043-5.jpg, mc043-6.jpg
b.
mc043-7.jpg, mc043-8.jpg, mc043-9.jpg
c.
mc043-10.jpg, mc043-11.jpg, mc043-12.jpg
d.
mc043-13.jpg, mc043-14.jpg, mc043-15.jpg
 

 44. 
mc044-1.jpg
a.
2.8
b.
–2.8
 

 45. 
Which number line model can you use to simplify –5 + 6?
a.
mc045-1.jpg
–5 + 6 = 11
b.
mc045-2.jpg
–5 + 6 = 1
c.
mc045-3.jpg
–5 + 6 = –11
d.
mc045-4.jpg
–5 + 6 = 11
 

 46. 
A mountain climber ascends a mountain to its peak. The peak is 12,740 ft above sea level. The climber then descends 200 ft to meet a fellow climber. Find the climber’s elevation above sea level after meeting the other climber.
a.
12,540 ft
b.
–12,540 ft
c.
10,740 ft
d.
12,940 ft
 

 47. 
Evaluate –x + 2.7 for x = 0.9.
a.
–1.8
b.
–3.6
c.
1.8
d.
3.6
 

 48. 
The temperature on a summer afternoon is 85°F. Define a variable and write an expression to find the temperature after it changes. Then evaluate your expression for a decrease of 11 degrees Fahrenheit.
a.
11 + c; 11 + (–85) = 96
c.
11 – c; 11 – (–85) = 74
b.
85 + c; 85 + (–11) = 74
d.
85 – c; 85 – (–11) = 96
 

 49. 
Simplify 9 – 10 using a number line.
a.
mc049-1.jpg
b.
mc049-2.jpg
c.
mc049-3.jpg
d.
mc049-4.jpg
 

 50. 
Evaluate b – 2a – c for a = –7, b = 3, and c = –7.
a.
24
b.
3
c.
10
d.
–18
 

 51. 
The closing price of a share of stock in Company XYZ is $25.69 on Thursday. If the change from the closing price on Wednesday is –$0.75, find the closing price on Wednesday.
a.
$26.44
b.
$24.94
c.
$25.75
d.
$25.06
 

 52. 
You made two deposits to your bank account this month. One deposit was $17.92, and the second deposit was $15.33. Your balance at the end of the month is $72.31, and you made no withdrawals. Write and evaluate an expression for your balance at the beginning of the month.
a.
$72.31 + ($17.92 – $15.33); $74.90
b.
$72.31 – $17.92 – $15.33; $39.06
c.
$72.31 + $17.92 + $15.33; $105.56
d.
$72.31 – ($17.92 – $15.33); $69.72
 

 53. 
Evaluate x(–y + z) for x = 3, y = 3, and z = 1.
a.
–6
b.
10
c.
12
d.
–8
 

 54. 
The expression mc054-1.jpgcan be used to calculate the change in temperature in degrees Fahrenheit for an increase in altitude a, measured in feet. A plane starts on the ground and then rises 23,000 ft. Find the change in temperature at the altitude of the plane.
a.
126.5 degrees
c.
–125 degrees
b.
–126.5 degrees
d.
125 degrees
 

 55. 
The product of two negative numbers is ____ positive.
a.
always
b.
sometimes
c.
never
 

 56. 
–12 ¸ (–2)
a.
24
b.
–6
c.
–24
d.
6
 

 57. 
Evaluate mc057-1.jpg for m = –4, n = 2, and p = 1.5.
a.
–10
b.
–19
c.
–30
d.
–22
 

 58. 
If a is a negative number, then mc058-1.jpg is ____ equal to –1.
a.
always
b.
sometimes
c.
never
 

 59. 
Evaluate mc059-1.jpg for a = mc059-2.jpg and b = mc059-3.jpg.
a.
mc059-4.jpg
b.
mc059-5.jpg
c.
mc059-6.jpg
d.
mc059-7.jpg
 

 60. 
Simplify 7(499) using the Distributive Property.
a.
3500
b.
3493
c.
3514
d.
3486
 

 61. 
Use the Distributive Property to find the price of 7 CDs that cost $14.99 each.
a.
$105.00
b.
$98.00
c.
$104.93
d.
$105.70
 

 62. 
For every real number x, y, and z, the statement mc062-1.jpg is ____ true.
a.
always
b.
sometimes
c.
never
 

 63. 
–10z – 28z
a.
38z
b.
–38z
c.
18
d.
18z
 
 
Name the property the equation illustrates.
 

 64. 
mc064-1.jpg
a.
Inverse Property of Multiplication
b.
Multiplication Property of –1
c.
Identity Property of Addition
d.
Identity Property of Multiplication
 

 65. 
0 + x = x
a.
Identity Property of Addition
b.
Multiplication Property of 0
c.
Commutative Property of Addition
d.
Inverse Property of Multiplication
 

 66. 
8 ´ mc066-1.jpg = 1
a.
Identity Property of Division
b.
Inverse Property of Addition
c.
Inverse Property of Multiplication
d.
Multiplication Property of –1
 

 67. 
8.2 + (–8.2) = 0
a.
Inverse Property of Addition
b.
Addition Property of 0
c.
Identity Property of Addition
d.
Inverse Property of Multiplication
 

 68. 
8 + 3.4 = 3.4 + 8
a.
Inverse Property of Addition
b.
Associative Property of Addition
c.
Commutative Property of Addition
d.
Inverse Property of Multiplication
 

 69. 
7 + (4 + 4) = (7 + 4) + 4
a.
Inverse Property of Addition
b.
Associative Property of Addition
c.
Commutative Property of Multiplication
d.
Commutative Property of Addition
 

 70. 
mc070-1.jpg
a.
Associative Property of Addition
b.
Commutative Property of Multiplication
c.
Inverse Property of Multiplication
d.
Commutative Property of Addition
 

 71. 
(ab)3 = a(b3)
a.
Inverse Property of Multiplication
b.
Associative Property of Addition
c.
Associative Property of Multiplication
d.
Commutative Property of Multiplication
 

 72. 
At the grocery store, you buy a carton of milk for $1.95, a loaf of bread for $0.85, and a bag of cookies for $2.05. Use mental math to find the total cost of the groceries.
a.
$5.15
b.
$4.90
c.
$5.00
d.
$4.85
 

 73. 
What are the coordinates of point A?
mc073-1.jpg
a.
(–1, 1)
b.
(1, 1)
c.
(–1, –1)
d.
(1, –1)
 

 74. 
In which quadrant or on which axis would you find the point (–2, –4)?
a.
Quadrant III
b.
Quadrant II
c.
Quadrant IV
d.
y-axis
 

 75. 
The point (a, b) is ____ in Quadrant II when a < 0.
a.
always
b.
sometimes
c.
never
 

 76. 
Which of the scatter plots shows a positive correlation?
a.
mc076-1.jpg
c.
mc076-3.jpg
b.
mc076-2.jpg
d.
mc076-4.jpg
 

 77. 
Write the coordinates of the point that is 9 units to the left of the y-axis and 6 units above the x-axis.
a.
(–9, 6)
b.
(9, 6)
c.
(–9, –6)
d.
(6, –9)
 

Short Answer
 

 78. 
a. Write an equation to show how the amount of money in a jar of nickels is related to the number of nickels in the jar.
b. If the jar contains 40 nickels, how much money is this?
 

 79. 
Graph the points on the same coordinate plane.
A(4, 4), B(3, –1), C(–4, –1)

sa079-1.jpg
 

 80. 
The population of an endangered animal species has been increasing. Make a scatter plot using the data given in the table.

Year
Population
1
230
2
670
3
620
4
840
5
1400
6
1580

sa080-1.jpg
 

Essay
 

 81. 
a. Simplify the following expressions.
es081-1.jpg
b. What is the sign of the final answer when the exponent is odd? When the exponent is even?
c. Use your answer from part (b) to simplify es081-2.jpg.
 

 82. 
Justify each step.
a. 7 + 2(x – 3) + 5x = 7 + 2x – 6 + 5x
b.= 7 + 2x + (–6) + 5x
c.= 7 + (–6) + 2x + 5x
d.= 7 + (–6) + (2 + 5)x
e.= 7 + (–6) + 7x
f.= 1 + 7x
g.= 7x + 1
 

 83. 
Simplify the expression. Justify each step.
13x – 4 + 9x
 

Other
 

 84. 
Is the statement below true or false? If the statement is false, give a counterexample.
All real numbers are rational.
 

 85. 
Is the following statement true or false for all values of a and b? If false, give a counterexample.
ot085-1.jpg
 



 
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