Ch. 0 Chapter P: Prerequisites: Fundamental Concepts of Algebra
0.1 Algebraic Expressions, Mathematical Models, and Real Numbers
1 Evaluate Algebraic Expressions
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Evaluate the algebraic expression for the given value or values of the variable(s).
1) 8x + 3; x = 2
A) 19 B) 32 C) 11 D) 13
2) 3x + 6; x = -3
A) -3 B) 15 C) -15 D) 3
3) 2(x + 3) + 17; x = -11
A) 1 B) -1 C) 55 D) -21
4) 4x2 + 8y; x = 7 and y = 9
A) 268 B) 856 C) 2052 D) 380
5) (x + 4y)2; x = 2 and y = 2
A) 100 B) 10 C) 20 D) 36
6) 6 + 5(x - 2)3; x = 4
A) 46 B) 16 C) 88 D) -34
7) x2 - 3(x - y); x = 8 and y = 2
A) 46 B) 38 C) 42 D) -82
8) 7(x + 1)
2x + 4 ; x = 5
A) 3 B) 2 C) 6 D) 7
2
9) y - 2x
3x + xy ; x = -4 and y = 1
A) - 9
16 B) 7
16 C) 7
8 D) - 1
16
2 Use Mathematical Models
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve.
1) The formula C = 5
9 (F - 32) expresses the relationship between Fahrenheit temperature, F, and Celsius
temperature, C. Use the formula to convert 86°F to its equivalent temperature on the Celsius scale.
A) 30°C B) 6°C C) 66°C D) 97°C
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2) A stone is dropped from a tower that is 740 feet high. The formula h = 740 - 16t2 describes the stoneʹs height
above the ground, h, in feet, t seconds after it was dropped. What is the stoneʹs height 5 seconds after it is
released?
A) 340 ft B) 350 ft C) 315 ft D) 365 ft
3) If a rock falls from a height of 70 meters above the ground, the height H (in meters) after x seconds can be
approximated using the formula H = 70 - 4.9x2. What is the height of the rock after 3 seconds?
A) 25.9 m B) 585.9 m C) -146.09 m D) 55.3 m
4) As the relative humidity increases, the temperature seems higher than it is. The formula T = 0.101x + 82.57
approximates the apparent temperature for an actual temperature of 90°F, where x is the relative humidity.
What is the apparent temperature (to the nearest degree) for a relative humidity of 80%?
A) 91°F B) 667°F C) 163°F D) 83°F
5) The winning times (in seconds) in a speed-skating event for men can be represented by the formula
T = 46.97 - 0.099x, where x represents the year, with x = 0 corresponding to 1920. (For example in 1992, x would
be 1992 - 1920 = 72.) According to the formula, what was the winning time in 1997? Round to the nearest
hundredth.
A) 39.35 sec B) 3609.07 sec C) 40.34 sec D) 41.33 sec
6) It is estimated that y, the number of items of a particular commodity (in millions) sold in the United States in
year x, where x represents the number of years since 1990, is given by the formula y = 1.23x + 4.5. That is, x = 0
represents 1990, x = 1 represents 1991, and so on. According to the formula, how many items sold in 1996?
A) 11.88 millions B) 4.5 millions C) 34.38 millions D) 13.11 millions
3 Find the Intersection of Two Sets
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the intersection of the two sets.
1) {1, 7, 4, 9} ∩ {4, 6, 1}
A) {1, 4} B) {1} C) {1, 4, 9, 7, 6} D) ∅
2) {1, 3, 9} ∩ {5, 6}
A) ∅ B) {3, 9} C) {1, 5, 9, 3, 6} D) {1, 9}
3) {6, 8, 9, 11} ∩ ∅
A) ∅ B) {6, 8, 9, 11} C) {6, 8} D) {9, 11}
4 Find the Union of Two Sets
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the union of the two sets.
1) {1, 4, 8, 11} ∪ {1, 4, 13}
A) {1, 4, 8, 11, 13} B) {1, 4} C) {8, 11, 13} D) ∅
2) {1, 11} ∪ {1, 4, 9}
A) {1, 4, 9, 11} B) {1} C) {4, 9, 11} D) ∅
3) {4, 6, 7, 9} ∪ ∅
A) {4, 6, 7, 9} B) {4, 6} C) {7, 9} D) ∅
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5 Recognize Subsets of the Real Numbers
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
List all numbers from the given set B that are members of the given Real Number subset.
1) B = {6, 7, -11, 0, 0.9, 9} Integers
A) 6, -11, 0, 9 B) 6, 0 C) 6, -11, 0 D) 6, 0, 9
2) B = {17, 7, -15, 0, 0.7, 9} Whole numbers
A) 17, 0, 9 B) 17, -15, 0 C) 17, -15, 0, 9 D) 17, 0
3) B = {17, 5, -18, 0, 0.8, 4} Natural numbers
A) 17, 4 B) 17, 0, 4 C) 17, 0 D) 17
4) B = {14, 6, -19, 0, 5
6 , 16, 0.8, 0.62} Rational numbers
A) 14, -19, 0, 5
6 , 16, 0.62, 0.8 B) 14, 0, 16
C) 6, 16 D) 6, 5
6 , 0.62
5) B = {3, 8, -15, 0, 4
5 , 4, 0.6, 0.7} Irrational numbers
A) 8 B) 8, 0.6 C) 8, 4, 0.6 D) 8, 4, 0.7
6) B = {5, 8, 0, 5
6 , 16, -0.9, 0.17, -11} Real numbers
A) 5, 8, 0, 5
6 , 16, -0.9, 0.17, -11 B) 5, 8, 0, 5
6 , 16, 0.17
C) 5, 8, 5
6 , 16, -0.9, 0.17, -11 D) 5, 0, 5
6 , -0.9, 0.17, -11
6 Use Inequality Symbols
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Determine whether the statement is true or false.
1) 12 > 21
A) False B) True
2) 14 ≥ 4
A) True B) False
3) -26 < 0
A) True B) False
4) 19 < -8
A) False B) True
5) 16 ≤ 11
A) False B) True
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6) -7 ≤ 7
A) True B) False
7) 12 > 2
A) True B) False
8) -2 ≥ 6
A) False B) True
9) -π ≥ -π
A) True B) False
10) π < 3
A) False B) True
7 Evaluate Absolute Value
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Rewrite the expression without absolute value bars.
1) |9|
A) 9 B) -9 C) 18 D) 0
2) |-7|
A) 7 B) -7 C) 14 D) 0
3) 10
1
A) 10 B) -1 C) 1 D) -10
4) 6 - 17
A) 17 - 6 B) 6 - 17 C) -11 D) 11
5) |3 + (-8)|
A) 5 B) 11 C) -5 D) -11
6) -4 - -8
A) 4 B) 12 C) -4 D) -12
7) -1 + -4
A) 5 B) 3 C) -3 D) -5
Evaluate the expression for the given values of x and y.
8) |x|
x + |y|
y ; x = 2 and y = -1
A) 0 B) 2 C) 1 D) -1
8 Use Absolute Value to Express Distance
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute
value expression.
1) 38 and 96
A) |38 - 96| = 58 B) -|96 - 38| = -58 C) |38 + 96| = 134 D) -|38 + 96| = -134
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2) -59 and -73
A) |(-59) - (-73)| = 14 B) |(-73) - (-59)| = -14
C) |(-73) + (-59)| = -132 D) |-(-59) + (-73)| = 132
3) 89 and -90
A) |89 - (-90)| = 179 B) |(-90) - 89| = -179
C) |89 + (-90)| = -1 D) |-89 + (-90)| = 1
4) 33.2 and 45.5
A) |33.2 - 45.5| = 12.3 B) |45.5 - 33.2| = -12.3
C) |33.2 + 45.5| = 78.7 D) |-33.2 + 45.5| = -78.7
5) -45.1 and 40.5
A) |-45.1 - 40.5| = 85.6 B) |40.5 + (-45.1)| = -85.6
C) |40.5 - (-45.1)| = -4.6 D) |-45.1 + (-40.5)| = 4.6
6) 8.2 and 17.9
A) |8.2 - 17.9| = 9.7 B) |17.9 - 8.2| = -9.7
C) |17.9 + 8.2| = 26.1 D) -|8.2 + 17.9| = -26.1
9 Identify Properties of the Real Numbers
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
State the name of the property illustrated.
1) 6 + (-9) = (-9) + 6
A) Commutative property of addition
B) Associative property of addition
C) Distributive property of multiplication over addition
D) Identity property of addition
2) 17 · (6 + 3) = 17 · 6 + 17 · 3
A) Distributive property of multiplication over addition
B) Commutative property of multiplication
C) Associative property of multiplication
D) Commutative property of addition
3) 18 + (15 + 9) = (18 + 15) + 9
A) Associative property of addition
B) Commutative property of addition
C) Distributive property of multiplication over addition
D) Identity property of addition
4) (5 + 9) + 6 = (9 + 5) + 6
A) Commutative property of addition
B) Associative property of addition
C) Distributive property of multiplication over addition
D) Inverse property of addition
5) 7 · (2 · 12) = 7 · (12 · 2)
A) Commutative property of multiplication
B) Associative property of multiplication
C) Distributive property of multiplication over addition
D) Identity property of multiplication
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6) (6 + 1) + (3 + 16) = (3 + 16) + (6 + 1)
A) Commutative property of addition
B) Associative property of addition
C) Distributive property of multiplication over addition
D) Inverse property of addition
7) 7 · (18 · 1) = (18 · 1) · 7
A) Commutative property of multiplication
B) Associative property of multiplication
C) Distributive property of multiplication over addition
D) Identity property of multiplication
8) (1 · 14) · 5 = 1 · (14 · 5)
A) Associative property of multiplication
B) Commutative property of multiplication
C) Distributive property of multiplication over addition
D) Identity property of multiplication
9) 5(x + 3) = 5x + 5 · 3
A) Distributive property of multiplication over addition
B) Commutative property of multiplication
C) Associative property of multiplication
D) Identity property of multiplication
10) 6(-6 + 4) = -36 + 24
A) Distributive property of multiplication over addition
B) Associative property of multiplication
C) Associative property of addition
D) Commutative property of multiplication
11) -7(2 + 5) = -14 + (-35)
A) Distributive property of multiplication over addition
B) Associative property of multiplication
C) Associative property of addition
D) Commutative property of multiplication
12) 1
(x + 2) (x + 2) = 1, x ≠ -2
A) Inverse property of multiplication B) Inverse property of addition
C) Commutative property of multiplication D) Identity property of multiplication
13) (x + 8) + [-(x + 8)] = 0
A) Inverse property of addition B) Inverse property of multiplication
C) Commutative property of addition D) Identity property of multiplication
10 Simplify Algebraic Expressions
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Simplify the algebraic expression.
1) -9(5r + 8) + 2(10r + 9)
A) -25r - 54 B) -4r - 1 C) -25r + 8 D) -117r
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2) (9z + 10) - (2z - 8)
A) 7z + 18 B) 7z + 2 C) 11z + 18 D) 7z - 18
3) -3(2x - 10) - 4x + 9
A) -10x + 39 B) 2x + 39 C) 10x + 39 D) -10x - 21
Write the algebraic expression without parentheses.
4) -(73w)
A) -73w B) 73w C) -73 - w D) 73 - w
5) -7(-5z)
A) 35z B) -35z C) 35 - 7z D) 35 + z
6) -(6x - 2)
A) -6x + 2 B) 6x - 2 C) -6x - 2 D) 12x
7) -(-7 + 7y)
A) 7 - 7y B) 7 + 7y C) -7 + 7y D) 49y
8) - (6z - 7w + 3y)
A) -6z + 7w - 3y B) -6z + 7w + 3y C) -6z - 7w + 3y D) -6z - 7w - 3y
9) 1
5 (5x) + [(-3x) + (3x)]
A) x B) -5x C) 7x D) 1
0.2 Exponents and Scientific Notation
1 Use Properties of Exponents
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Evaluate the exponential expression.
1) 33 · 10
A) 270 B) 90 C) 27,000 D) 37
2) (-7)3
A) -343 B) 343 C) -21 D) 21
3) -34
A) -81 B) 12 C) 81 D) -12
4) 90
A) 1 B) -1 C) 0 D) 9
5) (-7)0
A) 1 B) -1 C) 0 D) 7
6) -60
A) -1 B) 1 C) 0 D) 6
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7) 3-4
A) 1
81 B) -81 C) 81 D) 1
12
8) (-3)-4
A) 1
81 B) -81 C) 81 D) - 1
81
9) -2-4
A) - 1
16 B) -16 C) 16 D) 1
8
10) 96 · 99
A) 915 B) 954 C) 8115 D) 8154
11) (42)3
A) 4096 B) 1024 C) 24 D) 48
12) (42)-3
A) 1
4096 B) 1
1024 C) -24 D) -48
13) 5-3 · 5
A) 1
25 B) 1
125 C) 25 D) 125
14) 56 · 5-7
A) 1
5 B) -5 C) 1.220703125e+09 D) - 1
5
15) 44
42
A) 16 B) 1
16 C) 240 D) 2
2 Simplify Exponential Expressions
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Simplify the exponential expression.
1) x · x6
A) x7 B) 2x6 C) x6 D) 2x7
2) x-4y
A) y
x4 B) -x4y C) - y
x4 D) 1
x4y
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3) x5y0
A) x5 B) 1 C) 0 D) 1
x5
4) x5 · x3
A) x8 B) x15 C) 8x D) 15x
5) x9 · x-3
A) x6 B) 1
x6 C) -x6 D) - 1
x6
6) x-5 · x2
A) 1
x3 B) -x3 C) x3 D) - 1
x3
7) (x2)7
A) x14 B) x9 C) 7x2 D) 7x14
8) (x-3)6
A) 1
x18 B) -x18 C) -3x6 D) -3x18
9) (x4)-6
A) 1
x24 B) - x24 C) -6x4 D) -6x24
10) (x-5)-3
A) x15 B) 1
x15 C) 1
x8 D) -x8
11) x14
x4
A) x10 B) x18 C) x6 D) 1
x10
12) x2
x5
A) 1
x3 B) -x3 C) x3 D) - 1
x3
13) x-7
x2
A) 1
x9 B) 1
x14 C) 1
x5 D) x9
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14) x-5
y-2
A) y2
x5 B) 1
x5y2 C) x5y2 D) x5
y2
15) (2x)4
A) 16x4 B) 8x C) 16x D) 8x4
16) (-5x)2
A) 25x2 B) -10x C) 25x D) -10x2
17) (5x4)2
A) 25x8 B) 5x8 C) 25x4 D) 5x6
18) -8y0
A) -8 B) 1 C) 0 D) -7
19) (7b)0
A) 1 B) 0 C) b D) 7
20) (x9y)4
A) x36y4 B) x36y C) x13y5 D) x13y
21) (6x9)(7x6)
A) 42x15 B) -42x15 C) 42x54 D) -42x54
22) (-5x3y)(-9x6y5)
A) 45x9y6 B) -45x9y5 C) -14x9y5 D) 45x18y5
23) 4x7
x5
A) 4x2 B) 16x2 C) 4x12 D) 8x
24) 14x13
2x4
A) 7x9 B) x8 C) x9 D) 7x8
25) -48x7
8x12
A) -6
x5 B) -6x5 C) -6
x4 D) -6x4
26) x
4
3
A) x3
64 B) x4
256 C) x
4 D) x3
4
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27) - 4
x
2
A) 16
x2 B) - 16
x2 C) 16
x D) 4
x2
28) x3
4
2
A) x6
16 B) x6
4 C) x5
16 D) x5
4
29) -3x
y
2
A) 9x2
y2 B) 9x
y2 C) -6x2
y2 D) -6x
y
30) x13y9
x10y2
A) x3y7 B) x2y6 C) xy7 D) x2y7
31) 48x12y10
8x4y2
A) 6x8y8 B) x8y8 C) 6x7y8 D) 6x7y7
32) x2y-5
A) x2
y5 B) y5x2 C) x2
y11 D) y11x2
33) 3x-8y5
A) 3y5
x8 B) 3
x8y5 C) y5
3x8 D) 3x8
y5
34) x8y-5
z-9
A) x8z9
y5 B) z9
x8y5 C) y5
x8z9 D) x8z5
y9
35) 35x11y15
5x10y-10
A) 7xy25 B) 35xy25 C) 7x21y25 D) 7xy5
36) -36x13y13z7
4x8y6z6
A) -9x5y7z B) x5y7z C) -9x4y6z D) -9x5y7
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37) -25x12y10
5x2y3
0
A) 1 B) x10y7 C) -5x10y7 D) 0
38) (-11x8y8)2
A) 121x16y16 B) -11x16y16 C) -121x16y16 D) 121x10y10
39) (6x8)-2
A) 1
36x16 B) 1
6x16 C) 36x16 D) 36
x16
40) (x-4y6)-1-1
A) x4
y6 B) x-5
y5 C) 1
x4y6 D) y5
x-5
41) (2x-7y4z-8)-1
A) x7z8
2y4 B) y5
2x8z9 C) x7z8
-2y-4 D) y5
-2x8z9
42) 2x3y4
z4
2
A) 4x6y8
z8 B) 2x6y8
z8 C) 4x5y6
z6 D) 2x6y8
z6
43) -12x10y7
6x14y-2
3
A) -8y27
x12 B) 8y27
x12 C) -8y15
x12 D) -8
x12y27
44) x-3
y6
-3
A) x9y18 B) x-6
y3 C) 1
x9y18 D) y3
x-6
45) 4x3
y2
-5
A) y10
1024x15 B) 1024x15
y10 C) 1024y10
x15 D) y2
1024x15
46) (4x4)3
x15
A) 64
x3 B) 4
x3 C) 64
x8 D) 64
x27
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47) (-4x4y-5)(2x-1y)
A) -8x3
y4 B) -8x3y6 C) -2x3
y4 D) -8x5
y6
48) 2-8x-4y2
2-5x-7y4
A) x3
8y2 B) 1
8x7y2 C) 3x3
y2 D) 8
x3y2
49) xy5
x3y
-2
A) x4
y8 B) 1
x5y11 C) 1
x8y12 D) y8
x4
50) 12x-5y-3z4
3xy-3z-4
-1
A) x6
4z8 B) x4
4z8 C) 4x6
z8 D) x6y6
4z8
3 Use Scientific Notation
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Write the number in decimal notation without the use of exponents.
1) 9 × 10-3
A) 0.009 B) 9000 C) 0.09 D) 900
2) 2 × 103
A) 2000 B) 0.002 C) 20,000 D) 0.0002
3) 1.19 × 107
A) 11,900,000 B) 119,000,000 C) 1,190,000 D) 83.3
4) 7.34 × 10-4
A) 0.000734 B) 0.00734 C) 0.0000734 D) -734,000
5) 2.714 × 10-6
A) 0.000002714 B) 0.00002714 C) 0.0000002714 D) -2,714,000
6) -7.84 × 107
A) -78,400,000 B) -784,000,000 C) -7,840,000 D) 78,400,000
7) -7.1039 × 105
A) -710,390 B) -7,103,900 C) -71,039 D) -355.195
Write the number in scientific notation.
8) 7,781,440
A) 7.78144 × 106 B) 7.78144 × 107 C) 7.78144 × 10-6 D) 7.78144 × 101
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9) 36,000
A) 3.6 × 104 B) 3.6 × 10-4 C) 3.6 × 103 D) 3.6 × 10-3
10) 52,000,000
A) 5.2 × 107 B) 5.2 × 10-7 C) 5.2 × 106 D) 5.2 × 10-6
11) 8,546,930
A) 8.54693 × 106 B) 8.54693 × 107 C) 8.54693 × 10-6 D) 8.54693 × 101
12) 0.000576
A) 5.76 × 10-4 B) 5.76 × 104 C) 5.76 × 10-5 D) 5.76 × 10-3
13) 0.00002686
A) 2.686 × 10-5 B) 2.686 × 105 C) 2.686 × 10-4 D) 2.686 × 104
14) 0.000000041701
A) 4.1701 × 10-8 B) 4.1701 × 108 C) 4.1701 × 10-7 D) 4.1701 × 10-9
Perform the indicated computation. Write the answer in scientific notation.
15) (9 × 10-8)(2.1 × 10-7)
A) 1.89 × 10-14 B) 18.9 × 10-14 C) 189 × 10-15 D) 1.89 × 1056
16) (2 × 105)(3.6 × 108)
A) 7.2 × 1013 B) 7.2 × 1014 C) 72 × 1013 D) 7.2 × 1040
17) 10 × 10-8
2 × 10-3
A) 5 × 10-5 B) 5 × 10-11 C) 10 × 10-5 D) 10 × 10-11
18) 14.05 × 107
5 × 10-8
A) 2.81 × 1015 B) 2.81 × 10-1 C) 5.62 × 1015 D) 5.62 × 10-1
19) 8.37 × 10-3
3.1 × 10-8
A) 2.7 × 105 B) 2.7 × 10-11 C) 5.4 × 105 D) 5.4 × 10-11
20) 80,000,000,000
0.000004
A) 2 × 1016 B) 2 × 1015 C) 4 × 1016 D) 4 × 1015
21) 0.00016 × 0.0003
0.0008
A) 6 × 10-5 B) 6 × 105 C) 48 × 106 D) 48 × 10-6
Solve. Express the result in scientific notation. If necessary, round the decimal factor to two decimal places.
22) In a state with a population of 9,000,000 people, the average citizen spends $6,000 on housing each year. What
is the total spent on housing for the state?
A) $5.4 × 1010 B) $5.4 × 109 C) $54 × 1011 D) $54 × 1010
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23) Approximately 4 × 103 employees of a certain company average $30,000 each year in salary. What is the total
amount earned by all the employees of this company per year?
A) $1.2 × 108 B) $12 × 108 C) $1.2 × 109 D) $12 × 109
0.3 Radicals and Rational Exponents
1 Evaluate Square Roots
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Evaluate the expression or indicate that the root is not a real number.
1) 4
A) 2 B) 16 C) 1
4 D) Not a real number
2) - 361
A) -19 B) 19 C) -180 D) Not a real number
3) -144
A) 12
144 B) 20,736 C) 12 D) Not a real number
4) 64 + 36
A) 10 B) 14 C) 100 D) 28
5) 169 - 25
A) 12 B) 17 C) 144 D) 119
6) 64 + 36
A) 14 B) 10 C) 100 D) 28
2 Simplify Expressions of the Form SqRt(a^2)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Evaluate the expression or indicate that the root is not a real number.
1) (3)2
A) 3 B) 81 C) 1
9 D) Not a real number
2) (-14)2
A) 14 B) 196 C) -14 D) Not a real number
3 Use the Product Rule to Simplify Square Roots
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use the product rule to simplify the expression.
1) 18
A) 3 2 B) 2 3 C) 6 D) 4
2) 26
A) 26 B) 2 13 C) 13 2 D) 13
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Precalculus Essentials, 4th Edition Test Bank

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