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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) 9x + 8; x = 7
A) 71 B) 126 C) 17 D) 55
2) 8x + 3; x = -2
A) -13 B) 19 C) -19 D) 13
3) 2(x + 1) + 21; x = -4
A) 15 B) -15 C) 35 D) 7
4) 6x2 + 8y; x = 7 and y = 5
A) 334 B) 1804 C) 1710 D) 206
5) (x + 4y)2; x = 4 and y = 2
A) 144 B) 12 C) 24 D) 64
6) 2 + 6(x - 6)3; x = 8
A) 50 B) 14 C) 64 D) -46
7) x2 - 4(x - y); x = 6 and y = 2
A) 20 B) 10 C) 14 D) -52
8) 6(x + 3)
2x + 2 ; x = 5
A) 4 B) 1 C) 8 D) 11
2
9) y - 4x
7x + xy ; x = -1 and y = 3
A) - 7
10 B) 1
10 C) 1
4 D) - 9
10
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 68°F to its equivalent temperature on the Celsius scale.
A) 20°C B) 4°C C) 56°C D) 65°C
Page 1
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) 9x + 8; x = 7
A) 71 B) 126 C) 17 D) 55
2) 8x + 3; x = -2
A) -13 B) 19 C) -19 D) 13
3) 2(x + 1) + 21; x = -4
A) 15 B) -15 C) 35 D) 7
4) 6x2 + 8y; x = 7 and y = 5
A) 334 B) 1804 C) 1710 D) 206
5) (x + 4y)2; x = 4 and y = 2
A) 144 B) 12 C) 24 D) 64
6) 2 + 6(x - 6)3; x = 8
A) 50 B) 14 C) 64 D) -46
7) x2 - 4(x - y); x = 6 and y = 2
A) 20 B) 10 C) 14 D) -52
8) 6(x + 3)
2x + 2 ; x = 5
A) 4 B) 1 C) 8 D) 11
2
9) y - 4x
7x + xy ; x = -1 and y = 3
A) - 7
10 B) 1
10 C) 1
4 D) - 9
10
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 68°F to its equivalent temperature on the Celsius scale.
A) 20°C B) 4°C C) 56°C D) 65°C
Page 1
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) 9x + 8; x = 7
A) 71 B) 126 C) 17 D) 55
2) 8x + 3; x = -2
A) -13 B) 19 C) -19 D) 13
3) 2(x + 1) + 21; x = -4
A) 15 B) -15 C) 35 D) 7
4) 6x2 + 8y; x = 7 and y = 5
A) 334 B) 1804 C) 1710 D) 206
5) (x + 4y)2; x = 4 and y = 2
A) 144 B) 12 C) 24 D) 64
6) 2 + 6(x - 6)3; x = 8
A) 50 B) 14 C) 64 D) -46
7) x2 - 4(x - y); x = 6 and y = 2
A) 20 B) 10 C) 14 D) -52
8) 6(x + 3)
2x + 2 ; x = 5
A) 4 B) 1 C) 8 D) 11
2
9) y - 4x
7x + xy ; x = -1 and y = 3
A) - 7
10 B) 1
10 C) 1
4 D) - 9
10
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 68°F to its equivalent temperature on the Celsius scale.
A) 20°C B) 4°C C) 56°C D) 65°C
Page 1
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) 9x + 8; x = 7
A) 71 B) 126 C) 17 D) 55
2) 8x + 3; x = -2
A) -13 B) 19 C) -19 D) 13
3) 2(x + 1) + 21; x = -4
A) 15 B) -15 C) 35 D) 7
4) 6x2 + 8y; x = 7 and y = 5
A) 334 B) 1804 C) 1710 D) 206
5) (x + 4y)2; x = 4 and y = 2
A) 144 B) 12 C) 24 D) 64
6) 2 + 6(x - 6)3; x = 8
A) 50 B) 14 C) 64 D) -46
7) x2 - 4(x - y); x = 6 and y = 2
A) 20 B) 10 C) 14 D) -52
8) 6(x + 3)
2x + 2 ; x = 5
A) 4 B) 1 C) 8 D) 11
2
9) y - 4x
7x + xy ; x = -1 and y = 3
A) - 7
10 B) 1
10 C) 1
4 D) - 9
10
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 68°F to its equivalent temperature on the Celsius scale.
A) 20°C B) 4°C C) 56°C D) 65°C
Page 1
2) A stone is dropped from a tower that is 770 feet high. The formula h = 770 - 16t2 describes the stone's
height above the ground, h, in feet, t seconds after it was dropped. What is the stone's height 4 seconds
after it is released?
A) 514 ft B) 524 ft C) 489 ft D) 539 ft
3) If a rock falls from a height of 50 meters above the ground, the height H (in meters) after x seconds can be
approximated using the formula H = 50 - 4.9x2. What is the height of the rock after 3 seconds?
A) 5.9 m B) 405.9 m C) -166.09 m D) 35.3 m
4) As the relative humidity increases, the temperature seems higher than it is. The formula T = 0.113x + 77.98
approximates the apparent temperature for an actual temperature of 85°F, where x is the relative
humidity. What is the apparent temperature (to the nearest degree) for a relative humidity of 40%?
A) 83°F B) 352°F C) 118°F D) 78°F
5) The winning times (in seconds) in a speed-skating event for men can be represented by the formula
T = 46.18 - 0.095x, 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 1998? Round to the
nearest hundredth.
A) 38.77 sec B) 3594.63 sec C) 39.72 sec D) 40.67 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 = 1.3x + 3.07. That
is, x = 0 represents 1990, x = 1 represents 1991, and so on. According to the formula, how many items sold
in 1995?
A) 9.57 millions B) 3.07 millions C) 21.85 millions D) 10.87 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, 3, 5, 8} ∩ {5, 11, 1}
A) {1, 5} B) {1} C) {1, 5, 8, 3, 11} D) ∅
2) {2, 10, 8} ∩ {4, 6}
A) ∅ B) {10, 8} C) {2, 4, 8, 10, 6} D) {2, 8}
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) {2, 5, 8, 10} ∪ {2, 5, 12}
A) {2, 5, 8, 10, 12} B) {2, 5} C) {8, 10, 12} D) ∅
2) {2, 10} ∪ {2, 4, 8}
A) {2, 4, 8, 10} B) {2} C) {4, 8, 10} D) ∅
3) {1, 3, 4, 6} ∪ ∅
A) {1, 3, 4, 6} B) {1, 3} C) {4, 6} D) ∅
Page 2
height above the ground, h, in feet, t seconds after it was dropped. What is the stone's height 4 seconds
after it is released?
A) 514 ft B) 524 ft C) 489 ft D) 539 ft
3) If a rock falls from a height of 50 meters above the ground, the height H (in meters) after x seconds can be
approximated using the formula H = 50 - 4.9x2. What is the height of the rock after 3 seconds?
A) 5.9 m B) 405.9 m C) -166.09 m D) 35.3 m
4) As the relative humidity increases, the temperature seems higher than it is. The formula T = 0.113x + 77.98
approximates the apparent temperature for an actual temperature of 85°F, where x is the relative
humidity. What is the apparent temperature (to the nearest degree) for a relative humidity of 40%?
A) 83°F B) 352°F C) 118°F D) 78°F
5) The winning times (in seconds) in a speed-skating event for men can be represented by the formula
T = 46.18 - 0.095x, 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 1998? Round to the
nearest hundredth.
A) 38.77 sec B) 3594.63 sec C) 39.72 sec D) 40.67 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 = 1.3x + 3.07. That
is, x = 0 represents 1990, x = 1 represents 1991, and so on. According to the formula, how many items sold
in 1995?
A) 9.57 millions B) 3.07 millions C) 21.85 millions D) 10.87 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, 3, 5, 8} ∩ {5, 11, 1}
A) {1, 5} B) {1} C) {1, 5, 8, 3, 11} D) ∅
2) {2, 10, 8} ∩ {4, 6}
A) ∅ B) {10, 8} C) {2, 4, 8, 10, 6} D) {2, 8}
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) {2, 5, 8, 10} ∪ {2, 5, 12}
A) {2, 5, 8, 10, 12} B) {2, 5} C) {8, 10, 12} D) ∅
2) {2, 10} ∪ {2, 4, 8}
A) {2, 4, 8, 10} B) {2} C) {4, 8, 10} D) ∅
3) {1, 3, 4, 6} ∪ ∅
A) {1, 3, 4, 6} B) {1, 3} C) {4, 6} D) ∅
Page 2
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 = {17, 5, -22, 0, 0.6, 25} Integers
A) 17, -22, 0, 25 B) 17, 0 C) 17, -22, 0 D) 17, 0, 25
2) B = {11, 6, -16, 0, 0.1, 4} Whole numbers
A) 11, 0, 4 B) 11, -16, 0 C) 11, -16, 0, 4 D) 11, 0
3) B = {10, 6, -9, 0, 0.6, 9} Natural numbers
A) 10, 9 B) 10, 0, 9 C) 10, 0 D) 10
4) B = {16, 5, -2, 0, 8
9 , 25, 0.3, 0.73} Rational numbers
A) 16, -2, 0, 8
9 , 25, 0.73, 0.3 B) 16, 0, 25
C) 5, 25 D) 5, 8
9 , 0.73
5) B = {11, 7, -11, 0, 5
6 , 4, 0.7, 0.35} Irrational numbers
A) 7 B) 7, 0.7 C) 7, 4, 0.7 D) 7, 4, 0.35
6) B = {4, 8, 0, 5
6 , 9, -0.9, 0.53, -23} Real numbers
A) 4, 8, 0, 5
6 , 9, -0.9, 0.53, -23 B) 4, 8, 0, 5
6 , 9, 0.53
C) 4, 8, 5
6 , 9, -0.9, 0.53, -23 D) 4, 0, 5
6 , -0.9, 0.53, -23
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) 21 > 24
A) False B) True
2) 17 ≥ 4
A) True B) False
3) -81 < 0
A) True B) False
4) 24 < -6
A) False B) True
5) 12 ≤ 11
A) False B) True
Page 3
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 = {17, 5, -22, 0, 0.6, 25} Integers
A) 17, -22, 0, 25 B) 17, 0 C) 17, -22, 0 D) 17, 0, 25
2) B = {11, 6, -16, 0, 0.1, 4} Whole numbers
A) 11, 0, 4 B) 11, -16, 0 C) 11, -16, 0, 4 D) 11, 0
3) B = {10, 6, -9, 0, 0.6, 9} Natural numbers
A) 10, 9 B) 10, 0, 9 C) 10, 0 D) 10
4) B = {16, 5, -2, 0, 8
9 , 25, 0.3, 0.73} Rational numbers
A) 16, -2, 0, 8
9 , 25, 0.73, 0.3 B) 16, 0, 25
C) 5, 25 D) 5, 8
9 , 0.73
5) B = {11, 7, -11, 0, 5
6 , 4, 0.7, 0.35} Irrational numbers
A) 7 B) 7, 0.7 C) 7, 4, 0.7 D) 7, 4, 0.35
6) B = {4, 8, 0, 5
6 , 9, -0.9, 0.53, -23} Real numbers
A) 4, 8, 0, 5
6 , 9, -0.9, 0.53, -23 B) 4, 8, 0, 5
6 , 9, 0.53
C) 4, 8, 5
6 , 9, -0.9, 0.53, -23 D) 4, 0, 5
6 , -0.9, 0.53, -23
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) 21 > 24
A) False B) True
2) 17 ≥ 4
A) True B) False
3) -81 < 0
A) True B) False
4) 24 < -6
A) False B) True
5) 12 ≤ 11
A) False B) True
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6) -5 ≤ 8
A) True B) False
7) 15 > 13
A) True B) False
8) -8 ≥ 15
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) |13|
A) 13 B) -13 C) 26 D) 0
2) |-2|
A) 2 B) -2 C) 4 D) 0
3) 19
-1
A) 19 B) -1 C) 1 D) -19
4) 10 - 13
A) 13 - 10 B) 10 - 13 C) -3 D) 3
5) |5 + (-10)|
A) 5 B) 15 C) -5 D) -15
6) -4 - -9
A) 5 B) 13 C) -5 D) -13
7) -6 + -8
A) 14 B) 2 C) -2 D) -14
Evaluate the expression for the given values of x and y.
8) |x|
x + |y|
y ; x = 6 and y = -3
A) 0 B) 2 C) 1 D) -1
Page 4
A) True B) False
7) 15 > 13
A) True B) False
8) -8 ≥ 15
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) |13|
A) 13 B) -13 C) 26 D) 0
2) |-2|
A) 2 B) -2 C) 4 D) 0
3) 19
-1
A) 19 B) -1 C) 1 D) -19
4) 10 - 13
A) 13 - 10 B) 10 - 13 C) -3 D) 3
5) |5 + (-10)|
A) 5 B) 15 C) -5 D) -15
6) -4 - -9
A) 5 B) 13 C) -5 D) -13
7) -6 + -8
A) 14 B) 2 C) -2 D) -14
Evaluate the expression for the given values of x and y.
8) |x|
x + |y|
y ; x = 6 and y = -3
A) 0 B) 2 C) 1 D) -1
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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) 26 and 34
A) |26 - 34| = 8 B) -|34 - 26| = -8 C) |26 + 34| = 60 D) -|26 + 34| = -60
2) -18 and -34
A) |(-18) - (-34)| = 16 B) |(-34) - (-18)| = -16
C) |(-34) + (-18)| = -52 D) |-(-18) + (-34)| = 52
3) 72 and -9
A) |72 - (-9)| = 81 B) |(-9) - 72| = -81 C) |72 + (-9)| = 63 D) |-72 + (-9)| = -63
4) 28.9 and 23.7
A) |28.9 - 23.7| = 5.2 B) |23.7 - 28.9| = -5.2
C) |28.9 + 23.7| = 52.6 D) |-28.9 + 23.7| = -52.6
5) -14.7 and 24.3
A) |-14.7 - 24.3| = 39.0 B) |24.3 + (-14.7)| = -39.0
C) |24.3 - (-14.7)| = 9.6 D) |-14.7 + (-24.3)| = -9.6
6) 1.5 and 48.3
A) |1.5 - 48.3| = 46.8 B) |48.3 - 1.5| = -46.8
C) |48.3 + 1.5| = 49.8 D) -|1.5 + 48.3| = -49.8
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 + (-7) = (-7) + 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 + 8) = 17 · 6 + 17 · 8
A) Distributive property of multiplication over addition
B) Commutative property of multiplication
C) Associative property of multiplication
D) Commutative property of addition
3) 2 + (8 + 7) = (2 + 8) + 7
A) Associative property of addition
B) Commutative property of addition
C) Distributive property of multiplication over addition
D) Identity property of addition
Page 5
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) 26 and 34
A) |26 - 34| = 8 B) -|34 - 26| = -8 C) |26 + 34| = 60 D) -|26 + 34| = -60
2) -18 and -34
A) |(-18) - (-34)| = 16 B) |(-34) - (-18)| = -16
C) |(-34) + (-18)| = -52 D) |-(-18) + (-34)| = 52
3) 72 and -9
A) |72 - (-9)| = 81 B) |(-9) - 72| = -81 C) |72 + (-9)| = 63 D) |-72 + (-9)| = -63
4) 28.9 and 23.7
A) |28.9 - 23.7| = 5.2 B) |23.7 - 28.9| = -5.2
C) |28.9 + 23.7| = 52.6 D) |-28.9 + 23.7| = -52.6
5) -14.7 and 24.3
A) |-14.7 - 24.3| = 39.0 B) |24.3 + (-14.7)| = -39.0
C) |24.3 - (-14.7)| = 9.6 D) |-14.7 + (-24.3)| = -9.6
6) 1.5 and 48.3
A) |1.5 - 48.3| = 46.8 B) |48.3 - 1.5| = -46.8
C) |48.3 + 1.5| = 49.8 D) -|1.5 + 48.3| = -49.8
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 + (-7) = (-7) + 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 + 8) = 17 · 6 + 17 · 8
A) Distributive property of multiplication over addition
B) Commutative property of multiplication
C) Associative property of multiplication
D) Commutative property of addition
3) 2 + (8 + 7) = (2 + 8) + 7
A) Associative property of addition
B) Commutative property of addition
C) Distributive property of multiplication over addition
D) Identity property of addition
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4) (7 + 3) + 4 = (3 + 7) + 4
A) Commutative property of addition
B) Associative property of addition
C) Distributive property of multiplication over addition
D) Inverse property of addition
5) 5 · (6 · 17) = 5 · (17 · 6)
A) Commutative property of multiplication
B) Associative property of multiplication
C) Distributive property of multiplication over addition
D) Identity property of multiplication
6) (9 + 6) + (7 + 19) = (7 + 19) + (9 + 6)
A) Commutative property of addition
B) Associative property of addition
C) Distributive property of multiplication over addition
D) Inverse property of addition
7) 3 · (19 · 2) = (19 · 2) · 3
A) Commutative property of multiplication
B) Associative property of multiplication
C) Distributive property of multiplication over addition
D) Identity property of multiplication
8) (8 · 12) · 7 = 8 · (12 · 7)
A) Associative property of multiplication
B) Commutative property of multiplication
C) Distributive property of multiplication over addition
D) Identity property of multiplication
9) 7(x + 6) = 7x + 7 · 6
A) Distributive property of multiplication over addition
B) Commutative property of multiplication
C) Associative property of multiplication
D) Identity property of multiplication
10) 3(-5 + 7) = -15 + 21
A) Distributive property of multiplication over addition
B) Associative property of multiplication
C) Associative property of addition
D) Commutative property of multiplication
11) -7(6 + 7) = -42 + (-49)
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
Page 6
A) Commutative property of addition
B) Associative property of addition
C) Distributive property of multiplication over addition
D) Inverse property of addition
5) 5 · (6 · 17) = 5 · (17 · 6)
A) Commutative property of multiplication
B) Associative property of multiplication
C) Distributive property of multiplication over addition
D) Identity property of multiplication
6) (9 + 6) + (7 + 19) = (7 + 19) + (9 + 6)
A) Commutative property of addition
B) Associative property of addition
C) Distributive property of multiplication over addition
D) Inverse property of addition
7) 3 · (19 · 2) = (19 · 2) · 3
A) Commutative property of multiplication
B) Associative property of multiplication
C) Distributive property of multiplication over addition
D) Identity property of multiplication
8) (8 · 12) · 7 = 8 · (12 · 7)
A) Associative property of multiplication
B) Commutative property of multiplication
C) Distributive property of multiplication over addition
D) Identity property of multiplication
9) 7(x + 6) = 7x + 7 · 6
A) Distributive property of multiplication over addition
B) Commutative property of multiplication
C) Associative property of multiplication
D) Identity property of multiplication
10) 3(-5 + 7) = -15 + 21
A) Distributive property of multiplication over addition
B) Associative property of multiplication
C) Associative property of addition
D) Commutative property of multiplication
11) -7(6 + 7) = -42 + (-49)
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
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13) (x + 3) + [-(x + 3)] = 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) -8(6r + 3) + 4(9r + 4)
A) -12r - 8 B) -2r - 5 C) -12r + 3 D) -72r
2) (11z + 6) - (4z - 4)
A) 7z + 10 B) 7z + 2 C) 15z + 10 D) 7z - 10
3) -6(2x - 9) - 4x + 5
A) -16x + 59 B) 8x + 59 C) 16x + 59 D) -16x - 49
Write the algebraic expression without parentheses.
4) -(49x)
A) -49x B) 49x C) -49 - x D) 49 - x
5) -8(-8z)
A) 64z B) -64z C) 64 - 8z D) 64 + z
6) -(3x - 9)
A) -3x + 9 B) 3x - 9 C) -3x - 9 D) 27x
7) -(-9 + 5y)
A) 9 - 5y B) 9 + 5y C) -9 + 5y D) 45y
8) - (7z - 2w + 6y)
A) -7z + 2w - 6y B) -7z + 2w + 6y C) -7z - 2w + 6y D) -7z - 2w - 6y
9) 1
5 (5x) + [(4x) + (-4x)]
A) x B) 9x C) -7x D) 1
0.2 Exponents and Scientific Notation
1 Use the Product Rule
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Simplify the exponential expression.
1) 83 · 88
A) 811 B) 824 C) 6411 D) 6424
2) y · y11
A) y12 B) 2y11 C) y11 D) 2y12
3) x8 · x9
A) x17 B) x72 C) 17x D) 72x
Page 7
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) -8(6r + 3) + 4(9r + 4)
A) -12r - 8 B) -2r - 5 C) -12r + 3 D) -72r
2) (11z + 6) - (4z - 4)
A) 7z + 10 B) 7z + 2 C) 15z + 10 D) 7z - 10
3) -6(2x - 9) - 4x + 5
A) -16x + 59 B) 8x + 59 C) 16x + 59 D) -16x - 49
Write the algebraic expression without parentheses.
4) -(49x)
A) -49x B) 49x C) -49 - x D) 49 - x
5) -8(-8z)
A) 64z B) -64z C) 64 - 8z D) 64 + z
6) -(3x - 9)
A) -3x + 9 B) 3x - 9 C) -3x - 9 D) 27x
7) -(-9 + 5y)
A) 9 - 5y B) 9 + 5y C) -9 + 5y D) 45y
8) - (7z - 2w + 6y)
A) -7z + 2w - 6y B) -7z + 2w + 6y C) -7z - 2w + 6y D) -7z - 2w - 6y
9) 1
5 (5x) + [(4x) + (-4x)]
A) x B) 9x C) -7x D) 1
0.2 Exponents and Scientific Notation
1 Use the Product Rule
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Simplify the exponential expression.
1) 83 · 88
A) 811 B) 824 C) 6411 D) 6424
2) y · y11
A) y12 B) 2y11 C) y11 D) 2y12
3) x8 · x9
A) x17 B) x72 C) 17x D) 72x
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4) (3x4)(9x9)
A) 27x13 B) -27x13 C) 27x36 D) -27x36
5) (-8x5y)(-3x3y6)
A) 24x8y7 B) -24x8y6 C) -11x8y6 D) 24x15y6
2 Use the Quotient Rule
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Simplify the exponential expression.
1) 55
56
A) 1
5 B) 5 C) -12,500 D) 5
6
2) x14
x10
A) x4 B) x24 C) x8 D) 1
x4
3) x2
x6
A) 1
x4 B) -x4 C) x4 D) - 1
x4
4) 6x10
x7
A) 6x3 B) 216x3 C) 6x17 D) 18x
5) -30x11
5x8
A) -6x3 B) x2 C) x3 D) -6x2
6) x13y13
x2y2
A) x11y11 B) x10y10 C) xy11 D) x10y11
7) -32x12y11
8x8y3
A) -4x4y8 B) x4y8 C) -4x3y4 D) -4x3y7
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A) 27x13 B) -27x13 C) 27x36 D) -27x36
5) (-8x5y)(-3x3y6)
A) 24x8y7 B) -24x8y6 C) -11x8y6 D) 24x15y6
2 Use the Quotient Rule
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Simplify the exponential expression.
1) 55
56
A) 1
5 B) 5 C) -12,500 D) 5
6
2) x14
x10
A) x4 B) x24 C) x8 D) 1
x4
3) x2
x6
A) 1
x4 B) -x4 C) x4 D) - 1
x4
4) 6x10
x7
A) 6x3 B) 216x3 C) 6x17 D) 18x
5) -30x11
5x8
A) -6x3 B) x2 C) x3 D) -6x2
6) x13y13
x2y2
A) x11y11 B) x10y10 C) xy11 D) x10y11
7) -32x12y11
8x8y3
A) -4x4y8 B) x4y8 C) -4x3y4 D) -4x3y7
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8) -27x7
3x10
A) -9
x3 B) -9x3 C) -9
x2 D) -9x2
9) -10x13y12z6
5x7y3z5
A) -2x6y9z B) x6y9z C) -2x5y8z D) -2x6y9
3 Use the Zero-Exponent Rule
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Simplify the exponential expression.
1) 40
A) 1 B) -1 C) 0 D) 4
2) (-2)0
A) 1 B) -1 C) 0 D) 2
3) -60
A) -1 B) 1 C) 0 D) 6
4) x6y0
A) x6 B) 1 C) 0 D) 1
x6
5) -7y0
A) -7 B) 1 C) 0 D) -6
6) (7b)0
A) 1 B) 0 C) b D) 7
7) -72x9y13
8x3y4
0
A) 1 B) x6y9 C) -9x6y9 D) 0
4 Use the Negative-Exponent Rule
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Simplify the exponential expression.
1) 3-4
A) 1
81 B) -81 C) 81 D) 1
12
2) (-3)-2
A) 1
9 B) -9 C) 9 D) - 1
9
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3x10
A) -9
x3 B) -9x3 C) -9
x2 D) -9x2
9) -10x13y12z6
5x7y3z5
A) -2x6y9z B) x6y9z C) -2x5y8z D) -2x6y9
3 Use the Zero-Exponent Rule
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Simplify the exponential expression.
1) 40
A) 1 B) -1 C) 0 D) 4
2) (-2)0
A) 1 B) -1 C) 0 D) 2
3) -60
A) -1 B) 1 C) 0 D) 6
4) x6y0
A) x6 B) 1 C) 0 D) 1
x6
5) -7y0
A) -7 B) 1 C) 0 D) -6
6) (7b)0
A) 1 B) 0 C) b D) 7
7) -72x9y13
8x3y4
0
A) 1 B) x6y9 C) -9x6y9 D) 0
4 Use the Negative-Exponent Rule
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Simplify the exponential expression.
1) 3-4
A) 1
81 B) -81 C) 81 D) 1
12
2) (-3)-2
A) 1
9 B) -9 C) 9 D) - 1
9
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3) -4-3
A) - 1
64 B) -64 C) 64 D) 1
12
4) 3-3 · 3
A) 1
9 B) 1
27 C) 9 D) 27
5) 33 · 3-4
A) 1
3 B) -3 C) 2187 D) - 1
3
6) x7 · x-2
A) x5 B) 1
x5 C) -x5 D) - 1
x5
7) x-9 · x7
A) 1
x2 B) -x2 C) x2 D) - 1
x2
8) x2y-3
A) x2
y3 B) y3x2 C) x2
y15 D) y15x2
9) 8x-8y2
A) 8y2
x8 B) 8
x8y2 C) y2
8x8 D) 8x8
y2
10) x-6
x4
A) 1
x10 B) 1
x24 C) 1
x2 D) x10
11) x-3
y-2
A) y2
x3 B) 1
x3y2 C) x3y2 D) x3
y2
12) x8y-3
z-8
A) x8z8
y3 B) z8
x8y3 C) y3
x8z8 D) x8z3
y8
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A) - 1
64 B) -64 C) 64 D) 1
12
4) 3-3 · 3
A) 1
9 B) 1
27 C) 9 D) 27
5) 33 · 3-4
A) 1
3 B) -3 C) 2187 D) - 1
3
6) x7 · x-2
A) x5 B) 1
x5 C) -x5 D) - 1
x5
7) x-9 · x7
A) 1
x2 B) -x2 C) x2 D) - 1
x2
8) x2y-3
A) x2
y3 B) y3x2 C) x2
y15 D) y15x2
9) 8x-8y2
A) 8y2
x8 B) 8
x8y2 C) y2
8x8 D) 8x8
y2
10) x-6
x4
A) 1
x10 B) 1
x24 C) 1
x2 D) x10
11) x-3
y-2
A) y2
x3 B) 1
x3y2 C) x3y2 D) x3
y2
12) x8y-3
z-8
A) x8z8
y3 B) z8
x8y3 C) y3
x8z8 D) x8z3
y8
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13) 10x3y14
5x2y-10
A) 2xy24 B) 10xy24 C) 2x5y24 D) 2xy4
5 Use the Power Rule
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Simplify the exponential expression.
1) (34)2
A) 6561 B) 729 C) 24 D) 162
2) (43)-2
A) 1
4096 B) 1
1024 C) -24 D) -128
3) (x7)8
A) x56 B) x15 C) 8x7 D) 8x56
4) (x-6)4
A) 1
x24 B) -x24 C) -6x4 D) -6x24
5) (x9)-6
A) 1
x54 B) - x54 C) -6x9 D) -6x54
6) (x-4)-3
A) x12 B) 1
x12 C) 1
x7 D) -x7
6 Find the Power of a Product
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Simplify the exponential expression.
1) (5x)3
A) 125x3 B) 15x C) 125x D) 15x3
2) (-2x)5
A) -32x5 B) -10x C) -32x D) -10x5
3) (6x3)2
A) 36x6 B) 6x6 C) 36x3 D) 6x5
4) (x7y)4
A) x28y4 B) x28y C) x11y5 D) x11y
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5x2y-10
A) 2xy24 B) 10xy24 C) 2x5y24 D) 2xy4
5 Use the Power Rule
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Simplify the exponential expression.
1) (34)2
A) 6561 B) 729 C) 24 D) 162
2) (43)-2
A) 1
4096 B) 1
1024 C) -24 D) -128
3) (x7)8
A) x56 B) x15 C) 8x7 D) 8x56
4) (x-6)4
A) 1
x24 B) -x24 C) -6x4 D) -6x24
5) (x9)-6
A) 1
x54 B) - x54 C) -6x9 D) -6x54
6) (x-4)-3
A) x12 B) 1
x12 C) 1
x7 D) -x7
6 Find the Power of a Product
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Simplify the exponential expression.
1) (5x)3
A) 125x3 B) 15x C) 125x D) 15x3
2) (-2x)5
A) -32x5 B) -10x C) -32x D) -10x5
3) (6x3)2
A) 36x6 B) 6x6 C) 36x3 D) 6x5
4) (x7y)4
A) x28y4 B) x28y C) x11y5 D) x11y
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5) (-6x4y5)2
A) 36x8y10 B) -6x8y10 C) -36x8y10 D) 36x6y7
6) (4x3)-2
A) 1
16x6 B) 1
4x6 C) 16x6 D) 16
x6
7) (x-1y4)-2
A) x2
y8 B) x-3
y2 C) 1
x2y8 D) y2
x-3
8) (3x-6y2z-5)-3
A) x18z15
27y6 B) y5
27x9z8 C) x18z15
-9y-6 D) y5
-9x9z8
7 Find the Power of a Quotient
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Simplify the exponential expression.
1) x
6
3
A) x3
216 B) x4
1296 C) x
6 D) x3
6
2) - 5
x
3
A) - 125
x3 B) 125
x3 C) - 125
x D) - 5
x3
3) x4
2
2
A) x8
4 B) x8
2 C) x6
4 D) x6
2
4) -3x
y
2
A) 9x2
y2 B) 9x
y2 C) -6x2
y2 D) -6x
y
5) 3x4y2
z2
3
A) 27x12y6
z6 B) 3x12y6
z6 C) 27x7y5
z5 D) 3x12y6
z5
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A) 36x8y10 B) -6x8y10 C) -36x8y10 D) 36x6y7
6) (4x3)-2
A) 1
16x6 B) 1
4x6 C) 16x6 D) 16
x6
7) (x-1y4)-2
A) x2
y8 B) x-3
y2 C) 1
x2y8 D) y2
x-3
8) (3x-6y2z-5)-3
A) x18z15
27y6 B) y5
27x9z8 C) x18z15
-9y-6 D) y5
-9x9z8
7 Find the Power of a Quotient
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Simplify the exponential expression.
1) x
6
3
A) x3
216 B) x4
1296 C) x
6 D) x3
6
2) - 5
x
3
A) - 125
x3 B) 125
x3 C) - 125
x D) - 5
x3
3) x4
2
2
A) x8
4 B) x8
2 C) x6
4 D) x6
2
4) -3x
y
2
A) 9x2
y2 B) 9x
y2 C) -6x2
y2 D) -6x
y
5) 3x4y2
z2
3
A) 27x12y6
z6 B) 3x12y6
z6 C) 27x7y5
z5 D) 3x12y6
z5
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6) -21x12y6
7x17y-2
3
A) -27y24
x15 B) 27y24
x15 C) -27y12
x15 D) -27
x15y24
7) x-1
y5
-3
A) x3y15 B) x-4
y2 C) 1
x3y15 D) y2
x-4
8) 2x3
y2
-3
A) y6
8x9 B) 8x9
y6 C) 8y6
x9 D) y2
8x9
8 Simplify Exponential Expressions
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Simplify the exponential expression. Assume that variables represent nonzero real numbers.
1) 33 · 5
A) 135 B) 45 C) 3375 D) 32
2) (-5)3
A) -125 B) 125 C) -15 D) 15
3) -63
A) -216 B) 18 C) 216 D) -18
4) (3x3)3
x15
A) 27
x6 B) 3
x6 C) 27
x9 D) 27
x24
5) (-5x4y-5)(3x-1y)
A) -15x3
y4 B) -15x3y6 C) -2x3
y4 D) -15x5
y6
6) 5-9x-2y3
5-6x-5y6
A) x3
125y3 B) 1
125x5y3 C) 3x3
y3 D) 125
x3y3
Page 13
7x17y-2
3
A) -27y24
x15 B) 27y24
x15 C) -27y12
x15 D) -27
x15y24
7) x-1
y5
-3
A) x3y15 B) x-4
y2 C) 1
x3y15 D) y2
x-4
8) 2x3
y2
-3
A) y6
8x9 B) 8x9
y6 C) 8y6
x9 D) y2
8x9
8 Simplify Exponential Expressions
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Simplify the exponential expression. Assume that variables represent nonzero real numbers.
1) 33 · 5
A) 135 B) 45 C) 3375 D) 32
2) (-5)3
A) -125 B) 125 C) -15 D) 15
3) -63
A) -216 B) 18 C) 216 D) -18
4) (3x3)3
x15
A) 27
x6 B) 3
x6 C) 27
x9 D) 27
x24
5) (-5x4y-5)(3x-1y)
A) -15x3
y4 B) -15x3y6 C) -2x3
y4 D) -15x5
y6
6) 5-9x-2y3
5-6x-5y6
A) x3
125y3 B) 1
125x5y3 C) 3x3
y3 D) 125
x3y3
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7) xy6
x6y
-2
A) x10
y10 B) 1
x8y13 C) 1
x14y14 D) y10
x10
8) 6x-4y-2z3
2xy-2z-3
-1
A) x5
3z6 B) x3
3z6 C) 3x5
z6 D) x5y4
3z6
9 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) 4 × 10-4
A) 0.0004 B) 40,000 C) 0.004 D) 4000
2) 2 × 105
A) 200,000 B) 0.00002 C) 2,000,000 D) 0.000002
3) 5.01 × 107
A) 50,100,000 B) 501,000,000 C) 5,010,000 D) 350.7
4) 4.14 × 10-4
A) 0.000414 B) 0.00414 C) 0.0000414 D) -414,000
5) 5.201 × 10-6
A) 0.000005201 B) 0.00005201 C) 0.0000005201 D) -5,201,000
6) -6.77 × 104
A) -67,700 B) -677,000 C) -6770 D) 67,700
7) -1.0077 × 104
A) -10,077 B) -100,770 C) -1007.7 D) -40.308
Write the number in scientific notation.
8) 2,012,310
A) 2.01231 × 106 B) 2.01231 × 107 C) 2.01231 × 10-6 D) 2.01231 × 101
9) 24,000
A) 2.4 × 104 B) 2.4 × 10-4 C) 2.4 × 103 D) 2.4 × 10-3
10) 57,000,000
A) 5.7 × 107 B) 5.7 × 10-7 C) 5.7 × 108 D) 5.7 × 10-8
11) 472
A) 4.72 × 102 B) 4.72 × 103 C) 4.72 × 10-2 D) 4.72 × 101
Page 14
x6y
-2
A) x10
y10 B) 1
x8y13 C) 1
x14y14 D) y10
x10
8) 6x-4y-2z3
2xy-2z-3
-1
A) x5
3z6 B) x3
3z6 C) 3x5
z6 D) x5y4
3z6
9 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) 4 × 10-4
A) 0.0004 B) 40,000 C) 0.004 D) 4000
2) 2 × 105
A) 200,000 B) 0.00002 C) 2,000,000 D) 0.000002
3) 5.01 × 107
A) 50,100,000 B) 501,000,000 C) 5,010,000 D) 350.7
4) 4.14 × 10-4
A) 0.000414 B) 0.00414 C) 0.0000414 D) -414,000
5) 5.201 × 10-6
A) 0.000005201 B) 0.00005201 C) 0.0000005201 D) -5,201,000
6) -6.77 × 104
A) -67,700 B) -677,000 C) -6770 D) 67,700
7) -1.0077 × 104
A) -10,077 B) -100,770 C) -1007.7 D) -40.308
Write the number in scientific notation.
8) 2,012,310
A) 2.01231 × 106 B) 2.01231 × 107 C) 2.01231 × 10-6 D) 2.01231 × 101
9) 24,000
A) 2.4 × 104 B) 2.4 × 10-4 C) 2.4 × 103 D) 2.4 × 10-3
10) 57,000,000
A) 5.7 × 107 B) 5.7 × 10-7 C) 5.7 × 108 D) 5.7 × 10-8
11) 472
A) 4.72 × 102 B) 4.72 × 103 C) 4.72 × 10-2 D) 4.72 × 101
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12) 0.000585
A) 5.85 × 10-4 B) 5.85 × 104 C) 5.85 × 10-5 D) 5.85 × 10-3
13) 0.000048919
A) 4.8919 × 10-5 B) 4.8919 × 105 C) 4.8919 × 10-4 D) 4.8919 × 104
14) 0.000000088007
A) 8.8007 × 10-8 B) 8.8007 × 108 C) 8.8007 × 10-7 D) 8.8007 × 10-9
Perform the indicated computation. Write the answer in scientific notation.
15) (5 × 10-9)(7 × 10-4)
A) 3.5 × 10-12 B) 35 × 10-12 C) 350 × 10-13 D) 3.5 × 1036
16) (2 × 10-4)(3.2 × 10-7)
A) 6.4 × 10-11 B) 6.4 × 10-10 C) 64 × 10-11 D) 6.4 × 1028
17) 8 × 102
4 × 103
A) 2 × 10-1 B) 2 × 105 C) 4 × 10-1 D) 4 × 105
18) 17.15 × 10-6
5 × 10-3
A) 3.43 × 10-3 B) 3.43 × 10-9 C) 6.86 × 10-3 D) 6.86 × 10-9
19) 5.52 × 101
2.4 × 10-8
A) 2.3 × 109 B) 2.3 × 10-7 C) 4.6 × 109 D) 4.6 × 10-7
20) 30,000,000,000
0.00006
A) 5 × 1014 B) 5 × 1013 C) 24 × 1014 D) 24 × 1013
21) 0.00018 × 0.0003
0.0009
A) 6 × 10-5 B) 6 × 105 C) 54 × 106 D) 54 × 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 5,000,000 people, the average citizen spends $6,000 on housing each year.
What is the total spent on housing for the state?
A) $3 × 1010 B) $3 × 109 C) $30 × 1011 D) $30 × 1010
23) Approximately 8 × 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) $2.4 × 108 B) $24 × 108 C) $2.4 × 109 D) $24 × 109
Page 15
A) 5.85 × 10-4 B) 5.85 × 104 C) 5.85 × 10-5 D) 5.85 × 10-3
13) 0.000048919
A) 4.8919 × 10-5 B) 4.8919 × 105 C) 4.8919 × 10-4 D) 4.8919 × 104
14) 0.000000088007
A) 8.8007 × 10-8 B) 8.8007 × 108 C) 8.8007 × 10-7 D) 8.8007 × 10-9
Perform the indicated computation. Write the answer in scientific notation.
15) (5 × 10-9)(7 × 10-4)
A) 3.5 × 10-12 B) 35 × 10-12 C) 350 × 10-13 D) 3.5 × 1036
16) (2 × 10-4)(3.2 × 10-7)
A) 6.4 × 10-11 B) 6.4 × 10-10 C) 64 × 10-11 D) 6.4 × 1028
17) 8 × 102
4 × 103
A) 2 × 10-1 B) 2 × 105 C) 4 × 10-1 D) 4 × 105
18) 17.15 × 10-6
5 × 10-3
A) 3.43 × 10-3 B) 3.43 × 10-9 C) 6.86 × 10-3 D) 6.86 × 10-9
19) 5.52 × 101
2.4 × 10-8
A) 2.3 × 109 B) 2.3 × 10-7 C) 4.6 × 109 D) 4.6 × 10-7
20) 30,000,000,000
0.00006
A) 5 × 1014 B) 5 × 1013 C) 24 × 1014 D) 24 × 1013
21) 0.00018 × 0.0003
0.0009
A) 6 × 10-5 B) 6 × 105 C) 54 × 106 D) 54 × 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 5,000,000 people, the average citizen spends $6,000 on housing each year.
What is the total spent on housing for the state?
A) $3 × 1010 B) $3 × 109 C) $30 × 1011 D) $30 × 1010
23) Approximately 8 × 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) $2.4 × 108 B) $24 × 108 C) $2.4 × 109 D) $24 × 109
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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) 16
A) 4 B) 256 C) 1
16 D) Not a real number
2) - 625
A) -25 B) 25 C) -312 D) Not a real number
3) -144
A) 12
144 B) 20,736 C) 12 D) Not a real number
4) 16 + 9
A) 5 B) 7 C) 25 D) 7
5) 25 - 9
A) 4 B) 7 C) 16 D) 7
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) (7)2
A) 7 B) 2401 C) 1
49 D) Not a real number
2) (-5)2
A) 5 B) 25 C) -5 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) 96
A) 4 6 B) 6 4 C) 24 D) 9
2) 15
A) 15 B) 5 3 C) 3 5 D) 3
3) 175
A) 5 7 B) 175 C) 35 D) 25 7
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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) 16
A) 4 B) 256 C) 1
16 D) Not a real number
2) - 625
A) -25 B) 25 C) -312 D) Not a real number
3) -144
A) 12
144 B) 20,736 C) 12 D) Not a real number
4) 16 + 9
A) 5 B) 7 C) 25 D) 7
5) 25 - 9
A) 4 B) 7 C) 16 D) 7
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) (7)2
A) 7 B) 2401 C) 1
49 D) Not a real number
2) (-5)2
A) 5 B) 25 C) -5 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) 96
A) 4 6 B) 6 4 C) 24 D) 9
2) 15
A) 15 B) 5 3 C) 3 5 D) 3
3) 175
A) 5 7 B) 175 C) 35 D) 25 7
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4) 192x2
A) 8 x 3 B) 8 3x C) 192x D) 3x2 8
5) 448x2
A) 8 x 7 B) 8 7x2 C) 8x2 7 D) 8 7
6) 14x · 28x
A) 14 x 2 B) 14 2x C) 14x2 2 D) 14 2x2
7) 7x2 · 21x
A) 7 x 3x B) 7 x 3 C) 7x2 3x D) 7 x 3x2
Solve the problem.
8) Racing cyclists use the algebraic expression 4 x to determine the maximum speed, in miles per hour, to
turn a corner of radius x, in feet, without tipping over. Find the maximum speed at which a cyclist should
travel around a corner of radius 38 feet without tipping over. Write the answer in simplified radical form.
A) 4 38 miles per hour B) 24 2 miles per hour
C) 24 + 2 miles per hour D) 4(6 + 2)
x miles per hour
9) The formula v = 2.5r models the safe maximum speed, v, in miles per hour, at which a car can travel on a
curved road with radius of curvature, r, in feet. A highway crew measures the radius of curvature at an
exit ramp as 490 feet. What is the maximum safe speed?
A) 35 miles per hour B) 49 miles per hour C) 40 miles per hour D) 32 miles per hour
10) The formula v = 20L can be used to estimate the speed of a car, v, in miles per hour, based on the length,
L, in feet, of its skid marks upon sudden braking on a dry asphalt road. If a car is involved in an accident
and its skid marks measure 245 feet, at what estimated speed was the car traveling when it applied its
brakes just prior to the accident?
A) 70 miles per hour B) 75 miles per hour C) 65 miles per hour D) 80 miles per hour
11) The average height of a boy in the United States, from birth through 60 months, can be modeled by
y = 2.9 x + 20.1 where y is the average height, in inches, of boys who are x months of age. What would be
the expected difference in height between a child 36 months of age and a child 25 months of age?
A) 2.9 inches B) 43.1 inches C) 17.4 inches D) 4.9 inches
4 Use the Quotient Rule to Simplify Square Roots
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use the quotient rule to simplify the expression.
1) 1
4
A) 1
2 B) 1
16 C) 2 D) 4
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A) 8 x 3 B) 8 3x C) 192x D) 3x2 8
5) 448x2
A) 8 x 7 B) 8 7x2 C) 8x2 7 D) 8 7
6) 14x · 28x
A) 14 x 2 B) 14 2x C) 14x2 2 D) 14 2x2
7) 7x2 · 21x
A) 7 x 3x B) 7 x 3 C) 7x2 3x D) 7 x 3x2
Solve the problem.
8) Racing cyclists use the algebraic expression 4 x to determine the maximum speed, in miles per hour, to
turn a corner of radius x, in feet, without tipping over. Find the maximum speed at which a cyclist should
travel around a corner of radius 38 feet without tipping over. Write the answer in simplified radical form.
A) 4 38 miles per hour B) 24 2 miles per hour
C) 24 + 2 miles per hour D) 4(6 + 2)
x miles per hour
9) The formula v = 2.5r models the safe maximum speed, v, in miles per hour, at which a car can travel on a
curved road with radius of curvature, r, in feet. A highway crew measures the radius of curvature at an
exit ramp as 490 feet. What is the maximum safe speed?
A) 35 miles per hour B) 49 miles per hour C) 40 miles per hour D) 32 miles per hour
10) The formula v = 20L can be used to estimate the speed of a car, v, in miles per hour, based on the length,
L, in feet, of its skid marks upon sudden braking on a dry asphalt road. If a car is involved in an accident
and its skid marks measure 245 feet, at what estimated speed was the car traveling when it applied its
brakes just prior to the accident?
A) 70 miles per hour B) 75 miles per hour C) 65 miles per hour D) 80 miles per hour
11) The average height of a boy in the United States, from birth through 60 months, can be modeled by
y = 2.9 x + 20.1 where y is the average height, in inches, of boys who are x months of age. What would be
the expected difference in height between a child 36 months of age and a child 25 months of age?
A) 2.9 inches B) 43.1 inches C) 17.4 inches D) 4.9 inches
4 Use the Quotient Rule to Simplify Square Roots
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use the quotient rule to simplify the expression.
1) 1
4
A) 1
2 B) 1
16 C) 2 D) 4
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2) 64
25
A) 8
5 B) 1 C) 8
5 D) 8
5
3) 32x3
2x
A) 4 x B) 4 x 2 C) 2x2 D) 4x2
2
4) 100x4
5x
A) 2 x 5x B) 100x3 C) 5 x x D) x2 100
5
Solve the problem.
5) The time, in seconds, that it takes an object to fall a distance d, in feet, is given by the algebraic expression
d
16 . Find how long it will take a ball dropped from the top of a building 83 feet tall to hit the ground.
Write the answer in simplified radical form.
A) 83
4 seconds B) 9 2
4 seconds C) 83
16 seconds D) 9 + 2
4 seconds
5 Add and Subtract Square Roots
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Add or subtract terms whenever possible.
1) 6 3 + 2 3
A) 8 3 B) 12 6 C) 8 6 D) 4 3
2) 7 6 + 5 54
A) 22 6 B) 8 6 C) 12 6 D) -22 6
3) 8 3x + 3 3x
A) 11 3x B) 24 6x C) 11x 6 D) 5 3
4) 3 3 + 9 12
A) 21 3 B) 15 3 C) 12 3 D) -21 3
5) -6 162 + 2 128 + 7 98
A) 11 2 B) -6 2 C) 66 2 D) -66 2
6) 16 + 245 + 4 + 405
A) 16 5 + 6 B) 16 5 + 16 + 4 C) 245 + 405 + 6 D) 130 5 + 6
7) 5x - 5 45x + 2 80x
A) -6 5x B) -6 130x C) -3 130x D) -3 5x
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25
A) 8
5 B) 1 C) 8
5 D) 8
5
3) 32x3
2x
A) 4 x B) 4 x 2 C) 2x2 D) 4x2
2
4) 100x4
5x
A) 2 x 5x B) 100x3 C) 5 x x D) x2 100
5
Solve the problem.
5) The time, in seconds, that it takes an object to fall a distance d, in feet, is given by the algebraic expression
d
16 . Find how long it will take a ball dropped from the top of a building 83 feet tall to hit the ground.
Write the answer in simplified radical form.
A) 83
4 seconds B) 9 2
4 seconds C) 83
16 seconds D) 9 + 2
4 seconds
5 Add and Subtract Square Roots
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Add or subtract terms whenever possible.
1) 6 3 + 2 3
A) 8 3 B) 12 6 C) 8 6 D) 4 3
2) 7 6 + 5 54
A) 22 6 B) 8 6 C) 12 6 D) -22 6
3) 8 3x + 3 3x
A) 11 3x B) 24 6x C) 11x 6 D) 5 3
4) 3 3 + 9 12
A) 21 3 B) 15 3 C) 12 3 D) -21 3
5) -6 162 + 2 128 + 7 98
A) 11 2 B) -6 2 C) 66 2 D) -66 2
6) 16 + 245 + 4 + 405
A) 16 5 + 6 B) 16 5 + 16 + 4 C) 245 + 405 + 6 D) 130 5 + 6
7) 5x - 5 45x + 2 80x
A) -6 5x B) -6 130x C) -3 130x D) -3 5x
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6 Rationalize Denominators
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Rationalize the denominator.
1) 1
17
A) 17
17 B) 17 C) 1 + 17 D) 1 + 17
17
2) 10
10
A) 10 B) 10 10 C) 10 D) 1
3) 144
11
A) 12 11
11 B) 12 11 C) 144 11
11 D) 133
4) 144
11
A) 12 11
11 B) 12 11 C) 144 11
11 D) 133
5) 3
7
A) 21
7 B) 21
49 C) 21 D) 3
6) 5
8 - 10
A) 40 + 5 10
54 B) 40 - 5 10
54 C) 40 + 5 10
2 D) 5
8 - 5
10
7) 6
17 + 2
A) 102 - 2 6
13 B) 102 + 2 6
13 C) 102 - 2 6
19 D) 3 102 + 17 34
6
8) 3
4 - 2
A) 12 + 3 2
14 B) 12 - 3 2
14 C) 12 + 3 2
2 D) 3
4 - 3
2
9) 5
6 + 11
A) 11 - 6 B) 6 - 11 C) 11 + 6 D) 5
Page 19
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Rationalize the denominator.
1) 1
17
A) 17
17 B) 17 C) 1 + 17 D) 1 + 17
17
2) 10
10
A) 10 B) 10 10 C) 10 D) 1
3) 144
11
A) 12 11
11 B) 12 11 C) 144 11
11 D) 133
4) 144
11
A) 12 11
11 B) 12 11 C) 144 11
11 D) 133
5) 3
7
A) 21
7 B) 21
49 C) 21 D) 3
6) 5
8 - 10
A) 40 + 5 10
54 B) 40 - 5 10
54 C) 40 + 5 10
2 D) 5
8 - 5
10
7) 6
17 + 2
A) 102 - 2 6
13 B) 102 + 2 6
13 C) 102 - 2 6
19 D) 3 102 + 17 34
6
8) 3
4 - 2
A) 12 + 3 2
14 B) 12 - 3 2
14 C) 12 + 3 2
2 D) 3
4 - 3
2
9) 5
6 + 11
A) 11 - 6 B) 6 - 11 C) 11 + 6 D) 5
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7 Evaluate and Perform Operations with Higher Roots
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Evaluate the radical expressions or indicate that the root is not a real number.
1) 3 64
A) 4 B) -4 C) 64 D) not a real number
2) 3 (-3)3
A) -3 B) 3 C) -27 D) not a real number
3) 4 625
A) 5 B) -5 C) 625 D) not a real number
4) 4 (-3)4
A) 3 B) -3 C) 81 D) not a real number
Simplify the radical expression.
5) 3 x4
A) x 3 x B) x2 3 x C) x 3 x2 D) x2 3 x2
6) 3 14 · 3 4
A) 2 3 7 B) 3 56 C) 2 3 14 D) 6 56
Add or subtract terms whenever possible.
7) 2 3 40 + 3 320
A) 8 3 5 B) 2 3 360 C) 3 3 360 D) 6 3 5
8) y 3 192x - 3 24xy3
A) 2y 3 3x B) 4y 3 3x - 192 3 3xy3
C) (y + 1) 3 26 D) y 3 -22xy3
8 Understand and Use Rational Exponents
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Evaluate the expression without using a calculator.
1) 1441/2
A) 12 B) 24 C) 6 D) 48
2) 2561/4
A) 4 B) 16 C) 64 D) 1024
3) 84/3
A) 16 B) 64 C) 32 D) 128
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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Evaluate the radical expressions or indicate that the root is not a real number.
1) 3 64
A) 4 B) -4 C) 64 D) not a real number
2) 3 (-3)3
A) -3 B) 3 C) -27 D) not a real number
3) 4 625
A) 5 B) -5 C) 625 D) not a real number
4) 4 (-3)4
A) 3 B) -3 C) 81 D) not a real number
Simplify the radical expression.
5) 3 x4
A) x 3 x B) x2 3 x C) x 3 x2 D) x2 3 x2
6) 3 14 · 3 4
A) 2 3 7 B) 3 56 C) 2 3 14 D) 6 56
Add or subtract terms whenever possible.
7) 2 3 40 + 3 320
A) 8 3 5 B) 2 3 360 C) 3 3 360 D) 6 3 5
8) y 3 192x - 3 24xy3
A) 2y 3 3x B) 4y 3 3x - 192 3 3xy3
C) (y + 1) 3 26 D) y 3 -22xy3
8 Understand and Use Rational Exponents
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Evaluate the expression without using a calculator.
1) 1441/2
A) 12 B) 24 C) 6 D) 48
2) 2561/4
A) 4 B) 16 C) 64 D) 1024
3) 84/3
A) 16 B) 64 C) 32 D) 128
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4) 16-3/2
A) 1
64 B) - 1
64 C) 64 D) -64
Simplify using properties of exponents.
5) (7x3/4)(10x1/2)
A) 70x5/4 B) 70x1/2 C) 70x5/3 D) 70x3/4
6) 50x3/2
10x1/3
A) 5x7/6 B) 5x1/3 C) 40x1/3 D) 5x7/2
7) (25x4y6)1/2
A) 5x2y3 B) 625x8y6 C) 5
2 x2y3 D) 25x2y3
Simplify by reducing the index of the radical.
8) 10 x4
A) 5 x2 B) x2 C) 5 x D) x
9) 6 27x3
A) 3x B) 3 3x C) 3 3x D) 1
9x
Solve the problem.
10) The algebraic expression 0.07d3/2 describes the duration of a storm, in hours, whose diameter is d miles.
Use a calculator to determine the duration of a storm with a diameter of 5 miles. Round to the nearest
hundredth.
A) 0.78 hours B) 0.16 hours C) 11.18 hours D) 0.21 hours
0.4 Polynomials
1 Understand the Vocabulary of Polynomials
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Is the algebraic expression a polynomial? If it is, write the polynomial in standard form.
1) 4x-1 - 8 + 7x
A) No B) Yes; 7x + 4x-1 - 8
2) 2x - 3 + 5x2
A) Yes; 5x2 + 2x - 3 B) No
3) 2x - 7
x
A) No B) Yes; 7
x - 2
Page 21
A) 1
64 B) - 1
64 C) 64 D) -64
Simplify using properties of exponents.
5) (7x3/4)(10x1/2)
A) 70x5/4 B) 70x1/2 C) 70x5/3 D) 70x3/4
6) 50x3/2
10x1/3
A) 5x7/6 B) 5x1/3 C) 40x1/3 D) 5x7/2
7) (25x4y6)1/2
A) 5x2y3 B) 625x8y6 C) 5
2 x2y3 D) 25x2y3
Simplify by reducing the index of the radical.
8) 10 x4
A) 5 x2 B) x2 C) 5 x D) x
9) 6 27x3
A) 3x B) 3 3x C) 3 3x D) 1
9x
Solve the problem.
10) The algebraic expression 0.07d3/2 describes the duration of a storm, in hours, whose diameter is d miles.
Use a calculator to determine the duration of a storm with a diameter of 5 miles. Round to the nearest
hundredth.
A) 0.78 hours B) 0.16 hours C) 11.18 hours D) 0.21 hours
0.4 Polynomials
1 Understand the Vocabulary of Polynomials
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Is the algebraic expression a polynomial? If it is, write the polynomial in standard form.
1) 4x-1 - 8 + 7x
A) No B) Yes; 7x + 4x-1 - 8
2) 2x - 3 + 5x2
A) Yes; 5x2 + 2x - 3 B) No
3) 2x - 7
x
A) No B) Yes; 7
x - 2
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4) x2 + x4 - x3 + 9
A) Yes; x4 - x3 + x2 + 9 B) No
Find the degree of the polynomial.
5) -6x - 8x7 - 5
A) degree 7 B) degree 8 C) degree -6 D) degree -8
6) -7x + 3x8 + 4x7 - 16
A) degree 8 B) degree 4 C) degree 3 D) degree 7
7) -15x4 + 2x3 + 2x - 4x5 - 3
A) degree 5 B) degree 4 C) degree -15 D) degree 3
8) x5 - 3x4y7 + 8xy - 10x + 6
A) degree 11 B) degree 5 C) degree 18 D) degree -3
2 Add and Subtract Polynomials
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Perform the indicated operations. Write the resulting polynomial in standard form.
1) (7x5 + 6x2 - 9x) + (3x5 - 3x2 - 9x)
A) 10x5 + 3x2 - 18x B) -6x5 + 4x2 - 3x C) 10x + 3x5 - 18x2 D) -5x8
2) (6x4 + 9x3 - 3x2 - 4) + (3x4 + 7x3 - 9x2 + 5)
A) 9x4 + 16x3 - 12x2 + 1 B) 9x8 + 16x6 - 12x4 + 1
C) 13x18 + 1 D) 3x4 + 3x3 + 11x2 + 12
3) (-6x5 + 18x3 + 15) + (8x5 + 4x3 - 11)
A) 2x5 + 22x3 + 4 B) 2x5 + 10x3 - 26 C) 2x5 + 22x3 - 26 D) 28x8
4) (-4x5 - 8x4 - 2x3 + 6) + (6x5 + 2x4 + 9x3 + 5)
A) 2x5 - 6x4 +
A) Yes; x4 - x3 + x2 + 9 B) No
Find the degree of the polynomial.
5) -6x - 8x7 - 5
A) degree 7 B) degree 8 C) degree -6 D) degree -8
6) -7x + 3x8 + 4x7 - 16
A) degree 8 B) degree 4 C) degree 3 D) degree 7
7) -15x4 + 2x3 + 2x - 4x5 - 3
A) degree 5 B) degree 4 C) degree -15 D) degree 3
8) x5 - 3x4y7 + 8xy - 10x + 6
A) degree 11 B) degree 5 C) degree 18 D) degree -3
2 Add and Subtract Polynomials
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Perform the indicated operations. Write the resulting polynomial in standard form.
1) (7x5 + 6x2 - 9x) + (3x5 - 3x2 - 9x)
A) 10x5 + 3x2 - 18x B) -6x5 + 4x2 - 3x C) 10x + 3x5 - 18x2 D) -5x8
2) (6x4 + 9x3 - 3x2 - 4) + (3x4 + 7x3 - 9x2 + 5)
A) 9x4 + 16x3 - 12x2 + 1 B) 9x8 + 16x6 - 12x4 + 1
C) 13x18 + 1 D) 3x4 + 3x3 + 11x2 + 12
3) (-6x5 + 18x3 + 15) + (8x5 + 4x3 - 11)
A) 2x5 + 22x3 + 4 B) 2x5 + 10x3 - 26 C) 2x5 + 22x3 - 26 D) 28x8
4) (-4x5 - 8x4 - 2x3 + 6) + (6x5 + 2x4 + 9x3 + 5)
A) 2x5 - 6x4 +
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3 Multiply Polynomials
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the product.
1) (x + 2)(x2 - 2x + 4)
A) x3 + 8 B) x3 - 8 C) x3 + 4x2 + 4x + 8 D) x3 - 4x2 - 4x + 8
2) (x - 12)(x2 + 2x - 7)
A) x3 - 10x2 - 31x + 84 B) x3 + 14x2 + 17x - 84
C) x3 - 10x2 - 17x - 84 D) x3 + 14x2 + 31x + 84
3) (x + 6)(x2 + 8x - 5)
A) x3 + 14x2 + 43x - 30 B) x4 + 6x3 + 8x2 + 43x - 30
C) x3 + 14x2 + 53x - 30 D) x3 + 14x2 + 53x + 30
4) (x + 4)(2x2 + 5x + 9)
A) 2x3 + 13x2 + 29x + 36 B) 2x3 + 8x2 + 20x + 36
C) 10x3 + 25x2 + 45x D) 40x4 + 2x3 + 180x2 + 36
5) (7x - 1)(x2 - 4x + 1)
A) 7x3 - 29x2 + 11x - 1 B) 7x3 - 27x2 + 3x - 1
C) 7x3 - 28x2 + 7x + 1 D) 7x3 + 29x2 - 11x + 1
4 Use FOIL in Polynomial Multiplication
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the product.
1) (x + 9)(x - 5)
A) x2 + 4x - 45 B) x2 - 45x + 4 C) x2 + 3x - 45 D) x2 + 4x + 4
2) (2x - 7)(x + 6)
A) 2x2 + 5x - 42 B) x2 - 42x + 5 C) 2x2 + 4x - 42 D) x2 + 5x + 4
3) (2x - 7)(5x - 1)
A) 10x2 - 37x + 7 B) 7x2 - 37x + 7 C) 10x2 - 37x - 37 D) 7x2 - 37x -
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the product.
1) (x + 2)(x2 - 2x + 4)
A) x3 + 8 B) x3 - 8 C) x3 + 4x2 + 4x + 8 D) x3 - 4x2 - 4x + 8
2) (x - 12)(x2 + 2x - 7)
A) x3 - 10x2 - 31x + 84 B) x3 + 14x2 + 17x - 84
C) x3 - 10x2 - 17x - 84 D) x3 + 14x2 + 31x + 84
3) (x + 6)(x2 + 8x - 5)
A) x3 + 14x2 + 43x - 30 B) x4 + 6x3 + 8x2 + 43x - 30
C) x3 + 14x2 + 53x - 30 D) x3 + 14x2 + 53x + 30
4) (x + 4)(2x2 + 5x + 9)
A) 2x3 + 13x2 + 29x + 36 B) 2x3 + 8x2 + 20x + 36
C) 10x3 + 25x2 + 45x D) 40x4 + 2x3 + 180x2 + 36
5) (7x - 1)(x2 - 4x + 1)
A) 7x3 - 29x2 + 11x - 1 B) 7x3 - 27x2 + 3x - 1
C) 7x3 - 28x2 + 7x + 1 D) 7x3 + 29x2 - 11x + 1
4 Use FOIL in Polynomial Multiplication
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the product.
1) (x + 9)(x - 5)
A) x2 + 4x - 45 B) x2 - 45x + 4 C) x2 + 3x - 45 D) x2 + 4x + 4
2) (2x - 7)(x + 6)
A) 2x2 + 5x - 42 B) x2 - 42x + 5 C) 2x2 + 4x - 42 D) x2 + 5x + 4
3) (2x - 7)(5x - 1)
A) 10x2 - 37x + 7 B) 7x2 - 37x + 7 C) 10x2 - 37x - 37 D) 7x2 - 37x -
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Solve the problem.
6) Write a polynomial in standard form that represents the volume of the open box.
x
11 - 6x
9 - 6x
A) 36x3 - 120x2 + 99x B) 36x3 + 120x2 + 99x
C) 36x2 - 120x + 99 D) 6x3 - 120x2 + 99x
7) Write a polynomial in standard form that represents the area of the shaded region.
x + 7
x + 5
x + 3 x + 2
A) 3x + 11 B) 17x + 31 C) x2 + 14x + 11 D) -3x - 11
5 Use Special Products in Polynomial Multiplication
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the product.
1) (x + 7)(x - 7)
A) x2 - 49 B) x2 - 14 C) x2 - 14x - 49 D) x2 + 14x - 49
2) (9x + 5)(9x - 5)
A) 81x2 - 25 B) x2 - 25 C) 81x2 - 90x - 25 D) 81x2 + 90x - 25
3) (3 + 11x)(3 - 11x)
A) 9 - 121x2 B) 9 - 66x - 121x2 C) 121x2 - 9 D) 9 + 66x - 121x2
4) (5x2 + 7x)(5x2 - 7x)
A) 25x4 - 49x2 B) 25x4 - 70x3 - 49x2
C) 10x4 - 14x2 D) 25x4 + 70x3 - 49x2
5) (1 + x3)(1 - x3)
A) 1 - x6 B) 2 - x6 C) 2 - x9 D) 1 - x9
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6) Write a polynomial in standard form that represents the volume of the open box.
x
11 - 6x
9 - 6x
A) 36x3 - 120x2 + 99x B) 36x3 + 120x2 + 99x
C) 36x2 - 120x + 99 D) 6x3 - 120x2 + 99x
7) Write a polynomial in standard form that represents the area of the shaded region.
x + 7
x + 5
x + 3 x + 2
A) 3x + 11 B) 17x + 31 C) x2 + 14x + 11 D) -3x - 11
5 Use Special Products in Polynomial Multiplication
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the product.
1) (x + 7)(x - 7)
A) x2 - 49 B) x2 - 14 C) x2 - 14x - 49 D) x2 + 14x - 49
2) (9x + 5)(9x - 5)
A) 81x2 - 25 B) x2 - 25 C) 81x2 - 90x - 25 D) 81x2 + 90x - 25
3) (3 + 11x)(3 - 11x)
A) 9 - 121x2 B) 9 - 66x - 121x2 C) 121x2 - 9 D) 9 + 66x - 121x2
4) (5x2 + 7x)(5x2 - 7x)
A) 25x4 - 49x2 B) 25x4 - 70x3 - 49x2
C) 10x4 - 14x2 D) 25x4 + 70x3 - 49x2
5) (1 + x3)(1 - x3)
A) 1 - x6 B) 2 - x6 C) 2 - x9 D) 1 - x9
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6) (12 - y3)(12 + y3)
A) 144 - y6 B) 144 - y9 C) 144 - y3 D) y6 - 144
7) (x + 3)2
A) x2 + 6x + 9 B) x2 + 9 C) 9x2 + 6x + 9 D) x + 9
8) (x - 12)2
A) x2 - 24x + 144 B) x2 + 144 C) 144x2 - 24x + 144 D) x + 144
9) (7x + 9)2
A) 49x2 + 126x + 81 B) 49x2 + 81 C) 7x2 + 126x + 81 D) 7x2 + 81
10) (6x - 1)2
A) 36x2 - 12x + 1 B) 36x2 + 1 C) 6x2 - 12x + 1 D) 6x2 + 1
11) (3x2 + 4)2
A) 9x4 + 24x2 + 16 B) 9x2 + 24x + 16 C) 3x4 + 24x2 + 16 D) 9x4 + 16
12) (9x2 - 2)2
A) 81x4 - 36x2 + 4 B) 81x4 + 36x2 + 4 C) 81x4 - 36x2 - 4 D) 81x2 - 36x + 4
13) (5 + 3x)2
A) 25 + 30x + 9x2 B) 25 + 9x2 C) 25x2 + 30x + 9 D) 25 + 30x + 3x2
14) (9 - 5x)2
A) 81 - 90x + 25x2 B) 81 + 25x2 C) 81x2 - 90x + 25 D) 81 - 90x - 25x2
15) (x - 3)3
A) x3 - 9x2 + 27x - 27 B) x3 - 3x2 + 15x - 27
C) x3 - 9x2 + 15x - 27 D) x3 - 9x2 + 9x - 27
16) (3x + 5)3
A) 27x3 + 135x2 + 225x + 125 B) 27x3 + 135x2 + 135x + 125
C) 9x6 + 15x3 + 15,625 D) 9x2 + 30x + 25
17) (4x - 5)3
A) 64x3 - 240x2 + 300x - 125 B) 64x3 - 240x2 + 240x - 125
C) 64x3
A) 144 - y6 B) 144 - y9 C) 144 - y3 D) y6 - 144
7) (x + 3)2
A) x2 + 6x + 9 B) x2 + 9 C) 9x2 + 6x + 9 D) x + 9
8) (x - 12)2
A) x2 - 24x + 144 B) x2 + 144 C) 144x2 - 24x + 144 D) x + 144
9) (7x + 9)2
A) 49x2 + 126x + 81 B) 49x2 + 81 C) 7x2 + 126x + 81 D) 7x2 + 81
10) (6x - 1)2
A) 36x2 - 12x + 1 B) 36x2 + 1 C) 6x2 - 12x + 1 D) 6x2 + 1
11) (3x2 + 4)2
A) 9x4 + 24x2 + 16 B) 9x2 + 24x + 16 C) 3x4 + 24x2 + 16 D) 9x4 + 16
12) (9x2 - 2)2
A) 81x4 - 36x2 + 4 B) 81x4 + 36x2 + 4 C) 81x4 - 36x2 - 4 D) 81x2 - 36x + 4
13) (5 + 3x)2
A) 25 + 30x + 9x2 B) 25 + 9x2 C) 25x2 + 30x + 9 D) 25 + 30x + 3x2
14) (9 - 5x)2
A) 81 - 90x + 25x2 B) 81 + 25x2 C) 81x2 - 90x + 25 D) 81 - 90x - 25x2
15) (x - 3)3
A) x3 - 9x2 + 27x - 27 B) x3 - 3x2 + 15x - 27
C) x3 - 9x2 + 15x - 27 D) x3 - 9x2 + 9x - 27
16) (3x + 5)3
A) 27x3 + 135x2 + 225x + 125 B) 27x3 + 135x2 + 135x + 125
C) 9x6 + 15x3 + 15,625 D) 9x2 + 30x + 25
17) (4x - 5)3
A) 64x3 - 240x2 + 300x - 125 B) 64x3 - 240x2 + 240x - 125
C) 64x3
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2) (4x2y - 12xy + 10) + (-3x2y + 8xy - 5)
A) x2y - 4xy + 5 B) -x2y - 20xy + 15 C) -4x3y2 + 5 D) 7x2y + 20xy + 15
3) (12x4y2 - 7x2y2 + 5xy) + (11x4y2 - 8x2y2 + 10xy)
A) 23x4y2 - 15x2y2 + 15xy B) -15x4y2 + 23x2y2 + 15xy
C) 23x4y2 + 15x2y2 + 15xy D) 15x4y2 - 23x2y2 + 15xy
4) (x3 + 9xy - 6y2) - (8x3 + 6xy + y2)
A) -7x3 + 3xy - 7y2 B) 9x3 + 3xy - 7y2 C) -7x3 + 3xy - 5y2 D) 7x3 - 3xy - 5y2
5) (9x4 + 7xy - y3) - (x4 + 5xy + 7y3)
A) 8x4 + 2xy - 8y3 B) 10x4 + 13xy + 6y3 C) 9x4
A) x2y - 4xy + 5 B) -x2y - 20xy + 15 C) -4x3y2 + 5 D) 7x2y + 20xy + 15
3) (12x4y2 - 7x2y2 + 5xy) + (11x4y2 - 8x2y2 + 10xy)
A) 23x4y2 - 15x2y2 + 15xy B) -15x4y2 + 23x2y2 + 15xy
C) 23x4y2 + 15x2y2 + 15xy D) 15x4y2 - 23x2y2 + 15xy
4) (x3 + 9xy - 6y2) - (8x3 + 6xy + y2)
A) -7x3 + 3xy - 7y2 B) 9x3 + 3xy - 7y2 C) -7x3 + 3xy - 5y2 D) 7x3 - 3xy - 5y2
5) (9x4 + 7xy - y3) - (x4 + 5xy + 7y3)
A) 8x4 + 2xy - 8y3 B) 10x4 + 13xy + 6y3 C) 9x4
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15) (3xy2 - 13y)(3xy2 + 13y)
A) 9x2y4 - 169y2 B) 3x2y4 - 13y2
C) 9x2y4 - 78xy3 - 169y2 D) 9x2y4 + 78xy3 - 169y2
0.5 Factoring Polynomials
1 Factor Out the Greatest Common Factor of a Polynomial
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Factor out the greatest common factor.
1) 2x + 12
A) 2(x + 6) B) 2(x + 12) C) 2x(x + 6) D) 2x(6)
2) 4x2 + 28x
A) 4x(x + 7) B) x(4x + 28) C) 4(x2 + 7x) D) 4x(x + 7x)
3) 21x4 - 9x3 + 12x2
A) 3x2(7x2 - 3x + 4) B) 3(7x4 - 3x3 + 4x2) C) x2(21x2 - 9x + 12) D) 3x(7x3 - 3x2 + 4x)
4) x(x + 13) + 5(x +13)
A) (x +13)(x + 5) B) (x2 + 13x) + (5x + 65)
C) 5x(x +13) D) 13x(x + 5)
5) x(5x + 4) - 2(5x + 4)
A) (5x + 4)(x - 2) B) (5x + 4)(x + 2) C) (5x - 2)(x + 4) D) -2x(5x + 4)
6) x2(x - 3) - (x - 3)
A) (x - 3)(x2 - 1) B) (x - 3)(x2 + 1) C) x2(x - 3) D) (x3 - 3x2) - (x - 3)
2 Factor by Grouping
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Factor by grouping. Assume any variable exponents represent whole numbers.
1) x3 - 4x2 - 3x + 12
A) (x - 4)(x2 - 3) B) (x - 3)(x2 - 4) C) (x + 4)(x2 + 3) D) (x - 4)(x - 3)
2) x3 + 7x + 2x2 + 14
A) (x + 2)(x2 + 7) B) (x - 2)(x2 + 7) C) (x + 2)(x2 - 7) D) (x + 2)(x + 7)
3) 5x3 - 25x2 + 8x - 40
A) (x - 5)(5x2 + 8) B) (x + 5)(5x2 + 8) C) (x - 5)(5x2 - 8) D) (x - 5)(5x +
A) 9x2y4 - 169y2 B) 3x2y4 - 13y2
C) 9x2y4 - 78xy3 - 169y2 D) 9x2y4 + 78xy3 - 169y2
0.5 Factoring Polynomials
1 Factor Out the Greatest Common Factor of a Polynomial
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Factor out the greatest common factor.
1) 2x + 12
A) 2(x + 6) B) 2(x + 12) C) 2x(x + 6) D) 2x(6)
2) 4x2 + 28x
A) 4x(x + 7) B) x(4x + 28) C) 4(x2 + 7x) D) 4x(x + 7x)
3) 21x4 - 9x3 + 12x2
A) 3x2(7x2 - 3x + 4) B) 3(7x4 - 3x3 + 4x2) C) x2(21x2 - 9x + 12) D) 3x(7x3 - 3x2 + 4x)
4) x(x + 13) + 5(x +13)
A) (x +13)(x + 5) B) (x2 + 13x) + (5x + 65)
C) 5x(x +13) D) 13x(x + 5)
5) x(5x + 4) - 2(5x + 4)
A) (5x + 4)(x - 2) B) (5x + 4)(x + 2) C) (5x - 2)(x + 4) D) -2x(5x + 4)
6) x2(x - 3) - (x - 3)
A) (x - 3)(x2 - 1) B) (x - 3)(x2 + 1) C) x2(x - 3) D) (x3 - 3x2) - (x - 3)
2 Factor by Grouping
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Factor by grouping. Assume any variable exponents represent whole numbers.
1) x3 - 4x2 - 3x + 12
A) (x - 4)(x2 - 3) B) (x - 3)(x2 - 4) C) (x + 4)(x2 + 3) D) (x - 4)(x - 3)
2) x3 + 7x + 2x2 + 14
A) (x + 2)(x2 + 7) B) (x - 2)(x2 + 7) C) (x + 2)(x2 - 7) D) (x + 2)(x + 7)
3) 5x3 - 25x2 + 8x - 40
A) (x - 5)(5x2 + 8) B) (x + 5)(5x2 + 8) C) (x - 5)(5x2 - 8) D) (x - 5)(5x +
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2) x2 - 3x - 28
A) (x + 4)(x - 7) B) (x - 4)(x - 7) C) (x - 4)(x + 1) D) prime
3) x2 - 8x + 15
A) (x - 3)(x - 5) B) (x + 3)(x - 5) C) (x + 3)(x + 1) D) prime
4) x2 + 10x - 24
A) (x + 12)(x - 2) B) (x - 12)(x + 2) C) (x - 12)(x + 1) D) prime
5) x2 - x - 6
A) (x + 2)(x - 3) B) (x + 3)(x - 2) C) (x + 1)(x - 5) D) prime
6) x2 - x - 35
A) (x - 35)(x + 1) B) (x + 5)(x - 7) C) (x - 5)(x + 7) D) prime
7) 5x2 + 18x + 16
A) (5x + 8)(x + 2) B) (5x + 2)(x + 8) C) (5x + 8)(5x + 2) D) prime
8) 7x2 - 44x + 12
A) (7x - 2)(x - 6) B) 7(x - 2)(x - 6) C) (7x + 6)(x - 2) D) (7x - 2)(7x + 6)
9) 7x2 + 2x - 5
A) (7x - 5)(x + 1) B) (7x + 1)(x
A) (x + 4)(x - 7) B) (x - 4)(x - 7) C) (x - 4)(x + 1) D) prime
3) x2 - 8x + 15
A) (x - 3)(x - 5) B) (x + 3)(x - 5) C) (x + 3)(x + 1) D) prime
4) x2 + 10x - 24
A) (x + 12)(x - 2) B) (x - 12)(x + 2) C) (x - 12)(x + 1) D) prime
5) x2 - x - 6
A) (x + 2)(x - 3) B) (x + 3)(x - 2) C) (x + 1)(x - 5) D) prime
6) x2 - x - 35
A) (x - 35)(x + 1) B) (x + 5)(x - 7) C) (x - 5)(x + 7) D) prime
7) 5x2 + 18x + 16
A) (5x + 8)(x + 2) B) (5x + 2)(x + 8) C) (5x + 8)(5x + 2) D) prime
8) 7x2 - 44x + 12
A) (7x - 2)(x - 6) B) 7(x - 2)(x - 6) C) (7x + 6)(x - 2) D) (7x - 2)(7x + 6)
9) 7x2 + 2x - 5
A) (7x - 5)(x + 1) B) (7x + 1)(x
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4 Factor the Difference of Squares
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Factor the difference of two squares.
1) x2 - 9
A) (x + 3)(x - 3) B) (x + 3)2 C) (x - 3)2 D) prime
2) 16x2 - 49
A) (4x + 7)(4x - 7) B) (4x - 7)2 C) (4x + 7)2 D) prime
3) 16x2 - 121y2
A) (4x + 11y)(4x - 11y) B) (4x - 11y)2
C) (4x + 11y)2 D) prime
4) x4 - 256
A) (x2 + 16)(x + 4)(x - 4) B) (x2 + 16)(x2 + 16)
C) (x2 - 16)(x2 - 16) D) prime
5) (16x4 - 81)
A) (4x2 + 9)(2x + 3)(2x - 3) B) (4x2 + 9)(4x2 - 9)
C) (2x + 3)2(2x - 3)2 D) (4x2 + 9)(4x2 + 9)
5 Factor Perfect Square Trinomials
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Factor the perfect square trinomial.
1) x2 - 10x + 25
A) (x - 5)2 B) (x + 5)2 C) (x - 5)(x + 5) D) prime
2) x2 - 20x + 400
A) (x - 20)2 B) (x + 20)2 C) (x + 20)(x - 20) D) prime
3) 36x2 + 12x + 1
A) (6x + 1)2 B) (6x + 1)(6x - 1) C) (x + 6)2 D) prime
6 Factor the Sum or Difference of Two Cubes
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Factor using the formula for the sum or difference of two cubes.
1) x3 - 125
A) (x - 5)(x2 + 5x + 25) B) (x + 5)(x2 - 5x + 25)
C) (x + 125)(x2 - 1) D) prime
2) x3 + 64
A) (x + 4)(x2 - 4x + 16) B) (x - 4)(x2 + 4x + 16)
C) (x + 4)(x2 + 16) D) prime
Page 29
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Factor the difference of two squares.
1) x2 - 9
A) (x + 3)(x - 3) B) (x + 3)2 C) (x - 3)2 D) prime
2) 16x2 - 49
A) (4x + 7)(4x - 7) B) (4x - 7)2 C) (4x + 7)2 D) prime
3) 16x2 - 121y2
A) (4x + 11y)(4x - 11y) B) (4x - 11y)2
C) (4x + 11y)2 D) prime
4) x4 - 256
A) (x2 + 16)(x + 4)(x - 4) B) (x2 + 16)(x2 + 16)
C) (x2 - 16)(x2 - 16) D) prime
5) (16x4 - 81)
A) (4x2 + 9)(2x + 3)(2x - 3) B) (4x2 + 9)(4x2 - 9)
C) (2x + 3)2(2x - 3)2 D) (4x2 + 9)(4x2 + 9)
5 Factor Perfect Square Trinomials
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Factor the perfect square trinomial.
1) x2 - 10x + 25
A) (x - 5)2 B) (x + 5)2 C) (x - 5)(x + 5) D) prime
2) x2 - 20x + 400
A) (x - 20)2 B) (x + 20)2 C) (x + 20)(x - 20) D) prime
3) 36x2 + 12x + 1
A) (6x + 1)2 B) (6x + 1)(6x - 1) C) (x + 6)2 D) prime
6 Factor the Sum or Difference of Two Cubes
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Factor using the formula for the sum or difference of two cubes.
1) x3 - 125
A) (x - 5)(x2 + 5x + 25) B) (x + 5)(x2 - 5x + 25)
C) (x + 125)(x2 - 1) D) prime
2) x3 + 64
A) (x + 4)(x2 - 4x + 16) B) (x - 4)(x2 + 4x + 16)
C) (x + 4)(x2 + 16) D) prime
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3) 27x3 - 1
A) (3x - 1)(9x2 + 3x + 1) B) (3x - 1)(9x2 + 1)
C) (3x + 1)(9x2 - 3x + 1) D) prime
4) 8x3 + 1
A) (2x + 1)(4x2 - 2x + 1) B) (2x - 1)(4x2 + 1)
C) (2x - 1)(4x2 + 2x + 1) D) prime
5) 27x3 + 64
A) (3x + 4)(9x2 - 12x + 16) B) (3x - 4)(9x2 + 12x + 16)
C) (3x + 4)(9x2 + 12x + 16) D) (3x + 4)(9x2 + 16)
6) 125x3 - 8
A) (5x - 2)(25x2 + 10x + 4) B) (5x + 2)(25x2 - 10x + 4)
C) (5x - 2)(25x2 - 10x + 4) D) (5x - 2)(25x2 + 4)
7 Use a General Strategy for Factoring Polynomials
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Factor completely, or state that the polynomial is prime.
1) 4x3 - 16x
A) 4x(x + 2)(x - 2) B) 4(x + 2)(x2 - 2x) C) x(x + 2)(4x - 8) D) prime
2) 50x2 - 32
A) 2(5x + 4)(5x - 4) B) 2(5x - 4)2 C) 2(5x + 4)2 D) prime
3) 4x2 + 16x + 12
A) 4(x + 1)(x + 3) B) (4x + 4)(x + 3) C) (x + 1)(4x + 12) D) 4(x2 + 4x + 3)
4) 6x4 - 6
A) 6(x2 + 1)(x + 1)(x - 1) B) 6(x2 + 1)(x2 - 1)
C) 6(x + 1)2(x - 1)2 D) prime
5) x3 - 2x2 - 25x + 50
A) (x - 2)(x + 5)(x - 5) B) (x + 2)(x
A) (3x - 1)(9x2 + 3x + 1) B) (3x - 1)(9x2 + 1)
C) (3x + 1)(9x2 - 3x + 1) D) prime
4) 8x3 + 1
A) (2x + 1)(4x2 - 2x + 1) B) (2x - 1)(4x2 + 1)
C) (2x - 1)(4x2 + 2x + 1) D) prime
5) 27x3 + 64
A) (3x + 4)(9x2 - 12x + 16) B) (3x - 4)(9x2 + 12x + 16)
C) (3x + 4)(9x2 + 12x + 16) D) (3x + 4)(9x2 + 16)
6) 125x3 - 8
A) (5x - 2)(25x2 + 10x + 4) B) (5x + 2)(25x2 - 10x + 4)
C) (5x - 2)(25x2 - 10x + 4) D) (5x - 2)(25x2 + 4)
7 Use a General Strategy for Factoring Polynomials
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Factor completely, or state that the polynomial is prime.
1) 4x3 - 16x
A) 4x(x + 2)(x - 2) B) 4(x + 2)(x2 - 2x) C) x(x + 2)(4x - 8) D) prime
2) 50x2 - 32
A) 2(5x + 4)(5x - 4) B) 2(5x - 4)2 C) 2(5x + 4)2 D) prime
3) 4x2 + 16x + 12
A) 4(x + 1)(x + 3) B) (4x + 4)(x + 3) C) (x + 1)(4x + 12) D) 4(x2 + 4x + 3)
4) 6x4 - 6
A) 6(x2 + 1)(x + 1)(x - 1) B) 6(x2 + 1)(x2 - 1)
C) 6(x + 1)2(x - 1)2 D) prime
5) x3 - 2x2 - 25x + 50
A) (x - 2)(x + 5)(x - 5) B) (x + 2)(x
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