Deck 12: Prerequisites: Fundamental Concepts of Algebra

Question 1

Evaluate the algebraic expression for the given value or values of the variable(s).
$2 ( x + 1 ) + 21 ; \quad x = - 4$

A) 15
В) $- 15$
C) 35
D) 7

Answer 1

A

Question 2

Find the Intersection of Two Sets
$\{ 2,10,8 \} \cap \{ 4,6 \}$

A) $\varnothing$
B) $\{ 10,8 \}$
C) $\{ 2,4,8,10,6 \}$
D) $\{ 2,8 \}$

Answer 2

A

Question 3

Use Mathematical Models
The formula $\mathrm { C } = \frac { 5 } { 9 } ( \mathrm {~F} - 32 )$ expresses the relationship between Fahrenheit temperature, $\mathrm { F }$ , and Celsius temperature, C. Use the formula to convert $68 ^ { \circ } \mathrm { F }$ to its equivalent temperature on the Celsius scale.

A) $20 ^ { \circ } \mathrm { C }$
B) $4 ^ { \circ } \mathrm { C }$
C) $56 ^ { \circ } \mathrm { C }$
D) $65 ^ { \circ } \mathrm { C }$

Answer 3

A

Question 4

Find the Intersection of Two Sets
$\{ 1,3,5,8 \} \cap \{ 5,11,1 \}$

A) $\{ 1,5 \}$
B) $\{ 1 \}$
C) $\{ 1,5,8,3,11 \}$
D) $\varnothing$

Question 5

Use Mathematical Models
A stone is dropped from a tower that is 770 feet high. The formula $h = 770 - 16 t ^ { 2 }$ 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) $514 \mathrm { ft }$
B) $524 \mathrm { ft }$
C) $489 \mathrm { ft }$
D) $539 \mathrm { ft }$

Question 6

Use Mathematical Models
The winning times (in seconds) in a speed-skating event for men can be represented by the formula $\mathrm { T } = 46.18 - 0.095 \mathrm { x }$ , where $\mathrm { x }$ represents the year, with $\mathrm { x } = 0$ corresponding to 1920 . (For example in $1992 , \mathrm { x }$ would be $1992 - 1920 = 72$ .) According to the formula, what was the winning time in 1998 ? Round to the nearest hundredth.

A) $38.77 \mathrm { sec }$
B) $3594.63 \mathrm { sec }$
C) $39.72 \mathrm { sec }$
D) $40.67 \mathrm { sec }$

Question 7

Find the Union of Two Sets
$\{ 2,5,8,10 \} \cup \{ 2,5,12 \}$

A) $\{ 2,5,8,10,12 \}$
B) $\{ 2,5 \}$
C) $\{ 8,10,12 \}$
D) $\varnothing$

Question 8

Find the Intersection of Two Sets
$\{ 6,8,9,11 \} \cap \varnothing$

A) $\varnothing$
B) $\{ 6,8,9,11 \}$
C) $\{ 6,8 \}$
D) $\{ 9,11 \}$

Question 9

Evaluate the algebraic expression for the given value or values of the variable(s).
$8 x + 3 ; \quad x = - 2$

A) $- 13$
B) 19
C) $- 19$
D) 13

Question 10

Find the Union of Two Sets
$\{ 2,10 \} \cup \{ 2,4,8 \}$

A) $\{ 2,4,8,10 \}$
B) $\{ 2 \}$
C) $\{ 4,8,10 \}$
D) $\varnothing$

Question 11

Evaluate the algebraic expression for the given value or values of the variable(s).
$\frac { y - 4 x } { 7 x + x y } ; \quad x = - 1$ and $y = 3$

A) $- \frac { 7 } { 10 }$
B) $\frac { 1 } { 10 }$
C) $\frac { 1 } { 4 }$
D) $- \frac { 9 } { 10 }$

Question 12

Use Mathematical Models
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 $y = 1.3 x + 3.07$ . 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

Question 13

Use Mathematical Models
As the relative humidity increases, the temperature seems higher than it is. The formula $\mathrm { T } = 0.113 \mathrm { x } + 77.98$ approximates the apparent temperature for an actual temperature of $85 ^ { \circ } \mathrm { F }$ , where $x$ is the relative humidity. What is the apparent temperature (to the nearest degree) for a relative humidity of $40 \%$ ?

A) $83 ^ { \circ } \mathrm { F }$
B) $352 ^ { \circ } \mathrm { F }$
C) $118 ^ { \circ } \mathrm { F }$
D) $78 ^ { \circ } \mathrm { F }$

Question 14

Evaluate the algebraic expression for the given value or values of the variable(s).
$x ^ { 2 } - 4 ( x - y ) ; \quad x = 6$ and $y = 2$

A) 20
B) 10
C) 14
D) $- 52$

Question 15

Evaluate the algebraic expression for the given value or values of the variable(s).
$$\frac { 6 ( x + 3 ) } { 2 x + 2 } ; \quad x = 5$$

A) 4
B) 1
C) 8
D) $\frac { 11 } { 2 }$

Question 16

Evaluate the algebraic expression for the given value or values of the variable(s).
$6 x ^ { 2 } + 8 y ; \quad x = 7$ and $y = 5$

A) 334
B) 1804
C) 1710
D) 206

Question 17

Use Mathematical Models
If a rock falls from a height of 50 meters above the ground, the height $\mathrm { H }$ (in meters) after x seconds can be approximated using the formula $\mathrm { H } = 50 - 4.9 \mathrm { x } ^ { 2 }$ . What is the height of the rock after 3 seconds?

A) $5.9 \mathrm {~m}$
B) $405.9 \mathrm {~m}$
C) $- 166.09 \mathrm {~m}$
D) $35.3 \mathrm {~m}$

Question 18

Evaluate the algebraic expression for the given value or values of the variable(s).
$$9 x + 8 ; \quad x = 7$$

A) 71
B) 126
C) 17
D) 55

Question 19

Evaluate the algebraic expression for the given value or values of the variable(s).
$( x + 4 y ) ^ { 2 } ; \quad x = 4$ and $y = 2$

A) 144
B) 12
C) 24
D) 64

Question 20

Evaluate the algebraic expression for the given value or values of the variable(s).
$2 + 6 ( x - 6 ) ^ { 3 } ; \quad x = 8$

A) 50
B) 14
C) 64
D) $- 46$

Question 21

Use Inequality Symbols
$$17 \geq 4$$

Question 22

Use Inequality Symbols
$$15 > 13$$

Question 23

Use Inequality Symbols
$$24 < - 6$$

Question 24

Find the Union of Two Sets
$\{ 1,3,4,6 \} \cup \varnothing$

A) $\{ 1,3,4,6 \}$
B) $\{ 1,3 \}$
C) $\{ 4,6 \}$
D) $\varnothing$

Question 25

Use Inequality Symbols
$$- \pi \geq - \pi$$

Question 26

Recognize Subsets of the Real Numbers
$\mathrm { B } = \{ 17 , \sqrt { 5 } , - 22,0,0 . \overline { 6 } , \sqrt { 25 } \}$ Integers

A) $17 , - 22,0 , \sqrt { 25 }$
B) 17,0
C) $17 , - 22,0$
D) $17,0 , \sqrt { 25 }$

Question 27

Evaluate Absolute Value
$$\frac { 19 } { | - 1 | }$$

A) 19
B) -1C)1
D)-19

Question 28

Use Inequality Symbols
$$12 \leq 11$$

Question 29

Use Inequality Symbols
$$- 81 < 0$$

Question 30

Evaluate Absolute Value
$$| 13 |$$

A) 13
B) -13
C) 26
D) 0

Question 31

Use Inequality Symbols
$$\pi < 3$$

Question 32

Use Inequality Symbols
$$- 5 \leq 8$$

Question 33

Recognize Subsets of the Real Numbers
$\mathrm { B } = \left\{ 4 , \sqrt { 8 } , 0 , \frac { 5 } { 6 } , \sqrt { 9 } , - 0 . \overline { 9 } , 0.53 , - 23 \right\}$ Real numbers

A) $4 , \sqrt { 8 } , 0 , \frac { 5 } { 6 } , \sqrt { 9 } , - 0 . \overline { 9 } , 0.53 , - 23$
B) $4 , \sqrt { 8 } , 0 , \frac { 5 } { 6 } , \sqrt { 9 } , 0.53$
C) $4 , \sqrt { 8 } , \frac { 5 } { 6 } , \sqrt { 9 } , - 0 . \overline { 9 } , 0.53 , - 23$
D) $4,0 , \frac { 5 } { 6 } , - 0 . \overline { 9 } , 0.53 , - 23$

Question 34

Recognize Subsets of the Real Numbers
$B = \{ 10 , \sqrt { 6 } , - 9,0,0 . \overline { 6 } , \sqrt { 9 } \}$ Natural numbers

A) $10 , \sqrt { 9 }$
B) $10,0 , \sqrt { 9 }$
C) 10,0
D) 10 )10

Question 35

Use Inequality Symbols
$$21 > 24$$

Question 36

Recognize Subsets of the Real Numbers
$B = \left\{ 16 , \sqrt { 5 } , - 2,0 , \frac { 8 } { 9 } , \sqrt { 25 } , 0 . \overline { 3 } , 0.73 \right\}$ Rational numbers

A) $16 , - 2,0 , \frac { 8 } { 9 } , \sqrt { 25 } , 0.73,0 . \overline { 3 }$
B) $16,0 , \sqrt { 25 }$
C) $\sqrt { 5 } , \sqrt { 25 }$
D) $\sqrt { 5 } , \frac { 8 } { 9 } , 0.73$

Question 37

Recognize Subsets of the Real Numbers
$\mathrm { B } = \{ 11 , \sqrt { 6 } , - 16,0,0 . \overline { 1 } , \sqrt { 4 } \}$ Whole numbers

A) $11,0 , \sqrt { 4 }$
B) $11 , - 16,0$
C) $11 , - 16,0 , \sqrt { 4 }$
D) 11,0

Question 38

Use Inequality Symbols
$$- 8 \geq 15$$

Question 39

Recognize Subsets of the Real Numbers
$B = \left\{ 11 , \sqrt { 7 } , - 11,0 , \frac { 5 } { 6 } , \sqrt { 4 } , 0 . \overline { 7 } , 0.35 \right\}$ Irrational numbers

A) $\sqrt { 7 }$
B) $\sqrt { 7 } , 0 . \overline { 7 }$
C) $\sqrt { 7 } , \sqrt { 4 } , 0 . \overline { 7 }$
D) $\sqrt { 7 } , \sqrt { 4 } , 0.35$

Question 40

Evaluate Absolute Value
$$| - 2 |$$

A) 2
B) -2
C) 4
D) 0

Question 41

Evaluate Absolute Value
$| \sqrt { 10 } - 13 |$

A) $13 - \sqrt { 10 }$
B) $\sqrt { 10 } - 13$
C) $- 3$
D) 3 )3

Question 42

Identify Properties of the Real Numbers
$17 \cdot ( 6 + 8 ) = 17 \cdot 6 + 17 \cdot 8$

A) Distributive property of multiplication over addition
B) Commutative property of multiplication
C) Associative property of multiplication
D) Commutative property of addition

Question 43

Use Absolute Value to Express Distance
$- 18$ and $- 34$

A) $| ( - 18 ) - ( - 34 ) | = 16$
B) $| ( - 34 ) - ( - 18 ) | = - 16$
C) $| ( - 34 ) + ( - 18 ) | = - 52$
D) $| - ( - 18 ) + ( - 34 ) | = 52$

Question 44

Identify Properties of the Real Numbers
$$( 8 \cdot 12 ) \cdot 7 = 8 \cdot ( 12 \cdot 7 )$$

A) Associative property of multiplication
B) Commutative property of multiplication
C) Distributive property of multiplication over addition
D) Identity property of multiplication

Question 45

Use Absolute Value to Express Distance
$28.9$ 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) $| - 28.9 + 23.7 | = - 52.6$

Question 46

Identify Properties of the Real Numbers
$$( 7 + 3 ) + 4 = ( 3 + 7 ) + 4$$

A) Commutative property of addition
B) Associative property of addition
C) Distributive property of multiplication over addition
D) Inverse property of addition

Question 47

Identify Properties of the Real Numbers
$$6 + ( - 7 ) = ( - 7 ) + 6$$

A) Commutative property of addition
B) Associative property of addition
C) Distributive property of multiplication over addition
D) Identity property of addition

Question 48

Identify Properties of the Real Numbers
$$7 ( x + 6 ) = 7 x + 7 \cdot 6$$

A) Distributive property of multiplication over addition
B) Commutative property of multiplication
C) Associative property of multiplication
D) Identity property of multiplication

Question 49

Evaluate Absolute Value
$$| | - 6 | + | - 8 | |$$

A) 14
B) 2
C) $- 2$
D) $- 14$ ) Evaluate the expression for the given values of x and y.

Question 50

Use Absolute Value to Express Distance
72 and $- 9$

A) $| 72 - ( - 9 ) | = 81$
В) $| ( - 9 ) - 72 | = - 81$
C) $| 72 + ( - 9 ) | = 63$
D) $| - 72 + ( - 9 ) | = - 63$

Question 51

Identify Properties of the Real Numbers
$$( 9 + 6 ) + ( 7 + 19 ) = ( 7 + 19 ) + ( 9 + 6 )$$

A) Commutative property of addition
B) Associative property of addition
C) Distributive property of multiplication over addition
D) Inverse property of addition

Question 52

Identify Properties of the Real Numbers
$$3 \cdot ( 19 \cdot 2 ) = ( 19 \cdot 2 ) \cdot 3$$

A) Commutative property of multiplication
B) Associative property of multiplication
C) Distributive property of multiplication over addition
D) Identity property of multiplication

Question 53

Identify Properties of the Real Numbers
$$2 + ( 8 + 7 ) = ( 2 + 8 ) + 7$$

A) Associative property of addition
B) Commutative property of addition
C) Distributive property of multiplication over addition
D) Identity property of addition

Question 54

Use Absolute Value to Express Distance
$1.5$ 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) $- | 1.5 + 48.3 | = - 49.8$

Question 55

Identify Properties of the Real Numbers
$$5 \cdot ( 6 \cdot 17 ) = 5 \cdot ( 17 \cdot 6 )$$

A) Commutative property of multiplication
B) Associative property of multiplication
C) Distributive property of multiplication over addition
D) Identity property of multiplication

Question 56

Use Absolute Value to Express Distance
$- 14.7$ 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) $| - 14.7 + ( - 24.3 ) | = - 9.6$

Question 57

Evaluate Absolute Value
$$| 5 + ( - 10 ) |$$

A) 5
B) 15
C) $- 5$
D) $- 15$ )

Question 58

Evaluate Absolute Value
$\frac { | x | } { x } + \frac { | y | } { y } ; \quad x = 6$ and $y = - 3$

A) 0
B) 2
C) 1
D) $- 1$

Question 59

Evaluate Absolute Value
$$| | - 4 | - | - 9 | |$$

A) 5
B) 13
C) $- 5$
D) $- 13$ )

Question 60

Use Absolute Value to Express Distance
26 and 34

A) $| 26 - 34 | = 8$
B) $- | 34 - 26 | = - 8$
C) $| 26 + 34 | = 60$
D) $- | 26 + 34 | = - 60$

Question 61

Identify Properties of the Real Numbers
$$3 ( - 5 + 7 ) = - 15 + 21$$

A) Distributive property of multiplication over addition
B) Associative property of multiplication
C) Associative property of addition
D) Commutative property of multiplication

Question 62

Identify Properties of the Real Numbers
$- ( 49 x )$

A) $- 49 x$
B) $49 x$
C) $- 49 - x$
D) $49 - x$

Question 63

Identify Properties of the Real Numbers
$$( 11 z + 6 ) - ( 4 z - 4 )$$

A) $7 z + 10$
B) $7 \mathrm { z } + 2$
C) $15 z + 10$
D) $7 \mathrm { z } - 10$

Question 64

Identify Properties of the Real Numbers
$$- 6 ( 2 x - 9 ) - 4 x + 5$$

A) $- 16 x + 59$
B) $8 x + 59$
C) $16 x + 59$
D) $- 16 x - 49$ Write the algebraic expression without parentheses.

Question 65

Exponents and Scientific Notation
1 Use the Product Rule
$$\left( 3 x ^ { 4 } \right) \left( 9 x ^ { 9 } \right)$$

A) $27 x ^ { 13 }$
В) $- 27 x + 13$
C) $27 x ^ { 36 }$
D) $- 27 x ^ { 36 }$

Question 66

Identify Properties of the Real Numbers
$$- 7 ( 6 + 7 ) = - 42 + ( - 49 )$$

A) Distributive property of multiplication over addition
B) Associative property of multiplication
C) Associative property of addition
D) Commutative property of multiplication

Question 67

Identify Properties of the Real Numbers
$$- ( 3 x - 9 )$$

A) $- 3 x + 9$
B) $3 x - 9$
C) $- 3 x - 9$
D) $27 x$

Question 68

Identify Properties of the Real Numbers
$- ( 7 z - 2 w + 6 y )$

A) $- 7 z + 2 w - 6 y$
B) $- 7 z + 2 w + 6 y$
C) $- 7 z - 2 w + 6 y$
D) $- 7 z - 2 w - 6 y$

Question 69

Identify Properties of the Real Numbers
$$- 8 ( 6 r + 3 ) + 4 ( 9 r + 4 )$$

A) $- 12 r - 8$
B) $- 2 r - 5$
C) $- 12 r + 3$
D) $- 72 \mathrm { r }$ )

Question 70

Identify Properties of the Real Numbers
$$- 8 ( - 8 z )$$

A) $64 \mathrm { z }$
B) $- 64 z$
C) $64 - 8 z$
D) $64 + z$

Question 71

Exponents and Scientific Notation
1 Use the Product Rule
$83 \cdot 8 ^ { 8 }$

A) 8¹¹
B) 8²⁴
C) 64¹¹
D) 64²⁴

Question 72

Exponents and Scientific Notation
1 Use the Product Rule
$$y \cdot y ^ { 11 }$$

A) $\mathrm { y } ^ { 12 }$
B) $2 y ^ { 11 }$
C) $\mathrm { y } ^ { 11 }$
D) $2 \mathrm { y } ^ { 12 }$

Question 73

Use the Quotient Rule
$\frac { x ^ { 14 } } { x ^ { 10 } }$

A) $x ^ { 4 }$
B) $x ^ { 24 }$
C) $x ^ { 8 }$
D) $\frac { 1 } { x ^ { 4 } }$

Question 74

Exponents and Scientific Notation
1 Use the Product Rule
$$x ^ { 8 } \cdot x ^ { 9 }$$

A) $x ^ { 17 }$
B) $x ^ { 72 }$
C) $17 x$
D) $72 \mathrm { x }$

Question 75

Identify Properties of the Real Numbers
$- ( - 9 + 5 y )$

A) $9 - 5 y$
B) $9 + 5 y$
C) $- 9 + 5 y$
D) $45 \mathrm { y }$

Question 76

Identify Properties of the Real Numbers
$$\frac { 1 } { ( x + 2 ) } ( x + 2 ) = 1 , x \neq - 2$$
A) Inverse property of multiplication
B) Inverse property of addition
C) Commutative property of multiplication
D) Identity property of multiplication 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

Question 77

Use the Quotient Rule
$\frac { x ^ { 2 } } { x ^ { 6 } }$

A) $\frac { 1 } { { } ^ { 4} x}$
B) $- x ^ { 4 }$
C) $x ^ { 4 }$
D) $- \frac { 1 } { x ^ { 4 } }$

Question 78

Identify Properties of the Real Numbers
$$\frac { 1 } { 5 } ( 5 x ) + [ ( 4 x ) + ( - 4 x ) ]$$

A) $x$
B) $9 x$
C) $- 7 x$
D) 1 0.2 Exponents and Scientific Notation

Question 79

Use the Quotient Rule
$\frac { 5 ^ { 5 } } { 5 ^ { 6 } }$

A) $\frac { 1 } { 5 }$
B) 5
C) $- 12,500$
D) $\frac { 5 } { 6 }$

Question 80

Exponents and Scientific Notation
1 Use the Product Rule
$$\left( - 8 x ^ { 5 } y \right) \left( - 3 x ^ { 3 } y ^ { 6 } \right)$$

A) $24 x ^ { 8 } y ^ { 7 }$
B) $- 24 x ^ { 8 } y ^ { 6 }$
C) $- 11 x ^ { 8 } y ^ { 6 }$
D) $24 \mathrm { x } ^ { 15 } \mathrm { y }^ 6$