Deck 1: Algebra, Mathematical Models, and Problem Solving

Question 1

Determine whether the statement is true or false.
Some whole numbers are not integers.

Answer 1

False

Question 2

Determine whether the statement is true or false.
All natural numbers are whole numbers.

Answer 2

True

Question 3

Evaluate the expression for the given values.
3x + 6, for x = 6

A) 36
B) 12
C) 9
D) 24

Answer 3

D

Question 4

Write the English phrase as an algebraic expression. Let x represent the number.
5 less than 3 times a number

A) 5 - 3x
B) 3x - 5
C) 3 - 5x
D) 5x - 3

Question 5

Solve.
Forensic scientists use the lengths of certain bones to calculate the height of a person. When the femur (the bone from the knee to the hip socket) is used, the following formula applies for men: h = 69.09 + 2.24f, where h is the height and f is the length of the femur (both in centimeters). Find the height of a man with a femur measuring 51 centimeters.

A) 3637.83 cm
B) 183.33 cm
C) 120.09 cm
D) 8.08 cm

Question 6

Solve.
The formula $C = \frac { 5 } { 9 } ( F - 32 )$ converts Fahrenheit to Celsius degrees. The high temperature in a certain city was $59 ^ { \circ } \mathrm { F }$ . Find the corresponding Celsius temperature (to the nearest degree).

A) 33°C
B) 15°C
C) 49°C
D) 1°C

Question 7

Solve.
If a rock falls from a height of 80 meters above the ground, the height H (in meters) after x seconds is approximately H = 80 - 4.9x². What is the height of the rock after 2 seconds? (Round your answer to the nearest tenth.)

A) 70.2 m
B) 300.4 m
C) -16.04 m
D) 60.4 m

Question 8

Write the English phrase as an algebraic expression. Let x represent the number.
A number divided by 50

A) $\frac { 50 } { x }$
B) 50x
C) x 50
D) $\frac { x } { 50 }$
-

Question 9

Determine whether the statement is true or false.
Some whole numbers are not natural numbers.

Question 10

Write the English phrase as an algebraic expression. Let x represent the number.
The sum of a number and 131

A) 131x
B) 131 - x
C) 131 + x
D) 131

Question 11

Evaluate the expression for the given values.
$( x + 3 y ) ^ { 2 } , \text { for } x = 2 , y = 4$

A) 25
B) 14
C) 196
D) 28

Question 12

Write the English phrase as an algebraic expression. Let x represent the number.
89 less than a number

A) 89
B) x + 89
C) 89x
D) 89 - x

Question 13

Write the English phrase as an algebraic expression. Let x represent the number.
8 more than 4 times a number

A) 8x + 4
B) 4(8 + x)
C) 12x
D) 4x + 8

Question 14

Determine whether the statement is true or false.
Every irrational number is a rational number.

Question 15

Evaluate the expression for the given values.
$7 x ^ { 2 } + 5 y , \text { for } x = 8 , y = 3$

A) 103
B) 1449
C) 3151
D) 463

Question 16

Determine whether the statement is true or false.
Every rational number is an integer.

Question 17

Write the English phrase as an algebraic expression. Let x represent the number.
The quotient of 64 and a number

A) 64 - x
B) $\frac { 64 } { x }$
C) x - 64
D) $\frac { x } { 64 }$

Question 18

Evaluate the expression for the given values.
3x - y, for x = 9 and y = 5

A) 54
B) 32
C) 22
D) 8

Question 19

Determine whether the statement is true or false.
Some real numbers are integers.

Question 20

Write the English phrase as an algebraic expression. Let x represent the number.
A number decreased by 78

A) 78x
B) x - 78
C) 78
D) 78 - x

Question 21

By definition, an "and" statement is true only when the statements before and after the "and" connective are both true. Use this definition to determine whether the given statement is true or false.
$$\text { Six times the sum of a number and eight is represented by } 6 ( x + 8 ) \text { and } \frac { 6 } { 13 } \in \{ x \mid x \text { is a rational number } \}$$

Question 22

By definition, an "and" statement is true only when the statements before and after the "and" connective are both true. Use this definition to determine whether the given statement is true or false.
$$\left( \frac { 11 } { 12 } - \frac { 23 } { 12 } \right) \in \{ x \mid x \text { is an integer } \} \text { and the value of } 1 x ^ { 2 } ( x + 11 ) - 1 ( x + 11 ) x ^ { 2 } , \text { for } x = 100 \text { is } 0$$

Question 23

By definition, an "and" statement is true only when the statements before and after the "and" connective are both true. Use this definition to determine whether the given statement is true or false.
$$5 \in \{ 1,2,3 , \ldots . . \} \text { and } - 9 \notin \{ 1,2,3 , \ldots . \}$$

Question 24

Determine whether the statement is true or false.
Every real number is either an integer or irrational.

Question 25

Determine whether the statement is true or false.
Every real number is either rational or irrational.

Question 26

Determine whether the statement is true or false.
Some square roots are not irrational.

Question 27

By definition, an "and" statement is true only when the statements before and after the "and" connective are both true. Use this definition to determine whether the given statement is true or false.
$$\text { Five times the difference of a number and nine is represented by } 5 x - 9 \text { and } \pi \in \{ x \mid x \text { is an irrational number }$$

Question 28

Use the roster method to list the elements in the set.
{x | x is a whole number between 4 and 8}

A) {5, 6, 7, 8}
B) {4, 5, 6, 7}
C) {5, 6, 7}
D) {4, 5, 6, 7, 8}

Question 29

Use the roster method to list the elements in the set.
{x | x is an integer greater than -4}

A) {-3, -2, -1, . . .}
B) {-5, -6, -7, . . .}
C) {-5, -6, -7}
D) {-3, -2, -1, 0}

Question 30

Use the roster method to list the elements in the set.
{x  x is a natural number less than 9}

A) {0, 1, 2, 3, 4, 5, 6, 7, 8}
B) {1, 2, 3, 4, 5, 6, 7, 8}
C) {1, 2, 3, 4, 5, 6, 7, 8, 9}
D) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

Question 31

By definition, an "and" statement is true only when the statements before and after the "and" connective are both true. Use this definition to determine whether the given statement is true or false.
$$- 4000 \in \{ x \mid x \text { is an integer } \} \text { and twelve subtracted from four times a number is represented by } 4 x - 12 .$$

Question 32

Determine whether the statement is true or false.
All whole numbers are positive.

Question 33

Use the roster method to list the elements in the set.
{x | x is an integer between 5 and 9}

A) {6, 7, 8}
B) {5, 6, 7, 8}
C) {6, 7, 8, 9}
D) {5, 6, 7, 8, 9}

Question 34

Use the roster method to list the elements in the set.
{x | x is a natural number multiple of 5}

A) {5, 10, 15, . . .}
B) {-15, -10, -5, 0, 5, 10, 15,. . .}
C) {0, 5, 10, 15,. . .}
D) {10, 15, 20, . . .}

Question 35

By definition, an "and" statement is true only when the statements before and after the "and" connective are both true. Use this definition to determine whether the given statement is true or false.
$$\text { Three times the sum of a number and eight is represented by } 3 ( x + 8 ) \text { and } 0 \in \{ x \mid x \text { is a natural number } \}$$

Question 36

By definition, an "and" statement is true only when the statements before and after the "and" connective are both true. Use this definition to determine whether the given statement is true or false.
$$\left( \frac { 10 } { 66 } + \frac { 17 } { 66 } \right) \in \{ x \mid x \text { is a whole number } \} \text { and the value of } 9 x ^ { 2 } ( x + 22 ) - 9 x ^ { 2 } ( 22 + x ) \text {, for } x = 100 \text { is } 0 \text {. }$$

Question 37

By definition, an "and" statement is true only when the statements before and after the "and" connective are both true. Use this definition to determine whether the given statement is true or false.
The quotient of a number and the sum of the number and 7 is represented by $\frac { x } { x + 7 }$ and $\sqrt { 2 } \notin \{ x \mid x$ is a rational number $\}$

Question 38

Determine whether the statement is true or false.
Some integers are not positive.

Question 39

By definition, an "and" statement is true only when the statements before and after the "and" connective are both true. Use this definition to determine whether the given statement is true or false.
$$27 \in \{ 1,2,3 , \ldots \} \text { and } \{ 1 \} \in \{ 1,2,3,4 \}$$

Question 40

By definition, an "and" statement is true only when the statements before and after the "and" connective are both true. Use this definition to determine whether the given statement is true or false.
$$- 30,000 \in \{ x \mid x \text { is a whole number } \} \text { and nine subtracted from three times a number is represented by } 3 x - 9 .$$

Question 41

Express the interval in set builder notation and graph the interval on a number line.
$[ - 7 , \infty )$

A) $\{ x \mid x > - 7 \}$

B) $\{ x \mid x \geq - 7 \}$

C) $\{ x \mid x \geq - 7 \}$

D) $\{ x \mid x > - 7 \}$

Question 42

Express the interval in set builder notation and graph the interval on a number line.
$( 2.5 , \infty )$

A) $\{ x \mid x > 2.5 \}$

B) $\{ x \mid x \geq 2.5 \}$

C) $\{ x \mid x \leq 2.5 \}$

D) $\{ x \mid x < 2.5 \}$

Question 43

Express the interval in set builder notation and graph the interval on a number line.
$$[ - 4,7 ]$$

A) $\{ x \mid - 4 < x < 7 \}$

B) $\{ x \mid - 4 \leq x \leq 7 \}$

C) $\{ x \mid - 4 < x \leq 7 \}$

D) $\{ x \mid - 4 \leq x < 7 \}$

Question 44

Find the absolute value.
$$- | - 14 |$$

A) -14
B) 0
C) 14
D) 28

Question 45

Express the interval in set builder notation and graph the interval on a number line.
$$( - \infty , 2 ]$$

A) $\{ x \mid x \leq 2 \}$

B) $\{ x \mid x \leq 2 \}$

C) $\{ x \mid x < 2 \}$

D) $\{ x \mid x < 2 \}$

Question 46

Find the absolute value.
$| - 1.9 |$

A) 3.8
B) 0
C) -1.9
D) 1.9

Question 47

Find the absolute value.
$| 2.9 |$

A) -2.9
B) 0
C) 5.8
D) 2.9

Question 48

Find the absolute value.
$| - 22 |$

A) $- 22$
B) 0
C) 22
D) 44

Question 49

Find the absolute value.
$| - \sqrt { 5 } |$

A) $- \sqrt { 5 }$
B) $\sqrt { 5 }$
C) 5
D) $- 5$

Question 50

Express the interval in set builder notation and graph the interval on a number line.
$$[ - 5,1 )$$

A) $\{ x \mid - 5 < x \leq 1 \}$

B) $\{ x \mid - 5 \leq x \leq 1 \}$

C) $\{ x \mid x < 1 \}$

D) $\{ x \mid - 5 \leq x < 1 \}$

Question 51

Express the interval in set builder notation and graph the interval on a number line.
$$( - \infty , 6.5 ]$$

A) $\{ x \mid x \geq 6.5 \}$

B) $\{ x \mid x \leq 6.5 \}$

C) $\{ x \mid x > 6.5 \}$

D) $\{ x \mid x < 6.5 \}$

Question 52

Express the interval in set builder notation and graph the interval on a number line.
(-9, 6] A) $\{ x \mid - 9 \leq x \leq 6 \}$

B) $\{ x \mid - 9 < x < 6 \}$

C) $\{ x \mid - 9 < x \leq 6 \}$

D) $\{ x \mid x \leq 6 \}$

Question 53

Find the absolute value.
$| 0 |$

A) 10
B) -1
C) 0
D) 1

Question 54

Express the interval in set builder notation and graph the interval on a number line.
$$( - 6 , \infty )$$

A) $\{ x \mid x \geq - 6 \}$

B) $\{ x \mid x > - 6 \}$

C) $\{ x \mid x > - 6 \}$

D) $\{ x \mid x \geq - 6 \}$

Question 55

Express the interval in set builder notation and graph the interval on a number line.
$$( - \infty , 8 )$$

A) $\{ x \mid x < 8 \}$

B) $\{ x \mid x < 8 \}$

C) $\{ x \mid x \leq 8 \}$

D) $\{ x \mid x \leq 8 \}$

Question 56

Find the absolute value.
$- | 15 |$

A) -30
B) 0
C) 15
D) -15

Question 57

Express the interval in set builder notation and graph the interval on a number line.
$[ 2.5 , \infty )$

A) $\{ x \mid x \leq 2.5 \}$

B) $\{ x \mid x > 2.5 \}$

C) $\{ x \mid x \geq 2.5 \}$

D) $\{ x \mid x < 2.5 \}$

Question 58

Express the interval in set builder notation and graph the interval on a number line.
$$( - 4,7 )$$

A) $\{ x \mid - 4 < x < 7 \}$

B) $\{ x \mid - 4 \leq x \leq 7 \}$

C) $\{ x \mid - 4 \leq x < 7 \}$

D) $\{ x \mid - 4 < x \leq 7 \}$

Question 59

Express the interval in set builder notation and graph the interval on a number line.
$( - \infty , 2.5 )$

A) $\{ x \mid x \geq 2.5 \}$

B) $\{ x \mid x > 2.5 \}$

C) $\{ x \mid x < 2.5 \}$

D) $\{ x \mid x \leq 2.5 \}$

Question 60

Find the absolute value.
$| 7 |$

A) $- 7$
B) 0
C) 14
D) 7

Question 61

Find -x for the given value of x.
$$x = \frac { 1 } { 2 }$$

A) $- \frac { 1 } { 2 }$
B) 2
C) 0
D) $\frac { 1 } { 2 }$

Question 62

0 + (-11.3 )

A) 11.3
B) 0
C) -11.3
D) 4.7

Question 63

14.7 + (-14.7)

A) 2
B) 0
C) 14.7
D) -14.7

Question 64

Find the absolute value.
$$- \left| - \frac { 13 } { 3 } \right|$$

A) 10
B) $- 16$
C) $= \frac { 13 } { 3 }$
D) $\frac { 13 } { 3 }$

Question 65

Find -x for the given value of x.
$$x = - \frac { 5 } { 9 }$$

A) $\frac { 5 } { 9 }$
B) $- \frac { 9 } { 5 }$
C) 0
D) $- \frac { 5 } { 9 }$

Question 66

Find -x for the given value of x.
$$x = - \sqrt { 10 }$$

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

Question 67

Add as indicated.
-12 + 8

A) 20
B) -4
C) 4
D) -20

Question 68

Subtract as indicated.
1 - 12

A) 11
B) -13
C) -11
D) 13

Question 69

-14.9 + (-13.7)

A) 28.6
B) -28.6
C) 1.2
D) -1.2

Question 70

$- \frac { 5 } { 9 } - \frac { 3 } { 4 }$

A) $- \frac { 8 } { 13 }$
B) $- \frac { 2 } { 9 }$
C) $- \frac { 19 } { 12 }$
D) $- \frac { 47 } { 36 }$

Question 71

Find -x for the given value of x.
$$x = - 26$$

A) $- 26$
B) $- \frac { 1 } { 26 }$
C) 0
D) 26

Question 72

Find -x for the given value of x.
$$x = - \frac { 11 } { 7 }$$

A) $\frac { 7 } { 11 }$
B) $\frac { 11 } { 7 }$
C) $- \frac { 7 } { 11 }$
D) $- \frac { 11 } { 7 }$

Question 73

Add as indicated.
-16 + (-17)

A) 1
B) -33
C) -1
D) 33

Question 74

$\frac { 2 } { 3 } + \left( - \frac { 5 } { 9 } \right)$

A) $\frac { 11 } { 9 }$
B) $\frac { 1 } { 9 }$
$C ) = \frac { 1 } { 9 }$
D) $- \frac { 11 } { 9 }$

Question 75

Find -x for the given value of x.
$$x = \frac { 3 } { 8 }$$

A) $- \frac { 3 } { 8 }$
B) $\frac { 8 } { 3 }$
C) $\frac { 3 } { 8 }$
D) $- \frac { 8 } { 3 }$

Question 76

Add as indicated.
11 + (-14)

A) -25
B) 3
C) -3
D) 25

Question 77

Add as indicated.
-5.4 + 5.2

A) 10.6
B) -0.2
C) 0.2
D) -10.6

Question 78

Find -x for the given value of x.
$$x = 21$$

A) 21
B) $\frac { 1 } { 21 }$
C) $- 21$
D) 0

Question 79

Find -x for the given value of x.
$$x = - 2.2$$

A) $- 2.2$
B) $2.2$
C) $\frac { 1 } { - 2.2 }$
D) 0

Question 80

Find -x for the given value of x.
x = 23 A) $- 23$
B) 23
C) $\frac { 1 } { 23 }$
D) 0