Deck 1: A Review of Basic Algebra

Question 1

Estimate the height of the candle after it has burned for $5 \frac { 1 } { 2 }$ hours. Please round the answer to the nearest inch.

A) 4
B) 6
C) 7
D) 1
E) 3

Answer 1

3

Question 2

The formula for the cost C of renting a banquet room is given by C = 150 x + 300 where x is the number of hours the room is rented. Find the cost of renting the room for 4 hours.

A) $975.00
B) $9750.00
C) $5335.00
D) none of these

Answer 2

$975.00

Question 3

Translate the verbal model into a mathematical model. The quotient of the number of clients c and seventy-five gives the number of social workers w needed.

A) $w = \frac { c } { 75 }$
B) $w = c - 75$
C) $w = 75 - c$
D) $c = \frac { w } { 75 }$
E) $w = 75 + c$

Answer 3

$w = \frac { c } { 75 }$

Question 4

Use the given formula to complete the table. $c = \frac { p } { 13 }$
$\begin{array} { | c | c | } \hline \begin{array} { c } \text { Number of packages } \\p\end{array} & \begin{array} { c } \text { Cartons } \\c\end{array} \\\hline 52 & 4 \\\hline 91 & ? \\\hline 156 & 12 \\\hline\end{array}$

A) 7
B) 10
C) 11
D) 5
E) 6

Question 5

Translate the verbal model into a mathematical model. The product of the number of boxes b of crayons in a case and 12 gives the number of crayons c in a case.

A) $c = 12 b$
B) $c = \frac { b } { 12 }$
C) $c = \frac { 12 } { b }$
D) $c = 12 + b$
E) $c = 12 - b$

Question 6

A(n) __________ is a letter that is used to stand for a number.

A) equation
B) variable
C) expression
D) formula
E) number

Question 7

Use the given formula to complete the table. $n = 30.44 - K$
$\begin{array} {| c | c| } \hline K & n \\\hline 0 & 30.44 \\\hline 1,01 & ? \\\hline 30.44 & 0 \\\hline\end{array}$

A) 26.43
B) 28.43
C) 31.43
D) 29.43
E) 33.43

Question 8

Variables and/or numbers can be combined with mathematical operations to create algebraic __________.

A) variables
B) expressions
C) sets
D) verbal models
E) numbers

Question 9

Translate the verbal model into a mathematical model. The weight of a super-size s order of French Fries is three times that of a regular-size r order.

A) $s = 3 + r$
B) $s = 3 r$
C) $s = \frac { 3 } { r }$
D) $s = 3 - r$
E) $s = \frac { r } { 3 }$

Question 10

Use the given formula to complete the table. $y = x + 11$
$\begin{array} { | c | c | } \hline x & y \\\hline 0 & 11 \\\hline 11 & ? \\\hline 22 & 33 \\\hline\end{array}$

A) 21
B) 18
C) 20
D) 22
E) 19

Question 11

Choose the correct mathematical model for the following. Five less than the product of 5 and x is 7.

A) 5 - 5 x = 7
B) $\frac { 5 } { x } - 5 = 7$
C) $5 - \frac { 5 } { x } = 7$
D) 5 x - 5 = 7

Question 12

A(n) __________ is a mathematical sentence that contains an = symbol.

A) expression
B) formula
C) variable
D) equation

Question 13

Translate the verbal model into a mathematical model. The cost c each semester is the sum of $10 times the number of units u taken and a student services fee of $23.

A) $c = 10 u - 23$
B) $c = 10 u + 23$
C) $u = 23 c - 10$
D) $c = 23 u - 10$
E) $u = 23 c + 10$

Question 14

Choose the correct mathematical model for the following. A triangle has an area of 29 in². The height is the quotient of twice the area and the base.

A) $h = 58 b$
B) $h = \frac { 58 } { b }$
C) $h = \frac { b } { 58 }$
D) $h = 58 - b$

Question 15

Translate the verbal model into a mathematical model. Each test score t was increased by 16 points to give a new adjusted test score A .

A) $A = 16 t$
B) $A = \frac { t } { 16 }$
C) $A = t + 16$
D) $A = t - 16$
E) $A = \frac { 16 } { t }$

Question 16

Choose the correct mathematical model for the following statement. The cost C (in dollars) to rent a truck is the sum of $30 and $0.58 a mile.

A) $C = 30 - 0.58 m$
B) $C = 58 + 30 m$
C) $C = 30 + 0.58 m$
D) $C = \frac { 30 } { 0.58 m }$

Question 17

Translate the verbal model into a mathematical model. The perimeter P of an equilateral triangle can be found by tripling the length of one of its sides s .

A) $\rho = 3 - s$
B) $p = 3 + s$
C) $P = \frac { 3 } { s }$
D) $P = 3 s$
E) $P = \frac { s } { 3 }$

Question 18

Use the given formula to complete the table. y=100c
$\begin{array} { | c | c | } \hline \begin{array}{c}\text { Number of centuries } \\c\end{array} & \begin{array}{c}\text { Years } \\y\end{array} \\\hline 2 & 200 \\\hline 8 & ? \\\hline 21 & 2,100 \\\hline\end{array}$

A) 830
B) 790
C) 800
D) 780
E) 760

Question 19

Estimate the amount of the least average expenditure.

A) $670
B) $780
C) $600
D) $830
E) $650

Question 20

Classify the following as an expression or an equation.
$\sqrt { 2 x ^ { 2 } }$

A) expression
B) equation

Question 21

Translate the verbal model into a mathematical model. The product of the number of boxes b of crayons in a case and 11 gives the number of crayons c in a case.

Question 22

Translate the verbal model into a mathematical model. The quotient of the number of clients c and seventy-five gives the number of social workers w needed.

Question 23

If

Question 24

Translate the verbal model into a mathematical model. 20% of a number

A) 0.2 x
B) 2 x
C) 0.02 x
D) $\frac { x } { 0.2 }$

Question 25

Translate the verbal model into a mathematical model. Each test score t was increased by 19 points to give a new adjusted test score A .

Question 26

Classify the following as an expression or an equation. $\sqrt { 3 x - 5 }$

A) equation
B) expression

Question 27

Given the formula $t = \frac { d } { 40 }$ . If d=8 , find t .

A) t=5
B) t= $\frac{1}{5}$
C) t=4
D) t= $\frac{1}{64}$

Question 28

In what year was the average expenditure the least?
__________ Estimate the amount. __________ In what year was it the greatest?
__________ Estimate the amount. __________

Question 29

Expressions that express a relationship between two or more variables are called __________.

Question 30

Estimate the height of the candle after it has burned for the given times. Please round the answer to the nearest inch. For hours. __________ in. For 9 hours. __________ in.

Question 31

A(n) __________ is a letter that is used to stand for a number.

Question 32

Phrases such as decreased by and less than are used to indicate the operation of __________.

Question 33

Translate the verbal model into a mathematical model. The weight of a super-size s order of French Fries is four times that of a regular-size r order.

Question 34

Choose the correct mathematical model for the following statement. Eight less than the quotient of six and x is three.

A) $8 - \frac { 6 } { x } = 3$
B) $\frac { 6 } { x } - 8 = 3$
C) 8 x - 6 = 3
D) 8 - 6 x = 3

Question 35

Translate the verbal model into a mathematical model. The perimeter P of an equilateral triangle can be found by tripling the length of one of its sides s .

Question 36

A(n) __________ is a mathematical sentence that contains an = symbol.

Question 37

Translate the verbal model into a mathematical model. 8 less than the square of a number

A) $\sqrt { x } - 8$
B) $8 - \sqrt { x }$
C) $8 - x ^ { 2 }$
D) $x ^ { 2 } - 8$

Question 38

Variables and/or numbers can be combined with mathematical operations to create algebraic __________ .

Question 39

Translate the verbal model into a mathematical model. The cost c each semester is the sum of $12 times the number of units u taken and a student services fee of $23.

Question 40

Translate the following verbal model into a mathematical model. The cost C (in dollars) to rent a limousine is $300 plus $0.46 a mile. Let m = number of miles driven.

Question 41

List the elements of $\left\{ - 3 , - \frac { 8 } { 3 } , 0 , \frac { 2 } { 3 } , 1 , \sqrt { 5 } , 2 , \pi , 4.45,9,16 . \overline { 6 } \right\}$ that belong to the set of rational numbers.

A) $- 3,0,1,2,9$
B) $\sqrt { 5 } , \pi$
C) $- 3 , - \frac { 8 } { 3 } , 0 , \frac { 2 } { 3 } , 1,2,4.45,9,16 . \overline { 6 }$
D) $- 3 , - \frac { 8 } { 3 } , 0 , \frac { 2 } { 3 } , 1 , \sqrt { 5 } , 2 , \pi , 4.45,9,16 . \overline { 6 }$
E) $0,1,2,9$

Question 42

List the elements of $\left\{ - 2 , - \frac { 8 } { 5 } , 0 , \frac { 1 } { 3 } , 1 , \sqrt { 3 } , 4 , \pi , 4.55,9,13 . \overline { 6 } \right\}$ that belong to the set of integers.

A) $0,1 , \sqrt { 3 } , 4 , \pi , 9$
B) $0,1,4,9$
C) $- 2,0,1,4,9$
D) $0 , \frac { 1 } { 3 } , 1 , \sqrt { 3 } , 4 , \pi , 4.55,9,13 . \overline { 6 }$
E) $- \frac { 8 } { 5 } , \frac { 1 } { 3 } , 4.55,13 . \overline { 6 }$

Question 43

A(n) __________ number is a whole number greater than 1 that has only itself and 1 as factors. A(n) __________ number is a whole number greater than 1 that is not prime.

A) rational, composite
B) irrational, rational
C) prime, composite
D) prime, rational
E) rational, irrational

Question 44

List the elements of $\left\{ - 2 , - \frac { 8 } { 5 } , 0 , \frac { 1 } { 3 } , 1 , \sqrt { 3 } , 2 , \pi , 4.65,9,16 . \overline { 6 } \right\}$ that belong to the set of whole numbers.

A) $0 , \frac { 1 } { 3 } , 1 , \sqrt { 3 } , 2 , \pi , 4.65,9,16 . \overline { 6 }$
B) $0,1,2,9$
C) $0,1 , \sqrt { 3 } , 2 , \pi , 9$
D) $- 2,0,1,2,9$
E) $- \frac { 8 } { 5 } , \frac { 1 } { 3 } , 4.65,16 . \overline { 6 }$

Question 45

Find the decimal equivalent of the fraction and determine whether the decimal is terminating or repeating. $\frac { 5 } { 8 }$

A) $0.63$ , terminating
B) $0.62 \overline { 5 }$ , terminating
C) $0.625$ , repeating
D) $0.62 \overline { 5 }$ , terminating.
E) $0.625$ , repeating.

Question 46

Determine whether the statement is true or false. $-25 \in \mathbb{N}$

Question 47

List the elements of $\left\{ - 3 , - \frac { 8 } { 5 } , 0 , \frac { 2 } { 3 } , 1 , \sqrt { 3 } , 2 , \pi , 4.45,7,15 . \overline { 6 } \right\}$ that belong to the set of real numbers.

A) $- 3 , - \frac { 8 } { 5 } , 0 , \frac { 2 } { 3 } , 1,2,4.45,7,15 . \overline { 6 }$
B) $0,1,2,7$
C) $- 3 , - \frac { 8 } { 5 } , 0 , \frac { 2 } { 3 } , 1 , \sqrt { 3 } , 2 , \pi , 4.45,7,15 . \overline { 6 }$
D) $\sqrt { 3 } , \pi$
E) $- 3,0,1,2,7$

Question 48

Change the fraction into a decimal. Is the result terminating or repeating? $\frac { 19 } { 16 }$

A) terminating
B) repeating

Question 49

Graph the set on a number line. The set of composite numbers less than .

A)
B)
C)
D)
E)

Question 50

Insert either a > or a symbol to make a true statement. |- 4| ____ - (- 5)

A) <
B) >

Question 51

Determine whether the statement is true or false. $$\mathbb { N } \subset \mathbb { Q }$$

Question 52

Graph the set on a number line. The set of integers between - 7 and 0.

A)
B)
C)
D)
E)

Question 53

__________ numbers are nonterminating, nonrepeating decimals.

A) Real
B) Rational
C) Negative
D) Positive
E) Irrational

Question 54

Determine whether the statement is true or false. $$\sqrt { 10 } \in { Q }$$

Question 55

Graph the set on a number line. $\left\{ - \frac { 5 } { 2 } , - 0.5,2.142765 \ldots , \frac { \pi } { 4 } , - \sqrt { 11 } , 2 \sqrt { 3 } \right\}$

A)
B)
C)
D)
E)

Question 56

A(n) __________ number is any number that can be written as a fraction with an integer numerator and a nonzero integer denominator.

A) composite
B) rational
C) prime
D) irrational
E) whole

Question 57

For any real number c , $\left\{ \begin{array} { l } \text { If } c \geq 0 , \text { then } | c | = \underline { \quad\quad\quad } \\\text { If } c < 0 , \text { then } | c | =\underline { \quad\quad\quad } \end{array} \right.$

A) $\left\{ \begin{array} { r } 0 \\- c\end{array} \right.$
B) $\left\{ \begin{array} { r } - c \\c\end{array} \right.$
C) $\left\{ \begin{array} { l } c \\c\end{array} \right.$
D) $\left\{ \begin{array} { l } - c \\- c\end{array} \right.$
E) $\left\{ \begin{array} { r } c \\- c\end{array} \right.$

Question 58

If

Question 59

The set of rational numbers together with the set of irrational numbers form the set of __________ numbers.

A) real
B) negative
C) integer
D) prime
E) composite

Question 60

List the elements of $\left\{ - 3 , - \frac { 8 } { 5 } , 0 , \frac { 1 } { 3 } , 1 , \sqrt { 3 } , 2 , \pi , 4.65,9,14 . \overline { 6 } \right\}$ that belong to the set of irrational numbers.

A) $- 3 , - \frac { 8 } { 5 } , 0 , \frac { 1 } { 3 } , 1,2,4.65,9,14 . \overline { 6 }$
B) $\sqrt { 3 } , \pi$
C) $\sqrt { 3 }$
D) $- 3,0,1,2,9$
E) $- 3 , - \frac { 8 } { 5 } , 0 , \frac { 1 } { 3 } , 1 , \sqrt { 3 } , 2 , \pi , 4.65,9,14 . \overline { 6 }$

Question 61

__________ numbers are nonterminating, nonrepeating decimals.

Question 62

$- \frac { 5 \pi } { 3 }$ is located between which of the following two numbers on the number line?

A) $- 5 \text { and } - 4$
B) $- 6 \text { and } - 5$
C) $- 7 \text { and } - 6$
D) $- 8 \text { and } - 7$

Question 63

Find the value of the expression. |- 7.9|

Question 64

Which of the following numbers is an integer?

A) -1
B) $\frac{5}{4}$
C) $\sqrt { 6 }$
D) 2.87

Question 65

Insert either a or a symbol to make a true statement. ____

A) <
B) >

Question 66

is an example of a(n) ___________ number.

A) irrational
B) rational
C) integer
D) whole

Question 67

Which of the following elements is an irrational number: $\left\{ - 2 , - \frac { 2 } { 9 } , .1 \overline { 5 } , \sqrt { 4 } , \sqrt { 6 } \right\}$

A) $\sqrt { 6 }$
B) $\sqrt { 4 }$
C) $1 \overline { 5 }$
D) -2

Question 68

Find the value of the expression. |- 20|

Question 69

The set of rational numbers together with the set of irrational numbers form the set of __________ numbers.

Question 70

The number $\sqrt { 0.42 }$ is an example of a(n) __________.

A) irrational number
B) rational number
C) integer
D) whole number

Question 71

Find the value of the expression. |- 20|

A) 20
B) - 20
C) 0
D) - 1
E) 1

Question 72

Find the value of the expression. - |- 9|

Question 73

A(n) __________ number is any number that can be written as a fraction with an integer numerator and a nonzero integer denominator.

Question 74

Graph the set of whole numbers less that 3.

A)
B)
C)
D)

Question 75

Which of the following is a true inequality?

A) $- 20 > - 6$
B) $| - 20 | < 6$
C) $0 < - 7$
D) $- 20 < - 6$

Question 76

Insert either a > or a symbol to make a true statement. 5.999 ____ 5.1

A) <
B) >

Question 77

Find the value of the expression. |6.9|

A) 1
B) 0
C) 6.9
D) - 1
E) - 6.9

Question 78

Evaluate: $| - ( - 5 ) |$

A) 5
B) -5
C) $\frac{1}{5}$
D) $- \frac{1}{5}$

Question 79

A number that can be written as $\frac { a } { b }$ , where a and b represent integers and b ? 0 is a(n) __________.

A) irrational number
B) whole number
C) integer
D) rational number

Question 80

Find the value of the expression. - |- 4|

A) - 4
B) - 1
C) 4
D) 0
E) 1