Deck 1: Algebraic Representations

Question 1

Add: $$\frac { 5 } { 8 } + \frac { 11 } { 16 }$$

A) $1 \frac { 5 } { 24 }$
B) $\frac { 13 } { 8 }$
C) $\frac { 5 } { 16 }$
D) $1 \frac { 5 } { 16 }$
E) $2 \frac { 5 } { 16 }$

Answer 1

$1 \frac { 5 } { 16 }$

Question 2

Add: $$\begin{array} { r } 2 \frac { 7 } { 8 } \\+ \quad 2 \frac { 5 } { 6 } \\\hline\end{array}$$

A) $6 \frac { 17 } { 144 }$
B) $6 \frac { 17 } { 24 }$
C) $6 \frac { 17 } { 32 }$
D) $5 \frac { 17 } { 144 }$
E) $5 \frac { 17 } { 24 }$

Answer 2

$5 \frac { 17 } { 24 }$

Question 3

When we combine the even numbers and the odd numbers, we get which set of real numbers?

A) natural numbers
B) integers
C) negative real numbers
D) rational numbers
E) irrational numbers

Answer 3

integers

Question 4

Subtract: $$\begin{array} { r } \frac { 3 } { 10 } \\- \quad \frac { 1 } { 4 } \\\hline\end{array}$$

A) $\frac { 1 } { 20 }$
B) $\frac { 1 } { 50 }$
C) $\frac { 1 } { 60 }$
D) $\frac { 1 } { 40 }$
E) $\frac { 1 } { 8 }$

Question 5

Add: $$\frac { 1 } { 8 } + \frac { 3 } { 22 }$$

A) $1 \frac { 23 } { 88 }$
B) $\frac { 23 } { 88 }$
C) $\frac { 23 } { 176 }$
D) $2 \frac { 23 } { 176 }$
E) $1 \frac { 23 } { 176 }$

Question 6

From the set $\left\{ \frac { 4 } { 5 } , - 4,0,4,3 \right\}$ , select a number that fits the statement below. This rational number is not defined in the set of integers.

A) -4
B) 4
C) $3$
D) 0
E) $\frac { 4 } { 5 }$

Question 7

Change the following fraction into a mixed number. $$\frac { 16 } { 9 }$$

A) $1 \frac { 7 } { 9 }$
B) $1 \frac { 1 } { 9 }$
C) $1 \frac { 2 } { 9 }$
D) $2 \frac { 8 } { 9 }$
E) $2 \frac { 5 } { 9 }$

Question 8

Subtract: $$\begin{array} { r } \frac { 4 } { 7 } \\- \quad \frac { 1 } { 6 } \\\hline\end{array}$$

A) $\frac { 17 } { 294 }$
B) $\frac { 17 } { 252 }$
C) $\frac { 17 } { 126 }$
D) $\frac { 17 } { 42 }$
E) $\frac { 17 } { 84 }$

Question 9

Calculate the course load for student with the following schedule: 18 credit hours and 26 hours of employment.

A) 80
B) 46
C) 98
D) 44
E) 62

Question 10

Write the phrases using the correct operation symbol $( + , - , \cdot , \div )$ and then do the operation. Write answers as fractions and decimals, where appropriate. Round decimals to the nearest thousandth. Assume the second number is subtracted from or divided into the first number. Find the quotient of of 4 and $\frac { 1 } { 5 }$ .

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

Question 11

Find two numbers that have the product of 14 and the sum of 9.

A) 1 and 7
B) 1 and 6
C) 2 and 9
D) 2 and 6
E) 2 and 7

Question 12

Read "What to Expect from This Text" and "Beginning the New Term: First Day" What are three alternative approaches to thinking algebraically?

A) verbal
B) visual
C) kinesthetic
D) all the above
E) none of these

Question 13

Write the phrases using the correct operation symbol $( + , - , \cdot , \div )$ and then do the operation. Write answers as fractions and decimals, where appropriate. Round decimals to the nearest thousandth. Assume the second number is subtracted from or divided Into the first number. Find the sum of $\frac { 5 } { 4 }$ and $\frac { 1 } { 2 }$ .

A) $\frac { 7 } { 2 } , 3.500$
B) $\frac { 7 } { 4 } , 1.750$
C) $\frac { 5 } { 4 } , 1.25$
D) $\frac { 7 } { 2 } , 3.5$
E) $\frac { 5 } { 2 } , 2.5$

Question 14

Subtract: $$\begin{array} { r } 12 \frac { 11 } { 17 } \\- \quad 9 \frac { 6 } { 17 } \\\hline\end{array}$$

A) $3 \frac { 5 } { 17 }$
B) $4 \frac { 5 } { 17 }$
C) $4 \frac { 5 } { 11 }$
D) $3 \frac { 5 } { 11 }$
E) $3 \frac { 5 } { 187 }$

Question 15

Kelsey is setting up the Events Center for a petting zoo. She builds the pens along a long wall. She starts in a corner, making the first pen with two panels and needing two more panels for each additional pen. Build an input-output table for the number of panels needed for 1 to 5 pens. How many panels are needed for 10 pens?

A) 10 panels
B) 16 panels
C) 20 panels
D) 19 panels
E) 21 panels

Question 16

What is the rule in words? What is the output when the input is 100? Write the rule as an equation. $$\begin{array} { l l l l l } \text { Input, } x & 7 & 8 & 9 & 100 \\\text { Output, } y & 5 & 6 & 7 & ?\end{array}$$

A) The output is five less than the input; 95; y = x-5
B) The output is seven less than the input; 93; y = x-7
C) The output is six less than the input; 94; y = x-6
D) The output is two less than the input; 98; y = x-2

Question 17

Make an input-output for the following tuition model: Tuition is $55 per credit hour for 1 to 11 hours; $1050 for 12 to 18 hours; and an additional $30 per credit hour for each hour above 18 hours. Stop at 20 hours. Use your table to find the tuition cost for 8 hours, 13 hours, and 20 hours.

A) $440, $715, $1100
B) $55, $1050, $30
C) $55, $1050, $1080
D) $240, $390, $600
E) $440, $1050, $1110

Question 18

What is the rule in words? What is the output when the input is 100? Write the rule as an equation. $$\begin{array} { l l l l l l } \text { Input, } x & 2 & 3 & 4 & 20 & 100 \\\text { Output, } y & 8 & 12 & 16 & 80 & ?\end{array}$$

A) The output if four times the input; 400; y = 4x
B) The output if six times the input; 400; y = 8x
C) The output if eight times the input; 400; y = 16x
D) The output if seven times the input; 400; y = 42x
E) The output if six times the input; 400; y = 80x

Question 19

Calculate the course load for student with the following schedule: 13 credit hours and 20 hours of employment.

A) 19
B) 36
C) 86
D) 59
E) 99

Question 20

Calculate the course load for student with the following schedule: 18 credit hours and no hours of employment.

A) 23
B) 36
C) 54
D) 13
E) 72

Question 21

Write an expression in symbol for word phase. Let n be the input. To find a difference or quotient, write the numbers in the order in which they are stated.
The product of five and the input

A) $\frac { 5 } { n }$
B) 5
C) 7n
D) 5n
E) 6n

Question 22

Write the phrases using the correct operation symbol $( + , - , \cdot , \div )$ and then do the operation. Write answers as fractions and decimals, where appropriate. Round decimals to the nearest thousandth. Assume the second number is subtracted from or divided Into the first number. Find the sum of 0.5 and $\frac { 7 } { 2 }$ .

A) 8
B) 7
C) 5
D) 6
E) 4

Question 23

Change from equations into sentences. $$y = 11 - \frac { x } { 4 }$$

A) The output is four less the quotient of the input and four.
B) The output is four greater the quotient of the input and eleven.
C) The output is eleven less the quotient of the input and four.
D) The output is four less the quotient of the input and eleven.
E) The output is eleven greater quotient of the input and four.

Question 24

Identify the operation (addition, subtraction, multiplication, division) Implies by question. One family ate $5 \frac { 3 } { 4 }$ pizzas; another family ate $2 \frac { 1 } { 5 }$ pizzas. How much more did the first family eat?

A) addition
B) subtraction
C) division
D) multiplication
E) data insufficient

Question 25

Change the decimals to percents 0.09

A) 9%
B) 9.09%
C) 0.009%
D) 0.1%
E) 0.9%

Question 26

Write 4.78 as a percent.

A) 4.78 %
B) 47.8 %
C) 478 %
D) 0.0478 %
E) 0.478 %

Question 27

Write the phrases using the correct operation symbol $( + , - , \cdot , \div )$ and then do the operation. Write answers as fractions and decimals, where appropriate. Round decimals to the nearest thousandth. Assume the second number is subtracted from or divided Into the first number. Find the difference between $7 \frac { 1 } { 4 }$ and $3 \frac { 1 } { 2 }$ .

A) $3 \frac { 1 } { 4 }$ , 3.250
B) $3 \frac { 1 } { 2 }$ , 3.500
C) $3 \frac { 1 } { 3 }$ , 3.333
D) $3 \frac { 2 } { 3 }$ , 3.667
E) $3 \frac { 3 } { 4 }$ , 3.750

Question 28

Change these sentence to equation. Use n as the variable. The quotient of six and a number is ten.

A) $\frac { 6 } { n } = 10$
B) $\frac { n } { 6 } = 10$
C) $\frac { 6 } { n } = 6$
D) $\frac { n } { 6 } = 6$
E) $6 n = 10$

Question 29

California community colleges are considered financially secure if college reserves are 6% of their total budget.Write this percent as a fraction and as a decimal.

A) $\frac { 7 } { 100 }$ , 0.07
B) $\frac { 1 } { 20 }$ , 0.05
C) $\frac { 2 } { 25 }$ , 0.08
D) $\frac { 9 } { 100 }$ , 0.09
E) $\frac { 3 } { 50 }$ , $0.06$

Question 30

Write 4.033 as a percent.

A) 0.4033 %
B) 40.33 %
C) 4.033 %
D) 0.04033 %
E) 403.3 %

Question 31

Write 115% as a fraction and as a decimal.

A) $1 \frac { 3 } { 20 }$ ; 0.15
B) $1 \frac { 3 } { 20 }$ ; 1.15
C) $\frac { 20 } { 23 }$ ; 0.115
D) $\frac { 23 } { 200 }$ ; 11.5
E) $1 \frac { 3 } { 20 }$ ; 115

Question 32

Write percent statement as an expression. 70% of $n$

A) 0.07 $n$
B) 7000 $n$
C) 700 $n$
D) 7 $n$
E) 0.7 $n$

Question 33

Change these sentence to equation. Use n as the variable. Seventeen is the difference between eleven and five tenths and a number.

A) 17 = 11.5 - n
B) 17 = 11 - n
C) 11.5 = 17 - n
D) 11.5 = 11 - n
E) 11 = 11.5 - n

Question 34

Identity the constants numerical coefficients, and variables in the expression $x ^ { 2 } - 8$ .

A) -8 constant; x, variable
B) 1, constant and numerical coefficient; 8 constant; x, variable
C) 1, constant and numerical coefficient; -8 constant; x, variable
D) 8 constant; x, variable
E) none of these

Question 35

Write 95% as a fraction and as a decimal.

A) $\frac { 19 } { 2 }$ ; 95
B) $\frac { 20 } { 19 }$ ; 0.95
C) $\frac { 19 } { 20 }$ ; 0.95
D) $\frac { 1 } { 95 }$ ; 9.5
E) $\frac { 2 } { 19 }$ ; 9.5

Question 36

Write 81% as a fraction and as a decimal.

A) $\frac { 10 } { 81 }$ ; 8.1
B) $\frac { 81 } { 100 }$ ; 81
C) $\frac { 1 } { 81 }$ ; 8.1
D) $\frac { 81 } { 100 }$ ; 0.81
E) $\frac { 81 } { 100 }$ ; 8100

Question 37

A study reported by Science News (Nov,26,2005,p.347) found that 25% of all medication taken in space is sleeping pills. Write this percent as a fraction and as a decimal.

A) $\frac { 13 } { 50 }$ , $0.26$
B) $\frac { 6 } { 25 }$ , $0.24$
C) $\frac { 1 } { 4 }$ , $0.25$
D) $\frac { 27 } { 100 }$ , $0.27$
E) $\frac { 23 } { 100 }$ , $0.23$

Question 38

Write $\frac { 24 } { 25 }$ as a percent.

A) 24 %
B) 96 %
C) 1.04 %
D) 240 %
E) 9.6 %

Question 39

Identity the constants numerical coefficients, and variables in the expression $\pi \mathrm { r }$ .

A) r, variable
B) $\pi$ , constant and numerical
C) $\pi$ , constant and numerical coefficient: r, constant
D) $\pi$ , constant and numerical coefficient: r, variable
E) data insufficient

Question 40

Change the decimals to percents 0.7

A) 7%
B) 700%
C) 70%
D) 0.007%
E) 0.9%

Question 41

Make a graph for the following rule. Use integer inputs of 0 to 5. The output is 5 more than twice the input.

A)
B)
C)
D)
E)

Question 42

Graph the ordered pairs (2, 8) and (4, 16). Draw a straight line through them. Name an ordered pair on the same line.

A) (3, 27)
B) (12, 3)
C) (3, 9)
D) (1, 4)
E) (5, 15)

Question 43

Name the quadrant in which the point is located. $( 2 , - 5 )$

A) I
B) II
C) III
D) IV

Question 44

Write the percent statement as an expression. $32 \frac { 1 } { 2 } \% \text { of } x$

A) $0.425 x$
B) $0.315 x$
C) $0.325 x$
D) $0.125 x$
E) $0.265 x$

Question 45

Write percent statement as an expression. $31 \frac { 1 } { 2 }$ % of $n$

A) 1.315
B) 0.315
C) 3.315
D) 4.315
E) 2.315

Question 46

Name the quadrant in which the point is located. $( - 4 , - 4 )$

A) I
B) III
C) IV
D) II

Question 47

The ATT low-use plane for Internet and email costs $15 for the first 200 MB (megabytes) plus $0.10 for each additional MB. Use your Graph to estimate the cost of these usages: 40 MB, 195 MB, 270 MB.

A) $16$ , $16$ , $2$
B) $14$ , $14$ , $21$
C) $15$ , $15$ , $22$
D) $17$ , $14$ , $24$
E) $13$ , $16$ , $20$

Question 48

Change the decimal to percent. 0.3

A) $30$ %
B) $29.9$ %
C) $30.1$ %
D) $30.2$ %
E) $30.3$ %

Question 49

Name the quadrant in which the point is located. $( - 2,5 )$

A) I
B) II
C) IV
D) III

Question 50

Name the quadrant in which the point is located. $( - 6 , - 4 )$

A) I
B) III
C) II
D) IV

Question 51

Name the axis on which the point is located. $( 0,2 )$

A) Vertical
B) Horizontal

Question 52

How do you find the ordered pair describing a point?

A) For the ordered pair (x,y), trace vertically to the vertical axis to find x, horizontally to the horizontal axis to find y.
B) For the ordered pair (x,y), trace vertically to the horizontal axis to find x, horizontally to the vertically axis to find y.
C) For the ordered pair (x,y), trace horizontally to the vertical axis to find x, vertically to the horizontal axis to find y.
D) For the ordered pair (x,y), trace vertically to the vertical axis to find y, horizontally to the horizontal axis to find x.
E) For the ordered pair (x,y), trace vertically to the horizontal axis to find y, horizontally to the vertical axis to find x.

Question 53

How do you find on which axis an ordered pair (a, 0) or (0, b) is located?

A) The first number is zero on the horizontal axis, the second number is zero on the vertical axis.
B) The second number is zero on the horizontal axis, the first number is zero on the vertical axis.
C) The second number is one on the horizontal axis, the first number is zero on the vertical axis.
D) The second number is zero on the horizontal axis, the first number is one on the vertical axis.
E) The second number is one on the horizontal axis, the first number is one on the vertical axis.

Question 54

In the bulk foods department, candy costs $2.29 per pound. Use your graph to estimate the total cost of these candy purchase: $1 \frac { 1 } { 2 }$ pounds, $3 \frac { 3 } { 4 }$ pounds, $3 \frac { 1 } { 4 }$ pounds.

A) $ $4.43$ , $ $9.59$ , $ $8.44$
B) $ $2.43$ , $ $7.59$ , $ $6.44$
C) $ $5.43$ , $ $10.59$ , $ $9.44$
D) $ $1.43$ , $ $6.59$ , $ $5.44$
E) $ $3.43$ , $ $8.59$ , $ $7.44$

Question 55

Graph the ordered pairs (3, 8) and (5, 10). Draw a straight line through them. Name an ordered pair on the same line.

A) (0, 7)
B) (0, 6)
C) (2, 5)
D) (7, 2)
E) (1, 6)

Question 56

Is x a negative number? Explain.

A) Not necessarily; x is a variable that may represent a positive number or negative number or zero.
B) Yes, because there is a positive sign before x.
C) No, because there is no positive sign before x.
D) No, because there is no negative sign before x.
E) No, because negative means opposite and the opposite of x is y.

Question 57

The ATT high use plane for Internet and email cost $40 for the first 5000 MB (megabytes) plus $0.06 for each additional MB. (FYI, the ATT plan list 5000 MB as 5 GB.) Use your graph to estimate the cost of these usages: 4000 MB, 4900 MB, 5900 MB.

A) $41$ , $41$ , $95$
B) $39$ , $39$ , $93$
C) $42$ , $39$ , $96$
D) $40$ , $40$ , $94$
E) $38$ , $41$ , $92$

Question 58

Make a table for the following rule. Use integer inputs of 0 to 5. The output is 5 more than twice the input.

A) $\begin{array} { | c | l | } \hline \text { Input } & \text { Output } \\\hline 0 & 0 \\1 & 0.5 \\2 & 1 \\3 & 1.5 \\4 & 2 \\5 & 2.5 \\\hline\end{array}$
B) $\begin{array} { | c | c | } \hline \text { Input } & \text { Output } \\\hline 0 & - 2 \\1 & 1 \\2 & 4 \\3 & 7 \\4 & 10 \\5 & 13 \\\hline\end{array}$
C) $\begin{array} { | c | c | } \hline \text { Input } & \text { Output } \\\hline 0 & 8 \\1 & 7 \\2 & 6 \\3 & 5 \\4 & 4 \\5 & 3 \\\hline\end{array}$
D) $\begin{array} { | c | c | } \hline \text { Input } & \text { Output } \\\hline 0 & 10 \\1 & 8 \\2 & 6 \\3 & 4 \\4 & 2 \\5 & 0 \\\hline\end{array}$
E) $\begin{array} { | c | c | } \hline \text { Input } & \text { Output } \\\hline 0 & 5 \\1 & 7 \\2 & 9 \\3 & 11 \\4 & 13 \\5 & 15 \\\hline\end{array}$

Question 59

Write the percent statement as an expression. $$3 \frac { 1 } { 4 } \% \text { of } x$$

A) $0.0315 x$
B) $3.25 x$
C) $0.00325 x$
D) $0.325 x$
E) $0.0325 x$

Question 60

Draw a graph from the following input-output table. $$\begin{array} { | c | c | } \hline \begin{array} { c } \text { Input } \\x\end{array} & \begin{array} { c } \text { Output } \\y\end{array} \\\hline - 2 & 5 \\- 1 & 2 \\0 & - 1 \\1 & - 4 \\2 & - 7 \\\hline\end{array}$$

A)
B)
C)
D)
E)