Question 1

Use the data shown in the scatter plot to determine whether the data should be modeled by a linear function.
-

Accepted Answer

A)  No, data points do not lie close to a line 
B)  Yes, exactly linear 
C)  Yes, approximately linear 
A)  No, data points do not lie close to a line 
B)  Yes, exactly linear 
C)  Yes, approximately linear

Question 2

Translate the sentence to an algebraic inequality.
-If the formula P $\mathrm { P } = 0.5643 \mathrm { Y } - 1092.57$ 2.57 can be used to predict the average price of a theater ticket after 1945, for what years will the average theater ticket price be at least 43 dollars? (Y is the actual year.)

Accepted Answer

A)  2011 or after 
B)  2015 or after 
C)  2023 or after 
D)  2013 or after 
A)  2011 or after 
B)  2015 or after 
C)  2023 or after 
D)  2013 or after

Question 3

Solve the system of equations by elimination, if a solution exists.
-$$\left\{ \begin{array} { l } 
x - 6 y = - 30 \
- 5 x - 5 y = - 25
\end{array} \right.$$

Accepted Answer

A)  $x = - 5 , y = 0$ 
B)  No solution 
C)  $x = 1 , y = 4$ 
D)  $x = 0 , y = 5$ 
A)  $x = - 5 , y = 0$ 
B)  No solution 
C)  $x = 1 , y = 4$ 
D)  $x = 0 , y = 5$

Question 4

Solve the inequality and draw a number line graph of the solution.
-$$\frac { 5 x - 3 } { - 7 } < - \frac { 32 } { 5 }$$

Accepted Answer

A)  $x > - \frac { 32 } { 25 }$

$$- \frac { 32 } { 25 }$$ 
B)  $x  \frac { 239 } { 5 }$

$$\frac { 239 } { 5 }$$ 
D)  $x > \frac { 239 } { 25 }$

$$\frac { 239 } { 25 }$$ 
A)  $x > - \frac { 32 } { 25 }$

$$- \frac { 32 } { 25 }$$ 
B)  $x  \frac { 239 } { 5 }$

$$\frac { 239 } { 5 }$$ 
D)  $x > \frac { 239 } { 25 }$

$$\frac { 239 } { 25 }$$

Question 5

Solve the formula for the specified variable.
-$- 6 \mathrm { k } + \mathrm { ar } = \mathrm { r } - 9 \mathrm { y }$ for $\mathrm { r }$

Accepted Answer

A)  $r = \frac { a - 1 } { 6 k - 9 y }$ or $r = \frac { 1 - a } { - 6 k + 9 y }$ 
B)  $r = \frac { - 6 k + a } { 1 - 9 y }$ or $r = \frac { 6 k - a } { 9 y - 1 }$ 
C)  $r = \frac { 6 k - 9 y } { a - 1 }$ or $r = \frac { - 6 k + 9 y } { 1 - a }$ 
D)  $r = \frac { - 6 k + 9 y } { a - 1 }$ or $r = \frac { 6 k - 9 y } { 1 - a }$ 
A)  $r = \frac { a - 1 } { 6 k - 9 y }$ or $r = \frac { 1 - a } { - 6 k + 9 y }$ 
B)  $r = \frac { - 6 k + a } { 1 - 9 y }$ or $r = \frac { 6 k - a } { 9 y - 1 }$ 
C)  $r = \frac { 6 k - 9 y } { a - 1 }$ or $r = \frac { - 6 k + 9 y } { 1 - a }$ 
D)  $r = \frac { - 6 k + 9 y } { a - 1 }$ or $r = \frac { 6 k - 9 y } { 1 - a }$

Question 6

Solve the double inequality.
-$- 28 \leq - 4 c + 4 < - 4$

Accepted Answer

A)  $- 8 \leq c < - 2$ 
B)  $- 8 < c \leq - 2$ 
C)  $2 < \mathrm { c } \leq 8$ 
D)  $2 \leq c < 8$ 
A)  $- 8 \leq c < - 2$ 
B)  $- 8 < c \leq - 2$ 
C)  $2 < \mathrm { c } \leq 8$ 
D)  $2 \leq c < 8$

Question 7

The table below gives the quantity of a product demanded and the quantity supplied for various prices. Solve the
problem.
-Find the market equilibrium price. $$\begin{array} { l | l | l } 
\text { Price (dollars) } & \text { Quantity Demanded } & \text { Quantity Supplied } \
\hline 100 & 250 & 0 \
120 & 210 & 40 \
140 & 170 & 80 \
160 & 130 & 120 \
180 & 90 & 160
\end{array}$$

Accepted Answer

A)  $162.50 
B)  $167.50 
C)  $125.00 
D)  $157.50 
A)  $162.50 
B)  $167.50 
C)  $125.00 
D)  $157.50

Question 8

Solve the formula for the specified variable.
-$\mathrm { P } = \mathrm { a } + \mathrm { b } + \mathrm { c }$ for $a$

Accepted Answer

A)  $a = P - b - c$ 
B)  $a = b + c - P$ 
C)  $a = b + P - c$ 
D)  $a = P + b + c$ 
A)  $a = P - b - c$ 
B)  $a = b + c - P$ 
C)  $a = b + P - c$ 
D)  $a = P + b + c$

Question 9

Translate the sentence to an algebraic inequality.
-The equation y $y = 0.003 x + 0.50$ can be used to determine the approximate profit, y in dollars, of producing x items. How many items must be produced so the profit will be at least $2937?

Accepted Answer

A)  $x \geq 978,834$ 
B)  $x \geq 979,167$ 
C)  $0 < x \leq 978,833$ 
D)  $x \leq 978,834$ 
A)  $x \geq 978,834$ 
B)  $x \geq 979,167$ 
C)  $0 < x \leq 978,833$ 
D)  $x \leq 978,834$

Question 10

Translate the sentence to an algebraic inequality.
-DG's Plumbing and Heating charges $50 plus $60 per hour for emergency service. Bill remembers being billed just over $400 for an emergency call. How long to the nearest hour was the plumber at Bill's house?

Accepted Answer

A)  6 hours 
B)  14 hours 
C)  8 hours 
D)  10 hours 
A)  6 hours 
B)  14 hours 
C)  8 hours 
D)  10 hours

Question 11

Solve the equation for y.
-$$6 x + 9 y = 17$$

Accepted Answer

A)  $y = \frac { 2 } { 3 } x - \frac { 17 } { 9 }$ 
B)  $y = 6 x - 17$ 
C)  $y = - \frac { 2 } { 3 } x + \frac { 17 } { 9 }$ 
D)  $y = \frac { 2 } { 3 } x + \frac { 17 } { 9 }$ 
A)  $y = \frac { 2 } { 3 } x - \frac { 17 } { 9 }$ 
B)  $y = 6 x - 17$ 
C)  $y = - \frac { 2 } { 3 } x + \frac { 17 } { 9 }$ 
D)  $y = \frac { 2 } { 3 } x + \frac { 17 } { 9 }$

Question 12

Write the best-fit linear model for the data.
-Two different tests are designed to measure employee productivity and dexterity. Several employees are randomly selected and tested with these results. Find the linear function to model this data. $\begin{array}{cc|c|c|c|c|c|c|c|c|c}
\text { Productivity } & 23 & 25 & 28 & 21 & 21 & 25 & 26 & 30 & 34 & 36 \
\hline \text { Dexterity } & 49 & 53 & 59 & 42 & 47 & 53 & 55 & 63 & 67 & 75
\end{array}$

Accepted Answer

A)  $y = 10.7 + 1.53 x$ 
B)  $y = 2.36 + 2.03 x$ 
C)  $y = 75.3 - 0.329 x$ 
D)  $y = 5.05 + 1.91 x$ 
A)  $y = 10.7 + 1.53 x$ 
B)  $y = 2.36 + 2.03 x$ 
C)  $y = 75.3 - 0.329 x$ 
D)  $y = 5.05 + 1.91 x$

Question 13

Solve the equation.
-$$- 4.6 = y + 8$$

Accepted Answer

A)  $- 3.4$ 
B)  $3.4$ 
C)  $12.6$ 
D)  $- 12.6$ 
A)  $- 3.4$ 
B)  $3.4$ 
C)  $12.6$ 
D)  $- 12.6$

Question 14

To find the number of units that gives break-even for the product, solve the equation R $$\mathbf { R } = \mathbf { C }$$ ound your answer to the
nearest whole unit.
-Mardi received an inheritance of $50,000. She invested part of it at 12% and the rest at 11%. Her total annual income from the investments was $5900. Find the amount invested at 12%.

Accepted Answer

A)  $39,000 
B)  $20,000 
C)  $44,100 
D)  $40,000 
A)  $39,000 
B)  $20,000 
C)  $44,100 
D)  $40,000

Question 15

Translate the sentence to an algebraic inequality.
-Suppose that the sales of a particular brand of appliance satisfy the relationship $S ( x ) = 120 x + 1600$, where $S ( x )$ represents the number of sales in year $x$, with $x = 0$ corresponding to 1990 . For what years will sales be between 1960 and 2320 ?

Accepted Answer

A)  Between 1992 and 1995 
B)  Between 1993 and 1996 
C)  Between 1993 and 1995 
D)  Between 4 and 7 
A)  Between 1992 and 1995 
B)  Between 1993 and 1996 
C)  Between 1993 and 1995 
D)  Between 4 and 7

Question 16

The graph of a certain function $y = f ( x )$ and the zero of that function is given. Using this graph, find a) the $x$-intercept of the graph of $y = f ( x )$ and b) the solution to the equation $f ( x ) = 0$.
-

Accepted Answer

A)  a. 0
b. $x = 2.5$ 
B)  a. $2.5$
b. $x = 0$ 
C)  a. $- 2.5$
b. $x = - 2.5$ 
D)  a. $2.5$
b. $x = 2.5$ 
A)  a. 0
b. $x = 2.5$ 
B)  a. $2.5$
b. $x = 0$ 
C)  a. $- 2.5$
b. $x = - 2.5$ 
D)  a. $2.5$
b. $x = 2.5$

Question 17

Construct a scatter plot of the data in the table.
-$\begin{array}{r|r|r|r|r|r|r|r|r}
\mathrm{x} & 0.75 & 0.86 & 0.33 & 0.25 & -0.12 & 0.97 & 0.71 & -0.05 \
\hline \mathrm{y} & 0.57 & 0.1 & 0.72 & 0.12 & -0.91 & 0.54 & 0.1 & 0.13
\end{array}$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 18

Without graphing, determine whether the following data set is exactly linear, approximately linear or nonlinear.
-$$\begin{array} { c | c c c c c c c c c } 
\text { Height (inches) } & 57 & 60 & 72 & 59 & 63 & 65 & 66 & 68 & 61 \
\hline \text { Time (seconds) } & 32.9 & 40.1 & 35.7 & 41.8 & 47.4 & 37.3 & 39.1 & 41.5 & 32.8
\end{array}$$

Accepted Answer

A)  exactly linear 
B)  nonlinear 
C)  approximately linear 
A)  exactly linear 
B)  nonlinear 
C)  approximately linear

Question 19

Without graphing, determine whether the following data set is exactly linear, approximately linear or nonlinear.
-$$\begin{array} { l | l l l l l l l l l } 
\text { Foot Length } ( \mathrm { cm } ) & 25 & 26 & 28 & 29 & 30 & 31 & 32 & 33 & 37 \
\hline \text { Forearm Length } ( \mathrm { cm } ) & 24 & 25 & 28 & 30 & 31 & 30 & 31 & 33 & 37
\end{array}$$

Accepted Answer

A)  exactly linear 
B)  nonlinear 
C)  approximately linear 
A)  exactly linear 
B)  nonlinear 
C)  approximately linear

Question 20

Solve the equation using graphical methods. Round to the nearest thousandth when appropriate.
-$$( 8 x - 3 ) + 5 = 9 ( x - 3 )$$

Accepted Answer

A)  $x = - 29$ 
B)  $x = - 19$ 
C)  $x = - 5$ 
D)  $x = 29$ 
A)  $x = - 29$ 
B)  $x = - 19$ 
C)  $x = - 5$ 
D)  $x = 29$

Use the data shown in the scatter plot to determine whether the data should be modeled by a linear function. -

Translate the sentence to an algebraic inequality. -If the formula P $\mathrm { P } = 0.5643 \mathrm { Y } - 1092.57$ 2.57 can be used to predict the average price of a theater ticket after 1945, for what years will the average theater ticket price be at least 43 dollars? (Y is the actual year.)

Solve the system of equations by elimination, if a solution exists. - $\left\{ \begin{array} { l } x - 6 y = - 30 \\- 5 x - 5 y = - 25\end{array} \right.$

Solve the inequality and draw a number line graph of the solution. - $\frac { 5 x - 3 } { - 7 } < - \frac { 32 } { 5 }$ $Solve the inequality and draw a number line graph of the solution. - \frac { 5 x - 3 } { - 7 } < - \frac { 32 } { 5 }$

Solve the formula for the specified variable. - $- 6 \mathrm { k } + \mathrm { ar } = \mathrm { r } - 9 \mathrm { y }$ for $\mathrm { r }$

Solve the double inequality. - $- 28 \leq - 4 c + 4 < - 4$

The table below gives the quantity of a product demanded and the quantity supplied for various prices. Solve the problem. -Find the market equilibrium price. Price (dollars) Quantity Demanded Quantity Supplied 100 250 0 120 210 40 140 170 80 160 130 120 180 90 160

Solve the formula for the specified variable. - $\mathrm { P } = \mathrm { a } + \mathrm { b } + \mathrm { c }$ for $a$

Translate the sentence to an algebraic inequality. -The equation y $y = 0.003 x + 0.50$ can be used to determine the approximate profit, y in dollars, of producing x items. How many items must be produced so the profit will be at least $2937?

Translate the sentence to an algebraic inequality. -DG's Plumbing and Heating charges $50 plus $60 per hour for emergency service. Bill remembers being billed just over $400 for an emergency call. How long to the nearest hour was the plumber at Bill's house?

Solve the equation for y. - $6 x + 9 y = 17$

Solve the equation. - $- 4.6 = y + 8$

The graph of a certain function $y = f ( x )$ and the zero of that function is given. Using this graph, find a) the $x$ -intercept of the graph of $y = f ( x )$ and b) the solution to the equation $f ( x ) = 0$ . -

Without graphing, determine whether the following data set is exactly linear, approximately linear or nonlinear. - Height (inches) 57 60 72 59 63 65 66 68 61 Time (seconds) 32.9 40.1 35.7 41.8 47.4 37.3 39.1 41.5 32.8

Without graphing, determine whether the following data set is exactly linear, approximately linear or nonlinear. - Foot Length () 25 26 28 29 30 31 32 33 37 Forearm Length () 24 25 28 30 31 30 31 33 37

Solve the equation using graphical methods. Round to the nearest thousandth when appropriate. - $( 8 x - 3 ) + 5 = 9 ( x - 3 )$

Functions, Graphs, and Models; Linear Functions

Quadratic, Piecewise-Defined, and Power Functions

Additional Topics With Functions

Exponential and Logarithmic Functions

Higher-Degree Polynomial and Rational Functions

Systems of Equations and Matrices

Special Topics in Algebra

Filters

Exam 2: Linear Models, Equations, and Inequalities

Use the data shown in the scatter plot to determine whether the data should be modeled by a linear function. -

Solve the system of equations by elimination, if a solution exists. - {x−6y=−30−5x−5y=−25\left\{ \begin{array} { l } x - 6 y = - 30 \\- 5 x - 5 y = - 25\end{array} \right.{x−6y=−30−5x−5y=−25​

Solve the inequality and draw a number line graph of the solution. - 5x−3−7<−325\frac { 5 x - 3 } { - 7 } < - \frac { 32 } { 5 }−75x−3​<−532​

Solve the formula for the specified variable. - −6k+ar=r−9y- 6 \mathrm { k } + \mathrm { ar } = \mathrm { r } - 9 \mathrm { y }−6k+ar=r−9y for r\mathrm { r }r

Solve the double inequality. - −28≤−4c+4<−4- 28 \leq - 4 c + 4 < - 4−28≤−4c+4<−4