Question 1

Find the partial fraction decomposition for the rational expression.
$\frac { 22 x ^ { 2 } - 105 x + 132 } { ( x - 4 ) ( 2 x - 4 ) ^ { 2 } }$

Accepted Answer

A)  $\frac { 5 } { ( 2 x - 4 ) ^ { 2 } } + \frac { 3 } { 2 x - 4 } + \frac { - 4 } { x - 4 }$ 
B)  $\frac { 3 } { 2 x - 4 } + \frac { - 5 } { ( 2 x - 4 ) ^ { 2 } } + \frac { 4 } { x - 4 }$ 
C)  $\frac { - 4 } { ( 2 x - 4 ) ^ { 2 } } + \frac { 3 } { 2 x - 4 } + \frac { 5 } { x - 4 }$ 
D)  $\frac { - 5 } { ( 2 x - 4 ) ^ { 2 } } + \frac { 3 } { 2 x - 4 } + \frac { 4 } { x - 4 }$ 
A)  $\frac { 5 } { ( 2 x - 4 ) ^ { 2 } } + \frac { 3 } { 2 x - 4 } + \frac { - 4 } { x - 4 }$ 
B)  $\frac { 3 } { 2 x - 4 } + \frac { - 5 } { ( 2 x - 4 ) ^ { 2 } } + \frac { 4 } { x - 4 }$ 
C)  $\frac { - 4 } { ( 2 x - 4 ) ^ { 2 } } + \frac { 3 } { 2 x - 4 } + \frac { 5 } { x - 4 }$ 
D)  $\frac { - 5 } { ( 2 x - 4 ) ^ { 2 } } + \frac { 3 } { 2 x - 4 } + \frac { 4 } { x - 4 }$

Question 2

Graph the solution set of the system of inequalities.
-$\begin{array}{c}
2 x+y \leq 4 \
y-1 \leq 0
\end{array}$

Accepted Answer

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

Question 3

Le Boulangerie, a bakery, sells four main items: sweet rolls, bread, cakes, and pies. The amount of each ingredient (in cups, except for eggs) required for these items is given by matrix A.   The cost (in cents) for each ingredient when purchased in large lots or small lots is given in matrix B.  
 Use matrix multiplication to find a matrix giving the comparative cost per bakery item for the two purchase options.

Accepted Answer

A) 
$$\left[ \begin{array} { l l } 
33.75 & 43 \
40.75 & 55 \
86 & 106 \
41 & 59.33
\end{array} \right]$$ 
B) 
$$\left[ \begin{array} { l l } 
32.75 & 43 \
40.75 & 54 \
87 & 106 \
41 & 55.33
\end{array} \right]$$ 
C)  $$\left[ \begin{array} { l l } 
35.75 & 43 \
0 & 0 \
87 & 106 \
0 & 0
\end{array} \right]$$ 
D)  These matrices cannot be multiplied. 
A) 
$$\left[ \begin{array} { l l } 
33.75 & 43 \
40.75 & 55 \
86 & 106 \
41 & 59.33
\end{array} \right]$$ 
B) 
$$\left[ \begin{array} { l l } 
32.75 & 43 \
40.75 & 54 \
87 & 106 \
41 & 55.33
\end{array} \right]$$ 
C)  $$\left[ \begin{array} { l l } 
35.75 & 43 \
0 & 0 \
87 & 106 \
0 & 0
\end{array} \right]$$ 
D)  These matrices cannot be multiplied.

Question 4

Linda invests $25,000 for one year. Part is invested at 5%, another part at 6%, and the rest at 8%. The total income from all 3 investments is $1600. The combined income from the 5% and 6% investments is the same as
The income from the 8% investment. Find the amount invested at each rate.

Accepted Answer

A)  $10,000 at 5%; $10,000 at 6%; $5000 at 8% 
B)  $10,000 at 5%; $5000 at 6%; $10,000 at 8% 
C)  $5000 at 5%; $10,000 at 6%; $10,000 at 8% 
D)  $8000 at 5%; $10,000 at 6%; $7000 at 8% 
A)  $10,000 at 5%; $10,000 at 6%; $5000 at 8% 
B)  $10,000 at 5%; $5000 at 6%; $10,000 at 8% 
C)  $5000 at 5%; $10,000 at 6%; $10,000 at 8% 
D)  $8000 at 5%; $10,000 at 6%; $7000 at 8%

Question 5

Graph the solution set of the system of inequalities.
-$\begin{array}{l}
\frac{x^{2}}{36}-\frac{y^{2}}{9} \geq 1 \
y \geq|x-8|
\end{array}$

Accepted Answer

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

Question 6

Solve the system.
$\begin{array} { l } 
\frac { 6 } { x } + \frac { 5 } { y } + \frac { 1 } { z } = - \frac { 1 } { 4 } \
\frac { 3 } { x } + \frac { 1 } { y } - \frac { 7 } { z } = \frac { 11 } { 8 } \
\frac { 1 } { x } + \frac { 1 } { y } + \frac { 4 } { z } = - \frac { 17 } { 24 }
\end{array}$

Accepted Answer

A)  $\{ ( 8 , - 6,6 ) \}$ 
B)  $\left\{ \left( \frac { 1 } { 8 } , - \frac { 1 } { 6 } , - \frac { 1 } { 6 } \right) \right\}$ 
C)  $\left\{ \left( \frac { 1 } { 8 } , - \frac { 1 } { 6 } , \frac { 1 } { 6 } \right) \right\}$ 
D)  $\{ ( 8 , - 6 , - 6 ) \}$ 
A)  $\{ ( 8 , - 6,6 ) \}$ 
B)  $\left\{ \left( \frac { 1 } { 8 } , - \frac { 1 } { 6 } , - \frac { 1 } { 6 } \right) \right\}$ 
C)  $\left\{ \left( \frac { 1 } { 8 } , - \frac { 1 } { 6 } , \frac { 1 } { 6 } \right) \right\}$ 
D)  $\{ ( 8 , - 6 , - 6 ) \}$

Question 7

Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 164 \
x ^ { 2 } - y ^ { 2 } = 36
\end{array}$

Accepted Answer

A)  {(10,8),(-10,8),(10,-8),(-10,-8)} 
B)  {(-10,-8),(-8,-10)} 
C)  {(10,8),(8,10),(-10,-8),(-8,-10)} 
D)  {(10,-8),(10,8)} 
A)  {(10,8),(-10,8),(10,-8),(-10,-8)} 
B)  {(-10,-8),(-8,-10)} 
C)  {(10,8),(8,10),(-10,-8),(-8,-10)} 
D)  {(10,-8),(10,8)}

Question 8

Use a graphing calculator to Express solutions with approximations to the nearest thousandth.
-$$\sqrt { 2 } x + \sqrt { 7 } y - 3 = 0$$
$\sqrt { 3 } x - y - \sqrt { 6 } = 0$

Accepted Answer

A)  $\{ ( 1.670,0.443 ) \}$ 
B)  $\{ ( 1.581,0.289 ) \}$ 
C)  $\varnothing$ 
D)  $\{ ( 1.099,0.547 ) \}$ 
A)  $\{ ( 1.670,0.443 ) \}$ 
B)  $\{ ( 1.581,0.289 ) \}$ 
C)  $\varnothing$ 
D)  $\{ ( 1.099,0.547 ) \}$

Question 9

Find the partial fraction decomposition for the rational expression.
$\frac { 5 x ^ { 2 } + 20 x - 10 } { \left( 2 x ^ { 2 } + 1 \right) ( 3 - x ) }$

Accepted Answer

A)  $\frac { 99 x - 83 } { 2 x ^ { 2 } + 1 } + \frac { - 59 } { x - 3 }$ 
B)  $\frac { 5 x - 5 } { 2 x ^ { 2 } + 1 } + \frac { - 5 } { x - 3 }$ 
C)  $\frac { 99 x + 83 } { 2 x ^ { 2 } + 1 } + \frac { - 59 } { x - 3 }$ 
D)  $\frac { 5 x - 5 } { 2 x ^ { 2 } + 1 } + \frac { 5 } { x - 3 }$ 
A)  $\frac { 99 x - 83 } { 2 x ^ { 2 } + 1 } + \frac { - 59 } { x - 3 }$ 
B)  $\frac { 5 x - 5 } { 2 x ^ { 2 } + 1 } + \frac { - 5 } { x - 3 }$ 
C)  $\frac { 99 x + 83 } { 2 x ^ { 2 } + 1 } + \frac { - 59 } { x - 3 }$ 
D)  $\frac { 5 x - 5 } { 2 x ^ { 2 } + 1 } + \frac { 5 } { x - 3 }$

Question 10

Solve the system.
$\begin{array} { c } 
x + y + z = - 6 \
x - y + 5 z = 2 \
5 x + y + z = - 26
\end{array}$

Accepted Answer

A)  $\{ ( 1 , - 5 , - 2 ) \}$ 
B)  $\{ ( - 5 , - 2,1 ) \}$ 
C)  $\phi$ 
D)  $\{ ( 1 , - 2 , - 5 ) \}$ 
A)  $\{ ( 1 , - 5 , - 2 ) \}$ 
B)  $\{ ( - 5 , - 2,1 ) \}$ 
C)  $\phi$ 
D)  $\{ ( 1 , - 2 , - 5 ) \}$

Question 11

Find the matrix product when possible.
-$$\left[ \begin{array} { r r } 
- 2 & 3 \
3 & 2
\end{array} \right] \left[ \begin{array} { l l } 
- 2 & 0 \
- 1 & 1
\end{array} \right]$$

Accepted Answer

A) 
$$\left[ \begin{array} { r r } 
1 & 3 \
- 8 & 2
\end{array} \right]$$ 
B) 
$\left[\begin{array}{rr}
4 & 0 \
-3 & 2
\end{array}\right]$ 
C) 
$$\left[ \begin{array} { r r } 
3 & 1 \
2 & - 8
\end{array} \right]$$ 
D) 
$\left[\begin{array}{rr}
4 & -6 \
-4 & -1
\end{array}\right]$ 
A) 
$$\left[ \begin{array} { r r } 
1 & 3 \
- 8 & 2
\end{array} \right]$$ 
B) 
$\left[\begin{array}{rr}
4 & 0 \
-3 & 2
\end{array}\right]$ 
C) 
$$\left[ \begin{array} { r r } 
3 & 1 \
2 & - 8
\end{array} \right]$$ 
D) 
$\left[\begin{array}{rr}
4 & -6 \
-4 & -1
\end{array}\right]$

Question 12

Provide an appropriate response.
-Suppose that A and B are two matrices such th $A + B , A - B$ B, and AB all exist. What can you conclude about the dimensions of A and B?

Accepted Answer

A)  A is a row matrix, and B is a column matrix. 
B)  A and B are square matrices of the same dimension. 
C)  A and B have the same dimension but are not necessarily square matrices. 
D)  There are no dimensions of A and B that would make this possible. 
A)  A is a row matrix, and B is a column matrix. 
B)  A and B are square matrices of the same dimension. 
C)  A and B have the same dimension but are not necessarily square matrices. 
D)  There are no dimensions of A and B that would make this possible.

Question 13

Solve the system.
$\begin{array} { l } 
x - y + z = 0 \
x + y + z = - 4 \
x + y - z = - 6
\end{array}$

Accepted Answer

A)  $\{ ( 1 , - 3 , - 2 ) \}$ 
B)  $\{ ( - 3,1 , - 2 ) \}$ 
C)  $\{ ( - 3 , - 2,1 ) \}$ 
D)  $\phi$ 
A)  $\{ ( 1 , - 3 , - 2 ) \}$ 
B)  $\{ ( - 3,1 , - 2 ) \}$ 
C)  $\{ ( - 3 , - 2,1 ) \}$ 
D)  $\phi$

Question 14

Determine the inequality which matches the calculator graph. Do not use your calculator. Instead, use your knowledge of
the concepts involved in graphing inequalities.
-

Accepted Answer

A)  $y \leq - 3 x - 2$ 
B)  $y \geq 3 x - 2$ 
C)  $y \leq 3 x - 2$ 
D)  $y \geq - 3 x - 2$ 
A)  $y \leq - 3 x - 2$ 
B)  $y \geq 3 x - 2$ 
C)  $y \leq 3 x - 2$ 
D)  $y \geq - 3 x - 2$

Question 15

Perform the operation or operations when possible.
-$$\left[ \begin{array} { r r } 
- 1 & 2 \
0 & 4 \
7 & - 4
\end{array} \right] - \left[ \begin{array} { l l } 
2 & 1 \
7 & 4 \
4 & 2
\end{array} \right]$$

Accepted Answer

A) 
$$\left[ \begin{array} { r r } 
3 & - 1 \
7 & 0 \
- 3 & 6
\end{array} \right]$$ 
B) 
$\left[ \begin{array} { r r } 1 & 1 \ 7 & 0 \ 3 & - 2 \end{array} \right]$ 
C) 
$\left[ \begin{array} { r r } - 3 & 1 \ - 7 & 0 \ 3 & - 6 \end{array} \right]$ 
D) 
$$\left[ \begin{array} { r r } 
1 & 3 \
7 & 8 \
11 & 1
\end{array} \right]$$ 
A) 
$$\left[ \begin{array} { r r } 
3 & - 1 \
7 & 0 \
- 3 & 6
\end{array} \right]$$ 
B) 
$\left[ \begin{array} { r r } 1 & 1 \ 7 & 0 \ 3 & - 2 \end{array} \right]$ 
C) 
$\left[ \begin{array} { r r } - 3 & 1 \ - 7 & 0 \ 3 & - 6 \end{array} \right]$ 
D) 
$$\left[ \begin{array} { r r } 
1 & 3 \
7 & 8 \
11 & 1
\end{array} \right]$$

Question 16

Determine the inequality which matches the calculator graph. Do not use your calculator. Instead, use your knowledge of
the concepts involved in graphing inequalities.
-

Accepted Answer

A)  $y \leq x$ 
B)  $y \geq x$ 
C)  $y \leq - x$ 
D)  $y \geq - x$ 
A)  $y \leq x$ 
B)  $y \geq x$ 
C)  $y \leq - x$ 
D)  $y \geq - x$

Question 17

Determine the system of inequalities illustrated in the graph. Write inequalities in standard form.
-

Accepted Answer

A) $x - 4 y > - 2$ $3 x + y - 2$ $3 x + y < 0$ D) $x - 4 y < - 2$ $3 x + y < 0$ A) $x - 4 y > - 2$ $3 x + y - 2$ $3 x + y < 0$ D) $x - 4 y < - 2$ $3 x + y < 0$

Question 18

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the solution with y arbitrary.
-$$\begin{array} { l } 
9 x - 7 y = - 14 \
- 7 x + 4 y = 8
\end{array}$$

Accepted Answer

A)  $\{ ( - 1,3 ) \}$ 
B)  $\varnothing$ 
C)  $\{ ( 0,2 ) \}$ 
D)  $\{ ( 0,3 ) \}$ 
A)  $\{ ( - 1,3 ) \}$ 
B)  $\varnothing$ 
C)  $\{ ( 0,2 ) \}$ 
D)  $\{ ( 0,3 ) \}$

Question 19

If the graphs of a system of two equations are a circle and a parabola, what are the possible numbers of
solutions (with real coordinates) of this system?

Accepted Answer

The answer of If the graphs of a system of...

Question 20

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth.
-$$\begin{array} { l } 
y = e ^ { 2 x + 3 } \
2 x + y = 3
\end{array}$$

Accepted Answer

A)  $\{ ( - 0.75,4.50 ) \}$ 
B)  $\{ ( - 0.75 , - 4.50 ) \}$ 
C)  $\{ ( 0.75 , - 4.50 ) \}$ 
D)  $\{ ( 0.75,4.50 ) \}$ 
A)  $\{ ( - 0.75,4.50 ) \}$ 
B)  $\{ ( - 0.75 , - 4.50 ) \}$ 
C)  $\{ ( 0.75 , - 4.50 ) \}$ 
D)  $\{ ( 0.75,4.50 ) \}$

Find the partial fraction decomposition for the rational expression. $\frac { 22 x ^ { 2 } - 105 x + 132 } { ( x - 4 ) ( 2 x - 4 ) ^ { 2 } }$

Graph the solution set of the system of inequalities. - 2x+y\leq4 y-1\leq0 $Graph the solution set of the system of inequalities. - \begin{array}{c} 2 x+y \leq 4 \\ y-1 \leq 0 \end{array}$

Linda invests $25,000 for one year. Part is invested at 5%, another part at 6%, and the rest at 8%. The total income from all 3 investments is $1600. The combined income from the 5% and 6% investments is the same as The income from the 8% investment. Find the amount invested at each rate.

Graph the solution set of the system of inequalities. - -\geq1 y\geq|x-8| $Graph the solution set of the system of inequalities. - \begin{array}{l} \frac{x^{2}}{36}-\frac{y^{2}}{9} \geq 1 \\ y \geq|x-8| \end{array}$

Solve the system. ++=- +-= ++=-

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. +=164 -=36

Use a graphing calculator to Express solutions with approximations to the nearest thousandth. - $\sqrt { 2 } x + \sqrt { 7 } y - 3 = 0$ $\sqrt { 3 } x - y - \sqrt { 6 } = 0$

Find the partial fraction decomposition for the rational expression. $\frac { 5 x ^ { 2 } + 20 x - 10 } { \left( 2 x ^ { 2 } + 1 \right) ( 3 - x ) }$

Solve the system. x+y+z=-6 x-y+5z=2 5x+y+z=-26

Find the matrix product when possible. - $\left[ \begin{array} { r r } - 2 & 3 \\3 & 2\end{array} \right] \left[ \begin{array} { l l } - 2 & 0 \\- 1 & 1\end{array} \right]$

Provide an appropriate response. -Suppose that A and B are two matrices such th $A + B , A - B$ B, and AB all exist. What can you conclude about the dimensions of A and B?

Solve the system. x-y+z=0 x+y+z=-4 x+y-z=-6

Determine the inequality which matches the calculator graph. Do not use your calculator. Instead, use your knowledge of the concepts involved in graphing inequalities. -

Perform the operation or operations when possible. - $\left[ \begin{array} { r r } - 1 & 2 \\0 & 4 \\7 & - 4\end{array} \right] - \left[ \begin{array} { l l } 2 & 1 \\7 & 4 \\4 & 2\end{array} \right]$

Determine the inequality which matches the calculator graph. Do not use your calculator. Instead, use your knowledge of the concepts involved in graphing inequalities. -

Determine the system of inequalities illustrated in the graph. Write inequalities in standard form. -

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the solution with y arbitrary. - 9x-7y=-14 -7x+4y=8

If the graphs of a system of two equations are a circle and a parabola, what are the possible numbers of solutions (with real coordinates) of this system?

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth. - y= 2x+y=3

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 6: Systems and Matrices

Find the partial fraction decomposition for the rational expression. 22x2−105x+132(x−4)(2x−4)2\frac { 22 x ^ { 2 } - 105 x + 132 } { ( x - 4 ) ( 2 x - 4 ) ^ { 2 } }(x−4)(2x−4)222x2−105x+132​

Graph the solution set of the system of inequalities. - 2x+y\leq4 y-1\leq0

Linda invests $25,000 for one year. Part is invested at 5%, another part at 6%, and the rest at 8%. The total income from all 3 investments is $1600. The combined income from the 5% and 6% investments is the same as The income from the 8% investment. Find the amount invested at each rate.

Graph the solution set of the system of inequalities. - -\geq1 y\geq|x-8|

Solve the system. ++=- +-= ++=-

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. +=164 -=36

Use a graphing calculator to Express solutions with approximations to the nearest thousandth. - 2x+7y−3=0\sqrt { 2 } x + \sqrt { 7 } y - 3 = 02​x+7​y−3=0 3x−y−6=0\sqrt { 3 } x - y - \sqrt { 6 } = 03​x−y−6​=0

Find the partial fraction decomposition for the rational expression. 5x2+20x−10(2x2+1)(3−x)\frac { 5 x ^ { 2 } + 20 x - 10 } { \left( 2 x ^ { 2 } + 1 \right) ( 3 - x ) }(2x2+1)(3−x)5x2+20x−10​

Solve the system. x+y+z=-6 x-y+5z=2 5x+y+z=-26

Find the matrix product when possible. - [−2332][−20−11]\left[ \begin{array} { r r } - 2 & 3 \\3 & 2\end{array} \right] \left[ \begin{array} { l l } - 2 & 0 \\- 1 & 1\end{array} \right][−23​32​][−2−1​01​]

Provide an appropriate response. -Suppose that A and B are two matrices such th A+B,A−BA + B , A - BA+B,A−B B, and AB all exist. What can you conclude about the dimensions of A and B?

Solve the system. x-y+z=0 x+y+z=-4 x+y-z=-6

Determine the inequality which matches the calculator graph. Do not use your calculator. Instead, use your knowledge of the concepts involved in graphing inequalities. -

Perform the operation or operations when possible. - [−12047−4]−[217442]\left[ \begin{array} { r r } - 1 & 2 \\0 & 4 \\7 & - 4\end{array} \right] - \left[ \begin{array} { l l } 2 & 1 \\7 & 4 \\4 & 2\end{array} \right]​−107​24−4​​−​274​142​​

Determine the inequality which matches the calculator graph. Do not use your calculator. Instead, use your knowledge of the concepts involved in graphing inequalities. -

Determine the system of inequalities illustrated in the graph. Write inequalities in standard form. -

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the solution with y arbitrary. - 9x-7y=-14 -7x+4y=8

If the graphs of a system of two equations are a circle and a parabola, what are the possible numbers of solutions (with real coordinates) of this system?

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth. - y= 2x+y=3

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Arithmetic Sequence: Common Difference and First n Terms

Filters

Find the partial fraction decomposition for the rational expression. $\frac { 22 x ^ { 2 } - 105 x + 132 } { ( x - 4 ) ( 2 x - 4 ) ^ { 2 } }$

Graph the solution set of the system of inequalities. - 2x+y\leq4 y-1\leq0 $Graph the solution set of the system of inequalities. - \begin{array}{c} 2 x+y \leq 4 \\ y-1 \leq 0 \end{array}$

Graph the solution set of the system of inequalities. - -\geq1 y\geq|x-8| $Graph the solution set of the system of inequalities. - \begin{array}{l} \frac{x^{2}}{36}-\frac{y^{2}}{9} \geq 1 \\ y \geq|x-8| \end{array}$

Use a graphing calculator to Express solutions with approximations to the nearest thousandth. - $\sqrt { 2 } x + \sqrt { 7 } y - 3 = 0$ $\sqrt { 3 } x - y - \sqrt { 6 } = 0$

Find the partial fraction decomposition for the rational expression. $\frac { 5 x ^ { 2 } + 20 x - 10 } { \left( 2 x ^ { 2 } + 1 \right) ( 3 - x ) }$

Find the matrix product when possible. - $\left[ \begin{array} { r r } - 2 & 3 \\3 & 2\end{array} \right] \left[ \begin{array} { l l } - 2 & 0 \\- 1 & 1\end{array} \right]$

Provide an appropriate response. -Suppose that A and B are two matrices such th $A + B , A - B$ B, and AB all exist. What can you conclude about the dimensions of A and B?

Perform the operation or operations when possible. - $\left[ \begin{array} { r r } - 1 & 2 \\0 & 4 \\7 & - 4\end{array} \right] - \left[ \begin{array} { l l } 2 & 1 \\7 & 4 \\4 & 2\end{array} \right]$