Question 1

Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
$\begin{array} { l } 
y = 10 | x | - 25 \
y = x ^ { 2 }
\end{array}$

Accepted Answer

A)  {(5,25),(-5,25)} 
B)  {(-5,25)} 
C)  {(5,25)} 
D)  {(0,-25),(-5,25)} 
A)  {(5,25),(-5,25)} 
B)  {(-5,25)} 
C)  {(5,25)} 
D)  {(0,-25),(-5,25)}

Question 2

Use a graphing calculator to find the value of the determinant.
-$$\left| \begin{array} { r r r } 
- 5 & 3 & 5 \
0 & 5 & - 3 \
- 5 & - 2 & - 5
\end{array} \right|$$

Accepted Answer

A)  $- 325$ 
B)  15 
C)  325 
D)  235 
A)  $- 325$ 
B)  15 
C)  325 
D)  235

Question 3

Use a graphing calculator to find the inverse of the matrix. Give five decimal places, if necessary.
-$$A = \left[ \begin{array} { c c } 
\sqrt { 3 } & - 4 \
\frac { 2 } { 7 } & 0.932
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { c c } 0.33803 & 1.45078 \ - 0.10363 & 0.62821 \end{array} \right]$ 
B) 
$\left[ \begin{array} { c c } 0.57735 & - 0.25 \ 3.5 & 1.07296 \end{array} \right]$ 
C) 
$$\left[ \begin{array} { l r } 
1.97703 & - 8.48511 \
- 0.60608 & 3.67416
\end{array} \right]$$ 
D) 
$$\left[ \begin{array} { l l } 
0 & 1 \
1 & 0
\end{array} \right]$$ 
A)  $\left[ \begin{array} { c c } 0.33803 & 1.45078 \ - 0.10363 & 0.62821 \end{array} \right]$ 
B) 
$\left[ \begin{array} { c c } 0.57735 & - 0.25 \ 3.5 & 1.07296 \end{array} \right]$ 
C) 
$$\left[ \begin{array} { l r } 
1.97703 & - 8.48511 \
- 0.60608 & 3.67416
\end{array} \right]$$ 
D) 
$$\left[ \begin{array} { l l } 
0 & 1 \
1 & 0
\end{array} \right]$$

Question 4

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

Question 5

Matt bought 3 pounds of oranges and 2 pounds of apples and paid $\$ 4.14$, before tax. Andy bought 4 pounds of oranges and 3 pounds of apples and paid $\$ 5.83$, before tax. Use this information to set up a matrix equation of the form $\mathrm { AX } = \mathrm { B }$, which can be solved to determine the price per pound for oranges and apples. Solve this matrix equation to find the price per pound of oranges.
Use the fact that for $A = \left[ \begin{array} { l l } 3 & 2 \ 4 & 3 \end{array} \right] , A ^ { - 1 } = \left[ \begin{array} { r r } 3 & - 2 \ - 4 & 3 \end{array} \right]$.

Accepted Answer

A)  $0.72 per pound 
B)  $0.76 per pound 
C)  $0.79 per pound 
D)  $0.74 per pound 
A)  $0.72 per pound 
B)  $0.76 per pound 
C)  $0.79 per pound 
D)  $0.74 per pound

Question 6

Write the system of equations associated with the augmented matrix. Do not solve.
-$\left[ \begin{array} { l l l | r } 1 & 0 & 0 & - 8 \ 0 & 1 & 0 & - 9 \ 0 & 0 & 1 & 5 \end{array} \right]$

Accepted Answer

A)  $x = - 13$
$y = - 14$
$\mathrm { z } = 0$ 
B)  $x = - 8$
$y = - 9$
$\mathrm { z } = 5$ 
C)  $x = 0$
$y = - 17$
$\mathrm { z } = - 3$ 
D)  $x = 8$
$y = 9$
$\mathrm { z } = - 5$ 
A)  $x = - 13$
$y = - 14$
$\mathrm { z } = 0$ 
B)  $x = - 8$
$y = - 9$
$\mathrm { z } = 5$ 
C)  $x = 0$
$y = - 17$
$\mathrm { z } = - 3$ 
D)  $x = 8$
$y = 9$
$\mathrm { z } = - 5$

Question 7

Evaluate the determinant.
$\left| \begin{array} { r r r } 
2 & - 7 & 5 \
- 1 & - 7 & - 9 \
0 & 0 & 0
\end{array} \right|$

Accepted Answer

A)  14 
B)  0 
C)   -49 
D)   -77 
A)  14 
B)  0 
C)   -49 
D)   -77

Question 8

A triangle with vertices at (x1, y1), (x2, y2), and (x3, y3) has area equal to the absolute value of D, where $$D = \frac { 1 } { 2 } \left| \begin{array} { l l l } 
x _ { 1 } & y _ { 1 } & 1 \
x _ { 2 } & y _ { 2 } & 1 \
x _ { 3 } & y _ { 3 } & 1
\end{array} \right|$$ Find the area of the triangle having vertices at P, Q, and R.
-$$\mathrm { P } ( - 3 , - 3 ) , \mathrm { Q } ( 0,0 ) , \mathrm { R } ( 5 , - 1 )$$

Accepted Answer

A)  12 
B)  18 
C)  0 
D)  9 
A)  12 
B)  18 
C)  0 
D)  9

Question 9

Find the partial fraction decomposition for the rational expression.
$\frac { 2 x ^ { 3 } - 7 x ^ { 2 } + 5 x - 3 } { x ^ { 2 } + x - 2 }$

Accepted Answer

A)  $2 x - 9 + \frac { 19 } { x + 2 } - \frac { - 1 } { x - 1 }$ 
B)  $2 x + 9 + \frac { - 13 } { x + 2 } + \frac { 7 } { x - 1 }$ 
C)  $2 x + 5 + \frac { - 7 / 3 } { x + 2 } + \frac { 13 / 3 } { x - 1 }$ 
D)  $2 x - 9 + \frac { - 5 / 3 } { x + 2 } + \frac { 1 / 3 } { x - 1 }$ 
A)  $2 x - 9 + \frac { 19 } { x + 2 } - \frac { - 1 } { x - 1 }$ 
B)  $2 x + 9 + \frac { - 13 } { x + 2 } + \frac { 7 } { x - 1 }$ 
C)  $2 x + 5 + \frac { - 7 / 3 } { x + 2 } + \frac { 13 / 3 } { x - 1 }$ 
D)  $2 x - 9 + \frac { - 5 / 3 } { x + 2 } + \frac { 1 / 3 } { x - 1 }$

Question 10

Find the value of the determinant.
-$\left| \begin{array} { l l } - 1 & 1 \ - 2 & - 3 \end{array} \right|$

Accepted Answer

A)  $- 5$ 
B)  5 
C)  $- 7$ 
D)  1 
A)  $- 5$ 
B)  5 
C)  $- 7$ 
D)  1

Question 11

Provide an appropriate response.
-Which of the following inequalities satisfies the following description: the region inside an ellipse centered at the origin, with $x$-intercepts at $( - 8,0 )$ and $( 8,0 )$, and $y$-intercepts at $( 0 , - 4 )$ and $( 0,4 )$ ?

Accepted Answer

A)  $\frac { x ^ { 2 } } { 8 } + \frac { y ^ { 2 } } { 4 }  1$ 
C)  $\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 16 } < 1$ 
D)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 16 } < 1$ 
A)  $\frac { x ^ { 2 } } { 8 } + \frac { y ^ { 2 } } { 4 }  1$ 
C)  $\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 16 } < 1$ 
D)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 16 } < 1$

Question 12

Find the indicated matrix.
-Let $\mathrm { A } = \left[ \begin{array} { r r } - 3 & 1 \ 0 & 2 \end{array} \right]$. Find $2 \mathrm {~A}$.

Accepted Answer

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

Question 13

Solve the system by substitution.
9x + 4y = 3
9y = 26 + 2x

Accepted Answer

A)  $\left\{ \left\{ - \frac { 77 } { 89 } , - \frac { 130 } { 89 } \right) \right\}$ 
B)  $\left\{ \left( - \frac { 77 } { 89 } , \frac { 240 } { 89 } \right) \right\}$ 
C)  $\left\{ \left( - \frac { 77 } { 89 } , - \frac { 130 } { 801 } \right) \right\}$ 
D)  $\left\{ \left( \frac { 240 } { 89 } , - \frac { 77 } { 89 } \right) \right\}$ 
A)  $\left\{ \left\{ - \frac { 77 } { 89 } , - \frac { 130 } { 89 } \right) \right\}$ 
B)  $\left\{ \left( - \frac { 77 } { 89 } , \frac { 240 } { 89 } \right) \right\}$ 
C)  $\left\{ \left( - \frac { 77 } { 89 } , - \frac { 130 } { 801 } \right) \right\}$ 
D)  $\left\{ \left( \frac { 240 } { 89 } , - \frac { 77 } { 89 } \right) \right\}$

Question 14

Solve the system.
$\begin{array} { l } 
\frac { 6 } { x } + \frac { 4 } { y } = - \frac { 2 } { 21 } \
\frac { 7 } { x } - \frac { 3 } { y } = - \frac { 76 } { 63 }
\end{array}$

Accepted Answer

A)  $\left\{ \left( - \frac { 4221 } { 106 } , 7 \right) \right\}$ 
B)  $\{ ( - 9,7 ) \}$ 
C)  $\{ ( 9 , - 7 ) \}$ 
D)  $\{ ( 7 , - 9 ) \}$ 
A)  $\left\{ \left( - \frac { 4221 } { 106 } , 7 \right) \right\}$ 
B)  $\{ ( - 9,7 ) \}$ 
C)  $\{ ( 9 , - 7 ) \}$ 
D)  $\{ ( 7 , - 9 ) \}$

Question 15

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

Accepted Answer

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

Question 16

Decide whether or not the matrices are inverses of each other.
-$$\left[ \begin{array} { l l } 
9 & 4 \
4 & 4
\end{array} \right] \text { and } \left[ \begin{array} { r r } 
- .2 & .2 \
.2 & - .45
\end{array} \right]$$

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 17

Choose the one alternative that best completes the statement or answers the question.
Graph the inequality.
$(x-4)^{2}+(y+3)^{2} \leq 4$

Accepted Answer

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

Question 18

The following table shows the number of rectifiers, in thousands, produced by Allied Electronics in the three years considered. For a function of the form $f ( x ) = a x ^ { 2 } + b x + c$ that fits this data, what is the value of $b$ ?

Accepted Answer

A)  11 
B)  12 
C)  10 
D)  9 
A)  11 
B)  12 
C)  10 
D)  9

Question 19

Let A be a $3 \times 2$ matrix. Write a matrix B such that AB can be found.

Accepted Answer

Answers wi

Question 20

Find the cofactor of the indicated element.
$a_{22}$
$\left|\begin{array}{rrr}
1 & 1 & 4 \
-2 & -1 & 1 \
4 & 3 & 1
\end{array}\right|$

Accepted Answer

A)  13 
B)  15 
C)  -15 
D)  -13 
A)  13 
B)  15 
C)  -15 
D)  -13

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. y=10|x|-25 y=

Use a graphing calculator to find the value of the determinant. - $\left| \begin{array} { r r r } - 5 & 3 & 5 \\0 & 5 & - 3 \\- 5 & - 2 & - 5\end{array} \right|$

Use a graphing calculator to find the inverse of the matrix. Give five decimal places, if necessary. - $A = \left[ \begin{array} { c c } \sqrt { 3 } & - 4 \\\frac { 2 } { 7 } & 0.932\end{array} \right]$

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

Write the system of equations associated with the augmented matrix. Do not solve. - $\left[ \begin{array} { l l l | r } 1 & 0 & 0 & - 8 \\ 0 & 1 & 0 & - 9 \\ 0 & 0 & 1 & 5 \end{array} \right]$

Evaluate the determinant. $\left| \begin{array} { r r r } 2 & - 7 & 5 \\- 1 & - 7 & - 9 \\0 & 0 & 0\end{array} \right|$

Find the partial fraction decomposition for the rational expression. $\frac { 2 x ^ { 3 } - 7 x ^ { 2 } + 5 x - 3 } { x ^ { 2 } + x - 2 }$

Find the value of the determinant. - $\left| \begin{array} { l l } - 1 & 1 \\ - 2 & - 3 \end{array} \right|$

Provide an appropriate response. -Which of the following inequalities satisfies the following description: the region inside an ellipse centered at the origin, with $x$ -intercepts at $( - 8,0 )$ and $( 8,0 )$ , and $y$ -intercepts at $( 0 , - 4 )$ and $( 0,4 )$ ?

Find the indicated matrix. -Let $\mathrm { A } = \left[ \begin{array} { r r } - 3 & 1 \\ 0 & 2 \end{array} \right]$ . Find $2 \mathrm {~A}$ .

Solve the system by substitution. 9x + 4y = 3 9y = 26 + 2x

Solve the system. +=- -=-

Graph the solution set of the system of inequalities. - x-2y\leq2 x+y\leq0 $Graph the solution set of the system of inequalities. - \begin{array}{c} x-2 y \leq 2 \\ x+y \leq 0 \end{array}$

Decide whether or not the matrices are inverses of each other. - $\left[ \begin{array} { l l } 9 & 4 \\4 & 4\end{array} \right] \text { and } \left[ \begin{array} { r r } - .2 & .2 \\.2 & - .45\end{array} \right]$

Choose the one alternative that best completes the statement or answers the question. Graph the inequality. $(x-4)^{2}+(y+3)^{2} \leq 4$ $Choose the one alternative that best completes the statement or answers the question. Graph the inequality. (x-4)^{2}+(y+3)^{2} \leq 4$

Let A be a $3 \times 2$ matrix. Write a matrix B such that AB can be found.

Find the cofactor of the indicated element. $a_{22}$ $\left|\begin{array}{rrr}1 & 1 & 4 \\-2 & -1 & 1 \\4 & 3 & 1\end{array}\right|$

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

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. y=10|x|-25 y=

Use a graphing calculator to find the value of the determinant. - ∣−53505−3−5−2−5∣\left| \begin{array} { r r r } - 5 & 3 & 5 \\0 & 5 & - 3 \\- 5 & - 2 & - 5\end{array} \right|​−50−5​35−2​5−3−5​​

Use a graphing calculator to find the inverse of the matrix. Give five decimal places, if necessary. - A=[3−4270.932]A = \left[ \begin{array} { c c } \sqrt { 3 } & - 4 \\\frac { 2 } { 7 } & 0.932\end{array} \right]A=[3​72​​−40.932​]

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

Write the system of equations associated with the augmented matrix. Do not solve. - [100−8010−90015]\left[ \begin{array} { l l l | r } 1 & 0 & 0 & - 8 \\ 0 & 1 & 0 & - 9 \\ 0 & 0 & 1 & 5 \end{array} \right]​100​010​001​−8−95​​

Evaluate the determinant. ∣2−75−1−7−9000∣\left| \begin{array} { r r r } 2 & - 7 & 5 \\- 1 & - 7 & - 9 \\0 & 0 & 0\end{array} \right|​2−10​−7−70​5−90​​

Find the partial fraction decomposition for the rational expression. 2x3−7x2+5x−3x2+x−2\frac { 2 x ^ { 3 } - 7 x ^ { 2 } + 5 x - 3 } { x ^ { 2 } + x - 2 }x2+x−22x3−7x2+5x−3​

Find the value of the determinant. - ∣−11−2−3∣\left| \begin{array} { l l } - 1 & 1 \\ - 2 & - 3 \end{array} \right|​−1−2​1−3​​

Find the indicated matrix. -Let A=[−3102]\mathrm { A } = \left[ \begin{array} { r r } - 3 & 1 \\ 0 & 2 \end{array} \right]A=[−30​12​] . Find 2 A2 \mathrm {~A}2 A .

Solve the system by substitution. 9x + 4y = 3 9y = 26 + 2x

Solve the system. +=- -=-

Graph the solution set of the system of inequalities. - x-2y\leq2 x+y\leq0

Decide whether or not the matrices are inverses of each other. - [9444] and [−.2.2.2−.45]\left[ \begin{array} { l l } 9 & 4 \\4 & 4\end{array} \right] \text { and } \left[ \begin{array} { r r } - .2 & .2 \\.2 & - .45\end{array} \right][94​44​] and [−.2.2​.2−.45​]

Choose the one alternative that best completes the statement or answers the question. Graph the inequality. (x−4)2+(y+3)2≤4(x-4)^{2}+(y+3)^{2} \leq 4(x−4)2+(y+3)2≤4

The following table shows the number of rectifiers, in thousands, produced by Allied Electronics in the three years considered. For a function of the form f(x)=ax2+bx+cf ( x ) = a x ^ { 2 } + b x + cf(x)=ax2+bx+c that fits this data, what is the value of bbb ?

Let A be a 3×23 \times 23×2 matrix. Write a matrix B such that AB can be found.

Find the cofactor of the indicated element. a22a_{22}a22​ ∣114−2−11431∣\left|\begin{array}{rrr}1 & 1 & 4 \\-2 & -1 & 1 \\4 & 3 & 1\end{array}\right|​1−24​1−13​411​​

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

Use a graphing calculator to find the value of the determinant. - $\left| \begin{array} { r r r } - 5 & 3 & 5 \\0 & 5 & - 3 \\- 5 & - 2 & - 5\end{array} \right|$

Use a graphing calculator to find the inverse of the matrix. Give five decimal places, if necessary. - $A = \left[ \begin{array} { c c } \sqrt { 3 } & - 4 \\\frac { 2 } { 7 } & 0.932\end{array} \right]$

Write the system of equations associated with the augmented matrix. Do not solve. - $\left[ \begin{array} { l l l | r } 1 & 0 & 0 & - 8 \\ 0 & 1 & 0 & - 9 \\ 0 & 0 & 1 & 5 \end{array} \right]$

Evaluate the determinant. $\left| \begin{array} { r r r } 2 & - 7 & 5 \\- 1 & - 7 & - 9 \\0 & 0 & 0\end{array} \right|$

Find the partial fraction decomposition for the rational expression. $\frac { 2 x ^ { 3 } - 7 x ^ { 2 } + 5 x - 3 } { x ^ { 2 } + x - 2 }$

Find the value of the determinant. - $\left| \begin{array} { l l } - 1 & 1 \\ - 2 & - 3 \end{array} \right|$

Find the indicated matrix. -Let $\mathrm { A } = \left[ \begin{array} { r r } - 3 & 1 \\ 0 & 2 \end{array} \right]$ . Find $2 \mathrm {~A}$ .

Graph the solution set of the system of inequalities. - x-2y\leq2 x+y\leq0 $Graph the solution set of the system of inequalities. - \begin{array}{c} x-2 y \leq 2 \\ x+y \leq 0 \end{array}$

Decide whether or not the matrices are inverses of each other. - $\left[ \begin{array} { l l } 9 & 4 \\4 & 4\end{array} \right] \text { and } \left[ \begin{array} { r r } - .2 & .2 \\.2 & - .45\end{array} \right]$

Choose the one alternative that best completes the statement or answers the question. Graph the inequality. $(x-4)^{2}+(y+3)^{2} \leq 4$ $Choose the one alternative that best completes the statement or answers the question. Graph the inequality. (x-4)^{2}+(y+3)^{2} \leq 4$

Let A be a $3 \times 2$ matrix. Write a matrix B such that AB can be found.

Find the cofactor of the indicated element. $a_{22}$ $\left|\begin{array}{rrr}1 & 1 & 4 \\-2 & -1 & 1 \\4 & 3 & 1\end{array}\right|$