Question 1

Find the value of the determinant.
$\left| \begin{array} { r r r } 
9 & 0 & 0 \
8 & - 1 & 0 \
- 1 & 6 & 3
\end{array} \right|$

Accepted Answer

A)  27 
B)   -21 
C)   -27 
D)   -75 
A)  27 
B)   -21 
C)   -27 
D)   -75

Question 2

If the graphs of a system of two equations are a line 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 3

Solve the system using a graphing calculator capable of performing row operations. Give solutions with values correct to
the nearest thousandth.
-\[\begin{array}{l}
\sqrt { 3 } x - 0.9 y + z = - 8\
\frac { 2 } { 3 } x - y + 2 z = \frac { 5 } { 6 }\
6.2 x + 16 y - 5 z = \sqrt { 7 }\

Accepted Answer

A)  	ext {  } \{ ( - 4.259,3.107,2.517 ) \}\ 
B)  	ext {  } \{ ( 4.729,7.426,3.652 ) \}\ 
C)  	ext {  } \{ ( 3.628,5.029,3.719 ) \}\ 
D)  	ext {  } \{ ( - 5.072,3.306,3.760 ) \}
\end{array}\] 
A)  	ext {  } \{ ( - 4.259,3.107,2.517 ) \}\ 
B)  	ext {  } \{ ( 4.729,7.426,3.652 ) \}\ 
C)  	ext {  } \{ ( 3.628,5.029,3.719 ) \}\ 
D)  	ext {  } \{ ( - 5.072,3.306,3.760 ) \}
\end{array}\]

Question 4

Find the values of the variables for which the statement is true, if possible.
-$\left[ \begin{array} { l l l } 7 & \mathrm { p } + 3 & \mathrm { q } - 7 \end{array} \right] = \left[ \begin{array} { l l l } \mathrm { k } + 2 & 5 & - 7 \end{array} \right]$

Accepted Answer

A)  $\mathrm { k } = 2 ; \mathrm { p } = 7 ; \mathrm { q } = - 7$ 
B)  $\mathrm { k } = 5 ; \mathrm { p } = 2 ; \mathrm { q } = 0$ 
C)  $\mathrm { k } = - 5 ; \mathrm { p } = - 2 ; \mathrm { q } = 0$ 
D)  $k = 5 ; p = 0 ; q = 0$ 
A)  $\mathrm { k } = 2 ; \mathrm { p } = 7 ; \mathrm { q } = - 7$ 
B)  $\mathrm { k } = 5 ; \mathrm { p } = 2 ; \mathrm { q } = 0$ 
C)  $\mathrm { k } = - 5 ; \mathrm { p } = - 2 ; \mathrm { q } = 0$ 
D)  $k = 5 ; p = 0 ; q = 0$

Question 5

Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
$\begin{array} { l } 
x ^ { 2 } + 3 x y + y ^ { 2 } = 4 \
x ^ { 2 } - 3 x y - y ^ { 2 } = 4
\end{array}$

Accepted Answer

A)  {(0,2),(0,-2),(2,-6),(-2,6)} 
B)  {(2,-6),(-2,6)} 
C)  {(2,0),(-2,0)} 
D)  {(2,0),(-2,0),(2,-6),(-2,6)} 
A)  {(0,2),(0,-2),(2,-6),(-2,6)} 
B)  {(2,-6),(-2,6)} 
C)  {(2,0),(-2,0)} 
D)  {(2,0),(-2,0),(2,-6),(-2,6)}

Question 6

Solve the system by using the inverse of the coefficient matrix.
-$$\begin{array} { c } 
5 x + 4 y = 8 \
4 x - 2 y = 22
\end{array}$$

Accepted Answer

A)  $\{ ( - 3,4 ) \}$ 
B)  $\{ ( 4 , - 3 ) \}$ 
C)  $\{ ( 3 , - 4 ) \}$ 
D)  $\{ ( - 4,3 ) \}$ 
A)  $\{ ( - 3,4 ) \}$ 
B)  $\{ ( 4 , - 3 ) \}$ 
C)  $\{ ( 3 , - 4 ) \}$ 
D)  $\{ ( - 4,3 ) \}$

Question 7

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

Accepted Answer

A)  {(6,0)} 
B)  {(6,0),(-6,0)} 
C)  {(0,6),(0,-6)} 
D)  {(0,-6)} 
A)  {(6,0)} 
B)  {(6,0),(-6,0)} 
C)  {(0,6),(0,-6)} 
D)  {(0,-6)}

Question 8

Graph the solution set of the system of inequalities.
-$$\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 25 } \leq 1$$
$$\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 9 } \geq 1$$

Accepted Answer

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

Question 9

If the system has infinitely many solutions, write the solution set with x arbitrary.
-$$\begin{array} { c } 
x + y - 2 z - 8 = 0 \
3 x + z + 6 = 0 \
2 x - y + 3 z + 14 = 0
\end{array}$$

Accepted Answer

A)  $\{ ( x , - 7 x + 4 , - 3 x - 6 ) \}$ 
B)  $\{ ( x , 7 x + 4 , - 3 x - 6 ) \}$ 
C)  $\{ ( x , 7 x - 4 , - 3 x - 6 ) \}$ 
D)  $\{ ( x , - 7 x - 4 , - 3 x - 6 ) \}$ 
A)  $\{ ( x , - 7 x + 4 , - 3 x - 6 ) \}$ 
B)  $\{ ( x , 7 x + 4 , - 3 x - 6 ) \}$ 
C)  $\{ ( x , 7 x - 4 , - 3 x - 6 ) \}$ 
D)  $\{ ( x , - 7 x - 4 , - 3 x - 6 ) \}$

Question 10

Find the cofactor of the indicated element.
$\begin{array} { l } 
\text { a } 33 \
\left| \begin{array} { r r r } 
4 & 3 & 2 \
5 & 4 & 2 \
- 1 & - 1 & 4
\end{array} \right|
\end{array}$

Accepted Answer

A)  -1 
B)  1 
C)  -2 
D)  2 
A)  -1 
B)  1 
C)  -2 
D)  2

Question 11

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

Question 12

Suppose that you are solving a system of three linear equations by the Gauss-Jordan method and obtain the following augmented matrix. $$\left[ \begin{array} { r r r | r } 
1 & - 11 & - 13 & - 30 \
0 & - 14 & - 3 & 1 \
0 & 5 & - 9 & - 26
\end{array} \right]$$
What row operation would you perform next?

Accepted Answer

A)  Multiply row 1 by $- \frac { 1 } { 11 }$. 
B)  Add $- 5$ times row 1 to $- 11$ times row 3 to obtain a zero in the third row, second column position. 
C)  Add row 1 to row $2 .$ 
D)  Multiply row 2 by $- \frac { 1 } { 14 }$. 
A)  Multiply row 1 by $- \frac { 1 } { 11 }$. 
B)  Add $- 5$ times row 1 to $- 11$ times row 3 to obtain a zero in the third row, second column position. 
C)  Add row 1 to row $2 .$ 
D)  Multiply row 2 by $- \frac { 1 } { 14 }$.

Question 13

Find the dimensions of a rectangular garden with perimeter 62 yd an $220 \mathrm { yd } ^ { 2 }$

Accepted Answer

A)  20 yd by 11 yd 
B)  10 yd by 22 yd 
C)  20 yd by 22 yd 
D)  10 yd by 11 yd 
A)  20 yd by 11 yd 
B)  10 yd by 22 yd 
C)  20 yd by 22 yd 
D)  10 yd by 11 yd

Question 14

Choose the one alternative that best completes the statement or answers the question.
Graph the inequality.
$x-y<-2$

Accepted Answer

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

Question 15

Solve the system in terms of the arbitrary variable x.
-$$\begin{array} { c } 
x + y + z = 9 \
4 x - 3 y + 2 z = 7
\end{array}$$

Accepted Answer

A)  $\left\{ \left( x , \frac { 2 x + 11 } { 5 } , \frac { x + 34 } { 5 } \right) \right\}$ 
B)  $\left\{ \left( x , \frac { 2 x + 11 } { 5 } , \frac { - 7 x + 34 } { 5 } \right) \right\}$ 
C)  $\left\{ \left\{ x , \frac { 2 x - 11 } { 5 } , \frac { - 7 x + 34 } { 5 } \right) \right\}$ 
D)  $\varnothing$ 
A)  $\left\{ \left( x , \frac { 2 x + 11 } { 5 } , \frac { x + 34 } { 5 } \right) \right\}$ 
B)  $\left\{ \left( x , \frac { 2 x + 11 } { 5 } , \frac { - 7 x + 34 } { 5 } \right) \right\}$ 
C)  $\left\{ \left\{ x , \frac { 2 x - 11 } { 5 } , \frac { - 7 x + 34 } { 5 } \right) \right\}$ 
D)  $\varnothing$

Question 16

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

Accepted Answer

A)  $x + y \geq 2$
$2 x + y \leq 5$ 
B)  $x - y \geq 2$
$2 x + y \leq 5$ 
C)  $x - y \leq 2$
$2 x + y \geq 5$ 
D)  $x + y \leq 2$
$2 x + y \geq 5$ 
A)  $x + y \geq 2$
$2 x + y \leq 5$ 
B)  $x - y \geq 2$
$2 x + y \leq 5$ 
C)  $x - y \leq 2$
$2 x + y \geq 5$ 
D)  $x + y \leq 2$
$2 x + y \geq 5$

Question 17

Use the given row transformation to change the matrix as indicated.
-$\left[ \begin{array} { r r } - 1 & 4 \ 7 & 0 \end{array} \right] ; 7$ times row 1 added to row 2

Accepted Answer

A) 
$\left[ \begin{array} { r r } - 1 & 4 \ 0 & 28 \end{array} \right]$ 
B)

$\left[ \begin{array} { r r } - 1 & - 3 \ 0 & 28 \end{array} \right]$ 
C) 
$\left[ \begin{array} { r r } - 7 & 28 \ 7 & 0 \end{array} \right]$ 
D) 
$\left[ \begin{array} { r r } - 1 & 4 \ 7 & 28 \end{array} \right]$ 
A) 
$\left[ \begin{array} { r r } - 1 & 4 \ 0 & 28 \end{array} \right]$ 
B)

$\left[ \begin{array} { r r } - 1 & - 3 \ 0 & 28 \end{array} \right]$ 
C) 
$\left[ \begin{array} { r r } - 7 & 28 \ 7 & 0 \end{array} \right]$ 
D) 
$\left[ \begin{array} { r r } - 1 & 4 \ 7 & 28 \end{array} \right]$

Question 18

Write the word or phrase that best completes each statement or answers the question.
Which method should be used to solve the system? Explain your answer, including a description of the first step.
$$\begin{array} { r } 
5 x ^ { 2 } - 6 y ^ { 2 } = 16 \
- 7 x - 7 y = - 7
\end{array}$$

Accepted Answer

Substitution should be used, b

Question 19

Graph the solution set of the system of inequalities.
-$\begin{array}{l}
y \geq-x^{2} \
y \leq x+1 \
y \geq-5 \
x \leq-4
\end{array}$

Accepted Answer

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

Question 20

Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
$\begin{array} { r } 
5 x ^ { 2 } + 3 x y - 5 y ^ { 2 } = - 9 \
x ^ { 2 } - x y - y ^ { 2 } = - 5
\end{array}$

Accepted Answer

A)  $\left\{ ( - 1 , - 2 ) , ( 1,2 ) , \left( 2 \mathrm { i } \sqrt { 2 } , - \frac { \mathrm { i } \sqrt { 2 } } { 2 } \right) , \left( - 2 \mathrm { i } \sqrt { 2 } , \frac { \mathrm { i } \sqrt { 2 } } { 2 } \right) \right\}$ 
B)  $\{ ( - 1,2 ) , ( 1 , - 2 ) , ( 2 \mathrm { i } , \mathrm { i } ) , ( - 2 \mathrm { i } , - \mathrm { i } ) \}$ 
C)  $\{ ( - 1 , - 2 ) , ( 1,2 ) , ( 2 i , - i ) , ( - 2 i , i ) \}$ 
D)  $\left\{ ( - 1,2 ) , ( 1 , - 2 ) , \left( 2 \mathrm { i } \sqrt { 2 } , \frac { \mathrm { i } \sqrt { 2 } } { 2 } \right) , \left( - 2 \mathrm { i } \sqrt { 2 } , - \frac { \mathrm { i } \sqrt { 2 } } { 2 } \right) \right\}$ 
A)  $\left\{ ( - 1 , - 2 ) , ( 1,2 ) , \left( 2 \mathrm { i } \sqrt { 2 } , - \frac { \mathrm { i } \sqrt { 2 } } { 2 } \right) , \left( - 2 \mathrm { i } \sqrt { 2 } , \frac { \mathrm { i } \sqrt { 2 } } { 2 } \right) \right\}$ 
B)  $\{ ( - 1,2 ) , ( 1 , - 2 ) , ( 2 \mathrm { i } , \mathrm { i } ) , ( - 2 \mathrm { i } , - \mathrm { i } ) \}$ 
C)  $\{ ( - 1 , - 2 ) , ( 1,2 ) , ( 2 i , - i ) , ( - 2 i , i ) \}$ 
D)  $\left\{ ( - 1,2 ) , ( 1 , - 2 ) , \left( 2 \mathrm { i } \sqrt { 2 } , \frac { \mathrm { i } \sqrt { 2 } } { 2 } \right) , \left( - 2 \mathrm { i } \sqrt { 2 } , - \frac { \mathrm { i } \sqrt { 2 } } { 2 } \right) \right\}$

Find the value of the determinant. $\left| \begin{array} { r r r } 9 & 0 & 0 \\8 & - 1 & 0 \\- 1 & 6 & 3\end{array} \right|$

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

Solve the system using a graphing calculator capable of performing row operations. Give solutions with values correct to the nearest thousandth. - \[\begin{array}{l} \sqrt { 3 } x - 0.9 y + z = - 8\\ \frac { 2 } { 3 } x - y + 2 z = \frac { 5 } { 6 }\\ 6.2 x + 16 y - 5 z = \sqrt { 7 }\\

Find the values of the variables for which the statement is true, if possible. - $\left[ \begin{array} { l l l } 7 & \mathrm { p } + 3 & \mathrm { q } - 7 \end{array} \right] = \left[ \begin{array} { l l l } \mathrm { k } + 2 & 5 & - 7 \end{array} \right]$

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. +3xy+=4 -3xy-=4

Solve the system by using the inverse of the coefficient matrix. - 5x+4y=8 4x-2y=22

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

If the system has infinitely many solutions, write the solution set with x arbitrary. - x+y-2z-8=0 3x+z+6=0 2x-y+3z+14=0

Find the cofactor of the indicated element. a 33 4 3 2 5 4 2 -1 -1 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. -

Suppose that you are solving a system of three linear equations by the Gauss-Jordan method and obtain the following augmented matrix. $\left[ \begin{array} { r r r | r } 1 & - 11 & - 13 & - 30 \\0 & - 14 & - 3 & 1 \\0 & 5 & - 9 & - 26\end{array} \right]$ What row operation would you perform next?

Find the dimensions of a rectangular garden with perimeter 62 yd an $220 \mathrm { yd } ^ { 2 }$

Choose the one alternative that best completes the statement or answers the question. Graph the inequality. $x-y<-2$

Solve the system in terms of the arbitrary variable x. - x+y+z=9 4x-3y+2z=7

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

Use the given row transformation to change the matrix as indicated. - $\left[ \begin{array} { r r } - 1 & 4 \\ 7 & 0 \end{array} \right] ; 7$ times row 1 added to row 2

Write the word or phrase that best completes each statement or answers the question. Which method should be used to solve the system? Explain your answer, including a description of the first step. 5-6=16 -7x-7y=-7

Graph the solution set of the system of inequalities. - y\geq- y\leqx+1 y\geq-5 x\leq-4 $Graph the solution set of the system of inequalities. - \begin{array}{l} y \geq-x^{2} \\ y \leq x+1 \\ y \geq-5 \\ x \leq-4 \end{array}$

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. 5+3xy-5=-9 -xy-=-5

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 value of the determinant. ∣9008−10−163∣\left| \begin{array} { r r r } 9 & 0 & 0 \\8 & - 1 & 0 \\- 1 & 6 & 3\end{array} \right|​98−1​0−16​003​​

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

Solve the system using a graphing calculator capable of performing row operations. Give solutions with values correct to the nearest thousandth. - \[\begin{array}{l} \sqrt { 3 } x - 0.9 y + z = - 8\\ \frac { 2 } { 3 } x - y + 2 z = \frac { 5 } { 6 }\\ 6.2 x + 16 y - 5 z = \sqrt { 7 }\\

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. +3xy+=4 -3xy-=4

Solve the system by using the inverse of the coefficient matrix. - 5x+4y=8 4x-2y=22

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

Graph the solution set of the system of inequalities. - x29+y225≤1\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 25 } \leq 19x2​+25y2​≤1 x225+y29≥1\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 9 } \geq 125x2​+9y2​≥1

If the system has infinitely many solutions, write the solution set with x arbitrary. - x+y-2z-8=0 3x+z+6=0 2x-y+3z+14=0

Find the cofactor of the indicated element. a 33 4 3 2 5 4 2 -1 -1 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. -

Find the dimensions of a rectangular garden with perimeter 62 yd an 220yd2220 \mathrm { yd } ^ { 2 }220yd2

Choose the one alternative that best completes the statement or answers the question. Graph the inequality. x−y<−2x-y<-2x−y<−2

Solve the system in terms of the arbitrary variable x. - x+y+z=9 4x-3y+2z=7

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

Use the given row transformation to change the matrix as indicated. - [−1470];7\left[ \begin{array} { r r } - 1 & 4 \\ 7 & 0 \end{array} \right] ; 7[−17​40​];7 times row 1 added to row 2

Write the word or phrase that best completes each statement or answers the question. Which method should be used to solve the system? Explain your answer, including a description of the first step. 5-6=16 -7x-7y=-7

Graph the solution set of the system of inequalities. - y\geq- y\leqx+1 y\geq-5 x\leq-4

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. 5+3xy-5=-9 -xy-=-5

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 value of the determinant. $\left| \begin{array} { r r r } 9 & 0 & 0 \\8 & - 1 & 0 \\- 1 & 6 & 3\end{array} \right|$

Find the dimensions of a rectangular garden with perimeter 62 yd an $220 \mathrm { yd } ^ { 2 }$

Choose the one alternative that best completes the statement or answers the question. Graph the inequality. $x-y<-2$

Use the given row transformation to change the matrix as indicated. - $\left[ \begin{array} { r r } - 1 & 4 \\ 7 & 0 \end{array} \right] ; 7$ times row 1 added to row 2

Graph the solution set of the system of inequalities. - y\geq- y\leqx+1 y\geq-5 x\leq-4 $Graph the solution set of the system of inequalities. - \begin{array}{l} y \geq-x^{2} \\ y \leq x+1 \\ y \geq-5 \\ x \leq-4 \end{array}$