Question 1

Provide an appropriate response.
-Which one of the following is a description of the graph of the inequality? $$( x + 3 ) ^ { 2 } + ( y + 7 ) ^ { 2 } > 9$$

Accepted Answer

A)  The region outside a circle with center $( - 3 , - 7 )$ and radius 3 
B)  The region outside a circle with center $( 3,7 )$ and radius 3 
C)  The region inside a circle with center $( - 3 , - 7 )$ and radius 3 
D)  The region inside the circle with center $( 3,7 )$ and radius 3 
A)  The region outside a circle with center $( - 3 , - 7 )$ and radius 3 
B)  The region outside a circle with center $( 3,7 )$ and radius 3 
C)  The region inside a circle with center $( - 3 , - 7 )$ and radius 3 
D)  The region inside the circle with center $( 3,7 )$ and radius 3

Question 2

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

Accepted Answer

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

Question 3

Choose the one alternative that best completes the statement or answers the question.
Graph the inequality.
$x^{2}+(y+3)^{2} \leq 25$

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the
solution with y arbitrary.
$\begin{array} { l } 
4 x - 2 y - 10 = 0 \
8 x + y - 25 = 0
\end{array}$

Accepted Answer

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

Question 6

Find the matrix product when possible.
-$$\left[ \begin{array} { r r r } 
- 8 & - 5 & - 8 \
- 5 & - 1 & 7 \
- 6 & - 4 & 9
\end{array} \right] \left[ \begin{array} { r r r } 
4 & 7 & - 2 \
4 & - 7 & 2 \
8 & - 7 & - 7
\end{array} \right]$$

Accepted Answer

A) 
$\left[\begin{array}{rrr}
-8 & -5 & -8 \
-5 & -1 & 7 \
-6 & -4 & 9 \
4 & 7 & -2 \
4 & -7 & 2 \
8 & -7 & -7
\end{array}\right]$ 
B) 
$\left[\begin{array}{rrr}
-116 & 32 & 32 \
35 & -77 & -77 \
62 & -41 & -59
\end{array}\right]$ 
C) 
$\left[\begin{array}{rrr}
-32 & -35 & 16 \
-20 & 7 & 14 \
-48 & 28 & -63
\end{array}\right]$ 
D) 
$$\left[ \begin{array} { r r r } 
- 116 & 35 & 62 \
32 & - 77 & - 41 \
32 & - 77 & - 59
\end{array} \right]$$ 
A) 
$\left[\begin{array}{rrr}
-8 & -5 & -8 \
-5 & -1 & 7 \
-6 & -4 & 9 \
4 & 7 & -2 \
4 & -7 & 2 \
8 & -7 & -7
\end{array}\right]$ 
B) 
$\left[\begin{array}{rrr}
-116 & 32 & 32 \
35 & -77 & -77 \
62 & -41 & -59
\end{array}\right]$ 
C) 
$\left[\begin{array}{rrr}
-32 & -35 & 16 \
-20 & 7 & 14 \
-48 & 28 & -63
\end{array}\right]$ 
D) 
$$\left[ \begin{array} { r r r } 
- 116 & 35 & 62 \
32 & - 77 & - 41 \
32 & - 77 & - 59
\end{array} \right]$$

Question 7

Find the inverse, if it exists, for the matrix.
-$$\left[ \begin{array} { r r r } 
0 & 1 & 1 \
- 5 & 0 & 5 \
0 & 7 & 0
\end{array} \right]$$

Accepted Answer

A)  The inverse does not exist. 
B)  $$\left[ \begin{array} { r r r } 
1 & 0 & 1 \
- \frac { 1 } { 5 } & 0 & 0 \
- \frac { 1 } { 7 } & \frac { 1 } { 7 } & - \frac { 1 } { 7 }
\end{array} \right]$$ 
C) 
$$\left[ \begin{array} { r r r } 
1 & - \frac { 1 } { 5 } & - \frac { 1 } { 7 } \
0 & 0 & \frac { 1 } { 7 } \
1 & 0 & - \frac { 1 } { 7 }
\end{array} \right]$$ 
D) 
$$\left[ \begin{array} { r r r } 
- 1 & - \frac { 1 } { 5 } & - \frac { 1 } { 7 } \
- \frac { 1 } { 7 } & 0 & \frac { 1 } { 7 } \
1 & 0 & 0
\end{array} \right]$$ 
A)  The inverse does not exist. 
B)  $$\left[ \begin{array} { r r r } 
1 & 0 & 1 \
- \frac { 1 } { 5 } & 0 & 0 \
- \frac { 1 } { 7 } & \frac { 1 } { 7 } & - \frac { 1 } { 7 }
\end{array} \right]$$ 
C) 
$$\left[ \begin{array} { r r r } 
1 & - \frac { 1 } { 5 } & - \frac { 1 } { 7 } \
0 & 0 & \frac { 1 } { 7 } \
1 & 0 & - \frac { 1 } { 7 }
\end{array} \right]$$ 
D) 
$$\left[ \begin{array} { r r r } 
- 1 & - \frac { 1 } { 5 } & - \frac { 1 } { 7 } \
- \frac { 1 } { 7 } & 0 & \frac { 1 } { 7 } \
1 & 0 & 0
\end{array} \right]$$

Question 8

Find the value of the determinant.
$\left| \begin{array} { l l l } 
0 & 1 & 5 \
2 & 3 & 2 \
1 & 2 & 5
\end{array} \right|$

Accepted Answer

A)   -7 
B)  47 
C)   -3 
D)  3 
A)   -7 
B)  47 
C)   -3 
D)  3

Question 9

Solve the equation for x.
-$$\left| \begin{array} { r r } 
3 & x \
2 & - 1
\end{array} \right| = 3$$

Accepted Answer

A)  $\{ 3 \}$ 
B)  $\{ 1 \rangle$ 
C)  $\{ - 3 \}$ 
D)  $\left\{ \frac { 3 } { 2 } \right\}$ 
A)  $\{ 3 \}$ 
B)  $\{ 1 \rangle$ 
C)  $\{ - 3 \}$ 
D)  $\left\{ \frac { 3 } { 2 } \right\}$

Question 10

Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set.
8x +5y=32 
3x - 2y=12

Accepted Answer

A)  Cramer's rule does not apply since $\mathrm { D } = 0 ; \varnothing$ 
B)  $\{ ( 4,0 ) \}$ 
C)  $\{ ( 4,1 ) \}$ 
D)  $\{ ( 3,1 ) \}$ 
A)  Cramer's rule does not apply since $\mathrm { D } = 0 ; \varnothing$ 
B)  $\{ ( 4,0 ) \}$ 
C)  $\{ ( 4,1 ) \}$ 
D)  $\{ ( 3,1 ) \}$

Question 11

Solve the problem using matrices.
-Anne and Nancy use a metal alloy that is 18.8% copper to make jewelry. How many ounces of an alloy that is 16% copper must be mixed with an alloy that is 20% copper to form 80 ounces of the desired alloy?

Accepted Answer

A)  61 oz 
B)  24 oz 
C)  26 oz 
D)  56 oz 
A)  61 oz 
B)  24 oz 
C)  26 oz 
D)  56 oz

Question 12

The solution set of the system $y _ { 1 } = - x + 5$ and $y _ { 2 } = - 2 x + 7$ is $\{ ( 2,3 ) \}$. Using slopes and $y$-intercepts, determine which of the two calculator-generated screens, left or right, is the appropriate one for this system.

Accepted Answer

A)  Right 
B)  Left 
C)  Neither is correct. 
D)  Both could be correct. 
A)  Right 
B)  Left 
C)  Neither is correct. 
D)  Both could be correct.

Question 13

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth.
$\begin{array} { l } 
x ^ { 2 } - y ^ { 2 } = 7.82 \
x = 2 y - 5
\end{array}$

Accepted Answer

A)  {(-2.97,-1.01),(6.31,-5.65)} 
B)  {(-2.97,1.01),(6.31,5.65)} 
C)  {(-6.31,-5.65),(2.97,-1.01)} 
D)  {(-6.31,5.65),(2.97,1.01)} 
A)  {(-2.97,-1.01),(6.31,-5.65)} 
B)  {(-2.97,1.01),(6.31,5.65)} 
C)  {(-6.31,-5.65),(2.97,-1.01)} 
D)  {(-6.31,5.65),(2.97,1.01)}

Question 14

Evaluate the determinant.
$\left| \begin{array} { l l l } 
2 & 8 & 5 \
3 & 9 & 8 \
8 & 6 & 2
\end{array} \right|$

Accepted Answer

A)  134 
B)   -890 
C)   -134 
D)  1142 
A)  134 
B)   -890 
C)   -134 
D)  1142

Question 15

Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set.
x+y=4 
5x +5y =20

Accepted Answer

A)  $\{ ( 5 , - 1 ) \}$ 
B)  Cramer's rule does not apply since $D = 0 ; \phi$ 
C)  $\{ ( 0,0 ) \}$ 
D)  Cramer's rule does not apply since $\mathrm { D } = 0 ; \{ ( 4 - \mathrm { y } , \mathrm { y } ) \}$ 
A)  $\{ ( 5 , - 1 ) \}$ 
B)  Cramer's rule does not apply since $D = 0 ; \phi$ 
C)  $\{ ( 0,0 ) \}$ 
D)  Cramer's rule does not apply since $\mathrm { D } = 0 ; \{ ( 4 - \mathrm { y } , \mathrm { y } ) \}$

Question 16

Provide an appropriate response.
-$$\begin{array} { l } 
5 x + 3 y = 19 \
7 x + 8 y = 48
\end{array}$$ If your friend were going to solve this system of equations by first eliminating y, what general suggestions
would you make so your friend could start on this in a systematic way?

Accepted Answer

Answers may vary. One possibility: Multi

Question 17

Use a graphing calculator to Express solutions with approximations to the nearest thousandth.
-$$\begin{array} { l } 
\sqrt { 2 } x - y = 7 \
100 x + y = 9
\end{array}$$

Accepted Answer

A)  $\{ ( 0.157 , - 6.686 ) \}$ 
B)  $\{ ( 0.154 , - 6.444 ) \}$ 
C)  $\{ ( 0.158 , - 6.777 ) \}$ 
D)  $\{ ( 0.020,6.971 ) \}$ 
A)  $\{ ( 0.157 , - 6.686 ) \}$ 
B)  $\{ ( 0.154 , - 6.444 ) \}$ 
C)  $\{ ( 0.158 , - 6.777 ) \}$ 
D)  $\{ ( 0.020,6.971 ) \}$

Question 18

The sizes of two matrices are given. Find the size of the product AB and the size of the product BA, if the given product
can be calculated.
-$A$ is $4 \times 4$; B is $4 \times 4$.

Accepted Answer

A)  $\mathrm { AB }$ is $1 \times 1$; BA is $1 \times 1$. 
B)  $\mathrm { AB }$ is $4 \times 4$; BA is $4 \times 4$. 
C)  $\mathrm { AB }$ is $8 \times 4$; $\mathrm { BA }$ is $8 \times 4$. 
D)  $\mathrm { AB }$ is $4 \times 8$; BA is $4 \times 8$. 
A)  $\mathrm { AB }$ is $1 \times 1$; BA is $1 \times 1$. 
B)  $\mathrm { AB }$ is $4 \times 4$; BA is $4 \times 4$. 
C)  $\mathrm { AB }$ is $8 \times 4$; $\mathrm { BA }$ is $8 \times 4$. 
D)  $\mathrm { AB }$ is $4 \times 8$; BA is $4 \times 8$.

Question 19

The sum of the squares of the digits of a positive two-digit number is 13, and the units digit is 1 more than the tens digit. Find the number.

Accepted Answer

A)  23 
B)  32 
C)  34 
D)  43 
A)  23 
B)  32 
C)  34 
D)  43

Question 20

Graph the solution set of the system of inequalities.
-$$\begin{array} { l } 
\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 16 } \leq 1 \
x ^ { 2 } + y ^ { 2 } \leq 36
\end{array}$$

Accepted Answer

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

Provide an appropriate response. -Which one of the following is a description of the graph of the inequality? $( x + 3 ) ^ { 2 } + ( y + 7 ) ^ { 2 } > 9$

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

Choose the one alternative that best completes the statement or answers the question. Graph the inequality. $x^{2}+(y+3)^{2} \leq 25$ $Choose the one alternative that best completes the statement or answers the question. Graph the inequality. x^{2}+(y+3)^{2} \leq 25$

Graph the solution set of the system of inequalities. - +\leq1 +\leq1 $Graph the solution set of the system of inequalities. - \begin{array}{l} \frac{x^{2}}{9}+\frac{y^{2}}{25} \leq 1 \\ \frac{x^{2}}{25}+\frac{y^{2}}{9} \leq 1 \end{array}$

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the solution with y arbitrary. 4x-2y-10=0 8x+y-25=0

Find the matrix product when possible. - $\left[ \begin{array} { r r r } - 8 & - 5 & - 8 \\- 5 & - 1 & 7 \\- 6 & - 4 & 9\end{array} \right] \left[ \begin{array} { r r r } 4 & 7 & - 2 \\4 & - 7 & 2 \\8 & - 7 & - 7\end{array} \right]$

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { r r r } 0 & 1 & 1 \\- 5 & 0 & 5 \\0 & 7 & 0\end{array} \right]$

Find the value of the determinant. $\left| \begin{array} { l l l } 0 & 1 & 5 \\2 & 3 & 2 \\1 & 2 & 5\end{array} \right|$

Solve the equation for x. - $\left| \begin{array} { r r } 3 & x \\2 & - 1\end{array} \right| = 3$

Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set. 8x +5y=32 3x - 2y=12

Solve the problem using matrices. -Anne and Nancy use a metal alloy that is 18.8% copper to make jewelry. How many ounces of an alloy that is 16% copper must be mixed with an alloy that is 20% copper to form 80 ounces of the desired alloy?

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth. -=7.82 x=2y-5

Evaluate the determinant. $\left| \begin{array} { l l l } 2 & 8 & 5 \\3 & 9 & 8 \\8 & 6 & 2\end{array} \right|$

Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set. x+y=4 5x +5y =20

Provide an appropriate response. - 5x+3y=19 7x+8y=48 If your friend were going to solve this system of equations by first eliminating y, what general suggestions would you make so your friend could start on this in a systematic way?

Use a graphing calculator to Express solutions with approximations to the nearest thousandth. - x-y=7 100x+y=9

The sizes of two matrices are given. Find the size of the product AB and the size of the product BA, if the given product can be calculated. - $A$ is $4 \times 4$ ; B is $4 \times 4$ .

The sum of the squares of the digits of a positive two-digit number is 13, and the units digit is 1 more than the tens digit. Find the number.

Graph the solution set of the system of inequalities. - -\leq1 +\leq36 $Graph the solution set of the system of inequalities. - \begin{array} { l } \frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 16 } \leq 1 \\ x ^ { 2 } + y ^ { 2 } \leq 36 \end{array}$

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

Provide an appropriate response. -Which one of the following is a description of the graph of the inequality? (x+3)2+(y+7)2>9( x + 3 ) ^ { 2 } + ( y + 7 ) ^ { 2 } > 9(x+3)2+(y+7)2>9

Choose the one alternative that best completes the statement or answers the question. Graph the inequality. y≤2x−x2y \leq 2 x-x^{2}y≤2x−x2

Choose the one alternative that best completes the statement or answers the question. Graph the inequality. x2+(y+3)2≤25x^{2}+(y+3)^{2} \leq 25x2+(y+3)2≤25

Graph the solution set of the system of inequalities. - +\leq1 +\leq1

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the solution with y arbitrary. 4x-2y-10=0 8x+y-25=0

Find the inverse, if it exists, for the matrix. - [011−505070]\left[ \begin{array} { r r r } 0 & 1 & 1 \\- 5 & 0 & 5 \\0 & 7 & 0\end{array} \right]​0−50​107​150​​

Find the value of the determinant. ∣015232125∣\left| \begin{array} { l l l } 0 & 1 & 5 \\2 & 3 & 2 \\1 & 2 & 5\end{array} \right|​021​132​525​​

Solve the equation for x. - ∣3x2−1∣=3\left| \begin{array} { r r } 3 & x \\2 & - 1\end{array} \right| = 3​32​x−1​​=3

Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set. 8x +5y=32 3x - 2y=12

Solve the problem using matrices. -Anne and Nancy use a metal alloy that is 18.8% copper to make jewelry. How many ounces of an alloy that is 16% copper must be mixed with an alloy that is 20% copper to form 80 ounces of the desired alloy?

The solution set of the system y1=−x+5y _ { 1 } = - x + 5y1​=−x+5 and y2=−2x+7y _ { 2 } = - 2 x + 7y2​=−2x+7 is {(2,3)}\{ ( 2,3 ) \}{(2,3)} . Using slopes and yyy -intercepts, determine which of the two calculator-generated screens, left or right, is the appropriate one for this system.

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth. -=7.82 x=2y-5

Evaluate the determinant. ∣285398862∣\left| \begin{array} { l l l } 2 & 8 & 5 \\3 & 9 & 8 \\8 & 6 & 2\end{array} \right|​238​896​582​​

Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set. x+y=4 5x +5y =20

Provide an appropriate response. - 5x+3y=19 7x+8y=48 If your friend were going to solve this system of equations by first eliminating y, what general suggestions would you make so your friend could start on this in a systematic way?

Use a graphing calculator to Express solutions with approximations to the nearest thousandth. - x-y=7 100x+y=9

The sizes of two matrices are given. Find the size of the product AB and the size of the product BA, if the given product can be calculated. - AAA is 4×44 \times 44×4 ; B is 4×44 \times 44×4 .

The sum of the squares of the digits of a positive two-digit number is 13, and the units digit is 1 more than the tens digit. Find the number.

Graph the solution set of the system of inequalities. - -\leq1 +\leq36

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

Provide an appropriate response. -Which one of the following is a description of the graph of the inequality? $( x + 3 ) ^ { 2 } + ( y + 7 ) ^ { 2 } > 9$

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

Choose the one alternative that best completes the statement or answers the question. Graph the inequality. $x^{2}+(y+3)^{2} \leq 25$ $Choose the one alternative that best completes the statement or answers the question. Graph the inequality. x^{2}+(y+3)^{2} \leq 25$

Graph the solution set of the system of inequalities. - +\leq1 +\leq1 $Graph the solution set of the system of inequalities. - \begin{array}{l} \frac{x^{2}}{9}+\frac{y^{2}}{25} \leq 1 \\ \frac{x^{2}}{25}+\frac{y^{2}}{9} \leq 1 \end{array}$

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { r r r } 0 & 1 & 1 \\- 5 & 0 & 5 \\0 & 7 & 0\end{array} \right]$

Find the value of the determinant. $\left| \begin{array} { l l l } 0 & 1 & 5 \\2 & 3 & 2 \\1 & 2 & 5\end{array} \right|$

Solve the equation for x. - $\left| \begin{array} { r r } 3 & x \\2 & - 1\end{array} \right| = 3$

Evaluate the determinant. $\left| \begin{array} { l l l } 2 & 8 & 5 \\3 & 9 & 8 \\8 & 6 & 2\end{array} \right|$

The sizes of two matrices are given. Find the size of the product AB and the size of the product BA, if the given product can be calculated. - $A$ is $4 \times 4$ ; B is $4 \times 4$ .

Graph the solution set of the system of inequalities. - -\leq1 +\leq36 $Graph the solution set of the system of inequalities. - \begin{array} { l } \frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 16 } \leq 1 \\ x ^ { 2 } + y ^ { 2 } \leq 36 \end{array}$