Question 1

Solve the equation for x.
-$\mathrm { P } ( 0,3 ) , \mathrm { Q } ( 5,8 ) , \mathrm { R } ( 7,3 )$

Accepted Answer

A)  0 
B)  5 
C)  $\frac { 35 } { 2 }$ 
D)  35 
A)  0 
B)  5 
C)  $\frac { 35 } { 2 }$ 
D)  35

Question 2

Provide an appropriate response
-If the graphs of a system of two equations are both circles, what are the possible numbers 
of solutions (with real coordinates) of this system?

Accepted Answer

0, 1, 2, o

Question 3

Provide an appropriate response.
-Suppose that you attempt to solve a system of equations and find that D = 0. What can you conclude about the solutions of this system?

Accepted Answer

A)  The system has no solution. 
B)  The system has exactly one solution. 
C)  The system has an infinite number of solutions. 
D)  The system has either no solution or an infinite number of solutions. 
A)  The system has no solution. 
B)  The system has exactly one solution. 
C)  The system has an infinite number of solutions. 
D)  The system has either no solution or an infinite number of solutions.

Question 4

Provide an appropriate response.
-Suppose that you are solving a system of three linear equations by the Gauss-Jordan method and obtain the following augmented matrix. $$\left[ \begin{array} { r r r | r } 
1 & 11 & - 7 & - 22 \
0 & 1 & 9 & 26 \
0 & - 15 & 5 & 27
\end{array} \right]$$
What row operation would you perform next?

Accepted Answer

A)  Add 15 times row 1 to 11 times row 3 to obtain a zero in the third row, second column position. 
B)  Add row 1 to row 2. 
C)  Multiply row 1 by $\frac { 1 } { 11 }$. 
D)  Multiply row 2 by 1 . 
A)  Add 15 times row 1 to 11 times row 3 to obtain a zero in the third row, second column position. 
B)  Add row 1 to row 2. 
C)  Multiply row 1 by $\frac { 1 } { 11 }$. 
D)  Multiply row 2 by 1 .

Question 5

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

Question 6

Use a graphing calculator and the method of matrix inverses to Give five decimal places, if necessary.
-A basketball fieldhouse seats 15,000 . Courtside seats sell for $\$ 10$, endzone for $\$ 6$, and balcony for $\$$ 5. Total revenue for a sell-out is $\$ 92,000$. If half the courtside and balcony and all the endzone seats are sold, the total revenue is $\$ 52,000$. How many of each type of seat are there in the fieldhouse?

Accepted Answer

A)  4,000 courtside; 3,000 endzone; 8,000 balcony 
B)  2,000 courtside; 5,000 endzone; 8,000 balcony 
C)  3,000 courtside; 2,000 endzone; 10,000 balcony 
D)  3,200 courtside; 1,800 endzone; 10,000 balcony 
A)  4,000 courtside; 3,000 endzone; 8,000 balcony 
B)  2,000 courtside; 5,000 endzone; 8,000 balcony 
C)  3,000 courtside; 2,000 endzone; 10,000 balcony 
D)  3,200 courtside; 1,800 endzone; 10,000 balcony

Question 7

Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set.
-$$\begin{aligned}
x - y & + 5 z = 5 \
3 x & + z = 0 \
x + 4 y & + z = - 20
\end{aligned}$$

Accepted Answer

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

Question 8

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth.
-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)  34 
B)  23 
C)  32 
D)  43 
A)  34 
B)  23 
C)  32 
D)  43

Question 9

Which method should be used to solve the system? Explain your answer, including a description of the first step.
-$$\begin{array} { c } 
3 x ^ { 2 } - 6 y ^ { 2 } = 49 \
x + 2 y = 1
\end{array}$$

Accepted Answer

Substitution should be used, b

Question 10

Which method should be used to solve the system? Explain your answer, including a description of the first step.
-$$\begin{array} { l } 
x ^ { 2 } - y ^ { 2 } = 49 \
x - 4 y = 9
\end{array}$$

Accepted Answer

Substitution should be used, b

Question 11

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth.
-The sum of the squares of the digits of a positive two-digit number is 85 , and the tens digit is 1 less than the units digit. Find the number.

Accepted Answer

A)  76 
B)  65 
C)  67 
D)  56 
A)  76 
B)  65 
C)  67 
D)  56

Question 12

Provide an appropriate response.
-Consider the matrix
$$A = \left[ \begin{array} { r r r } 
2 & 9 & 3 \
4 & 10 & 0 \
- 2 & - 7 & 0
\end{array} \right]$$
Without using a calculator, determine whether $\mathrm { A } ^ { - 1 }$ exists. Explain your reasoning.

Accepted Answer

Expanding

Question 13

If the system has infinitely many solutions, write the solution set with x arbitrary.
-$$\begin{array} { l } 
7 x + 8 y = 7 \
14 x + 16 y = 5
\end{array}$$

Accepted Answer

A)  $\left\{ \left\{ x , \frac { 7 } { 8 } - \frac { 7 } { 8 } x \right) \right\}$ 
B)  $\varnothing$ 
C)  $\left\{ \left\{ x , \frac { 1 } { 2 } - \frac { 7 } { 8 } x \right) \right\}$ 
D)  $\{ ( 0,0 ) \}$ 
A)  $\left\{ \left\{ x , \frac { 7 } { 8 } - \frac { 7 } { 8 } x \right) \right\}$ 
B)  $\varnothing$ 
C)  $\left\{ \left\{ x , \frac { 1 } { 2 } - \frac { 7 } { 8 } x \right) \right\}$ 
D)  $\{ ( 0,0 ) \}$

Question 14

Which method should be used to solve the system? Explain your answer, including a description of the first step.
-$$x \geq - 3$$

Accepted Answer

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

Question 15

Provide an appropriate response.
-Indicate whether the following statement is If every element of a 9 × 9 matrix is 
multiplied by 6, the determinant of the new matrix is 6 times the determinant of the original
matrix.

Accepted Answer

A) True 
 B)False

Question 16

Provide an appropriate response
-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 Provide an appropriate response
-If the graphs of...

Question 17

Provide an appropriate response.
-Which one of the following is a description of the graph of the solution set for the system below?
$$\begin{array} { l } 
4 x ^ { 2 } + 36 y ^ { 2 } < 144 \
y < - 5
\end{array}$$

Accepted Answer

A)  Inside the ellipse and above the line 
B)  Outside the ellipse and above the line 
C)  Inside the ellipse and below the line 
D)  Outside the ellipse and below the line 
A)  Inside the ellipse and above the line 
B)  Outside the ellipse and above the line 
C)  Inside the ellipse and below the line 
D)  Outside the ellipse and below the line

Question 18

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)  $y \leq - 3 x + 5$ 
B)  $y \leq 3 x + 5$ 
C)  $y \geq 3 x + 5$ 
D)  $y \geq - 3 x + 5$ 
A)  $y \leq - 3 x + 5$ 
B)  $y \leq 3 x + 5$ 
C)  $y \geq 3 x + 5$ 
D)  $y \geq - 3 x + 5$

Question 19

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

Accepted Answer

A)  6 
B)  $- 12$ 
C)  0 
D)  $- 6$ 
A)  6 
B)  $- 12$ 
C)  0 
D)  $- 6$

Question 20

Perform the operation or operations when possible.
-$\left[ \begin{array} { l l l } - 1 & 8 & 4 \end{array} \right] - \left[ \begin{array} { l l } 4 & 3 \end{array} \right]$

Accepted Answer

A)  $\left[ \begin{array} { l l l } - 5 & 5 & 1 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l l } - 5 & 8 & 1 \end{array} \right]$ 
C)  $\left[ \begin{array} { l l l } - 5 & 5 & 4 \end{array} \right]$ 
D)  They cannot be subtracted. 
A)  $\left[ \begin{array} { l l l } - 5 & 5 & 1 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l l } - 5 & 8 & 1 \end{array} \right]$ 
C)  $\left[ \begin{array} { l l l } - 5 & 5 & 4 \end{array} \right]$ 
D)  They cannot be subtracted.

Solve the equation for x. - $\mathrm { P } ( 0,3 ) , \mathrm { Q } ( 5,8 ) , \mathrm { R } ( 7,3 )$

Provide an appropriate response -If the graphs of a system of two equations are both circles, what are the possible numbers of solutions (with real coordinates) of this system?

Provide an appropriate response. -Suppose that you attempt to solve a system of equations and find that D = 0. What can you conclude about the solutions of this system?

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

Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set. - x-y +5z=5 3x +z=0 x+4y +z=-20

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

Which method should be used to solve the system? Explain your answer, including a description of the first step. - 3-6=49 x+2y=1

Which method should be used to solve the system? Explain your answer, including a description of the first step. - -=49 x-4y=9

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth. -The sum of the squares of the digits of a positive two-digit number is 85 , and the tens digit is 1 less than the units digit. Find the number.

Provide an appropriate response. -Consider the matrix $A = \left[ \begin{array} { r r r } 2 & 9 & 3 \\4 & 10 & 0 \\- 2 & - 7 & 0\end{array} \right]$ Without using a calculator, determine whether $\mathrm { A } ^ { - 1 }$ exists. Explain your reasoning.

If the system has infinitely many solutions, write the solution set with x arbitrary. - 7x+8y=7 14x+16y=5

Which method should be used to solve the system? Explain your answer, including a description of the first step. - $x \geq - 3$ $Which method should be used to solve the system? Explain your answer, including a description of the first step. - x \geq - 3$

Provide an appropriate response. -Indicate whether the following statement is If every element of a 9 × 9 matrix is multiplied by 6, the determinant of the new matrix is 6 times the determinant of the original matrix.

Provide an appropriate response -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?

Provide an appropriate response. -Which one of the following is a description of the graph of the solution set for the system below? 4+36<144 y<-5

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

Perform the operation or operations when possible. - $\left[ \begin{array} { l l l } - 1 & 8 & 4 \end{array} \right] - \left[ \begin{array} { l l } 4 & 3 \end{array} \right]$

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Analytic Geometry

Further Topics in Algebra

Filters

Exam 10: Systems and Matrices

Solve the equation for x. - P(0,3),Q(5,8),R(7,3)\mathrm { P } ( 0,3 ) , \mathrm { Q } ( 5,8 ) , \mathrm { R } ( 7,3 )P(0,3),Q(5,8),R(7,3)

Provide an appropriate response -If the graphs of a system of two equations are both circles, what are the possible numbers of solutions (with real coordinates) of this system?

Provide an appropriate response. -Suppose that you attempt to solve a system of equations and find that D = 0. What can you conclude about the solutions of this system?

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

Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set. - x-y +5z=5 3x +z=0 x+4y +z=-20

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

Which method should be used to solve the system? Explain your answer, including a description of the first step. - 3-6=49 x+2y=1

Which method should be used to solve the system? Explain your answer, including a description of the first step. - -=49 x-4y=9

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth. -The sum of the squares of the digits of a positive two-digit number is 85 , and the tens digit is 1 less than the units digit. Find the number.

If the system has infinitely many solutions, write the solution set with x arbitrary. - 7x+8y=7 14x+16y=5

Which method should be used to solve the system? Explain your answer, including a description of the first step. - x≥−3x \geq - 3x≥−3

Provide an appropriate response. -Indicate whether the following statement is If every element of a 9 × 9 matrix is multiplied by 6, the determinant of the new matrix is 6 times the determinant of the original matrix.

Provide an appropriate response -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?

Provide an appropriate response. -Which one of the following is a description of the graph of the solution set for the system below? 4+36<144 y<-5

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 value of the determinant. - ∣3003−10−122∣\left| \begin{array} { r r r } 3 & 0 & 0 \\3 & - 1 & 0 \\- 1 & 2 & 2\end{array} \right|​33−1​0−12​002​​

Perform the operation or operations when possible. - [−184]−[43]\left[ \begin{array} { l l l } - 1 & 8 & 4 \end{array} \right] - \left[ \begin{array} { l l } 4 & 3 \end{array} \right][−1​8​4​]−[4​3​]

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Analytic Geometry

Further Topics in Algebra

Filters

Solve the equation for x. - $\mathrm { P } ( 0,3 ) , \mathrm { Q } ( 5,8 ) , \mathrm { R } ( 7,3 )$

Which method should be used to solve the system? Explain your answer, including a description of the first step. - $x \geq - 3$ $Which method should be used to solve the system? Explain your answer, including a description of the first step. - x \geq - 3$

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

Perform the operation or operations when possible. - $\left[ \begin{array} { l l l } - 1 & 8 & 4 \end{array} \right] - \left[ \begin{array} { l l } 4 & 3 \end{array} \right]$