Question 1

Find the value of the determinant.
-$$\left| \begin{array} { l l l } 
4 & 4 & 5 \
1 & 0 & 2 \
2 & 1 & 5
\end{array} \right|$$

Accepted Answer

A)  7 
B)  49 
C)  $- 7$ 
D)  $- 39$ 
A)  7 
B)  49 
C)  $- 7$ 
D)  $- 39$

Question 2

Solve the problem.
-The perimeter of a triangle is 81 cm. The triangle is isosceles now, but if its base were lengthened by 4 cm and each leg were shortened by 5 cm, it would be equilateral. Find the length of the base
Of the original triangle.

Accepted Answer

A)  25 cm 
B)  20 cm 
C)  21 cm 
D)  30 cm 
A)  25 cm 
B)  20 cm 
C)  21 cm 
D)  30 cm

Question 3

Find the values of the variables for which the statement is true, if possible.
-$$\left[ \begin{array} { r r r } 
- 2 & 2 & - 6 \
1 & \mathrm {~m} & - 2
\end{array} \right] = \left[ \begin{array} { l l l } 
\mathrm { x } & \mathrm { y } & - 6 \
1 & 1 & - 2
\end{array} \right]$$

Accepted Answer

A)  $x = 2 ; y = - 2 ; m = 1$ 
B)  $x = 2 ; y = - 2 ; m = - 1$ 
C)  $\mathrm { x } = - 2 ; \mathrm { y } = 2 ; \mathrm { m } = 1$ 
D)  $x = 2 ; y = 2 ; m = - 1$ 
A)  $x = 2 ; y = - 2 ; m = 1$ 
B)  $x = 2 ; y = - 2 ; m = - 1$ 
C)  $\mathrm { x } = - 2 ; \mathrm { y } = 2 ; \mathrm { m } = 1$ 
D)  $x = 2 ; y = 2 ; m = - 1$

Question 4

Use Cramerʹs rule to solve the system of equations. If D = 0, use another method to determine the solution set.
-$$\begin{array} { c } 
x + y = 5 \
5 x + 5 y = 25
\end{array}$$

Accepted Answer

A)  Cramer's rule does not apply since $D = 0 ; \varnothing$ 
B)  Cramer's rule does not apply since $D = 0 ; \{ ( 5 - y , y ) \}$ 
C)  $\{ ( 0,0 ) \}$ 
D)  $\{ ( 6 , - 1 ) \}$ 
A)  Cramer's rule does not apply since $D = 0 ; \varnothing$ 
B)  Cramer's rule does not apply since $D = 0 ; \{ ( 5 - y , y ) \}$ 
C)  $\{ ( 0,0 ) \}$ 
D)  $\{ ( 6 , - 1 ) \}$

Question 5

Solve the system for x and y using Cramerʹs rule. Assume a and b are nonzero constants.
-$$\begin{array} { l } 
\frac { 1 } { a } x + \frac { 1 } { b } y = a b \
x + y = a
\end{array}$$

Accepted Answer

A)  $\left. \left\{ \frac { a ( b - a ) \left( b ^ { 2 } - 1 \right) } { a b ^ { 2 } } , \frac { ( b - a ) ( 1 - a b ) } { a b } \right) \right\}$ 
B)  $\left\{ \left( a b ( 1 - a b ) , a ^ { 2 } \left( b ^ { 2 } - 1 \right) \right) \right\}$ 
C)  $\left\{ \left( \frac { a ^ { 2 } \left( b ^ { 2 } - 1 \right) } { b - a } , \frac { a b ( 1 - a b ) } { b - a } \right) \right\}$ 
D)  $\left\{ \left( \frac { a ^ { 2 } b \left( b ^ { 2 } - 1 \right) } { b - a } , \frac { a b ( 1 - a b ) } { b - a } \right) \right\}$ 
A)  $\left. \left\{ \frac { a ( b - a ) \left( b ^ { 2 } - 1 \right) } { a b ^ { 2 } } , \frac { ( b - a ) ( 1 - a b ) } { a b } \right) \right\}$ 
B)  $\left\{ \left( a b ( 1 - a b ) , a ^ { 2 } \left( b ^ { 2 } - 1 \right) \right) \right\}$ 
C)  $\left\{ \left( \frac { a ^ { 2 } \left( b ^ { 2 } - 1 \right) } { b - a } , \frac { a b ( 1 - a b ) } { b - a } \right) \right\}$ 
D)  $\left\{ \left( \frac { a ^ { 2 } b \left( b ^ { 2 } - 1 \right) } { b - a } , \frac { a b ( 1 - a b ) } { b - a } \right) \right\}$

Question 6

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.
-$\mathrm { P } ( - 4,2 ) , \mathrm { Q } ( - 2 , - 5 ) , \mathrm { R } ( 4 , - 3 )$

Accepted Answer

A)  46 
B)  0 
C)  23 
D)  11 
A)  46 
B)  0 
C)  23 
D)  11

Question 7

Use the shading capabilities of your graphing calculator to graph the inequality or system of inequalities.
-

Accepted Answer

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

Question 8

Solve the system.
-$$\begin{array} { l } 
\frac { 7 } { x } - \frac { 5 } { y } = \frac { 7 } { 2 } \
\frac { 6 } { x } + \frac { 5 } { y } = - \frac { 23 } { 14 }
\end{array}$$

Accepted Answer

A)  $\{ ( - 2 , - 7 ) \}$ 
B)  $\{ ( 7,2 ) \}$ 
C)  $\left\{ \left( - \frac { 329 } { 240 } , - 2 \right) \right\}$ 
D)  $\{ ( 7 , - 2 ) \}$ 
A)  $\{ ( - 2 , - 7 ) \}$ 
B)  $\{ ( 7,2 ) \}$ 
C)  $\left\{ \left( - \frac { 329 } { 240 } , - 2 \right) \right\}$ 
D)  $\{ ( 7 , - 2 ) \}$

Question 9

Which method should be used to solve the system? Explain your answer, including a description of the first step.
-$$x ^ { 2 } + y ^ { 2 } = 25$$

Accepted Answer

Substitution should be used, b

Question 10

Find the cofactor of the indicated element.
-$\text { a11 }$
$\left|\begin{array}{rrr}
-1 & 0 & 2 \
2 & 2 & 4 \
2 & 5 & 1
\end{array}\right|$

Accepted Answer

A)  6 
B)  18 
C)  $- 18$ 
D)  $- 2$ 
A)  6 
B)  18 
C)  $- 18$ 
D)  $- 2$

Question 11

Write the system of equations associated with the augmented matrix. Do not solve.
-$\left[ \begin{array} { r r r | r } 1 & 0 & 0 & 4 \ 0 & 1 & 0 & - 8 \ 0 & 0 & 1 & 2 \end{array} \right]$

Accepted Answer

A)  $x = - 4$
$\mathrm { y } = 8$
$\mathrm { z } = - 2$ 
B)  $x = 0$
$y = - 4$
$z = 6$ 
C)  $x = 2$
$y = - 10$
$z = 0$ 
D)  $x = 4$
$y = - 8$
$z = 2$ 
A)  $x = - 4$
$\mathrm { y } = 8$
$\mathrm { z } = - 2$ 
B)  $x = 0$
$y = - 4$
$z = 6$ 
C)  $x = 2$
$y = - 10$
$z = 0$ 
D)  $x = 4$
$y = - 8$
$z = 2$

Question 12

Find the indicated matrix.
-Let $C = \left[ \begin{array} { r } 4 \ - 2 \ 8 \end{array} \right]$. Find $\frac { 1 } { 2 } C$

Accepted Answer

A) 
$\left[ \begin{array} { r } 8 \ - 4 \ 16 \end{array} \right]$ 
B) 
$\left[ \begin{array} { r } 2 \ - 1 \ 4 \end{array} \right]$ 
C) 
$\left[ \begin{array} { r } 2 \ - 2 \ 8 \end{array} \right]$ 
D) 
$\left[ \begin{array} { r } 4 \ - 1 \ 8 \end{array} \right]$ 
A) 
$\left[ \begin{array} { r } 8 \ - 4 \ 16 \end{array} \right]$ 
B) 
$\left[ \begin{array} { r } 2 \ - 1 \ 4 \end{array} \right]$ 
C) 
$\left[ \begin{array} { r } 2 \ - 2 \ 8 \end{array} \right]$ 
D) 
$\left[ \begin{array} { r } 4 \ - 1 \ 8 \end{array} \right]$

Question 13

Find the inverse, if it exists, for the matrix.
-$\left[ \begin{array} { l l l } 1 & 0 & 8 \ 1 & 2 & 3 \ 2 & 5 & 3 \end{array} \right]$

Accepted Answer

A)  The inverse does not exist. 
B) 
$$\left[ \begin{array} { r r r } 
9 & - 40 & 16 \
- 3 & 13 & - 5 \
- 1 & 5 & - 2
\end{array} \right]$$ 
C) 
$\left[ \begin{array} { l l l } 1 & 1 & 2 \ 0 & 2 & 5 \ 8 & 3 & 3 \end{array} \right]$ 
D) 
$$\left[ \begin{array} { r r r } 
- 1 & 0 & - 8 \
- 1 & - 2 & - 3 \
- 2 & - 5 & - 3
\end{array} \right]$$ 
A)  The inverse does not exist. 
B) 
$$\left[ \begin{array} { r r r } 
9 & - 40 & 16 \
- 3 & 13 & - 5 \
- 1 & 5 & - 2
\end{array} \right]$$ 
C) 
$\left[ \begin{array} { l l l } 1 & 1 & 2 \ 0 & 2 & 5 \ 8 & 3 & 3 \end{array} \right]$ 
D) 
$$\left[ \begin{array} { r r r } 
- 1 & 0 & - 8 \
- 1 & - 2 & - 3 \
- 2 & - 5 & - 3
\end{array} \right]$$

Question 14

A nonlinear system is given, along with the graphs of both equations in the system. Determine if the points of
intersection specified on the graph are solutions of the system by substituting directly into both equations.
-$$\begin{array} { l } 
y = \ln ( 4 x + 2 ) \
y = \sqrt { ( x - 3 ) ^ { 3 } + 0.5 ( x - 7 ) }
\end{array}$$

Accepted Answer

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

Question 15

Solve the system for x and y using Cramerʹs rule. Assume a and b are nonzero constants.
-$$\begin{array} { l } 
a ^ { 2 } x + b ^ { 2 } y = b ^ { 2 } \
a x + b y = a
\end{array}$$

Accepted Answer

A)  $\left\{ \left( - \frac { b } { a } , \frac { a + b } { b } \right) \right\}$ 
B)  $\left\{ \left( \frac { b } { a } , \frac { a - b } { b } \right) \right\}$ 
C)  $\left\{ \left( \frac { \mathrm { a } } { \mathrm { b } } , \frac { \mathrm { a } - \mathrm { b } } { \mathrm { b } } \right) \right\}$ 
D)  $\left\{ \left( \frac { b } { a } , \frac { a + b } { b } \right) \right\}$ 
A)  $\left\{ \left( - \frac { b } { a } , \frac { a + b } { b } \right) \right\}$ 
B)  $\left\{ \left( \frac { b } { a } , \frac { a - b } { b } \right) \right\}$ 
C)  $\left\{ \left( \frac { \mathrm { a } } { \mathrm { b } } , \frac { \mathrm { a } - \mathrm { b } } { \mathrm { b } } \right) \right\}$ 
D)  $\left\{ \left( \frac { b } { a } , \frac { a + b } { b } \right) \right\}$

Question 16

Provide an appropriate response.
-What is the value of
$$\left| \begin{array} { l l l } 
\mathrm { m } & \mathrm { n } & \mathrm { p } \
0 & 0 & 0 \
\mathrm { q } & \mathrm { r } & \mathrm { s }
\end{array} \right|$$
for any values of the variables?

Accepted Answer

A)  1 
B)  undefined 
C)  -1 
D)  0 
A)  1 
B)  undefined 
C)  -1 
D)  0

Question 17

Graph the inequality.
-$y \geq-6 x^{2}-3$

Accepted Answer

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

Question 18

Graph the solution set of the system of inequalities.
-$$\begin{array} { c } 
3 x - 2 y \leq 6 \
x - 1 \geq 0
\end{array}$$

Accepted Answer

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

Question 19

Use a graphing calculator to find the value of the determinant.
-$$\left| \begin{array} { r r r } 
0 & - 4 & - 3 \
5 & 4 & 5 \
1 & - 5 & - 5
\end{array} \right|$$

Accepted Answer

A)  33 
B)  $- 33$ 
C)  7 
D)  143 
A)  33 
B)  $- 33$ 
C)  7 
D)  143

Question 20

Solve the problem using matrices.
-John has a jarful of quarters and nickels. There are 88 coins in the jar. The value of the coins is $\$ 12.40$. How many of each type of coin are there?

Accepted Answer

A)  45 quarters ; 43 nickels 
B)  40 quarters; 48 nickels 
C)  83 quarters; 5 nickels 
D)  48 quarters; 40 nickels 
A)  45 quarters ; 43 nickels 
B)  40 quarters; 48 nickels 
C)  83 quarters; 5 nickels 
D)  48 quarters; 40 nickels

Find the value of the determinant. - $\left| \begin{array} { l l l } 4 & 4 & 5 \\1 & 0 & 2 \\2 & 1 & 5\end{array} \right|$

Solve the problem. -The perimeter of a triangle is 81 cm. The triangle is isosceles now, but if its base were lengthened by 4 cm and each leg were shortened by 5 cm, it would be equilateral. Find the length of the base Of the original triangle.

Find the values of the variables for which the statement is true, if possible. - $\left[ \begin{array} { r r r } - 2 & 2 & - 6 \\1 & \mathrm {~m} & - 2\end{array} \right] = \left[ \begin{array} { l l l } \mathrm { x } & \mathrm { y } & - 6 \\1 & 1 & - 2\end{array} \right]$

Use Cramerʹs rule to solve the system of equations. If D = 0, use another method to determine the solution set. - x+y=5 5x+5y=25

Solve the system for x and y using Cramerʹs rule. Assume a and b are nonzero constants. - x+y=ab x+y=a

Use the shading capabilities of your graphing calculator to graph the inequality or system of inequalities. -

Solve the system. - -= +=-

Which method should be used to solve the system? Explain your answer, including a description of the first step. - $x ^ { 2 } + y ^ { 2 } = 25$

Find the cofactor of the indicated element. - $\text { a11 }$ $\left|\begin{array}{rrr}-1 & 0 & 2 \\2 & 2 & 4 \\2 & 5 & 1\end{array}\right|$

Write the system of equations associated with the augmented matrix. Do not solve. - $\left[ \begin{array} { r r r | r } 1 & 0 & 0 & 4 \\ 0 & 1 & 0 & - 8 \\ 0 & 0 & 1 & 2 \end{array} \right]$

Find the indicated matrix. -Let $C = \left[ \begin{array} { r } 4 \\ - 2 \\ 8 \end{array} \right]$ . Find $\frac { 1 } { 2 } C$

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { l l l } 1 & 0 & 8 \\ 1 & 2 & 3 \\ 2 & 5 & 3 \end{array} \right]$

Solve the system for x and y using Cramerʹs rule. Assume a and b are nonzero constants. - x+y= ax+by=a

Provide an appropriate response. -What is the value of $\left| \begin{array} { l l l } \mathrm { m } & \mathrm { n } & \mathrm { p } \\0 & 0 & 0 \\\mathrm { q } & \mathrm { r } & \mathrm { s }\end{array} \right|$ for any values of the variables?

Graph the inequality. - $y \geq-6 x^{2}-3$ $Graph the inequality. - y \geq-6 x^{2}-3$

Graph the solution set of the system of inequalities. - 3x-2y\leq6 x-1\geq0 $Graph the solution set of the system of inequalities. - \begin{array} { c } 3 x - 2 y \leq 6 \\ x - 1 \geq 0 \end{array}$

Use a graphing calculator to find the value of the determinant. - $\left| \begin{array} { r r r } 0 & - 4 & - 3 \\5 & 4 & 5 \\1 & - 5 & - 5\end{array} \right|$

Solve the problem using matrices. -John has a jarful of quarters and nickels. There are 88 coins in the jar. The value of the coins is $\$ 12.40$ . How many of each type of coin are there?

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

Review of Basic Concepts

Filters

Exam 9: Systems and Matrices

Find the value of the determinant. - ∣445102215∣\left| \begin{array} { l l l } 4 & 4 & 5 \\1 & 0 & 2 \\2 & 1 & 5\end{array} \right|​412​401​525​​

Solve the problem. -The perimeter of a triangle is 81 cm. The triangle is isosceles now, but if its base were lengthened by 4 cm and each leg were shortened by 5 cm, it would be equilateral. Find the length of the base Of the original triangle.

Use Cramerʹs rule to solve the system of equations. If D = 0, use another method to determine the solution set. - x+y=5 5x+5y=25

Solve the system for x and y using Cramerʹs rule. Assume a and b are nonzero constants. - x+y=ab x+y=a

Use the shading capabilities of your graphing calculator to graph the inequality or system of inequalities. -

Solve the system. - -= +=-

Which method should be used to solve the system? Explain your answer, including a description of the first step. - x2+y2=25x ^ { 2 } + y ^ { 2 } = 25x2+y2=25

Find the cofactor of the indicated element. - a11 \text { a11 } a11 ∣−102224251∣\left|\begin{array}{rrr}-1 & 0 & 2 \\2 & 2 & 4 \\2 & 5 & 1\end{array}\right|​−122​025​241​​

Write the system of equations associated with the augmented matrix. Do not solve. - [1004010−80012]\left[ \begin{array} { r r r | r } 1 & 0 & 0 & 4 \\ 0 & 1 & 0 & - 8 \\ 0 & 0 & 1 & 2 \end{array} \right]​100​010​001​4−82​​

Find the indicated matrix. -Let C=[4−28]C = \left[ \begin{array} { r } 4 \\ - 2 \\ 8 \end{array} \right]C=​4−28​​ . Find 12C\frac { 1 } { 2 } C21​C

Find the inverse, if it exists, for the matrix. - [108123253]\left[ \begin{array} { l l l } 1 & 0 & 8 \\ 1 & 2 & 3 \\ 2 & 5 & 3 \end{array} \right]​112​025​833​​

A nonlinear system is given, along with the graphs of both equations in the system. Determine if the points of intersection specified on the graph are solutions of the system by substituting directly into both equations. - y=(4x+2) y=

Solve the system for x and y using Cramerʹs rule. Assume a and b are nonzero constants. - x+y= ax+by=a

Provide an appropriate response. -What is the value of ∣mnp000qrs∣\left| \begin{array} { l l l } \mathrm { m } & \mathrm { n } & \mathrm { p } \\0 & 0 & 0 \\\mathrm { q } & \mathrm { r } & \mathrm { s }\end{array} \right|​m0q​n0r​p0s​​ for any values of the variables?

Graph the inequality. - y≥−6x2−3y \geq-6 x^{2}-3y≥−6x2−3

Graph the solution set of the system of inequalities. - 3x-2y\leq6 x-1\geq0

Use a graphing calculator to find the value of the determinant. - ∣0−4−35451−5−5∣\left| \begin{array} { r r r } 0 & - 4 & - 3 \\5 & 4 & 5 \\1 & - 5 & - 5\end{array} \right|​051​−44−5​−35−5​​

Solve the problem using matrices. -John has a jarful of quarters and nickels. There are 88 coins in the jar. The value of the coins is $12.40\$ 12.40$12.40 . How many of each type of coin are there?

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

Review of Basic Concepts

Filters

Find the value of the determinant. - $\left| \begin{array} { l l l } 4 & 4 & 5 \\1 & 0 & 2 \\2 & 1 & 5\end{array} \right|$

Which method should be used to solve the system? Explain your answer, including a description of the first step. - $x ^ { 2 } + y ^ { 2 } = 25$

Find the cofactor of the indicated element. - $\text { a11 }$ $\left|\begin{array}{rrr}-1 & 0 & 2 \\2 & 2 & 4 \\2 & 5 & 1\end{array}\right|$

Write the system of equations associated with the augmented matrix. Do not solve. - $\left[ \begin{array} { r r r | r } 1 & 0 & 0 & 4 \\ 0 & 1 & 0 & - 8 \\ 0 & 0 & 1 & 2 \end{array} \right]$

Find the indicated matrix. -Let $C = \left[ \begin{array} { r } 4 \\ - 2 \\ 8 \end{array} \right]$ . Find $\frac { 1 } { 2 } C$

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { l l l } 1 & 0 & 8 \\ 1 & 2 & 3 \\ 2 & 5 & 3 \end{array} \right]$

Provide an appropriate response. -What is the value of $\left| \begin{array} { l l l } \mathrm { m } & \mathrm { n } & \mathrm { p } \\0 & 0 & 0 \\\mathrm { q } & \mathrm { r } & \mathrm { s }\end{array} \right|$ for any values of the variables?

Graph the inequality. - $y \geq-6 x^{2}-3$ $Graph the inequality. - y \geq-6 x^{2}-3$

Graph the solution set of the system of inequalities. - 3x-2y\leq6 x-1\geq0 $Graph the solution set of the system of inequalities. - \begin{array} { c } 3 x - 2 y \leq 6 \\ x - 1 \geq 0 \end{array}$

Use a graphing calculator to find the value of the determinant. - $\left| \begin{array} { r r r } 0 & - 4 & - 3 \\5 & 4 & 5 \\1 & - 5 & - 5\end{array} \right|$

Solve the problem using matrices. -John has a jarful of quarters and nickels. There are 88 coins in the jar. The value of the coins is $\$ 12.40$ . How many of each type of coin are there?