Question 1

Find the partial fraction decomposition.
-$$\frac { 3 x - 1 } { x ( x + 1 ) } = \frac { A } { x } + \frac { B } { x + 1 }$$

Accepted Answer

A)  $\mathrm { A } = - 1 , \mathrm {~B} = 4$ 
B)  $A = 1 , B = 4$ 
C)  $\mathrm { A } = - 1 , \mathrm {~B} = - 4$ 
D)  $\mathrm { A } = 1 , \mathrm {~B} = - 4$ 
A)  $\mathrm { A } = - 1 , \mathrm {~B} = 4$ 
B)  $A = 1 , B = 4$ 
C)  $\mathrm { A } = - 1 , \mathrm {~B} = - 4$ 
D)  $\mathrm { A } = 1 , \mathrm {~B} = - 4$

Question 2

Use division to write the rational function in the form q(x) + r(x)/d(x), where the degree of r(x) is less than the degree of
d(x). Then find the partial fraction decomposition of r(x)/d(x).
-$$\frac { 2 x ^ { 3 } - 7 x ^ { 2 } + 5 x - 3 } { x ^ { 2 } + x - 2 }$$

Accepted Answer

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

Question 3

Find the determinant of the given matrix.
-$$\left[ \begin{array} { l l l l } 
0 & 1 & 5 & 5 \
0 & 9 & 2 & 8 \
5 & 2 & 9 & 1 \
7 & 1 & 5 & 2
\end{array} \right]$$

Accepted Answer

A)  30 
B)  $- 1805$ 
C)  $- 15$ 
D)  $- 40$ 
A)  30 
B)  $- 1805$ 
C)  $- 15$ 
D)  $- 40$

Question 4

Find the indicated matrix product or state that the product is undefined.
-$$A = \left[ \begin{array} { r r } 
1 & 2 \
- 4 & 8
\end{array} \right] , B = \left[ \begin{array} { r r r } 
- 7 & - 4 & - 7 \
1 & 6 & - 6
\end{array} \right]$$
BA

Accepted Answer

A) 
$\left[\begin{array}{rrr}
-5 & 8 & -19 \
36 & 64 & -20
\end{array}\right]$ 
B) 
$\left[\begin{array}{rrr}
-7 & -4 & -14 \
-4 & 6 & -48
\end{array}\right]$ 
C) 
$\left[\begin{array}{cc}
-7 & -8 \
-4 & 48
\end{array}\right]$ 
D)  Undefined 
A) 
$\left[\begin{array}{rrr}
-5 & 8 & -19 \
36 & 64 & -20
\end{array}\right]$ 
B) 
$\left[\begin{array}{rrr}
-7 & -4 & -14 \
-4 & 6 & -48
\end{array}\right]$ 
C) 
$\left[\begin{array}{cc}
-7 & -8 \
-4 & 48
\end{array}\right]$ 
D)  Undefined

Question 5

Use the graph to estimate any solutions of the system.
-$$\begin{array} { l } 
5 x - 3 y = 13 \
2 x + y = 3
\end{array}$$

$[ - 5,5 ]$ by $[ - 5,5 ]$

Accepted Answer

A)  $( 2.5 , - 0.5 )$ 
B)  $( 2,1 )$ 
C)  $( 2 , - 1 )$ 
D)  $( 2.5 , - 1 )$ 
A)  $( 2.5 , - 0.5 )$ 
B)  $( 2,1 )$ 
C)  $( 2 , - 1 )$ 
D)  $( 2.5 , - 1 )$

Question 6

Determine which inequality matches the graph.
-

Accepted Answer

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

Question 7

Determine whether the matrices are inverses.
-$$\left[ \begin{array} { l l } 
5 & 3 \
3 & 2
\end{array} \right] , \left[ \begin{array} { r r } 
2 & - 3 \
- 3 & 5
\end{array} \right]$$

Accepted Answer

A) True 
 B)False

Question 8

Solve the system of equations.
-x + 2y + z = -3 x + y + 3z + w = -5

Accepted Answer

A)  (-5z - 2w - 10, 2z + w + 2, z, w) 
B)  (-5z - 2w - 7, 2z + w + 2, z, w) 
C)  No solution 
D)  (-w - 7, w + 1, -w + 2, w) 
A)  (-5z - 2w - 10, 2z + w + 2, z, w) 
B)  (-5z - 2w - 7, 2z + w + 2, z, w) 
C)  No solution 
D)  (-w - 7, w + 1, -w + 2, w)

Question 9

Graph the inequality.
-$y \leq 2\left(x^{2}-1\right)+3$

Accepted Answer

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

Question 10

Find the determinant of the given matrix.
-$$\left[ \begin{array} { l l l l } 
7 & 5 & 4 & 9 \
2 & 5 & 7 & 3 \
5 & 7 & 9 & 2 \
3 & 7 & 7 & 6
\end{array} \right]$$

Accepted Answer

A)  $- 51$ 
B)  $- 304$ 
C)  $- 73$ 
D)  $- 39$ 
A)  $- 51$ 
B)  $- 304$ 
C)  $- 73$ 
D)  $- 39$

Question 11

Solve the problem.
-Find the maximum value of $f = 2 x + 5 y$ subject to the following constraints.
$$\begin{array} { l } 
3 x + 2 y \leq 6 \
- 2 x + 4 y \leq 8 \
x \geq 0 \
y \geq 0
\end{array}$$

Accepted Answer

A)  Maximum of $\frac { 34 } { 3 }$ 
B)  Maximum of $\frac { 49 } { 4 }$ 
C)  Maximum of 19 
D)  Maximum of 10 
A)  Maximum of $\frac { 34 } { 3 }$ 
B)  Maximum of $\frac { 49 } { 4 }$ 
C)  Maximum of 19 
D)  Maximum of 10

Question 12

Find the inverse of A if it has one, or state that the inverse does not exist.
-$$A = \left[ \begin{array} { l l l } 
1 & 3 & 2 \
1 & 3 & 3 \
2 & 7 & 8
\end{array} \right]$$

Accepted Answer

A) 
$$\left[ \begin{array} { l l l } 
1 & \frac { 1 } { 3 } & \frac { 1 } { 2 } \
1 & \frac { 1 } { 3 } & \frac { 1 } { 3 } \
\frac { 1 } { 2 } & \frac { 1 } { 7 } & \frac { 1 } { 8 }
\end{array} \right]$$ 
B)  Inverse does not exist 
C) 
$$\left[ \begin{array} { r r r } 
- 3 & 10 & - 3 \
2 & - 4 & 1 \
- 1 & 1 & 0
\end{array} \right]$$ 
D) 
$$\left[ \begin{array} { l l l } 
- 1 & - 3 & - 2 \
- 1 & - 3 & - 3 \
- 2 & - 7 & - 8
\end{array} \right]$$ 
A) 
$$\left[ \begin{array} { l l l } 
1 & \frac { 1 } { 3 } & \frac { 1 } { 2 } \
1 & \frac { 1 } { 3 } & \frac { 1 } { 3 } \
\frac { 1 } { 2 } & \frac { 1 } { 7 } & \frac { 1 } { 8 }
\end{array} \right]$$ 
B)  Inverse does not exist 
C) 
$$\left[ \begin{array} { r r r } 
- 3 & 10 & - 3 \
2 & - 4 & 1 \
- 1 & 1 & 0
\end{array} \right]$$ 
D) 
$$\left[ \begin{array} { l l l } 
- 1 & - 3 & - 2 \
- 1 & - 3 & - 3 \
- 2 & - 7 & - 8
\end{array} \right]$$

Question 13

Find the indicated matrix product or state that the product is undefined.
-$$
A=\left[\begin{array}{lll}
0 & 0 & 1 \
0 & 1 & 0 \
1 & 0 & 0
\end{array}\right], B=\left[\begin{array}{rrr}
4 & 2 & -1 \
7 & -5 & -9 \
3 & 4 & -7
\end{array}\right]
$$

Accepted Answer

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

Question 14

Solve the system of equations by using an inverse matrix.
-$$\begin{aligned}
9 x - y + 9 z & = 92 \
- 7 x + 3 z & = - 27 \
7 y + z & = 54
\end{aligned}$$

Accepted Answer

A)  $\varnothing$ 
B)  $( 6,5,7 )$ 
C)  $( - 6,7,12 )$ 
D)  $( 6,7,5 )$ 
A)  $\varnothing$ 
B)  $( 6,5,7 )$ 
C)  $( - 6,7,12 )$ 
D)  $( 6,7,5 )$

Question 15

Determine which elementary row operation(s) applied to the first matrix will yield the second matrix.
-

Accepted Answer

The answer of Determine which elementary row operation(s) applied to...

Question 16

Solve the system graphically.
-$$\begin{array} { l } 
y = e ^ { 2 x + 3 } \
2 x + y = 3
\end{array}$$

Accepted Answer

A)  $\approx ( 0.75,4.5 )$ 
B)  $\approx ( - 0.75 , - 4.5 )$ 
C)  $\approx ( - 0.75,4.5 )$ 
D)  $\approx ( 0.75 , - 4.5 )$ 
A)  $\approx ( 0.75,4.5 )$ 
B)  $\approx ( - 0.75 , - 4.5 )$ 
C)  $\approx ( - 0.75,4.5 )$ 
D)  $\approx ( 0.75 , - 4.5 )$

Question 17

Solve the system algebraically.
-$$\begin{array} { l } 
y = 25 x ^ { 2 } + x \
9 x + y = 8
\end{array}$$

Accepted Answer

A)  $\left( \frac { 2 } { 5 } , \frac { 22 } { 5 } \right)$ and $\left( \frac { 4 } { 5 } , \frac { 84 } { 5 } \right)$ 
B)  $\left( - \frac { 2 } { 5 } , \frac { 18 } { 5 } \right)$ and $\left( - \frac { 4 } { 5 } , \frac { 76 } { 5 } \right)$ 
C)  $\left( - \frac { 2 } { 5 } , \frac { 18 } { 5 } \right)$ and $\left( \frac { 4 } { 5 } , \frac { 84 } { 5 } \right)$ 
D)  $\left( \frac { 2 } { 5 } , \frac { 22 } { 5 } \right)$ and $\left( - \frac { 4 } { 5 } , \frac { 76 } { 5 } \right)$ 
A)  $\left( \frac { 2 } { 5 } , \frac { 22 } { 5 } \right)$ and $\left( \frac { 4 } { 5 } , \frac { 84 } { 5 } \right)$ 
B)  $\left( - \frac { 2 } { 5 } , \frac { 18 } { 5 } \right)$ and $\left( - \frac { 4 } { 5 } , \frac { 76 } { 5 } \right)$ 
C)  $\left( - \frac { 2 } { 5 } , \frac { 18 } { 5 } \right)$ and $\left( \frac { 4 } { 5 } , \frac { 84 } { 5 } \right)$ 
D)  $\left( \frac { 2 } { 5 } , \frac { 22 } { 5 } \right)$ and $\left( - \frac { 4 } { 5 } , \frac { 76 } { 5 } \right)$

Question 18

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

Accepted Answer

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

Question 19

Graph the linear inequality.
-$x-y<-5$

Accepted Answer

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

Question 20

Solve the system of equations by finding the reduced row echelon form for the augmented matrix.
-$$\begin{array} { r } 
w - x + 2 y + z = 1 \
x + y = 5 \
y - z = 4
\end{array}$$

Accepted Answer

A)  No solution 
B)  $( - 10,0,5,1 )$ 
C)  $( - 6,1,4 , z )$ 
D)  $( - 6 - 4 z , 1 - z , 4 + z , z )$ 
A)  No solution 
B)  $( - 10,0,5,1 )$ 
C)  $( - 6,1,4 , z )$ 
D)  $( - 6 - 4 z , 1 - z , 4 + z , z )$

Find the partial fraction decomposition. - $\frac { 3 x - 1 } { x ( x + 1 ) } = \frac { A } { x } + \frac { B } { x + 1 }$

Use division to write the rational function in the form q(x) + r(x)/d(x), where the degree of r(x) is less than the degree of d(x). Then find the partial fraction decomposition of r(x)/d(x). - $\frac { 2 x ^ { 3 } - 7 x ^ { 2 } + 5 x - 3 } { x ^ { 2 } + x - 2 }$

Find the determinant of the given matrix. - $\left[ \begin{array} { l l l l } 0 & 1 & 5 & 5 \\0 & 9 & 2 & 8 \\5 & 2 & 9 & 1 \\7 & 1 & 5 & 2\end{array} \right]$

Find the indicated matrix product or state that the product is undefined. - $A = \left[ \begin{array} { r r } 1 & 2 \\- 4 & 8\end{array} \right] , B = \left[ \begin{array} { r r r } - 7 & - 4 & - 7 \\1 & 6 & - 6\end{array} \right]$ BA

Use the graph to estimate any solutions of the system. - 5x-3y=13 2x+y=3 $Use the graph to estimate any solutions of the system. - \begin{array} { l } 5 x - 3 y = 13 \\ 2 x + y = 3 \end{array} [ - 5,5 ] by [ - 5,5 ]$ $[ - 5,5 ]$ by $[ - 5,5 ]$

Determine which inequality matches the graph. -

Determine whether the matrices are inverses. - $\left[ \begin{array} { l l } 5 & 3 \\3 & 2\end{array} \right] , \left[ \begin{array} { r r } 2 & - 3 \\- 3 & 5\end{array} \right]$

Solve the system of equations. -x + 2y + z = -3 x + y + 3z + w = -5

Graph the inequality. - $y \leq 2\left(x^{2}-1\right)+3$ $Graph the inequality. - y \leq 2\left(x^{2}-1\right)+3$

Find the determinant of the given matrix. - $\left[ \begin{array} { l l l l } 7 & 5 & 4 & 9 \\2 & 5 & 7 & 3 \\5 & 7 & 9 & 2 \\3 & 7 & 7 & 6\end{array} \right]$

Solve the problem. -Find the maximum value of $f = 2 x + 5 y$ subject to the following constraints. 3x+2y\leq6 -2x+4y\leq8 x\geq0 y\geq0

Find the inverse of A if it has one, or state that the inverse does not exist. - $A = \left[ \begin{array} { l l l } 1 & 3 & 2 \\1 & 3 & 3 \\2 & 7 & 8\end{array} \right]$

Find the indicated matrix product or state that the product is undefined. - $A=\left[\begin{array}{lll}0 & 0 & 1 \\0 & 1 & 0 \\1 & 0 & 0\end{array}\right], B=\left[\begin{array}{rrr}4 & 2 & -1 \\7 & -5 & -9 \\3 & 4 & -7\end{array}\right]$

Solve the system of equations by using an inverse matrix. - 9x-y+9z =92 -7x+3z =-27 7y+z =54

Determine which elementary row operation(s) applied to the first matrix will yield the second matrix. -

Solve the system graphically. - y= 2x+y=3

Solve the system algebraically. - y=25+x 9x+y=8

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

Graph the linear inequality. - $x-y<-5$

Solve the system of equations by finding the reduced row echelon form for the augmented matrix. - w-x+2y+z=1 x+y=5 y-z=4

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Exam 7: Systems and Matrices

Find the partial fraction decomposition. - 3x−1x(x+1)=Ax+Bx+1\frac { 3 x - 1 } { x ( x + 1 ) } = \frac { A } { x } + \frac { B } { x + 1 }x(x+1)3x−1​=xA​+x+1B​

Find the determinant of the given matrix. - [0155092852917152]\left[ \begin{array} { l l l l } 0 & 1 & 5 & 5 \\0 & 9 & 2 & 8 \\5 & 2 & 9 & 1 \\7 & 1 & 5 & 2\end{array} \right]​0057​1921​5295​5812​​

Use the graph to estimate any solutions of the system. - 5x-3y=13 2x+y=3 [−5,5][ - 5,5 ][−5,5] by [−5,5][ - 5,5 ][−5,5]

Determine which inequality matches the graph. -

Determine whether the matrices are inverses. - [5332],[2−3−35]\left[ \begin{array} { l l } 5 & 3 \\3 & 2\end{array} \right] , \left[ \begin{array} { r r } 2 & - 3 \\- 3 & 5\end{array} \right][53​32​],[2−3​−35​]

Solve the system of equations. -x + 2y + z = -3 x + y + 3z + w = -5

Graph the inequality. - y≤2(x2−1)+3y \leq 2\left(x^{2}-1\right)+3y≤2(x2−1)+3

Find the determinant of the given matrix. - [7549257357923776]\left[ \begin{array} { l l l l } 7 & 5 & 4 & 9 \\2 & 5 & 7 & 3 \\5 & 7 & 9 & 2 \\3 & 7 & 7 & 6\end{array} \right]​7253​5577​4797​9326​​

Solve the problem. -Find the maximum value of f=2x+5yf = 2 x + 5 yf=2x+5y subject to the following constraints. 3x+2y\leq6 -2x+4y\leq8 x\geq0 y\geq0

Find the inverse of A if it has one, or state that the inverse does not exist. - A=[132133278]A = \left[ \begin{array} { l l l } 1 & 3 & 2 \\1 & 3 & 3 \\2 & 7 & 8\end{array} \right]A=​112​337​238​​

Solve the system of equations by using an inverse matrix. - 9x-y+9z =92 -7x+3z =-27 7y+z =54

Determine which elementary row operation(s) applied to the first matrix will yield the second matrix. -

Solve the system graphically. - y= 2x+y=3

Solve the system algebraically. - y=25+x 9x+y=8

Graph the inequality. - y≤3x−x2y \leq 3 x-x^{2}y≤3x−x2

Graph the linear inequality. - x−y<−5x-y<-5x−y<−5

Solve the system of equations by finding the reduced row echelon form for the augmented matrix. - w-x+2y+z=1 x+y=5 y-z=4

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Find the partial fraction decomposition. - $\frac { 3 x - 1 } { x ( x + 1 ) } = \frac { A } { x } + \frac { B } { x + 1 }$

Find the determinant of the given matrix. - $\left[ \begin{array} { l l l l } 0 & 1 & 5 & 5 \\0 & 9 & 2 & 8 \\5 & 2 & 9 & 1 \\7 & 1 & 5 & 2\end{array} \right]$

Use the graph to estimate any solutions of the system. - 5x-3y=13 2x+y=3 $Use the graph to estimate any solutions of the system. - \begin{array} { l } 5 x - 3 y = 13 \\ 2 x + y = 3 \end{array} [ - 5,5 ] by [ - 5,5 ]$ $[ - 5,5 ]$ by $[ - 5,5 ]$

Determine whether the matrices are inverses. - $\left[ \begin{array} { l l } 5 & 3 \\3 & 2\end{array} \right] , \left[ \begin{array} { r r } 2 & - 3 \\- 3 & 5\end{array} \right]$

Graph the inequality. - $y \leq 2\left(x^{2}-1\right)+3$ $Graph the inequality. - y \leq 2\left(x^{2}-1\right)+3$

Find the determinant of the given matrix. - $\left[ \begin{array} { l l l l } 7 & 5 & 4 & 9 \\2 & 5 & 7 & 3 \\5 & 7 & 9 & 2 \\3 & 7 & 7 & 6\end{array} \right]$

Solve the problem. -Find the maximum value of $f = 2 x + 5 y$ subject to the following constraints. 3x+2y\leq6 -2x+4y\leq8 x\geq0 y\geq0

Find the inverse of A if it has one, or state that the inverse does not exist. - $A = \left[ \begin{array} { l l l } 1 & 3 & 2 \\1 & 3 & 3 \\2 & 7 & 8\end{array} \right]$

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

Graph the linear inequality. - $x-y<-5$