Question 1

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 2

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

Accepted Answer

A)  $( 0,0 )$ and $( 1,2 )$ 
B)  $( 0,0 )$ and $( 1,1 )$ 
C)  $( 1,2 )$ 
D)  $( 0,0 )$ and $( 3,18 )$ 
A)  $( 0,0 )$ and $( 1,2 )$ 
B)  $( 0,0 )$ and $( 1,1 )$ 
C)  $( 1,2 )$ 
D)  $( 0,0 )$ and $( 3,18 )$

Question 3

Perform the indicated elementary row operations.
-$\begin{array}{l}
\text { (6)R2 } \
{\left[\begin{array}{rrr}
-1 & 4 & -4 \
-3 & -5 & -9 \
-11 & 8 & -7
\end{array}\right]}
\end{array}$

Accepted Answer

A) $\begin{array}{l}
\
{\left[\begin{array}{rrr}
-1 & 4 & -4 \
-3 & -5 & -9 \
-11 & 8 & -7
\end{array}\right]}
\end{array}$ 
B) $\left[\begin{array}{rrr}
-6 & 24 & -24 \
-18 & -30 & -54 \
-66 & 48 & -42
\end{array}\right]$ 
C) $\left[\begin{array}{rrr}
-1 & 4 & -4 \
3 & 1 & -3 \
-11 & 8 & -7
\end{array}\right]$ 
D) $\left[\begin{array}{rrr}
-1 & 4 & -4 \
-18 & -30 & -54 \
-11 & 8 & -7
\end{array}\right]$ 
A) $\begin{array}{l}
\
{\left[\begin{array}{rrr}
-1 & 4 & -4 \
-3 & -5 & -9 \
-11 & 8 & -7
\end{array}\right]}
\end{array}$ 
B) $\left[\begin{array}{rrr}
-6 & 24 & -24 \
-18 & -30 & -54 \
-66 & 48 & -42
\end{array}\right]$ 
C) $\left[\begin{array}{rrr}
-1 & 4 & -4 \
3 & 1 & -3 \
-11 & 8 & -7
\end{array}\right]$ 
D) $\left[\begin{array}{rrr}
-1 & 4 & -4 \
-18 & -30 & -54 \
-11 & 8 & -7
\end{array}\right]$

Question 4

Solve the system by elimination.
--x + 2y = -3 2x - 4y = 6

Accepted Answer

A)  (2y - 3, y) 
B)  (3, 0) 
C)  (2y + 3, y) 
D)  (0, - 32 ) 
A)  (2y - 3, y) 
B)  (3, 0) 
C)  (2y + 3, y) 
D)  (0, - 32 )

Question 5

Use a graph to determine the number of solutions the system has.
-$$\begin{array} { l } 
x - 5 y = 3 \
4 x + 5 y = - 13
\end{array}$$

Accepted Answer

A)  Infinitely many solutions 
B)  No solution 
C)  One solution 
A)  Infinitely many solutions 
B)  No solution 
C)  One solution

Question 6

Solve the system algebraically.
-$$\begin{array} { l } 
y = x ^ { 3 } - x ^ { 2 } \
y = 5 x ^ { 2 }
\end{array}$$

Accepted Answer

A)  $( 0,0 )$ and $( 4,80 )$ 
B)  $( 0,0 )$ and $( 6,180 )$ 
C)  $( 0,0 )$ and $( 6,216 )$ 
D)  $( 6,180 )$ 
A)  $( 0,0 )$ and $( 4,80 )$ 
B)  $( 0,0 )$ and $( 6,180 )$ 
C)  $( 0,0 )$ and $( 6,216 )$ 
D)  $( 6,180 )$

Question 7

Solve the system of inequalities.
-$\begin{aligned}
3 x-2 y & \geq-6 \
x-1 & \leq 0
\end{aligned}$

Accepted Answer

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

Question 8

Solve the problem.
-Michael's bank contains only nickels, dimes, and quarters. There are 65 coins in all, valued at $5.35. The number of nickels is 7 short of being three times the sum of the number of dimes and quarters together. How many
Dimes are in the bank?

Accepted Answer

A)  8 
B)  47 
C)  15 
D)  10 
A)  8 
B)  47 
C)  15 
D)  10

Question 9

Determine the order of the matrix.
-$$\left[ \begin{array} { r r r } 
6 & 5 & - 2 \
- 4 & - 5 & 1
\end{array} \right]$$

Accepted Answer

A)  $3 \times 2$ 
B)  6 
C)  $2 \times 3$ 
D)  3 
A)  $3 \times 2$ 
B)  6 
C)  $2 \times 3$ 
D)  3

Question 10

Solve the system graphically.
-$$\begin{array} { l } 
y = \sqrt [ 4 ] { 2 x + 9 } \
x ^ { 2 } + y ^ { 2 } = 5.7
\end{array}$$

Accepted Answer

A)  $\approx ( - 1.50 , - 1.86 )$ and $\approx ( 1.84 , - 1.52 )$ 
B)  $\approx ( - 1.84,1.52 )$ and $\approx ( 1.50,1.86 )$ 
C)  $\approx ( - 1.84 , - 1.52 )$ and $\approx ( 1.50 , - 1.86 )$ 
D)  $\approx ( - 1.50,1.86 )$ and $\approx ( 1.84,1.52 )$ 
A)  $\approx ( - 1.50 , - 1.86 )$ and $\approx ( 1.84 , - 1.52 )$ 
B)  $\approx ( - 1.84,1.52 )$ and $\approx ( 1.50,1.86 )$ 
C)  $\approx ( - 1.84 , - 1.52 )$ and $\approx ( 1.50 , - 1.86 )$ 
D)  $\approx ( - 1.50,1.86 )$ and $\approx ( 1.84,1.52 )$

Question 11

Solve the system of inequalities.
-$\begin{array}{r}
3 x+3 y \leq 18 \
2 x+4 y \leq 24 \
x+y \geq 2 \
x \geq 0 \
y \geq 0
\end{array}$

Accepted Answer

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

Question 12

Perform the indicated elementary row operations.
-$\begin{array} { l } 
(9)\mathrm { R } _ { 1 } + \mathrm { R } _ { 2 } \
{ \left[ \begin{array} { r r } 
8 & 5 \
- 8 & - 1
\end{array} \right] }
\end{array}$

Accepted Answer

A) $\left[\begin{array}{rr}
-64 & -4 \
-8 & -1
\end{array}\right]$ 
B) $\left[\begin{array}{rr}
8 & 5 \
64 & 44
\end{array}\right]$ 
C) $\left[\begin{array}{rr}
72 & 45 \
-8 & -1
\end{array}\right]$ 
D) $\left[\begin{array}{rr}
8 & 77 \
-8 & -73
\end{array}\right]$ 
A) $\left[\begin{array}{rr}
-64 & -4 \
-8 & -1
\end{array}\right]$ 
B) $\left[\begin{array}{rr}
8 & 5 \
64 & 44
\end{array}\right]$ 
C) $\left[\begin{array}{rr}
72 & 45 \
-8 & -1
\end{array}\right]$ 
D) $\left[\begin{array}{rr}
8 & 77 \
-8 & -73
\end{array}\right]$

Question 13

Use Gaussian elimination to solve the system of equations.
-$$x - y + 3 z = - 1$$
$5 \mathrm { x } + \mathrm { z } = 1$
$x + 5 y + z = 21$

Accepted Answer

A)  $( 1,0,4 )$ 
B)  No solution 
C)  $( 0,4,1 )$ 
D)  $( 1,4,0 )$ 
A)  $( 1,0,4 )$ 
B)  No solution 
C)  $( 0,4,1 )$ 
D)  $( 1,4,0 )$

Question 14

Find the determinant of the given matrix.
-$$\left[ \begin{array} { r r r } 
6 & - 3 & 6 \
0 & 9 & 3 \
0 & 0 & - 4
\end{array} \right]$$

Accepted Answer

A)  $- 216$ 
B)  207 
C)  216 
D)  $- 225$ 
A)  $- 216$ 
B)  207 
C)  216 
D)  $- 225$

Question 15

Solve the problem.
-Find the maximum value of $\mathrm { f } = 8 \mathrm { x } + 12 \mathrm { y }$ subject to the following constraints.
$$\begin{array} { l } 
40 x + 80 y \leq 560 \
6 x + 8 y \leq 72 \
x \geq 0 \
y \geq 0
\end{array}$$

Accepted Answer

A)  Maximum of 92 
B)  Maximum of 120 
C)  Maximum of 96 
D)  Maximum of 100 
A)  Maximum of 92 
B)  Maximum of 120 
C)  Maximum of 96 
D)  Maximum of 100

Question 16

Determine whether the matrices are inverses.
-$$\left[ \begin{array} { r r } 
- 5 & - 1 \
6 & 0
\end{array} \right] , \left[ \begin{array} { c } 
0 \frac { 1 } { 6 } \
- 1 \frac { 5 } { 6 }
\end{array} \right]$$

Accepted Answer

A) True 
 B)False

Question 17

Find the inverse of A if it has one, or state that the inverse does not exist.
-$$A = \left[ \begin{array} { r r } 
2 & 8 \
3 & 12
\end{array} \right]$$

Accepted Answer

A) 
$$\left[ \begin{array} { r r } 
12 & - 8 \
- 5 & 3
\end{array} \right]$$ 
B)  Inverse does not exist 
C) 
$$\left[ \begin{array} { r r } 
12 & - 8 \
- 3 & 2
\end{array} \right]$$ 
D) 
$$\left[ \begin{array} { c c } 
\frac { 1 } { 2 } & 0 \
0 & \frac { 1 } { 12 }
\end{array} \right]$$ 
A) 
$$\left[ \begin{array} { r r } 
12 & - 8 \
- 5 & 3
\end{array} \right]$$ 
B)  Inverse does not exist 
C) 
$$\left[ \begin{array} { r r } 
12 & - 8 \
- 3 & 2
\end{array} \right]$$ 
D) 
$$\left[ \begin{array} { c c } 
\frac { 1 } { 2 } & 0 \
0 & \frac { 1 } { 12 }
\end{array} \right]$$

Question 18

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).
-$\frac { 5 x ^ { 2 } - x - 10 } { x ^ { 2 } - 4 }$

Accepted Answer

A)  $5 + \frac { 2 } { x - 2 } - \frac { 3 } { x + 2 }$ 
B)  $\frac { 2 } { x - 2 } - \frac { 3 } { x + 2 }$ 
C)  $5 + \frac { 3 } { x - 2 } - \frac { 2 } { x + 2 }$ 
D)  $5 + \frac { 2 } { x - 2 } + \frac { 3 } { x - 2 }$ 
A)  $5 + \frac { 2 } { x - 2 } - \frac { 3 } { x + 2 }$ 
B)  $\frac { 2 } { x - 2 } - \frac { 3 } { x + 2 }$ 
C)  $5 + \frac { 3 } { x - 2 } - \frac { 2 } { x + 2 }$ 
D)  $5 + \frac { 2 } { x - 2 } + \frac { 3 } { x - 2 }$

Question 19

Find the partial fraction decomposition.
-$$\frac { 3 } { x ^ { 2 } + 4 x + 3 } = \frac { A } { x + 3 } + \frac { B } { x + 1 }$$

Accepted Answer

A)  $A = - \frac { 3 } { 2 } , B = - \frac { 3 } { 2 }$ 
B)  $A = \frac { 3 } { 2 } , B = \frac { 3 } { 2 }$ 
C)  $\mathrm { A } = \frac { 3 } { 2 } , \mathrm {~B} = - \frac { 3 } { 2 }$ 
D)  $\mathrm { A } = - \frac { 3 } { 2 } , \mathrm {~B} = \frac { 3 } { 2 }$ 
A)  $A = - \frac { 3 } { 2 } , B = - \frac { 3 } { 2 }$ 
B)  $A = \frac { 3 } { 2 } , B = \frac { 3 } { 2 }$ 
C)  $\mathrm { A } = \frac { 3 } { 2 } , \mathrm {~B} = - \frac { 3 } { 2 }$ 
D)  $\mathrm { A } = - \frac { 3 } { 2 } , \mathrm {~B} = \frac { 3 } { 2 }$

Question 20

Solve the system of equations by using an inverse matrix.
-$$\begin{aligned}
- 5 x - y + 2 z & = - 29 \
8 x + 8 y + 2 z & = 90 \
- 7 x - 6 y + z & = - 70
\end{aligned}$$

Accepted Answer

A)  $( 5,6,1 )$ 
B)  $\varnothing$ 
C)  $( 5,1,6 )$ 
D)  $( - 5,6,10 )$ 
A)  $( 5,6,1 )$ 
B)  $\varnothing$ 
C)  $( 5,1,6 )$ 
D)  $( - 5,6,10 )$

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?

Solve the system algebraically. - y=+ y=2

Perform the indicated elementary row operations. - (6)R2 -1 4 -4 -3 -5 -9 -11 8 -7

Solve the system by elimination. --x + 2y = -3 2x - 4y = 6

Use a graph to determine the number of solutions the system has. - x-5y=3 4x+5y=-13

Solve the system algebraically. - y=- y=5

Solve the system of inequalities. - 3x-2y \geq-6 x-1 \leq0 $Solve the system of inequalities. - \begin{aligned} 3 x-2 y & \geq-6 \\ x-1 & \leq 0 \end{aligned}$

Solve the problem. -Michael's bank contains only nickels, dimes, and quarters. There are 65 coins in all, valued at $5.35. The number of nickels is 7 short of being three times the sum of the number of dimes and quarters together. How many Dimes are in the bank?

Determine the order of the matrix. - $\left[ \begin{array} { r r r } 6 & 5 & - 2 \\- 4 & - 5 & 1\end{array} \right]$

Solve the system graphically. - y= +=5.7

Solve the system of inequalities. - 3x+3y\leq18 2x+4y\leq24 x+y\geq2 x\geq0 y\geq0 $Solve the system of inequalities. - \begin{array}{r} 3 x+3 y \leq 18 \\ 2 x+4 y \leq 24 \\ x+y \geq 2 \\ x \geq 0 \\ y \geq 0 \end{array}$

Perform the indicated elementary row operations. - (9)+ 8 5 -8 -1

Use Gaussian elimination to solve the system of equations. - $x - y + 3 z = - 1$ $5 \mathrm { x } + \mathrm { z } = 1$ $x + 5 y + z = 21$

Find the determinant of the given matrix. - $\left[ \begin{array} { r r r } 6 & - 3 & 6 \\0 & 9 & 3 \\0 & 0 & - 4\end{array} \right]$

Solve the problem. -Find the maximum value of $\mathrm { f } = 8 \mathrm { x } + 12 \mathrm { y }$ subject to the following constraints. 40x+80y\leq560 6x+8y\leq72 x\geq0 y\geq0

Determine whether the matrices are inverses. - $\left[ \begin{array} { r r } - 5 & - 1 \\6 & 0\end{array} \right] , \left[ \begin{array} { c } 0 \frac { 1 } { 6 } \\- 1 \frac { 5 } { 6 }\end{array} \right]$

Find the inverse of A if it has one, or state that the inverse does not exist. - $A = \left[ \begin{array} { r r } 2 & 8 \\3 & 12\end{array} \right]$

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). - $\frac { 5 x ^ { 2 } - x - 10 } { x ^ { 2 } - 4 }$

Find the partial fraction decomposition. - $\frac { 3 } { x ^ { 2 } + 4 x + 3 } = \frac { A } { x + 3 } + \frac { B } { x + 1 }$

Solve the system of equations by using an inverse matrix. - -5x-y+2z =-29 8x+8y+2z =90 -7x-6y+z =-70

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