Question 1

Solve the system of inequalities.
-$\begin{array}{r}
2 x+y \leq 4 \
y-1 \leq 0
\end{array}$

Accepted Answer

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

Question 2

Solve the system by substitution.
-x + 9y = 9 -4x + 10y = 10

Accepted Answer

A)  (-1, 0) 
B)  (0, 1) 
C)  (1, 0) 
D)  No solution 
A)  (-1, 0) 
B)  (0, 1) 
C)  (1, 0) 
D)  No solution

Question 3

Solve the problem.
-Factories A and B sent rice to stores 1 and 2. A sent 12 loads and B sent 23. Store 1 used 19 loads and store 2 used 16. It cost $200 to ship from A to 1, $350 from A to 2, $300 from B to 1, and $250 from B to 2. $8500 was spent.
How many loads went where?

Accepted Answer

A)  11 from A to 1 
B)  0 from A to 1 
C)  10 from A to 1 
D)  12 from A to 1 1 from A to 2 12 from A to 2 2 from A to 2 0 from A to 2
8 from B to 1 16 from B to 1 9 from B to 1 7 from B to 1
4 from B to 2 7 from B to 2 14 from B to 2 16 from B to 2 
A)  11 from A to 1 
B)  0 from A to 1 
C)  10 from A to 1 
D)  12 from A to 1 1 from A to 2 12 from A to 2 2 from A to 2 0 from A to 2
8 from B to 1 16 from B to 1 9 from B to 1 7 from B to 1
4 from B to 2 7 from B to 2 14 from B to 2 16 from B to 2

Question 4

Identify the element specified for the matrix.
-$$\left[ \begin{array} { r } 
8 \
9 \
1 \
2 \
- 4
\end{array} \right]$$
a51

Accepted Answer

A)  8 
B)  Does not exist 
C)  $- 4$ 
D)  2 
A)  8 
B)  Does not exist 
C)  $- 4$ 
D)  2

Question 5

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 If the graphs of a system of...

Question 6

Find the matrix product, if possible.
-$$\left[ \begin{array} { r r r } 
7 & - 9 & - 3 \
2 & 4 & 2
\end{array} \right] \left[ \begin{array} { r } 
- 2 \
3 \
4
\end{array} \right]$$

Accepted Answer

A) 
$$\left[ \begin{array} { r r r } 
7 & - 9 & - 3 \
2 & 4 & 2 \
- 2 & 3 & 4
\end{array} \right]$$ 
B) 
$\left[\begin{array}{r}
16 \
-53
\end{array}\right]$ 
C) 
[-53 16] 
D) 
$$\left[ \begin{array} { r } 
- 53 \
16
\end{array} \right]$$ 
A) 
$$\left[ \begin{array} { r r r } 
7 & - 9 & - 3 \
2 & 4 & 2 \
- 2 & 3 & 4
\end{array} \right]$$ 
B) 
$\left[\begin{array}{r}
16 \
-53
\end{array}\right]$ 
C) 
[-53 16] 
D) 
$$\left[ \begin{array} { r } 
- 53 \
16
\end{array} \right]$$

Question 7

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).
-$$\frac { 4 x ^ { 3 } + 8 x ^ { 2 } - 6 x + 2 } { 2 x ^ { 2 } - x - 1 }$$

Accepted Answer

A)  $2 x + 5 - \frac { 13 / 3 } { 2 x + 1 } + \frac { 8 / 3 } { x - 1 }$ 
B)  $2 x - 5 - \frac { 13 } { 2 x + 1 } + \frac { 7 } { x - 1 }$ 
C)  $2 x + 5 - \frac { 7 / 3 } { 2 x + 1 } + \frac { 13 / 3 } { x - 1 }$ 
D)  $2 x - 5 - \frac { 5 / 3 } { 2 x + 1 } + \frac { 1 / 3 } { x - 1 }$ 
A)  $2 x + 5 - \frac { 13 / 3 } { 2 x + 1 } + \frac { 8 / 3 } { x - 1 }$ 
B)  $2 x - 5 - \frac { 13 } { 2 x + 1 } + \frac { 7 } { x - 1 }$ 
C)  $2 x + 5 - \frac { 7 / 3 } { 2 x + 1 } + \frac { 13 / 3 } { x - 1 }$ 
D)  $2 x - 5 - \frac { 5 / 3 } { 2 x + 1 } + \frac { 1 / 3 } { x - 1 }$

Question 8

Solve the system of equations by finding the reduced row echelon form for the augmented matrix.
-$$\begin{array} { c } 
x - y + 3 z = - 3 \
3 x + z = 0 \
x + 5 y + z = 15
\end{array}$$

Accepted Answer

A)  $( 0,0,3 )$ 
B)  $( 0,3 , - 3 )$ 
C)  No solution 
D)  $( 0,3,0 )$ 
A)  $( 0,0,3 )$ 
B)  $( 0,3 , - 3 )$ 
C)  No solution 
D)  $( 0,3,0 )$

Question 9

Identify the element specified for the matrix.
-$$\left[ \begin{array} { r r r r } 
- 5 & 2 & 4 & - 9 \
- 3 & 0 & 7 & - 7 \
- 4 & 2 & 2 & 5 \
6 & - 3 & 9 & - 4
\end{array} \right]$$
a 14

Accepted Answer

A)  6 
B)  $- 4$ 
C)  $- 3$ 
D)  $- 9$ 
A)  6 
B)  $- 4$ 
C)  $- 3$ 
D)  $- 9$

Question 10

Solve the system graphically.
-$$\begin{array} { l } 
y = 2 \sin x \
y - 3 x = 4
\end{array}$$

Accepted Answer

A)  $\approx ( - 1.95 , - 1.86 )$ 
B)  $\approx ( - 1.91 , - 1.88 )$ 
C)  $\approx ( - 1.88 , - 1.90 )$ 
D)  $\approx ( - 1.98 , - 1.84 )$ 
A)  $\approx ( - 1.95 , - 1.86 )$ 
B)  $\approx ( - 1.91 , - 1.88 )$ 
C)  $\approx ( - 1.88 , - 1.90 )$ 
D)  $\approx ( - 1.98 , - 1.84 )$

Question 11

Solve the system of equations by using an inverse matrix.
-$$\begin{array} { l } 
3 x + 5 y = - 10 \
- 2 x - 4 y = 6
\end{array}$$

Accepted Answer

A)  $( 5 , - 1 )$ 
B)  $( 1 , - 5 )$ 
C)  $( - 1,5 )$ 
D)  $( - 5,1 )$ 
A)  $( 5 , - 1 )$ 
B)  $( 1 , - 5 )$ 
C)  $( - 1,5 )$ 
D)  $( - 5,1 )$

Question 12

Solve the problem.
-The total number of cars sold at a used car lot for the years 1996 and 1997 was 1184. From 1996 to 1997 the number of cars sold declined by 158. How many cars were sold in 1996?

Accepted Answer

A)  659 
B)  671 
C)  677 
D)  649 
A)  659 
B)  671 
C)  677 
D)  649

Question 13

Graph the linear inequality.
-$y \geq 2$

Accepted Answer

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

Question 14

Use Gaussian elimination to solve the system of equations.
-x - y + z = 3 x + y + z = 9
X + y - z = 1

Accepted Answer

A)  (4, 2, 3) 
B)  (2, 4, 3) 
C)  No solution 
D)  (2, 3, 4) 
A)  (4, 2, 3) 
B)  (2, 4, 3) 
C)  No solution 
D)  (2, 3, 4)

Question 15

Solve the system of equations.
-x + 2.5y = 8.5 4.5x + z = 0.5
Y - 2.25z = 12

Accepted Answer

A)  No solution 
B)  (1, 3, -4) 
C)  (2, 3, -8.5) 
D)  (1, 3, -3) 
A)  No solution 
B)  (1, 3, -4) 
C)  (2, 3, -8.5) 
D)  (1, 3, -3)

Question 16

Answer the question.
-Find $a , b$, and $c$ so that the graph of the equation $y = a x ^ { 2 } + b x + c$ passes through the points $( - 5 , - 115 ) , ( - 4 , - 73 )$, and $( - 2 , - 19 )$.

Accepted Answer

A)  $y = - 5 x ^ { 2 } - 3 x + 5$ 
B)  $y = - 5 x ^ { 2 } - 3 x - 5$ 
C)  $y = 5 x ^ { 2 } - 3 x - 5$ 
D)  $y = - 5 x ^ { 2 } + 3 x - 5$ 
A)  $y = - 5 x ^ { 2 } - 3 x + 5$ 
B)  $y = - 5 x ^ { 2 } - 3 x - 5$ 
C)  $y = 5 x ^ { 2 } - 3 x - 5$ 
D)  $y = - 5 x ^ { 2 } + 3 x - 5$

Question 17

Write a system of inequalities whose solution set is the region shown.
-

Accepted Answer

A)  $x \geq 0 , y \geq 0 , y \geq \frac { 1 } { 2 } x + 7 , y \geq \frac { 5 } { 2 } x + 15$ 
B)  $x \geq 0 , y \geq 0 , y \geq - \frac { 1 } { 2 } x + 7 , y \geq - \frac { 5 } { 2 } x + 6$ 
C)  $x \geq 0 , y \geq 0 , y \leq - \frac { 1 } { 2 } x + 7 , y \leq - \frac { 5 } { 2 } x + 6$ 
D)  $x \geq 0 , y \geq 0 , y \geq - \frac { 1 } { 2 } x + 7 , y \geq - \frac { 5 } { 2 } x + 15$ 
A)  $x \geq 0 , y \geq 0 , y \geq \frac { 1 } { 2 } x + 7 , y \geq \frac { 5 } { 2 } x + 15$ 
B)  $x \geq 0 , y \geq 0 , y \geq - \frac { 1 } { 2 } x + 7 , y \geq - \frac { 5 } { 2 } x + 6$ 
C)  $x \geq 0 , y \geq 0 , y \leq - \frac { 1 } { 2 } x + 7 , y \leq - \frac { 5 } { 2 } x + 6$ 
D)  $x \geq 0 , y \geq 0 , y \geq - \frac { 1 } { 2 } x + 7 , y \geq - \frac { 5 } { 2 } x + 15$

Question 18

Perform the indicated elementary row operations.
-$\begin{array} { l } 
\mathrm { R } _ { 3 } + \mathrm { R } _ { 2 } \
{ \left[ \begin{array} { r r r } 
3 & - 8 & - 9 \
- 7 & 5 & - 6 \
8 & 4 & 6
\end{array} \right] }
\end{array}$

Accepted Answer

A) $\left[\begin{array}{rrr}
3 & -8 & -9 \
-7 & 5 & -6 \
1 & 9 & 0
\end{array}\right]$ 
B) $\left[\begin{array}{rrr}
3 & -8 & -9 \
8 & 4 & 6 \
-7 & 5 & -6
\end{array}\right]$ 
C) $\left[\begin{array}{rrr}
3 & -17 & -9 \
-7 & -1 & -6 \
8 & 12 & 6
\end{array}\right]$ 
D) $\left[\begin{array}{rrr}
3 & -8 & -9 \
1 & 9 & 0 \
8 & 4 & 6
\end{array}\right]$ 
A) $\left[\begin{array}{rrr}
3 & -8 & -9 \
-7 & 5 & -6 \
1 & 9 & 0
\end{array}\right]$ 
B) $\left[\begin{array}{rrr}
3 & -8 & -9 \
8 & 4 & 6 \
-7 & 5 & -6
\end{array}\right]$ 
C) $\left[\begin{array}{rrr}
3 & -17 & -9 \
-7 & -1 & -6 \
8 & 12 & 6
\end{array}\right]$ 
D) $\left[\begin{array}{rrr}
3 & -8 & -9 \
1 & 9 & 0 \
8 & 4 & 6
\end{array}\right]$

Question 19

Identify the element specified for the matrix.
-$$\left[ \begin{array} { r r r } 
0 & - 4 & 6 \
- 9 & - 7 & - 6 \
- 5 & 5 & 1 \
1 & 3 & - 5
\end{array} \right]$$
a33

Accepted Answer

A)  5 
B)  $- 6$ 
C)  $- 7$ 
D)  1 
A)  5 
B)  $- 6$ 
C)  $- 7$ 
D)  1

Question 20

For any augmented matrix of a system of linear equations, which of the following row transformations will not necessarily result in a matrix of an equivalent system?
(i) Adding to the elements of any row a multiple of the corresponding elements of another row.
(ii) Interchanging any two columns.
(iii) Multiplying the elements of any row by the corresponding elements of another row.
(iv) Multiplying the elements of any row by any nonzero number.

Accepted Answer

A)  (ii) 
B)  (ii), (iii) 
C)  (ii), (iii), (iv) 
D)  (i), (iv) 
A)  (ii) 
B)  (ii), (iii) 
C)  (ii), (iii), (iv) 
D)  (i), (iv)

Solve the system of inequalities. - 2x+y\leq4 y-1\leq0 $Solve the system of inequalities. - \begin{array}{r} 2 x+y \leq 4 \\ y-1 \leq 0 \end{array}$

Solve the system by substitution. -x + 9y = 9 -4x + 10y = 10

Solve the problem. -Factories A and B sent rice to stores 1 and 2. A sent 12 loads and B sent 23. Store 1 used 19 loads and store 2 used 16. It cost $200 to ship from A to 1, $350 from A to 2, $300 from B to 1, and $250 from B to 2. $8500 was spent. How many loads went where?

Identify the element specified for the matrix. - $\left[ \begin{array} { r } 8 \\9 \\1 \\2 \\- 4\end{array} \right]$ a51

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?

Find the matrix product, if possible. - $\left[ \begin{array} { r r r } 7 & - 9 & - 3 \\2 & 4 & 2\end{array} \right] \left[ \begin{array} { r } - 2 \\3 \\4\end{array} \right]$

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). - $\frac { 4 x ^ { 3 } + 8 x ^ { 2 } - 6 x + 2 } { 2 x ^ { 2 } - x - 1 }$

Solve the system of equations by finding the reduced row echelon form for the augmented matrix. - x-y+3z=-3 3x+z=0 x+5y+z=15

Identify the element specified for the matrix. - $\left[ \begin{array} { r r r r } - 5 & 2 & 4 & - 9 \\- 3 & 0 & 7 & - 7 \\- 4 & 2 & 2 & 5 \\6 & - 3 & 9 & - 4\end{array} \right]$ a 14

Solve the system graphically. - y=2x y-3x=4

Solve the system of equations by using an inverse matrix. - 3x+5y=-10 -2x-4y=6

Solve the problem. -The total number of cars sold at a used car lot for the years 1996 and 1997 was 1184. From 1996 to 1997 the number of cars sold declined by 158. How many cars were sold in 1996?

Graph the linear inequality. - $y \geq 2$ $Graph the linear inequality. - y \geq 2$

Use Gaussian elimination to solve the system of equations. -x - y + z = 3 x + y + z = 9 X + y - z = 1

Solve the system of equations. -x + 2.5y = 8.5 4.5x + z = 0.5 Y - 2.25z = 12

Answer the question. -Find $a , b$ , and $c$ so that the graph of the equation $y = a x ^ { 2 } + b x + c$ passes through the points $( - 5 , - 115 ) , ( - 4 , - 73 )$ , and $( - 2 , - 19 )$ .

Write a system of inequalities whose solution set is the region shown. -

Perform the indicated elementary row operations. - + 3 -8 -9 -7 5 -6 8 4 6

Identify the element specified for the matrix. - $\left[ \begin{array} { r r r } 0 & - 4 & 6 \\- 9 & - 7 & - 6 \\- 5 & 5 & 1 \\1 & 3 & - 5\end{array} \right]$ a33

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

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Exam 7: Systems and Matrices

Solve the system of inequalities. - 2x+y\leq4 y-1\leq0