Question 1

The graph below shows a system of equations. How many solutions exist for this system?

Accepted Answer

A)  3 
B)  0 
C)  4 
D)  2 
E)  1

Question 2

Write the system of equations that corresponds to the following augmented matrix: $ \left[\begin{array}{cccc}4 & -9 & 0 & 5 \ 8 & 4 & -7 & 2 \ 0 & 4 & 0 & 3\end{array}\right] $

Accepted Answer

A)  $ \left\{\begin{array}{r}4 x-9=5 \ 8 x+4 y-7=2 \ 4 y=3\end{array}\right. $ 
B)  $ \left\{\begin{array}{r}4 x+9 y=5 \ 8 x+4 y+7 z=2 \ 4 y=3\end{array}\right. $ 
C)  $ \left\{\begin{array}{r}4 x-9 y+z=5 \ 8 x+4 y-7 z=2 \ x++y+4 z=3\end{array}\right. $ 
D)  $ \left\{\begin{array}{r}4 x-9 y=5 \ 8 x+4 y-7 z=2 \ 4 y=3\end{array}\right. $ 
E)  $ \left\{\begin{array}{r}4 x+8 y=0 \ -9 x+4 y=4 \ -7 y=0 \ 5 x+2 y=3\end{array}\right. $

Question 3

A chemistry class takes a survey of the number of hours they studied for an exam and the exam score. Of the students who studied less than two hours, 8 students got a score below 60, 3 students got a score between 60 and 80, and 1 above 80. Of the students who studied two to four hours, 3 students got a score below 60, 5 between 60 and 80, and 5 above 80. Of the students who studied more than four hours, 2 student got a score below 60, 1 between 60 and 80, and 4 above 80. Which of the following matrices organizes this data with the columns representing the number of hours students studied and the rows representing the exam score.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 4

Perform the matrix operation as indicated.

Accepted Answer

A)   
B)  None of the above 
C)   
D)   
E)

Question 5

Which one of the following is the augmented matrix in row-echelon form for the system below?

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 6

Perform the matrix operation as indicated.

Accepted Answer

A)   
B)  Not possible 
C)   
D)   
E)

Question 7

Which one of the following is the variable matrix for the following systems of equations? $\left\{\begin{array}{r}
5 x-2 y+6 z=9 \
6 x+2 z=4 \
2 y=3
\end{array}\right.$

Accepted Answer

A)  $\left[\begin{array}{lll}
x & y & z \
x & y & z \
x & y & z
\end{array}\right]$ 
B)  $\left[\begin{array}{l}
9 \
4 \
3
\end{array}\right]$ 
C)  $\left[\begin{array}{lll}
x & y & z
\end{array}\right]$ 
D)  $\left[\begin{array}{ccc}
5 x & -2 y & 6 z \
6 x & 0 y & 2 z \
0 x & 2 y & 0 z
\end{array}\right]$ 
E)  $\left[\begin{array}{l}
x \
y \
z
\end{array}\right]$

Question 8

An investor has $45,000 to invest in three types of accounts. Account A pays 4% annually, Account B pays 6%, and Account C pays 8%. The investor wishes to have a total return of $3000 on the investment, with equal amounts invested in Account B and Account C. How much should be invested in each type of account to satisfy the investor's wishes? Round to the nearest hundredth.

Accepted Answer

A)  Account A = $15,000, Account B = $15,000, Account C = $15,000 
B)  Account A = $25,000, Account B = $10,00, Account C = $10,000 
C)  Account A = $5,000, Account B = $20,000, Account C = $20,000 
D)  There are infinitely many solutions 
E)  No solution

Question 9

A college conducted a survey of students satisfaction with three academic courses: mathematics, English, and science. The results are tabulated in the data matrix below. How many students rate math as average or above?

Accepted Answer

A)  9 
B)  8 
C)  3 
D)  11 
E)  20

Question 10

A family sold jewelry during an art festival over a weekend. They sold bracelets, earrings, and necklaces created by 3 different family members. The matrices  and  tabulate the number of each piece of jewelry sold on Saturday and Sunday. The matrix  gives the price per piece of jewelry (in dollars) for each type sold. Find  .

Accepted Answer

A)   
B)   
C)   
D)  Not possible 
E)

Question 11

Which one of the following is the augmented matrix for the following system of equations.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 12

Find the inverse matrix of  .

Accepted Answer

A)  Not invertible 
B)  $\left[\begin{array}{ccc}
9 & -3 & 5 \
-3 & 1 & -5
\end{array}\right]$ 
C)  $\left[\begin{array}{ccc}
1 / 9 & -1 / 3 & 1 / 5 \
-1 / 3 & 1 & -1 / 5
\end{array}\right]$ 
D)  $\left[\begin{array}{lll}
1 & 0 & 0 \
0 & 1 & 1
\end{array}\right]$ 
E)  $\left[\begin{array}{cc}
9 & -3 \
-3 & 1 \
5 & -5
\end{array}\right]$

Question 13

Find the inverse matrix of  .

Accepted Answer

A)   
B)   
C)  Not invertible 
D)   
E)

Question 14

A college conducted a survey of students satisfaction with three academic courses: mathematics, English, and science. The results are tabulated in the data matrix below. Of the students who were surveyed regarding math, what proportion rated math as excellent?

Accepted Answer

A)  7 
B)  0.41 
C)  2.57 
D)  0.39 
E)  18

Question 15

Solve the system of linear equations. Round to the nearest hundredth.

Accepted Answer

A)  No solution 
B)   
C)   
D)   
E)

Question 16

The cost of a movie ticket at a local theater is $6.50 per child under 12 years old and $11.75 per adult. On a given day, 3000 people purchased a movie ticket, and the ticket costs collected totaled $26,000. How many children and how many adults purchased a movie ticket that day? (Rounded to the nearest whole number.)

Accepted Answer

A)  507 children and 2,493 adults 
B)  1,762 children and 1,238 adults 
C)  1,500 children and 1,500 adults 
D)  5,667 children and 8,667 adults 
E)  1,951 children and 4,951 adults

Question 17

Perform the matrix operation as indicated.

Accepted Answer

A)   
B)   
C)   
D)   
E)  None of the above

Question 18

Which one of the following is the constant matrix for the following systems of equations? $\left\{\begin{array}{r}
4 x-9 y+3 z=8 \
4 x+2 z=3 \
7 y=7
\end{array}\right.$

Accepted Answer

A)  $\left[\begin{array}{ccc}
4 & -9 & 3 \
4 & 0 & 2 \
0 & 7 & 0
\end{array}\right]$ 
B)  $\left[\begin{array}{lll}
8 & 3 & 7
\end{array}\right]$ 
C)  $\left[\begin{array}{l}
8 \
3 \
7
\end{array}\right]$ 
D)  $\left[\begin{array}{l}
x \
y \
z
\end{array}\right]$ 
E)

Question 19

When multiplying 3 matrices, the dimensions of all matrices must be the same.

Accepted Answer

A) True 
 B)False

Question 20

Perform the matrix operation as indicated.

Accepted Answer

A)   
B)   
C)   
D)   
E)  Not possible

Exam 7: Systems of Equations and Data in Categories

The graph below shows a system of equations. How many solutions exist for this system?

Write the system of equations that corresponds to the following augmented matrix: $\left[\begin{array}{cccc}4 & -9 & 0 & 5 \\ 8 & 4 & -7 & 2 \\ 0 & 4 & 0 & 3\end{array}\right]$

Perform the matrix operation as indicated.

Which one of the following is the augmented matrix in row-echelon form for the system below?

Perform the matrix operation as indicated.

Which one of the following is the variable matrix for the following systems of equations? $\left\{\begin{array}{r}5 x-2 y+6 z=9 \\6 x+2 z=4 \\2 y=3\end{array}\right.$

A college conducted a survey of students satisfaction with three academic courses: mathematics, English, and science. The results are tabulated in the data matrix below. How many students rate math as average or above?

Which one of the following is the augmented matrix for the following system of equations.

Find the inverse matrix of .

A college conducted a survey of students satisfaction with three academic courses: mathematics, English, and science. The results are tabulated in the data matrix below. Of the students who were surveyed regarding math, what proportion rated math as excellent?

Solve the system of linear equations. Round to the nearest hundredth.

Perform the matrix operation as indicated.

Which one of the following is the constant matrix for the following systems of equations? $\left\{\begin{array}{r}4 x-9 y+3 z=8 \\4 x+2 z=3 \\7 y=7\end{array}\right.$

When multiplying 3 matrices, the dimensions of all matrices must be the same.

Perform the matrix operation as indicated.

Exam 7: Systems of Equations and Data in Categories

The graph below shows a system of equations. How many solutions exist for this system?

Write the system of equations that corresponds to the following augmented matrix: [4−90584−720403] \left[\begin{array}{cccc}4 & -9 & 0 & 5 \\ 8 & 4 & -7 & 2 \\ 0 & 4 & 0 & 3\end{array}\right] ​480​−944​0−70​523​​

Perform the matrix operation as indicated.

Which one of the following is the augmented matrix in row-echelon form for the system below?

Perform the matrix operation as indicated.

Which one of the following is the variable matrix for the following systems of equations? {5x−2y+6z=96x+2z=42y=3\left\{\begin{array}{r}5 x-2 y+6 z=9 \\6 x+2 z=4 \\2 y=3\end{array}\right.⎩⎨⎧​5x−2y+6z=96x+2z=42y=3​

A college conducted a survey of students satisfaction with three academic courses: mathematics, English, and science. The results are tabulated in the data matrix below. How many students rate math as average or above?

Which one of the following is the augmented matrix for the following system of equations.

Find the inverse matrix of .

Find the inverse matrix of .

A college conducted a survey of students satisfaction with three academic courses: mathematics, English, and science. The results are tabulated in the data matrix below. Of the students who were surveyed regarding math, what proportion rated math as excellent?

Solve the system of linear equations. Round to the nearest hundredth.

Perform the matrix operation as indicated.

Which one of the following is the constant matrix for the following systems of equations? {4x−9y+3z=84x+2z=37y=7\left\{\begin{array}{r}4 x-9 y+3 z=8 \\4 x+2 z=3 \\7 y=7\end{array}\right.⎩⎨⎧​4x−9y+3z=84x+2z=37y=7​

When multiplying 3 matrices, the dimensions of all matrices must be the same.

Perform the matrix operation as indicated.

Write the system of equations that corresponds to the following augmented matrix: $\left[\begin{array}{cccc}4 & -9 & 0 & 5 \\ 8 & 4 & -7 & 2 \\ 0 & 4 & 0 & 3\end{array}\right]$

Which one of the following is the variable matrix for the following systems of equations? $\left\{\begin{array}{r}5 x-2 y+6 z=9 \\6 x+2 z=4 \\2 y=3\end{array}\right.$

Which one of the following is the constant matrix for the following systems of equations? $\left\{\begin{array}{r}4 x-9 y+3 z=8 \\4 x+2 z=3 \\7 y=7\end{array}\right.$