Question 1

Determine the sum or difference in the given clock arithmetic.
-2 + (4 - 5) (clock 6)

Accepted Answer

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

Question 2

Decide whether the given set of numbers is a commutative group under the given operation.
-Rational numbers; multiplication

Accepted Answer

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

Question 3

Perform the indicated operation.
-$$\left[ \begin{array} { r r } 
- 1 & 0 \
3 & 3
\end{array} \right] - \left[ \begin{array} { r r } 
- 1 & 3 \
3 & 1
\end{array} \right]$$

Accepted Answer

A)  $[ - 1 ]$ 
B)  $\left[ \begin{array} { r r } 0 & 3 \ 0 & - 2 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } - 2 & 3 \ 6 & 4 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } 0 & - 3 \ 0 & 2 \end{array} \right]$ 
A)  $[ - 1 ]$ 
B)  $\left[ \begin{array} { r r } 0 & 3 \ 0 & - 2 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } - 2 & 3 \ 6 & 4 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } 0 & - 3 \ 0 & 2 \end{array} \right]$

Question 4

Perform the indicated operation.
-Let $\mathrm { A } = \left[ \begin{array} { r r r } - 4 & 2 & 5 \ 6 & - 1 & 6 \ - 4 & 7 & 7 \end{array} \right]$ and $\mathrm { B } = \left[ \begin{array} { r r r } 1 & - 4 & 4 \ 5 & 3 & 2 \ - 9 & 6 & 7 \end{array} \right]$. Find $\mathrm { A } + \mathrm { B }$.

Accepted Answer

A)  $\left[ \begin{array} { l r r } - 2 & - 3 & 9 \ 11 & 2 & 8 \ - 13 & 13 & 14 \end{array} \right]$ 
B)  $\left[ \begin{array} { l r r } - 3 & - 2 & 9 \ 11 & 2 & 8 \ - 13 & 13 & 14 \end{array} \right]$ 
C)  $\left[ \begin{array} { l r r } - 3 & - 2 & 9 \ 11 & 2 & 8 \ - 13 & 14 & 13 \end{array} \right]$ 
D)  $\left[ \begin{array} { l r r } - 3 & - 2 & 9 \ 11 & - 4 & 8 \ - 13 & 13 & 14 \end{array} \right]$ 
A)  $\left[ \begin{array} { l r r } - 2 & - 3 & 9 \ 11 & 2 & 8 \ - 13 & 13 & 14 \end{array} \right]$ 
B)  $\left[ \begin{array} { l r r } - 3 & - 2 & 9 \ 11 & 2 & 8 \ - 13 & 13 & 14 \end{array} \right]$ 
C)  $\left[ \begin{array} { l r r } - 3 & - 2 & 9 \ 11 & 2 & 8 \ - 13 & 14 & 13 \end{array} \right]$ 
D)  $\left[ \begin{array} { l r r } - 3 & - 2 & 9 \ 11 & - 4 & 8 \ - 13 & 13 & 14 \end{array} \right]$

Question 5

Find the modulo class to which the number belongs for the given modulo system.
-57, mod 13

Accepted Answer

A)  9 
B)  1 
C)  5 
D)  12 
A)  9 
B)  1 
C)  5 
D)  12

Question 6

Decide whether the given set of numbers is a commutative group under the given operation.
-Prime numbers; multiplication

Accepted Answer

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

Question 7

Determine the sum or difference in clock 12 arithmetic.
-(5 + 12) + 7

Accepted Answer

A)  10 
B)  5 
C)  12 
D)  1 
A)  10 
B)  5 
C)  12 
D)  1

Question 8

Find the product, AB, if possible.
-$$A = \left[ \begin{array} { r r } 
- 1 & 3 \
3 & 2
\end{array} \right] , B = \left[ \begin{array} { l l l } 
0 & - 2 & 4 \
1 & - 3 & 2
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { r r r } 0 & - 6 & 12 \ 3 & - 6 & 4 \end{array} \right]$ 
B)  $A B$ is not defined. 
C)  $\left[ \begin{array} { r r } 3 & 2 \ - 7 & - 12 \ 2 & 16 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r } 3 & - 7 & 2 \ 2 & - 12 & 16 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r r } 0 & - 6 & 12 \ 3 & - 6 & 4 \end{array} \right]$ 
B)  $A B$ is not defined. 
C)  $\left[ \begin{array} { r r } 3 & 2 \ - 7 & - 12 \ 2 & 16 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r } 3 & - 7 & 2 \ 2 & - 12 & 16 \end{array} \right]$

Question 9

Solve the problem.
-A company makes three chocolate candies: cherry, almond, and raisin. Matrix A gives the amount Of ingredients in one batch. Matrix B gives the costs of ingredients from suppliers X and Y. Multiply the matrices. $\begin{array} { c } 
\text { sugar choc milk } \quad\quad\quad\quad X\quad Y\\
A = \left[ \begin{array} { l l l } 
4 & 6 & 1 \
5 & 3 & 1 \
3 & 3 & 1
\end{array} \right] \begin{array} { l } 
\text { cherry } \
\text { almond } \
\text { raisin }
\end{array} \quad B = \left[ \begin{array} { l l } 
3 & 2 \
3 & 4 \
2 & 2
\end{array} \right] \begin{array} { l } 
\text { sugar } \
\text { choc } \
\text { milk }
\end{array}
\end{array}$

Accepted Answer

A)  
$\begin{array} { l } 
 \quad\quad\quad\quad \mathrm { X }\quad\quad  Y \
\mathrm { AB } = \left[ \begin{array} { l l } 
32 & 34 \
26 & 24 \
20 & 20
\end{array} \right] \begin{array} { l } 
\text { cherry } \
\text { almond } \
\text { raisin }
\end{array} \
\end{array}$ 
B)  
  
C) 
  
D) 
  
A)  
$\begin{array} { l } 
 \quad\quad\quad\quad \mathrm { X }\quad\quad  Y \
\mathrm { AB } = \left[ \begin{array} { l l } 
32 & 34 \
26 & 24 \
20 & 20
\end{array} \right] \begin{array} { l } 
\text { cherry } \
\text { almond } \
\text { raisin }
\end{array} \
\end{array}$ 
B)  
  
C) 
  
D)

Question 10

Determine the sum or difference in the given clock arithmetic.
-2 + (4 - 4) (clock 7)

Accepted Answer

A)  5 
B)  4 
C)  3 
D)  2 
A)  5 
B)  4 
C)  3 
D)  2

Question 11

Solve the problem.
-If October is your starting month, what month will it be 18 months from October?

Accepted Answer

A)  January 
B)  May 
C)  April 
D)  August 
A)  January 
B)  May 
C)  April 
D)  August

Question 12

Decide whether or not the modulo system forms a group.
-{0, 1, 2, 3, 4, 5, 6}; addition modulo 7

Accepted Answer

A)  Not a group 
B)  Group 
A)  Not a group 
B)  Group

Question 13

Decide whether the given set of numbers is a group under the given operation.
-Natural numbers; addition

Accepted Answer

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

Question 14

Find the product, AB, if possible.
-$A = \left[ \begin{array} { r r } 3 & - 1 \ 3 & 0 \end{array} \right] , B = \left[ \begin{array} { r r } 0 & - 1 \ 3 & 6 \end{array} \right]$

Accepted Answer

A)  $\left[ \begin{array} { l l } 0 & 1 \ 9 & 0 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r } - 3 & 0 \ 27 & - 3 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } - 9 & - 3 \ - 3 & 0 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } - 3 & - 9 \ 0 & - 3 \end{array} \right]$ 
A)  $\left[ \begin{array} { l l } 0 & 1 \ 9 & 0 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r } - 3 & 0 \ 27 & - 3 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } - 9 & - 3 \ - 3 & 0 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } - 3 & - 9 \ 0 & - 3 \end{array} \right]$

Question 15

Find the modulo class to which the number belongs for the given modulo system.
--14, mod 4

Accepted Answer

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

Question 16

Determine the sum or difference in clock 12 arithmetic.
-6 - 5

Accepted Answer

A)  3 
B)  1 
C)  7 
D)  2 
A)  3 
B)  1 
C)  7 
D)  2

Question 17

Decide which of the 5 properties of a commutative group (closure, identity, inverse, associative, commutative) hold for
the given system.
-$$\begin{array} { c | c c c c } 
‡ & 4 & 9 & 14 & 19 \ 
\hline 4 & 14 & 19 & 4 & 9 \
9 & 19 & 4 & 9 & 14 \
14 & 4 & 9 & 14 & 19 \
19 & 9 & 14 & 19 & 4
\end{array}$$

Accepted Answer

A)  Closure, identity, inverse, and commutative only 
B)  Closure, identity, associative, and commutative only 
C)  Closure, identity, inverse, and associative only 
D)  All of them 
A)  Closure, identity, inverse, and commutative only 
B)  Closure, identity, associative, and commutative only 
C)  Closure, identity, inverse, and associative only 
D)  All of them

Question 18

Perform the modular arithmetic operation.
-10 + 13 (mod 8)

Accepted Answer

A)  2 
B)  6 
C)  7 
D)  8 
A)  2 
B)  6 
C)  7 
D)  8

Question 19

Decide whether the given set of numbers is a group under the given operation.
-Rational numbers; multiplication

Accepted Answer

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

Question 20

Provide an appropriate response.
-Is the set of integers closed under the operation of subtraction? Support your claim with an example.

Accepted Answer

Yes; examples will v

Determine the sum or difference in the given clock arithmetic. -2 + (4 - 5) (clock 6)

Decide whether the given set of numbers is a commutative group under the given operation. -Rational numbers; multiplication

Perform the indicated operation. - $\left[ \begin{array} { r r } - 1 & 0 \\3 & 3\end{array} \right] - \left[ \begin{array} { r r } - 1 & 3 \\3 & 1\end{array} \right]$

Find the modulo class to which the number belongs for the given modulo system. -57, mod 13

Decide whether the given set of numbers is a commutative group under the given operation. -Prime numbers; multiplication

Determine the sum or difference in clock 12 arithmetic. -(5 + 12) + 7

Find the product, AB, if possible. - $A = \left[ \begin{array} { r r } - 1 & 3 \\3 & 2\end{array} \right] , B = \left[ \begin{array} { l l l } 0 & - 2 & 4 \\1 & - 3 & 2\end{array} \right]$

Determine the sum or difference in the given clock arithmetic. -2 + (4 - 4) (clock 7)

Solve the problem. -If October is your starting month, what month will it be 18 months from October?

Decide whether or not the modulo system forms a group. -{0, 1, 2, 3, 4, 5, 6}; addition modulo 7

Decide whether the given set of numbers is a group under the given operation. -Natural numbers; addition

Find the product, AB, if possible. - $A = \left[ \begin{array} { r r } 3 & - 1 \\ 3 & 0 \end{array} \right] , B = \left[ \begin{array} { r r } 0 & - 1 \\ 3 & 6 \end{array} \right]$

Find the modulo class to which the number belongs for the given modulo system. --14, mod 4

Determine the sum or difference in clock 12 arithmetic. -6 - 5

Decide which of the 5 properties of a commutative group (closure, identity, inverse, associative, commutative) hold for the given system. - ‡ 4 9 14 19 4 14 19 4 9 9 19 4 9 14 14 4 9 14 19 19 9 14 19 4

Perform the modular arithmetic operation. -10 + 13 (mod 8)

Decide whether the given set of numbers is a group under the given operation. -Rational numbers; multiplication

Provide an appropriate response. -Is the set of integers closed under the operation of subtraction? Support your claim with an example.

Critical Thinking Skills

Sets

Logic

Systems of Numeration

Number Theory and the Real Number System

Algebra, Graphs, and Functions

The Metric System

Consumer Mathematics

Probability

Voting and Apportionment

Filters

Exam 9: Geometry

Determine the sum or difference in the given clock arithmetic. -2 + (4 - 5) (clock 6)

Decide whether the given set of numbers is a commutative group under the given operation. -Rational numbers; multiplication

Perform the indicated operation. - [−1033]−[−1331]\left[ \begin{array} { r r } - 1 & 0 \\3 & 3\end{array} \right] - \left[ \begin{array} { r r } - 1 & 3 \\3 & 1\end{array} \right][−13​03​]−[−13​31​]

Find the modulo class to which the number belongs for the given modulo system. -57, mod 13

Decide whether the given set of numbers is a commutative group under the given operation. -Prime numbers; multiplication

Determine the sum or difference in clock 12 arithmetic. -(5 + 12) + 7

Find the product, AB, if possible. - A=[−1332],B=[0−241−32]A = \left[ \begin{array} { r r } - 1 & 3 \\3 & 2\end{array} \right] , B = \left[ \begin{array} { l l l } 0 & - 2 & 4 \\1 & - 3 & 2\end{array} \right]A=[−13​32​],B=[01​−2−3​42​]

Determine the sum or difference in the given clock arithmetic. -2 + (4 - 4) (clock 7)

Solve the problem. -If October is your starting month, what month will it be 18 months from October?

Decide whether or not the modulo system forms a group. -{0, 1, 2, 3, 4, 5, 6}; addition modulo 7

Decide whether the given set of numbers is a group under the given operation. -Natural numbers; addition

Find the product, AB, if possible. - A=[3−130],B=[0−136]A = \left[ \begin{array} { r r } 3 & - 1 \\ 3 & 0 \end{array} \right] , B = \left[ \begin{array} { r r } 0 & - 1 \\ 3 & 6 \end{array} \right]A=[33​−10​],B=[03​−16​]

Find the modulo class to which the number belongs for the given modulo system. --14, mod 4

Determine the sum or difference in clock 12 arithmetic. -6 - 5

Decide which of the 5 properties of a commutative group (closure, identity, inverse, associative, commutative) hold for the given system. - ‡ 4 9 14 19 4 14 19 4 9 9 19 4 9 14 14 4 9 14 19 19 9 14 19 4

Perform the modular arithmetic operation. -10 + 13 (mod 8)

Decide whether the given set of numbers is a group under the given operation. -Rational numbers; multiplication

Provide an appropriate response. -Is the set of integers closed under the operation of subtraction? Support your claim with an example.

Critical Thinking Skills

Sets

Logic

Systems of Numeration

Number Theory and the Real Number System

Algebra, Graphs, and Functions

The Metric System

Consumer Mathematics

Probability

Voting and Apportionment

Filters

Perform the indicated operation. - $\left[ \begin{array} { r r } - 1 & 0 \\3 & 3\end{array} \right] - \left[ \begin{array} { r r } - 1 & 3 \\3 & 1\end{array} \right]$

Find the product, AB, if possible. - $A = \left[ \begin{array} { r r } - 1 & 3 \\3 & 2\end{array} \right] , B = \left[ \begin{array} { l l l } 0 & - 2 & 4 \\1 & - 3 & 2\end{array} \right]$

Find the product, AB, if possible. - $A = \left[ \begin{array} { r r } 3 & - 1 \\ 3 & 0 \end{array} \right] , B = \left[ \begin{array} { r r } 0 & - 1 \\ 3 & 6 \end{array} \right]$