Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

Determine the sum or difference in clock 12 arithmetic.
-10 + 2

Accepted Answer

A)  0 
B)  24 
C)  undefined 
D)  12 
A)  0 
B)  24 
C)  undefined 
D)  12

Question 4

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. What is The cost of 100 batches from supplier X? $ \quad \quad \quad \quad \quad\text { sugar choc milk } \ \quad \quad \quad \quad \quad  \quad \quad \quad  \quad\quad X \quad Y$

$$A = \left[ \begin{array} { r r r } 
4 & 6 & 1 \
5 & 3 & 1 \
3 & 3 & 1
\end{array} \right] \text { cherry } \text { almond } \quad B = \left[ \begin{array} { l l } 
3 & 2 \
3 & 4 \
2 & 2
\end{array} \right]  \begin{array} { l } \text { sugar }\
\text { milk } \
\text { moc }
\end{array}$$

Accepted Answer

A)  $6600 
B)  $3300 
C)  $7800 
D)  $4800 
A)  $6600 
B)  $3300 
C)  $7800 
D)  $4800

Question 5

Determine the sum or difference in clock 12 arithmetic.
-11 + 4

Accepted Answer

A)  4 
B)  3 
C)  7 
D)  15 
A)  4 
B)  3 
C)  7 
D)  15

Question 6

Determine the sum or difference in the given clock arithmetic.
-(1 - 6) - 2 (clock 7)

Accepted Answer

A)  1 
B)  7 
C)  5 
D)  3 
A)  1 
B)  7 
C)  5 
D)  3

Question 7

Decide whether or not the modulo system forms a group.
-{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}; Addition modulo 10

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

Solve the problem.
-If November is your starting month, what month will it be 16 years from November?

Accepted Answer

A)  July 
B)  March 
C)  November 
D)  April 
A)  July 
B)  March 
C)  November 
D)  April

Question 11

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

Accepted Answer

A)  Closure, identity, and commutative only 
B)  Closure, identity, inverse, and associative only 
C)  Closure, identity, associative, and commutative only 
D)  None of them 
A)  Closure, identity, and commutative only 
B)  Closure, identity, inverse, and associative only 
C)  Closure, identity, associative, and commutative only 
D)  None of them

Question 12

Decide which of the 5 properties of a commutative group (closure, identity, inverse, associative, commutative) hold for
the given system.
-$$\begin{array} { c | c c c c } 
/ & 5 & 11 & 16 & 8 \
\hline 5 & 11 & 16 & 8 & 5 \
11 & 16 & 8 & 5 & 11 \
16 & 8 & 5 & 11 & 16 \
8 & 5 & 11 & 16 & 8
\end{array}$$

Accepted Answer

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

Question 13

Decide which of the 5 properties of a commutative group (closure, identity, inverse, associative, commutative) hold for
the given system.
-$$\begin{array} { c | c c c c } 
?? & 2 & 8 & 11 & 16 \ 
\hline 2 & 8 & 11 & 16 & 2 \
8 & 11 & 16 & 2 & 8 \
11 & 16 & 2 & 8 & 11 \
16 & 2 & 16 & 11 & 8
\end{array}$$

Accepted Answer

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

Question 14

Find all replacements (less than the modulus) for the question mark that make the statement true.
-6 ∙ ? ≡ 8 (mod 10)

Accepted Answer

A)  1, 9 
B)  3 
C)  3, 8 
D) 4, 8 
A)  1, 9 
B)  3 
C)  3, 8 
D) 4, 8

Question 15

Perform the indicated operation.
-$$\left[ \begin{array} { l l } 
5 & 4
\end{array} \right] + \left[ \begin{array} { r } 
- 2 \
5
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { l l } 3 & 9 \end{array} \right]$ 
B)  $\left[ \begin{array} { l } 3 \ 9 \end{array} \right]$ 
C)  Not defined 
D)  $\left[ \begin{array} { r r } 5 & - 2 \ 4 & 5 \end{array} \right]$ 
A)  $\left[ \begin{array} { l l } 3 & 9 \end{array} \right]$ 
B)  $\left[ \begin{array} { l } 3 \ 9 \end{array} \right]$ 
C)  Not defined 
D)  $\left[ \begin{array} { r r } 5 & - 2 \ 4 & 5 \end{array} \right]$

Question 16

Perform the indicated operation.
-$$\left[ \begin{array} { r } 
3 \
- 1 \
- 4
\end{array} \right] + \left[ \begin{array} { r } 
- 5 \
6 \
9
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { r r } 3 & - 5 \ - 1 & 6 \ - 4 & 9 \end{array} \right]$ 
B)  $\left[ \begin{array} { l } 2 \ 5 \ 6 \end{array} \right]$ 
C)  $\left[ \begin{array} { l l l } - 2 & 5 & 5 \end{array} \right]$ 
D)  $\left[ \begin{array} { r } - 2 \ 5 \ 5 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r } 3 & - 5 \ - 1 & 6 \ - 4 & 9 \end{array} \right]$ 
B)  $\left[ \begin{array} { l } 2 \ 5 \ 6 \end{array} \right]$ 
C)  $\left[ \begin{array} { l l l } - 2 & 5 & 5 \end{array} \right]$ 
D)  $\left[ \begin{array} { r } - 2 \ 5 \ 5 \end{array} \right]$

Question 17

Perform the indicated operation.
-Let $\mathrm { C } = \left[ \begin{array} { r } 2 \ - 2 \ 10 \end{array} \right]$. Find (1/2) $\mathrm { C }$.

Accepted Answer

A)  $\left[ \begin{array} { r } 2 \ - 1 \ 10 \end{array} \right]$ 
B)  $\left[ \begin{array} { r } 4 \ - 4 \ 20 \end{array} \right]$ 
C)  $\left[ \begin{array} { r } 1 \ - 2 \ 10 \end{array} \right]$ 
D)  $\left[ \begin{array} { r } 1 \ - 1 \ 5 \end{array} \right]$ 
A)  $\left[ \begin{array} { r } 2 \ - 1 \ 10 \end{array} \right]$ 
B)  $\left[ \begin{array} { r } 4 \ - 4 \ 20 \end{array} \right]$ 
C)  $\left[ \begin{array} { r } 1 \ - 2 \ 10 \end{array} \right]$ 
D)  $\left[ \begin{array} { r } 1 \ - 1 \ 5 \end{array} \right]$

Question 18

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

Accepted Answer

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

Question 19

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

Accepted Answer

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

Question 20

Perform the indicated operation.
-Let $\mathrm { A } = \left[ \begin{array} { r r } - 3 & 1 \ 0 & 2 \end{array} \right]$. Find $3 \mathrm {~A}$.

Accepted Answer

A)  $\left[ \begin{array} { r r } - 9 & 3 \ 0 & 2 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l } 0 & 4 \ 3 & 5 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } - 9 & 3 \ 0 & 6 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } - 9 & 1 \ 0 & 2 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r } - 9 & 3 \ 0 & 2 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l } 0 & 4 \ 3 & 5 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } - 9 & 3 \ 0 & 6 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } - 9 & 1 \ 0 & 2 \end{array} \right]$

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

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

Determine the sum or difference in clock 12 arithmetic. -10 + 2

Determine the sum or difference in clock 12 arithmetic. -11 + 4

Determine the sum or difference in the given clock arithmetic. -(1 - 6) - 2 (clock 7)

Decide whether or not the modulo system forms a group. -{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}; Addition modulo 10

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

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

Solve the problem. -If November is your starting month, what month will it be 16 years from November?

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

Decide which of the 5 properties of a commutative group (closure, identity, inverse, associative, commutative) hold for the given system. - / 5 11 16 8 5 11 16 8 5 11 16 8 5 11 16 8 5 11 16 8 5 11 16 8

Decide which of the 5 properties of a commutative group (closure, identity, inverse, associative, commutative) hold for the given system. - ?? 2 8 11 16 2 8 11 16 2 8 11 16 2 8 11 16 2 8 11 16 2 16 11 8

Find all replacements (less than the modulus) for the question mark that make the statement true. -6 ∙ ? ≡ 8 (mod 10)

Perform the indicated operation. - $\left[ \begin{array} { l l } 5 & 4\end{array} \right] + \left[ \begin{array} { r } - 2 \\5\end{array} \right]$

Perform the indicated operation. - $\left[ \begin{array} { r } 3 \\- 1 \\- 4\end{array} \right] + \left[ \begin{array} { r } - 5 \\6 \\9\end{array} \right]$

Perform the indicated operation. -Let $\mathrm { C } = \left[ \begin{array} { r } 2 \\ - 2 \\ 10 \end{array} \right]$ . Find (1/2) $\mathrm { C }$ .

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

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

Perform the indicated operation. -Let $\mathrm { A } = \left[ \begin{array} { r r } - 3 & 1 \\ 0 & 2 \end{array} \right]$ . Find $3 \mathrm {~A}$ .

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

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

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

Determine the sum or difference in clock 12 arithmetic. -10 + 2

Determine the sum or difference in clock 12 arithmetic. -11 + 4

Determine the sum or difference in the given clock arithmetic. -(1 - 6) - 2 (clock 7)

Decide whether or not the modulo system forms a group. -{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}; Addition modulo 10

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

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

Solve the problem. -If November is your starting month, what month will it be 16 years from November?

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

Decide which of the 5 properties of a commutative group (closure, identity, inverse, associative, commutative) hold for the given system. - / 5 11 16 8 5 11 16 8 5 11 16 8 5 11 16 8 5 11 16 8 5 11 16 8

Decide which of the 5 properties of a commutative group (closure, identity, inverse, associative, commutative) hold for the given system. - ?? 2 8 11 16 2 8 11 16 2 8 11 16 2 8 11 16 2 8 11 16 2 16 11 8

Find all replacements (less than the modulus) for the question mark that make the statement true. -6 ∙ ? ≡ 8 (mod 10)

Perform the indicated operation. - [54]+[−25]\left[ \begin{array} { l l } 5 & 4\end{array} \right] + \left[ \begin{array} { r } - 2 \\5\end{array} \right][5​4​]+[−25​]

Perform the indicated operation. - [3−1−4]+[−569]\left[ \begin{array} { r } 3 \\- 1 \\- 4\end{array} \right] + \left[ \begin{array} { r } - 5 \\6 \\9\end{array} \right]​3−1−4​​+​−569​​

Perform the indicated operation. -Let C=[2−210]\mathrm { C } = \left[ \begin{array} { r } 2 \\ - 2 \\ 10 \end{array} \right]C=​2−210​​ . Find (1/2) C\mathrm { C }C .

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

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

Perform the indicated operation. -Let A=[−3102]\mathrm { A } = \left[ \begin{array} { r r } - 3 & 1 \\ 0 & 2 \end{array} \right]A=[−30​12​] . Find 3 A3 \mathrm {~A}3 A .

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. - $\left[ \begin{array} { l l } 5 & 4\end{array} \right] + \left[ \begin{array} { r } - 2 \\5\end{array} \right]$

Perform the indicated operation. - $\left[ \begin{array} { r } 3 \\- 1 \\- 4\end{array} \right] + \left[ \begin{array} { r } - 5 \\6 \\9\end{array} \right]$

Perform the indicated operation. -Let $\mathrm { C } = \left[ \begin{array} { r } 2 \\ - 2 \\ 10 \end{array} \right]$ . Find (1/2) $\mathrm { C }$ .

Perform the indicated operation. -Let $\mathrm { A } = \left[ \begin{array} { r r } - 3 & 1 \\ 0 & 2 \end{array} \right]$ . Find $3 \mathrm {~A}$ .