Question 1

Determine the sum or difference in clock 12 arithmetic.
-(7 + 10) + (12 + 9)

Accepted Answer

A)  8 
B)  2 
C)  1 
D)  38 
A)  8 
B)  2 
C)  1 
D)  38

Question 2

Determine the sum or difference in clock 12 arithmetic.
-(2 + 1) + (1 + 8)

Accepted Answer

A)  12 
B)  4 
C)  2 
D)  1 
A)  12 
B)  4 
C)  2 
D)  1

Question 3

Solve the problem.
-If May is your starting month, what month will it be 73 months from May?

Accepted Answer

A)  April 
B)  June 
C)  December 
D)  March 
A)  April 
B)  June 
C)  December 
D)  March

Question 4

Decide which of the 5 properties of a commutative group (closure, identity, inverse, associative, commutative) hold for
the given system.
-$$\begin{array} { c | c c c c } 
\| & 4 & 7 & 12 & 19 \
\hline 4 & 4 & 7 & 12 & 19 \
7 & 7 & 12 & 19 & 4 \
12 & 12 & 19 & 4 & 7 \
19 & 19 & 4 & 7 & 12
\end{array}$$

Accepted Answer

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

Question 5

Provide an appropriate response.
-Is there an identity element for the operation of division over the set of integers? Support your claim with an example.

Accepted Answer

Yes; examples will vary. One e

Question 6

Provide an appropriate response.
-Does the commutative property hold for the set of real numbers under the operation of subtraction? Support your claim with an example.

Accepted Answer

No; examples will va

Question 7

Find the modulo class to which the number belongs for the given modulo system.
--2, mod 11

Accepted Answer

A)  9 
B)  5 
C)  1 
D)  0 
A)  9 
B)  5 
C)  1 
D)  0

Question 8

Find the modulo class to which the number belongs for the given modulo system.
-13, mod 4

Accepted Answer

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

Question 9

Find the modulo class to which the number belongs for the given modulo system.
-69, mod 16

Accepted Answer

A)  5 
B)  13 
C)  10 
D)  8 
A)  5 
B)  13 
C)  10 
D)  8

Question 10

Determine the sum or difference in the given clock arithmetic.
-(3 - 4) - 6 (clock 6)

Accepted Answer

A)  5 
B)  2 
C)  6 
D)  3 
A)  5 
B)  2 
C)  6 
D)  3

Question 11

Solve the problem.
-Does the commutative property of multiplication, A × B = B × A, hold for matrices A and B? $$A = \left[ \begin{array} { r r r } 
- 9 & 7 & 2 \
3 & 5 & 1 \
9 & - 4 & 9
\end{array} \right] , B = \left[ \begin{array} { l l l } 
1 & 0 & 0 \
0 & 1 & 0 \
0 & 0 & 1
\end{array} \right]$$

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

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

Accepted Answer

A)  $\left[ \begin{array} { r r } 2 & - 2 \ - 11 & 3 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r } 0 & 4 \ - 4 & 3 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } - 2 & 2 \ - 5 & - 11 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } - 8 & - 6 \ 4 & 5 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r } 2 & - 2 \ - 11 & 3 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r } 0 & 4 \ - 4 & 3 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } - 2 & 2 \ - 5 & - 11 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } - 8 & - 6 \ 4 & 5 \end{array} \right]$

Question 14

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

Accepted Answer

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

Question 15

Solve the problem.
-If April is your starting month, what month will it be 5 years and 2 months from April?

Accepted Answer

A)  August 
B)  June 
C)  October 
D)  May 
A)  August 
B)  June 
C)  October 
D)  May

Question 16

Find all replacements (less than the modulus) for the question mark that make the statement true.
-2 - ? ≡ 9 (mod 9)

Accepted Answer

A)  2 
B)  7 
C)  3 
D)  4 
A)  2 
B)  7 
C)  3 
D)  4

Question 17

Find all replacements (less than the modulus) for the question mark that make the statement true.
-9 ∙ 4 ≡ ? (mod 7)

Accepted Answer

A)  4 
B)  6 
C)  2 
D)  1 
A)  4 
B)  6 
C)  2 
D)  1

Question 18

Solve the problem.
-Are the matrices A and B multiplicative inverses? $$A = \left[ \begin{array} { l l } 
5 & 3 \
3 & 2
\end{array} \right] , B = \left[ \begin{array} { r r } 
2 & - 3 \
- 3 & 5
\end{array} \right]$$

Accepted Answer

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

Question 19

Find all replacements (less than the modulus) for the question mark that make the statement true.
-5 + 5 ≡ ? (mod 5)

Accepted Answer

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

Question 20

Solve the problem.
-Barnes and Able sell life, health, and auto insurance. Sales for May and June are given in the
Matrices. 
$\quad $$\quad $$\quad $$\quad $$\text {Life}$ $\quad $$\quad $$\text {Health}$$\quad $ $\text {Auto}$
$\begin{array} { l } 
M = \left[ \begin{array} { r r r } 
20,000 & 15,000 & 6000 \
30,000 & 0 & 17,000
\end{array} \right] \begin{array} { l } 
\text { Able } \
\text { Barnes }
\end{array} \
\end{array}$

$J = \left[ \begin{array} { r r r } 
70,000 & 0 & 14,000 \
30,000 & 23,000 & 32,000
\end{array} \right] \begin{array} { l } 
\text { Able } \
\text { Barnes }
\end{array}$

Use matrix addition to determine the total sales for each type of insurance for each salesperson.

Accepted Answer

A) $\quad $$\text {Life}$ $\quad $$\quad $$\text {Health}$$\quad $ $\text {Auto}$
$\left[ \begin{array} { l l l } 
150,000 & 38,000 & 69,000
\end{array} \right]$ 
B) $\quad $$\text {Life}$ $\quad $$\text {Health}$$\quad $ $\text {Auto}$
$\begin{array} { l }

{ \left[ \begin{array} { l l l } 
90,000 & 0 & 20,000 \
60,000 & 0 & 49,000
\end{array} \right] \begin{array} { l } 
\text { Able } \
\text { Barnes }
\end{array} } \
\end{array}$ 
C) $\quad $$\text {Life}$ $\quad $$\quad $$\text {Health}$$\quad $ $\text {Auto}$
$\left[ \begin{array} { l l l } 
90,000 & 15,000 & 20,000 \
60,000 & 23,000 & 49,000
\end{array} \right] \begin{array} { l } 
\text { Able } \
\text { Barnes }
\end{array}$ 
D)  $\quad $$\text {Life}$ $\quad $$\quad $$\text {Health}$$\quad $ $\text {Auto}$
$\left[ \begin{array} { l l l } 
90,000 & 15,000 & 20,000 \
60,000 & 23,000 & 32,000
\end{array} \right] \begin{array} { l } 
\text { Able } \
\text { Barnes }
\end{array}$ 
A) $\quad $$\text {Life}$ $\quad $$\quad $$\text {Health}$$\quad $ $\text {Auto}$
$\left[ \begin{array} { l l l } 
150,000 & 38,000 & 69,000
\end{array} \right]$ 
B) $\quad $$\text {Life}$ $\quad $$\text {Health}$$\quad $ $\text {Auto}$
$\begin{array} { l }

{ \left[ \begin{array} { l l l } 
90,000 & 0 & 20,000 \
60,000 & 0 & 49,000
\end{array} \right] \begin{array} { l } 
\text { Able } \
\text { Barnes }
\end{array} } \
\end{array}$ 
C) $\quad $$\text {Life}$ $\quad $$\quad $$\text {Health}$$\quad $ $\text {Auto}$
$\left[ \begin{array} { l l l } 
90,000 & 15,000 & 20,000 \
60,000 & 23,000 & 49,000
\end{array} \right] \begin{array} { l } 
\text { Able } \
\text { Barnes }
\end{array}$ 
D)  $\quad $$\text {Life}$ $\quad $$\quad $$\text {Health}$$\quad $ $\text {Auto}$
$\left[ \begin{array} { l l l } 
90,000 & 15,000 & 20,000 \
60,000 & 23,000 & 32,000
\end{array} \right] \begin{array} { l } 
\text { Able } \
\text { Barnes }
\end{array}$

Determine the sum or difference in clock 12 arithmetic. -(7 + 10) + (12 + 9)

Determine the sum or difference in clock 12 arithmetic. -(2 + 1) + (1 + 8)

Solve the problem. -If May is your starting month, what month will it be 73 months from May?

Decide which of the 5 properties of a commutative group (closure, identity, inverse, associative, commutative) hold for the given system. - \| 4 7 12 19 4 4 7 12 19 7 7 12 19 4 12 12 19 4 7 19 19 4 7 12

Provide an appropriate response. -Is there an identity element for the operation of division over the set of integers? Support your claim with an example.

Provide an appropriate response. -Does the commutative property hold for the set of real numbers under the operation of subtraction? Support your claim with an example.

Find the modulo class to which the number belongs for the given modulo system. --2, mod 11

Find the modulo class to which the number belongs for the given modulo system. -13, mod 4

Find the modulo class to which the number belongs for the given modulo system. -69, mod 16

Determine the sum or difference in the given clock arithmetic. -(3 - 4) - 6 (clock 6)

Solve the problem. -Does the commutative property of multiplication, A × B = B × A, hold for matrices A and B? $A = \left[ \begin{array} { r r r } - 9 & 7 & 2 \\3 & 5 & 1 \\9 & - 4 & 9\end{array} \right] , B = \left[ \begin{array} { l l l } 1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1\end{array} \right]$

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

Decide which of the 5 properties of a commutative group (closure, identity, inverse, associative, commutative) hold for the given system. - ? \vee ¥ \Theta \vee \vee \Theta ¥ ¥ \Theta ¥ \vee \Theta ¥ £ \vee

Solve the problem. -If April is your starting month, what month will it be 5 years and 2 months from April?

Find all replacements (less than the modulus) for the question mark that make the statement true. -2 - ? ≡ 9 (mod 9)

Find all replacements (less than the modulus) for the question mark that make the statement true. -9 ∙ 4 ≡ ? (mod 7)

Solve the problem. -Are the matrices A and B multiplicative inverses? $A = \left[ \begin{array} { l l } 5 & 3 \\3 & 2\end{array} \right] , B = \left[ \begin{array} { r r } 2 & - 3 \\- 3 & 5\end{array} \right]$

Find all replacements (less than the modulus) for the question mark that make the statement true. -5 + 5 ≡ ? (mod 5)

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