Question 1

Perform the modular arithmetic operation.
-9 ∙ 9 (mod 7)

Accepted Answer

A)  3 
B)  7 
C)  11 
D)  4 
A)  3 
B)  7 
C)  11 
D)  4

Question 2

Solve the problem.
-If Tuesday is your starting day, what day will it be 3 years, 348 days from Tuesday? (Assume no Leap years.)

Accepted Answer

A)  Tuesday 
B)  Monday 
C)  Sunday 
D)  Wednesday 
A)  Tuesday 
B)  Monday 
C)  Sunday 
D)  Wednesday

Question 3

Perform the indicated operation.
-$$\left[ \begin{array} { r r } 
- 1 & 3 \
0 & 4 \
7 & - 4
\end{array} \right] - \left[ \begin{array} { l l } 
2 & 1 \
7 & 4 \
4 & 2
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { r r } 1 & 2 \ 7 & 0 \ 3 & - 2 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r } 3 & - 2 \ 7 & 0 \ - 3 & 6 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } 1 & 4 \ 7 & 8 \ 11 & 0 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } - 3 & 2 \ - 7 & 0 \ 3 & - 6 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r } 1 & 2 \ 7 & 0 \ 3 & - 2 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r } 3 & - 2 \ 7 & 0 \ - 3 & 6 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } 1 & 4 \ 7 & 8 \ 11 & 0 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } - 3 & 2 \ - 7 & 0 \ 3 & - 6 \end{array} \right]$

Question 4

Solve the problem.
-An intensive-care nurse works 3 days of 12-hour shifts and then has 3 days off. If today is the Nurseʹs 3rd day off, will he be working 51 days from now?

Accepted Answer

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

Question 5

Provide an appropriate response.
-Give the additive and multiplicative inverses of -2 for the set of rational numbers.

Accepted Answer

The answer of Provide an appropriate response.
-Give the additive and...

Question 6

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

Accepted Answer

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

Question 7

Perform the modular arithmetic operation.
-124 + 125 (mod 12)

Accepted Answer

A)  9 
B)  13 
C)  8 
D)  20 
A)  9 
B)  13 
C)  8 
D)  20

Question 8

Perform the modular arithmetic operation.
-[(11 ∙ 4) + 4] (mod 8)

Accepted Answer

A)  7 
B)  1 
C)  0 
D)  3 
A)  7 
B)  1 
C)  0 
D)  3

Question 9

Find all replacements (less than the modulus) for the question mark that make the statement true.
-7 - 2 ≡ ? (mod 6)

Accepted Answer

A)  1 
B)  3 
C)  0 
D)  5 
A)  1 
B)  3 
C)  0 
D)  5

Question 10

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

Accepted Answer

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

Question 11

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 R and S. What is The cost of 100 batches from supplier S?

Accepted Answer

A)  $13,200 
B)  $12,000 
C)  $16,500 
D)  $6,600 
A)  $13,200 
B)  $12,000 
C)  $16,500 
D)  $6,600

Question 12

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

Accepted Answer

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

Question 13

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

Accepted Answer

A)  $\left[ \begin{array} { r r r } 0 & 4 & - 2 \ - 3 & 3 & 15 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } 0 & - 6 & - 8 \ 0 & - 6 & 3 \end{array} \right]$ 
C)  $\mathrm { AB }$ is not defined. 
D)  $\left[ \begin{array} { r r } 0 & - 3 \ 4 & 3 \ - 2 & 15 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r r } 0 & 4 & - 2 \ - 3 & 3 & 15 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } 0 & - 6 & - 8 \ 0 & - 6 & 3 \end{array} \right]$ 
C)  $\mathrm { AB }$ is not defined. 
D)  $\left[ \begin{array} { r r } 0 & - 3 \ 4 & 3 \ - 2 & 15 \end{array} \right]$

Question 14

Determine the sum or difference in the given clock arithmetic.
-2 + 5 (clock 7)

Accepted Answer

A)  5 
B)  7 
C)  1 
D)  2 
A)  5 
B)  7 
C)  1 
D)  2

Question 15

Find all replacements (less than the modulus) for the question mark that make the statement true.
-4 ∙ ? ≡ 3 (mod 12)

Accepted Answer

A)  0 
B)  1, 3, 5 
C) 2, 4 
D) No solution 
A)  0 
B)  1, 3, 5 
C) 2, 4 
D) No solution

Question 16

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

Accepted Answer

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

Question 17

Solve the problem.
-A machine operator works both day and evening shifts. She works the day shift for 5 consecutive Days, then the evening shift for 3 consecutive days, then the day shift for 2 consecutive days and Then the evening shift for 4 consecutive days. If she is in day 3 of the 5-day consecutive day shift, What shift will she be working 79 days from now?

Accepted Answer

A)  Day 
B)  Evening 
A)  Day 
B)  Evening

Question 18

Find the product, AB, if possible.
-$A = \left[ \begin{array} { l l l } - 6 & 2 & 3 \end{array} \right] , B = \left[ \begin{array} { r } 9 \ 0 \ - 3 \end{array} \right]$

Accepted Answer

A)  $[ 156 ]$ 
B)  $A B$ is not defined. 
C)  $[ - 63 ]$ 
D)  $\left[ \begin{array} { l l l } - 54 & 0 & - 9 \end{array} \right]$ 
A)  $[ 156 ]$ 
B)  $A B$ is not defined. 
C)  $[ - 63 ]$ 
D)  $\left[ \begin{array} { l l l } - 54 & 0 & - 9 \end{array} \right]$

Question 19

Perform the indicated operation.
-Let $\mathrm { A } = \left[ \begin{array} { l l } 2 & 3 \ 2 & 6 \end{array} \right]$ and $\mathrm { B } = \left[ \begin{array} { r r } 0 & 4 \ - 1 & 6 \end{array} \right]$. Find $4 \mathrm {~A} + \mathrm { B }$.

Accepted Answer

A)  $\left[ \begin{array} { l l } 8 & 16 \ 7 & 30 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r } 8 & 7 \ 7 & 12 \end{array} \right]$ 
C)  $\left[ \begin{array} { l l } 8 & 28 \ 4 & 48 \end{array} \right]$ 
D)  $\left[ \begin{array} { l l } 8 & 16 \ 1 & 12 \end{array} \right]$ 
A)  $\left[ \begin{array} { l l } 8 & 16 \ 7 & 30 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r } 8 & 7 \ 7 & 12 \end{array} \right]$ 
C)  $\left[ \begin{array} { l l } 8 & 28 \ 4 & 48 \end{array} \right]$ 
D)  $\left[ \begin{array} { l l } 8 & 16 \ 1 & 12 \end{array} \right]$

Question 20

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

Accepted Answer

A)  $\left[ \begin{array} { r r } 12 & 0 \ 0 & 12 \end{array} \right]$ 
B)  $A B$ is not defined. 
C)  $\left[ \begin{array} { r r r } 12 & - 8 & 4 \ - 6 & 16 & - 11 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } 12 & - 6 \ - 8 & 16 \ 4 & - 11 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r } 12 & 0 \ 0 & 12 \end{array} \right]$ 
B)  $A B$ is not defined. 
C)  $\left[ \begin{array} { r r r } 12 & - 8 & 4 \ - 6 & 16 & - 11 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } 12 & - 6 \ - 8 & 16 \ 4 & - 11 \end{array} \right]$

Perform the modular arithmetic operation. -9 ∙ 9 (mod 7)

Solve the problem. -If Tuesday is your starting day, what day will it be 3 years, 348 days from Tuesday? (Assume no Leap years.)

Perform the indicated operation. - $\left[ \begin{array} { r r } - 1 & 3 \\0 & 4 \\7 & - 4\end{array} \right] - \left[ \begin{array} { l l } 2 & 1 \\7 & 4 \\4 & 2\end{array} \right]$

Solve the problem. -An intensive-care nurse works 3 days of 12-hour shifts and then has 3 days off. If today is the Nurseʹs 3rd day off, will he be working 51 days from now?

Provide an appropriate response. -Give the additive and multiplicative inverses of -2 for the set of rational numbers.

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

Perform the modular arithmetic operation. -124 + 125 (mod 12)

Perform the modular arithmetic operation. -[(11 ∙ 4) + 4] (mod 8)

Find all replacements (less than the modulus) for the question mark that make the statement true. -7 - 2 ≡ ? (mod 6)

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

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 R and S. What is The cost of 100 batches from supplier S?

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

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

Determine the sum or difference in the given clock arithmetic. -2 + 5 (clock 7)

Find all replacements (less than the modulus) for the question mark that make the statement true. -4 ∙ ? ≡ 3 (mod 12)

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

Find the product, AB, if possible. - $A = \left[ \begin{array} { l l l } - 6 & 2 & 3 \end{array} \right] , B = \left[ \begin{array} { r } 9 \\ 0 \\ - 3 \end{array} \right]$

Perform the indicated operation. -Let $\mathrm { A } = \left[ \begin{array} { l l } 2 & 3 \\ 2 & 6 \end{array} \right]$ and $\mathrm { B } = \left[ \begin{array} { r r } 0 & 4 \\ - 1 & 6 \end{array} \right]$ . Find $4 \mathrm {~A} + \mathrm { B }$ .

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

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