Question 1

Convert from binary form to the indicated base.
-$11000000 _ { \text {two } }$ to base eight

Accepted Answer

A) $200_{\text {eight }}$ 
B) $400_{\text {eight }}$ 
C)  $300_{\text {eight }}$ 
D)  $1600_{\text {eight }}$ 
A) $200_{\text {eight }}$ 
B) $400_{\text {eight }}$ 
C)  $300_{\text {eight }}$ 
D)  $1600_{\text {eight }}$

Question 2

Convert the Hindu-Arabic numeral to Roman form.
-649

Accepted Answer

A) DCLIX 
B) DXLIX 
C) MCXLIX 
D) DCXLIX 
A) DCLIX 
B) DXLIX 
C) MCXLIX 
D) DCXLIX

Question 3

Identify the largest number expressible in a simple grouping system with the specified base and specified number of distinct symbols.
-base nine, d distinct symbols

Accepted Answer

A)  $\mathrm { d } ^ { 9 } - 1$ 
B)  $9 d - 1$ 
C)  $9^ d$ 
D)  $9^ d _ { - 1 }$ 
A)  $\mathrm { d } ^ { 9 } - 1$ 
B)  $9 d - 1$ 
C)  $9^ d$ 
D)  $9^ d _ { - 1 }$

Question 4

Perform the operation in expanded notation. Write your answer in simplified form.
-729 + 513

Accepted Answer

A) 1262 
B) 7074 
C) 1242 
D) 1252 
A) 1262 
B) 7074 
C) 1242 
D) 1252

Question 5

Determine the letters or numbers.
-Translate the word "couch" into an ASCII string of binary digits.

Accepted Answer

A)  11000111101101111010111100111101010 
B)  11000111101111111010111000111101000 
C)  10111001100110011011101111000110011 
D)  11000111101111111010110001111101000 
A)  11000111101101111010111100111101010 
B)  11000111101111111010111000111101000 
C)  10111001100110011011101111000110011 
D)  11000111101111111010110001111101000

Question 6

Decide whether the congruence statement is true or false.

-5 ≡ 21 (mod 5)

Accepted Answer

A) True 
 B)False

Question 7

Determine the letters or numbers.
-Translate "Mexico" into an ASCII string of binary digits.

Accepted Answer

A) 100110101001011111000110100111000111101111 
B) 100110111001011111000110100111000111101111 
C) 100110111011011101000110100111000111110011 
D) 110110111001011011011100111000111111001101 
A) 100110101001011111000110100111000111101111 
B) 100110111001011111000110100111000111101111 
C) 100110111011011101000110100111000111110011 
D) 110110111001011011011100111000111111001101

Question 8

Perform the addition or subtraction and give your answer in Hindu-Arabic form.
-

Accepted Answer

A)  52 
B)  502 
C)  602 
D)  62 
A)  52 
B)  502 
C)  602 
D)  62

Question 9

Decide whether the congruence statement is true or false.

-3 ≡ 13 (mod 11)

Accepted Answer

A) True 
 B)False

Question 10

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

Accepted Answer

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

Question 11

Convert the Hindu-Arabic numeral to Chinese.
-2000

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 12

Perform the modular arithmetic operation.
-[(3 ·7)- 5](mod 4)

Accepted Answer

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

Question 13

Identify the number represented on the abacus.
-

Accepted Answer

A)  55,555 
B)  66,666 
C)  99,999 
D)  11,111 
A)  55,555 
B)  66,666 
C)  99,999 
D)  11,111

Question 14

Identify the number represented on the abacus.
-

Accepted Answer

A)  8,761 
B)  9,871 
C)  9,870 
D)  8,760 
A)  8,761 
B)  9,871 
C)  9,870 
D)  8,760

Question 15

Perform the modular arithmetic operation.
-(49 - 25)(mod 5)

Accepted Answer

A) 0 
B) 4 
C) 3 
D) 120 
A) 0 
B) 4 
C) 3 
D) 120

Question 16

Write the number in expanded form.
-806

Accepted Answer

A)  $\left( 8 \cdot 10 ^ { 2 } \right) + \left( 0 \cdot 10 ^ { 1 } \right) + \left( 6 \cdot 10 ^ { 0 } \right)$ 
B)  $\left( 8 \cdot 10 ^ { 3 } \right) + \left( 0 \cdot 10 ^ { 2 } \right) + \left( 6 \cdot 10 ^ { 1 } \right)$ 
C)  $\left( 8 \cdot 10 ^ { 1 } \right) + \left( 0 \cdot 10 ^ { 2 } \right) + \left( 6 \cdot 10 ^ { 3 } \right)$ 
D)  $\left( 8 \cdot 10 ^ { 0 } \right) + \left( 0 \cdot 10 ^ { 1 } \right) + \left( 6 \cdot 10 ^ { 2 } \right)$ 
A)  $\left( 8 \cdot 10 ^ { 2 } \right) + \left( 0 \cdot 10 ^ { 1 } \right) + \left( 6 \cdot 10 ^ { 0 } \right)$ 
B)  $\left( 8 \cdot 10 ^ { 3 } \right) + \left( 0 \cdot 10 ^ { 2 } \right) + \left( 6 \cdot 10 ^ { 1 } \right)$ 
C)  $\left( 8 \cdot 10 ^ { 1 } \right) + \left( 0 \cdot 10 ^ { 2 } \right) + \left( 6 \cdot 10 ^ { 3 } \right)$ 
D)  $\left( 8 \cdot 10 ^ { 0 } \right) + \left( 0 \cdot 10 ^ { 1 } \right) + \left( 6 \cdot 10 ^ { 2 } \right)$

Question 17

Convert the number to decimal form.
-$10110 _ { \text {two } }$

Accepted Answer

A)  44 
B)  20,220 
C)  6 
D)  22 
A)  44 
B)  20,220 
C)  6 
D)  22

Question 18

Convert from binary form to the indicated base.
-$11100_{\text {two }}$two to base eight

Accepted Answer

A)  $168 _\text { eight }$ 
B)  $42 _\text { eight }$ 
C)  $34 _\text { eight }$ 
D)  $21 _\text { eight }$ 
A)  $168 _\text { eight }$ 
B)  $42 _\text { eight }$ 
C)  $34 _\text { eight }$ 
D)  $21 _\text { eight }$

Question 19

Decide whether the congruence statement is true or false.

-6 ≡ 13 (mod 2)

Accepted Answer

A) True 
 B)False

Question 20

Write the number in expanded form.
-eighty-five thousand, six hundred seventeen

Accepted Answer

A)  $\left( 5 \cdot 10 ^ { 5 } \right) + \left( 8 \cdot 10 ^ { 4 } \right) + \left( 6 \cdot 10 ^ { 3 } \right) + \left( 0 \cdot 10 ^ { 2 } \right) + \left( 7 \cdot 10 ^ { 1 } \right)$ 
B)  $\left( 8 \cdot 10 ^ { 5 } \right) + \left( 5 \cdot 10 ^ { 4 } \right) + \left( 6 \cdot 10 ^ { 3 } \right) + \left( 1 \cdot 10 ^ { 2 } \right) + \left( 7 \cdot 10 ^ { 1 } \right)$ 
C)  $\left( 8 \cdot 10 ^ { 4 } \right) + \left( 5 \cdot 10 ^ { 3 } \right) + \left( 6 \cdot 10 ^ { 2 } \right) + \left( 1 \cdot 10 ^ { 1 } \right) + \left( 7 \cdot 10 ^ { 0 } \right)$ 
D)  $\left( 8 \cdot 10 ^ { 4 } \right) + \left( 5 \cdot 10 ^ { 3 } \right) + \left( 6 \cdot 10 ^ { 2 } \right) + \left( 7 \cdot 10 ^ { 1 } \right) + \left( 0 \cdot 10 ^ { 0 } \right)$ 
A)  $\left( 5 \cdot 10 ^ { 5 } \right) + \left( 8 \cdot 10 ^ { 4 } \right) + \left( 6 \cdot 10 ^ { 3 } \right) + \left( 0 \cdot 10 ^ { 2 } \right) + \left( 7 \cdot 10 ^ { 1 } \right)$ 
B)  $\left( 8 \cdot 10 ^ { 5 } \right) + \left( 5 \cdot 10 ^ { 4 } \right) + \left( 6 \cdot 10 ^ { 3 } \right) + \left( 1 \cdot 10 ^ { 2 } \right) + \left( 7 \cdot 10 ^ { 1 } \right)$ 
C)  $\left( 8 \cdot 10 ^ { 4 } \right) + \left( 5 \cdot 10 ^ { 3 } \right) + \left( 6 \cdot 10 ^ { 2 } \right) + \left( 1 \cdot 10 ^ { 1 } \right) + \left( 7 \cdot 10 ^ { 0 } \right)$ 
D)  $\left( 8 \cdot 10 ^ { 4 } \right) + \left( 5 \cdot 10 ^ { 3 } \right) + \left( 6 \cdot 10 ^ { 2 } \right) + \left( 7 \cdot 10 ^ { 1 } \right) + \left( 0 \cdot 10 ^ { 0 } \right)$

Convert from binary form to the indicated base. - $11000000 _ { \text {two } }$ to base eight

Convert the Hindu-Arabic numeral to Roman form. -649

Identify the largest number expressible in a simple grouping system with the specified base and specified number of distinct symbols. -base nine, d distinct symbols

Perform the operation in expanded notation. Write your answer in simplified form. -729 + 513

Determine the letters or numbers. -Translate the word "couch" into an ASCII string of binary digits.

Decide whether the congruence statement is true or false. -5 ≡ 21 (mod 5)

Determine the letters or numbers. -Translate "Mexico" into an ASCII string of binary digits.

Perform the addition or subtraction and give your answer in Hindu-Arabic form. -

Decide whether the congruence statement is true or false. -3 ≡ 13 (mod 11)

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

Convert the Hindu-Arabic numeral to Chinese. -2000

Perform the modular arithmetic operation. -[(3 ·7)- 5](mod 4)

Identify the number represented on the abacus. -

Identify the number represented on the abacus. -

Perform the modular arithmetic operation. -(49 - 25)(mod 5)

Write the number in expanded form. -806

Convert the number to decimal form. - $10110 _ { \text {two } }$

Convert from binary form to the indicated base. - $11100_{\text {two }}$ two to base eight

Decide whether the congruence statement is true or false. -6 ≡ 13 (mod 2)

Write the number in expanded form. -eighty-five thousand, six hundred seventeen

The Art of Problem Solving

The Basic Concepts of Set Theory

Introduction to Logic

Number Theory

The Real Numbers and Their Representations

The Basic Concepts of Algebra

Graphs, Functions, and Systems of Equations and Inequalities

Geometry

Counting Methods

Probability

Statistics

Personal Financial Management

Trigonometry Formerly

Graph Theory

Voting and Apportionment

Filters

Exam 4: Numeration Systems

Convert from binary form to the indicated base. - 11000000two 11000000 _ { \text {two } }11000000two ​ to base eight

Convert the Hindu-Arabic numeral to Roman form. -649

Identify the largest number expressible in a simple grouping system with the specified base and specified number of distinct symbols. -base nine, d distinct symbols

Perform the operation in expanded notation. Write your answer in simplified form. -729 + 513

Determine the letters or numbers. -Translate the word "couch" into an ASCII string of binary digits.

Decide whether the congruence statement is true or false. -5 ≡ 21 (mod 5)

Determine the letters or numbers. -Translate "Mexico" into an ASCII string of binary digits.

Perform the addition or subtraction and give your answer in Hindu-Arabic form. -

Decide whether the congruence statement is true or false. -3 ≡ 13 (mod 11)

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

Convert the Hindu-Arabic numeral to Chinese. -2000

Perform the modular arithmetic operation. -[(3 ·7)- 5](mod 4)

Identify the number represented on the abacus. -

Identify the number represented on the abacus. -

Perform the modular arithmetic operation. -(49 - 25)(mod 5)

Write the number in expanded form. -806

Convert the number to decimal form. - 10110two 10110 _ { \text {two } }10110two ​

Convert from binary form to the indicated base. - 11100two 11100_{\text {two }}11100two ​ two to base eight

Decide whether the congruence statement is true or false. -6 ≡ 13 (mod 2)

Write the number in expanded form. -eighty-five thousand, six hundred seventeen

The Art of Problem Solving

The Basic Concepts of Set Theory

Introduction to Logic

Number Theory

The Real Numbers and Their Representations

The Basic Concepts of Algebra

Graphs, Functions, and Systems of Equations and Inequalities

Geometry

Counting Methods

Probability

Statistics

Personal Financial Management

Trigonometry Formerly

Graph Theory

Voting and Apportionment

Filters

Convert from binary form to the indicated base. - $11000000 _ { \text {two } }$ to base eight

Convert the number to decimal form. - $10110 _ { \text {two } }$

Convert from binary form to the indicated base. - $11100_{\text {two }}$ two to base eight