Question 1

Remove or add parentheses as indicated.
-Place parentheses to make the equation $a \cdot b \div b + 5 b = a + 5 b$ true.

Accepted Answer

A)  $( a \cdot b ) \div ( b + 5 b ) = a + 5 b$ 
B)  None needed. 
C)  $a \cdot ( b \div b + 5 b ) = a + 5 b$ 
D)  $a \cdot b \div ( b + 5 b ) = a + 5 b$ 
A)  $( a \cdot b ) \div ( b + 5 b ) = a + 5 b$ 
B)  None needed. 
C)  $a \cdot ( b \div b + 5 b ) = a + 5 b$ 
D)  $a \cdot b \div ( b + 5 b ) = a + 5 b$

Question 2

Convert the following.
-632 seconds to minutes and seconds

Accepted Answer

A) 11 min and 32 sec 
B) 12 min and 32 sec 
C) 13 min and 32 sec 
D) 10 min and 32 sec 
A) 11 min and 32 sec 
B) 12 min and 32 sec 
C) 13 min and 32 sec 
D) 10 min and 32 sec

Question 3

Solve the problem.
-Pat withdrew $495 from an ATM. If the ATM gives $100, $20, and $5 bills such that the total number of bills is the least, then how many of each type of bill did Pat get?

Accepted Answer

A) 4 $100-bills, 3 $20-bills, and 7 $5-bills 
B) 5 $100-bills, zero $20-bills, and 3 $5-bills 
C) 4 $100-bills, 4 $20-bills, and 3 $5-bills 
D) 3 $100-bills, 9 $20-bills, and 3 $5-bills 
A) 4 $100-bills, 3 $20-bills, and 7 $5-bills 
B) 5 $100-bills, zero $20-bills, and 3 $5-bills 
C) 4 $100-bills, 4 $20-bills, and 3 $5-bills 
D) 3 $100-bills, 9 $20-bills, and 3 $5-bills

Question 4

Find the missing numbers.
-

Accepted Answer

A)  $( a ) = 3 , ( b ) = 2 , ( c ) = 8$ 
B)  $( a ) = 1 , ( b ) = 2 , ( c ) = 8$ 
C)  (a) $= 4 , ( b ) = 3 , ( c ) = 9$ 
D)  $( a ) = 2 , ( b ) = 2 , ( c ) = 8$ 
A)  $( a ) = 3 , ( b ) = 2 , ( c ) = 8$ 
B)  $( a ) = 1 , ( b ) = 2 , ( c ) = 8$ 
C)  (a) $= 4 , ( b ) = 3 , ( c ) = 9$ 
D)  $( a ) = 2 , ( b ) = 2 , ( c ) = 8$

Question 5

Solve the problem.
-James doubled his profit compared with that of last year. Last year he doubled his profit from the previous year. If his profit this year was $12,000, then what was his profit last year and the year Before that?

Accepted Answer

A) $9000; $6000 
B) $9000; $3000 
C) $3000; $1500 
D) $6000; $3000 
A) $9000; $6000 
B) $9000; $3000 
C) $3000; $1500 
D) $6000; $3000

Question 6

For the given Hindu-Arabic numeral, write an equivalent numeral in the indicated system.
-72,302; Mayan

Accepted Answer

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

Question 7

Convert the following.
-44 inches to feet and inches

Accepted Answer

A) 3 ft and 8 in. 
B) 3 ft and 9 in. 
C) 4 ft and 8 in. 
D) 5 ft and 8 in. 
A) 3 ft and 8 in. 
B) 3 ft and 9 in. 
C) 4 ft and 8 in. 
D) 5 ft and 8 in.

Question 8

If $n ( A ) = 5 , n ( B ) = 11$ and $n ( A \cap B ) = 3$, what do you know about $n ( A \cup B )$ ?

Accepted Answer

A)  $n ( A \cup B ) = 12$ 
B)  $n ( A \cup B ) = 16$ 
C)  $n ( A \cup B ) = 14$ 
D)  $n ( A \cup B ) = 13$ 
A)  $n ( A \cup B ) = 12$ 
B)  $n ( A \cup B ) = 16$ 
C)  $n ( A \cup B ) = 14$ 
D)  $n ( A \cup B ) = 13$

Question 9

Decide whether or not the set is closed under addition.
-{2}

Accepted Answer

A) Closed 
B) Not closed 
A) Closed 
B) Not closed

Question 10

Estimate the following mentally.
-$$3 + 57 + 44 + 36$$

Accepted Answer

A)  140 
B)  150 
C)  110 
D)  160 
A)  140 
B)  150 
C)  110 
D)  160

Question 11

Rewrite the problem as a multiplication problem.
-n ÷ m = 30

Accepted Answer

A) n ·m = 30 
B) n ·30 = m 
C) n = 30 · m 
D) m ·n = 30 
A) n ·m = 30 
B) n ·30 = m 
C) n = 30 · m 
D) m ·n = 30

Question 12

Decide whether or not the set is closed under addition.
-{2, 4, 6, 8, . . .}

Accepted Answer

A) Closed 
B) Not closed 
A) Closed 
B) Not closed

Question 13

Find the solution.
-3x + 3 = x + 19

Accepted Answer

A) 13 
B) 32 
C) 11 
D) 8 
A) 13 
B) 32 
C) 11 
D) 8

Question 14

Write the place value of the underlined numeral.
-

Accepted Answer

A)  Hundreds 
B)  Units 
C)  Thousands 
D)  Tens 
A)  Hundreds 
B)  Units 
C)  Thousands 
D)  Tens

Question 15

Provide an appropriate response.
-If $\mathrm { A } , \mathrm { B } , \mathrm { C }$, and $\mathrm { D }$ each stand for a different single digit from 1 to 9 , and $\mathrm { A } + \mathrm { B } + \mathrm { C } = \mathrm { D }$, what is the smallest value that $\mathrm { D }$ can have? What digits can $\mathrm { A } , \mathrm { B }$, and $\mathrm { C }$ never be?

Accepted Answer

6. The maximum value of D is 9

Question 16

Provide an appropriate response.
-$$\text { Is it possible to have } 8 _ { \text {seven? } } \text { ? If not, how should you write this number? }$$

Accepted Answer

The answer of Provide an appropriate response.
-\[\text { Is it...

Question 17

Perform the indicated operation.
-

Accepted Answer

A)  5 gross $2 \mathrm { dz } 3$ ones 
B)  4 gross $9 \mathrm { dz } 9$ ones 
C)  4 gross $10 \mathrm { dz } 9$ ones 
D)  4 gross $7 \mathrm { dz } 7$ ones 
A)  5 gross $2 \mathrm { dz } 3$ ones 
B)  4 gross $9 \mathrm { dz } 9$ ones 
C)  4 gross $10 \mathrm { dz } 9$ ones 
D)  4 gross $7 \mathrm { dz } 7$ ones

Question 18

Provide an appropriate response.
-$$\text { Show that } 1010 _ { \text {two } } = 20 _{\text { five. }}$$

Accepted Answer

The answer of Provide an appropriate response.
-\[\text { Show that...

Question 19

Use the distributive property to factor the following.
-$$( y + 1 ) x + ( y + 1 )$$

Accepted Answer

A)  $x ^ { 2 } ( y + 1 )$ 
B)  $( y + 1 ) ( x + 1 )$ 
C)  $x ( y + 1 )$ 
D)  $x ( y + 1 ) ^ { 2 }$ 
A)  $x ^ { 2 } ( y + 1 )$ 
B)  $( y + 1 ) ( x + 1 )$ 
C)  $x ( y + 1 )$ 
D)  $x ( y + 1 ) ^ { 2 }$

Question 20

Provide an appropriate response.
-$$\begin{array}{l}
\text { What base is being used in a 3-digit numeral having place values as depicted in the table. }\
\begin{array} { l | l | l } 
\text { 3rd position } & \text { 2nd position } & \text { 1st position } \
\hline \text { pairs of pairs } & \text { pairs } & \text { ones }
\end{array}
\end{array}$$

Accepted Answer

The answer of Provide an appropriate response.
-\[\begin{array}{l}
\text { What base...

Remove or add parentheses as indicated. -Place parentheses to make the equation $a \cdot b \div b + 5 b = a + 5 b$ true.

Convert the following. -632 seconds to minutes and seconds

Solve the problem. -Pat withdrew $495 from an ATM. If the ATM gives $100, $20, and $5 bills such that the total number of bills is the least, then how many of each type of bill did Pat get?

Find the missing numbers. -

Solve the problem. -James doubled his profit compared with that of last year. Last year he doubled his profit from the previous year. If his profit this year was $12,000, then what was his profit last year and the year Before that?

For the given Hindu-Arabic numeral, write an equivalent numeral in the indicated system. -72,302; Mayan

Convert the following. -44 inches to feet and inches

If $n ( A ) = 5 , n ( B ) = 11$ and $n ( A \cap B ) = 3$ , what do you know about $n ( A \cup B )$ ?

Decide whether or not the set is closed under addition. -{2}

Estimate the following mentally. - $3 + 57 + 44 + 36$

Rewrite the problem as a multiplication problem. -n ÷ m = 30

Decide whether or not the set is closed under addition. -{2, 4, 6, 8, . . .}

Find the solution. -3x + 3 = x + 19

Write the place value of the underlined numeral. -

Provide an appropriate response. - $\text { Is it possible to have } 8 _ { \text {seven? } } \text { ? If not, how should you write this number? }$

Perform the indicated operation. -

Provide an appropriate response. - $\text { Show that } 1010 _ { \text {two } } = 20 _{\text { five. }}$

Use the distributive property to factor the following. - $( y + 1 ) x + ( y + 1 )$

Provide an appropriate response. - What base is being used in a 3-digit numeral having place values as depicted in the table. 3rd position 2nd position 1st position pairs of pairs pairs ones

An Introduction to Problem Solving

Introduction to Logic and Sets

Number Theory

Integers

Rational Numbers and Proportional Reasoning

Rational Numbers As Decimals and Percents

Real Numbers and Algebraic Thinking

Probability

Data Analysisstatistics: an Introduction

Introductory Geometry

Congruence and Similarity With Constructions

Congruence and Similarity With Transformations

Area, Pythagorean Theorem, and Volume

Filters

Exam 3: Numeration Systems and Whole Number Operations

Remove or add parentheses as indicated. -Place parentheses to make the equation a⋅b÷b+5b=a+5ba \cdot b \div b + 5 b = a + 5 ba⋅b÷b+5b=a+5b true.