Question 1

Use the method suggested to compute mentally.
-Use breaking and bridging. $\begin{array}{r}
86 \
+\quad 69 \
\hline
\end{array}$

Accepted Answer

A)  157 
B)  154 
C)  155 
D)  153 
A)  157 
B)  154 
C)  155 
D)  153

Question 2

Rewrite the subtraction problem as an equivalent addition problem.
-x - 55 = 77

Accepted Answer

A) x = 77 + 55 
B) x + 77 = 55 
C) x + 55 = 77 
D) x - 77 = 55 
A) x = 77 + 55 
B) x + 77 = 55 
C) x + 55 = 77 
D) x - 77 = 55

Question 3

Use the distributive property to factor the following.
-$$x ^ { 2 } y + x y ^ { 2 }$$

Accepted Answer

A)  $x y ( x + y )$ 
B)  $x ( x y + y )$ 
C)  $x ^ { 2 } \left( y + y ^ { 2 } \right)$ 
D)  $x ^ { 2 } ( y + x y )$ 
A)  $x y ( x + y )$ 
B)  $x ( x y + y )$ 
C)  $x ^ { 2 } \left( y + y ^ { 2 } \right)$ 
D)  $x ^ { 2 } ( y + x y )$

Question 4

Write the place value of the underlined numeral.
-

Accepted Answer

A)  Thousands 
B)  Hundreds 
C)  Tens 
D)  Hundred thousands 
A)  Thousands 
B)  Hundreds 
C)  Tens 
D)  Hundred thousands

Question 5

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

Accepted Answer

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

Question 6

Find the missing numbers.
-

Accepted Answer

A)  $( \mathrm { a } ) = 3 , ( \mathrm {~b} ) = 1 , ( \mathrm { c } ) = 9 , ( \mathrm {~d} ) = 4$ 
B)  $( \mathrm { a } ) = 5 , ( \mathrm {~b} ) = 2 , ( \mathrm { c } ) = 1 , ( \mathrm {~d} ) = 6$ 
C)  $( \mathrm { a } ) = 4 , ( \mathrm {~b} ) = 1 , ( \mathrm { c } ) = 9 , ( \mathrm {~d} ) = 4$ 
D)  $( a ) = 9 , ( b ) = 1 , ( c ) = 0 , ( d ) = 5$ 
A)  $( \mathrm { a } ) = 3 , ( \mathrm {~b} ) = 1 , ( \mathrm { c } ) = 9 , ( \mathrm {~d} ) = 4$ 
B)  $( \mathrm { a } ) = 5 , ( \mathrm {~b} ) = 2 , ( \mathrm { c } ) = 1 , ( \mathrm {~d} ) = 6$ 
C)  $( \mathrm { a } ) = 4 , ( \mathrm {~b} ) = 1 , ( \mathrm { c } ) = 9 , ( \mathrm {~d} ) = 4$ 
D)  $( a ) = 9 , ( b ) = 1 , ( c ) = 0 , ( d ) = 5$

Question 7

Find, if possible, the whole number that makes the equation true.
-$45 \div \square + 6 = 21$

Accepted Answer

A)  3 
B)  1 
C)  15 
D)  6 
A)  3 
B)  1 
C)  15 
D)  6

Question 8

For the given Hindu-Arabic numeral, write an equivalent numeral in the indicated system.
-999; Roman

Accepted Answer

A) IM 
B) CMXCIX 
C) MCXCIX 
D) IXM 
A) IM 
B) CMXCIX 
C) MCXCIX 
D) IXM

Question 9

Solve the problem.
-You work 2 hours each weekday, and sometimes you work 8 hours on Saturday. What is the maximum number of hours you might work during any given week?

Accepted Answer

A) 10 
B) 40 
C) 18 
D) 26 
A) 10 
B) 40 
C) 18 
D) 26

Question 10

Provide an appropriate response.
-What is the smallest 3-digit number in base seven?

Accepted Answer

The answer of Provide an appropriate response.
-What is the smallest...

Question 11

Provide an appropriate response.
-Given that the counting  represents the number 7 , where the value of each dot is represented by the number in the box below the dot, what does the counting frame   epresent?

Accepted Answer

The answer of Provide an appropriate response.
-Given that the counting...

Question 12

Solve the problem.
-Indicate which digit in 54,972 has place value thousands.

Accepted Answer

A) 0 
B) 7 
C) 4 
D) 9 
A) 0 
B) 7 
C) 4 
D) 9

Question 13

Decide which property of addition is illustrated.
-2 + 8 = 8 + 2

Accepted Answer

A) Associative 
B) Commutative 
A) Associative 
B) Commutative

Question 14

Convert the base-ten number to a number in the indicated base.
-2,874 to base five

Accepted Answer

A) 42,444five 
B) 42,422five 
C) 42,424five 
D) 42,222five 
A) 42,444five 
B) 42,422five 
C) 42,424five 
D) 42,222five

Question 15

Find the solutions in the set W.
-x - 3 = x + 6

Accepted Answer

A) no solution 
B) 9 
C) 0 
D) all whole numbers 
A) no solution 
B) 9 
C) 0 
D) all whole numbers

Question 16

Use the method suggested to compute mentally.
-Use breaking and bridging. $\begin{array}{r}
82 \
-\quad 49 \
\hline
\end{array}$

Accepted Answer

A)  32 
B)  34 
C)  31 
D)  33 
A)  32 
B)  34 
C)  31 
D)  33

Question 17

Write the base-four numeral for the base-four blocks shown.

Accepted Answer

A)  3120 four 
B)  2013 four 
C)  213 four 
D)  312 four 
A)  3120 four 
B)  2013 four 
C)  213 four 
D)  312 four

Question 18

Remove or add parentheses as indicated.
-Rewrite $( x + y + z ) ( x - y )$ without parentheses.

Accepted Answer

A)  $x ^ { 2 } + y ^ { 2 } + x z - y z + 2 x y$ 
B)  $x ^ { 2 } - y ^ { 2 } + x z - y z - 2 x y$ 
C)  $x ^ { 2 } - y ^ { 2 } + x z - y z$ 
D)  $x ^ { 2 } - y ^ { 2 } + x z - y z + 2 x y$ 
A)  $x ^ { 2 } + y ^ { 2 } + x z - y z + 2 x y$ 
B)  $x ^ { 2 } - y ^ { 2 } + x z - y z - 2 x y$ 
C)  $x ^ { 2 } - y ^ { 2 } + x z - y z$ 
D)  $x ^ { 2 } - y ^ { 2 } + x z - y z + 2 x y$

Question 19

Rewrite the problem as a multiplication problem.
-70 ÷ 7 = x

Accepted Answer

A) 70 ÷ x = 7 
B) 70 ·7 = x 
C) 10 ·7 = x 
D) 70 = x ·7 
A) 70 ÷ x = 7 
B) 70 ·7 = x 
C) 10 ·7 = x 
D) 70 = x ·7

Question 20

Solve the problem.
-You have two times as many dimes as quarters and the same number of quarters and nickels in your pocket. If there are 4 quarters in your pocket, what is the maximum number of single dollar
Bills you can get in exchange for your loose change? Would you have any change left over?

Accepted Answer

A) 2, Yes 
B) 3, No 
C) 3, Yes 
D) 2, No 
A) 2, Yes 
B) 3, No 
C) 3, Yes 
D) 2, No

Use the method suggested to compute mentally. -Use breaking and bridging. 86 +69

Rewrite the subtraction problem as an equivalent addition problem. -x - 55 = 77

Use the distributive property to factor the following. - $x ^ { 2 } y + x y ^ { 2 }$

Write the place value of the underlined numeral. -

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

Find the missing numbers. -

Find, if possible, the whole number that makes the equation true. - $45 \div \square + 6 = 21$

For the given Hindu-Arabic numeral, write an equivalent numeral in the indicated system. -999; Roman

Solve the problem. -You work 2 hours each weekday, and sometimes you work 8 hours on Saturday. What is the maximum number of hours you might work during any given week?

Provide an appropriate response. -What is the smallest 3-digit number in base seven?

Provide an appropriate response. -Given that the counting framerepresents the number 7 , where the value of each dot is represented by the number in the box below the dot, what does the counting frame epresent?

Solve the problem. -Indicate which digit in 54,972 has place value thousands.

Decide which property of addition is illustrated. -2 + 8 = 8 + 2

Convert the base-ten number to a number in the indicated base. -2,874 to base five

Find the solutions in the set W. -x - 3 = x + 6

Use the method suggested to compute mentally. -Use breaking and bridging. 82 -49

Write the base-four numeral for the base-four blocks shown.

Remove or add parentheses as indicated. -Rewrite $( x + y + z ) ( x - y )$ without parentheses.

Rewrite the problem as a multiplication problem. -70 ÷ 7 = x

Solve the problem. -You have two times as many dimes as quarters and the same number of quarters and nickels in your pocket. If there are 4 quarters in your pocket, what is the maximum number of single dollar Bills you can get in exchange for your loose change? Would you have any change left over?

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

Use the method suggested to compute mentally. -Use breaking and bridging. 86 +69

Rewrite the subtraction problem as an equivalent addition problem. -x - 55 = 77

Use the distributive property to factor the following. - x2y+xy2x ^ { 2 } y + x y ^ { 2 }x2y+xy2

Write the place value of the underlined numeral. -

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

Find the missing numbers. -

Find, if possible, the whole number that makes the equation true. - 45÷□+6=2145 \div \square + 6 = 2145÷□+6=21

For the given Hindu-Arabic numeral, write an equivalent numeral in the indicated system. -999; Roman

Solve the problem. -You work 2 hours each weekday, and sometimes you work 8 hours on Saturday. What is the maximum number of hours you might work during any given week?

Provide an appropriate response. -What is the smallest 3-digit number in base seven?

Provide an appropriate response. -Given that the counting framerepresents the number 7 , where the value of each dot is represented by the number in the box below the dot, what does the counting frame epresent?

Solve the problem. -Indicate which digit in 54,972 has place value thousands.

Decide which property of addition is illustrated. -2 + 8 = 8 + 2

Convert the base-ten number to a number in the indicated base. -2,874 to base five

Find the solutions in the set W. -x - 3 = x + 6

Use the method suggested to compute mentally. -Use breaking and bridging. 82 -49

Write the base-four numeral for the base-four blocks shown.

Remove or add parentheses as indicated. -Rewrite (x+y+z)(x−y)( x + y + z ) ( x - y )(x+y+z)(x−y) without parentheses.

Rewrite the problem as a multiplication problem. -70 ÷ 7 = x

Solve the problem. -You have two times as many dimes as quarters and the same number of quarters and nickels in your pocket. If there are 4 quarters in your pocket, what is the maximum number of single dollar Bills you can get in exchange for your loose change? Would you have any change left over?

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

Use the distributive property to factor the following. - $x ^ { 2 } y + x y ^ { 2 }$

Find, if possible, the whole number that makes the equation true. - $45 \div \square + 6 = 21$

Remove or add parentheses as indicated. -Rewrite $( x + y + z ) ( x - y )$ without parentheses.