Question 1

Evaluate the expression.
-$- ( - 2 ) ^ { 3 }$

Accepted Answer

A)  8 
B)  $- 8$ 
C)  6 
D)  $- 6$ 
A)  8 
B)  $- 8$ 
C)  6 
D)  $- 6$

Question 2

Solve the inequality, then graph the solution.
-$- 6 < - 3 b + 3 \leq 6$

Accepted Answer

A)  $( - 3,1 ]$
  
B)  $[ - 1,3 )$
  
C)  $[ - 3,1 )$
  
D)  $( - 1,3 ]$
  
A)  $( - 3,1 ]$
  
B)  $[ - 1,3 )$
  
C)  $[ - 3,1 )$
  
D)  $( - 1,3 ]$

Question 3

Solve the problem.
-Suppose the sales of a particular brand of appliance satisfy the relationship S(x)= 240x + 2000, where S(x)represents the number of sales in year x, with x = 0 corresponding to 1982. In what year Would the sales be 4880?

Accepted Answer

A) 1992 
B) 1994 
C) 1991 
D) 1997 
A) 1992 
B) 1994 
C) 1991 
D) 1997

Question 4

Answer the question based on the given graph.
- 
In which month(s) does the percentage of earthquakes exceed $10 \%$ ?

Accepted Answer

A)  November and December 
B)  September 
C)  August and September 
D)  September and November 
A)  November and December 
B)  September 
C)  August and September 
D)  September and November

Question 5

Solve the equation.
-$15 ( 9 c - 8 ) = 2 c - 2$

Accepted Answer

A)  $\left\{ - \frac { 118 } { 133 } \right\}$ 
B)  $\left\{ \frac { 122 } { 133 } \right\}$ 
C)  $\left\{ \frac { 118 } { 133 } \right\}$ 
D)  $\left\{ \frac { 118 } { 137 } \right\}$ 
A)  $\left\{ - \frac { 118 } { 133 } \right\}$ 
B)  $\left\{ \frac { 122 } { 133 } \right\}$ 
C)  $\left\{ \frac { 118 } { 133 } \right\}$ 
D)  $\left\{ \frac { 118 } { 137 } \right\}$

Question 6

Decide whether the equation is "conditional," an "identity," or a "contradiction." Give its solution set.
-$2 [ 3 - ( 9 - 5 r ) ] - r = - 18 + 3 ( 2 + 3 r )$

Accepted Answer

A)  Conditional; $\{ 18 \}$ 
B)  Conditional; $\{ - 9 \}$ 
C)  Contradiction; $\varnothing$ 
D)  Identity; {all real numbers $\}$ 
A)  Conditional; $\{ 18 \}$ 
B)  Conditional; $\{ - 9 \}$ 
C)  Contradiction; $\varnothing$ 
D)  Identity; {all real numbers $\}$

Question 7

Solve the inequality, giving its solution set in both interval and graph forms.
-$f - 3 < - 5$

Accepted Answer

A)  $( - \infty , - 2 )$
  
B)  $[ - 2 , \infty )$
  
C)  $( - 2 , \infty )$
  
D)  $( - \infty , - 2 ]$
  
A)  $( - \infty , - 2 )$
  
B)  $[ - 2 , \infty )$
  
C)  $( - 2 , \infty )$
  
D)  $( - \infty , - 2 ]$

Question 8

Translate the verbal phrase into a mathematical expression. Use x to represent the unknown number.
-Twice some number

Accepted Answer

A)  $2 + x$ 
B)  $\frac { 2 } { x }$ 
C)  $2 - x$ 
D)  $2 x$ 
A)  $2 + x$ 
B)  $\frac { 2 } { x }$ 
C)  $2 - x$ 
D)  $2 x$

Question 9

There were 35,000 people at a ball game in Los Angeles. The day's receipts were $247,000. How many people paid $14.00 for reserved seats and how many paid $5.00 for general admission?

Accepted Answer

A) 8000 paid $14 and 27,000 paid $5 
B) 17,000 paid $14 and 18,000 paid $5 
C) 27,000 paid $14 and 8000 paid $5 
D) 18,000 paid $14 and 17,000 paid $5 
A) 8000 paid $14 and 27,000 paid $5 
B) 17,000 paid $14 and 18,000 paid $5 
C) 27,000 paid $14 and 8000 paid $5 
D) 18,000 paid $14 and 17,000 paid $5

Question 10

In a chemistry class, 6 liters of a 4% silver iodide solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed?

Accepted Answer

A) 6 liters 
B) 4 liters 
C) 2 liters 
D) 3 liters 
A) 6 liters 
B) 4 liters 
C) 2 liters 
D) 3 liters

Question 11

A bank teller has some five-dollar bills and some twenty-dollar bills. The teller has 5 more of the twenties. The total value of the money is $675. Find the number of five-dollar bills that the teller
Has.

Accepted Answer

A) 18 five-dollar bills 
B) 23 five-dollar bills 
C) 28 five-dollar bills 
D) 33 five-dollar bills 
A) 18 five-dollar bills 
B) 23 five-dollar bills 
C) 28 five-dollar bills 
D) 33 five-dollar bills

Question 12

The weight of a liquid varies directly as its volume V. If the weight of the liquid in a cubical container 4 cm on a side is 128 g, find the weight of the liquid in a cubical container 5 cm on a side.

Accepted Answer

A) 105 g 
B) 10 g 
C) 250 g 
D) 125 g 
A) 105 g 
B) 10 g 
C) 250 g 
D) 125 g

Question 13

Evaluate the expression.
-$- \left( - \frac { 3 } { 4 } \right) ^ { 3 }$

Accepted Answer

A)  $- \frac { 9 } { 12 }$ 
B)  $- \frac { 27 } { 64 }$ 
C)  $\frac { 27 } { 64 }$ 
D)  $\frac { 64 } { 27 }$ 
A)  $- \frac { 9 } { 12 }$ 
B)  $- \frac { 27 } { 64 }$ 
C)  $\frac { 27 } { 64 }$ 
D)  $\frac { 64 } { 27 }$

Question 14

Solve the formula for the specified variable.
-$A = \frac { 1 } { 2 } b h ;$ for $b$

Accepted Answer

A)  $b = \frac { 2 A } { h }$ 
B)  $b = \frac { A } { 2 h }$ 
C)  $b = \frac { \mathrm { Ah } } { 2 }$ 
D)  $b = \frac { h } { 2 \mathrm {~A} }$ 
A)  $b = \frac { 2 A } { h }$ 
B)  $b = \frac { A } { 2 h }$ 
C)  $b = \frac { \mathrm { Ah } } { 2 }$ 
D)  $b = \frac { h } { 2 \mathrm {~A} }$

Question 15

Decide whether the equation is "conditional," an "identity," or a "contradiction." Give its solution set.
-$3 ( 5 f + 9 ) = 15 f + 27$

Accepted Answer

A)  Conditional; {all real numbers } 
B)  Identity; {all real numbers } 
C)  Contradiction; $\varnothing$ 
D)  Identity; $\varnothing$ 
A)  Conditional; {all real numbers } 
B)  Identity; {all real numbers } 
C)  Contradiction; $\varnothing$ 
D)  Identity; $\varnothing$

Question 16

Decide whether the proportion is true or false.
-$\frac { 50 } { 78 } = \frac { 150 } { 234 }$

Accepted Answer

A) True 
 B)False

Question 17

Solve the equation.
-$25 \mathrm {~b} + 24 = 13 \mathrm {~b}$

Accepted Answer

A)  $\{ - 2 \}$ 
B)  $\{ 2 \}$ 
C)  $\left\{ - \frac { 3 } { 38 } \right\}$ 
D)  $\left\{ - \frac { 1 } { 2 } \right\}$ 
A)  $\{ - 2 \}$ 
B)  $\{ 2 \}$ 
C)  $\left\{ - \frac { 3 } { 38 } \right\}$ 
D)  $\left\{ - \frac { 1 } { 2 } \right\}$

Question 18

A convention manager finds that she has $1540, made up of twenties and fifties. She has a total of 50 bills. How many fifty-dollar bills does the manager have?

Accepted Answer

A) 50 fifty-dollar bills 
B) 18 fifty-dollar bills 
C) 12 fifty-dollar bills 
D) 32 fifty-dollar bills 
A) 50 fifty-dollar bills 
B) 18 fifty-dollar bills 
C) 12 fifty-dollar bills 
D) 32 fifty-dollar bills

Question 19

Evaluate the expression.
-$\left( \frac { 2 } { 3 } \right) ^ { - 2 }$

Accepted Answer

A)  $\frac { 9 } { 4 }$ 
B)  $- \frac { 4 } { 9 }$ 
C)  $- \frac { 9 } { 4 }$ 
D)  $\frac { 4 } { 9 }$ 
A)  $\frac { 9 } { 4 }$ 
B)  $- \frac { 4 } { 9 }$ 
C)  $- \frac { 9 } { 4 }$ 
D)  $\frac { 4 } { 9 }$

Question 20

The gravitational attraction A between two masses varies inversely as the square of the distance between them. If the force of attraction is 9 lb when the masses are 2 ft apart, what is the attraction
When the masses are 6 ft apart?

Accepted Answer

A) 4 lb 
B) 3 lb 
C) 2 lb 
D) 1 lb 
A) 4 lb 
B) 3 lb 
C) 2 lb 
D) 1 lb

Evaluate the expression. - $- ( - 2 ) ^ { 3 }$

Solve the inequality, then graph the solution. - $- 6 < - 3 b + 3 \leq 6$ $Solve the inequality, then graph the solution. - - 6 < - 3 b + 3 \leq 6$

Solve the problem. -Suppose the sales of a particular brand of appliance satisfy the relationship S(x)= 240x + 2000, where S(x)represents the number of sales in year x, with x = 0 corresponding to 1982. In what year Would the sales be 4880?

Answer the question based on the given graph. - $Answer the question based on the given graph. - In which month(s) does the percentage of earthquakes exceed 10 \% ?$ In which month(s) does the percentage of earthquakes exceed $10 \%$ ?

Solve the equation. - $15 ( 9 c - 8 ) = 2 c - 2$

Decide whether the equation is "conditional," an "identity," or a "contradiction." Give its solution set. - $2 [ 3 - ( 9 - 5 r ) ] - r = - 18 + 3 ( 2 + 3 r )$

Solve the inequality, giving its solution set in both interval and graph forms. - $f - 3 < - 5$

Translate the verbal phrase into a mathematical expression. Use x to represent the unknown number. -Twice some number

There were 35,000 people at a ball game in Los Angeles. The day's receipts were $247,000. How many people paid $14.00 for reserved seats and how many paid $5.00 for general admission?

In a chemistry class, 6 liters of a 4% silver iodide solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed?

A bank teller has some five-dollar bills and some twenty-dollar bills. The teller has 5 more of the twenties. The total value of the money is $675. Find the number of five-dollar bills that the teller Has.

The weight of a liquid varies directly as its volume V. If the weight of the liquid in a cubical container 4 cm on a side is 128 g, find the weight of the liquid in a cubical container 5 cm on a side.

Evaluate the expression. - $- \left( - \frac { 3 } { 4 } \right) ^ { 3 }$

Solve the formula for the specified variable. - $A = \frac { 1 } { 2 } b h ;$ for $b$

Decide whether the equation is "conditional," an "identity," or a "contradiction." Give its solution set. - $3 ( 5 f + 9 ) = 15 f + 27$

Decide whether the proportion is true or false. - $\frac { 50 } { 78 } = \frac { 150 } { 234 }$

Solve the equation. - $25 \mathrm {~b} + 24 = 13 \mathrm {~b}$

A convention manager finds that she has $1540, made up of twenties and fifties. She has a total of 50 bills. How many fifty-dollar bills does the manager have?

Evaluate the expression. - $\left( \frac { 2 } { 3 } \right) ^ { - 2 }$

The gravitational attraction A between two masses varies inversely as the square of the distance between them. If the force of attraction is 9 lb when the masses are 2 ft apart, what is the attraction When the masses are 6 ft apart?

The Art of Problem Solving

The Basic Concepts of Set Theory

Introduction to Logic

Numeration Systems

Number Theory

The Real Numbers and Their Representations

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 7: The Basic Concepts of Algebra

Evaluate the expression. - −(−2)3- ( - 2 ) ^ { 3 }−(−2)3

Solve the inequality, then graph the solution. - −6<−3b+3≤6- 6 < - 3 b + 3 \leq 6−6<−3b+3≤6

Solve the problem. -Suppose the sales of a particular brand of appliance satisfy the relationship S(x)= 240x + 2000, where S(x)represents the number of sales in year x, with x = 0 corresponding to 1982. In what year Would the sales be 4880?

Answer the question based on the given graph. - In which month(s) does the percentage of earthquakes exceed 10%10 \%10% ?

Solve the equation. - 15(9c−8)=2c−215 ( 9 c - 8 ) = 2 c - 215(9c−8)=2c−2

Decide whether the equation is "conditional," an "identity," or a "contradiction." Give its solution set. - 2[3−(9−5r)]−r=−18+3(2+3r)2 [ 3 - ( 9 - 5 r ) ] - r = - 18 + 3 ( 2 + 3 r )2[3−(9−5r)]−r=−18+3(2+3r)

Solve the inequality, giving its solution set in both interval and graph forms. - f−3<−5f - 3 < - 5f−3<−5

Translate the verbal phrase into a mathematical expression. Use x to represent the unknown number. -Twice some number

There were 35,000 people at a ball game in Los Angeles. The day's receipts were $247,000. How many people paid $14.00 for reserved seats and how many paid $5.00 for general admission?

In a chemistry class, 6 liters of a 4% silver iodide solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed?

A bank teller has some five-dollar bills and some twenty-dollar bills. The teller has 5 more of the twenties. The total value of the money is $675. Find the number of five-dollar bills that the teller Has.

The weight of a liquid varies directly as its volume V. If the weight of the liquid in a cubical container 4 cm on a side is 128 g, find the weight of the liquid in a cubical container 5 cm on a side.

Evaluate the expression. - −(−34)3- \left( - \frac { 3 } { 4 } \right) ^ { 3 }−(−43​)3

Solve the formula for the specified variable. - A=12bh;A = \frac { 1 } { 2 } b h ;A=21​bh; for bbb

Decide whether the equation is "conditional," an "identity," or a "contradiction." Give its solution set. - 3(5f+9)=15f+273 ( 5 f + 9 ) = 15 f + 273(5f+9)=15f+27

Decide whether the proportion is true or false. - 5078=150234\frac { 50 } { 78 } = \frac { 150 } { 234 }7850​=234150​

Solve the equation. - 25 b+24=13 b25 \mathrm {~b} + 24 = 13 \mathrm {~b}25 b+24=13 b

A convention manager finds that she has $1540, made up of twenties and fifties. She has a total of 50 bills. How many fifty-dollar bills does the manager have?

Evaluate the expression. - (23)−2\left( \frac { 2 } { 3 } \right) ^ { - 2 }(32​)−2

The gravitational attraction A between two masses varies inversely as the square of the distance between them. If the force of attraction is 9 lb when the masses are 2 ft apart, what is the attraction When the masses are 6 ft apart?

The Art of Problem Solving

The Basic Concepts of Set Theory

Introduction to Logic

Numeration Systems

Number Theory

The Real Numbers and Their Representations

Graphs, Functions, and Systems of Equations and Inequalities

Geometry

Counting Methods

Probability

Statistics

Personal Financial Management

Trigonometry Formerly

Graph Theory

Voting and Apportionment

Filters

Evaluate the expression. - $- ( - 2 ) ^ { 3 }$

Solve the inequality, then graph the solution. - $- 6 < - 3 b + 3 \leq 6$ $Solve the inequality, then graph the solution. - - 6 < - 3 b + 3 \leq 6$

Answer the question based on the given graph. - $Answer the question based on the given graph. - In which month(s) does the percentage of earthquakes exceed 10 \% ?$ In which month(s) does the percentage of earthquakes exceed $10 \%$ ?

Solve the equation. - $15 ( 9 c - 8 ) = 2 c - 2$

Decide whether the equation is "conditional," an "identity," or a "contradiction." Give its solution set. - $2 [ 3 - ( 9 - 5 r ) ] - r = - 18 + 3 ( 2 + 3 r )$

Solve the inequality, giving its solution set in both interval and graph forms. - $f - 3 < - 5$

Evaluate the expression. - $- \left( - \frac { 3 } { 4 } \right) ^ { 3 }$

Solve the formula for the specified variable. - $A = \frac { 1 } { 2 } b h ;$ for $b$

Decide whether the equation is "conditional," an "identity," or a "contradiction." Give its solution set. - $3 ( 5 f + 9 ) = 15 f + 27$

Decide whether the proportion is true or false. - $\frac { 50 } { 78 } = \frac { 150 } { 234 }$

Solve the equation. - $25 \mathrm {~b} + 24 = 13 \mathrm {~b}$

Evaluate the expression. - $\left( \frac { 2 } { 3 } \right) ^ { - 2 }$