Question 1

Evaluate the expression.
-$\frac { 1 } { 4 ^ { - 3 } }$

Accepted Answer

A)  12 
B)  16 
C)  64 
D)  256 
A)  12 
B)  16 
C)  64 
D)  256

Question 2

Decide whether the proportion is true or false.
-$\frac { \frac { 1 } { 7 } } { 17 } = \frac { 1 } { 119 }$

Accepted Answer

A) True 
 B)False

Question 3

Solve the problem.
-The mathematical model C = 600x + 80,000 represents the cost in dollars a company has in manufacturing x items during a month. How many items were produced if costs reached $440,000?

Accepted Answer

A) 467 items 
B) 867 items 
C) 600 items 
D) 439,400 items 
A) 467 items 
B) 867 items 
C) 600 items 
D) 439,400 items

Question 4

Mardi received an inheritance of $60,000. She invested part at 8% and deposited the remainder in tax-free bonds at 12%. Her total annual income from the investments was $6000. Find the amount
Invested at 8%.

Accepted Answer

A) $15,000 
B) $54,000 
C) $29,000 
D) $30,000 
A) $15,000 
B) $54,000 
C) $29,000 
D) $30,000

Question 5

Evaluate the expression.
-$3 ^ { - 1 } + 4 ^ { - 1 }$

Accepted Answer

A)  $\frac { 12 } { 7 }$ 
B)  2 
C)  $- 1$ 
D)  $\frac { 7 } { 12 }$ 
A)  $\frac { 12 } { 7 }$ 
B)  2 
C)  $- 1$ 
D)  $\frac { 7 } { 12 }$

Question 6

At the end of the day, a storekeeper had $1712 in the cash register, counting both the sale of goods and the sales tax of 7%. Find the amount of the tax.

Accepted Answer

A) $102 
B) $112 
C) $107 
D) $117 
A) $102 
B) $112 
C) $107 
D) $117

Question 7

A tree casts a shadow 34 m long. At the same time, the shadow cast by a 41-cm tall statue is 88 cm long. Find the height of the tree. Round results to the nearest unit.

Accepted Answer

A) 14 m 
B) 16 m 
C) 71 m 
D) 73 m 
A) 14 m 
B) 16 m 
C) 71 m 
D) 73 m

Question 8

Decide whether the statement translates into an expression or an equation.
-66% of a number decreased by 14.

Accepted Answer

A) Expression 
B) Equation 
A) Expression 
B) Equation

Question 9

Solve the equation.
-$- 9 x + 5 ( - 3 x - 2 ) = - 30 - 4 x$

Accepted Answer

A)  $\left\{ \frac { 10 } { 7 } \right\}$ 
B)  $\{ 1 \rangle$ 
C)  $\{ - 1 \}$ 
D)  $\{ 2 \}$ 
A)  $\left\{ \frac { 10 } { 7 } \right\}$ 
B)  $\{ 1 \rangle$ 
C)  $\{ - 1 \}$ 
D)  $\{ 2 \}$

Question 10

Solve the equation.
-$\frac { x } { 45 } = \frac { 4 } { 15 }$

Accepted Answer

A) 168.8 
B) 12 
C) 1.3 
D) 16 
A) 168.8 
B) 12 
C) 1.3 
D) 16

Question 11

Solve the inequality, giving its solution set in both interval and graph forms.
-$\frac { 8 x + 3 } { 8 } < \frac { 61 } { 8 }$

Accepted Answer

A)  $\left( - \infty , \frac { 29 } { 4 } \right)$
  
B)  $\left( - \infty , \frac { 61 } { 8 } \right)$
  
C)  $\left( \frac { 29 } { 4 } , \infty \right)$
  
D)  $\left( \frac { 61 } { 8 } , \infty \right)$
  
A)  $\left( - \infty , \frac { 29 } { 4 } \right)$
  
B)  $\left( - \infty , \frac { 61 } { 8 } \right)$
  
C)  $\left( \frac { 29 } { 4 } , \infty \right)$
  
D)  $\left( \frac { 61 } { 8 } , \infty \right)$

Question 12

Solve the problem.
-The ratio of the distances a pitching wedge and an 8-iron will drive a golf ball is 4 to 5. If a golfer averages 88 yards with a pitching wedge, how far should she average with an 8-iron?

Accepted Answer

A) 110 yd 
B) 70 yd 
C) 79 yd 
D) 97 yd 
A) 110 yd 
B) 70 yd 
C) 79 yd 
D) 97 yd

Question 13

Solve the equation.
-$7 [ - 6 z - 3 + 5 ( z + 1 ) ] = 4 z + 2$

Accepted Answer

A)  $\{ 9 \}$ 
B)  $\left\{ \frac { 54 } { 11 } \right\}$ 
C)  $\left\{ \frac { 12 } { 11 } \right\}$ 
D)  $\{ 2 \}$ 
A)  $\{ 9 \}$ 
B)  $\left\{ \frac { 54 } { 11 } \right\}$ 
C)  $\left\{ \frac { 12 } { 11 } \right\}$ 
D)  $\{ 2 \}$

Question 14

Decide whether the statement translates into an expression or an equation.
-a number divided by 11

Accepted Answer

A) Equation 
B) Expression 
A) Equation 
B) Expression

Question 15

Decide whether the equation is "conditional," an "identity," or a "contradiction." Give its solution set.
-$- 20 s + 47 + 5 ( 4 s - 8 ) = 0$

Accepted Answer

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

Question 16

Evaluate the expression.
-$( - 3 ) ^ { - 4 }$

Accepted Answer

A)  $\frac { 1 } { 81 }$ 
B)  $\frac { 1 } { - 81 }$ 
C)  $- 81$ 
D)  81 
A)  $\frac { 1 } { 81 }$ 
B)  $\frac { 1 } { - 81 }$ 
C)  $- 81$ 
D)  81

Question 17

Solve the formula for the specified variable.
-$P = 2 L + 2 W ; \text { for } L$

Accepted Answer

A)  $\mathrm { L } = \frac { \mathrm { P } - \mathrm { W } } { 2 }$ 
B)  $L = P - W$ 
C)  $L = \frac { P - 2 W } { 2 }$ 
D)  $L = d - 2 W$ 
A)  $\mathrm { L } = \frac { \mathrm { P } - \mathrm { W } } { 2 }$ 
B)  $L = P - W$ 
C)  $L = \frac { P - 2 W } { 2 }$ 
D)  $L = d - 2 W$

Question 18

Translate the verbal phrase into a mathematical expression. Use x to represent the unknown number.
-The product of 22 and a number

Accepted Answer

A)  $22 + x$ 
B)  $\frac { 22 } { x }$ 
C)  $22 - x$ 
D)  $22 x$ 
A)  $22 + x$ 
B)  $\frac { 22 } { x }$ 
C)  $22 - x$ 
D)  $22 x$

Question 19

Solve the equation.
-$10 y = 4 y + 3 + 5 y$

Accepted Answer

A)  $\{ - 30 \}$ 
B)  $\{ 30 \}$ 
C)  $\{ - 3 \}$ 
D)  $\{ 3 \}$ 
A)  $\{ - 30 \}$ 
B)  $\{ 30 \}$ 
C)  $\{ - 3 \}$ 
D)  $\{ 3 \}$

Question 20

Solve the problem.
-The sides of a triangle are 8 inches, 11 inches, and 14 inches. If the shortest side of a similar triangle is 48 inches, find its longest side.

Accepted Answer

A) 84 inches 
B) 11 inches 
C) 66 inches 
D) 65 inches 
A) 84 inches 
B) 11 inches 
C) 66 inches 
D) 65 inches

Evaluate the expression. - $\frac { 1 } { 4 ^ { - 3 } }$

Decide whether the proportion is true or false. - $\frac { \frac { 1 } { 7 } } { 17 } = \frac { 1 } { 119 }$

Solve the problem. -The mathematical model C = 600x + 80,000 represents the cost in dollars a company has in manufacturing x items during a month. How many items were produced if costs reached $440,000?

Mardi received an inheritance of $60,000. She invested part at 8% and deposited the remainder in tax-free bonds at 12%. Her total annual income from the investments was $6000. Find the amount Invested at 8%.

Evaluate the expression. - $3 ^ { - 1 } + 4 ^ { - 1 }$

At the end of the day, a storekeeper had $1712 in the cash register, counting both the sale of goods and the sales tax of 7%. Find the amount of the tax.

A tree casts a shadow 34 m long. At the same time, the shadow cast by a 41-cm tall statue is 88 cm long. Find the height of the tree. Round results to the nearest unit.

Decide whether the statement translates into an expression or an equation. -66% of a number decreased by 14.

Solve the equation. - $- 9 x + 5 ( - 3 x - 2 ) = - 30 - 4 x$

Solve the equation. - $\frac { x } { 45 } = \frac { 4 } { 15 }$

Solve the inequality, giving its solution set in both interval and graph forms. - $\frac { 8 x + 3 } { 8 } < \frac { 61 } { 8 }$ $Solve the inequality, giving its solution set in both interval and graph forms. - \frac { 8 x + 3 } { 8 } < \frac { 61 } { 8 }$

Solve the problem. -The ratio of the distances a pitching wedge and an 8-iron will drive a golf ball is 4 to 5. If a golfer averages 88 yards with a pitching wedge, how far should she average with an 8-iron?

Solve the equation. - $7 [ - 6 z - 3 + 5 ( z + 1 ) ] = 4 z + 2$

Decide whether the statement translates into an expression or an equation. -a number divided by 11

Decide whether the equation is "conditional," an "identity," or a "contradiction." Give its solution set. - $- 20 s + 47 + 5 ( 4 s - 8 ) = 0$

Evaluate the expression. - $( - 3 ) ^ { - 4 }$

Solve the formula for the specified variable. - $P = 2 L + 2 W ; \text { for } L$

Translate the verbal phrase into a mathematical expression. Use x to represent the unknown number. -The product of 22 and a number

Solve the equation. - $10 y = 4 y + 3 + 5 y$

Solve the problem. -The sides of a triangle are 8 inches, 11 inches, and 14 inches. If the shortest side of a similar triangle is 48 inches, find its longest side.

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. - 14−3\frac { 1 } { 4 ^ { - 3 } }4−31​

Decide whether the proportion is true or false. - 1717=1119\frac { \frac { 1 } { 7 } } { 17 } = \frac { 1 } { 119 }1771​​=1191​

Solve the problem. -The mathematical model C = 600x + 80,000 represents the cost in dollars a company has in manufacturing x items during a month. How many items were produced if costs reached $440,000?

Mardi received an inheritance of $60,000. She invested part at 8% and deposited the remainder in tax-free bonds at 12%. Her total annual income from the investments was $6000. Find the amount Invested at 8%.

Evaluate the expression. - 3−1+4−13 ^ { - 1 } + 4 ^ { - 1 }3−1+4−1

At the end of the day, a storekeeper had $1712 in the cash register, counting both the sale of goods and the sales tax of 7%. Find the amount of the tax.

A tree casts a shadow 34 m long. At the same time, the shadow cast by a 41-cm tall statue is 88 cm long. Find the height of the tree. Round results to the nearest unit.

Decide whether the statement translates into an expression or an equation. -66% of a number decreased by 14.

Solve the equation. - −9x+5(−3x−2)=−30−4x- 9 x + 5 ( - 3 x - 2 ) = - 30 - 4 x−9x+5(−3x−2)=−30−4x

Solve the equation. - x45=415\frac { x } { 45 } = \frac { 4 } { 15 }45x​=154​

Solve the inequality, giving its solution set in both interval and graph forms. - 8x+38<618\frac { 8 x + 3 } { 8 } < \frac { 61 } { 8 }88x+3​<861​

Solve the problem. -The ratio of the distances a pitching wedge and an 8-iron will drive a golf ball is 4 to 5. If a golfer averages 88 yards with a pitching wedge, how far should she average with an 8-iron?

Solve the equation. - 7[−6z−3+5(z+1)]=4z+27 [ - 6 z - 3 + 5 ( z + 1 ) ] = 4 z + 27[−6z−3+5(z+1)]=4z+2

Decide whether the statement translates into an expression or an equation. -a number divided by 11

Decide whether the equation is "conditional," an "identity," or a "contradiction." Give its solution set. - −20s+47+5(4s−8)=0- 20 s + 47 + 5 ( 4 s - 8 ) = 0−20s+47+5(4s−8)=0

Evaluate the expression. - (−3)−4( - 3 ) ^ { - 4 }(−3)−4

Solve the formula for the specified variable. - P=2L+2W; for LP = 2 L + 2 W ; \text { for } LP=2L+2W; for L

Translate the verbal phrase into a mathematical expression. Use x to represent the unknown number. -The product of 22 and a number

Solve the equation. - 10y=4y+3+5y10 y = 4 y + 3 + 5 y10y=4y+3+5y

Solve the problem. -The sides of a triangle are 8 inches, 11 inches, and 14 inches. If the shortest side of a similar triangle is 48 inches, find its longest side.

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. - $\frac { 1 } { 4 ^ { - 3 } }$

Decide whether the proportion is true or false. - $\frac { \frac { 1 } { 7 } } { 17 } = \frac { 1 } { 119 }$

Evaluate the expression. - $3 ^ { - 1 } + 4 ^ { - 1 }$

Solve the equation. - $- 9 x + 5 ( - 3 x - 2 ) = - 30 - 4 x$

Solve the equation. - $\frac { x } { 45 } = \frac { 4 } { 15 }$

Solve the inequality, giving its solution set in both interval and graph forms. - $\frac { 8 x + 3 } { 8 } < \frac { 61 } { 8 }$ $Solve the inequality, giving its solution set in both interval and graph forms. - \frac { 8 x + 3 } { 8 } < \frac { 61 } { 8 }$

Solve the equation. - $7 [ - 6 z - 3 + 5 ( z + 1 ) ] = 4 z + 2$

Decide whether the equation is "conditional," an "identity," or a "contradiction." Give its solution set. - $- 20 s + 47 + 5 ( 4 s - 8 ) = 0$

Evaluate the expression. - $( - 3 ) ^ { - 4 }$

Solve the formula for the specified variable. - $P = 2 L + 2 W ; \text { for } L$

Solve the equation. - $10 y = 4 y + 3 + 5 y$