Question 1

Translate the verbal phrase into a mathematical expression. Use x to represent the unknown number.
-The quotient of a number and 73

Accepted Answer

A)  $73 + x$ 
B)  $73 - x$ 
C)  $\frac { x } { 73 }$ 
D)  $73 x$ 
A)  $73 + x$ 
B)  $73 - x$ 
C)  $\frac { x } { 73 }$ 
D)  $73 x$

Question 2

Solve the problem.
-The mathematical model C = 100x + 50,000 represents the cost in dollars a company has in manufacturing x items during a month. Based on this model, how much does it cost to produce 100 Items?

Accepted Answer

A) $500 
B) $60,000 
C) $5 
D) $10,000 
A) $500 
B) $60,000 
C) $5 
D) $10,000

Question 3

Solve the problem.
-A label printer prints 7 pages of labels in 2.9 seconds. How long will it take to print 406 pages of labels?

Accepted Answer

A) 168.2 sec 
B) 171.2 sec 
C) 172.2 sec 
D) 170.2 sec 
A) 168.2 sec 
B) 171.2 sec 
C) 172.2 sec 
D) 170.2 sec

Question 4

Solve the formula for the specified variable.
-$\mathrm { A } = \mathrm { P } ( 1 + \mathrm { nr } ) ;$ for $\mathrm { r }$

Accepted Answer

A)  $r = \frac { A } { n }$ 
B)  $r = \frac { P n } { A - P }$ 
C)  $r = \frac { P - A } { P n }$ 
D)  $r = \frac { A - P } { P n }$ 
A)  $r = \frac { A } { n }$ 
B)  $r = \frac { P n } { A - P }$ 
C)  $r = \frac { P - A } { P n }$ 
D)  $r = \frac { A - P } { P n }$

Question 5

Solve the formula for the specified variable.
-$\mathrm { F } = \frac { 9 } { 5 } \mathrm { C } + 32 ; \text { for } \mathrm { C }$

Accepted Answer

A)  $C = \frac { F - 32 } { 9 }$ 
B)  $C = \frac { 5 } { F - 32 }$ 
C)  $C = \frac { 5 } { 9 } ( F - 32 )$ 
D)  $C = \frac { 9 } { 5 } ( F - 32 )$ 
A)  $C = \frac { F - 32 } { 9 }$ 
B)  $C = \frac { 5 } { F - 32 }$ 
C)  $C = \frac { 5 } { 9 } ( F - 32 )$ 
D)  $C = \frac { 9 } { 5 } ( F - 32 )$

Question 6

Solve the equation.
-$22 \mathrm { t } - 30 = 8 \mathrm { t } - 12$

Accepted Answer

A)  $\left\{ - \frac { 5 } { 7 } \right\}$ 
B)  $\left\{ - \frac { 9 } { 7 } \right\}$ 
C)  $\left\{ \frac { 9 } { 7 } \right\}$ 
D)  $\left\{ - \frac { 30 } { 23 } \right\}$ 
A)  $\left\{ - \frac { 5 } { 7 } \right\}$ 
B)  $\left\{ - \frac { 9 } { 7 } \right\}$ 
C)  $\left\{ \frac { 9 } { 7 } \right\}$ 
D)  $\left\{ - \frac { 30 } { 23 } \right\}$

Question 7

The two largest oil spills together released 301 million gallons of oil into the oceans. The smaller of the two released 73 million gallons less than the larger of the two. How many million gallons did
The larger one release?

Accepted Answer

A) 228 million gal 
B) 114 million gal 
C) 130 million gal 
D) 187 million gal 
A) 228 million gal 
B) 114 million gal 
C) 130 million gal 
D) 187 million gal

Question 8

Solve and graph.
-$x - 2 ( x - 6 ) \leq 12 x$

Accepted Answer

A)  $\left[ - \infty , \frac { 12 } { 13 } \right]$
  
B)  $\left( - \infty , - \frac { 12 } { 13 } \right]$
  
C)  $\left[ - \frac { 12 } { 13 } , \infty \right]$
  
D)  $\left[ \frac { 12 } { 13 } , \infty \right]$
  
A)  $\left[ - \infty , \frac { 12 } { 13 } \right]$
  
B)  $\left( - \infty , - \frac { 12 } { 13 } \right]$
  
C)  $\left[ - \frac { 12 } { 13 } , \infty \right]$
  
D)  $\left[ \frac { 12 } { 13 } , \infty \right]$

Question 9

Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 300 miles in the same time that Dana travels 264 miles. If Chuck's rate of travel is 6 mph more than Dana's, and they
Travel the same length of time, at what speed does Chuck travel?

Accepted Answer

A) 58 mph 
B) 42 mph 
C) 44 mph 
D) 50 mph 
A) 58 mph 
B) 42 mph 
C) 44 mph 
D) 50 mph

Question 10

Pizzicato Pizza, Inc. finds that the cost to make $x$ pizzas (with one topping) is $C = 2 x + 1885$, while the revenue produced from them is $R = 16 x$ ( $C$ and $R$ are in dollars). What is the smallest whole number of pizzas, $x$, that must be sold for the company to show a profit?

Accepted Answer

A)  135 
B)  105 
C)  33,930 
D)  26,390 
A)  135 
B)  105 
C)  33,930 
D)  26,390

Question 11

Solve the formula for the specified variable.
-$A = \frac { 1 } { 2 } h \left( b _ { 1 } + b _ { 2 } \right) ; \quad$ for $b _ { 1 }$

Accepted Answer

A)  $b _ { 1 } = \frac { h \left( b _ { 2 } \right) - 2 A } { h }$ 
B)  $b _ { 1 } = \frac { A - h \left( b _ { 2 } \right) } { 2 h }$ 
C)  $b _ { 1 } = \frac { \left( b _ { 2 } \right) 2 \mathrm {~A} - \mathrm { h } } { \mathrm { h } }$ 
D)  $b _ { 1 } = \frac { 2 \mathrm {~A} - ( \mathrm { h } ) \left( \mathrm { b } _ { 2 } \right) } { \mathrm { h } }$ 
A)  $b _ { 1 } = \frac { h \left( b _ { 2 } \right) - 2 A } { h }$ 
B)  $b _ { 1 } = \frac { A - h \left( b _ { 2 } \right) } { 2 h }$ 
C)  $b _ { 1 } = \frac { \left( b _ { 2 } \right) 2 \mathrm {~A} - \mathrm { h } } { \mathrm { h } }$ 
D)  $b _ { 1 } = \frac { 2 \mathrm {~A} - ( \mathrm { h } ) \left( \mathrm { b } _ { 2 } \right) } { \mathrm { h } }$

Question 12

Translate the verbal phrase into a mathematical expression. Use x to represent the unknown number.
-68 more than a number

Accepted Answer

A) 68 - x 
B) 68 
C) 68x 
D) 68 + x 
A) 68 - x 
B) 68 
C) 68x 
D) 68 + x

Question 13

Evaluate the expression.
-$( - 2 ) ^ { - 1 }$

Accepted Answer

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

Question 14

Evaluate the expression.
-$2 ^ { 4 } + 2 ^ { 1 }$

Accepted Answer

A)  10 
B)  5 
C)  18 
D)  6 
A)  10 
B)  5 
C)  18 
D)  6

Question 15

One side of a triangle is twice as long as a second side. The third side of the triangle is 12 feet long. The perimeter of the triangle cannot be more than 48 feet. Find the longest possible values for the
Other two sides of the triangle.

Accepted Answer

A) 11 feet and 22 feet 
B) 30 feet and 30 feet 
C) 18 feet and 18 feet 
D) 12 feet and 24 feet 
A) 11 feet and 22 feet 
B) 30 feet and 30 feet 
C) 18 feet and 18 feet 
D) 12 feet and 24 feet

Question 16

Match the inequality with its correct representation.
-$\{ x \mid - 6 \leq x < 6 \}$

Accepted Answer

A)  $( - 6,6 )$ 
B)  $[ - 6,6 )$ 
C)  $[ - 6,6 ]$ 
D)  $( - 6,6 ]$ 
A)  $( - 6,6 )$ 
B)  $[ - 6,6 )$ 
C)  $[ - 6,6 ]$ 
D)  $( - 6,6 ]$

Question 17

A line from the top of a cliff to the ground passes just over the top of a pole 8.0 ft high and meets the ground at a point 5.0 ft from the base of the pole. If the point is 66 ft from the base of the cliff,
How high is the cliff? Round to the nearest unit.

Accepted Answer

A) 2640 ft 
B) 106 ft 
C) 528 ft 
D) 7 ft 
A) 2640 ft 
B) 106 ft 
C) 528 ft 
D) 7 ft

Question 18

Evaluate.
-$12 ^ { 0 } + 12 ^ { 0 }$

Accepted Answer

A)  1 
B)  24 
C)  0 
D)  2 
A)  1 
B)  24 
C)  0 
D)  2

Question 19

Decide whether the statement translates into an expression or an equation.
-16 is 3 less than a number.

Accepted Answer

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

Question 20

Solve and graph.
-$9 x - 15 > 3 ( 2 x - 6 )$

Accepted Answer

A)  $[ - 1 , \infty )$
  
B)  $(-\infty,-1)$
  
C) $(-1, \infty)$
  
D)  $( - 11 , \infty )$
  
A)  $[ - 1 , \infty )$
  
B)  $(-\infty,-1)$
  
C) $(-1, \infty)$
  
D)  $( - 11 , \infty )$

Translate the verbal phrase into a mathematical expression. Use x to represent the unknown number. -The quotient of a number and 73

Solve the problem. -The mathematical model C = 100x + 50,000 represents the cost in dollars a company has in manufacturing x items during a month. Based on this model, how much does it cost to produce 100 Items?

Solve the problem. -A label printer prints 7 pages of labels in 2.9 seconds. How long will it take to print 406 pages of labels?

Solve the formula for the specified variable. - $\mathrm { A } = \mathrm { P } ( 1 + \mathrm { nr } ) ;$ for $\mathrm { r }$

Solve the formula for the specified variable. - $\mathrm { F } = \frac { 9 } { 5 } \mathrm { C } + 32 ; \text { for } \mathrm { C }$

Solve the equation. - $22 \mathrm { t } - 30 = 8 \mathrm { t } - 12$

The two largest oil spills together released 301 million gallons of oil into the oceans. The smaller of the two released 73 million gallons less than the larger of the two. How many million gallons did The larger one release?

Solve and graph. - $x - 2 ( x - 6 ) \leq 12 x$ $Solve and graph. - x - 2 ( x - 6 ) \leq 12 x$

Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 300 miles in the same time that Dana travels 264 miles. If Chuck's rate of travel is 6 mph more than Dana's, and they Travel the same length of time, at what speed does Chuck travel?

Pizzicato Pizza, Inc. finds that the cost to make $x$ pizzas (with one topping) is $C = 2 x + 1885$ , while the revenue produced from them is $R = 16 x$ ( $C$ and $R$ are in dollars). What is the smallest whole number of pizzas, $x$ , that must be sold for the company to show a profit?

Solve the formula for the specified variable. - $A = \frac { 1 } { 2 } h \left( b _ { 1 } + b _ { 2 } \right) ; \quad$ for $b _ { 1 }$

Translate the verbal phrase into a mathematical expression. Use x to represent the unknown number. -68 more than a number

Evaluate the expression. - $( - 2 ) ^ { - 1 }$

Evaluate the expression. - $2 ^ { 4 } + 2 ^ { 1 }$

One side of a triangle is twice as long as a second side. The third side of the triangle is 12 feet long. The perimeter of the triangle cannot be more than 48 feet. Find the longest possible values for the Other two sides of the triangle.

Match the inequality with its correct representation. - $\{ x \mid - 6 \leq x < 6 \}$

A line from the top of a cliff to the ground passes just over the top of a pole 8.0 ft high and meets the ground at a point 5.0 ft from the base of the pole. If the point is 66 ft from the base of the cliff, How high is the cliff? Round to the nearest unit.

Evaluate. - $12 ^ { 0 } + 12 ^ { 0 }$

Decide whether the statement translates into an expression or an equation. -16 is 3 less than a number.

Solve and graph. - $9 x - 15 > 3 ( 2 x - 6 )$

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

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Exam 7: The Basic Concepts of Algebra