Question 1

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

Accepted Answer

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

Question 2

Solve the radical equation, and check all proposed solutions.
-$$\sqrt { 28 x + 28 } = x + 8$$

Accepted Answer

A)  $\{ - 6 \}$ 
B)  $\{ 6 \}$ 
C)  $\{ 7 \}$ 
D)  $\{ - 5 \}$ 
A)  $\{ - 6 \}$ 
B)  $\{ 6 \}$ 
C)  $\{ 7 \}$ 
D)  $\{ - 5 \}$ B

Question 3

Solve the equation by the method of your choice.
-$$4 x ^ { 2 } - 19 x - 5 = 0$$

Accepted Answer

A)  $\{ - 4,5 \}$ 
B)  $\left\{ - \frac { 1 } { 4 } , \frac { 1 } { 19 } \right\}$ 
C)  $\left\{ - \frac { 1 } { 4 } , 5 \right\}$ 
D)  $\left\{ - \frac { 1 } { 4 } , 4 \right\}$ 
A)  $\{ - 4,5 \}$ 
B)  $\left\{ - \frac { 1 } { 4 } , \frac { 1 } { 19 } \right\}$ 
C)  $\left\{ - \frac { 1 } { 4 } , 5 \right\}$ 
D)  $\left\{ - \frac { 1 } { 4 } , 4 \right\}$ C

Question 4

Express the interval in set-builder notation and graph the interval on a number line.
-$$( - 4,3 ]$$

Accepted Answer

A)  $\{ x \mid - 4 < x < 3 \}$
  
B)  $\{ x \mid - 4 < x \leq 3 \}$
  
C)  $\{ x \mid x \leq 3 \}$
  
D)  $\{ x \mid - 4 \leq x \leq 3 \}$
  
A)  $\{ x \mid - 4 < x < 3 \}$
  
B)  $\{ x \mid - 4 < x \leq 3 \}$
  
C)  $\{ x \mid x \leq 3 \}$
  
D)  $\{ x \mid - 4 \leq x \leq 3 \}$

Question 5

Solve the problem.
-For a culture of 70,000 bacteria of a certain strain, the number of bacteria $\mathrm { N }$ that will survive $x$ hours is modeled by the formula $N = 7000 \sqrt { 100 - x }$. After how many hours will 63,000 bacteria survive?

Accepted Answer

A)  $81 \mathrm { hr }$ 
B)  $37 \mathrm { hr }$ 
C)  $19 \mathrm { hr }$ 
D)  $91 \mathrm { hr }$ 
A)  $81 \mathrm { hr }$ 
B)  $37 \mathrm { hr }$ 
C)  $19 \mathrm { hr }$ 
D)  $91 \mathrm { hr }$

Question 6

Solve the absolute value equation or indicate that the equation has no solution.
-$$\left| \frac { 1 } { 2 } x + 2 \right| = \left| \frac { 3 } { 4 } x - 2 \right|$$

Accepted Answer

A)  $\{ 10,10 \}$ 
B)  $\{ 16,0 \}$ 
C)  $\{ 16,12 \}$ 
D)  $\varnothing$ 
A)  $\{ 10,10 \}$ 
B)  $\{ 16,0 \}$ 
C)  $\{ 16,12 \}$ 
D)  $\varnothing$

Question 7

Solve and check the linear equation.
-( - 9 x + 7 ) - 7 = - 8 ( x + 2 )

Accepted Answer

A)  {-16} 
B)  { 2 } 
C)  { 16 } 
D)  { - 30 } 
A)  {-16} 
B)  { 2 } 
C)  { 16 } 
D)  { - 30 }

Question 8

Find all values of x satisfying the given conditions.
-$y _ { 1 } = \frac { 1 } { x + 5 } , y _ { 2 } = \frac { 3 } { x + 4 } , y _ { 3 } = \frac { - 1 } { x ^ { 2 } + 9 x + 20 }$, and $y _ { 1 } + y _ { 2 } = y _ { 3 }$

Accepted Answer

A)  $\{ 4 \}$ 
B)  $\{ 0 \}$ 
C)  $\{ - 5 \}$ 
D)  $\varnothing$ 
A)  $\{ 4 \}$ 
B)  $\{ 0 \}$ 
C)  $\{ - 5 \}$ 
D)  $\varnothing$

Question 9

Solve the equation by the method of your choice.
-$$6 x ^ { 2 } + 72 x + 240 = 0$$

Accepted Answer

A)  $\{ - 8 , - 4 \}$ 
B)  $\{ - 6 - 4 i , - 6 + 4 i \}$ 
C)  $\{ - 6 + 2 i \}$ 
D)  $\{ - 6 - 2 i , - 6 + 2 i \}$ 
A)  $\{ - 8 , - 4 \}$ 
B)  $\{ - 6 - 4 i , - 6 + 4 i \}$ 
C)  $\{ - 6 + 2 i \}$ 
D)  $\{ - 6 - 2 i , - 6 + 2 i \}$

Question 10

Solve the equation.
-$ \frac{4 x}{5}-x=\frac{x}{45}-\frac{2}{9} $

Accepted Answer

A)  {1} 
B)  {{50} 
C)  {5/4} 
D)  { 1- } 
A)  {1} 
B)  {{50} 
C)  {5/4} 
D)  { 1- }

Question 11

Match the correct viewing rectangle dimensions with the figure.
-

Accepted Answer

A)  [ - 5,25,5 ] by [ - 20,40,5 ] 
B)  [ - 50,25,5 ] by [ - 50,25,5 ] 
C)  [ - 50,150,50 ] by [ - 2000,2500,500 ] 
D)  [ - 5,40,5 ] by [ - 5,40,5 ] 
A)  [ - 5,25,5 ] by [ - 20,40,5 ] 
B)  [ - 50,25,5 ] by [ - 50,25,5 ] 
C)  [ - 50,150,50 ] by [ - 2000,2500,500 ] 
D)  [ - 5,40,5 ] by [ - 5,40,5 ]

Question 12

Solve the problem.
-When making a long distance call from a certain pay phone, the first three minutes of a call cost $2.40. After that, each additional minute or portion of a minute of that call costs $0.30. Use an inequality to find the number
Of minutes one can call long distance for $4.20.

Accepted Answer

A) 9 minutes or fewer 
B) 14 minutes or fewer 
C) 2 minutes or fewer 
D) 6 minutes or fewer 
A) 9 minutes or fewer 
B) 14 minutes or fewer 
C) 2 minutes or fewer 
D) 6 minutes or fewer

Question 13

Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write
and factor the trinomial.
-$$x ^ { 2 } + \frac { 1 } { 4 } x$$

Accepted Answer

A)  $64 ; x ^ { 2 } + \frac { 1 } { 4 } x + 64 = ( x + 8 ) ^ { 2 }$ 
B)  $\frac { 1 } { 8 } ; x ^ { 2 } + \frac { 1 } { 4 } x + \frac { 1 } { 8 } = \left( x + \frac { 1 } { 4 } \right) ^ { 2 }$ 
C)  $\frac { 1 } { 64 } ; x ^ { 2 } + \frac { 1 } { 4 } x + \frac { 1 } { 64 } = \left( x + \frac { 1 } { 8 } \right) ^ { 2 }$ 
D)  $\frac { 1 } { 16 } ; x ^ { 2 } + \frac { 1 } { 4 } x + \frac { 1 } { 16 } = \left( x + \frac { 1 } { 4 } \right) ^ { 2 }$ 
A)  $64 ; x ^ { 2 } + \frac { 1 } { 4 } x + 64 = ( x + 8 ) ^ { 2 }$ 
B)  $\frac { 1 } { 8 } ; x ^ { 2 } + \frac { 1 } { 4 } x + \frac { 1 } { 8 } = \left( x + \frac { 1 } { 4 } \right) ^ { 2 }$ 
C)  $\frac { 1 } { 64 } ; x ^ { 2 } + \frac { 1 } { 4 } x + \frac { 1 } { 64 } = \left( x + \frac { 1 } { 8 } \right) ^ { 2 }$ 
D)  $\frac { 1 } { 16 } ; x ^ { 2 } + \frac { 1 } { 4 } x + \frac { 1 } { 16 } = \left( x + \frac { 1 } { 4 } \right) ^ { 2 }$

Question 14

Solve the problem.
-A bookcase is to be constructed as shown in the figure below. The height of the bookcase is 3 feet longer than the length of a shelf. If 18 feet of lumber is available for the entire unit (including the shelves, but NOT the back of the bookcase), find the length and height of the unit.

Accepted Answer

A)  length $= 3$ feet; height $= 6$ feet 
B)  length $= 2$ feet; height $= 6$ feet 
C)  length $= 2$ feet; height $= 5$ feet 
D)  length $= 7.5$ feet; height $= 9.0$ feet 
A)  length $= 3$ feet; height $= 6$ feet 
B)  length $= 2$ feet; height $= 6$ feet 
C)  length $= 2$ feet; height $= 5$ feet 
D)  length $= 7.5$ feet; height $= 9.0$ feet

Question 15

First, write the value(s) that make the denominator(s) zero. Then solve the equation.
-$ \frac{10}{x}=\frac{5}{2 x}+30 $

Accepted Answer

A)   
B)  No restrictions; { 2 } 
C)   
D)    
A)   
B)  No restrictions; { 2 } 
C)   
D)

Question 16

Find all values of x satisfying the given conditions.
-$y = 4 x ^ { 2 } - 7 x - 2$ and $y = 0$

Accepted Answer

A)  $- \frac { 1 } { 4 } , 2$ 
B)  $\frac { 1 } { 7 } , - \frac { 1 } { 4 }$ 
C)  $- \frac { 1 } { 4 } , 4$ 
D)  $- 4,2$ 
A)  $- \frac { 1 } { 4 } , 2$ 
B)  $\frac { 1 } { 7 } , - \frac { 1 } { 4 }$ 
C)  $- \frac { 1 } { 4 } , 4$ 
D)  $- 4,2$

Question 17

Use the five-step strategy for solving word problems to find the number or numbers described in the following exercise.
-When four times the number is added to 7 times the number, the result is 44. What is the number?

Accepted Answer

A) -6.3 
B) 0.7 
C) 4 
D) 6.3 
A) -6.3 
B) 0.7 
C) 4 
D) 6.3

Question 18

Solve the linear inequality. Other than $ \phi $, use interval notation to express the solution set and graph the solution set on a number line.
-$4 x + 4 \geq 3 x + 5$

Accepted Answer

A)  $[ 1 , \infty )$
  
B)  $(-\infty, 1]$
  
C) $( 9 , \infty )$
  
D)  $( - \infty , 1 )$
  
A)  $[ 1 , \infty )$
  
B)  $(-\infty, 1]$
  
C) $( 9 , \infty )$
  
D)  $( - \infty , 1 )$

Question 19

Match the correct viewing rectangle dimensions with the figure.
-

Accepted Answer

A) [ - 20,20,2 ] by [ - 20,20,2 ] 
B)  [ - 4,4,2 ] by [ - 80,80,8 ] 
C)  [ - 4,4,2 ] by [ - 4,4,2 ] 
D)  [ - 16,16,4 ] by [ - 4,4,2 ] 
A) [ - 20,20,2 ] by [ - 20,20,2 ] 
B)  [ - 4,4,2 ] by [ - 80,80,8 ] 
C)  [ - 4,4,2 ] by [ - 4,4,2 ] 
D)  [ - 16,16,4 ] by [ - 4,4,2 ]

Question 20

Determine whether the equation is an identity, a conditional equation, or an inconsistent equation.
--4(x + 6)+ 165 = 5x - 9(x - 9)

Accepted Answer

A) Identity 
B) Conditional equation 
C) Inconsistent equation 
A) Identity 
B) Conditional equation 
C) Inconsistent equation

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

Solve the radical equation, and check all proposed solutions. - $\sqrt { 28 x + 28 } = x + 8$

Solve the equation by the method of your choice. - $4 x ^ { 2 } - 19 x - 5 = 0$

Express the interval in set-builder notation and graph the interval on a number line. - $( - 4,3 ]$

Solve the problem. -For a culture of 70,000 bacteria of a certain strain, the number of bacteria $\mathrm { N }$ that will survive $x$ hours is modeled by the formula $N = 7000 \sqrt { 100 - x }$ . After how many hours will 63,000 bacteria survive?

Solve the absolute value equation or indicate that the equation has no solution. - $\left| \frac { 1 } { 2 } x + 2 \right| = \left| \frac { 3 } { 4 } x - 2 \right|$

Solve and check the linear equation. -( - 9 x + 7 ) - 7 = - 8 ( x + 2 )

Find all values of x satisfying the given conditions. - $y _ { 1 } = \frac { 1 } { x + 5 } , y _ { 2 } = \frac { 3 } { x + 4 } , y _ { 3 } = \frac { - 1 } { x ^ { 2 } + 9 x + 20 }$ , and $y _ { 1 } + y _ { 2 } = y _ { 3 }$

Solve the equation by the method of your choice. - $6 x ^ { 2 } + 72 x + 240 = 0$

Solve the equation. - $\frac{4 x}{5}-x=\frac{x}{45}-\frac{2}{9}$

Match the correct viewing rectangle dimensions with the figure. -

Solve the problem. -When making a long distance call from a certain pay phone, the first three minutes of a call cost $2.40. After that, each additional minute or portion of a minute of that call costs $0.30. Use an inequality to find the number Of minutes one can call long distance for $4.20.

Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. - $x ^ { 2 } + \frac { 1 } { 4 } x$

First, write the value(s) that make the denominator(s) zero. Then solve the equation. - $\frac{10}{x}=\frac{5}{2 x}+30$

Find all values of x satisfying the given conditions. - $y = 4 x ^ { 2 } - 7 x - 2$ and $y = 0$

Use the five-step strategy for solving word problems to find the number or numbers described in the following exercise. -When four times the number is added to 7 times the number, the result is 44. What is the number?

Match the correct viewing rectangle dimensions with the figure. -

Determine whether the equation is an identity, a conditional equation, or an inconsistent equation. --4(x + 6)+ 165 = 5x - 9(x - 9)

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Filters

Exam 1: Equations and Inequalities

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

Solve the radical equation, and check all proposed solutions. - 28x+28=x+8\sqrt { 28 x + 28 } = x + 828x+28​=x+8

Solve the equation by the method of your choice. - 4x2−19x−5=04 x ^ { 2 } - 19 x - 5 = 04x2−19x−5=0

Express the interval in set-builder notation and graph the interval on a number line. - (−4,3]( - 4,3 ](−4,3]

Solve the problem. -For a culture of 70,000 bacteria of a certain strain, the number of bacteria N\mathrm { N }N that will survive xxx hours is modeled by the formula N=7000100−xN = 7000 \sqrt { 100 - x }N=7000100−x​ . After how many hours will 63,000 bacteria survive?

Solve the absolute value equation or indicate that the equation has no solution. - ∣12x+2∣=∣34x−2∣\left| \frac { 1 } { 2 } x + 2 \right| = \left| \frac { 3 } { 4 } x - 2 \right|​21​x+2​=​43​x−2​

Solve and check the linear equation. -( - 9 x + 7 ) - 7 = - 8 ( x + 2 )

Solve the equation by the method of your choice. - 6x2+72x+240=06 x ^ { 2 } + 72 x + 240 = 06x2+72x+240=0

Solve the equation. - 4x5−x=x45−29 \frac{4 x}{5}-x=\frac{x}{45}-\frac{2}{9} 54x​−x=45x​−92​

Match the correct viewing rectangle dimensions with the figure. -

Solve the problem. -When making a long distance call from a certain pay phone, the first three minutes of a call cost $2.40. After that, each additional minute or portion of a minute of that call costs $0.30. Use an inequality to find the number Of minutes one can call long distance for $4.20.

Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. - x2+14xx ^ { 2 } + \frac { 1 } { 4 } xx2+41​x

First, write the value(s) that make the denominator(s) zero. Then solve the equation. - 10x=52x+30 \frac{10}{x}=\frac{5}{2 x}+30 x10​=2x5​+30

Find all values of x satisfying the given conditions. - y=4x2−7x−2y = 4 x ^ { 2 } - 7 x - 2y=4x2−7x−2 and y=0y = 0y=0

Use the five-step strategy for solving word problems to find the number or numbers described in the following exercise. -When four times the number is added to 7 times the number, the result is 44. What is the number?

Solve the linear inequality. Other than ϕ \phi ϕ , use interval notation to express the solution set and graph the solution set on a number line. - 4x+4≥3x+54 x + 4 \geq 3 x + 54x+4≥3x+5

Match the correct viewing rectangle dimensions with the figure. -

Determine whether the equation is an identity, a conditional equation, or an inconsistent equation. --4(x + 6)+ 165 = 5x - 9(x - 9)

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Filters

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

Solve the radical equation, and check all proposed solutions. - $\sqrt { 28 x + 28 } = x + 8$

Solve the equation by the method of your choice. - $4 x ^ { 2 } - 19 x - 5 = 0$

Express the interval in set-builder notation and graph the interval on a number line. - $( - 4,3 ]$

Solve the problem. -For a culture of 70,000 bacteria of a certain strain, the number of bacteria $\mathrm { N }$ that will survive $x$ hours is modeled by the formula $N = 7000 \sqrt { 100 - x }$ . After how many hours will 63,000 bacteria survive?

Solve the absolute value equation or indicate that the equation has no solution. - $\left| \frac { 1 } { 2 } x + 2 \right| = \left| \frac { 3 } { 4 } x - 2 \right|$

Solve the equation by the method of your choice. - $6 x ^ { 2 } + 72 x + 240 = 0$

Solve the equation. - $\frac{4 x}{5}-x=\frac{x}{45}-\frac{2}{9}$

Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. - $x ^ { 2 } + \frac { 1 } { 4 } x$

First, write the value(s) that make the denominator(s) zero. Then solve the equation. - $\frac{10}{x}=\frac{5}{2 x}+30$

Find all values of x satisfying the given conditions. - $y = 4 x ^ { 2 } - 7 x - 2$ and $y = 0$