Question 1

To solve for the lengths of the right triangle sides, which equation is correct?

Accepted Answer

A)  $( 2 x - 10 ) ^ { 2 } + x ^ { 2 } = ( 3 x ) ^ { 2 }$ 
B)  $x ^ { 2 } + ( 3 x ) ^ { 2 } = ( 2 x - 10 ) ^ { 2 }$ 
C)  $( 2 x - 10 ) ^ { 2 } = x ^ { 2 } + ( 3 x ) ^ { 2 }$ 
D)  $x ^ { 2 } = ( 3 x ) ^ { 2 } + ( 2 x - 10 ) ^ { 2 }$ 
A)  $( 2 x - 10 ) ^ { 2 } + x ^ { 2 } = ( 3 x ) ^ { 2 }$ 
B)  $x ^ { 2 } + ( 3 x ) ^ { 2 } = ( 2 x - 10 ) ^ { 2 }$ 
C)  $( 2 x - 10 ) ^ { 2 } = x ^ { 2 } + ( 3 x ) ^ { 2 }$ 
D)  $x ^ { 2 } = ( 3 x ) ^ { 2 } + ( 2 x - 10 ) ^ { 2 }$

Question 2

Graph the solution set.
-| $$- 7 x + 5 \mid = 16$$

Accepted Answer

A)  $\left\{ - \frac { 11 } { 7 } \right\}$ 
B)  $\left\{ - \frac { 11 } { 7 } , 3 \right\}$ 
C)  $\left\{ - 3 , \frac { 11 } { 7 } \right\}$ 
D)  $\left\{ \frac { 11 } { 7 } , - \frac { 11 } { 7 } \right\}$ 
A)  $\left\{ - \frac { 11 } { 7 } \right\}$ 
B)  $\left\{ - \frac { 11 } { 7 } , 3 \right\}$ 
C)  $\left\{ - 3 , \frac { 11 } { 7 } \right\}$ 
D)  $\left\{ \frac { 11 } { 7 } , - \frac { 11 } { 7 } \right\}$

Question 3

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex.
-$v ^ { 2 } - 5 v - 3 = 0$

Accepted Answer

A)  Two distinct nonreal complex solutions 
B)  Two distinct irrational solutions 
C)  One rational solution (a double solution) 
D)  Two distinct rational solutions 
A)  Two distinct nonreal complex solutions 
B)  Two distinct irrational solutions 
C)  One rational solution (a double solution) 
D)  Two distinct rational solutions

Question 4

Solve the equation using the quadratic formula.
-$$6 = - \frac { 6 } { x } - \frac { 1 } { x ^ { 2 } }$$

Accepted Answer

A)  $\left\{ \frac { - 3 \pm \sqrt { 3 } } { 6 } \right\}$ 
B)  $\left\{ \frac { - 6 \pm \sqrt { 3 } } { 6 } \right\}$ 
C)  $\left\{ \frac { - 3 \pm \sqrt { 3 } } { 12 } \right\}$ 
D)  $\left\{ \frac { - 3 \pm \sqrt { 15 } } { 6 } \right\}$ 
A)  $\left\{ \frac { - 3 \pm \sqrt { 3 } } { 6 } \right\}$ 
B)  $\left\{ \frac { - 6 \pm \sqrt { 3 } } { 6 } \right\}$ 
C)  $\left\{ \frac { - 3 \pm \sqrt { 3 } } { 12 } \right\}$ 
D)  $\left\{ \frac { - 3 \pm \sqrt { 15 } } { 6 } \right\}$

Question 5

Determine whether or not the equation is linear.
-$$7 x - 7 - 2 ( x + 1 ) = - ( - 3 x - 4 )$$

Accepted Answer

A)  $\left\{ \frac { 13 } { 7 } \right\}$ 
B)  $\left\{ \frac { 5 } { 7 } \right\}$ 
C)  $\left\{ \frac { 13 } { 2 } \right\}$ 
D)  $\left\{ \frac { 5 } { 2 } \right\}$ 
A)  $\left\{ \frac { 13 } { 7 } \right\}$ 
B)  $\left\{ \frac { 5 } { 7 } \right\}$ 
C)  $\left\{ \frac { 13 } { 2 } \right\}$ 
D)  $\left\{ \frac { 5 } { 2 } \right\}$

Question 6

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex.
-$2 - 5 a ^ { 2 } = 4 a - 3$

Accepted Answer

A)  Two distinct nonreal complex solutions 
B)  One rational solution (a double solution) 
C)  Two distinct rational solutions 
D)  Two distinct irrational solutions 
A)  Two distinct nonreal complex solutions 
B)  One rational solution (a double solution) 
C)  Two distinct rational solutions 
D)  Two distinct irrational solutions

Question 7

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex.
-$s ^ { 2 } + 3 s - 4 = 0$

Accepted Answer

A)  Two distinct irrational solutions 
B)  Two distinct rational solutions 
C)  Two distinct nonreal complex solutions 
D)  One rational solution (a double solution) 
A)  Two distinct irrational solutions 
B)  Two distinct rational solutions 
C)  Two distinct nonreal complex solutions 
D)  One rational solution (a double solution)

Question 8

Write the statement as an absolute value inequality.
-z is no less than 6 units from 17

Accepted Answer

A)  $| z - 17 | \geq 6$ 
B)  $| z - 17 | > 6$ 
C)  $| z - 17 | \leq 6$ 
D)  $| z - 6 | > 17$ 
A)  $| z - 17 | \geq 6$ 
B)  $| z - 17 | > 6$ 
C)  $| z - 17 | \leq 6$ 
D)  $| z - 6 | > 17$

Question 9

Solve the inequality. Write the solution set in interval notation.
-$$| 2 - 3 x | \geq 11$$

Accepted Answer

A)  $\left[ - \frac { 13 } { 3 } , 3 \right]$ 
B)  $( - \infty , 3 ] \cup \left[ \frac { 13 } { 3 } , \infty \right]$ 
C)  $( - \infty , - 3 ] \cup \left[ \frac { 13 } { 3 } , \infty \right)$ 
D)  $\left[ - 3 , \frac { 13 } { 3 } \right]$ 
A)  $\left[ - \frac { 13 } { 3 } , 3 \right]$ 
B)  $( - \infty , 3 ] \cup \left[ \frac { 13 } { 3 } , \infty \right]$ 
C)  $( - \infty , - 3 ] \cup \left[ \frac { 13 } { 3 } , \infty \right)$ 
D)  $\left[ - 3 , \frac { 13 } { 3 } \right]$

Question 10

Solve the formula for the indicated variable.
-$\mathrm { A } = \mathrm { bh }$, for $h$

Accepted Answer

A)  $h = A b$ 
B)  $h = A - b$ 
C)  $h = \frac { A } { b }$ 
D)  $h = \frac { b } { A }$ 
A)  $h = A b$ 
B)  $h = A - b$ 
C)  $h = \frac { A } { b }$ 
D)  $h = \frac { b } { A }$

Question 11

Solve the problem.
-A toy company uses the linear model y $y = - 2 x + 568$ to predict the decline in sales of a toy after it has been on the market more than one year. If x is the number of months after the first year and y is the number of toys sold in
Hundreds during that month, how many toys will be sold 11 months after the first year?

Accepted Answer

A)  59,000 toys 
B)  $- 27,850$ toys 
C)  $- 112,500$ toys 
D)  54,600 toys 
A)  59,000 toys 
B)  $- 27,850$ toys 
C)  $- 112,500$ toys 
D)  54,600 toys

Question 12

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\frac { 2 } { 5 x } - 8 = \frac { 3 } { 5 x }$$

Accepted Answer

A)  $\varnothing$ 
B)  $\left\{ - \frac { 5 } { 8 } \right\}$ 
C)  $\left\{ - \frac { 1 } { 40 } \right\}$ 
D)  $\left\{ - \frac { 3 } { 8 } \right\}$ 
A)  $\varnothing$ 
B)  $\left\{ - \frac { 5 } { 8 } \right\}$ 
C)  $\left\{ - \frac { 1 } { 40 } \right\}$ 
D)  $\left\{ - \frac { 3 } { 8 } \right\}$

Question 13

Solve the quadratic inequality. Write the solution set in interval notation.
-$$( x - 9 ) ( x + 8 ) > 0$$

Accepted Answer

A)  $( - \infty , - 9 ) \cup ( 8 , \infty )$ 
B)  $( - 8,9 )$ 
C)  $( - \infty , - 8 ) \cup ( 9 , \infty )$ 
D)  $( - 8 , \infty )$ 
A)  $( - \infty , - 9 ) \cup ( 8 , \infty )$ 
B)  $( - 8,9 )$ 
C)  $( - \infty , - 8 ) \cup ( 9 , \infty )$ 
D)  $( - 8 , \infty )$

Question 14

Decide what values of the variable cannot possibly be solutions for the equation.
-$$( 7 - 9 x ) ^ { 1 / 3 } - ( 8 + 3 x ) ^ { 1 / 3 } = 0$$

Accepted Answer

A)  $\left\{ \frac { 1 } { 12 } \right\}$ 
B)  $\varnothing$ 
C)  $\left\{ - \frac { 1 } { 12 } \right\}$ 
D)  $\{ - 12 \}$ 
A)  $\left\{ \frac { 1 } { 12 } \right\}$ 
B)  $\varnothing$ 
C)  $\left\{ - \frac { 1 } { 12 } \right\}$ 
D)  $\{ - 12 \}$

Question 15

Solve and graph the inequality. Give answer in interval notation.
-$$- 14 < - 3 x + 4 \leq - 2$$

Accepted Answer

A)  $[ 2,6 )$
  
B)  $( 2,6 ]$
  
C)  $( - 6 , - 2 ]$
  
D)  $[ - 6 , - 2 )$
  
A)  $[ 2,6 )$
  
B)  $( 2,6 ]$
  
C)  $( - 6 , - 2 ]$
  
D)  $[ - 6 , - 2 )$

Question 16

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex.
-$4 x ^ { 2 } + 12 x + 9 = 0$

Accepted Answer

A)  Two distinct nonreal complex solutions 
B)  Two distinct rational solutions 
C)  One rational solution (a double solution) 
D)  Two distinct irrational solutions 
A)  Two distinct nonreal complex solutions 
B)  Two distinct rational solutions 
C)  One rational solution (a double solution) 
D)  Two distinct irrational solutions

Question 17

Solve the quadratic inequality. Write the solution set in interval notation.
-$$x ^ { 2 } - 10 x + 20 \geq 0$$

Accepted Answer

A)  $( - \infty , 5 - \sqrt { 5 } ) \cup ( 5 + \sqrt { 5 } , \infty )$ 
B)  $( - \infty , - \sqrt { 5 } ] \cup [ \sqrt { 5 } , \infty )$ 
C)  $[ 5 - \sqrt { 5 } , 5 + \sqrt { 5 } ]$ 
D)  $( - \infty , 5 - \sqrt { 5 } ] \cup [ 5 + \sqrt { 5 } , \infty )$ 
A)  $( - \infty , 5 - \sqrt { 5 } ) \cup ( 5 + \sqrt { 5 } , \infty )$ 
B)  $( - \infty , - \sqrt { 5 } ] \cup [ \sqrt { 5 } , \infty )$ 
C)  $[ 5 - \sqrt { 5 } , 5 + \sqrt { 5 } ]$ 
D)  $( - \infty , 5 - \sqrt { 5 } ] \cup [ 5 + \sqrt { 5 } , \infty )$

Question 18

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set.
-$$4 ( 16 x + 20 ) = 16 ( 2 x - 13 )$$

Accepted Answer

A)  Contradiction; $\varnothing$ 
B)  Identity; \{all real numbers $\}$ 
C)  Conditional; $\{ 4 \}$ 
D)  Conditional; $\{ - 9 \}$ 
A)  Contradiction; $\varnothing$ 
B)  Identity; \{all real numbers $\}$ 
C)  Conditional; $\{ 4 \}$ 
D)  Conditional; $\{ - 9 \}$

Question 19

Solve the quadratic inequality. Write the solution set in interval notation.
-$$- 3 x ^ { 2 } + 2 x - 5 \leq 0$$

Accepted Answer

A)  $( - \infty , \infty )$ 
B)  $\left[ \frac { 1 } { 3 } , 5 \right]$ 
C)  $\varnothing$ 
D)  $\left[ - 3 , - \frac { 1 } { 5 } \right]$ 
A)  $( - \infty , \infty )$ 
B)  $\left[ \frac { 1 } { 3 } , 5 \right]$ 
C)  $\varnothing$ 
D)  $\left[ - 3 , - \frac { 1 } { 5 } \right]$

Question 20

Solve the rational inequality. Write the solution set in interval notation.
-$$\frac { x - 7 } { x + 8 } \leq 0$$

Accepted Answer

A)  $[ - 8,7 ]$ 
B)  $( - 8,7 ]$ 
C)  $( - 7,8 ]$ 
D)  $[ - 7,8 ]$ 
A)  $[ - 8,7 ]$ 
B)  $( - 8,7 ]$ 
C)  $( - 7,8 ]$ 
D)  $[ - 7,8 ]$

To solve for the lengths of the right triangle sides, which equation is correct?

Graph the solution set. -| $- 7 x + 5 \mid = 16$

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. - $v ^ { 2 } - 5 v - 3 = 0$

Solve the equation using the quadratic formula. - $6 = - \frac { 6 } { x } - \frac { 1 } { x ^ { 2 } }$

Determine whether or not the equation is linear. - $7 x - 7 - 2 ( x + 1 ) = - ( - 3 x - 4 )$

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. - $2 - 5 a ^ { 2 } = 4 a - 3$

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. - $s ^ { 2 } + 3 s - 4 = 0$

Write the statement as an absolute value inequality. -z is no less than 6 units from 17

Solve the inequality. Write the solution set in interval notation. - $| 2 - 3 x | \geq 11$

Solve the formula for the indicated variable. - $\mathrm { A } = \mathrm { bh }$ , for $h$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { 2 } { 5 x } - 8 = \frac { 3 } { 5 x }$

Solve the quadratic inequality. Write the solution set in interval notation. - $( x - 9 ) ( x + 8 ) > 0$

Decide what values of the variable cannot possibly be solutions for the equation. - $( 7 - 9 x ) ^ { 1 / 3 } - ( 8 + 3 x ) ^ { 1 / 3 } = 0$

Solve and graph the inequality. Give answer in interval notation. - $- 14 < - 3 x + 4 \leq - 2$ $Solve and graph the inequality. Give answer in interval notation. - - 14 < - 3 x + 4 \leq - 2$

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. - $4 x ^ { 2 } + 12 x + 9 = 0$

Solve the quadratic inequality. Write the solution set in interval notation. - $x ^ { 2 } - 10 x + 20 \geq 0$

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $4 ( 16 x + 20 ) = 16 ( 2 x - 13 )$

Solve the quadratic inequality. Write the solution set in interval notation. - $- 3 x ^ { 2 } + 2 x - 5 \leq 0$

Solve the rational inequality. Write the solution set in interval notation. - $\frac { x - 7 } { x + 8 } \leq 0$

Review of Basic Concepts

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 2: Equations and Inequalities

To solve for the lengths of the right triangle sides, which equation is correct?

Graph the solution set. -| −7x+5∣=16- 7 x + 5 \mid = 16−7x+5∣=16

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. - v2−5v−3=0v ^ { 2 } - 5 v - 3 = 0v2−5v−3=0

Solve the equation using the quadratic formula. - 6=−6x−1x26 = - \frac { 6 } { x } - \frac { 1 } { x ^ { 2 } }6=−x6​−x21​

Determine whether or not the equation is linear. - 7x−7−2(x+1)=−(−3x−4)7 x - 7 - 2 ( x + 1 ) = - ( - 3 x - 4 )7x−7−2(x+1)=−(−3x−4)

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. - 2−5a2=4a−32 - 5 a ^ { 2 } = 4 a - 32−5a2=4a−3

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. - s2+3s−4=0s ^ { 2 } + 3 s - 4 = 0s2+3s−4=0

Write the statement as an absolute value inequality. -z is no less than 6 units from 17

Solve the inequality. Write the solution set in interval notation. - ∣2−3x∣≥11| 2 - 3 x | \geq 11∣2−3x∣≥11

Solve the formula for the indicated variable. - A=bh\mathrm { A } = \mathrm { bh }A=bh , for hhh

Decide what values of the variable cannot possibly be solutions for the equation. - 25x−8=35x\frac { 2 } { 5 x } - 8 = \frac { 3 } { 5 x }5x2​−8=5x3​

Solve the quadratic inequality. Write the solution set in interval notation. - (x−9)(x+8)>0( x - 9 ) ( x + 8 ) > 0(x−9)(x+8)>0

Decide what values of the variable cannot possibly be solutions for the equation. - (7−9x)1/3−(8+3x)1/3=0( 7 - 9 x ) ^ { 1 / 3 } - ( 8 + 3 x ) ^ { 1 / 3 } = 0(7−9x)1/3−(8+3x)1/3=0

Solve and graph the inequality. Give answer in interval notation. - −14<−3x+4≤−2- 14 < - 3 x + 4 \leq - 2−14<−3x+4≤−2

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. - 4x2+12x+9=04 x ^ { 2 } + 12 x + 9 = 04x2+12x+9=0

Solve the quadratic inequality. Write the solution set in interval notation. - x2−10x+20≥0x ^ { 2 } - 10 x + 20 \geq 0x2−10x+20≥0

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - 4(16x+20)=16(2x−13)4 ( 16 x + 20 ) = 16 ( 2 x - 13 )4(16x+20)=16(2x−13)

Solve the quadratic inequality. Write the solution set in interval notation. - −3x2+2x−5≤0- 3 x ^ { 2 } + 2 x - 5 \leq 0−3x2+2x−5≤0

Solve the rational inequality. Write the solution set in interval notation. - x−7x+8≤0\frac { x - 7 } { x + 8 } \leq 0x+8x−7​≤0

Review of Basic Concepts

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Graph the solution set. -| $- 7 x + 5 \mid = 16$

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. - $v ^ { 2 } - 5 v - 3 = 0$

Solve the equation using the quadratic formula. - $6 = - \frac { 6 } { x } - \frac { 1 } { x ^ { 2 } }$

Determine whether or not the equation is linear. - $7 x - 7 - 2 ( x + 1 ) = - ( - 3 x - 4 )$

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. - $2 - 5 a ^ { 2 } = 4 a - 3$

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. - $s ^ { 2 } + 3 s - 4 = 0$

Solve the inequality. Write the solution set in interval notation. - $| 2 - 3 x | \geq 11$

Solve the formula for the indicated variable. - $\mathrm { A } = \mathrm { bh }$ , for $h$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { 2 } { 5 x } - 8 = \frac { 3 } { 5 x }$

Solve the quadratic inequality. Write the solution set in interval notation. - $( x - 9 ) ( x + 8 ) > 0$

Decide what values of the variable cannot possibly be solutions for the equation. - $( 7 - 9 x ) ^ { 1 / 3 } - ( 8 + 3 x ) ^ { 1 / 3 } = 0$

Solve and graph the inequality. Give answer in interval notation. - $- 14 < - 3 x + 4 \leq - 2$ $Solve and graph the inequality. Give answer in interval notation. - - 14 < - 3 x + 4 \leq - 2$

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. - $4 x ^ { 2 } + 12 x + 9 = 0$

Solve the quadratic inequality. Write the solution set in interval notation. - $x ^ { 2 } - 10 x + 20 \geq 0$

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $4 ( 16 x + 20 ) = 16 ( 2 x - 13 )$

Solve the quadratic inequality. Write the solution set in interval notation. - $- 3 x ^ { 2 } + 2 x - 5 \leq 0$

Solve the rational inequality. Write the solution set in interval notation. - $\frac { x - 7 } { x + 8 } \leq 0$