Question 1

Solve for the indicated variable.
-$\mathrm { Ve } = \frac { 1 } { 2 } \mathrm { mv } ^ { 2 }$, for $\mathrm { v }$

Accepted Answer

A)  $v = \frac { \pm \sqrt { 2 m V e } } { m }$ 
B)  $v = \pm \sqrt { 2 V e }$ 
C)  $v = \pm \sqrt { \frac { V e } { 2 m } }$ 
D)  $v = \pm 2 \frac { \sqrt { \mathrm { Ve } } } { \mathrm { m } }$ 
A)  $v = \frac { \pm \sqrt { 2 m V e } } { m }$ 
B)  $v = \pm \sqrt { 2 V e }$ 
C)  $v = \pm \sqrt { \frac { V e } { 2 m } }$ 
D)  $v = \pm 2 \frac { \sqrt { \mathrm { Ve } } } { \mathrm { m } }$

Question 2

Solve the inequality. Write the solution set in interval notation.
-$$x ^ { 3 } - 6 x ^ { 2 } > 0$$

Accepted Answer

A)  $( - \infty , 6 )$ 
B)  $( - \infty , 0 ) \cup ( 6 , \infty )$ 
C)  $( 0,6 )$ 
D)  $( 6 , \infty )$ 
A)  $( - \infty , 6 )$ 
B)  $( - \infty , 0 ) \cup ( 6 , \infty )$ 
C)  $( 0,6 )$ 
D)  $( 6 , \infty )$

Question 3

Solve the inequality. Write the solution set in interval notation.
-$$( x + 4 ) ( x + 3 ) ( x - 9 ) > 0$$

Accepted Answer

A)  $( - 4 , - 3 ) \cup ( 9 , \infty )$ 
B)  $( - \infty , - 3 )$ 
C)  $( - \infty , - 4 ) \cup ( - 3,9 )$ 
D)  $( 9 , \infty )$ 
A)  $( - 4 , - 3 ) \cup ( 9 , \infty )$ 
B)  $( - \infty , - 3 )$ 
C)  $( - \infty , - 4 ) \cup ( - 3,9 )$ 
D)  $( 9 , \infty )$

Question 4

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\frac { 10 } { x - 2 } = 1 + \frac { 12 } { x + 2 }$$

Accepted Answer

A)  $\{ - 6,8 \}$ 
B)  $\{ - 12,8 \}$ 
C)  $\{ 6 , - 8 \}$ 
D)  $\varnothing$ 
A)  $\{ - 6,8 \}$ 
B)  $\{ - 12,8 \}$ 
C)  $\{ 6 , - 8 \}$ 
D)  $\varnothing$

Question 5

Solve for y.
-Hannah borrowed $47,838 at 5% simple interest for 15 months. How much will the interest amount to? What is the total amount that she will have to pay back at the end of 15 months? Round answers to the nearest cent if
Necessary.

Accepted Answer

A)  $2790.55; $50,628.55 
B)  $3189.20; $51,027.20 
C)  $2989.88; $50,827.88 
D)  $3015.00; $50,853.00 
A)  $2790.55; $50,628.55 
B)  $3189.20; $51,027.20 
C)  $2989.88; $50,827.88 
D)  $3015.00; $50,853.00

Question 6

Solve the equation by the square root property.
-$$( 7 x + 4 ) ^ { 2 } = 4$$

Accepted Answer

A)  $\left\{ - \frac { 2 } { 7 } , - \frac { 6 } { 7 } \right\}$ 
B)  $\left\{ \frac { 0 } { 7 } \right\}$ 
C)  $\left\{ - \frac { 2 } { 7 } , 0 \right\}$ 
D)  $\left\{ \frac { 2 } { 7 } , \frac { 6 } { 7 } \right\}$ 
A)  $\left\{ - \frac { 2 } { 7 } , - \frac { 6 } { 7 } \right\}$ 
B)  $\left\{ \frac { 0 } { 7 } \right\}$ 
C)  $\left\{ - \frac { 2 } { 7 } , 0 \right\}$ 
D)  $\left\{ \frac { 2 } { 7 } , \frac { 6 } { 7 } \right\}$

Question 7

Determine whether or not the equation is linear.
-$$\frac { 7 x } { 9 } - 4 = x$$

Accepted Answer

A)  $\{ - 18 \}$ 
B)  $\{ 72 \}$ 
C)  $\{ 36 \}$ 
D)  $\{ 18 \}$ 
A)  $\{ - 18 \}$ 
B)  $\{ 72 \}$ 
C)  $\{ 36 \}$ 
D)  $\{ 18 \}$

Question 8

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set.
-$$2 ( 3 x + 20 ) - 6 x - 40 = 0$$

Accepted Answer

A)  Conditional; $\{ 0 \}$ 
B)  Contradiction; $\varnothing$ 
C)  Conditional; $\{ 3 \}$ 
D)  Identity; {all real numbers\} 
A)  Conditional; $\{ 0 \}$ 
B)  Contradiction; $\varnothing$ 
C)  Conditional; $\{ 3 \}$ 
D)  Identity; {all real numbers\}

Question 9

Graph the solution set.
-$$\left| x ^ { 2 } + 9 \right| = | 6 x |$$

Accepted Answer

A)  $\{ - 3,3 \}$ 
B)  $\varnothing$ 
C)  $\{ - 3 \}$ 
D)  $\{ 3 \}$ 
A)  $\{ - 3,3 \}$ 
B)  $\varnothing$ 
C)  $\{ - 3 \}$ 
D)  $\{ 3 \}$

Question 10

Solve the problem.
-Noah and Ben are running in the Walker Street Fun Run. Noah runs at 7 mph, Ben at 5 mph. If they start at the same time, how long (in minutes) will it be before they are $\frac { 1 } { 5 }$ mile apart?

Accepted Answer

A)  24 min 
B)  6 min 
C)  10 min 
D)  150 min 
A)  24 min 
B)  6 min 
C)  10 min 
D)  150 min

Question 11

The profit made when $t$ units are sold, $t > 0$, is given by $P = t ^ { 2 } - 33 t + 272$. Determine the number of units to be sold in order for $\mathrm { P } = 0$ (the break- even point).

Accepted Answer

A)  $t = 33$ 
B)  $t = 16$ or $t = 17$ 
C)  $t = - 16$ or $t = - 17$ 
D)  $t > 16$ 
A)  $t = 33$ 
B)  $t = 16$ or $t = 17$ 
C)  $t = - 16$ or $t = - 17$ 
D)  $t > 16$

Question 12

Solve the equation by the square root property.
-$$x ^ { 2 } = - 81$$

Accepted Answer

A)  $\{ \pm 9 \}$ 
B)  $\{ 40.5 \}$ 
C)  $\{ \pm 9 i \}$ 
D)  $\{ 9 \}$ 
A)  $\{ \pm 9 \}$ 
B)  $\{ 40.5 \}$ 
C)  $\{ \pm 9 i \}$ 
D)  $\{ 9 \}$

Question 13

Solve and graph the inequality. Give answer in interval notation.
-$$- 1 \leq \frac { x + 1 } { 2 } \leq 3$$

Accepted Answer

A)  $( - 7,1 )$
  
B)  $[ - 1,7 ]$
  
C)  $[ - 3,5 ]$
  
D)  $[ - 5,3 ]$
  
A)  $( - 7,1 )$
  
B)  $[ - 1,7 ]$
  
C)  $[ - 3,5 ]$
  
D)  $[ - 5,3 ]$

Question 14

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may
apply.
-$5 - 3 i$

Accepted Answer

A)  Complex, pure imaginary, nonreal complex 
B)  Complex 
C)  Nonreal complex 
D)  Real, complex 
A)  Complex, pure imaginary, nonreal complex 
B)  Complex 
C)  Nonreal complex 
D)  Real, complex

Question 15

Solve the inequality. Write the solution set in interval notation.
-$$| x + 3 | < 0$$

Accepted Answer

A)  $\{ 3 \}$ 
B)  $( - \infty , - 3 )$ 
C)  $\varnothing$ 
D)  $\{ - 3 \}$ 
A)  $\{ 3 \}$ 
B)  $( - \infty , - 3 )$ 
C)  $\varnothing$ 
D)  $\{ - 3 \}$

Question 16

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\sqrt { 3 x + 10 } = 5 - 2 x$$

Accepted Answer

A)  $\left\{ \frac { 3 } { 4 } , 5 \right\}$ 
B)  $\{ 5 \}$ 
C)  $\left\{ \frac { 5 } { 4 } , 9 \right\}$ 
D)  $\left\{ \frac { 3 } { 4 } \right\}$ 
A)  $\left\{ \frac { 3 } { 4 } , 5 \right\}$ 
B)  $\{ 5 \}$ 
C)  $\left\{ \frac { 5 } { 4 } , 9 \right\}$ 
D)  $\left\{ \frac { 3 } { 4 } \right\}$

Question 17

Solve the cubic equation using factoring and the quadratic formula.
-$$x ^ { 3 } - 64 = 0$$

Accepted Answer

A)  $\{ 4,2 \pm 2 \mathrm { i } \sqrt { 6 } \}$ 
B)  $\{ 4,2 \pm 2 \sqrt { 5 } \}$ 
C)  $\{ 4 , - 2 \pm 2 \mathrm { i } \}$ 
D)  $\{ 4 , - 2 \pm 2 \mathrm { i } \sqrt { 3 } \}$ 
A)  $\{ 4,2 \pm 2 \mathrm { i } \sqrt { 6 } \}$ 
B)  $\{ 4,2 \pm 2 \sqrt { 5 } \}$ 
C)  $\{ 4 , - 2 \pm 2 \mathrm { i } \}$ 
D)  $\{ 4 , - 2 \pm 2 \mathrm { i } \sqrt { 3 } \}$

Question 18

Decide what values of the variable cannot possibly be solutions for the equation.
-$$x = \sqrt { 2 x + 15 }$$

Accepted Answer

A)  $\{ 5 , - 3 \}$ 
B)  $\varnothing$ 
C)  $\{ 2 \}$ 
D)  $\{ 5 \}$ 
A)  $\{ 5 , - 3 \}$ 
B)  $\varnothing$ 
C)  $\{ 2 \}$ 
D)  $\{ 5 \}$

Question 19

Solve the equation by the square root property.
-Only one of the following equations does not require Step 1 of the method for completing the square. Which one is it?

Accepted Answer

A)  $2 x ^ { 2 } - 5 x - 6 = 0$ 
B)  $( 2 x - 5 ) ( x - 6 ) = 0$ 
C)  $x ^ { 2 } - x = 6$ 
D)  $( 2 x - 5 ) ^ { 2 } = 6$ 
A)  $2 x ^ { 2 } - 5 x - 6 = 0$ 
B)  $( 2 x - 5 ) ( x - 6 ) = 0$ 
C)  $x ^ { 2 } - x = 6$ 
D)  $( 2 x - 5 ) ^ { 2 } = 6$

Question 20

Write the inequality in interval notation.
-$1 < x$

Accepted Answer

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

Solve for the indicated variable. - $\mathrm { Ve } = \frac { 1 } { 2 } \mathrm { mv } ^ { 2 }$ , for $\mathrm { v }$

Solve the inequality. Write the solution set in interval notation. - $x ^ { 3 } - 6 x ^ { 2 } > 0$

Solve the inequality. Write the solution set in interval notation. - $( x + 4 ) ( x + 3 ) ( x - 9 ) > 0$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { 10 } { x - 2 } = 1 + \frac { 12 } { x + 2 }$

Solve for y. -Hannah borrowed $47,838 at 5% simple interest for 15 months. How much will the interest amount to? What is the total amount that she will have to pay back at the end of 15 months? Round answers to the nearest cent if Necessary.

Solve the equation by the square root property. - $( 7 x + 4 ) ^ { 2 } = 4$

Determine whether or not the equation is linear. - $\frac { 7 x } { 9 } - 4 = x$

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $2 ( 3 x + 20 ) - 6 x - 40 = 0$

Graph the solution set. - $\left| x ^ { 2 } + 9 \right| = | 6 x |$

Solve the problem. -Noah and Ben are running in the Walker Street Fun Run. Noah runs at 7 mph, Ben at 5 mph. If they start at the same time, how long (in minutes) will it be before they are $\frac { 1 } { 5 }$ mile apart?

The profit made when $t$ units are sold, $t > 0$ , is given by $P = t ^ { 2 } - 33 t + 272$ . Determine the number of units to be sold in order for $\mathrm { P } = 0$ (the break- even point).

Solve the equation by the square root property. - $x ^ { 2 } = - 81$

Solve and graph the inequality. Give answer in interval notation. - $- 1 \leq \frac { x + 1 } { 2 } \leq 3$ $Solve and graph the inequality. Give answer in interval notation. - - 1 \leq \frac { x + 1 } { 2 } \leq 3$

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply. - $5 - 3 i$

Solve the inequality. Write the solution set in interval notation. - $| x + 3 | < 0$

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt { 3 x + 10 } = 5 - 2 x$

Solve the cubic equation using factoring and the quadratic formula. - $x ^ { 3 } - 64 = 0$

Decide what values of the variable cannot possibly be solutions for the equation. - $x = \sqrt { 2 x + 15 }$

Solve the equation by the square root property. -Only one of the following equations does not require Step 1 of the method for completing the square. Which one is it?

Write the inequality in interval notation. - $1 < x$

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

Solve for the indicated variable. - Ve=12mv2\mathrm { Ve } = \frac { 1 } { 2 } \mathrm { mv } ^ { 2 }Ve=21​mv2 , for v\mathrm { v }v

Solve the inequality. Write the solution set in interval notation. - x3−6x2>0x ^ { 3 } - 6 x ^ { 2 } > 0x3−6x2>0

Solve the inequality. Write the solution set in interval notation. - (x+4)(x+3)(x−9)>0( x + 4 ) ( x + 3 ) ( x - 9 ) > 0(x+4)(x+3)(x−9)>0

Decide what values of the variable cannot possibly be solutions for the equation. - 10x−2=1+12x+2\frac { 10 } { x - 2 } = 1 + \frac { 12 } { x + 2 }x−210​=1+x+212​

Solve for y. -Hannah borrowed $47,838 at 5% simple interest for 15 months. How much will the interest amount to? What is the total amount that she will have to pay back at the end of 15 months? Round answers to the nearest cent if Necessary.

Solve the equation by the square root property. - (7x+4)2=4( 7 x + 4 ) ^ { 2 } = 4(7x+4)2=4

Determine whether or not the equation is linear. - 7x9−4=x\frac { 7 x } { 9 } - 4 = x97x​−4=x

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - 2(3x+20)−6x−40=02 ( 3 x + 20 ) - 6 x - 40 = 02(3x+20)−6x−40=0

Graph the solution set. - ∣x2+9∣=∣6x∣\left| x ^ { 2 } + 9 \right| = | 6 x |​x2+9​=∣6x∣

Solve the problem. -Noah and Ben are running in the Walker Street Fun Run. Noah runs at 7 mph, Ben at 5 mph. If they start at the same time, how long (in minutes) will it be before they are 15\frac { 1 } { 5 }51​ mile apart?

The profit made when ttt units are sold, t>0t > 0t>0 , is given by P=t2−33t+272P = t ^ { 2 } - 33 t + 272P=t2−33t+272 . Determine the number of units to be sold in order for P=0\mathrm { P } = 0P=0 (the break- even point).

Solve the equation by the square root property. - x2=−81x ^ { 2 } = - 81x2=−81

Solve and graph the inequality. Give answer in interval notation. - −1≤x+12≤3- 1 \leq \frac { x + 1 } { 2 } \leq 3−1≤2x+1​≤3

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply. - 5−3i5 - 3 i5−3i

Solve the inequality. Write the solution set in interval notation. - ∣x+3∣<0| x + 3 | < 0∣x+3∣<0

Decide what values of the variable cannot possibly be solutions for the equation. - 3x+10=5−2x\sqrt { 3 x + 10 } = 5 - 2 x3x+10​=5−2x

Solve the cubic equation using factoring and the quadratic formula. - x3−64=0x ^ { 3 } - 64 = 0x3−64=0

Decide what values of the variable cannot possibly be solutions for the equation. - x=2x+15x = \sqrt { 2 x + 15 }x=2x+15​