Question 1

Decide what values of the variable cannot possibly be solutions for the equation.
-$90 x ^ { - 2 } - 5 x ^ { - 1 } = 20$

Accepted Answer

A)  $\left\{ 2 , - \frac { 9 } { 4 } \right\}$ 
B)  $\left\{ \frac { 1 } { 2 } , - \frac { 4 } { 9 } \right\}$ 
C)  $\left\{ \frac { 1 } { 2 } , \frac { 4 } { 9 } \right\}$ 
D)  $\left\{ - \frac { 1 } { 2 } , - \frac { 4 } { 9 } \right\}$ 
A)  $\left\{ 2 , - \frac { 9 } { 4 } \right\}$ 
B)  $\left\{ \frac { 1 } { 2 } , - \frac { 4 } { 9 } \right\}$ 
C)  $\left\{ \frac { 1 } { 2 } , \frac { 4 } { 9 } \right\}$ 
D)  $\left\{ - \frac { 1 } { 2 } , - \frac { 4 } { 9 } \right\}$

Question 2

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set.
-$$- 0.9 ( x + 9 ) + 0.1 ( x + 9 ) = - 0.8 x - 7.2$$

Accepted Answer

A)  Conditional; $\{ - 0.8 \}$ 
B)  Identity; {all real numbers $\}$ 
C)  Contradiction; $\varnothing$ 
D)  Conditional; $\{ - 9 \}$ 
A)  Conditional; $\{ - 0.8 \}$ 
B)  Identity; {all real numbers $\}$ 
C)  Contradiction; $\varnothing$ 
D)  Conditional; $\{ - 9 \}$

Question 3

Solve for the indicated variable.
-$\mathrm { M } = \pi \mathrm { r } ^ { 2 } \mathrm { hd }$, for $\mathrm { r }$

Accepted Answer

A)  $r = \frac { \pm \mathrm { M } \sqrt { \pi h d } } { \pi h d }$ 
B)  $r = \frac { \pm \sqrt { \mathrm { M } \pi \mathrm { hd } } } { \pi \mathrm { hd } }$ 
C)  $r = \frac { \pm \sqrt { \pi \mathrm { Mhd } } } { \mathrm { hd } }$ 
D)  $r = \pm \sqrt { \pi \mathrm { Mhd } }$ 
A)  $r = \frac { \pm \mathrm { M } \sqrt { \pi h d } } { \pi h d }$ 
B)  $r = \frac { \pm \sqrt { \mathrm { M } \pi \mathrm { hd } } } { \pi \mathrm { hd } }$ 
C)  $r = \frac { \pm \sqrt { \pi \mathrm { Mhd } } } { \mathrm { hd } }$ 
D)  $r = \pm \sqrt { \pi \mathrm { Mhd } }$

Question 4

Solve the problem.
-A circular hole is filled with concrete to make a footing for a load-bearing pier. The hole measures 18 inches across and requires 1.5 bags of concrete in order to fill it to ground level. What is the depth of the hole? Round
Your answer to the nearest inch. (One bag of concrete, when mixed with the appropriate amount of water, makes 1800 in.3 of material.)

Accepted Answer

A)  11 in. 
B)  8 in. 
C)  15 in. 
D)  17 in. 
A)  11 in. 
B)  8 in. 
C)  15 in. 
D)  17 in.

Question 5

Simplify the power of i.
-$\frac { 1 } { i ^ { - 18 } }$

Accepted Answer

A)  $- 1$ 
B)  $- \mathrm { i }$ 
C)  $\mathrm { i }$ 
D)  1 
A)  $- 1$ 
B)  $- \mathrm { i }$ 
C)  $\mathrm { i }$ 
D)  1

Question 6

Solve the inequality. Write the solution set in interval notation.
-$| 7 + 6 x | > 8$

Accepted Answer

A)  $\left( - \infty , - \frac { 5 } { 2 } \right) \cup \left( \frac { 1 } { 6 } , \infty \right)$ 
B)  $\left( \frac { 1 } { 6 } , \frac { 5 } { 2 } \right)$ 
C)  $\left( - \frac { 5 } { 2 } , \frac { 1 } { 6 } \right)$ 
D)  $\left( - \infty , \frac { 1 } { 6 } \right) \cup \left( \frac { 17 } { 6 } , \infty \right)$ 
A)  $\left( - \infty , - \frac { 5 } { 2 } \right) \cup \left( \frac { 1 } { 6 } , \infty \right)$ 
B)  $\left( \frac { 1 } { 6 } , \frac { 5 } { 2 } \right)$ 
C)  $\left( - \frac { 5 } { 2 } , \frac { 1 } { 6 } \right)$ 
D)  $\left( - \infty , \frac { 1 } { 6 } \right) \cup \left( \frac { 17 } { 6 } , \infty \right)$

Question 7

Solve the rational inequality. Write the solution set in interval notation.
-$$\frac { x + 11 } { x + 4 } < 3$$

Accepted Answer

A)  $( - \infty , - 4 ) \cup \left( - \frac { 1 } { 2 } , \infty \right)$ 
B)  $\left( - \infty , - \frac { 1 } { 2 } \right) \cup ( 4 , \infty )$ 
C)  $\varnothing$ 
D)  $\left( - 4 , - \frac { 1 } { 2 } \right)$ 
A)  $( - \infty , - 4 ) \cup \left( - \frac { 1 } { 2 } , \infty \right)$ 
B)  $\left( - \infty , - \frac { 1 } { 2 } \right) \cup ( 4 , \infty )$ 
C)  $\varnothing$ 
D)  $\left( - 4 , - \frac { 1 } { 2 } \right)$

Question 8

Multiply or divide, as indicated. Simplify the answer.
-$$\frac { \sqrt { - 150 } } { \sqrt { 6 } }$$

Accepted Answer

A)  $- 5$ 
B)  5 
C)  $5 \mathrm { i }$ 
D)  $- 5 \mathrm { i }$ 
A)  $- 5$ 
B)  5 
C)  $5 \mathrm { i }$ 
D)  $- 5 \mathrm { i }$

Question 9

Solve the inequality. Write the solution set in interval notation.
-$$\left| x ^ { 4 } + 8 x ^ { 2 } + 16 \right| > 0$$

Accepted Answer

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

Question 10

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\frac { 1 } { x } + \frac { 2 } { 17 x } = - 2$$

Accepted Answer

A)  $\left\{ - \frac { 19 } { 2 } \right\}$ 
B)  $\left\{ - \frac { 3 } { 2 } \right\}$ 
C)  $\left\{ - \frac { 19 } { 34 } \right\}$ 
D)  $\varnothing$ 
A)  $\left\{ - \frac { 19 } { 2 } \right\}$ 
B)  $\left\{ - \frac { 3 } { 2 } \right\}$ 
C)  $\left\{ - \frac { 19 } { 34 } \right\}$ 
D)  $\varnothing$

Question 11

Solve the problem.
-Don James wants to invest $63,000 to earn $1547 per year. He can invest in B-rated bonds paying 3.9% per year or in a Certificate of Deposit (CD) paying 1.3% per year. How much money should be invested in each to realize
Exactly $1547 in interest per year?

Accepted Answer

A)  $29,000 in B-rated bonds and $34,000 in a CD 
B)  $34,000 in B-rated bonds and $29,000 in a CD 
C)  $35,000 in B-rated bonds and $28,000 in a CD 
D)  $28,000 in B-rated bonds and $35,000 in a CD 
A)  $29,000 in B-rated bonds and $34,000 in a CD 
B)  $34,000 in B-rated bonds and $29,000 in a CD 
C)  $35,000 in B-rated bonds and $28,000 in a CD 
D)  $28,000 in B-rated bonds and $35,000 in a CD

Question 12

Write the inequality in interval notation.
-

Accepted Answer

A)  $[ - 7,4 )$ 
B)  $( - 3,8 ]$ 
C)  $[ - 4,7 )$ 
D)  $( - 7,4 ]$ 
A)  $[ - 7,4 )$ 
B)  $( - 3,8 ]$ 
C)  $[ - 4,7 )$ 
D)  $( - 7,4 ]$

Question 13

Find the values of a, b, and c for which the quadratic equation $a x ^ { 2 } + b x + c = 0$ 0 has the given numbers as solutions. Then
use those values to write a quadratic equation.
-$- 5 + \sqrt { 5 } , - 5 - \sqrt { 5 }$

Accepted Answer

A)  $x ^ { 2 } + 10 x + 30 = 0$ 
B)  $x ^ { 2 } + 25 x + 30 = 0$ 
C)  $x ^ { 2 } - 10 x + 20 = 0$ 
D)  $x ^ { 2 } + 10 x + 20 = 0$ 
A)  $x ^ { 2 } + 10 x + 30 = 0$ 
B)  $x ^ { 2 } + 25 x + 30 = 0$ 
C)  $x ^ { 2 } - 10 x + 20 = 0$ 
D)  $x ^ { 2 } + 10 x + 20 = 0$

Question 14

Decide what values of the variable cannot possibly be solutions for the equation.
-$$x ^ { 1 / 2 } = - 3 x ^ { 1 / 4 }$$

Accepted Answer

A)  $\{ 0 , - 3 \}$ 
B)  $\{ 0,9 \}$ 
C)  $\{ 0 \}$ 
D)  $\varnothing$ 
A)  $\{ 0 , - 3 \}$ 
B)  $\{ 0,9 \}$ 
C)  $\{ 0 \}$ 
D)  $\varnothing$

Question 15

Decide what values of the variable cannot possibly be solutions for the equation.
-$25 x ^ { 4 } - 61 x ^ { 2 } + 36 = 0$

Accepted Answer

A)  $\left\{ - 1 , - \frac { 5 } { 6 } \right\}$ 
B)  $\left\{ - 1 , - \frac { 5 } { 6 } , \frac { 5 } { 6 } , 1 \right\}$ 
C)  $\left\{ - \frac { 6 } { 5 } , - 1,1 , \frac { 6 } { 5 } \right\}$ 
D)  $\left\{ 1 , \frac { 6 } { 5 } \right\}$ 
A)  $\left\{ - 1 , - \frac { 5 } { 6 } \right\}$ 
B)  $\left\{ - 1 , - \frac { 5 } { 6 } , \frac { 5 } { 6 } , 1 \right\}$ 
C)  $\left\{ - \frac { 6 } { 5 } , - 1,1 , \frac { 6 } { 5 } \right\}$ 
D)  $\left\{ 1 , \frac { 6 } { 5 } \right\}$

Question 16

Solve the problem.
-A computer company uses the linear model y $y = - 33 x + 35,836$ to predict the decline in sales of a computer 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 computers sold during that month, how many computers will be sold 9 months after the first year?

Accepted Answer

A)  1086 computers 
B)  35,143 computers 
C)  35,539 computers 
D)  36,133 computers 
A)  1086 computers 
B)  35,143 computers 
C)  35,539 computers 
D)  36,133 computers

Question 17

Your company uses the quadratic model y $y = - 11 x ^ { 2 } + 350 x$ represent how many units (y) of a new product will be sold (x) weeks after its release . How many units can you expect to sell in week 5?

Accepted Answer

A)  1695 units 
B)  2025 units 
C)  1805 units 
D)  1475 units 
A)  1695 units 
B)  2025 units 
C)  1805 units 
D)  1475 units

Question 18

Find the sum or difference. Write the answer in standard form.
-$$( - 1 + 9 i ) - ( 6 + 5 i ) - ( - 3 + 7 i )$$

Accepted Answer

A)  $- 4 + 21 \mathrm { i }$ 
B)  $2 + 21 \mathrm { i }$ 
C)  $- 4 - 3 \mathrm { i }$ 
D)  $- 10 + 11 \mathrm { i }$ 
A)  $- 4 + 21 \mathrm { i }$ 
B)  $2 + 21 \mathrm { i }$ 
C)  $- 4 - 3 \mathrm { i }$ 
D)  $- 10 + 11 \mathrm { i }$

Question 19

Solve the problem.
-Find the height of a moving box if its length is 30 in., its width is 33 in., and its surface area is $3618 \text { in } ^ { 2 }$ . Assume that the surface area includes the top of the moving box.

Accepted Answer

A)  12,870 in. 
B)  13 in. 
C)  33 in. 
D)  30 in. 
A)  12,870 in. 
B)  13 in. 
C)  33 in. 
D)  30 in.

Question 20

Use these equations to convert between the two systems. $C = \frac { 5 } { 9 } ( F - 32 ) \quad F = \frac { 9 } { 5 } C + 32$ Round answer to the nearest tenth of a degree if necessary.
-Find the length of a rectangular lot with a perimeter of 92 m if the length is 6 m more than the width.

Accepted Answer

A)  46 m 
B)  52 m 
C)  20 m 
D)  26 m 
A)  46 m 
B)  52 m 
C)  20 m 
D)  26 m

Decide what values of the variable cannot possibly be solutions for the equation. - $90 x ^ { - 2 } - 5 x ^ { - 1 } = 20$

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $- 0.9 ( x + 9 ) + 0.1 ( x + 9 ) = - 0.8 x - 7.2$

Solve for the indicated variable. - $\mathrm { M } = \pi \mathrm { r } ^ { 2 } \mathrm { hd }$ , for $\mathrm { r }$

Simplify the power of i. - $\frac { 1 } { i ^ { - 18 } }$

Solve the inequality. Write the solution set in interval notation. - $| 7 + 6 x | > 8$

Solve the rational inequality. Write the solution set in interval notation. - $\frac { x + 11 } { x + 4 } < 3$

Multiply or divide, as indicated. Simplify the answer. - $\frac { \sqrt { - 150 } } { \sqrt { 6 } }$

Solve the inequality. Write the solution set in interval notation. - $\left| x ^ { 4 } + 8 x ^ { 2 } + 16 \right| > 0$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { 1 } { x } + \frac { 2 } { 17 x } = - 2$

Solve the problem. -Don James wants to invest $63,000 to earn $1547 per year. He can invest in B-rated bonds paying 3.9% per year or in a Certificate of Deposit (CD) paying 1.3% per year. How much money should be invested in each to realize Exactly $1547 in interest per year?

Write the inequality in interval notation. -

Find the values of a, b, and c for which the quadratic equation $a x ^ { 2 } + b x + c = 0$ 0 has the given numbers as solutions. Then use those values to write a quadratic equation. - $- 5 + \sqrt { 5 } , - 5 - \sqrt { 5 }$

Decide what values of the variable cannot possibly be solutions for the equation. - $x ^ { 1 / 2 } = - 3 x ^ { 1 / 4 }$

Decide what values of the variable cannot possibly be solutions for the equation. - $25 x ^ { 4 } - 61 x ^ { 2 } + 36 = 0$

Your company uses the quadratic model y $y = - 11 x ^ { 2 } + 350 x$ represent how many units (y) of a new product will be sold (x) weeks after its release . How many units can you expect to sell in week 5?

Find the sum or difference. Write the answer in standard form. - $( - 1 + 9 i ) - ( 6 + 5 i ) - ( - 3 + 7 i )$

Solve the problem. -Find the height of a moving box if its length is 30 in., its width is 33 in., and its surface area is $3618 \text { in } ^ { 2 }$ . Assume that the surface area includes the top of the moving box.

Use these equations to convert between the two systems. $C = \frac { 5 } { 9 } ( F - 32 ) \quad F = \frac { 9 } { 5 } C + 32$ Round answer to the nearest tenth of a degree if necessary. -Find the length of a rectangular lot with a perimeter of 92 m if the length is 6 m more than the width.

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

Decide what values of the variable cannot possibly be solutions for the equation. - 90x−2−5x−1=2090 x ^ { - 2 } - 5 x ^ { - 1 } = 2090x−2−5x−1=20

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - −0.9(x+9)+0.1(x+9)=−0.8x−7.2- 0.9 ( x + 9 ) + 0.1 ( x + 9 ) = - 0.8 x - 7.2−0.9(x+9)+0.1(x+9)=−0.8x−7.2

Solve for the indicated variable. - M=πr2hd\mathrm { M } = \pi \mathrm { r } ^ { 2 } \mathrm { hd }M=πr2hd , for r\mathrm { r }r

Simplify the power of i. - 1i−18\frac { 1 } { i ^ { - 18 } }i−181​

Solve the inequality. Write the solution set in interval notation. - ∣7+6x∣>8| 7 + 6 x | > 8∣7+6x∣>8

Solve the rational inequality. Write the solution set in interval notation. - x+11x+4<3\frac { x + 11 } { x + 4 } < 3x+4x+11​<3

Multiply or divide, as indicated. Simplify the answer. - −1506\frac { \sqrt { - 150 } } { \sqrt { 6 } }6​−150​​

Solve the inequality. Write the solution set in interval notation. - ∣x4+8x2+16∣>0\left| x ^ { 4 } + 8 x ^ { 2 } + 16 \right| > 0​x4+8x2+16​>0

Decide what values of the variable cannot possibly be solutions for the equation. - 1x+217x=−2\frac { 1 } { x } + \frac { 2 } { 17 x } = - 2x1​+17x2​=−2

Solve the problem. -Don James wants to invest $63,000 to earn $1547 per year. He can invest in B-rated bonds paying 3.9% per year or in a Certificate of Deposit (CD) paying 1.3% per year. How much money should be invested in each to realize Exactly $1547 in interest per year?

Write the inequality in interval notation. -

Find the values of a, b, and c for which the quadratic equation ax2+bx+c=0a x ^ { 2 } + b x + c = 0ax2+bx+c=0 0 has the given numbers as solutions. Then use those values to write a quadratic equation. - −5+5,−5−5- 5 + \sqrt { 5 } , - 5 - \sqrt { 5 }−5+5​,−5−5​

Decide what values of the variable cannot possibly be solutions for the equation. - x1/2=−3x1/4x ^ { 1 / 2 } = - 3 x ^ { 1 / 4 }x1/2=−3x1/4

Decide what values of the variable cannot possibly be solutions for the equation. - 25x4−61x2+36=025 x ^ { 4 } - 61 x ^ { 2 } + 36 = 025x4−61x2+36=0

Your company uses the quadratic model y y=−11x2+350xy = - 11 x ^ { 2 } + 350 xy=−11x2+350x represent how many units (y) of a new product will be sold (x) weeks after its release . How many units can you expect to sell in week 5?

Find the sum or difference. Write the answer in standard form. - (−1+9i)−(6+5i)−(−3+7i)( - 1 + 9 i ) - ( 6 + 5 i ) - ( - 3 + 7 i )(−1+9i)−(6+5i)−(−3+7i)

Solve the problem. -Find the height of a moving box if its length is 30 in., its width is 33 in., and its surface area is 3618 in 23618 \text { in } ^ { 2 }3618 in 2 . Assume that the surface area includes the top of the moving box.

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

Decide what values of the variable cannot possibly be solutions for the equation. - $90 x ^ { - 2 } - 5 x ^ { - 1 } = 20$

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $- 0.9 ( x + 9 ) + 0.1 ( x + 9 ) = - 0.8 x - 7.2$

Solve for the indicated variable. - $\mathrm { M } = \pi \mathrm { r } ^ { 2 } \mathrm { hd }$ , for $\mathrm { r }$

Simplify the power of i. - $\frac { 1 } { i ^ { - 18 } }$

Solve the inequality. Write the solution set in interval notation. - $| 7 + 6 x | > 8$

Solve the rational inequality. Write the solution set in interval notation. - $\frac { x + 11 } { x + 4 } < 3$

Multiply or divide, as indicated. Simplify the answer. - $\frac { \sqrt { - 150 } } { \sqrt { 6 } }$

Solve the inequality. Write the solution set in interval notation. - $\left| x ^ { 4 } + 8 x ^ { 2 } + 16 \right| > 0$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { 1 } { x } + \frac { 2 } { 17 x } = - 2$

Find the values of a, b, and c for which the quadratic equation $a x ^ { 2 } + b x + c = 0$ 0 has the given numbers as solutions. Then use those values to write a quadratic equation. - $- 5 + \sqrt { 5 } , - 5 - \sqrt { 5 }$

Decide what values of the variable cannot possibly be solutions for the equation. - $x ^ { 1 / 2 } = - 3 x ^ { 1 / 4 }$

Decide what values of the variable cannot possibly be solutions for the equation. - $25 x ^ { 4 } - 61 x ^ { 2 } + 36 = 0$

Your company uses the quadratic model y $y = - 11 x ^ { 2 } + 350 x$ represent how many units (y) of a new product will be sold (x) weeks after its release . How many units can you expect to sell in week 5?

Find the sum or difference. Write the answer in standard form. - $( - 1 + 9 i ) - ( 6 + 5 i ) - ( - 3 + 7 i )$

Solve the problem. -Find the height of a moving box if its length is 30 in., its width is 33 in., and its surface area is $3618 \text { in } ^ { 2 }$ . Assume that the surface area includes the top of the moving box.