Question 1

Solve the formula for the indicated variable.
-$P = 21 + 2 w$, for 1

Accepted Answer

A)  $l = \frac { P } { 2 } - 2 w$ 
B)  $I = \frac { P } { 2 w + 2 }$ 
C)  $l = \frac { P - 2 w } { 2 }$ 
D)  $I = P - 2 w - 2$ 
A)  $l = \frac { P } { 2 } - 2 w$ 
B)  $I = \frac { P } { 2 w + 2 }$ 
C)  $l = \frac { P - 2 w } { 2 }$ 
D)  $I = P - 2 w - 2$

Question 2

A boat is 84 feet from the base of cliff. If the distance from the top of the cliff to the boat is 21 less than twice the height of the cliff to the water. Find the height of the cliff. Round to the nearest tenth of a foot if necessary.

Accepted Answer

A)  63 ft 
B)  49 ft 
C)  35 ft 
D)  105 ft 
A)  63 ft 
B)  49 ft 
C)  35 ft 
D)  105 ft

Question 3

Decide what values of the variable cannot possibly be solutions for the equation.
-One maid can clean the house in 5 hours. Another maid can do the job in 3 hours. How long will it take them to do the job working together?

Accepted Answer

A)  $\frac { 1 } { 15 } \mathrm { hr }$ 
B)  $\frac { 15 } { 8 } \mathrm { hr }$ 
C)  $\frac { 15 } { 2 } \mathrm { hr }$ 
D)  $\frac { 1 } { 8 } \mathrm { hr }$ 
A)  $\frac { 1 } { 15 } \mathrm { hr }$ 
B)  $\frac { 15 } { 8 } \mathrm { hr }$ 
C)  $\frac { 15 } { 2 } \mathrm { hr }$ 
D)  $\frac { 1 } { 8 } \mathrm { hr }$

Question 4

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\left( x ^ { 2 } - 3 \right) ^ { 1 / 2 } - ( x + 3 ) ^ { 1 / 2 } = 0$$

Accepted Answer

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

Question 5

Solve the equation by completing the square.
-$$8 x ^ { 2 } + 7 x = - 2$$

Accepted Answer

A)  $\left\{ \frac { 7 } { 16 } \pm \frac { \sqrt { 15 } } { 16 } \mathrm { i } \right\}$ 
B)  $\left\{ \frac { - 7 \pm \sqrt { 15 } } { 16 } \right\}$ 
C)  $\left\{ \frac { 7 \pm \sqrt { 15 } } { 16 } \right\}$ 
D)  $\left\{ - \frac { 7 } { 16 } \pm \frac { \sqrt { 15 } } { 16 } \mathrm { i } \right\}$ 
A)  $\left\{ \frac { 7 } { 16 } \pm \frac { \sqrt { 15 } } { 16 } \mathrm { i } \right\}$ 
B)  $\left\{ \frac { - 7 \pm \sqrt { 15 } } { 16 } \right\}$ 
C)  $\left\{ \frac { 7 \pm \sqrt { 15 } } { 16 } \right\}$ 
D)  $\left\{ - \frac { 7 } { 16 } \pm \frac { \sqrt { 15 } } { 16 } \mathrm { i } \right\}$

Question 6

Write the inequality in interval notation.
-$- 9 \leq x < - 3$

Accepted Answer

A)  $( - 9 , - 3 ]$ 
B)  $[ - 9 , - 3 )$ 
C)  $( - 9 , - 3 )$ 
D)  $[ - 9 , - 3 ]$ 
A)  $( - 9 , - 3 ]$ 
B)  $[ - 9 , - 3 )$ 
C)  $( - 9 , - 3 )$ 
D)  $[ - 9 , - 3 ]$

Question 7

Decide what values of the variable cannot possibly be solutions for the equation.
-$\sqrt [ 6 ] { x ^ { 2 } - 13 } = 1$

Accepted Answer

A)  $ \{\sqrt{13}\} $ 
B)  $\{ \sqrt { 14 } \}$ 
C)  $\{ - \sqrt { 14 } , \sqrt { 14 } \}$ 
D)  $\{ - \sqrt { 13 } , \sqrt { 13 } \}$ 
A)  $ \{\sqrt{13}\} $ 
B)  $\{ \sqrt { 14 } \}$ 
C)  $\{ - \sqrt { 14 } , \sqrt { 14 } \}$ 
D)  $\{ - \sqrt { 13 } , \sqrt { 13 } \}$

Question 8

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\frac { x } { x - 5 } - \frac { 5 } { x + 5 } = \frac { 50 } { x ^ { 2 } - 25 }$$

Accepted Answer

A)  $\{ \pm 5 i \}$ 
B)  $\left\{ \frac { 1 } { 5 } \right\}$ 
C)  $\varnothing$ 
D)  $\{ \pm 5 \}$ 
A)  $\{ \pm 5 i \}$ 
B)  $\left\{ \frac { 1 } { 5 } \right\}$ 
C)  $\varnothing$ 
D)  $\{ \pm 5 \}$

Question 9

Solve the inequality. Write the solution set in interval notation.
-$$| x + 2 | \leq 0$$

Accepted Answer

A)  $\{ - 2 \}$ 
B)  $( - \infty , - 2 )$ 
C)  $\{ 2 \}$ 
D)  $\varnothing$ 
A)  $\{ - 2 \}$ 
B)  $( - \infty , - 2 )$ 
C)  $\{ 2 \}$ 
D)  $\varnothing$

Question 10

Solve the cubic equation using factoring and the quadratic formula.
-$$x + 17 = 0$$

Accepted Answer

A)  17 
B)  $- \mathrm { i } \sqrt { 17 }$ 
C)  $- 17$ 
D)  $\mathrm { i } \sqrt { 17 }$ 
A)  17 
B)  $- \mathrm { i } \sqrt { 17 }$ 
C)  $- 17$ 
D)  $\mathrm { i } \sqrt { 17 }$

Question 11

Decide what values of the variable cannot possibly be solutions for the equation.
-$$( x + 6 ) ^ { 2 / 5 } = ( 25 x ) ^ { 1 / 5 }$$

Accepted Answer

A)  $\left\{ - \frac { 8 } { 21 } \right\}$ 
B)  $\{ 4,9 \}$ 
C)  $\{ 4 , - 9 \}$ 
D)  $\{ - 4,9 \}$ 
A)  $\left\{ - \frac { 8 } { 21 } \right\}$ 
B)  $\{ 4,9 \}$ 
C)  $\{ 4 , - 9 \}$ 
D)  $\{ - 4,9 \}$

Question 12

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set.
-$$0.2 ( x - 5 ) - 0.8 ( x - 5 ) = - 0.6 x + 3$$

Accepted Answer

A)  Conditional; $\{ 1 \}$ 
B)  Contradiction; $\varnothing$ 
C)  Conditional; $\{ - 5 \}$ 
D)  Identity; {all real numbers\} 
A)  Conditional; $\{ 1 \}$ 
B)  Contradiction; $\varnothing$ 
C)  Conditional; $\{ - 5 \}$ 
D)  Identity; {all real numbers\}

Question 13

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may
apply.
-$- 2$

Accepted Answer

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

Question 14

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set.
-$$4 x + 9 ( x + 1 ) + 2 = 11 - 6 x$$

Accepted Answer

A)  Conditional; $\{ 0 \}$ 
B)  Conditional; $\{ 1 \}$ 
C)  Identity; {all real numbers $\}$ 
D)  Contradiction; $\varnothing$ 
A)  Conditional; $\{ 0 \}$ 
B)  Conditional; $\{ 1 \}$ 
C)  Identity; {all real numbers $\}$ 
D)  Contradiction; $\varnothing$

Question 15

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set.
-$$20 x + 15 = 5 ( 2 x + 11 )$$

Accepted Answer

A)  Conditional; $\{ 4 \}$ 
B)  Contradiction; $\varnothing$ 
C)  Conditional; $\{ - 7 \}$ 
D)  Identity; \{all real numbers $\}$ 
A)  Conditional; $\{ 4 \}$ 
B)  Contradiction; $\varnothing$ 
C)  Conditional; $\{ - 7 \}$ 
D)  Identity; \{all real numbers $\}$

Question 16

Solve the quadratic inequality. Write the solution set in interval notation.
-$$( 7 + 4 x ) ^ { 2 } \leq - 1$$

Accepted Answer

A)  $\varnothing$ 
B)  $( - \infty , \infty )$ 
C)  $( - \infty , - 2 ) \cup \left( - \frac { 3 } { 2 } , \infty \right)$ 
D)  $\left[ - 2 , - \frac { 3 } { 2 } \right]$ 
A)  $\varnothing$ 
B)  $( - \infty , \infty )$ 
C)  $( - \infty , - 2 ) \cup \left( - \frac { 3 } { 2 } , \infty \right)$ 
D)  $\left[ - 2 , - \frac { 3 } { 2 } \right]$

Question 17

Solve the problem.
-In triangle ABC, the angle C is six times as large as angle A. The measure of angle B is 44° greater than that of angle A. Find the measure of the angles.

Accepted Answer

A)  $17 ^ { \circ } , 61 ^ { \circ }$ and $119 ^ { \circ }$ 
B)  $17 ^ { \circ } , 78 ^ { \circ }$ and $102 ^ { \circ }$ 
C)  $17 ^ { \circ } , 78 ^ { \circ }$ and $85 ^ { \circ }$ 
D)  $17 ^ { \circ } , 61 ^ { \circ }$ and $102 ^ { \circ }$ 
A)  $17 ^ { \circ } , 61 ^ { \circ }$ and $119 ^ { \circ }$ 
B)  $17 ^ { \circ } , 78 ^ { \circ }$ and $102 ^ { \circ }$ 
C)  $17 ^ { \circ } , 78 ^ { \circ }$ and $85 ^ { \circ }$ 
D)  $17 ^ { \circ } , 61 ^ { \circ }$ and $102 ^ { \circ }$

Question 18

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 corresponding Celsius temperature for a temperature of 242°F. Round to the nearest tenth, if necessary.

Accepted Answer

A)  $467.6 ^ { \circ } \mathrm { C }$ 
B)  $116.7 ^ { \circ } \mathrm { C }$ 
C)  $130.9 ^ { \circ } \mathrm { C }$ 
D)  $378 ^ { \circ } \mathrm { C }$ 
A)  $467.6 ^ { \circ } \mathrm { C }$ 
B)  $116.7 ^ { \circ } \mathrm { C }$ 
C)  $130.9 ^ { \circ } \mathrm { C }$ 
D)  $378 ^ { \circ } \mathrm { C }$

Question 19

Solve the equation for the indicated variable. Assume no denominator is 0.
-$r m = t ^ { 2 } - m t$, for $t$

Accepted Answer

A)  $t = \frac { m \pm \sqrt { m ^ { 2 } - 4 m r } } { 4 }$ 
B)  $t = \frac { m \pm \sqrt { m ^ { 2 } + 4 m r } } { 2 m }$ 
C)  $t = m \pm \sqrt { m ^ { 2 } + 4 r m }$ 
D)  $t = \sqrt { m r - m }$ 
A)  $t = \frac { m \pm \sqrt { m ^ { 2 } - 4 m r } } { 4 }$ 
B)  $t = \frac { m \pm \sqrt { m ^ { 2 } + 4 m r } } { 2 m }$ 
C)  $t = m \pm \sqrt { m ^ { 2 } + 4 r m }$ 
D)  $t = \sqrt { m r - m }$

Question 20

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\frac { 3 } { x + 5 } + \frac { 8 } { x + 2 } = \frac { 10 } { x ^ { 2 } + 7 x + 10 }$$

Accepted Answer

A)  $\varnothing$ 
B)  $\left\{ - \frac { 39 } { 7 } \right\}$ 
C)  $\left\{ - \frac { 36 } { 11 } \right\}$ 
D)  $\left\{ - \frac { 56 } { 11 } \right\}$ 
A)  $\varnothing$ 
B)  $\left\{ - \frac { 39 } { 7 } \right\}$ 
C)  $\left\{ - \frac { 36 } { 11 } \right\}$ 
D)  $\left\{ - \frac { 56 } { 11 } \right\}$

Solve the formula for the indicated variable. - $P = 21 + 2 w$ , for 1

A boat is 84 feet from the base of cliff. If the distance from the top of the cliff to the boat is 21 less than twice the height of the cliff to the water. Find the height of the cliff. Round to the nearest tenth of a foot if necessary.

Decide what values of the variable cannot possibly be solutions for the equation. -One maid can clean the house in 5 hours. Another maid can do the job in 3 hours. How long will it take them to do the job working together?

Decide what values of the variable cannot possibly be solutions for the equation. - $\left( x ^ { 2 } - 3 \right) ^ { 1 / 2 } - ( x + 3 ) ^ { 1 / 2 } = 0$

Solve the equation by completing the square. - $8 x ^ { 2 } + 7 x = - 2$

Write the inequality in interval notation. - $- 9 \leq x < - 3$

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt [ 6 ] { x ^ { 2 } - 13 } = 1$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { x } { x - 5 } - \frac { 5 } { x + 5 } = \frac { 50 } { x ^ { 2 } - 25 }$

Solve the inequality. Write the solution set in interval notation. - $| x + 2 | \leq 0$

Solve the cubic equation using factoring and the quadratic formula. - $x + 17 = 0$

Decide what values of the variable cannot possibly be solutions for the equation. - $( x + 6 ) ^ { 2 / 5 } = ( 25 x ) ^ { 1 / 5 }$

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $0.2 ( x - 5 ) - 0.8 ( x - 5 ) = - 0.6 x + 3$

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply. - $- 2$

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $4 x + 9 ( x + 1 ) + 2 = 11 - 6 x$

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $20 x + 15 = 5 ( 2 x + 11 )$

Solve the quadratic inequality. Write the solution set in interval notation. - $( 7 + 4 x ) ^ { 2 } \leq - 1$

Solve the problem. -In triangle ABC, the angle C is six times as large as angle A. The measure of angle B is 44° greater than that of angle A. Find the measure of the angles.

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 corresponding Celsius temperature for a temperature of 242°F. Round to the nearest tenth, if necessary.

Solve the equation for the indicated variable. Assume no denominator is 0. - $r m = t ^ { 2 } - m t$ , for $t$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { 3 } { x + 5 } + \frac { 8 } { x + 2 } = \frac { 10 } { x ^ { 2 } + 7 x + 10 }$

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 the formula for the indicated variable. - P=21+2wP = 21 + 2 wP=21+2w , for 1

A boat is 84 feet from the base of cliff. If the distance from the top of the cliff to the boat is 21 less than twice the height of the cliff to the water. Find the height of the cliff. Round to the nearest tenth of a foot if necessary.

Decide what values of the variable cannot possibly be solutions for the equation. -One maid can clean the house in 5 hours. Another maid can do the job in 3 hours. How long will it take them to do the job working together?

Decide what values of the variable cannot possibly be solutions for the equation. - (x2−3)1/2−(x+3)1/2=0\left( x ^ { 2 } - 3 \right) ^ { 1 / 2 } - ( x + 3 ) ^ { 1 / 2 } = 0(x2−3)1/2−(x+3)1/2=0

Solve the equation by completing the square. - 8x2+7x=−28 x ^ { 2 } + 7 x = - 28x2+7x=−2

Write the inequality in interval notation. - −9≤x<−3- 9 \leq x < - 3−9≤x<−3

Decide what values of the variable cannot possibly be solutions for the equation. - x2−136=1\sqrt [ 6 ] { x ^ { 2 } - 13 } = 16x2−13​=1

Decide what values of the variable cannot possibly be solutions for the equation. - xx−5−5x+5=50x2−25\frac { x } { x - 5 } - \frac { 5 } { x + 5 } = \frac { 50 } { x ^ { 2 } - 25 }x−5x​−x+55​=x2−2550​

Solve the inequality. Write the solution set in interval notation. - ∣x+2∣≤0| x + 2 | \leq 0∣x+2∣≤0

Solve the cubic equation using factoring and the quadratic formula. - x+17=0x + 17 = 0x+17=0

Decide what values of the variable cannot possibly be solutions for the equation. - (x+6)2/5=(25x)1/5( x + 6 ) ^ { 2 / 5 } = ( 25 x ) ^ { 1 / 5 }(x+6)2/5=(25x)1/5

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - 0.2(x−5)−0.8(x−5)=−0.6x+30.2 ( x - 5 ) - 0.8 ( x - 5 ) = - 0.6 x + 30.2(x−5)−0.8(x−5)=−0.6x+3

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply. - −2- 2−2

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - 4x+9(x+1)+2=11−6x4 x + 9 ( x + 1 ) + 2 = 11 - 6 x4x+9(x+1)+2=11−6x

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - 20x+15=5(2x+11)20 x + 15 = 5 ( 2 x + 11 )20x+15=5(2x+11)

Solve the quadratic inequality. Write the solution set in interval notation. - (7+4x)2≤−1( 7 + 4 x ) ^ { 2 } \leq - 1(7+4x)2≤−1

Solve the problem. -In triangle ABC, the angle C is six times as large as angle A. The measure of angle B is 44° greater than that of angle A. Find the measure of the angles.

Solve the equation for the indicated variable. Assume no denominator is 0. - rm=t2−mtr m = t ^ { 2 } - m trm=t2−mt , for ttt

Decide what values of the variable cannot possibly be solutions for the equation. - 3x+5+8x+2=10x2+7x+10\frac { 3 } { x + 5 } + \frac { 8 } { x + 2 } = \frac { 10 } { x ^ { 2 } + 7 x + 10 }x+53​+x+28​=x2+7x+1010​

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

Solve the formula for the indicated variable. - $P = 21 + 2 w$ , for 1

Decide what values of the variable cannot possibly be solutions for the equation. - $\left( x ^ { 2 } - 3 \right) ^ { 1 / 2 } - ( x + 3 ) ^ { 1 / 2 } = 0$

Solve the equation by completing the square. - $8 x ^ { 2 } + 7 x = - 2$

Write the inequality in interval notation. - $- 9 \leq x < - 3$

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt [ 6 ] { x ^ { 2 } - 13 } = 1$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { x } { x - 5 } - \frac { 5 } { x + 5 } = \frac { 50 } { x ^ { 2 } - 25 }$

Solve the inequality. Write the solution set in interval notation. - $| x + 2 | \leq 0$

Solve the cubic equation using factoring and the quadratic formula. - $x + 17 = 0$

Decide what values of the variable cannot possibly be solutions for the equation. - $( x + 6 ) ^ { 2 / 5 } = ( 25 x ) ^ { 1 / 5 }$

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $0.2 ( x - 5 ) - 0.8 ( x - 5 ) = - 0.6 x + 3$

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply. - $- 2$

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $4 x + 9 ( x + 1 ) + 2 = 11 - 6 x$

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $20 x + 15 = 5 ( 2 x + 11 )$

Solve the quadratic inequality. Write the solution set in interval notation. - $( 7 + 4 x ) ^ { 2 } \leq - 1$

Solve the equation for the indicated variable. Assume no denominator is 0. - $r m = t ^ { 2 } - m t$ , for $t$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { 3 } { x + 5 } + \frac { 8 } { x + 2 } = \frac { 10 } { x ^ { 2 } + 7 x + 10 }$