Question 1

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\sqrt { x + 7 } + 5 = x$$

Accepted Answer

A)  {2, 9} 
B)  {2} 
C)  {9} 
D)  {9, 18} 
A)  {2, 9} 
B)  {2} 
C)  {9} 
D)  {9, 18}

Question 2

A rectangular enclosure must have an area of at least $600 \mathrm { yd } ^ { 2 }$ . If 140 yd of fencing is to be used, and the width cannot exceed the length, within what limits must the width of the enclosure lie?

Accepted Answer

A)  $35 \leq w \leq 60$ 
B)  $0 \leq w \leq 10$ 
C)  $10 \leq w \leq 60$ 
D)  $10 \leq w \leq 35$ 
A)  $35 \leq w \leq 60$ 
B)  $0 \leq w \leq 10$ 
C)  $10 \leq w \leq 60$ 
D)  $10 \leq w \leq 35$

Question 3

Multiply or divide, as indicated. Simplify the answer.
-$\sqrt { - 5 } \cdot \sqrt { - 5 }$

Accepted Answer

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

Question 4

Find the sum or difference. Write the answer in standard form.
-$$( 2 + 6 i ) - ( - 8 - 6 i ) + ( 8 + 8 i )$$

Accepted Answer

A)  $18 + 20 \mathrm { i }$ 
B)  $- 18 + 4 i$ 
C)  $18 + 8 i$ 
D)  $2 + 8 i$ 
A)  $18 + 20 \mathrm { i }$ 
B)  $- 18 + 4 i$ 
C)  $18 + 8 i$ 
D)  $2 + 8 i$

Question 5

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\frac { 6 x } { x - 6 } - \frac { 4 } { x } = \frac { 24 } { x ^ { 2 } - 6 x }$$

Accepted Answer

A)  $\left\{ \frac { 2 } { 3 } \right\}$ 
B)  $\left\{ \frac { 3 } { 2 } \right\}$ 
C)  $\left\{ \frac { 2 } { 3 } , - \frac { 2 } { 3 } \right\}$ 
D)  $\left\{ 0 , \frac { 2 } { 3 } \right\}$ 
A)  $\left\{ \frac { 2 } { 3 } \right\}$ 
B)  $\left\{ \frac { 3 } { 2 } \right\}$ 
C)  $\left\{ \frac { 2 } { 3 } , - \frac { 2 } { 3 } \right\}$ 
D)  $\left\{ 0 , \frac { 2 } { 3 } \right\}$

Question 6

Indicate whether the statement is true always, sometimes, or never.
-The product of two imaginary numbers is a real number.

Accepted Answer

A)  Never 
B)  Always 
C)  Sometimes 
A)  Never 
B)  Always 
C)  Sometimes

Question 7

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\left( x ^ { 2 } + 2 \right) ^ { 1 / 2 } - ( 2 x + 5 ) ^ { 1 / 2 } = 0$$

Accepted Answer

A)  $\{ 3 , - 1 \}$ 
B)  $\{ 3 \}$ 
C)  $\varnothing$ 
D)  $\{ - 3,1 \}$ 
A)  $\{ 3 , - 1 \}$ 
B)  $\{ 3 \}$ 
C)  $\varnothing$ 
D)  $\{ - 3,1 \}$

Question 8

Solve the formula for the indicated variable.
-$\mathbf { I } =$ Prt, for $\mathrm { P }$

Accepted Answer

A)  $P = r$ - It 
B)  $P = \frac { r - I } { 1 + t }$ 
C)  $\mathrm { P } = \frac { \mathrm { r } - 1 } { \mathrm { It } }$ 
D)  $P = \frac { I } { r t }$ 
A)  $P = r$ - It 
B)  $P = \frac { r - I } { 1 + t }$ 
C)  $\mathrm { P } = \frac { \mathrm { r } - 1 } { \mathrm { It } }$ 
D)  $P = \frac { I } { r t }$

Question 9

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

Accepted Answer

A)  $- 3 + 6 i$ 
B)  $3 - 8 \mathrm { i }$ 
C)  $- 3 + 8 \mathrm { i }$ 
D)  $3 - 6 i$ 
A)  $- 3 + 6 i$ 
B)  $3 - 8 \mathrm { i }$ 
C)  $- 3 + 8 \mathrm { i }$ 
D)  $3 - 6 i$

Question 10

Simplify the power of i.
-Which one of the following equations is set up for direct use of the zero-factor property?

Accepted Answer

A)  $( 4 x + 5 ) ^ { 2 } = 8$ 
B)  $x ^ { 2 } + x = 8$ 
C)  $4 x ^ { 2 } + 5 x - 8 = 0$ 
D)  $( 4 x + 5 ) ( x - 8 ) = 0$ 
A)  $( 4 x + 5 ) ^ { 2 } = 8$ 
B)  $x ^ { 2 } + x = 8$ 
C)  $4 x ^ { 2 } + 5 x - 8 = 0$ 
D)  $( 4 x + 5 ) ( x - 8 ) = 0$

Question 11

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\sqrt { 2 x + 15 } - x = 6$$

Accepted Answer

A)  $\{ - 7 , - 3 \}$ 
B)  $\{ - 3 \}$ 
C)  $\{ - 7 \}$ 
D)  $\varnothing$ 
A)  $\{ - 7 , - 3 \}$ 
B)  $\{ - 3 \}$ 
C)  $\{ - 7 \}$ 
D)  $\varnothing$

Question 12

Solve the inequality. Write the solution set in interval notation.
-$$\left| x ^ { 4 } + 6 x ^ { 2 } + 9 \right| < 0$$

Accepted Answer

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

Question 13

Decide what values of the variable cannot possibly be solutions for the equation.
-$$( x - 4 ) ^ { 1 / 4 } + 10 = 0$$

Accepted Answer

A)  $\varnothing$ 
B)  $\{ 2500 \}$ 
C)  $\left\{ \frac { 5 } { 2 } \right\}$ 
D)  $\{ - 2500 \}$ 
A)  $\varnothing$ 
B)  $\{ 2500 \}$ 
C)  $\left\{ \frac { 5 } { 2 } \right\}$ 
D)  $\{ - 2500 \}$

Question 14

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\sqrt [ 4 ] { x - 3 } + 8 = 0$$

Accepted Answer

A)  $\varnothing$ 
B)  $\left\{ - \frac { 4096 } { 3 } \right\}$ 
C)  $\left\{ \frac { 4096 } { 3 } \right\}$ 
D)  $\left\{ \frac { 8 } { 3 } \right\}$ 
A)  $\varnothing$ 
B)  $\left\{ - \frac { 4096 } { 3 } \right\}$ 
C)  $\left\{ \frac { 4096 } { 3 } \right\}$ 
D)  $\left\{ \frac { 8 } { 3 } \right\}$

Question 15

Graph the solution set.
-$$| 9 x + 6 | = 5$$

Accepted Answer

A)  $\left\{ - \frac { 11 } { 9 } , \frac { 1 } { 9 } \right\}$ 
B)  $\left\{ \frac { 11 } { 9 } , \frac { 1 } { 9 } \right\}$ 
C)  $\left\{ - \frac { 1 } { 9 } \right\}$ 
D)  $\left\{ - \frac { 1 } { 9 } , - \frac { 11 } { 9 } \right\}$ 
A)  $\left\{ - \frac { 11 } { 9 } , \frac { 1 } { 9 } \right\}$ 
B)  $\left\{ \frac { 11 } { 9 } , \frac { 1 } { 9 } \right\}$ 
C)  $\left\{ - \frac { 1 } { 9 } \right\}$ 
D)  $\left\{ - \frac { 1 } { 9 } , - \frac { 11 } { 9 } \right\}$

Question 16

Graph the solution set.
-$$\left| x ^ { 2 } + 3 x - 10 \right| = 0$$

Accepted Answer

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

Question 17

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.
-$$- 8 + 4 \sqrt { 2 } , - 8 - 4 \sqrt { 2 }$$

Accepted Answer

A)  $x ^ { 2 } + 16 x + 32 = 0$ 
B)  $x ^ { 2 } - 32 x - 16 = 0$ 
C)  $x ^ { 2 } + 8 x + 56 = 0$ 
D)  $x ^ { 2 } - 64 x + 96 = 0$ 
A)  $x ^ { 2 } + 16 x + 32 = 0$ 
B)  $x ^ { 2 } - 32 x - 16 = 0$ 
C)  $x ^ { 2 } + 8 x + 56 = 0$ 
D)  $x ^ { 2 } - 64 x + 96 = 0$

Question 18

The temperatures in parts of Antarctica in degrees Celsius roughly satisfy the inequality $| C + 92 | \leq 53$. What range of temperatures corresponds to this inequality?

Accepted Answer

A)  $\left[ - 145 ^ { \circ } \mathrm { C } , - 39 ^ { \circ } \mathrm { C } \right]$ 
B)  $\left[ - 145 ^ { \circ } \mathrm { C } , 145 ^ { \circ } \mathrm { C } \right]$ 
C)  $\left[ - 39 ^ { \circ } \mathrm { C } , 145 ^ { \circ } \mathrm { C } \right]$ 
D)  $\left[ - 39 ^ { \circ } \mathrm { C } , 39 ^ { \circ } \mathrm { C } \right]$ 
A)  $\left[ - 145 ^ { \circ } \mathrm { C } , - 39 ^ { \circ } \mathrm { C } \right]$ 
B)  $\left[ - 145 ^ { \circ } \mathrm { C } , 145 ^ { \circ } \mathrm { C } \right]$ 
C)  $\left[ - 39 ^ { \circ } \mathrm { C } , 145 ^ { \circ } \mathrm { C } \right]$ 
D)  $\left[ - 39 ^ { \circ } \mathrm { C } , 39 ^ { \circ } \mathrm { C } \right]$

Question 19

Solve for the indicated variable.
-$\frac { 1 } { \mathrm {~A} } = \frac { 1 } { \mathrm {~m} } + \frac { 1 } { \mathrm { t } }$, for $\mathrm { t }$

Accepted Answer

A)  $t = \frac { m - A } { m A }$ 
B)  $t = 1 + \frac { m A } { m - A }$ 
C)  $t = 2 - \frac { m A } { m - A }$ 
D)  $t = \frac { m A } { m - A }$ 
A)  $t = \frac { m - A } { m A }$ 
B)  $t = 1 + \frac { m A } { m - A }$ 
C)  $t = 2 - \frac { m A } { m - A }$ 
D)  $t = \frac { m A } { m - A }$

Question 20

Solve the cubic equation using factoring and the quadratic formula.
-$$x ^ { 3 } - 8 = 0$$

Accepted Answer

A)  $\{ 2,1 \pm i \sqrt { 6 } \}$ 
B)  $\{ 2 , - 1 \pm \sqrt { 5 } \}$ 
C)  $\{ 2 , \pm 2 \mathrm { i } \}$ 
D)  $\{ 2 , - 1 \pm i \sqrt { 3 } \}$ 
A)  $\{ 2,1 \pm i \sqrt { 6 } \}$ 
B)  $\{ 2 , - 1 \pm \sqrt { 5 } \}$ 
C)  $\{ 2 , \pm 2 \mathrm { i } \}$ 
D)  $\{ 2 , - 1 \pm i \sqrt { 3 } \}$

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt { x + 7 } + 5 = x$

A rectangular enclosure must have an area of at least $600 \mathrm { yd } ^ { 2 }$ . If 140 yd of fencing is to be used, and the width cannot exceed the length, within what limits must the width of the enclosure lie?

Multiply or divide, as indicated. Simplify the answer. - $\sqrt { - 5 } \cdot \sqrt { - 5 }$

Find the sum or difference. Write the answer in standard form. - $( 2 + 6 i ) - ( - 8 - 6 i ) + ( 8 + 8 i )$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { 6 x } { x - 6 } - \frac { 4 } { x } = \frac { 24 } { x ^ { 2 } - 6 x }$

Indicate whether the statement is true always, sometimes, or never. -The product of two imaginary numbers is a real number.

Decide what values of the variable cannot possibly be solutions for the equation. - $\left( x ^ { 2 } + 2 \right) ^ { 1 / 2 } - ( 2 x + 5 ) ^ { 1 / 2 } = 0$

Solve the formula for the indicated variable. - $\mathbf { I } =$ Prt, for $\mathrm { P }$

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

Simplify the power of i. -Which one of the following equations is set up for direct use of the zero-factor property?

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt { 2 x + 15 } - x = 6$

Solve the inequality. Write the solution set in interval notation. - $\left| x ^ { 4 } + 6 x ^ { 2 } + 9 \right| < 0$

Decide what values of the variable cannot possibly be solutions for the equation. - $( x - 4 ) ^ { 1 / 4 } + 10 = 0$

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt [ 4 ] { x - 3 } + 8 = 0$

Graph the solution set. - $| 9 x + 6 | = 5$

Graph the solution set. - $\left| x ^ { 2 } + 3 x - 10 \right| = 0$

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. - $- 8 + 4 \sqrt { 2 } , - 8 - 4 \sqrt { 2 }$

The temperatures in parts of Antarctica in degrees Celsius roughly satisfy the inequality $| C + 92 | \leq 53$ . What range of temperatures corresponds to this inequality?

Solve for the indicated variable. - $\frac { 1 } { \mathrm {~A} } = \frac { 1 } { \mathrm {~m} } + \frac { 1 } { \mathrm { t } }$ , for $\mathrm { t }$

Solve the cubic equation using factoring and the quadratic formula. - $x ^ { 3 } - 8 = 0$

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

Decide what values of the variable cannot possibly be solutions for the equation. - x+7+5=x\sqrt { x + 7 } + 5 = xx+7​+5=x

A rectangular enclosure must have an area of at least 600yd2600 \mathrm { yd } ^ { 2 }600yd2 . If 140 yd of fencing is to be used, and the width cannot exceed the length, within what limits must the width of the enclosure lie?

Multiply or divide, as indicated. Simplify the answer. - −5⋅−5\sqrt { - 5 } \cdot \sqrt { - 5 }−5​⋅−5​

Find the sum or difference. Write the answer in standard form. - (2+6i)−(−8−6i)+(8+8i)( 2 + 6 i ) - ( - 8 - 6 i ) + ( 8 + 8 i )(2+6i)−(−8−6i)+(8+8i)

Decide what values of the variable cannot possibly be solutions for the equation. - 6xx−6−4x=24x2−6x\frac { 6 x } { x - 6 } - \frac { 4 } { x } = \frac { 24 } { x ^ { 2 } - 6 x }x−66x​−x4​=x2−6x24​

Indicate whether the statement is true always, sometimes, or never. -The product of two imaginary numbers is a real number.

Decide what values of the variable cannot possibly be solutions for the equation. - (x2+2)1/2−(2x+5)1/2=0\left( x ^ { 2 } + 2 \right) ^ { 1 / 2 } - ( 2 x + 5 ) ^ { 1 / 2 } = 0(x2+2)1/2−(2x+5)1/2=0

Solve the formula for the indicated variable. - I=\mathbf { I } =I= Prt, for P\mathrm { P }P

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

Simplify the power of i. -Which one of the following equations is set up for direct use of the zero-factor property?

Decide what values of the variable cannot possibly be solutions for the equation. - 2x+15−x=6\sqrt { 2 x + 15 } - x = 62x+15​−x=6

Solve the inequality. Write the solution set in interval notation. - ∣x4+6x2+9∣<0\left| x ^ { 4 } + 6 x ^ { 2 } + 9 \right| < 0​x4+6x2+9​<0

Decide what values of the variable cannot possibly be solutions for the equation. - (x−4)1/4+10=0( x - 4 ) ^ { 1 / 4 } + 10 = 0(x−4)1/4+10=0

Decide what values of the variable cannot possibly be solutions for the equation. - x−34+8=0\sqrt [ 4 ] { x - 3 } + 8 = 04x−3​+8=0

Graph the solution set. - ∣9x+6∣=5| 9 x + 6 | = 5∣9x+6∣=5

Graph the solution set. - ∣x2+3x−10∣=0\left| x ^ { 2 } + 3 x - 10 \right| = 0​x2+3x−10​=0

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. - −8+42,−8−42- 8 + 4 \sqrt { 2 } , - 8 - 4 \sqrt { 2 }−8+42​,−8−42​

The temperatures in parts of Antarctica in degrees Celsius roughly satisfy the inequality ∣C+92∣≤53| C + 92 | \leq 53∣C+92∣≤53 . What range of temperatures corresponds to this inequality?

Solve for the indicated variable. - 1 A=1 m+1t\frac { 1 } { \mathrm {~A} } = \frac { 1 } { \mathrm {~m} } + \frac { 1 } { \mathrm { t } } A1​= m1​+t1​ , for t\mathrm { t }t

Solve the cubic equation using factoring and the quadratic formula. - x3−8=0x ^ { 3 } - 8 = 0x3−8=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

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt { x + 7 } + 5 = x$

A rectangular enclosure must have an area of at least $600 \mathrm { yd } ^ { 2 }$ . If 140 yd of fencing is to be used, and the width cannot exceed the length, within what limits must the width of the enclosure lie?

Multiply or divide, as indicated. Simplify the answer. - $\sqrt { - 5 } \cdot \sqrt { - 5 }$

Find the sum or difference. Write the answer in standard form. - $( 2 + 6 i ) - ( - 8 - 6 i ) + ( 8 + 8 i )$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { 6 x } { x - 6 } - \frac { 4 } { x } = \frac { 24 } { x ^ { 2 } - 6 x }$

Decide what values of the variable cannot possibly be solutions for the equation. - $\left( x ^ { 2 } + 2 \right) ^ { 1 / 2 } - ( 2 x + 5 ) ^ { 1 / 2 } = 0$

Solve the formula for the indicated variable. - $\mathbf { I } =$ Prt, for $\mathrm { P }$

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

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt { 2 x + 15 } - x = 6$

Solve the inequality. Write the solution set in interval notation. - $\left| x ^ { 4 } + 6 x ^ { 2 } + 9 \right| < 0$

Decide what values of the variable cannot possibly be solutions for the equation. - $( x - 4 ) ^ { 1 / 4 } + 10 = 0$

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt [ 4 ] { x - 3 } + 8 = 0$

Graph the solution set. - $| 9 x + 6 | = 5$

Graph the solution set. - $\left| x ^ { 2 } + 3 x - 10 \right| = 0$

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. - $- 8 + 4 \sqrt { 2 } , - 8 - 4 \sqrt { 2 }$

The temperatures in parts of Antarctica in degrees Celsius roughly satisfy the inequality $| C + 92 | \leq 53$ . What range of temperatures corresponds to this inequality?

Solve for the indicated variable. - $\frac { 1 } { \mathrm {~A} } = \frac { 1 } { \mathrm {~m} } + \frac { 1 } { \mathrm { t } }$ , for $\mathrm { t }$

Solve the cubic equation using factoring and the quadratic formula. - $x ^ { 3 } - 8 = 0$