Question 1

Solve the equation.
-$$\frac { 16 } { x + 2 } = 1 + \frac { 2 } { x - 4 }$$

Accepted Answer

A)  $\varnothing$ 
B)  $\{ - 2,4 \}$ 
C)  $\{ - 12 \}$ 
D)  $\{ 6,10 \}$ 
A)  $\varnothing$ 
B)  $\{ - 2,4 \}$ 
C)  $\{ - 12 \}$ 
D)  $\{ 6,10 \}$

Question 2

Solve the equation.
-$$\sqrt [ 3 ] { 2 x - 3 } + 7 = 5$$

Accepted Answer

A)  $\{ - 11 \}$ 
B)  $\left\{ - \frac { 5 } { 2 } \right\}$ 
C)  $\{ - 4 \}$ 
D)  $\left\{ \frac { 3 } { 2 } \right\}$ 
A)  $\{ - 11 \}$ 
B)  $\left\{ - \frac { 5 } { 2 } \right\}$ 
C)  $\{ - 4 \}$ 
D)  $\left\{ \frac { 3 } { 2 } \right\}$

Question 3

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

Accepted Answer

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

Question 4

Solve the quadratic inequality. Write the solution set in interval notation.
-$$x ^ { 2 } - 8 x + 5 \geq 0$$

Accepted Answer

A)  $( - \infty , - \sqrt { 11 } ] \cup [ \sqrt { 11 } , \infty )$ 
B)  $( - \infty , 4 - \sqrt { 11 } ) \cup ( 4 + \sqrt { 11 } , \infty )$ 
C)  $( - \infty , 4 - \sqrt { 11 } ] \cup [ 4 + \sqrt { 11 } , \infty )$ 
D)  $[ 4 - \sqrt { 11 } , 4 + \sqrt { 11 } ]$ 
A)  $( - \infty , - \sqrt { 11 } ] \cup [ \sqrt { 11 } , \infty )$ 
B)  $( - \infty , 4 - \sqrt { 11 } ) \cup ( 4 + \sqrt { 11 } , \infty )$ 
C)  $( - \infty , 4 - \sqrt { 11 } ] \cup [ 4 + \sqrt { 11 } , \infty )$ 
D)  $[ 4 - \sqrt { 11 } , 4 + \sqrt { 11 } ]$

Question 5

Solve the problem.
-A square plywood platform has a perimeter which is 9 times the length of a side, decreased by 15 . Find the length of a side.

Accepted Answer

A)  8 
B)  3 
C)  1 
D)  5 
A)  8 
B)  3 
C)  1 
D)  5

Question 6

Solve the formula for the indicated variable.
-$\mathrm { P } = 2 \mathrm { l } + 2 \mathrm { w }$, for $w$

Accepted Answer

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

Question 7

Solve the equation by completing the square.
-$$2 x ^ { 2 } + 7 x + 3 = 0$$

Accepted Answer

A)  $\left\{ - 3 , - \frac { 1 } { 2 } \right\}$ 
B)  $\left\{ - 2 \pm \frac { \sqrt { 3 } } { 2 } \mathrm { i } \right\}$ 
C)  $\{ 3 , - 1 \}$ 
D)  $\left\{ \frac { - 7 \pm 2 \sqrt { 6 } } { 4 } \right\}$ 
A)  $\left\{ - 3 , - \frac { 1 } { 2 } \right\}$ 
B)  $\left\{ - 2 \pm \frac { \sqrt { 3 } } { 2 } \mathrm { i } \right\}$ 
C)  $\{ 3 , - 1 \}$ 
D)  $\left\{ \frac { - 7 \pm 2 \sqrt { 6 } } { 4 } \right\}$

Question 8

Simplify the power of i.
-$\frac { 1 } { \mathrm { i } ^ { 57 } }$

Accepted Answer

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

Question 9

Indicate whether the statement is true always, sometimes, or never.
-A complex number is an imaginary number.

Accepted Answer

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

Question 10

Solve the quadratic inequality. Write the solution set in interval notation.
-$$- 3 x ^ { 2 } + 4 x - 5 \leq 0$$

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 11

Find the quotient. Write the answer in standard form.
-$\frac { 2 } { 11 \mathrm { i } }$

Accepted Answer

A)  $\frac { 2 } { 11 }$ 
B)  $- \frac { 2 } { 11 } i$ 
C)  $- \frac { 2 } { 11 }$ 
D)  $\frac { 2 } { 11 } \mathrm { i }$ 
A)  $\frac { 2 } { 11 }$ 
B)  $- \frac { 2 } { 11 } i$ 
C)  $- \frac { 2 } { 11 }$ 
D)  $\frac { 2 } { 11 } \mathrm { i }$

Question 12

Solve the problem.
-Which one of the following equations is set up for direct use of the zero-factor property?

Accepted Answer

A)  $( 3 x - 5 ) ^ { 2 } = 6$ 
B)  $( 3 x - 5 ) ( x + 6 ) = 0$ 
C)  $3 x ^ { 2 } - 5 x + 6 = 0$ 
D)  $x ^ { 2 } - x = 6$ 
A)  $( 3 x - 5 ) ^ { 2 } = 6$ 
B)  $( 3 x - 5 ) ( x + 6 ) = 0$ 
C)  $3 x ^ { 2 } - 5 x + 6 = 0$ 
D)  $x ^ { 2 } - x = 6$

Question 13

Solve for the indicated variable.
-$\mathrm { A } = 2 \pi \mathrm { a } ^ { 2 }$, for $\mathrm { a }$

Accepted Answer

A)  $\mathrm { a } = \frac { \pm \sqrt { 2 \pi \mathrm { A } } } { 2 \pi }$ 
B)  $a = \sqrt { 2 \pi \mathrm { A } }$ 
C)  $\mathrm { a } = \frac { \pm \mathrm { A } \sqrt { 2 \pi } } { 2 \pi }$ 
D)  $\mathrm { a } = \frac { \pm \sqrt { \mathrm { A } \pi } } { 2 }$ 
A)  $\mathrm { a } = \frac { \pm \sqrt { 2 \pi \mathrm { A } } } { 2 \pi }$ 
B)  $a = \sqrt { 2 \pi \mathrm { A } }$ 
C)  $\mathrm { a } = \frac { \pm \mathrm { A } \sqrt { 2 \pi } } { 2 \pi }$ 
D)  $\mathrm { a } = \frac { \pm \sqrt { \mathrm { A } \pi } } { 2 }$

Question 14

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\frac { x } { x - 3 } + \frac { 11 x } { 9 x + 9 } = 0$$

Accepted Answer

A)  $- 9,3$ 
B)  $- 3,0,1$ 
C)  $- 3,9$ 
D)  $- 1,3$ 
A)  $- 9,3$ 
B)  $- 3,0,1$ 
C)  $- 3,9$ 
D)  $- 1,3$

Question 15

Solve the rational inequality. Write the solution set in interval notation.
-$$3 \geq \frac { 1 } { x }$$

Accepted Answer

A)  $\left( 0 , \frac { 1 } { 3 } \right)$ 
B)  $( - \infty , 0 ) \cup [ 3 , \infty )$ 
C)  $( - \infty , 0 ) \cup \left[ \frac { 1 } { 3 } , \infty \right]$ 
D)  $( 0,3 ]$ 
A)  $\left( 0 , \frac { 1 } { 3 } \right)$ 
B)  $( - \infty , 0 ) \cup [ 3 , \infty )$ 
C)  $( - \infty , 0 ) \cup \left[ \frac { 1 } { 3 } , \infty \right]$ 
D)  $( 0,3 ]$

Question 16

Find the quotient. Write the answer in standard form.
-$$\frac { 8 - 9 i } { 8 + 4 i }$$

Accepted Answer

A)  $5 + 2 i$ 
B)  $\frac { 7 } { 48 } + \frac { 13 } { 24 } \mathrm { i }$ 
C)  $\frac { 25 } { 12 } + \frac { 13 } { 24 } \mathrm { i }$ 
D)  $\frac { 7 } { 20 } - \frac { 13 } { 10 } \mathrm { i }$ 
A)  $5 + 2 i$ 
B)  $\frac { 7 } { 48 } + \frac { 13 } { 24 } \mathrm { i }$ 
C)  $\frac { 25 } { 12 } + \frac { 13 } { 24 } \mathrm { i }$ 
D)  $\frac { 7 } { 20 } - \frac { 13 } { 10 } \mathrm { i }$

Question 17

Solve the problem.
-A boat is 108 feet from the base of cliff. If the distance from the top of the cliff to the boat is 27 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)  81 ft 
C)  45 ft 
D)  135 ft 
A)  63 ft 
B)  81 ft 
C)  45 ft 
D)  135 ft

Question 18

Determine whether or not the equation is linear.
-0.03x + 0.07x = 0.90

Accepted Answer

A)  Linear 
B)  Not linear 
A)  Linear 
B)  Not linear

Question 19

Find the sum or difference. Write the answer in standard form.
-$$7 \sqrt { 2 } - ( 2 \sqrt { 2 } + i ) + 5 i - ( - 3 \sqrt { 2 } + 5 i )$$

Accepted Answer

A)  $8 \sqrt { 2 } + i$ 
B)  $8 - 9 \mathrm { i } \sqrt { 2 }$ 
C)  $8 \sqrt { 2 } - \mathrm { i }$ 
D)  $- 8 - 9 \mathrm { i } \sqrt { 2 }$ 
A)  $8 \sqrt { 2 } + i$ 
B)  $8 - 9 \mathrm { i } \sqrt { 2 }$ 
C)  $8 \sqrt { 2 } - \mathrm { i }$ 
D)  $- 8 - 9 \mathrm { i } \sqrt { 2 }$

Question 20

Find the quotient. Write the answer in standard form.
-$\frac { 2 + 8 i } { 9 + 8 i }$

Accepted Answer

A)  $\frac { 82 } { 17 } - \frac { 56 } { 17 } \mathrm { i }$ 
B)  $- \frac { 46 } { 17 } - \frac { 56 } { 17 } \mathrm { i }$ 
C)  $\frac { 82 } { 145 } + \frac { 56 } { 145 } \mathrm { i }$ 
D)  $- \frac { 46 } { 145 } - \frac { 88 } { 145 } \mathrm { i }$ 
A)  $\frac { 82 } { 17 } - \frac { 56 } { 17 } \mathrm { i }$ 
B)  $- \frac { 46 } { 17 } - \frac { 56 } { 17 } \mathrm { i }$ 
C)  $\frac { 82 } { 145 } + \frac { 56 } { 145 } \mathrm { i }$ 
D)  $- \frac { 46 } { 145 } - \frac { 88 } { 145 } \mathrm { i }$

Solve the equation. - $\frac { 16 } { x + 2 } = 1 + \frac { 2 } { x - 4 }$

Solve the equation. - $\sqrt [ 3 ] { 2 x - 3 } + 7 = 5$

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

Solve the quadratic inequality. Write the solution set in interval notation. - $x ^ { 2 } - 8 x + 5 \geq 0$

Solve the problem. -A square plywood platform has a perimeter which is 9 times the length of a side, decreased by 15 . Find the length of a side.

Solve the formula for the indicated variable. - $\mathrm { P } = 2 \mathrm { l } + 2 \mathrm { w }$ , for $w$

Solve the equation by completing the square. - $2 x ^ { 2 } + 7 x + 3 = 0$

Simplify the power of i. - $\frac { 1 } { \mathrm { i } ^ { 57 } }$

Indicate whether the statement is true always, sometimes, or never. -A complex number is an imaginary number.

Solve the quadratic inequality. Write the solution set in interval notation. - $- 3 x ^ { 2 } + 4 x - 5 \leq 0$

Find the quotient. Write the answer in standard form. - $\frac { 2 } { 11 \mathrm { i } }$

Solve the problem. -Which one of the following equations is set up for direct use of the zero-factor property?

Solve for the indicated variable. - $\mathrm { A } = 2 \pi \mathrm { a } ^ { 2 }$ , for $\mathrm { a }$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { x } { x - 3 } + \frac { 11 x } { 9 x + 9 } = 0$

Solve the rational inequality. Write the solution set in interval notation. - $3 \geq \frac { 1 } { x }$

Find the quotient. Write the answer in standard form. - $\frac { 8 - 9 i } { 8 + 4 i }$

Solve the problem. -A boat is 108 feet from the base of cliff. If the distance from the top of the cliff to the boat is 27 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.

Determine whether or not the equation is linear. -0.03x + 0.07x = 0.90

Find the sum or difference. Write the answer in standard form. - $7 \sqrt { 2 } - ( 2 \sqrt { 2 } + i ) + 5 i - ( - 3 \sqrt { 2 } + 5 i )$

Find the quotient. Write the answer in standard form. - $\frac { 2 + 8 i } { 9 + 8 i }$

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Exam 1: Equations and Inequalities

Solve the equation. - 16x+2=1+2x−4\frac { 16 } { x + 2 } = 1 + \frac { 2 } { x - 4 }x+216​=1+x−42​

Solve the equation. - 2x−33+7=5\sqrt [ 3 ] { 2 x - 3 } + 7 = 532x−3​+7=5

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

Solve the quadratic inequality. Write the solution set in interval notation. - x2−8x+5≥0x ^ { 2 } - 8 x + 5 \geq 0x2−8x+5≥0