Question 1

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

Accepted Answer

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

Question 2

Decide whether the statement is true or false.
--6 is a solution of -7x = 42.

Accepted Answer

A) True 
 B)False

Question 3

Determine whether or not the equation is linear.
-0.06x - 0.05x = 0.90

Accepted Answer

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

Question 4

Answer the question.
-The mat around the picture shown measures x inches across. Which one of the following equations says that the area of the picture itself is 700 square inches?

Accepted Answer

A)  $( 43 ) ( 34 ) - x ^ { 2 } = 700$ 
B)  $2 ( 43 - 2 x ) + 2 ( 34 - 2 x ) = 700$ 
C)  $( 43 - 2 x ) ( 34 - 2 x ) = 700$ 
D)  $( 43 - x ) ( 34 - x ) = 700$ 
A)  $( 43 ) ( 34 ) - x ^ { 2 } = 700$ 
B)  $2 ( 43 - 2 x ) + 2 ( 34 - 2 x ) = 700$ 
C)  $( 43 - 2 x ) ( 34 - 2 x ) = 700$ 
D)  $( 43 - x ) ( 34 - x ) = 700$

Question 5

Solve and graph the inequality. Give answer in interval notation.
-$$12 x + 11 \geq 11 x + 7$$

Accepted Answer

A)  $( - \infty , 12 )$
  
B)  $[ - 4 , \infty )$
  
C)  $( - \infty , - 4 ]$
  
D)  $( 12 , \infty )$
  
A)  $( - \infty , 12 )$
  
B)  $[ - 4 , \infty )$
  
C)  $( - \infty , - 4 ]$
  
D)  $( 12 , \infty )$

Question 6

Solve the equation using the quadratic formula.
-$$6 = - \frac { 6 } { x } - \frac { 1 } { x ^ { 2 } }$$

Accepted Answer

A)  $\left\{ \frac { - 3 \pm \sqrt { 3 } } { 6 } \right\}$ 
B)  $\left\{ \frac { - 3 \pm \sqrt { 3 } } { 12 } \right\}$ 
C)  $\left\{ \frac { - 3 \pm \sqrt { 15 } } { 6 } \right\}$ 
D)  $\left\{ \frac { - 6 \pm \sqrt { 3 } } { 6 } \right\}$ 
A)  $\left\{ \frac { - 3 \pm \sqrt { 3 } } { 6 } \right\}$ 
B)  $\left\{ \frac { - 3 \pm \sqrt { 3 } } { 12 } \right\}$ 
C)  $\left\{ \frac { - 3 \pm \sqrt { 15 } } { 6 } \right\}$ 
D)  $\left\{ \frac { - 6 \pm \sqrt { 3 } } { 6 } \right\}$

Question 7

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

Accepted Answer

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

Question 8

Solve the equation by the square root property.
-$$x ^ { 2 } = 18$$

Accepted Answer

A)  $\{ 9 \}$ 
B)  $\{ \pm 3 \sqrt { 2 } \}$ 
C)  $\{ 324 \}$ 
D)  $\{ \sqrt { 18 } \}$ 
A)  $\{ 9 \}$ 
B)  $\{ \pm 3 \sqrt { 2 } \}$ 
C)  $\{ 324 \}$ 
D)  $\{ \sqrt { 18 } \}$

Question 9

Solve the inequality. Write the solution set in interval notation.
-$$| 6 x - 7 | > - 4$$

Accepted Answer

A)  $\left( - \infty , - \frac { 1 } { 6 } \right) \cup \left( - \frac { 3 } { 2 } , \infty \right)$ 
B)  $\left( - \infty , \frac { 11 } { 6 } \right) \cup \left( \frac { 1 } { 2 } , \infty \right)$ 
C)  $\varnothing$ 
D)  $( - \infty , \infty )$ 
A)  $\left( - \infty , - \frac { 1 } { 6 } \right) \cup \left( - \frac { 3 } { 2 } , \infty \right)$ 
B)  $\left( - \infty , \frac { 11 } { 6 } \right) \cup \left( \frac { 1 } { 2 } , \infty \right)$ 
C)  $\varnothing$ 
D)  $( - \infty , \infty )$

Question 10

Decide what values of the variable cannot possibly be solutions for the equation.
-$$16 x = \sqrt { 1 - 24 x }$$

Accepted Answer

A)  $\left\{ - \frac { 1 } { 8 } \right\}$ 
B)  $\left\{ \frac { 1 } { 16 } \right\}$ 
C)  $\left\{ \frac { 1 } { 32 } \right\}$ 
D)  $\left\{ \frac { 1 } { 8 } \right\}$ 
A)  $\left\{ - \frac { 1 } { 8 } \right\}$ 
B)  $\left\{ \frac { 1 } { 16 } \right\}$ 
C)  $\left\{ \frac { 1 } { 32 } \right\}$ 
D)  $\left\{ \frac { 1 } { 8 } \right\}$

Question 11

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.
-$$C = 87 ^ { \circ }$$

Accepted Answer

A)  $F = 30.6 ^ { \circ }$ 
B)  $F = 188.6 ^ { \circ }$ 
C)  $\mathrm { F } = 214.2 ^ { \circ }$ 
D)  $\mathrm { F } = 66.1 ^ { \circ }$ 
A)  $F = 30.6 ^ { \circ }$ 
B)  $F = 188.6 ^ { \circ }$ 
C)  $\mathrm { F } = 214.2 ^ { \circ }$ 
D)  $\mathrm { F } = 66.1 ^ { \circ }$

Question 12

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\sqrt [ 3 ] { 4 x - 7 } + 9 = 5$$

Accepted Answer

A)  $\{ - 16 \}$ 
B)  $\left\{ \frac { 7 } { 4 } \right\}$ 
C)  $\left\{ - \frac { 57 } { 4 } \right\}$ 
D)  $\{ - 71 \}$ 
A)  $\{ - 16 \}$ 
B)  $\left\{ \frac { 7 } { 4 } \right\}$ 
C)  $\left\{ - \frac { 57 } { 4 } \right\}$ 
D)  $\{ - 71 \}$

Question 13

Solve the inequality. Write the solution set in interval notation.
-$$( x + 4 ) ( x + 1 ) ( x - 2 ) > 0$$

Accepted Answer

A)  $( - \infty , - 4 ) \cup ( - 1,2 )$ 
B)  $( 2 , \infty )$ 
C)  $( - 4 , - 1 ) \cup ( 2 , \infty )$ 
D)  $( - \infty , - 1 )$ 
A)  $( - \infty , - 4 ) \cup ( - 1,2 )$ 
B)  $( 2 , \infty )$ 
C)  $( - 4 , - 1 ) \cup ( 2 , \infty )$ 
D)  $( - \infty , - 1 )$

Question 14

Solve the equation.
-$$x ^ { 2 } = - 18$$

Accepted Answer

A)  $\pm 9 \mathrm { i } \sqrt { 2 }$ 
B)  $\pm 9 \sqrt { 2 }$ 
C)  $\pm 3 i \sqrt { 2 }$ 
D)  $\pm 3 \sqrt { 2 }$ 
A)  $\pm 9 \mathrm { i } \sqrt { 2 }$ 
B)  $\pm 9 \sqrt { 2 }$ 
C)  $\pm 3 i \sqrt { 2 }$ 
D)  $\pm 3 \sqrt { 2 }$

Question 15

Simplify the power of i.
-$\frac { 1 } { \mathrm { i } ^ { - 20 } }$

Accepted Answer

A)  i 
B)  1 
C)  -i 
D)  -1 
A)  i 
B)  1 
C)  -i 
D)  -1

Question 16

Solve the equation by the square root property.
-$$( x + 7 ) ^ { 2 } = 5$$

Accepted Answer

A)  $\{ \sqrt { 5 } + 7 , - \sqrt { 5 + 7 } \}$ 
B)  $\{ \sqrt { 5 } - \sqrt { 7 } \}$ 
C)  $\{ - 7 \pm \sqrt { 5 } \}$ 
D)  $\{ - 7 + \sqrt { 5 } \}$ 
A)  $\{ \sqrt { 5 } + 7 , - \sqrt { 5 + 7 } \}$ 
B)  $\{ \sqrt { 5 } - \sqrt { 7 } \}$ 
C)  $\{ - 7 \pm \sqrt { 5 } \}$ 
D)  $\{ - 7 + \sqrt { 5 } \}$

Question 17

Find the quotient. Write the answer in standard form.
-$$\frac { 2 + 3 i } { 5 + 2 i }$$

Accepted Answer

A)  $\frac { 16 } { 29 } + \frac { 11 } { 29 } \mathrm { i }$ 
B)  $\frac { 16 } { 21 } - \frac { 11 } { 21 } \mathrm { i }$ 
C)  $\frac { 4 } { 21 } - \frac { 11 } { 21 } \mathrm { i }$ 
D)  $\frac { 4 } { 29 } - \frac { 19 } { 29 } i$ 
A)  $\frac { 16 } { 29 } + \frac { 11 } { 29 } \mathrm { i }$ 
B)  $\frac { 16 } { 21 } - \frac { 11 } { 21 } \mathrm { i }$ 
C)  $\frac { 4 } { 21 } - \frac { 11 } { 21 } \mathrm { i }$ 
D)  $\frac { 4 } { 29 } - \frac { 19 } { 29 } i$

Question 18

Find the product. Write the answer in standard form.
-$$\mathrm { i } ( 9 - 3 \mathrm { i } ) ( 5 - 3 \mathrm { i } )$$

Accepted Answer

A)  $9 \mathrm { i } ^ { 3 } + 42 \mathrm { i } ^ { 2 } + 45 \mathrm { i }$ 
B)  $- 42 - 36 i$ 
C)  $54 + 12 \mathrm { i }$ 
D)  $42 + 36 i$ 
A)  $9 \mathrm { i } ^ { 3 } + 42 \mathrm { i } ^ { 2 } + 45 \mathrm { i }$ 
B)  $- 42 - 36 i$ 
C)  $54 + 12 \mathrm { i }$ 
D)  $42 + 36 i$

Question 19

Simplify the power of i.
-$\text { ¡69 }$

Accepted Answer

A)  1 
B)  i 
C)  -1 
D)  -i 
A)  1 
B)  i 
C)  -1 
D)  -i

Question 20

Solve the equation.
-$$\left| \frac { 7 x + 2 } { 4 x + 9 } \right| = 7$$

Accepted Answer

A)  $\left\{ - \frac { 61 } { 21 } , - \frac { 13 } { 7 } \right\}$ 
B)  $\left\{ - \frac { 65 } { 21 } , - \frac { 61 } { 35 } \right\}$ 
C)  $\left\{ \frac { 5 } { 7 } , - \frac { 9 } { 7 } \right\}$ 
D)  $\left\{ \frac { 61 } { 35 } , \frac { 3 } { 7 } \right\}$ 
A)  $\left\{ - \frac { 61 } { 21 } , - \frac { 13 } { 7 } \right\}$ 
B)  $\left\{ - \frac { 65 } { 21 } , - \frac { 61 } { 35 } \right\}$ 
C)  $\left\{ \frac { 5 } { 7 } , - \frac { 9 } { 7 } \right\}$ 
D)  $\left\{ \frac { 61 } { 35 } , \frac { 3 } { 7 } \right\}$

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

Decide whether the statement is true or false. --6 is a solution of -7x = 42.

Determine whether or not the equation is linear. -0.06x - 0.05x = 0.90

Answer the question. -The mat around the picture shown measures x inches across. Which one of the following equations says that the area of the picture itself is 700 square inches?

Solve and graph the inequality. Give answer in interval notation. - $12 x + 11 \geq 11 x + 7$ $Solve and graph the inequality. Give answer in interval notation. - 12 x + 11 \geq 11 x + 7$

Solve the equation using the quadratic formula. - $6 = - \frac { 6 } { x } - \frac { 1 } { x ^ { 2 } }$

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

Solve the equation by the square root property. - $x ^ { 2 } = 18$

Solve the inequality. Write the solution set in interval notation. - $| 6 x - 7 | > - 4$

Decide what values of the variable cannot possibly be solutions for the equation. - $16 x = \sqrt { 1 - 24 x }$

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. - $C = 87 ^ { \circ }$

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt [ 3 ] { 4 x - 7 } + 9 = 5$

Solve the inequality. Write the solution set in interval notation. - $( x + 4 ) ( x + 1 ) ( x - 2 ) > 0$

Solve the equation. - $x ^ { 2 } = - 18$

Simplify the power of i. - $\frac { 1 } { \mathrm { i } ^ { - 20 } }$

Solve the equation by the square root property. - $( x + 7 ) ^ { 2 } = 5$

Find the quotient. Write the answer in standard form. - $\frac { 2 + 3 i } { 5 + 2 i }$

Find the product. Write the answer in standard form. - $\mathrm { i } ( 9 - 3 \mathrm { i } ) ( 5 - 3 \mathrm { i } )$

Simplify the power of i. - $\text { ¡69 }$

Solve the equation. - $\left| \frac { 7 x + 2 } { 4 x + 9 } \right| = 7$

Review of Basic Concepts

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

Filters

Exam 2: Equations and Inequalities

Solve the equation by completing the square. - 2x2+7x+3=02 x ^ { 2 } + 7 x + 3 = 02x2+7x+3=0

Decide whether the statement is true or false. --6 is a solution of -7x = 42.

Determine whether or not the equation is linear. -0.06x - 0.05x = 0.90

Answer the question. -The mat around the picture shown measures x inches across. Which one of the following equations says that the area of the picture itself is 700 square inches?

Solve and graph the inequality. Give answer in interval notation. - 12x+11≥11x+712 x + 11 \geq 11 x + 712x+11≥11x+7

Solve the equation using the quadratic formula. - 6=−6x−1x26 = - \frac { 6 } { x } - \frac { 1 } { x ^ { 2 } }6=−x6​−x21​

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

Solve the equation by the square root property. - x2=18x ^ { 2 } = 18x2=18

Solve the inequality. Write the solution set in interval notation. - ∣6x−7∣>−4| 6 x - 7 | > - 4∣6x−7∣>−4

Decide what values of the variable cannot possibly be solutions for the equation. - 16x=1−24x16 x = \sqrt { 1 - 24 x }16x=1−24x​

Use these equations to convert between the two systems. C=59(F−32)F=95C+32C = \frac { 5 } { 9 } ( F - 32 ) \quad F = \frac { 9 } { 5 } C + 32C=95​(F−32)F=59​C+32 Round answer to the nearest tenth of a degree if necessary. - C=87∘C = 87 ^ { \circ }C=87∘

Decide what values of the variable cannot possibly be solutions for the equation. - 4x−73+9=5\sqrt [ 3 ] { 4 x - 7 } + 9 = 534x−7​+9=5

Solve the inequality. Write the solution set in interval notation. - (x+4)(x+1)(x−2)>0( x + 4 ) ( x + 1 ) ( x - 2 ) > 0(x+4)(x+1)(x−2)>0

Solve the equation. - x2=−18x ^ { 2 } = - 18x2=−18

Simplify the power of i. - 1i−20\frac { 1 } { \mathrm { i } ^ { - 20 } }i−201​

Solve the equation by the square root property. - (x+7)2=5( x + 7 ) ^ { 2 } = 5(x+7)2=5

Find the quotient. Write the answer in standard form. - 2+3i5+2i\frac { 2 + 3 i } { 5 + 2 i }5+2i2+3i​

Find the product. Write the answer in standard form. - i(9−3i)(5−3i)\mathrm { i } ( 9 - 3 \mathrm { i } ) ( 5 - 3 \mathrm { i } )i(9−3i)(5−3i)

Simplify the power of i. - ¡69 \text { ¡69 } ¡69

Solve the equation. - ∣7x+24x+9∣=7\left| \frac { 7 x + 2 } { 4 x + 9 } \right| = 7​4x+97x+2​​=7