Question 1

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

Accepted Answer

A)  $\{ 3,8 \}$ 
B)  $\{ 2,38 \}$ 
C)  $\{ 2 \}$ 
D)  $\{ - 2 \}$ 
A)  $\{ 3,8 \}$ 
B)  $\{ 2,38 \}$ 
C)  $\{ 2 \}$ 
D)  $\{ - 2 \}$

Question 2

Solve the inequality. Write the solution set in interval notation.
-$$| x + 3 | > 6$$

Accepted Answer

A)  $\varnothing$ 
B)  $( - \infty , - 9 ) \cup ( 3 , \infty )$ 
C)  $( - 9,3 )$ 
D)  $( 3 , \infty )$ 
A)  $\varnothing$ 
B)  $( - \infty , - 9 ) \cup ( 3 , \infty )$ 
C)  $( - 9,3 )$ 
D)  $( 3 , \infty )$

Question 3

Find the sum or difference. Write the answer in standard form.
-$$( 9 - 2 i ) + ( 6 + 5 i )$$

Accepted Answer

A)  $- 15 - 3 i$ 
B)  $15 - 3 i$ 
C)  $15 + 3 i$ 
D)  $3 + 7 i$ 
A)  $- 15 - 3 i$ 
B)  $15 - 3 i$ 
C)  $15 + 3 i$ 
D)  $3 + 7 i$

Question 4

Solve the equation using the quadratic formula.
-$$2 x ^ { 2 } + 12 x = - 7$$

Accepted Answer

A)  $\left\{ \frac { - 6 \pm \sqrt { 22 } } { 2 } \right\}$ 
B)  $\left\{ \frac { - 12 \pm \sqrt { 22 } } { 2 } \right\}$ 
C)  $\left\{ \frac { - 6 \pm \sqrt { 22 } } { 4 } \right\}$ 
D)  $\left\{ \frac { - 6 \pm \sqrt { 2 } } { 2 } \right\}$ 
A)  $\left\{ \frac { - 6 \pm \sqrt { 22 } } { 2 } \right\}$ 
B)  $\left\{ \frac { - 12 \pm \sqrt { 22 } } { 2 } \right\}$ 
C)  $\left\{ \frac { - 6 \pm \sqrt { 22 } } { 4 } \right\}$ 
D)  $\left\{ \frac { - 6 \pm \sqrt { 2 } } { 2 } \right\}$

Question 5

Decide whether the statement is true or false.
-$3 \text { is a solution of } - 6 x - 6 x = 4 \text {. }$

Accepted Answer

A) True 
 B)False

Question 6

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\frac { 1 } { 3 x } + \frac { 8 } { x } = 10$$

Accepted Answer

A)  0 
B)  $- 3$ 
C)  1,3 
D)  $0 , - \frac { 1 } { 3 }$ 
A)  0 
B)  $- 3$ 
C)  1,3 
D)  $0 , - \frac { 1 } { 3 }$

Question 7

Simplify the power of i.
-$\mathrm { i } ^ { 59 }$

Accepted Answer

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

Question 8

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.
-$4 i , - 4 i$

Accepted Answer

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

Question 9

Solve for y.
-$$y - 9 ( x + 5 ) = 6 + 2 y$$

Accepted Answer

A)  $y = - 9 x - 51$ 
B)  $y = - 9 x + 51$ 
C)  $y = 9 x + 39$ 
D)  $y = 9 x + 51$ 
A)  $y = - 9 x - 51$ 
B)  $y = - 9 x + 51$ 
C)  $y = 9 x + 39$ 
D)  $y = 9 x + 51$

Question 10

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 Fahrenheit temperature for a temperature of 84°C. Round to the nearest tenth, if necessary.

Accepted Answer

A)  $208.8 ^ { \circ } \mathrm { F }$ 
B)  $64.4 ^ { \circ } \mathrm { F }$ 
C)  $183.2 ^ { \circ } \mathrm { F }$ 
D)  $28.9 ^ { \circ } \mathrm { F }$ 
A)  $208.8 ^ { \circ } \mathrm { F }$ 
B)  $64.4 ^ { \circ } \mathrm { F }$ 
C)  $183.2 ^ { \circ } \mathrm { F }$ 
D)  $28.9 ^ { \circ } \mathrm { F }$

Question 11

A 16 ft by 18 ft rectangular garden is to have a gravel path of uniform width bordering it. How wide is the path if the total area covered by the garden and path is 440 $\mathrm { ft } ^ { 2 }$ ?

Accepted Answer

A)  2 ft 
B)  3.5 ft 
C)  1 ft 
D)  3 ft 
A)  2 ft 
B)  3.5 ft 
C)  1 ft 
D)  3 ft

Question 12

Solve the inequality. Write the solution set in interval notation.
-$$| - 2 x + 3 | > - 2$$

Accepted Answer

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

Question 13

Graph the solution set.
-$$\left| \frac { 5 } { x - 9 } \right| = 9$$

Accepted Answer

A)  $\{ 9 \}$ 
B)  $\left\{ - \frac { 86 } { 9 } , - \frac { 76 } { 9 } \right\}$ 
C)  $\left\{ - \frac { 76 } { 9 } , - \frac { 86 } { 9 } \right\}$ 
D)  $\left\{ \frac { 86 } { 9 } , \frac { 76 } { 9 } \right\}$ 
A)  $\{ 9 \}$ 
B)  $\left\{ - \frac { 86 } { 9 } , - \frac { 76 } { 9 } \right\}$ 
C)  $\left\{ - \frac { 76 } { 9 } , - \frac { 86 } { 9 } \right\}$ 
D)  $\left\{ \frac { 86 } { 9 } , \frac { 76 } { 9 } \right\}$

Question 14

A ladder is resting against a wall. The top of the ladder touches the wall at a height of 12 ft. Find the length of the ladder if the length is 4 ft more than its distance from the wall.

Accepted Answer

A)  20 ft 
B)  12 ft 
C)  24 ft 
D)  16 ft 
A)  20 ft 
B)  12 ft 
C)  24 ft 
D)  16 ft

Question 15

Solve the inequality. Write the solution set in interval notation.
-$| - 5 x + 3 | < 2$

Accepted Answer

A)  $\left( \frac { 1 } { 5 } , 1 \right)$ 
B)  $\left( \frac { 1 } { 5 } , - 1 \right)$ 
C)  $\left( - \infty , \frac { 1 } { 5 } \right) \cup ( 1 , \infty )$ 
D)  $\left( - \infty , - \frac { 7 } { 5 } \right) \cup \left( - \frac { 3 } { 5 } , \infty \right)$ 
A)  $\left( \frac { 1 } { 5 } , 1 \right)$ 
B)  $\left( \frac { 1 } { 5 } , - 1 \right)$ 
C)  $\left( - \infty , \frac { 1 } { 5 } \right) \cup ( 1 , \infty )$ 
D)  $\left( - \infty , - \frac { 7 } { 5 } \right) \cup \left( - \frac { 3 } { 5 } , \infty \right)$

Question 16

The sum of the squares of two consecutive odd integers is 1154. Find the integers.

Accepted Answer

A)  $23 , - 25$ 
B)  23,25 
C)  $- 23 , - 25$ 
D)  23,25 or $- 23 , - 25$ 
A)  $23 , - 25$ 
B)  23,25 
C)  $- 23 , - 25$ 
D)  23,25 or $- 23 , - 25$

Question 17

Solve the quadratic inequality. Write the solution set in interval notation.
-$$x ^ { 2 } - 7 x + 12 \geq 0$$

Accepted Answer

A)  $[ 3,4 ]$ 
B)  $( - \infty , 3 ]$ 
C)  $[ 4 , \infty )$ 
D)  $( - \infty , 3 ] \cup [ 4 , \infty )$ 
A)  $[ 3,4 ]$ 
B)  $( - \infty , 3 ]$ 
C)  $[ 4 , \infty )$ 
D)  $( - \infty , 3 ] \cup [ 4 , \infty )$

Question 18

Write the inequality in interval notation.
-$x \geq - 5$

Accepted Answer

A)  $( - 5 , \infty )$ 
B)  $[ - 5 , \infty )$ 
C)  $[ - 5 , \infty ]$ 
D)  $( - \infty , - 5 ]$ 
A)  $( - 5 , \infty )$ 
B)  $[ - 5 , \infty )$ 
C)  $[ - 5 , \infty ]$ 
D)  $( - \infty , - 5 ]$

Question 19

Solve the inequality. Write the solution set in interval notation.
-$$x ^ { 3 } + 4 x ^ { 2 } - 16 x \leq 64$$

Accepted Answer

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

Question 20

Graph the solution set.
-$| x | < 1$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

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

Solve the inequality. Write the solution set in interval notation. - $| x + 3 | > 6$

Find the sum or difference. Write the answer in standard form. - $( 9 - 2 i ) + ( 6 + 5 i )$

Solve the equation using the quadratic formula. - $2 x ^ { 2 } + 12 x = - 7$

Decide whether the statement is true or false. - $3 \text { is a solution of } - 6 x - 6 x = 4 \text {. }$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { 1 } { 3 x } + \frac { 8 } { x } = 10$

Simplify the power of i. - $\mathrm { i } ^ { 59 }$

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. - $4 i , - 4 i$

Solve for y. - $y - 9 ( x + 5 ) = 6 + 2 y$

A 16 ft by 18 ft rectangular garden is to have a gravel path of uniform width bordering it. How wide is the path if the total area covered by the garden and path is 440 $\mathrm { ft } ^ { 2 }$ ?

Solve the inequality. Write the solution set in interval notation. - $| - 2 x + 3 | > - 2$

Graph the solution set. - $\left| \frac { 5 } { x - 9 } \right| = 9$

A ladder is resting against a wall. The top of the ladder touches the wall at a height of 12 ft. Find the length of the ladder if the length is 4 ft more than its distance from the wall.

Solve the inequality. Write the solution set in interval notation. - $| - 5 x + 3 | < 2$

The sum of the squares of two consecutive odd integers is 1154. Find the integers.

Solve the quadratic inequality. Write the solution set in interval notation. - $x ^ { 2 } - 7 x + 12 \geq 0$

Write the inequality in interval notation. - $x \geq - 5$

Solve the inequality. Write the solution set in interval notation. - $x ^ { 3 } + 4 x ^ { 2 } - 16 x \leq 64$

Graph the solution set. - $| x | < 1$

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. - 2x+5−x−2=3\sqrt { 2 x + 5 } - \sqrt { x - 2 } = 32x+5​−x−2​=3

Solve the inequality. Write the solution set in interval notation. - ∣x+3∣>6| x + 3 | > 6∣x+3∣>6

Find the sum or difference. Write the answer in standard form. - (9−2i)+(6+5i)( 9 - 2 i ) + ( 6 + 5 i )(9−2i)+(6+5i)

Solve the equation using the quadratic formula. - 2x2+12x=−72 x ^ { 2 } + 12 x = - 72x2+12x=−7

Decide whether the statement is true or false. - 3 is a solution of −6x−6x=4. 3 \text { is a solution of } - 6 x - 6 x = 4 \text {. }3 is a solution of −6x−6x=4.

Decide what values of the variable cannot possibly be solutions for the equation. - 13x+8x=10\frac { 1 } { 3 x } + \frac { 8 } { x } = 103x1​+x8​=10

Simplify the power of i. - i59\mathrm { i } ^ { 59 }i59

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. - 4i,−4i4 i , - 4 i4i,−4i

Solve for y. - y−9(x+5)=6+2yy - 9 ( x + 5 ) = 6 + 2 yy−9(x+5)=6+2y

A 16 ft by 18 ft rectangular garden is to have a gravel path of uniform width bordering it. How wide is the path if the total area covered by the garden and path is 440 ft2\mathrm { ft } ^ { 2 }ft2 ?

Solve the inequality. Write the solution set in interval notation. - ∣−2x+3∣>−2| - 2 x + 3 | > - 2∣−2x+3∣>−2

Graph the solution set. - ∣5x−9∣=9\left| \frac { 5 } { x - 9 } \right| = 9​x−95​​=9

A ladder is resting against a wall. The top of the ladder touches the wall at a height of 12 ft. Find the length of the ladder if the length is 4 ft more than its distance from the wall.

Solve the inequality. Write the solution set in interval notation. - ∣−5x+3∣<2| - 5 x + 3 | < 2∣−5x+3∣<2

The sum of the squares of two consecutive odd integers is 1154. Find the integers.

Solve the quadratic inequality. Write the solution set in interval notation. - x2−7x+12≥0x ^ { 2 } - 7 x + 12 \geq 0x2−7x+12≥0

Write the inequality in interval notation. - x≥−5x \geq - 5x≥−5

Solve the inequality. Write the solution set in interval notation. - x3+4x2−16x≤64x ^ { 3 } + 4 x ^ { 2 } - 16 x \leq 64x3+4x2−16x≤64

Graph the solution set. - ∣x∣<1| x | < 1∣x∣<1

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. - $\sqrt { 2 x + 5 } - \sqrt { x - 2 } = 3$

Solve the inequality. Write the solution set in interval notation. - $| x + 3 | > 6$

Find the sum or difference. Write the answer in standard form. - $( 9 - 2 i ) + ( 6 + 5 i )$

Solve the equation using the quadratic formula. - $2 x ^ { 2 } + 12 x = - 7$

Decide whether the statement is true or false. - $3 \text { is a solution of } - 6 x - 6 x = 4 \text {. }$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { 1 } { 3 x } + \frac { 8 } { x } = 10$

Simplify the power of i. - $\mathrm { i } ^ { 59 }$

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. - $4 i , - 4 i$

Solve for y. - $y - 9 ( x + 5 ) = 6 + 2 y$

A 16 ft by 18 ft rectangular garden is to have a gravel path of uniform width bordering it. How wide is the path if the total area covered by the garden and path is 440 $\mathrm { ft } ^ { 2 }$ ?

Solve the inequality. Write the solution set in interval notation. - $| - 2 x + 3 | > - 2$

Graph the solution set. - $\left| \frac { 5 } { x - 9 } \right| = 9$

Solve the inequality. Write the solution set in interval notation. - $| - 5 x + 3 | < 2$

Solve the quadratic inequality. Write the solution set in interval notation. - $x ^ { 2 } - 7 x + 12 \geq 0$

Write the inequality in interval notation. - $x \geq - 5$

Solve the inequality. Write the solution set in interval notation. - $x ^ { 3 } + 4 x ^ { 2 } - 16 x \leq 64$

Graph the solution set. - $| x | < 1$