Question 1

Find two consecutive odd integers whose product is 899.

Accepted Answer

A)  $- 29 , - 31$ 
B)  29,31 or $- 29 , - 31$ 
C)  29,31 
D)  $29 , - 31$ 
A)  $- 29 , - 31$ 
B)  29,31 or $- 29 , - 31$ 
C)  29,31 
D)  $29 , - 31$

Question 2

Solve the inequality. Write the solution set in interval notation.
-$$| 8 x + 8 | < 1$$

Accepted Answer

A)  $\left( - \infty , - \frac { 9 } { 8 } \right) \cup \left( - \frac { 7 } { 8 } , \infty \right)$ 
B)  $\left( - \infty , - \frac { 9 } { 8 } \right)$ 
C)  $\left( - \frac { 9 } { 8 } , - \frac { 7 } { 8 } \right)$ 
D)  $( - \infty , 8 )$ 
A)  $\left( - \infty , - \frac { 9 } { 8 } \right) \cup \left( - \frac { 7 } { 8 } , \infty \right)$ 
B)  $\left( - \infty , - \frac { 9 } { 8 } \right)$ 
C)  $\left( - \frac { 9 } { 8 } , - \frac { 7 } { 8 } \right)$ 
D)  $( - \infty , 8 )$

Question 3

Decide whether the statement is true or false.
-$- 5 \text { is a solution of } 5 x - 6 = - 31 \text {. }$

Accepted Answer

A) True 
 B)False

Question 4

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set.
-$$5 ( 2 x - 31 ) = 10 x - 155$$

Accepted Answer

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

Question 5

Find the quotient. Write the answer in standard form.
-$$\frac { 4 + 2 i } { 7 - 9 i }$$

Accepted Answer

A)  $\frac { 46 } { 13 } + \frac { 22 } { 13 } \mathrm { i }$ 
B)  $- \frac { 23 } { 16 } + \frac { 5 } { 32 } \mathrm { i }$ 
C)  $\frac { 1 } { 13 } + \frac { 5 } { 13 } \mathrm { i }$ 
D)  $- \frac { 1 } { 32 } + \frac { 5 } { 32 } \mathrm { i }$ 
A)  $\frac { 46 } { 13 } + \frac { 22 } { 13 } \mathrm { i }$ 
B)  $- \frac { 23 } { 16 } + \frac { 5 } { 32 } \mathrm { i }$ 
C)  $\frac { 1 } { 13 } + \frac { 5 } { 13 } \mathrm { i }$ 
D)  $- \frac { 1 } { 32 } + \frac { 5 } { 32 } \mathrm { i }$

Question 6

Find the quotient. Write the answer in standard form.
-$$\frac { 7 + 3 i } { 6 - 9 i }$$

Accepted Answer

A)  $- \frac { 1 } { 9 } + \frac { 3 } { 5 } i$ 
B)  $\frac { 23 } { 13 } + \frac { 15 } { 13 } \mathrm { i }$ 
C)  $- \frac { 23 } { 15 } + \frac { 3 } { 5 } \mathrm { i }$ 
D)  $\frac { 5 } { 39 } + \frac { 9 } { 13 } \mathrm { i }$ 
A)  $- \frac { 1 } { 9 } + \frac { 3 } { 5 } i$ 
B)  $\frac { 23 } { 13 } + \frac { 15 } { 13 } \mathrm { i }$ 
C)  $- \frac { 23 } { 15 } + \frac { 3 } { 5 } \mathrm { i }$ 
D)  $\frac { 5 } { 39 } + \frac { 9 } { 13 } \mathrm { i }$

Question 7

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

Accepted Answer

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

Question 8

Solve the problem.
-A cylindrical container has a volume of $$1936 \pi \mathrm { cm } ^ { 3 }$$ and a radius of 11 cm. Find the height of the container.

Accepted Answer

A)  16 cm 
B)  11 cm 
C)  22 cm 
D)  4 cm 
A)  16 cm 
B)  11 cm 
C)  22 cm 
D)  4 cm

Question 9

Solve the inequality. Write the solution set in interval notation.
-$$| - 3 - 8 x | > 6$$

Accepted Answer

A)  $\left( \frac { 9 } { 8 } , - \frac { 3 } { 8 } \right)$ 
B)  $\left( - \frac { 3 } { 8 } , - \frac { 9 } { 8 } \right)$ 
C)  $\left( - \infty , - \frac { 9 } { 8 } \right) \cup \left( \frac { 3 } { 8 } , \infty \right)$ 
D)  $\left( - \infty , \frac { 7 } { 8 } \right) \cup \left( - \frac { 5 } { 8 } , \infty \right)$ 
A)  $\left( \frac { 9 } { 8 } , - \frac { 3 } { 8 } \right)$ 
B)  $\left( - \frac { 3 } { 8 } , - \frac { 9 } { 8 } \right)$ 
C)  $\left( - \infty , - \frac { 9 } { 8 } \right) \cup \left( \frac { 3 } { 8 } , \infty \right)$ 
D)  $\left( - \infty , \frac { 7 } { 8 } \right) \cup \left( - \frac { 5 } { 8 } , \infty \right)$

Question 10

Find two consecutive even integers whose product is 224.

Accepted Answer

A)  $- 14 , - 16$ 
B)  $14 , - 16$ 
C)  14,16 or $- 14 , - 16$ 
D)  14,16 
A)  $- 14 , - 16$ 
B)  $14 , - 16$ 
C)  14,16 or $- 14 , - 16$ 
D)  14,16

Question 11

Solve the inequality. Write the solution set in interval notation.
-$$x ^ { 2 } ( x + 64 ) ^ { 2 } \geq 0$$

Accepted Answer

A)  $\varnothing$ 
B)  $( - \infty , \infty )$ 
C)  $( - \infty , - 8 ] \cup [ 0,8 ]$ 
D)  $[ - 8,0 ] \cup [ 8 , \infty )$ 
A)  $\varnothing$ 
B)  $( - \infty , \infty )$ 
C)  $( - \infty , - 8 ] \cup [ 0,8 ]$ 
D)  $[ - 8,0 ] \cup [ 8 , \infty )$

Question 12

Solve and graph the inequality. Give answer in interval notation.
-$$4 x + 9 \geq 3 x + 13$$

Accepted Answer

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

Question 13

Determine whether or not the equation is linear.
-$$- 3 x + 1 = x - 5$$

Accepted Answer

A)  $\left\{ \frac { 4 } { 3 } \right\}$ 
B)  $\left\{ \frac { 3 } { 2 } \right\}$ 
C)  $\{ 1 \}$ 
D)  $\{ 2 \}$ 
A)  $\left\{ \frac { 4 } { 3 } \right\}$ 
B)  $\left\{ \frac { 3 } { 2 } \right\}$ 
C)  $\{ 1 \}$ 
D)  $\{ 2 \}$

Question 14

Find the product. Write the answer in standard form.
-$$( - 2 + 3 i ) ^ { 3 }$$

Accepted Answer

A)  $46 + 36 i + i ^ { 3 }$ 
B)  $46 + 9 \mathrm { i }$ 
C)  $46 + 107 i$ 
D)  $i ^ { 3 } - 54 i ^ { 2 } + 36 i + a ^ { 3 }$ 
A)  $46 + 36 i + i ^ { 3 }$ 
B)  $46 + 9 \mathrm { i }$ 
C)  $46 + 107 i$ 
D)  $i ^ { 3 } - 54 i ^ { 2 } + 36 i + a ^ { 3 }$

Question 15

Write the number as the product of a real number and i.
-$\sqrt { - 23 }$

Accepted Answer

A)  $\sqrt { 23 i }$ 
B)  $\mathrm { i } \sqrt { 23 }$ 
C)  $\mathrm { i } \sqrt { - 23 }$ 
D)  $- \mathrm { i } \sqrt { 23 }$ 
A)  $\sqrt { 23 i }$ 
B)  $\mathrm { i } \sqrt { 23 }$ 
C)  $\mathrm { i } \sqrt { - 23 }$ 
D)  $- \mathrm { i } \sqrt { 23 }$

Question 16

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\frac { x } { x - 5 } - \frac { 13 x } { 6 x + 6 } = 0$$

Accepted Answer

A)  $- 1,5$ 
B)  $- 5,6$ 
C)  $- 5,0,1$ 
D)  $- 6,5$ 
A)  $- 1,5$ 
B)  $- 5,6$ 
C)  $- 5,0,1$ 
D)  $- 6,5$

Question 17

Solve the rational inequality. Write the solution set in interval notation.
-$$\frac { 2 x + 7 } { x - 7 } \leq 0$$

Accepted Answer

A)  $\left[ - \frac { 7 } { 2 } , 7 \right)$ 
B)  $\left[ - \frac { 7 } { 2 } , 7 \right]$ 
C)  $\left[ - \infty , - \frac { 7 } { 2 } \right] \cup ( 7 , \infty )$ 
D)  $\left[ - \infty , - \frac { 7 } { 2 } \right] \cup [ 7 , \infty )$ 
A)  $\left[ - \frac { 7 } { 2 } , 7 \right)$ 
B)  $\left[ - \frac { 7 } { 2 } , 7 \right]$ 
C)  $\left[ - \infty , - \frac { 7 } { 2 } \right] \cup ( 7 , \infty )$ 
D)  $\left[ - \infty , - \frac { 7 } { 2 } \right] \cup [ 7 , \infty )$

Question 18

Solve the inequality. Write the solution set in interval notation.
-$$\left| \frac { 4 x + 1 } { x - 6 } \right| \geq 0$$

Accepted Answer

A)  $( - 6,6 )$ 
B)  $\left( - \infty , - \frac { 1 } { 4 } \right) \cup ( 6 , \infty )$ 
C)  $\left( - \frac { 1 } { 4 } , 6 \right)$ 
D)  $( - \infty , 6 ) \cup ( 6 , \infty )$ 
A)  $( - 6,6 )$ 
B)  $\left( - \infty , - \frac { 1 } { 4 } \right) \cup ( 6 , \infty )$ 
C)  $\left( - \frac { 1 } { 4 } , 6 \right)$ 
D)  $( - \infty , 6 ) \cup ( 6 , \infty )$

Question 19

Decide what values of the variable cannot possibly be solutions for the equation.
-$\sqrt { 3 x + 1 } = 3 + \sqrt { x - 4 }$

Accepted Answer

A)  $\varnothing$ 
B)  $\{ - 1 \}$ 
C)  $\{ - 5 , - 8 \}$ 
D)  $\{ 5,8 \}$ 
A)  $\varnothing$ 
B)  $\{ - 1 \}$ 
C)  $\{ - 5 , - 8 \}$ 
D)  $\{ 5,8 \}$

Question 20

Determine whether or not the equation is linear.
-$6 x - 5 x ( x - 2 ) = 11 x$

Accepted Answer

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

Find two consecutive odd integers whose product is 899.

Solve the inequality. Write the solution set in interval notation. - $| 8 x + 8 | < 1$

Decide whether the statement is true or false. - $- 5 \text { is a solution of } 5 x - 6 = - 31 \text {. }$

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $5 ( 2 x - 31 ) = 10 x - 155$

Find the quotient. Write the answer in standard form. - $\frac { 4 + 2 i } { 7 - 9 i }$

Find the quotient. Write the answer in standard form. - $\frac { 7 + 3 i } { 6 - 9 i }$

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

Solve the problem. -A cylindrical container has a volume of $1936 \pi \mathrm { cm } ^ { 3 }$ and a radius of 11 cm. Find the height of the container.

Solve the inequality. Write the solution set in interval notation. - $| - 3 - 8 x | > 6$

Find two consecutive even integers whose product is 224.

Solve the inequality. Write the solution set in interval notation. - $x ^ { 2 } ( x + 64 ) ^ { 2 } \geq 0$

Solve and graph the inequality. Give answer in interval notation. - $4 x + 9 \geq 3 x + 13$ $Solve and graph the inequality. Give answer in interval notation. - 4 x + 9 \geq 3 x + 13$

Determine whether or not the equation is linear. - $- 3 x + 1 = x - 5$

Find the product. Write the answer in standard form. - $( - 2 + 3 i ) ^ { 3 }$

Write the number as the product of a real number and i. - $\sqrt { - 23 }$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { x } { x - 5 } - \frac { 13 x } { 6 x + 6 } = 0$

Solve the rational inequality. Write the solution set in interval notation. - $\frac { 2 x + 7 } { x - 7 } \leq 0$

Solve the inequality. Write the solution set in interval notation. - $\left| \frac { 4 x + 1 } { x - 6 } \right| \geq 0$

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt { 3 x + 1 } = 3 + \sqrt { x - 4 }$

Determine whether or not the equation is linear. - $6 x - 5 x ( x - 2 ) = 11 x$

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

Find two consecutive odd integers whose product is 899.

Solve the inequality. Write the solution set in interval notation. - ∣8x+8∣<1| 8 x + 8 | < 1∣8x+8∣<1

Decide whether the statement is true or false. - −5 is a solution of 5x−6=−31. - 5 \text { is a solution of } 5 x - 6 = - 31 \text {. }−5 is a solution of 5x−6=−31.

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - 5(2x−31)=10x−1555 ( 2 x - 31 ) = 10 x - 1555(2x−31)=10x−155

Find the quotient. Write the answer in standard form. - 4+2i7−9i\frac { 4 + 2 i } { 7 - 9 i }7−9i4+2i​

Find the quotient. Write the answer in standard form. - 7+3i6−9i\frac { 7 + 3 i } { 6 - 9 i }6−9i7+3i​

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

Solve the problem. -A cylindrical container has a volume of 1936πcm31936 \pi \mathrm { cm } ^ { 3 }1936πcm3 and a radius of 11 cm. Find the height of the container.

Solve the inequality. Write the solution set in interval notation. - ∣−3−8x∣>6| - 3 - 8 x | > 6∣−3−8x∣>6

Find two consecutive even integers whose product is 224.

Solve the inequality. Write the solution set in interval notation. - x2(x+64)2≥0x ^ { 2 } ( x + 64 ) ^ { 2 } \geq 0x2(x+64)2≥0

Solve and graph the inequality. Give answer in interval notation. - 4x+9≥3x+134 x + 9 \geq 3 x + 134x+9≥3x+13

Determine whether or not the equation is linear. - −3x+1=x−5- 3 x + 1 = x - 5−3x+1=x−5

Find the product. Write the answer in standard form. - (−2+3i)3( - 2 + 3 i ) ^ { 3 }(−2+3i)3

Write the number as the product of a real number and i. - −23\sqrt { - 23 }−23​

Decide what values of the variable cannot possibly be solutions for the equation. - xx−5−13x6x+6=0\frac { x } { x - 5 } - \frac { 13 x } { 6 x + 6 } = 0x−5x​−6x+613x​=0

Solve the rational inequality. Write the solution set in interval notation. - 2x+7x−7≤0\frac { 2 x + 7 } { x - 7 } \leq 0x−72x+7​≤0

Solve the inequality. Write the solution set in interval notation. - ∣4x+1x−6∣≥0\left| \frac { 4 x + 1 } { x - 6 } \right| \geq 0​x−64x+1​​≥0

Decide what values of the variable cannot possibly be solutions for the equation. - 3x+1=3+x−4\sqrt { 3 x + 1 } = 3 + \sqrt { x - 4 }3x+1​=3+x−4​

Determine whether or not the equation is linear. - 6x−5x(x−2)=11x6 x - 5 x ( x - 2 ) = 11 x6x−5x(x−2)=11x

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 inequality. Write the solution set in interval notation. - $| 8 x + 8 | < 1$

Decide whether the statement is true or false. - $- 5 \text { is a solution of } 5 x - 6 = - 31 \text {. }$

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $5 ( 2 x - 31 ) = 10 x - 155$

Find the quotient. Write the answer in standard form. - $\frac { 4 + 2 i } { 7 - 9 i }$

Find the quotient. Write the answer in standard form. - $\frac { 7 + 3 i } { 6 - 9 i }$

Solve the problem. -A cylindrical container has a volume of $1936 \pi \mathrm { cm } ^ { 3 }$ and a radius of 11 cm. Find the height of the container.

Solve the inequality. Write the solution set in interval notation. - $| - 3 - 8 x | > 6$

Solve the inequality. Write the solution set in interval notation. - $x ^ { 2 } ( x + 64 ) ^ { 2 } \geq 0$

Solve and graph the inequality. Give answer in interval notation. - $4 x + 9 \geq 3 x + 13$ $Solve and graph the inequality. Give answer in interval notation. - 4 x + 9 \geq 3 x + 13$

Determine whether or not the equation is linear. - $- 3 x + 1 = x - 5$

Find the product. Write the answer in standard form. - $( - 2 + 3 i ) ^ { 3 }$

Write the number as the product of a real number and i. - $\sqrt { - 23 }$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { x } { x - 5 } - \frac { 13 x } { 6 x + 6 } = 0$

Solve the rational inequality. Write the solution set in interval notation. - $\frac { 2 x + 7 } { x - 7 } \leq 0$

Solve the inequality. Write the solution set in interval notation. - $\left| \frac { 4 x + 1 } { x - 6 } \right| \geq 0$

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt { 3 x + 1 } = 3 + \sqrt { x - 4 }$

Determine whether or not the equation is linear. - $6 x - 5 x ( x - 2 ) = 11 x$