Question 1

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

Accepted Answer

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

Question 2

Solve the problem
-The sum of the squares of two consecutive integers is 221. Find the integers.

Accepted Answer

A)  $10 , - 11$ 
B)  10,11 or $- 10 , - 11$ 
C)  10,11 
D)  $- 10 , - 11$ 
A)  $10 , - 11$ 
B)  10,11 or $- 10 , - 11$ 
C)  10,11 
D)  $- 10 , - 11$

Question 3

Decide whether or not the equations are equivalent.
-$\begin{array} { l } 
3 x - 1 = 7 \
- 3 x + 7 = - 1
\end{array}$

Accepted Answer

A)  Not equivalent 
B)  Equivalent 
A)  Not equivalent 
B)  Equivalent

Question 4

Solve the equation.
-$$| x - 5 | = 0$$

Accepted Answer

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

Question 5

Determine whether or not the equation is linear.
-$0.04 x ^ { 2 } + 0.07 x = 0.20$

Accepted Answer

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

Question 6

Find the product. Write the answer in standard form.
-$$- 4 i ( - 8 - 6 i ) ^ { 2 }$$

Accepted Answer

A)  $- 112 \mathrm { i }$ 
B)  $- 112 - 384 \mathrm { i }$ 
C)  $384 \mathrm { i } - 384 \mathrm { i } ^ { 2 } - 144 \mathrm { i } ^ { 3 }$ 
D)  $384 - 112 \mathrm { i }$ 
A)  $- 112 \mathrm { i }$ 
B)  $- 112 - 384 \mathrm { i }$ 
C)  $384 \mathrm { i } - 384 \mathrm { i } ^ { 2 } - 144 \mathrm { i } ^ { 3 }$ 
D)  $384 - 112 \mathrm { i }$

Question 7

Find the product. Write the answer in standard form.
-$( 2 - 4 i ) ^ { 3 }$

Accepted Answer

A)  $i ^ { 3 } + 96 i ^ { 2 } - 48 i + a ^ { 3 }$ 
B)  $- 88 - 48 i + i ^ { 3 }$ 
C)  $- 88 + 16 i$ 
D)  $- 88 - 145 \mathrm { i }$ 
A)  $i ^ { 3 } + 96 i ^ { 2 } - 48 i + a ^ { 3 }$ 
B)  $- 88 - 48 i + i ^ { 3 }$ 
C)  $- 88 + 16 i$ 
D)  $- 88 - 145 \mathrm { i }$

Question 8

Find the product. Write the answer in standard form.
-$$( - 1 - 3 \mathrm { i } ) ( - 1 + 3 \mathrm { i } )$$

Accepted Answer

A)  $- 8$ 
B)  $1 - 9 \mathrm { i } ^ { 2 }$ 
C)  $1 + 9 \mathrm { i } ^ { 2 }$ 
D)  10 
A)  $- 8$ 
B)  $1 - 9 \mathrm { i } ^ { 2 }$ 
C)  $1 + 9 \mathrm { i } ^ { 2 }$ 
D)  10

Question 9

Decide what values of the variable cannot possibly be solutions for the equation.
-$$( x - 2 ) ^ { 1 / 4 } + 9 = 0$$

Accepted Answer

A)  $\varnothing$ 
B)  $\left\{ \frac { 6561 } { 2 } \right\}$ 
C)  $\left\{ - \frac { 6561 } { 2 } \right\}$ 
D)  $\left\{ \frac { 9 } { 2 } \right\}$ 
A)  $\varnothing$ 
B)  $\left\{ \frac { 6561 } { 2 } \right\}$ 
C)  $\left\{ - \frac { 6561 } { 2 } \right\}$ 
D)  $\left\{ \frac { 9 } { 2 } \right\}$

Question 10

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

Accepted Answer

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

Question 11

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

Accepted Answer

A)  $\frac { 3 } { 5 }$ 
B)  $- \frac { 3 } { 5 }$ 
C)  $- \frac { 3 } { 5 } i$ 
D)  $\frac { 3 } { 5 } \mathrm { i }$ 
A)  $\frac { 3 } { 5 }$ 
B)  $- \frac { 3 } { 5 }$ 
C)  $- \frac { 3 } { 5 } i$ 
D)  $\frac { 3 } { 5 } \mathrm { i }$

Question 12

Simplify the power of i.
-$\frac { 1 } { \mathrm { i } ^ { 51 } }$

Accepted Answer

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

Question 13

Solve the problem.
-Find the corresponding Celsius temperature for a temperature of 290°F. Round to the nearest tenth, if necessary.

Accepted Answer

A)  157.6°C 
B)  464.4°C 
C)  143.3°C 
D)  554°C 
A)  157.6°C 
B)  464.4°C 
C)  143.3°C 
D)  554°C

Question 14

Find the sum or difference. Write the answer in standard form.
-$$( - 3 + 4 i ) - 4$$

Accepted Answer

A)  $7 - 4 \mathrm { i }$ 
B)  $- 7 + 4 i$ 
C)  $1 + 4 \mathrm { i }$ 
D)  $1 - 4 \mathrm { i }$ 
A)  $7 - 4 \mathrm { i }$ 
B)  $- 7 + 4 i$ 
C)  $1 + 4 \mathrm { i }$ 
D)  $1 - 4 \mathrm { i }$

Question 15

Decide what values of the variable cannot possibly be solutions for the equation.
-$$( 2 x + 5 ) ^ { 1 / 2 } - ( x - 2 ) ^ { 1 / 2 } = 3$$

Accepted Answer

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

Question 16

Solve the problem.
-The stadium vending company finds that sales of hot dogs average 48,000 hot dogs per game when the hot dogs sell for $2.50 each. For each 50 cent increase in the price, the sales per game drop by
5000 hot dogs. What price per hot dog should the vending company charge to realize the maximum
Revenue?

Accepted Answer

A)  $3.90 
B)  $2.30 
C)  $4.80 
D)  $3.65 
A)  $3.90 
B)  $2.30 
C)  $4.80 
D)  $3.65

Question 17

Graph the solution set.
-$| x | > - 2$

Accepted Answer

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

Question 18

Solve and graph the inequality. Give answer in interval notation.
-$$\frac { x } { 7 } - \frac { 1 } { 5 } \leq \frac { x } { 2 } + 3$$

Accepted Answer

A)  $\left[ - \infty , - \frac { 224 } { 25 } \right]$
  
B)  $\left[ - \frac { 224 } { 25 } , \infty \right)$
  
C)  $\left( - \frac { 224 } { 25 } , \infty \right)$
  
D)  $\left( - \infty , - \frac { 224 } { 25 } \right)$
  
A)  $\left[ - \infty , - \frac { 224 } { 25 } \right]$
  
B)  $\left[ - \frac { 224 } { 25 } , \infty \right)$
  
C)  $\left( - \frac { 224 } { 25 } , \infty \right)$
  
D)  $\left( - \infty , - \frac { 224 } { 25 } \right)$

Question 19

Solve the problem.
-A ladder is resting against a wall. The top of the ladder touches the wall at a height of 6 ft. Find the length of the ladder if the length is 2 ft more than its distance from the wall.

Accepted Answer

A)  6 ft 
B)  10 ft 
C)  12 ft 
D)  8 ft 
A)  6 ft 
B)  10 ft 
C)  12 ft 
D)  8 ft

Question 20

Decide what values of the variable cannot possibly be solutions for the equation.
-$\sqrt { 2 x + 3 } - \sqrt { x + 1 } = 1$

Accepted Answer

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

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

Solve the problem -The sum of the squares of two consecutive integers is 221. Find the integers.

Decide whether or not the equations are equivalent. - 3x-1=7 -3x+7=-1

Solve the equation. - $| x - 5 | = 0$

Determine whether or not the equation is linear. - $0.04 x ^ { 2 } + 0.07 x = 0.20$

Find the product. Write the answer in standard form. - $- 4 i ( - 8 - 6 i ) ^ { 2 }$

Find the product. Write the answer in standard form. - $( 2 - 4 i ) ^ { 3 }$

Find the product. Write the answer in standard form. - $( - 1 - 3 \mathrm { i } ) ( - 1 + 3 \mathrm { i } )$

Decide what values of the variable cannot possibly be solutions for the equation. - $( x - 2 ) ^ { 1 / 4 } + 9 = 0$

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

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

Simplify the power of i. - $\frac { 1 } { \mathrm { i } ^ { 51 } }$

Solve the problem. -Find the corresponding Celsius temperature for a temperature of 290°F. Round to the nearest tenth, if necessary.

Find the sum or difference. Write the answer in standard form. - $( - 3 + 4 i ) - 4$

Decide what values of the variable cannot possibly be solutions for the equation. - $( 2 x + 5 ) ^ { 1 / 2 } - ( x - 2 ) ^ { 1 / 2 } = 3$

Graph the solution set. - $| x | > - 2$

Solve and graph the inequality. Give answer in interval notation. - $\frac { x } { 7 } - \frac { 1 } { 5 } \leq \frac { x } { 2 } + 3$ $Solve and graph the inequality. Give answer in interval notation. - \frac { x } { 7 } - \frac { 1 } { 5 } \leq \frac { x } { 2 } + 3$

Solve the problem. -A ladder is resting against a wall. The top of the ladder touches the wall at a height of 6 ft. Find the length of the ladder if the length is 2 ft more than its distance from the wall.

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt { 2 x + 3 } - \sqrt { x + 1 } = 1$

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

Solve the problem -The sum of the squares of two consecutive integers is 221. Find the integers.

Decide whether or not the equations are equivalent. - 3x-1=7 -3x+7=-1

Solve the equation. - ∣x−5∣=0| x - 5 | = 0∣x−5∣=0

Determine whether or not the equation is linear. - 0.04x2+0.07x=0.200.04 x ^ { 2 } + 0.07 x = 0.200.04x2+0.07x=0.20

Find the product. Write the answer in standard form. - −4i(−8−6i)2- 4 i ( - 8 - 6 i ) ^ { 2 }−4i(−8−6i)2

Find the product. Write the answer in standard form. - (2−4i)3( 2 - 4 i ) ^ { 3 }(2−4i)3

Find the product. Write the answer in standard form. - (−1−3i)(−1+3i)( - 1 - 3 \mathrm { i } ) ( - 1 + 3 \mathrm { i } )(−1−3i)(−1+3i)

Decide what values of the variable cannot possibly be solutions for the equation. - (x−2)1/4+9=0( x - 2 ) ^ { 1 / 4 } + 9 = 0(x−2)1/4+9=0

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

Find the quotient. Write the answer in standard form. - 35i\frac { 3 } { 5 i }5i3​

Simplify the power of i. - 1i51\frac { 1 } { \mathrm { i } ^ { 51 } }i511​