Question 1

Graph the solution set.
-$$| x | = - 5$$

Accepted Answer

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

Question 2

Find the sum or difference. Write the answer in standard form.
-$$( 4 + 9 i ) - ( - 8 + i )$$

Accepted Answer

A)  $12 + 8 i$ 
B)  $- 4 + 10 \mathrm { i }$ 
C)  $- 12 - 8 i$ 
D)  $12 - 8 \mathrm { i }$ 
A)  $12 + 8 i$ 
B)  $- 4 + 10 \mathrm { i }$ 
C)  $- 12 - 8 i$ 
D)  $12 - 8 \mathrm { i }$

Question 3

Solve the equation by completing the square.
-$$4 x ^ { 2 } - 4 x - 8 = 0$$

Accepted Answer

A)  $\left\{ \frac { 1 } { 2 } , 1 \right\}$ 
B)  $\left\{ \frac { 1 } { 2 } , 0 \right\}$ 
C)  $\left\{ \frac { 1 } { 2 } , - 1 \right\}$ 
D)  $\{ 2 , - 1 \}$ 
A)  $\left\{ \frac { 1 } { 2 } , 1 \right\}$ 
B)  $\left\{ \frac { 1 } { 2 } , 0 \right\}$ 
C)  $\left\{ \frac { 1 } { 2 } , - 1 \right\}$ 
D)  $\{ 2 , - 1 \}$

Question 4

Solve the problem.
-The area of a square is numerically 117 more than the perimeter. Find the length of the side.

Accepted Answer

A)  85 units 
B)  338 units 
C)  52 units 
D)  13 units 
A)  85 units 
B)  338 units 
C)  52 units 
D)  13 units

Question 5

Solve for the indicated variable.
-$Z = A ( 1 + x ) ^ { 1 / 3 }$, for $x$

Accepted Answer

A)  $x = \left( \frac { Z } { A } \right) ^ { 3 }$ 
B)  $x = \left( \frac { Z } { A } \right) ^ { 3 } + 1$ 
C)  $x = \left( \frac { A } { Z } \right) ^ { 3 }$ 
D)  $x = \left( \frac { Z } { A } \right) ^ { 3 } - 1$ 
A)  $x = \left( \frac { Z } { A } \right) ^ { 3 }$ 
B)  $x = \left( \frac { Z } { A } \right) ^ { 3 } + 1$ 
C)  $x = \left( \frac { A } { Z } \right) ^ { 3 }$ 
D)  $x = \left( \frac { Z } { A } \right) ^ { 3 } - 1$

Question 6

Find the sum or difference. Write the answer in standard form.
-$$( 7 - 7 i ) - ( - 9 - 7 i ) + ( - 7 - 8 i )$$

Accepted Answer

A)  $- 9 - 22 \mathrm { i }$ 
B)  $9 - 8 \mathrm { i }$ 
C)  $- 9 + 8 i$ 
D)  $9 - 22 \mathrm { i }$ 
A)  $- 9 - 22 \mathrm { i }$ 
B)  $9 - 8 \mathrm { i }$ 
C)  $- 9 + 8 i$ 
D)  $9 - 22 \mathrm { i }$

Question 7

Simplify the power of i.
-$\mathrm { i } ^ { 43 }$

Accepted Answer

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

Question 8

Solve the rational inequality. Write the solution set in interval notation.
-$$\frac { 4 x } { - 3 x + 7 } \geq 11$$

Accepted Answer

A)  $\left( - \infty , \frac { 77 } { 37 } \right] \cup \left[ \frac { 77 } { 37 } , \infty \right)$ 
B)  $( - \infty , 0 ] \cup \left( \frac { 7 } { 3 } , \infty \right)$ 
C)  $\left[ 0 , \frac { 7 } { 3 } \right)$ 
D)  $\left[ \frac { 77 } { 37 } , \frac { 7 } { 3 } \right)$ 
A)  $\left( - \infty , \frac { 77 } { 37 } \right] \cup \left[ \frac { 77 } { 37 } , \infty \right)$ 
B)  $( - \infty , 0 ] \cup \left( \frac { 7 } { 3 } , \infty \right)$ 
C)  $\left[ 0 , \frac { 7 } { 3 } \right)$ 
D)  $\left[ \frac { 77 } { 37 } , \frac { 7 } { 3 } \right)$

Question 9

Solve the problem
-Find two consecutive integers whose product is 380. 252

Accepted Answer

A)  $- 19 , - 20$ 
B)  19,20 
C)  $19 , - 20$ 
D)  19,20 or $- 19 , - 20$ 
A)  $- 19 , - 20$ 
B)  19,20 
C)  $19 , - 20$ 
D)  19,20 or $- 19 , - 20$

Question 10

Solve the problem.
-Walt made an extra $7000 last year from a part-time job. He invested part of the money at 2% and the rest at 3.75%. He made a total of $192.50 in interest. How much was invested at 3.75%?

Accepted Answer

A)  $4000 
B)  $3500 
C)  $5000 
D)  $3000 
A)  $4000 
B)  $3500 
C)  $5000 
D)  $3000

Question 11

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set.
-$- 0.8 ( x + 3 ) + 0.1 ( x + 3 ) = - 0.7 x - 2.1$

Accepted Answer

A)  Conditional; $\{ - 0.7 \}$ 
B)  Identity; {all real numbers } 
C)  Contradiction; $\varnothing$ 
D)  Conditional; $\{ - 3 \}$ 
A)  Conditional; $\{ - 0.7 \}$ 
B)  Identity; {all real numbers } 
C)  Contradiction; $\varnothing$ 
D)  Conditional; $\{ - 3 \}$

Question 12

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are
rational, irrational, or nonreal complex.
-$8 y ^ { 2 } = - 7 y - 7$

Accepted Answer

A)  Two distinct irrational solutions 
B)  Two distinct rational solutions 
C)  One rational solution (a double solution) 
D)  Two distinct nonreal complex solutions 
A)  Two distinct irrational solutions 
B)  Two distinct rational solutions 
C)  One rational solution (a double solution) 
D)  Two distinct nonreal complex solutions

Question 13

Solve the problem
-The sum of the squares of two consecutive odd integers is 1802. Find the integers.

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 14

Solve the equation for the indicated variable. Assume no denominator is 0.
-$2 x ^ { 2 } - 4 x y + 3 y ^ { 2 } = 1$, for $y$

Accepted Answer

A)  $y = \frac { 2 x \pm 4 \sqrt { 3 - 2 x ^ { 2 } } } { 3 }$ 
B)  $y = \frac { 2 x \pm \sqrt { 3 - 2 x ^ { 2 } } } { 3 }$ 
C)  $y = \frac { 2 x \pm \sqrt { 6 - 4 x ^ { 2 } } } { 3 }$ 
D)  $y = \frac { 2 x \pm 2 \sqrt { 3 - 2 x ^ { 2 } } } { 3 }$ 
A)  $y = \frac { 2 x \pm 4 \sqrt { 3 - 2 x ^ { 2 } } } { 3 }$ 
B)  $y = \frac { 2 x \pm \sqrt { 3 - 2 x ^ { 2 } } } { 3 }$ 
C)  $y = \frac { 2 x \pm \sqrt { 6 - 4 x ^ { 2 } } } { 3 }$ 
D)  $y = \frac { 2 x \pm 2 \sqrt { 3 - 2 x ^ { 2 } } } { 3 }$

Question 15

Solve the inequality. Write the solution set in interval notation.
-$$| 4 x + 5 | + 4 < 6$$

Accepted Answer

A)  $\left( - \infty , - \frac { 7 } { 4 } \right) \cup \left( - \frac { 3 } { 4 } , \infty \right)$ 
B)  $\varnothing$ 
C)  $\left( - \infty , - \frac { 7 } { 4 } \right)$ 
D)  $\left( - \frac { 7 } { 4 } , - \frac { 3 } { 4 } \right)$ 
A)  $\left( - \infty , - \frac { 7 } { 4 } \right) \cup \left( - \frac { 3 } { 4 } , \infty \right)$ 
B)  $\varnothing$ 
C)  $\left( - \infty , - \frac { 7 } { 4 } \right)$ 
D)  $\left( - \frac { 7 } { 4 } , - \frac { 3 } { 4 } \right)$

Question 16

Find the sum or difference. Write the answer in standard form.
-$7 i + ( - 6 - i )$

Accepted Answer

A)  $- 6 + 8 i$ 
B)  $6 - 8 \mathrm { i }$ 
C)  $6 - 6 i$ 
D)  $- 6 + 6 i$ 
A)  $- 6 + 8 i$ 
B)  $6 - 8 \mathrm { i }$ 
C)  $6 - 6 i$ 
D)  $- 6 + 6 i$

Question 17

Graph the solution set.
-$$| x | > 8$$

Accepted Answer

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

Question 18

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are
rational, irrational, or nonreal complex.
-$v ^ { 2 } - 4 v - 7 = 0$

Accepted Answer

A)  One rational solution (a double solution) 
B)  Two distinct irrational solutions 
C)  Two distinct nonreal complex solutions 
D)  Two distinct rational solutions 
A)  One rational solution (a double solution) 
B)  Two distinct irrational solutions 
C)  Two distinct nonreal complex solutions 
D)  Two distinct rational solutions

Question 19

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\sqrt { 3 x + 10 } = 5 - 2 x$$

Accepted Answer

A)  $\left\{ \frac { 3 } { 4 } \right\}$ 
B)  $\left\{ \frac { 5 } { 4 } , 9 \right\}$ 
C)  $\{ 5 \}$ 
D)  $\left\{ \frac { 3 } { 4 } , 5 \right\}$ 
A)  $\left\{ \frac { 3 } { 4 } \right\}$ 
B)  $\left\{ \frac { 5 } { 4 } , 9 \right\}$ 
C)  $\{ 5 \}$ 
D)  $\left\{ \frac { 3 } { 4 } , 5 \right\}$

Question 20

Solve the equation.
-$$| - 9 x + 6 | = 5$$

Accepted Answer

A)  $\left\{ \frac { 1 } { 9 } , \frac { 11 } { 9 } \right\}$ 
B)  $\left\{ \frac { 1 } { 9 } \right\}$ 
C)  $\left\{ \frac { 11 } { 9 } , - \frac { 1 } { 9 } \right\}$ 
D)  $\left\{ - \frac { 11 } { 9 } , - \frac { 1 } { 9 } \right\}$ 
A)  $\left\{ \frac { 1 } { 9 } , \frac { 11 } { 9 } \right\}$ 
B)  $\left\{ \frac { 1 } { 9 } \right\}$ 
C)  $\left\{ \frac { 11 } { 9 } , - \frac { 1 } { 9 } \right\}$ 
D)  $\left\{ - \frac { 11 } { 9 } , - \frac { 1 } { 9 } \right\}$

Graph the solution set. - $| x | = - 5$

Find the sum or difference. Write the answer in standard form. - $( 4 + 9 i ) - ( - 8 + i )$

Solve the equation by completing the square. - $4 x ^ { 2 } - 4 x - 8 = 0$

Solve the problem. -The area of a square is numerically 117 more than the perimeter. Find the length of the side.

Solve for the indicated variable. - $Z = A ( 1 + x ) ^ { 1 / 3 }$ , for $x$

Find the sum or difference. Write the answer in standard form. - $( 7 - 7 i ) - ( - 9 - 7 i ) + ( - 7 - 8 i )$

Simplify the power of i. - $\mathrm { i } ^ { 43 }$

Solve the rational inequality. Write the solution set in interval notation. - $\frac { 4 x } { - 3 x + 7 } \geq 11$

Solve the problem -Find two consecutive integers whose product is 380. 252

Solve the problem. -Walt made an extra $7000 last year from a part-time job. He invested part of the money at 2% and the rest at 3.75%. He made a total of $192.50 in interest. How much was invested at 3.75%?

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $- 0.8 ( x + 3 ) + 0.1 ( x + 3 ) = - 0.7 x - 2.1$

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. - $8 y ^ { 2 } = - 7 y - 7$

Solve the problem -The sum of the squares of two consecutive odd integers is 1802. Find the integers.

Solve the equation for the indicated variable. Assume no denominator is 0. - $2 x ^ { 2 } - 4 x y + 3 y ^ { 2 } = 1$ , for $y$

Solve the inequality. Write the solution set in interval notation. - $| 4 x + 5 | + 4 < 6$

Find the sum or difference. Write the answer in standard form. - $7 i + ( - 6 - i )$

Graph the solution set. - $| x | > 8$

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. - $v ^ { 2 } - 4 v - 7 = 0$

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt { 3 x + 10 } = 5 - 2 x$

Solve the equation. - $| - 9 x + 6 | = 5$

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

Graph the solution set. - ∣x∣=−5| x | = - 5∣x∣=−5

Find the sum or difference. Write the answer in standard form. - (4+9i)−(−8+i)( 4 + 9 i ) - ( - 8 + i )(4+9i)−(−8+i)

Solve the equation by completing the square. - 4x2−4x−8=04 x ^ { 2 } - 4 x - 8 = 04x2−4x−8=0