Question 1

Solve the equation.
-$$\left( x ^ { 2 } + 2 \right) ^ { 1 / 2 } - ( 2 x + 5 ) ^ { 1 / 2 } = 0$$

Accepted Answer

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

Question 2

Solve the inequality. Write the solution set in interval notation.
-$$| 2 - 3 x | \leq 11$$

Accepted Answer

A)  $\left[ - \frac { 13 } { 3 } , 3 \right]$ 
B)  $( - \infty , - 3 ] \cup \left[ \frac { 13 } { 3 } , \infty \right)$ 
C)  $( - \infty , 3 ] \cup \left[ \frac { 13 } { 3 } , \infty \right)$ 
D)  $\left[ - 3 , \frac { 13 } { 3 } \right]$ 
A)  $\left[ - \frac { 13 } { 3 } , 3 \right]$ 
B)  $( - \infty , - 3 ] \cup \left[ \frac { 13 } { 3 } , \infty \right)$ 
C)  $( - \infty , 3 ] \cup \left[ \frac { 13 } { 3 } , \infty \right)$ 
D)  $\left[ - 3 , \frac { 13 } { 3 } \right]$

Question 3

Solve the equation.
-$$x ^ { 2 / 3 } = 5 x 1 / 3$$

Accepted Answer

A)  $\{ 0 , - 125 \}$ 
B)  $\{ 0,5 \}$ 
C)  $\varnothing$ 
D)  $\{ 0,125 \}$ 
A)  $\{ 0 , - 125 \}$ 
B)  $\{ 0,5 \}$ 
C)  $\varnothing$ 
D)  $\{ 0,125 \}$

Question 4

Solve the equation.
-$$| 9 x + 4 | = | 1 - 2 x |$$

Accepted Answer

A)  $\left\{ \frac { 5 } { 11 } , 1 \right\}$ 
B)  $\left\{ - \frac { 3 } { 11 } , - \frac { 5 } { 7 } \right\}$ 
C)  $\left\{ - \frac { 3 } { 7 } , - \frac { 5 } { 11 } \right\}$ 
D)  $\left\{ - \frac { 5 } { 11 } , 1 \right\}$ 
A)  $\left\{ \frac { 5 } { 11 } , 1 \right\}$ 
B)  $\left\{ - \frac { 3 } { 11 } , - \frac { 5 } { 7 } \right\}$ 
C)  $\left\{ - \frac { 3 } { 7 } , - \frac { 5 } { 11 } \right\}$ 
D)  $\left\{ - \frac { 5 } { 11 } , 1 \right\}$

Question 5

Solve the equation.
-$$\sqrt { 3 x + 1 } = 3 + \sqrt { x - 4 }$$

Accepted Answer

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

Question 6

Solve the problem.
-In a chemistry class, 7 liters of a 4% silver iodide solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed?

Accepted Answer

A)  3.5 L 
B) 7 L 
C)  4.5 L 
D)  2.5 L 
A)  3.5 L 
B) 7 L 
C)  4.5 L 
D)  2.5 L

Question 7

Solve the problem.
-One maid can clean the house in 5 hours. Another maid can do the job in 7 hours. How long will it take them to do the job working together?

Accepted Answer

A)  $\frac { 1 } { 12 } \mathrm { hr }$ 
B)  $\frac { 35 } { 12 } \mathrm { hr }$ 
C)  $\frac { 1 } { 35 } \mathrm { hr }$ 
D)  $\frac { 35 } { 2 } \mathrm { hr }$ 
A)  $\frac { 1 } { 12 } \mathrm { hr }$ 
B)  $\frac { 35 } { 12 } \mathrm { hr }$ 
C)  $\frac { 1 } { 35 } \mathrm { hr }$ 
D)  $\frac { 35 } { 2 } \mathrm { hr }$

Question 8

Solve the equation.
-$$| - 9 x + 8 | = 1$$

Accepted Answer

A)  $\left\{ \frac { 7 } { 9 } , 1 \right\}$ 
B)  $\left\{ \frac { 7 } { 9 } \right\}$ 
C)  $\left\{ 1 , - \frac { 7 } { 9 } \right\}$ 
D)  $\left\{ - 1 , - \frac { 7 } { 9 } \right\}$ 
A)  $\left\{ \frac { 7 } { 9 } , 1 \right\}$ 
B)  $\left\{ \frac { 7 } { 9 } \right\}$ 
C)  $\left\{ 1 , - \frac { 7 } { 9 } \right\}$ 
D)  $\left\{ - 1 , - \frac { 7 } { 9 } \right\}$

Question 9

Solve the inequality. Write the solution set in interval notation.
-$$\left| \frac { 5 } { 8 } - \frac { 1 } { 3 } x \right| > \frac { 2 } { 5 }$$

Accepted Answer

A)  $( - \infty , \infty )$ 
B)  $\left( - \infty , - \frac { 123 } { 40 } \right) \cup \left( \frac { 27 } { 40 } , \infty \right)$ 
C)  $\left( - \infty , \frac { 27 } { 40 } \right) \cup \left( \frac { 123 } { 40 } , \infty \right)$ 
D)  $\left( \frac { 27 } { 40 } , \frac { 123 } { 40 } \right)$ 
A)  $( - \infty , \infty )$ 
B)  $\left( - \infty , - \frac { 123 } { 40 } \right) \cup \left( \frac { 27 } { 40 } , \infty \right)$ 
C)  $\left( - \infty , \frac { 27 } { 40 } \right) \cup \left( \frac { 123 } { 40 } , \infty \right)$ 
D)  $\left( \frac { 27 } { 40 } , \frac { 123 } { 40 } \right)$

Question 10

Solve and graph the inequality. Give answer in interval notation.
-$-11 x+5 \geq-10 x+11$

Accepted Answer

A)  $[ 6 , \infty )$
  
B)  $( - \infty , - 6 ]$
  
C) $(-\infty,-11]$
  
D)  $( - 11 , \infty )$
  
A)  $[ 6 , \infty )$
  
B)  $( - \infty , - 6 ]$
  
C) $(-\infty,-11]$
  
D)  $( - 11 , \infty )$

Question 11

Solve the equation.
-$$x ^ { 2 } + 10 = 0$$

Accepted Answer

A)  $\pm 10 \mathrm { i }$ 
B)  $\pm \sqrt { 10 }$ 
C)  $\pm \mathrm { i } \sqrt { 10 }$ 
D)  $\pm 10$ 
A)  $\pm 10 \mathrm { i }$ 
B)  $\pm \sqrt { 10 }$ 
C)  $\pm \mathrm { i } \sqrt { 10 }$ 
D)  $\pm 10$

Question 12

Graph the solution set.
-$$| x | \neq 3$$

Accepted Answer

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

Question 13

Solve the equation.
-$$| 2 x - 5 | = | x - 1 |$$

Accepted Answer

A)  $\{ - 4 , - 2 \}$ 
B)  $\varnothing$ 
C)  $\{ 4 \}$ 
D)  $\{ 4,2 \}$ 
A)  $\{ - 4 , - 2 \}$ 
B)  $\varnothing$ 
C)  $\{ 4 \}$ 
D)  $\{ 4,2 \}$

Question 14

Solve the equation by completing the square.
-$$x ^ { 2 } + 4 x + 68 = 0$$

Accepted Answer

A)  $\{ 6 , - 10 \}$ 
B)  $\{ - 2 \pm 8 \mathrm { i } \}$ 
C)  $\{ 2 \pm 8 i \}$ 
D)  $\{ - 2 \pm 2 \sqrt { 17 } \}$ 
A)  $\{ 6 , - 10 \}$ 
B)  $\{ - 2 \pm 8 \mathrm { i } \}$ 
C)  $\{ 2 \pm 8 i \}$ 
D)  $\{ - 2 \pm 2 \sqrt { 17 } \}$

Question 15

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set.
-$$2 x + 5 ( x + 1 ) + 3 = 8 - 3 x$$

Accepted Answer

A)  Conditional; $\{ 1 \}$ 
B)  Contradiction; $\varnothing$ 
C)  Identity; $\{$ all real numbers $\}$ 
D)  Conditional; $\{ 0 \}$ 
A)  Conditional; $\{ 1 \}$ 
B)  Contradiction; $\varnothing$ 
C)  Identity; $\{$ all real numbers $\}$ 
D)  Conditional; $\{ 0 \}$

Question 16

Solve the problem.
-A rock falls from a tower that is $68.6 \mathrm {~m}$ high. As it is falling, its height is given by the formula $h = 68.6 - 4.9 t ^ { 2 }$, with $t$ in seconds. How many seconds will it take for the rock to hit the ground (h $= 0$ )?

Accepted Answer

A)  $960.4 \mathrm { sec }$ 
B)  $8 \mathrm { sec }$ 
C)  $3.7 \mathrm { sec }$ 
D)  $8.3 \mathrm { sec }$ 
A)  $960.4 \mathrm { sec }$ 
B)  $8 \mathrm { sec }$ 
C)  $3.7 \mathrm { sec }$ 
D)  $8.3 \mathrm { sec }$

Question 17

Solve for the indicated variable.
-$\mathrm { M } = \pi \mathrm { r } ^ { 2 } \mathrm { hd }$, for $\mathrm { r }$

Accepted Answer

A)  $\mathrm { r } = \frac { \pm \mathrm { M } \sqrt { \pi \mathrm { hd } } } { \pi \mathrm { hd } }$ 
B)  $r = \frac { \pm \sqrt { \mathrm { M } \pi \mathrm { hd } } } { \pi \mathrm { hd } }$ 
C)  $r = \pm \sqrt { \pi \mathrm { Mhd } }$ 
D)  $r = \frac { \pm \sqrt { \pi \mathrm { Mhd } } } { \mathrm { hd } }$ 
A)  $\mathrm { r } = \frac { \pm \mathrm { M } \sqrt { \pi \mathrm { hd } } } { \pi \mathrm { hd } }$ 
B)  $r = \frac { \pm \sqrt { \mathrm { M } \pi \mathrm { hd } } } { \pi \mathrm { hd } }$ 
C)  $r = \pm \sqrt { \pi \mathrm { Mhd } }$ 
D)  $r = \frac { \pm \sqrt { \pi \mathrm { Mhd } } } { \mathrm { hd } }$

Question 18

Solve the equation.
-$$\frac { 4 x + 4 } { 4 } - \frac { 4 x } { x - 4 } = x$$

Accepted Answer

A)  $\left\{ - \frac { 1 } { 3 } \right\}$ 
B)  $\left\{ - \frac { 4 } { 15 } \right\}$ 
C)  $\left\{ \frac { 4 } { 5 } \right\}$ 
D)  $\left\{ - \frac { 4 } { 3 } \right\}$ 
A)  $\left\{ - \frac { 1 } { 3 } \right\}$ 
B)  $\left\{ - \frac { 4 } { 15 } \right\}$ 
C)  $\left\{ \frac { 4 } { 5 } \right\}$ 
D)  $\left\{ - \frac { 4 } { 3 } \right\}$

Question 19

Find the values of a, b, and c for which the quadratic equation $$a x ^ { 2 } + b x + c = 0$$ has the given numbers as solutions. Then
use those values to write a quadratic equation.
-$5 , - 8$

Accepted Answer

A)  $x ^ { 2 } + 3 x - 40 = 0$ 
B)  $x ^ { 2 } - 40 x + 3 = 0$ 
C)  $x ^ { 2 } - 3 x - 40 = 0$ 
D)  $x ^ { 2 } - 40 x - 3 = 0$ 
A)  $x ^ { 2 } + 3 x - 40 = 0$ 
B)  $x ^ { 2 } - 40 x + 3 = 0$ 
C)  $x ^ { 2 } - 3 x - 40 = 0$ 
D)  $x ^ { 2 } - 40 x - 3 = 0$

Question 20

Find the values of a, b, and c for which the quadratic equation $$a x ^ { 2 } + b x + c = 0$$ has the given numbers as solutions. Then
use those values to write a quadratic equation.
-$- 9 , - 2$

Accepted Answer

A)  $x ^ { 2 } + 11 x + 18 = 0$ 
B)  $x ^ { 2 } + 18 x - 11 = 0$ 
C)  $x ^ { 2 } - 11 x + 18 = 0$ 
D)  $x ^ { 2 } + 18 x + 11 = 0$ 
A)  $x ^ { 2 } + 11 x + 18 = 0$ 
B)  $x ^ { 2 } + 18 x - 11 = 0$ 
C)  $x ^ { 2 } - 11 x + 18 = 0$ 
D)  $x ^ { 2 } + 18 x + 11 = 0$

Solve the equation. - $\left( x ^ { 2 } + 2 \right) ^ { 1 / 2 } - ( 2 x + 5 ) ^ { 1 / 2 } = 0$

Solve the inequality. Write the solution set in interval notation. - $| 2 - 3 x | \leq 11$

Solve the equation. - $x ^ { 2 / 3 } = 5 x 1 / 3$

Solve the equation. - $| 9 x + 4 | = | 1 - 2 x |$

Solve the equation. - $\sqrt { 3 x + 1 } = 3 + \sqrt { x - 4 }$

Solve the problem. -In a chemistry class, 7 liters of a 4% silver iodide solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed?

Solve the problem. -One maid can clean the house in 5 hours. Another maid can do the job in 7 hours. How long will it take them to do the job working together?

Solve the equation. - $| - 9 x + 8 | = 1$

Solve the inequality. Write the solution set in interval notation. - $\left| \frac { 5 } { 8 } - \frac { 1 } { 3 } x \right| > \frac { 2 } { 5 }$

Solve and graph the inequality. Give answer in interval notation. - $-11 x+5 \geq-10 x+11$ $Solve and graph the inequality. Give answer in interval notation. - -11 x+5 \geq-10 x+11$

Solve the equation. - $x ^ { 2 } + 10 = 0$

Graph the solution set. - $| x | \neq 3$ $Graph the solution set. - | x | \neq 3$

Solve the equation. - $| 2 x - 5 | = | x - 1 |$

Solve the equation by completing the square. - $x ^ { 2 } + 4 x + 68 = 0$

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $2 x + 5 ( x + 1 ) + 3 = 8 - 3 x$

Solve the problem. -A rock falls from a tower that is $68.6 \mathrm {~m}$ high. As it is falling, its height is given by the formula $h = 68.6 - 4.9 t ^ { 2 }$ , with $t$ in seconds. How many seconds will it take for the rock to hit the ground (h $= 0$ )?

Solve for the indicated variable. - $\mathrm { M } = \pi \mathrm { r } ^ { 2 } \mathrm { hd }$ , for $\mathrm { r }$

Solve the equation. - $\frac { 4 x + 4 } { 4 } - \frac { 4 x } { x - 4 } = x$

Find the values of a, b, and c for which the quadratic equation $a x ^ { 2 } + b x + c = 0$ has the given numbers as solutions. Then use those values to write a quadratic equation. - $5 , - 8$

Find the values of a, b, and c for which the quadratic equation $a x ^ { 2 } + b x + c = 0$ has the given numbers as solutions. Then use those values to write a quadratic equation. - $- 9 , - 2$

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

Review of Basic Concepts

Filters

Exam 1: Equations and Inequalities

Solve the equation. - (x2+2)1/2−(2x+5)1/2=0\left( x ^ { 2 } + 2 \right) ^ { 1 / 2 } - ( 2 x + 5 ) ^ { 1 / 2 } = 0(x2+2)1/2−(2x+5)1/2=0

Solve the inequality. Write the solution set in interval notation. - ∣2−3x∣≤11| 2 - 3 x | \leq 11∣2−3x∣≤11

Solve the equation. - x2/3=5x1/3x ^ { 2 / 3 } = 5 x 1 / 3x2/3=5x1/3

Solve the equation. - ∣9x+4∣=∣1−2x∣| 9 x + 4 | = | 1 - 2 x |∣9x+4∣=∣1−2x∣

Solve the equation. - 3x+1=3+x−4\sqrt { 3 x + 1 } = 3 + \sqrt { x - 4 }3x+1​=3+x−4​