Question 1

Decide what values of the variable cannot possibly be solutions for the equation.
-$\sqrt { 10 + x } + \sqrt { 11 - 5 x } = - 1$

Accepted Answer

A)  $\{ 1 \}$ 
B)  $\{ 0 \}$ 
C)  $\left\{ \frac { 11 } { 2 } \right\}$ 
D)  $\varnothing$ 
A)  $\{ 1 \}$ 
B)  $\{ 0 \}$ 
C)  $\left\{ \frac { 11 } { 2 } \right\}$ 
D)  $\varnothing$

Question 2

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.
-$$\mathrm { F } = 22 ^ { \circ }$$

Accepted Answer

A)  $C = 30 ^ { \circ }$ 
B)  $C = - 5.6 ^ { \circ }$ 
C)  $C = 8.7 ^ { \circ }$ 
D)  $C = - 18 ^ { \circ }$ 
A)  $C = 30 ^ { \circ }$ 
B)  $C = - 5.6 ^ { \circ }$ 
C)  $C = 8.7 ^ { \circ }$ 
D)  $C = - 18 ^ { \circ }$

Question 3

Solve the equation by completing the square.
-$$x ^ { 2 } + 4 x + 13 = 0$$

Accepted Answer

A)  $\{ 2 \pm 3 i \}$ 
B)  $\{ 1 , - 5 \}$ 
C)  $\{ - 2 \pm \sqrt { 13 } \}$ 
D)  $\{ - 2 \pm 3 i \}$ 
A)  $\{ 2 \pm 3 i \}$ 
B)  $\{ 1 , - 5 \}$ 
C)  $\{ - 2 \pm \sqrt { 13 } \}$ 
D)  $\{ - 2 \pm 3 i \}$

Question 4

Decide whether or not the equations are equivalent.
-$\begin{array} { l } 
2 x - 3 = 8 \
- 2 x + 8 = - 3
\end{array}$

Accepted Answer

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

Question 5

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.
-$w ^ { 2 } + 4 w + 5 = 0$

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 6

A square lawn has an area of 1152 square feet. A sprinkler placed at the center of the lawn sprays a water in a circular pattern that just covers the lawn. What is the radius of the circle?

Accepted Answer

A)  24 ft 
B)  16.97 ft 
C)  33.94 ft 
D)  48 ft 
A)  24 ft 
B)  16.97 ft 
C)  33.94 ft 
D)  48 ft

Question 7

Find the sum or difference. Write the answer in standard form.
-$$( 4 - 7 \mathrm { i } ) + ( - 8 + 2 \mathrm { i } ) + 2 \mathrm { i }$$

Accepted Answer

A)  $- 4 + 3 i$ 
B)  $- 4 - 3 \mathrm { i }$ 
C)  $- 2 - 3 \mathrm { i }$ 
D)  $12 - 5 \mathrm { i }$ 
A)  $- 4 + 3 i$ 
B)  $- 4 - 3 \mathrm { i }$ 
C)  $- 2 - 3 \mathrm { i }$ 
D)  $12 - 5 \mathrm { i }$

Question 8

Solve the rational inequality. Write the solution set in interval notation.
-$$\frac { 2 x } { - 5 x + 2 } \geq 14$$

Accepted Answer

A)  $\left[ \frac { 7 } { 18 } , \frac { 2 } { 5 } \right]$ 
B)  $( - \infty , 0 ] \cup \left( \frac { 2 } { 5 } , \infty \right)$ 
C)  $\left[ - \infty , \frac { 7 } { 18 } \right] \cup \left[ \frac { 7 } { 18 } , \infty \right)$ 
D)  $\left[ 0 , \frac { 2 } { 5 } \right]$ 
A)  $\left[ \frac { 7 } { 18 } , \frac { 2 } { 5 } \right]$ 
B)  $( - \infty , 0 ] \cup \left( \frac { 2 } { 5 } , \infty \right)$ 
C)  $\left[ - \infty , \frac { 7 } { 18 } \right] \cup \left[ \frac { 7 } { 18 } , \infty \right)$ 
D)  $\left[ 0 , \frac { 2 } { 5 } \right]$

Question 9

Solve the equation by the zero-factor property.
-$$x ^ { 2 } - 2 x - 24 = 0$$

Accepted Answer

A)  $\{ 6 , - 4 \}$ 
B)  $\{ - 20 , - 4 \}$ 
C)  $\{ 5 , - 5 \}$ 
D)  $\{ - 6,4 \}$ 
A)  $\{ 6 , - 4 \}$ 
B)  $\{ - 20 , - 4 \}$ 
C)  $\{ 5 , - 5 \}$ 
D)  $\{ - 6,4 \}$

Question 10

Solve the cubic equation using factoring and the quadratic formula.
-$$x ^ { 2 } = 44$$

Accepted Answer

A)  $\pm 4 \sqrt { 11 }$ 
B)  $\pm 2 \sqrt { 11 }$ 
C)  $\pm 2 \mathrm { i } \sqrt { 11 }$ 
D)  $\pm 4 \mathrm { i } \sqrt { 11 }$ 
A)  $\pm 4 \sqrt { 11 }$ 
B)  $\pm 2 \sqrt { 11 }$ 
C)  $\pm 2 \mathrm { i } \sqrt { 11 }$ 
D)  $\pm 4 \mathrm { i } \sqrt { 11 }$

Question 11

Graph the solution set.
-$$| 6 x - 6 | + 6 = 12$$

Accepted Answer

A)  $\{ - 2,0 \}$ 
B)  $\{ 2,0 \}$ 
C)  $\{ - 2,-1 \}$ 
D)  $\varnothing$ 
A)  $\{ - 2,0 \}$ 
B)  $\{ 2,0 \}$ 
C)  $\{ - 2,-1 \}$ 
D)  $\varnothing$

Question 12

Solve the quadratic inequality. Write the solution set in interval notation.
-$x ^ { 2 } - 7 x + 10 > 0$

Accepted Answer

A)  $( 5 , \infty )$ 
B)  $( 2,5 )$ 
C)  $( - \infty , 2 )$ 
D)  $( - \infty , 2 ) \cup ( 5 , \infty )$ 
A)  $( 5 , \infty )$ 
B)  $( 2,5 )$ 
C)  $( - \infty , 2 )$ 
D)  $( - \infty , 2 ) \cup ( 5 , \infty )$

Question 13

Solve for the indicated variable.
-$\frac { 1 } { A } = \frac { 1 } { B } + \frac { 1 } { C }$, for $A$

Accepted Answer

A)  $A = \frac { B C } { B + C }$ 
B)  $A = 4 + B + C$ 
C)  $A = \frac { B - C } { B C }$ 
D)  $A = \frac { B } { B + C }$ 
A)  $A = \frac { B C } { B + C }$ 
B)  $A = 4 + B + C$ 
C)  $A = \frac { B - C } { B C }$ 
D)  $A = \frac { B } { B + C }$

Question 14

Find the product. Write the answer in standard form.
-$$\mathrm { i } ( 7 - 3 \mathrm { i } ) ( 4 - 3 \mathrm { i } )$$

Accepted Answer

A)  $9 i ^ { 3 } + 33 i ^ { 2 } + 28 i$ 
B)  $- 33 - 19 i$ 
C)  $33 + 19 i$ 
D)  $37 + 9 i$ 
A)  $9 i ^ { 3 } + 33 i ^ { 2 } + 28 i$ 
B)  $- 33 - 19 i$ 
C)  $33 + 19 i$ 
D)  $37 + 9 i$

Question 15

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

Accepted Answer

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

Question 16

Solve the equation by the square root property.
-$$x ^ { 2 } = 225$$

Accepted Answer

A)  $\{ \pm 15 \}$ 
B)  $\{ 112.5 \}$ 
C)  $\{ 15 \}$ 
D)  $\{ \pm 15 \mathrm { i } \}$ 
A)  $\{ \pm 15 \}$ 
B)  $\{ 112.5 \}$ 
C)  $\{ 15 \}$ 
D)  $\{ \pm 15 \mathrm { i } \}$

Question 17

Solve and graph the inequality. Give answer in interval notation.
-$$- 4 < 3 x + 2 \leq 8$$

Accepted Answer

A)  $( - 2,2 ]$
  
B)  $[ - 2,2 )$
  
C)  $( - 2,2 )$
  
D)  $[ - 2,2 ]$
  
A)  $( - 2,2 ]$
  
B)  $[ - 2,2 )$
  
C)  $( - 2,2 )$
  
D)  $[ - 2,2 ]$

Question 18

Solve the cubic equation using factoring and the quadratic formula.
-$$x ^ { 2 } + 3 = 0$$

Accepted Answer

A)  $\pm 3$ 
B)  $\pm \sqrt { 3 }$ 
C)  $\pm 3 i$ 
D)  $\pm \mathrm { i } \sqrt { 3 }$ 
A)  $\pm 3$ 
B)  $\pm \sqrt { 3 }$ 
C)  $\pm 3 i$ 
D)  $\pm \mathrm { i } \sqrt { 3 }$

Question 19

Solve the cubic equation using factoring and the quadratic formula.
-Only one of the following equations is set up so that the values of a, b, and c can be determined immediately. Which one is it?

Accepted Answer

A)  $( 3 x + 5 ) ^ { 2 } = 1$ 
B)  $( 3 x + 5 ) ( x + 1 ) = 0$ 
C)  $3 x ^ { 2 } + 5 x + 1 = 0$ 
D)  $x ^ { 2 } + x = 1$ 
A)  $( 3 x + 5 ) ^ { 2 } = 1$ 
B)  $( 3 x + 5 ) ( x + 1 ) = 0$ 
C)  $3 x ^ { 2 } + 5 x + 1 = 0$ 
D)  $x ^ { 2 } + x = 1$

Question 20

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set.
-$$- 2 ( x + 7 ) + ( - 5 x ) = - 7 ( x - 7 ) + 5$$

Accepted Answer

A)  Contradiction; $\varnothing$ 
B)  Conditional; $\{ 5 \}$ 
C)  Conditional; $\{ 0 \}$ 
D)  Identity; \{all real numbers\} 
A)  Contradiction; $\varnothing$ 
B)  Conditional; $\{ 5 \}$ 
C)  Conditional; $\{ 0 \}$ 
D)  Identity; \{all real numbers\}

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt { 10 + x } + \sqrt { 11 - 5 x } = - 1$

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. - $\mathrm { F } = 22 ^ { \circ }$

Solve the equation by completing the square. - $x ^ { 2 } + 4 x + 13 = 0$

Decide whether or not the equations are equivalent. - 2x-3=8 -2x+8=-3

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. - $w ^ { 2 } + 4 w + 5 = 0$

A square lawn has an area of 1152 square feet. A sprinkler placed at the center of the lawn sprays a water in a circular pattern that just covers the lawn. What is the radius of the circle?

Find the sum or difference. Write the answer in standard form. - $( 4 - 7 \mathrm { i } ) + ( - 8 + 2 \mathrm { i } ) + 2 \mathrm { i }$

Solve the rational inequality. Write the solution set in interval notation. - $\frac { 2 x } { - 5 x + 2 } \geq 14$

Solve the equation by the zero-factor property. - $x ^ { 2 } - 2 x - 24 = 0$

Solve the cubic equation using factoring and the quadratic formula. - $x ^ { 2 } = 44$

Graph the solution set. - $| 6 x - 6 | + 6 = 12$

Solve the quadratic inequality. Write the solution set in interval notation. - $x ^ { 2 } - 7 x + 10 > 0$

Solve for the indicated variable. - $\frac { 1 } { A } = \frac { 1 } { B } + \frac { 1 } { C }$ , for $A$

Find the product. Write the answer in standard form. - $\mathrm { i } ( 7 - 3 \mathrm { i } ) ( 4 - 3 \mathrm { i } )$

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

Solve the equation by the square root property. - $x ^ { 2 } = 225$

Solve and graph the inequality. Give answer in interval notation. - $- 4 < 3 x + 2 \leq 8$ $Solve and graph the inequality. Give answer in interval notation. - - 4 < 3 x + 2 \leq 8$

Solve the cubic equation using factoring and the quadratic formula. - $x ^ { 2 } + 3 = 0$

Solve the cubic equation using factoring and the quadratic formula. -Only one of the following equations is set up so that the values of a, b, and c can be determined immediately. Which one is it?

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $- 2 ( x + 7 ) + ( - 5 x ) = - 7 ( x - 7 ) + 5$

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. - 10+x+11−5x=−1\sqrt { 10 + x } + \sqrt { 11 - 5 x } = - 110+x​+11−5x​=−1

Use these equations to convert between the two systems. C=59(F−32)F=95C+32C = \frac { 5 } { 9 } ( F - 32 ) \quad F = \frac { 9 } { 5 } C + 32C=95​(F−32)F=59​C+32 Round answer to the nearest tenth of a degree if necessary. - F=22∘\mathrm { F } = 22 ^ { \circ }F=22∘

Solve the equation by completing the square. - x2+4x+13=0x ^ { 2 } + 4 x + 13 = 0x2+4x+13=0

Decide whether or not the equations are equivalent. - 2x-3=8 -2x+8=-3

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. - w2+4w+5=0w ^ { 2 } + 4 w + 5 = 0w2+4w+5=0

A square lawn has an area of 1152 square feet. A sprinkler placed at the center of the lawn sprays a water in a circular pattern that just covers the lawn. What is the radius of the circle?

Find the sum or difference. Write the answer in standard form. - (4−7i)+(−8+2i)+2i( 4 - 7 \mathrm { i } ) + ( - 8 + 2 \mathrm { i } ) + 2 \mathrm { i }(4−7i)+(−8+2i)+2i

Solve the rational inequality. Write the solution set in interval notation. - 2x−5x+2≥14\frac { 2 x } { - 5 x + 2 } \geq 14−5x+22x​≥14

Solve the equation by the zero-factor property. - x2−2x−24=0x ^ { 2 } - 2 x - 24 = 0x2−2x−24=0

Solve the cubic equation using factoring and the quadratic formula. - x2=44x ^ { 2 } = 44x2=44

Graph the solution set. - ∣6x−6∣+6=12| 6 x - 6 | + 6 = 12∣6x−6∣+6=12

Solve the quadratic inequality. Write the solution set in interval notation. - x2−7x+10>0x ^ { 2 } - 7 x + 10 > 0x2−7x+10>0

Solve for the indicated variable. - 1A=1B+1C\frac { 1 } { A } = \frac { 1 } { B } + \frac { 1 } { C }A1​=B1​+C1​ , for AAA

Find the product. Write the answer in standard form. - i(7−3i)(4−3i)\mathrm { i } ( 7 - 3 \mathrm { i } ) ( 4 - 3 \mathrm { i } )i(7−3i)(4−3i)

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

Solve the equation by the square root property. - x2=225x ^ { 2 } = 225x2=225

Solve and graph the inequality. Give answer in interval notation. - −4<3x+2≤8- 4 < 3 x + 2 \leq 8−4<3x+2≤8

Solve the cubic equation using factoring and the quadratic formula. - x2+3=0x ^ { 2 } + 3 = 0x2+3=0

Solve the cubic equation using factoring and the quadratic formula. -Only one of the following equations is set up so that the values of a, b, and c can be determined immediately. Which one is it?

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - −2(x+7)+(−5x)=−7(x−7)+5- 2 ( x + 7 ) + ( - 5 x ) = - 7 ( x - 7 ) + 5−2(x+7)+(−5x)=−7(x−7)+5

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. - $\sqrt { 10 + x } + \sqrt { 11 - 5 x } = - 1$

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. - $\mathrm { F } = 22 ^ { \circ }$

Solve the equation by completing the square. - $x ^ { 2 } + 4 x + 13 = 0$

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. - $w ^ { 2 } + 4 w + 5 = 0$

Find the sum or difference. Write the answer in standard form. - $( 4 - 7 \mathrm { i } ) + ( - 8 + 2 \mathrm { i } ) + 2 \mathrm { i }$

Solve the rational inequality. Write the solution set in interval notation. - $\frac { 2 x } { - 5 x + 2 } \geq 14$

Solve the equation by the zero-factor property. - $x ^ { 2 } - 2 x - 24 = 0$

Solve the cubic equation using factoring and the quadratic formula. - $x ^ { 2 } = 44$

Graph the solution set. - $| 6 x - 6 | + 6 = 12$

Solve the quadratic inequality. Write the solution set in interval notation. - $x ^ { 2 } - 7 x + 10 > 0$

Solve for the indicated variable. - $\frac { 1 } { A } = \frac { 1 } { B } + \frac { 1 } { C }$ , for $A$

Find the product. Write the answer in standard form. - $\mathrm { i } ( 7 - 3 \mathrm { i } ) ( 4 - 3 \mathrm { i } )$

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

Solve the equation by the square root property. - $x ^ { 2 } = 225$

Solve and graph the inequality. Give answer in interval notation. - $- 4 < 3 x + 2 \leq 8$ $Solve and graph the inequality. Give answer in interval notation. - - 4 < 3 x + 2 \leq 8$

Solve the cubic equation using factoring and the quadratic formula. - $x ^ { 2 } + 3 = 0$

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $- 2 ( x + 7 ) + ( - 5 x ) = - 7 ( x - 7 ) + 5$