Question 1

The distance (in feet)that an object will fall in $t$ seconds is given by the formula $s = 16 t ^ { 2 }$ . How long will it take an object to fall 576 feet?

Accepted Answer

A) 6 sec 
B) 36 sec 
C) 8 sec 
D) 7 sec 
E) 35 sec 
A) 6 sec 
B) 36 sec 
C) 8 sec 
D) 7 sec 
E) 35 sec

Question 2

Write $\sqrt { 5 } \sqrt { - 49 }$ in terms of i , perform the indicated operations, and simplify.

Accepted Answer

A)  $7 i \sqrt { 5 }$ 
B)  $7 \sqrt { 5 }$ 
C)  $- 7 i \sqrt { 5 }$ 
D)  $7 \sqrt { 5 i }$ 
E)  $- 7 \sqrt { 5 }$ 
A)  $7 i \sqrt { 5 }$ 
B)  $7 \sqrt { 5 }$ 
C)  $- 7 i \sqrt { 5 }$ 
D)  $7 \sqrt { 5 i }$ 
E)  $- 7 \sqrt { 5 }$

Question 3

Solve the inequality. $\frac { x - 1 } { x - 5 } \leq 3$

Accepted Answer

A)  $x \in ( - \infty , - 7 ) \cup ( - 5 , \infty )$ 
B)  $x \in [ 5,7 ]$ 
C)  $x \in ( - \infty , 5 ) \cup [ 7 , \infty )$ 
D)  $x \in ( - \infty , 5 ] \cup [ 7 , \infty )$ 
E)  $x \in ( 5,7 )$ 
A)  $x \in ( - \infty , - 7 ) \cup ( - 5 , \infty )$ 
B)  $x \in [ 5,7 ]$ 
C)  $x \in ( - \infty , 5 ) \cup [ 7 , \infty )$ 
D)  $x \in ( - \infty , 5 ] \cup [ 7 , \infty )$ 
E)  $x \in ( 5,7 )$

Question 4

Solve the equation. $10 ( m + 3 ) ^ { - 2 } - 29 ( m + 3 ) ^ { - 1 } + 9 = 0$

Accepted Answer

A)  $\frac { 29 \pm \sqrt { 481 } } { 18 } - 3$ 
B)  $\frac { 29 \pm \sqrt { 481 } } { 18 } + 3$ 
C)  $$\frac { 29 \pm \sqrt { 481 } } { 20 } + 3$$ 
D)  $\frac { 29 \pm \sqrt { 481 } } { 20 } - 3$ 
A)  $\frac { 29 \pm \sqrt { 481 } } { 18 } - 3$ 
B)  $\frac { 29 \pm \sqrt { 481 } } { 18 } + 3$ 
C)  $$\frac { 29 \pm \sqrt { 481 } } { 20 } + 3$$ 
D)  $\frac { 29 \pm \sqrt { 481 } } { 20 } - 3$

Question 5

Use the quadratic formula to find all real solutions of the equation. $2 x ^ { 2 } + x = 5$

Accepted Answer

A)  $\frac { - 1 \pm \sqrt { 41 } } { 4 }$ 
B)  $\frac { - 1 \pm \sqrt { 41 } } { 2 }$ 
C)  $\frac { 1 \pm \sqrt { 41 } } { 2 }$ 
D)  $\frac { 1 \pm \sqrt { 41 } } { 4 }$ 
E) no real solutions 
A)  $\frac { - 1 \pm \sqrt { 41 } } { 4 }$ 
B)  $\frac { - 1 \pm \sqrt { 41 } } { 2 }$ 
C)  $\frac { 1 \pm \sqrt { 41 } } { 2 }$ 
D)  $\frac { 1 \pm \sqrt { 41 } } { 4 }$ 
E) no real solutions

Question 6

Solve the quadratic equation. $( n - 9 ) ^ { 2 } = 3$ Use the following property: For any real number a , $x ^ { 2 } = a$ if and only if $x = \sqrt { a }$ or $x = - \sqrt { a }$ .

Accepted Answer

A)  $\sqrt { 3 } - 9$ , $- \sqrt { 3 } - 9$ 
B)  $\sqrt { 3 } + 9$ , $0$ 
C)  $\sqrt { 3 } + 9$ , $\sqrt { 3 } - 9$ 
D)  $18$ , $0$ 
E)  $\sqrt { 3 } + 9$ , $- \sqrt { 3 } + 9$ 
A)  $\sqrt { 3 } - 9$ , $- \sqrt { 3 } - 9$ 
B)  $\sqrt { 3 } + 9$ , $0$ 
C)  $\sqrt { 3 } + 9$ , $\sqrt { 3 } - 9$ 
D)  $18$ , $0$ 
E)  $\sqrt { 3 } + 9$ , $- \sqrt { 3 } + 9$

Question 7

Refer to the illustration. Find $\text { c }$ if $a = 4$ and $$b = 3$$ .

Accepted Answer

A) 5 
B)  $\sqrt { 12 }$ 
C)  $\sqrt { 8 }$ 
D)  $\sqrt { 7 }$ 
E) 7 
A) 5 
B)  $\sqrt { 12 }$ 
C)  $\sqrt { 8 }$ 
D)  $\sqrt { 7 }$ 
E) 7

Question 8

Use the square root method to solve the equation. $3 x ^ { 2 } = 48$

Accepted Answer

A)  $\pm 4$ 
B)  $8$ 
C)  $\pm 8$ 
D)  $- 4$ 
E)  $4$ 
A)  $\pm 4$ 
B)  $8$ 
C)  $\pm 8$ 
D)  $- 4$ 
E)  $4$

Question 9

Solve the inequality. $$x ^ { 2 } + 11 x + 30 \geq 0$$

Accepted Answer

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

Question 10

Factor the trinomial square and use the square root method to solve the equation. $3 x ^ { 2 } + 7 x + 1 = 2$

Accepted Answer

A)  $\frac { ( - 10 + \sqrt { 61 } ) } { 7 }$ , $\frac { ( - 10 - \sqrt { 61 } ) } { 7 }$ 
B)  $\frac { ( - 6 + \sqrt { 61 } ) } { 7 }$ , $\frac { ( - 6 - \sqrt { 61 } ) } { 7 }$ 
C)  $\frac { ( - 7 + \sqrt { 61 } ) } { 6 }$ , $\frac { ( - 7 - \sqrt { 61 } ) } { 6 }$ 
D)  $\frac { ( - 8 \sqrt { 61 } ) } { 7 }$ , $\frac { ( - 8 - \sqrt { 61 } ) } { 7 }$ 
A)  $\frac { ( - 10 + \sqrt { 61 } ) } { 7 }$ , $\frac { ( - 10 - \sqrt { 61 } ) } { 7 }$ 
B)  $\frac { ( - 6 + \sqrt { 61 } ) } { 7 }$ , $\frac { ( - 6 - \sqrt { 61 } ) } { 7 }$ 
C)  $\frac { ( - 7 + \sqrt { 61 } ) } { 6 }$ , $\frac { ( - 7 - \sqrt { 61 } ) } { 6 }$ 
D)  $\frac { ( - 8 \sqrt { 61 } ) } { 7 }$ , $\frac { ( - 8 - \sqrt { 61 } ) } { 7 }$

Question 11

Solve the inequality. $\frac { 5 x - 2 } { x } \geq 0$

Accepted Answer

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

Question 12

When a wholesaler sells $n$ CD players, the revenue is $R = 130 n - \frac { 1 } { 2 } n ^ { 2 }$ . How many CD players would the wholesaler have to sell to receive $\$ 8,450$ ?

Accepted Answer

A)  $100$ CD players 
B)  $90$ CD players 
C)  $130$ CD players 
D)  $150$ CD players 
E)  $140$ CD players 
A)  $100$ CD players 
B)  $90$ CD players 
C)  $130$ CD players 
D)  $150$ CD players 
E)  $140$ CD players

Question 13

Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation. $$4 y ^ { 2 } + y + 5 = 0$$

Accepted Answer

A) rational, equal 
B) irrational, unequal 
C) irrational, equal 
D) nonreal complex numbers, complex conjugates 
E) rational, unequal 
A) rational, equal 
B) irrational, unequal 
C) irrational, equal 
D) nonreal complex numbers, complex conjugates 
E) rational, unequal

Question 14

Use the square root method to solve the equation. $x ^ { 2 } = 16$

Accepted Answer

A)  $\pm 4$ 
B)  $1$ 
C)  $4$ 
D)  $- 1$ 
E)  $- 4$ 
A)  $\pm 4$ 
B)  $1$ 
C)  $4$ 
D)  $- 1$ 
E)  $- 4$

Question 15

Solve the equation by completing the square. $x ^ { 2 } - 4 x - 5 = 0$

Accepted Answer

A)  $x = - 2$ , $x = 5$ 
B)  $x = 4$ , $x = 5$ 
C)  $x = 1$ , $x = 5$ 
D)  $x = - 1$ , $x = 5$ 
E)  $x = - 10$ , $x = 2$ 
A)  $x = - 2$ , $x = 5$ 
B)  $x = 4$ , $x = 5$ 
C)  $x = 1$ , $x = 5$ 
D)  $x = - 1$ , $x = 5$ 
E)  $x = - 10$ , $x = 2$

Question 16

Solve the equation by completing the square. $4 x ^ { 2 } = 20 - 32 x$

Accepted Answer

A)  $x = 32$ , $x = - \sqrt { 6 }$ 
B)  $x = - 4 \pm \sqrt { 21 }$ 
C)  $x = 6 \pm \sqrt { 6 }$ 
D)  $x = 4 \pm \sqrt { 21 }$ 
E)  $x = 4$ , $x = - 4$ 
A)  $x = 32$ , $x = - \sqrt { 6 }$ 
B)  $x = - 4 \pm \sqrt { 21 }$ 
C)  $x = 6 \pm \sqrt { 6 }$ 
D)  $x = 4 \pm \sqrt { 21 }$ 
E)  $x = 4$ , $x = - 4$

Question 17

Solve the equation. $6 ( x + 1 ) ^ { 2 } = ( x + 1 ) ^ { 2 } + 40$

Accepted Answer

A)  $1 \pm 2 \sqrt { 2 } ( - 1.8,3.8 )$ 
B)  $- 1 + 2 \sqrt { 2 } ( 1.8 )$ 
C)  $1 - 2 \sqrt { 2 } ( 3.8 )$ 
D)  $- 1 \pm 2 \sqrt { 2 } ( - 3.8,1.8 )$ 
E)  $- 1 - 2 \sqrt { 2 } ( - 3.8 )$ 
A)  $1 \pm 2 \sqrt { 2 } ( - 1.8,3.8 )$ 
B)  $- 1 + 2 \sqrt { 2 } ( 1.8 )$ 
C)  $1 - 2 \sqrt { 2 } ( 3.8 )$ 
D)  $- 1 \pm 2 \sqrt { 2 } ( - 3.8,1.8 )$ 
E)  $- 1 - 2 \sqrt { 2 } ( - 3.8 )$

Question 18

Write $\sqrt { - 4 }$ in terms of i and simplify.

Accepted Answer

A) 7 
B) 7+ i 
C) 7 i 
D) -7 i 
E) -7 
A) 7 
B) 7+ i 
C) 7 i 
D) -7 i 
E) -7

Question 19

Solve the inequality. $\frac { x + 5 } { x - 9 } > 0$

Accepted Answer

A)  $x \in ( - \infty , 5 ) \cup ( 9 , \infty )$ 
B)  $x \in ( - \infty , - 9 ] \cup [ 5 , \infty )$ 
C)  $x \in ( - \infty , - 5 ) \cup ( 9 , \infty )$ 
D)  $x \in ( - \infty , - 5 ] \cup [ 9 , \infty )$ 
E)  $x \in ( - \infty , 5 ] \cup [ 9 , \infty )$ 
A)  $x \in ( - \infty , 5 ) \cup ( 9 , \infty )$ 
B)  $x \in ( - \infty , - 9 ] \cup [ 5 , \infty )$ 
C)  $x \in ( - \infty , - 5 ) \cup ( 9 , \infty )$ 
D)  $x \in ( - \infty , - 5 ] \cup [ 9 , \infty )$ 
E)  $x \in ( - \infty , 5 ] \cup [ 9 , \infty )$

Question 20

Simplify the expression. Enter the answer in a + bi form. $( 6 + \sqrt { - 272 } ) + ( - 2 - \sqrt { - 17 } )$

Accepted Answer

A)  $4 + 3 \sqrt { 17 i }$ 
B)  $$4 - 3 \sqrt { 17 i }$$ 
C)  $( 4 - 3 \sqrt { 17 } ) i$ 
D)  $( 4 + 3 \sqrt { 17 } ) i$ 
A)  $4 + 3 \sqrt { 17 i }$ 
B)  $$4 - 3 \sqrt { 17 i }$$ 
C)  $( 4 - 3 \sqrt { 17 } ) i$ 
D)  $( 4 + 3 \sqrt { 17 } ) i$

The distance (in feet)that an object will fall in $t$ seconds is given by the formula $s = 16 t ^ { 2 }$ . How long will it take an object to fall 576 feet?

Write $\sqrt { 5 } \sqrt { - 49 }$ in terms of i , perform the indicated operations, and simplify.

Solve the inequality. $\frac { x - 1 } { x - 5 } \leq 3$

Solve the equation. $10 ( m + 3 ) ^ { - 2 } - 29 ( m + 3 ) ^ { - 1 } + 9 = 0$

Use the quadratic formula to find all real solutions of the equation. $2 x ^ { 2 } + x = 5$

Solve the quadratic equation. $( n - 9 ) ^ { 2 } = 3$ Use the following property: For any real number a , $x ^ { 2 } = a$ if and only if $x = \sqrt { a }$ or $x = - \sqrt { a }$ .

Refer to the illustration. Find $\text { c }$ if $a = 4$ and $b = 3$ . $Refer to the illustration. Find \text { c } if a = 4 and b = 3 .$

Use the square root method to solve the equation. $3 x ^ { 2 } = 48$

Solve the inequality. $x ^ { 2 } + 11 x + 30 \geq 0$

Factor the trinomial square and use the square root method to solve the equation. $3 x ^ { 2 } + 7 x + 1 = 2$

Solve the inequality. $\frac { 5 x - 2 } { x } \geq 0$

When a wholesaler sells $n$ CD players, the revenue is $R = 130 n - \frac { 1 } { 2 } n ^ { 2 }$ . How many CD players would the wholesaler have to sell to receive $\$ 8,450$ ?

Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation. $4 y ^ { 2 } + y + 5 = 0$

Use the square root method to solve the equation. $x ^ { 2 } = 16$

Solve the equation by completing the square. $x ^ { 2 } - 4 x - 5 = 0$

Solve the equation by completing the square. $4 x ^ { 2 } = 20 - 32 x$

Solve the equation. $6 ( x + 1 ) ^ { 2 } = ( x + 1 ) ^ { 2 } + 40$

Write $\sqrt { - 4 }$ in terms of i and simplify.

Solve the inequality. $\frac { x + 5 } { x - 9 } > 0$

Simplify the expression. Enter the answer in a + bi form. $( 6 + \sqrt { - 272 } ) + ( - 2 - \sqrt { - 17 } )$

Basic Concepts and Properties

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Exam 6: Quadratic Equations and Inequalities

The distance (in feet)that an object will fall in ttt seconds is given by the formula s=16t2s = 16 t ^ { 2 }s=16t2 . How long will it take an object to fall 576 feet?

Write 5−49\sqrt { 5 } \sqrt { - 49 }5​−49​ in terms of i , perform the indicated operations, and simplify.

Solve the inequality. x−1x−5≤3\frac { x - 1 } { x - 5 } \leq 3x−5x−1​≤3

Solve the equation. 10(m+3)−2−29(m+3)−1+9=010 ( m + 3 ) ^ { - 2 } - 29 ( m + 3 ) ^ { - 1 } + 9 = 010(m+3)−2−29(m+3)−1+9=0

Use the quadratic formula to find all real solutions of the equation. 2x2+x=52 x ^ { 2 } + x = 52x2+x=5

Solve the quadratic equation. (n−9)2=3( n - 9 ) ^ { 2 } = 3(n−9)2=3 Use the following property: For any real number a , x2=ax ^ { 2 } = ax2=a if and only if x=ax = \sqrt { a }x=a​ or x=−ax = - \sqrt { a }x=−a​ .

Refer to the illustration. Find c \text { c } c if a=4a = 4a=4 and b=3b = 3b=3 .

Use the square root method to solve the equation. 3x2=483 x ^ { 2 } = 483x2=48

Solve the inequality. x2+11x+30≥0x ^ { 2 } + 11 x + 30 \geq 0x2+11x+30≥0

Factor the trinomial square and use the square root method to solve the equation. 3x2+7x+1=23 x ^ { 2 } + 7 x + 1 = 23x2+7x+1=2

Solve the inequality. 5x−2x≥0\frac { 5 x - 2 } { x } \geq 0x5x−2​≥0

When a wholesaler sells nnn CD players, the revenue is R=130n−12n2R = 130 n - \frac { 1 } { 2 } n ^ { 2 }R=130n−21​n2 . How many CD players would the wholesaler have to sell to receive $8,450\$ 8,450$8,450 ?

Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation. 4y2+y+5=04 y ^ { 2 } + y + 5 = 04y2+y+5=0

Use the square root method to solve the equation. x2=16x ^ { 2 } = 16x2=16

Solve the equation by completing the square. x2−4x−5=0x ^ { 2 } - 4 x - 5 = 0x2−4x−5=0

Solve the equation by completing the square. 4x2=20−32x4 x ^ { 2 } = 20 - 32 x4x2=20−32x

Solve the equation. 6(x+1)2=(x+1)2+406 ( x + 1 ) ^ { 2 } = ( x + 1 ) ^ { 2 } + 406(x+1)2=(x+1)2+40

Write −4\sqrt { - 4 }−4​ in terms of i and simplify.

Solve the inequality. x+5x−9>0\frac { x + 5 } { x - 9 } > 0x−9x+5​>0

Simplify the expression. Enter the answer in a + bi form. (6+−272)+(−2−−17)( 6 + \sqrt { - 272 } ) + ( - 2 - \sqrt { - 17 } )(6+−272​)+(−2−−17​)

Basic Concepts and Properties

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The distance (in feet)that an object will fall in $t$ seconds is given by the formula $s = 16 t ^ { 2 }$ . How long will it take an object to fall 576 feet?

Write $\sqrt { 5 } \sqrt { - 49 }$ in terms of i , perform the indicated operations, and simplify.

Solve the inequality. $\frac { x - 1 } { x - 5 } \leq 3$

Solve the equation. $10 ( m + 3 ) ^ { - 2 } - 29 ( m + 3 ) ^ { - 1 } + 9 = 0$

Use the quadratic formula to find all real solutions of the equation. $2 x ^ { 2 } + x = 5$

Solve the quadratic equation. $( n - 9 ) ^ { 2 } = 3$ Use the following property: For any real number a , $x ^ { 2 } = a$ if and only if $x = \sqrt { a }$ or $x = - \sqrt { a }$ .

Refer to the illustration. Find $\text { c }$ if $a = 4$ and $b = 3$ . $Refer to the illustration. Find \text { c } if a = 4 and b = 3 .$

Use the square root method to solve the equation. $3 x ^ { 2 } = 48$

Solve the inequality. $x ^ { 2 } + 11 x + 30 \geq 0$

Factor the trinomial square and use the square root method to solve the equation. $3 x ^ { 2 } + 7 x + 1 = 2$

Solve the inequality. $\frac { 5 x - 2 } { x } \geq 0$

When a wholesaler sells $n$ CD players, the revenue is $R = 130 n - \frac { 1 } { 2 } n ^ { 2 }$ . How many CD players would the wholesaler have to sell to receive $\$ 8,450$ ?

Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation. $4 y ^ { 2 } + y + 5 = 0$

Use the square root method to solve the equation. $x ^ { 2 } = 16$

Solve the equation by completing the square. $x ^ { 2 } - 4 x - 5 = 0$

Solve the equation by completing the square. $4 x ^ { 2 } = 20 - 32 x$

Solve the equation. $6 ( x + 1 ) ^ { 2 } = ( x + 1 ) ^ { 2 } + 40$

Write $\sqrt { - 4 }$ in terms of i and simplify.

Solve the inequality. $\frac { x + 5 } { x - 9 } > 0$

Simplify the expression. Enter the answer in a + bi form. $( 6 + \sqrt { - 272 } ) + ( - 2 - \sqrt { - 17 } )$