Question 1

Write $\frac { \sqrt { - 96 } } { \sqrt { - 6 } }$ in terms of i , perform the indicated operations, and simplify.

Accepted Answer

A) 8 i 
B) -8 i 
C) -8 
D) 8 
E) 8 + i 
A) 8 i 
B) -8 i 
C) -8 
D) 8 
E) 8 + i D

Question 2

Factor the trinomial square and use the square root method to solve the equation. $x ^ { 2 } - 7 x + 5 = 5$

Accepted Answer

A)  $0$ 
B)  $\pm 7$ 
C)  $0 , - 7$ 
D)  $0,7$ 
E)  $7$ 
A)  $0$ 
B)  $\pm 7$ 
C)  $0 , - 7$ 
D)  $0,7$ 
E)  $7$ D

Question 3

Solve the inequality. $x ^ { 2 } + 8 x < - 16$

Accepted Answer

A)  $x \in ( - 4,4 )$ 
B)  $x \in ( - \infty , - 4 )$ 
C)  $x \in ( 4 , \infty )$ 
D)  $x \in ( - \infty , \infty )$ 
E) no solution 
A)  $x \in ( - 4,4 )$ 
B)  $x \in ( - \infty , - 4 )$ 
C)  $x \in ( 4 , \infty )$ 
D)  $x \in ( - \infty , \infty )$ 
E) no solution E

Question 4

Write $\sqrt { - \frac { 25 } { 4 } }$ in terms of i and simplify.

Accepted Answer

A)  $\frac { 5 } { 2 }$ 
B)  $- \frac { 5 } { 2 } + i$ 
C)  $\frac { 5 } { 2 } + i$ 
D)  $- \frac { 5 i } { 2 }$ 
E)  $\frac { 5 i } { 2 }$ 
A)  $\frac { 5 } { 2 }$ 
B)  $- \frac { 5 } { 2 } + i$ 
C)  $\frac { 5 } { 2 } + i$ 
D)  $- \frac { 5 i } { 2 }$ 
E)  $\frac { 5 i } { 2 }$

Question 5

Perform the operation. Write the answer in $a + b i$ form. $( 9 - 4 i ) - ( 3 + 6 i )$

Accepted Answer

A)  $6 + 10 i$ 
B)  $6 - 10 i$ 
C)  $6 i - 10$ 
D)  $6 i + 10$ 
A)  $6 + 10 i$ 
B)  $6 - 10 i$ 
C)  $6 i - 10$ 
D)  $6 i + 10$

Question 6

The height in feet $h$ of a rocket in flight is given by the formula $h = - 16 t ^ { 2 } + 224 t$ , where $t$ is the time of the flight in seconds. How long will it take for the rocket to hit the ground?

Accepted Answer

A) 13 sec 
B) 14 sec 
C) 16 sec 
D) 12 sec 
E) 11 sec 
A) 13 sec 
B) 14 sec 
C) 16 sec 
D) 12 sec 
E) 11 sec

Question 7

$| a + b i | =$ __________

Accepted Answer

A)  $a + b$ 
B)  $\sqrt { a + b }$ 
C)  $\sqrt { a ^ { 2 } - b ^ { 2 } }$ 
D)  $\sqrt { a - b }$ 
E)  $\sqrt { a ^ { 2 } + b ^ { 2 } }$ 
A)  $a + b$ 
B)  $\sqrt { a + b }$ 
C)  $\sqrt { a ^ { 2 } - b ^ { 2 } }$ 
D)  $\sqrt { a - b }$ 
E)  $\sqrt { a ^ { 2 } + b ^ { 2 } }$

Question 8

For this problem, use the triangle in the figure below. Express your two answers in simplest radical form.   If a = 8 ft, find b and c .

Accepted Answer

A)  $b = 3 \sqrt { 3 } \mathrm { ft } , c = 6 \sqrt { 3 } \mathrm { ft }$ 
B)  $b = 3 \mathrm { ft } , c = 6 \sqrt { 3 } \mathrm { ft }$ 
C)  $b = 3 \sqrt { 3 } \mathrm { ft } , c = 3 \sqrt { 3 } \mathrm { ft }$ 
D)  $b = 6 \mathrm { ft } , c = 6 \mathrm { ft }$ 
E)  $b = 3 \sqrt { 3 } \mathrm { ft } , c = 6 \mathrm { ft }$ 
A)  $b = 3 \sqrt { 3 } \mathrm { ft } , c = 6 \sqrt { 3 } \mathrm { ft }$ 
B)  $b = 3 \mathrm { ft } , c = 6 \sqrt { 3 } \mathrm { ft }$ 
C)  $b = 3 \sqrt { 3 } \mathrm { ft } , c = 3 \sqrt { 3 } \mathrm { ft }$ 
D)  $b = 6 \mathrm { ft } , c = 6 \mathrm { ft }$ 
E)  $b = 3 \sqrt { 3 } \mathrm { ft } , c = 6 \mathrm { ft }$

Question 9

Use the factoring method to solve the equation. $6 x ^ { 2 } + 11 x + 3 = 0$

Accepted Answer

A)  $- \frac { 3 } { 2 }$ , $- \frac { 1 } { 3 }$ 
B)  $\frac { 1 } { 3 }$ , $\frac { 3 } { 2 }$ 
C)  $- \frac { 1 } { 3 }$ , $\frac { 3 } { 2 }$ 
D)  $- \frac { 3 } { 2 }$ , $\frac { 3 } { 2 }$ 
E)  $- \frac { 3 } { 2 }$ , $\frac { 1 } { 3 }$ 
A)  $- \frac { 3 } { 2 }$ , $- \frac { 1 } { 3 }$ 
B)  $\frac { 1 } { 3 }$ , $\frac { 3 } { 2 }$ 
C)  $- \frac { 1 } { 3 }$ , $\frac { 3 } { 2 }$ 
D)  $- \frac { 3 } { 2 }$ , $\frac { 3 } { 2 }$ 
E)  $- \frac { 3 } { 2 }$ , $\frac { 1 } { 3 }$

Question 10

Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation. $$5 z ^ { 2 } + 6 z - 3 = 0$$

Accepted Answer

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

Question 11

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

Accepted Answer

A)  $x = 5$ , $x = 10$ 
B)  $x = 4$ , $x = 8$ 
C)  $x = - 8$ , $x = 4$ 
D)  $x = - 10$ , $x = 4$ 
E)  $x = 0$ , $x = 3$ 
A)  $x = 5$ , $x = 10$ 
B)  $x = 4$ , $x = 8$ 
C)  $x = - 8$ , $x = 4$ 
D)  $x = - 10$ , $x = 4$ 
E)  $x = 0$ , $x = 3$

Question 12

Refer to the illustration. Find $b$ if $a = 8$ and $c = 10$ .

Accepted Answer

A) 2 
B)  $\sqrt { 11 }$ 
C)  $\sqrt { 8 }$ 
D) 6 
E)  $\sqrt { 164 }$ 
A) 2 
B)  $\sqrt { 11 }$ 
C)  $\sqrt { 8 }$ 
D) 6 
E)  $\sqrt { 164 }$

Question 13

$a + b i$ and $a - b i$ are called complex __________.

Accepted Answer

A) part 
B) conjugates 
C) line 
A) part 
B) conjugates 
C) line

Question 14

Solve the equation. $z - 5 + \frac { 6 } { z } = 0$

Accepted Answer

A)  $$z = - 2 , - 3$$ 
B)  $z = 1 , - 5$ 
C)  $z = - 2,3$ 
D)  $z = 2,3$ 
E)  $z = 2 , - 3$ 
A)  $$z = - 2 , - 3$$ 
B)  $z = 1 , - 5$ 
C)  $z = - 2,3$ 
D)  $z = 2,3$ 
E)  $z = 2 , - 3$

Question 15

Simplify the expression. Enter the answer in a + bi form. $( - 5 + \sqrt { - 15 } ) ( 1 - \sqrt { - 15 } )$

Accepted Answer

A)  $10 - 6 \sqrt { 15 i }$ 
B)  $10 + 6 \sqrt { 15 i }$ 
C)  $- 20 + 6 \sqrt { 15 i }$ 
D)  $- 20 - 6 \sqrt { 15 } i$ 
A)  $10 - 6 \sqrt { 15 i }$ 
B)  $10 + 6 \sqrt { 15 i }$ 
C)  $- 20 + 6 \sqrt { 15 i }$ 
D)  $- 20 - 6 \sqrt { 15 } i$

Question 16

Write the expression in a + bi form. $\frac { 2 i } { 6 + i }$

Accepted Answer

A)  $\frac { 2 } { 37 } + \frac { 12 } { 37 } i$ 
B)  $\frac { 37 } { 2 } - \frac { 37 } { 12 } i$ 
C)  $\frac { 12 } { 37 } - \frac { 2 } { 37 } i$ 
D)  $\frac { 37 } { 12 } - \frac { 37 } { 2 } i$ 
A)  $\frac { 2 } { 37 } + \frac { 12 } { 37 } i$ 
B)  $\frac { 37 } { 2 } - \frac { 37 } { 12 } i$ 
C)  $\frac { 12 } { 37 } - \frac { 2 } { 37 } i$ 
D)  $\frac { 37 } { 12 } - \frac { 37 } { 2 } i$

Question 17

Write $\sqrt { - 49 } \sqrt { - 9 }$ in terms of i , perform the indicated operations, and simplify.

Accepted Answer

A) 28 
B) -28 
C) -28 i 
D) 28 + i 
E) 28 i 
A) 28 
B) -28 
C) -28 i 
D) 28 + i 
E) 28 i

Question 18

Simplify the expression. Enter the answer in a + bi form. $( 5 + i ) ( 2 - 3 i )$

Accepted Answer

A)  $7 + 13 i$ 
B)  $13 - 13 i$ 
C)  $13 + 13 i$ 
D)  $7 - 13 i$ 
A)  $7 + 13 i$ 
B)  $13 - 13 i$ 
C)  $13 + 13 i$ 
D)  $7 - 13 i$

Question 19

The complex conjugate of $3 - 4 i$ is _________.

Accepted Answer

The complex conjugate of a com

Question 20

Write the expression in a + bi form. $\frac { 6 - 5 i } { 6 + 5 i }$

Accepted Answer

A)  $\frac { 11 } { 61 } - \frac { 60 } { 61 } i$ 
B)  $\frac { 11 } { 61 } - \frac { 61 } { 60 } i$ 
C)  $\frac { 61 } { 11 } - \frac { 60 } { 61 } i$ 
D)  $\frac { 60 } { 61 } - \frac { 11 } { 61 } i$ 
A)  $\frac { 11 } { 61 } - \frac { 60 } { 61 } i$ 
B)  $\frac { 11 } { 61 } - \frac { 61 } { 60 } i$ 
C)  $\frac { 61 } { 11 } - \frac { 60 } { 61 } i$ 
D)  $\frac { 60 } { 61 } - \frac { 11 } { 61 } i$

Write $\frac { \sqrt { - 96 } } { \sqrt { - 6 } }$ in terms of i , perform the indicated operations, and simplify.

Factor the trinomial square and use the square root method to solve the equation. $x ^ { 2 } - 7 x + 5 = 5$

Solve the inequality. $x ^ { 2 } + 8 x < - 16$

Write $\sqrt { - \frac { 25 } { 4 } }$ in terms of i and simplify.

Perform the operation. Write the answer in $a + b i$ form. $( 9 - 4 i ) - ( 3 + 6 i )$

The height in feet $h$ of a rocket in flight is given by the formula $h = - 16 t ^ { 2 } + 224 t$ , where $t$ is the time of the flight in seconds. How long will it take for the rocket to hit the ground?

$| a + b i | =$ __________

For this problem, use the triangle in the figure below. Express your two answers in simplest radical form. If a = 8 ft, find b and c .

Use the factoring method to solve the equation. $6 x ^ { 2 } + 11 x + 3 = 0$

Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation. $5 z ^ { 2 } + 6 z - 3 = 0$

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

Refer to the illustration. Find $b$ if $a = 8$ and $c = 10$ .

$a + b i$ and $a - b i$ are called complex __________.

Solve the equation. $z - 5 + \frac { 6 } { z } = 0$

Simplify the expression. Enter the answer in a + bi form. $( - 5 + \sqrt { - 15 } ) ( 1 - \sqrt { - 15 } )$

Write the expression in a + bi form. $\frac { 2 i } { 6 + i }$

Write $\sqrt { - 49 } \sqrt { - 9 }$ in terms of i , perform the indicated operations, and simplify.

Simplify the expression. Enter the answer in a + bi form. $( 5 + i ) ( 2 - 3 i )$

The complex conjugate of $3 - 4 i$ is _________.

Write the expression in a + bi form. $\frac { 6 - 5 i } { 6 + 5 i }$

Basic Concepts and Properties

Equations, Inequalities, and Problem Solving

Polynomials

Rational Expressions

Exponents and Radicals

Equations and Inequalities in Two Variables

Conic Sections

Functions

Systems of Equations

Exponential and Logarithmic Functions

Filters

Exam 6: Quadratic Equations and Inequalities

Write −96−6\frac { \sqrt { - 96 } } { \sqrt { - 6 } }−6​−96​​ in terms of i , perform the indicated operations, and simplify.

Factor the trinomial square and use the square root method to solve the equation. x2−7x+5=5x ^ { 2 } - 7 x + 5 = 5x2−7x+5=5

Solve the inequality. x2+8x<−16x ^ { 2 } + 8 x < - 16x2+8x<−16

Write −254\sqrt { - \frac { 25 } { 4 } }−425​​ in terms of i and simplify.

Perform the operation. Write the answer in a+bia + b ia+bi form. (9−4i)−(3+6i)( 9 - 4 i ) - ( 3 + 6 i )(9−4i)−(3+6i)

The height in feet hhh of a rocket in flight is given by the formula h=−16t2+224th = - 16 t ^ { 2 } + 224 th=−16t2+224t , where ttt is the time of the flight in seconds. How long will it take for the rocket to hit the ground?

∣a+bi∣=| a + b i | =∣a+bi∣= __________

For this problem, use the triangle in the figure below. Express your two answers in simplest radical form. If a = 8 ft, find b and c .

Use the factoring method to solve the equation. 6x2+11x+3=06 x ^ { 2 } + 11 x + 3 = 06x2+11x+3=0

Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation. 5z2+6z−3=05 z ^ { 2 } + 6 z - 3 = 05z2+6z−3=0

Solve the equation by completing the square. x2=32−4xx ^ { 2 } = 32 - 4 xx2=32−4x

Refer to the illustration. Find bbb if a=8a = 8a=8 and c=10c = 10c=10 .

a+bia + b ia+bi and a−bia - b ia−bi are called complex __________.

Solve the equation. z−5+6z=0z - 5 + \frac { 6 } { z } = 0z−5+z6​=0

Simplify the expression. Enter the answer in a + bi form. (−5+−15)(1−−15)( - 5 + \sqrt { - 15 } ) ( 1 - \sqrt { - 15 } )(−5+−15​)(1−−15​)

Write the expression in a + bi form. 2i6+i\frac { 2 i } { 6 + i }6+i2i​

Write −49−9\sqrt { - 49 } \sqrt { - 9 }−49​−9​ in terms of i , perform the indicated operations, and simplify.

Simplify the expression. Enter the answer in a + bi form. (5+i)(2−3i)( 5 + i ) ( 2 - 3 i )(5+i)(2−3i)

The complex conjugate of 3−4i3 - 4 i3−4i is _________.

Write the expression in a + bi form. 6−5i6+5i\frac { 6 - 5 i } { 6 + 5 i }6+5i6−5i​

Basic Concepts and Properties

Equations, Inequalities, and Problem Solving

Polynomials

Rational Expressions

Exponents and Radicals

Equations and Inequalities in Two Variables

Conic Sections

Functions

Systems of Equations

Exponential and Logarithmic Functions

Filters

Write $\frac { \sqrt { - 96 } } { \sqrt { - 6 } }$ in terms of i , perform the indicated operations, and simplify.

Factor the trinomial square and use the square root method to solve the equation. $x ^ { 2 } - 7 x + 5 = 5$

Solve the inequality. $x ^ { 2 } + 8 x < - 16$

Write $\sqrt { - \frac { 25 } { 4 } }$ in terms of i and simplify.

Perform the operation. Write the answer in $a + b i$ form. $( 9 - 4 i ) - ( 3 + 6 i )$

The height in feet $h$ of a rocket in flight is given by the formula $h = - 16 t ^ { 2 } + 224 t$ , where $t$ is the time of the flight in seconds. How long will it take for the rocket to hit the ground?

$| a + b i | =$ __________

Use the factoring method to solve the equation. $6 x ^ { 2 } + 11 x + 3 = 0$

Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation. $5 z ^ { 2 } + 6 z - 3 = 0$

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

Refer to the illustration. Find $b$ if $a = 8$ and $c = 10$ .

$a + b i$ and $a - b i$ are called complex __________.

Solve the equation. $z - 5 + \frac { 6 } { z } = 0$

Simplify the expression. Enter the answer in a + bi form. $( - 5 + \sqrt { - 15 } ) ( 1 - \sqrt { - 15 } )$

Write the expression in a + bi form. $\frac { 2 i } { 6 + i }$

Write $\sqrt { - 49 } \sqrt { - 9 }$ in terms of i , perform the indicated operations, and simplify.

Simplify the expression. Enter the answer in a + bi form. $( 5 + i ) ( 2 - 3 i )$

The complex conjugate of $3 - 4 i$ is _________.

Write the expression in a + bi form. $\frac { 6 - 5 i } { 6 + 5 i }$