Question 1

Simplify. Write your answers in the form of a+bi, where a and b are real numbers.
-$$\frac { 1 - i } { - 9 + 6 i }$$

Accepted Answer

A)  $\frac { 5 } { 39 } + \frac { 1 } { 39 } \mathrm { i }$ 
B)  $\frac { 1 } { 39 } \mathrm { i }$ 
C)  $\frac { 1 } { 117 } + \frac { 1 } { 39 } \mathrm { i }$ 
D)  $- \frac { 5 } { 39 } + \frac { 1 } { 39 } \mathrm { i }$ 
A)  $\frac { 5 } { 39 } + \frac { 1 } { 39 } \mathrm { i }$ 
B)  $\frac { 1 } { 39 } \mathrm { i }$ 
C)  $\frac { 1 } { 117 } + \frac { 1 } { 39 } \mathrm { i }$ 
D)  $- \frac { 5 } { 39 } + \frac { 1 } { 39 } \mathrm { i }$

Question 2

Solve the problem.
-A ladder is resting against a wall. The top of the ladder touches the wall at a height of 12 ft. Find the length of the ladder if the length is 4 ft more than its distance from the wall.

Accepted Answer

A) 20 ft 
B) 24 ft 
C) 16 ft 
D) 12 ft 
A) 20 ft 
B) 24 ft 
C) 16 ft 
D) 12 ft

Question 3

Find the intervals on which the function is increasing and the intervals on which the function is decreasing.
-$$f ( x ) = - 2 x ^ { 2 } + 3 x + 1$$

Accepted Answer

A)  Increasing on $( - \infty , 1 )$; decreasing on $( - 1 , \infty )$ 
B)  Increasing on $( - \infty , 0 )$; decreasing on $( 0 , \infty )$ 
C)  Increasing on $\left( - \infty , \frac { 3 } { 4 } \right)$; decreasing on $\left( \frac { 3 } { 4 } , \infty \right)$ 
D)  Increasing on $\left( - \infty , \frac { 3 } { 8 } \right)$; decreasing on $\left( \frac { 3 } { 8 } , \infty \right)$ 
A)  Increasing on $( - \infty , 1 )$; decreasing on $( - 1 , \infty )$ 
B)  Increasing on $( - \infty , 0 )$; decreasing on $( 0 , \infty )$ 
C)  Increasing on $\left( - \infty , \frac { 3 } { 4 } \right)$; decreasing on $\left( \frac { 3 } { 4 } , \infty \right)$ 
D)  Increasing on $\left( - \infty , \frac { 3 } { 8 } \right)$; decreasing on $\left( \frac { 3 } { 8 } , \infty \right)$

Question 4

Find the zeros of the function. Give exact answers.
-$$f ( x ) = x ^ { 2 } - 5 x + 1$$

Accepted Answer

A)  $\frac { 5 \pm \sqrt { 21 } } { 2 }$ 
B)  $\frac { 5 \pm \sqrt { 29 } } { 2 }$ 
C)  $\frac { - 5 \pm \sqrt { 21 } \mathrm { i } } { 2 }$ 
D)  $\frac { 5 \pm \sqrt { 29 } \mathrm { i } } { 2 }$ 
A)  $\frac { 5 \pm \sqrt { 21 } } { 2 }$ 
B)  $\frac { 5 \pm \sqrt { 29 } } { 2 }$ 
C)  $\frac { - 5 \pm \sqrt { 21 } \mathrm { i } } { 2 }$ 
D)  $\frac { 5 \pm \sqrt { 29 } \mathrm { i } } { 2 }$

Question 5

Solve.
-$z ^ { 4 } - 11 z ^ { 2 } + 30 = 0$

Accepted Answer

A)  $\sqrt { 5 } , \sqrt { 6 }$ 
B)  $\sqrt { - 5 } , \sqrt { - 6 }$ 
C)  $\sqrt { - 5 } , \sqrt { 6 }$ 
D)  $\pm \sqrt { 5 } , \pm \sqrt { 6 }$ 
A)  $\sqrt { 5 } , \sqrt { 6 }$ 
B)  $\sqrt { - 5 } , \sqrt { - 6 }$ 
C)  $\sqrt { - 5 } , \sqrt { 6 }$ 
D)  $\pm \sqrt { 5 } , \pm \sqrt { 6 }$

Question 6

Simplify. Write your answers in the form of a+bi, where a and b are real numbers.
-$\frac { i } { 5 + i }$

Accepted Answer

A)  $\frac { 5 } { 26 } \mathrm { i }$ 
B)  $\frac { 1 } { 26 } + \frac { 5 } { 26 } \mathrm { i }$ 
C)  $\frac { 1 } { 26 } - \frac { 5 } { 26 } \mathrm { i }$ 
D)  $\frac { 1 } { 26 }$ 
A)  $\frac { 5 } { 26 } \mathrm { i }$ 
B)  $\frac { 1 } { 26 } + \frac { 5 } { 26 } \mathrm { i }$ 
C)  $\frac { 1 } { 26 } - \frac { 5 } { 26 } \mathrm { i }$ 
D)  $\frac { 1 } { 26 }$

Question 7

Solve.
-$\sqrt { 2 x + 3 } + \sqrt { 4 - x } = 4$

Accepted Answer

A)  $- 3$ 
B)  $3 , \frac { 11 } { 9 }$ 
C)  3 
D)  No solution 
A)  $- 3$ 
B)  $3 , \frac { 11 } { 9 }$ 
C)  3 
D)  No solution

Question 8

Simplify. Write your answers in the form of a+bi, where a and b are real numbers.
-$$( 3 + 3 i ) ( 3 - 3 i )$$

Accepted Answer

A)  $9 - 9 \mathrm { i }$ 
B)  $9 + 9 \mathrm { i }$ 
C)  0 
D)  18 
A)  $9 - 9 \mathrm { i }$ 
B)  $9 + 9 \mathrm { i }$ 
C)  0 
D)  18

Question 9

Simplify.
-$( - i ) ^ { 42 }$

Accepted Answer

A)  1 
B)  $- 1$ 
C)  $- \mathrm { i }$ 
D)  $\mathrm { i }$ 
A)  1 
B)  $- 1$ 
C)  $- \mathrm { i }$ 
D)  $\mathrm { i }$

Simplify. Write your answers in the form of a+bi, where a and b are real numbers. - $\frac { 1 - i } { - 9 + 6 i }$

Solve the problem. -A ladder is resting against a wall. The top of the ladder touches the wall at a height of 12 ft. Find the length of the ladder if the length is 4 ft more than its distance from the wall.

Find the intervals on which the function is increasing and the intervals on which the function is decreasing. - $f ( x ) = - 2 x ^ { 2 } + 3 x + 1$

Find the zeros of the function. Give exact answers. - $f ( x ) = x ^ { 2 } - 5 x + 1$

Solve. - $z ^ { 4 } - 11 z ^ { 2 } + 30 = 0$

Simplify. Write your answers in the form of a+bi, where a and b are real numbers. - $\frac { i } { 5 + i }$

Solve. - $\sqrt { 2 x + 3 } + \sqrt { 4 - x } = 4$

Simplify. Write your answers in the form of a+bi, where a and b are real numbers. - $( 3 + 3 i ) ( 3 - 3 i )$

Simplify. - $( - i ) ^ { 42 }$

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Exam 3: Quadratic Functions and Equations; Inequalities

Simplify. Write your answers in the form of a+bi, where a and b are real numbers. - 1−i−9+6i\frac { 1 - i } { - 9 + 6 i }−9+6i1−i​