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)  $- \frac { 5 } { 39 } + \frac { 1 } { 39 } \mathrm { i }$

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

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 $\left( \frac { 3 } { 8 } , \infty \right)$

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)  $\frac { 5 \pm \sqrt { 29 } \mathrm { i } } { 2 }$

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)  $\pm \sqrt { 5 } , \pm \sqrt { 6 }$

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)  $\frac { 1 } { 26 }$

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

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

Question 9

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

Accepted Answer

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

Exam 3: Quadratic Functions and Equations; Inequalities

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

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​

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) =−2x2+3x+1f ( x ) = - 2 x ^ { 2 } + 3 x + 1f(x) =−2x2+3x+1

Find the zeros of the function. Give exact answers. - f(x) =x2−5x+1f ( x ) = x ^ { 2 } - 5 x + 1f(x) =x2−5x+1

Solve. - z4−11z2+30=0z ^ { 4 } - 11 z ^ { 2 } + 30 = 0z4−11z2+30=0

Simplify. Write your answers in the form of a+bi, where a and b are real numbers. - i5+i\frac { i } { 5 + i }5+ii​

Solve. - 2x+3+4−x=4\sqrt { 2 x + 3 } + \sqrt { 4 - x } = 42x+3​+4−x​=4

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

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