Question 1

Solve the equation using the quadratic formula.
-$$( x + 6 ) ( x - 1 ) = 5$$

Accepted Answer

A)  $\left\{ - \frac { - 5 } { 2 } \pm \frac { i \sqrt { 69 } } { 2 } \right\}$ 
B)  $\left\{ \frac { - 5 \pm \sqrt { 69 } } { 2 } \right\}$ 
C)  $\left\{ \frac { 5 \pm \sqrt { 69 } } { 2 } \right\}$ 
D)  $\left\{ \frac { - 5 } { 2 } \pm \frac { \mathrm { i } \sqrt { 69 } } { 2 } \right\}$ 
A)  $\left\{ - \frac { - 5 } { 2 } \pm \frac { i \sqrt { 69 } } { 2 } \right\}$ 
B)  $\left\{ \frac { - 5 \pm \sqrt { 69 } } { 2 } \right\}$ 
C)  $\left\{ \frac { 5 \pm \sqrt { 69 } } { 2 } \right\}$ 
D)  $\left\{ \frac { - 5 } { 2 } \pm \frac { \mathrm { i } \sqrt { 69 } } { 2 } \right\}$

Question 2

Find the values of a, b, and c for which the quadratic equation $a x ^ { 2 } + b x + c = 0$ 0 has the given numbers as solutions. Then
use those values to write a quadratic equation.
-$- 2,9$

Accepted Answer

A)  $x ^ { 2 } + 7 x - 18 = 0$ 
B)  $x ^ { 2 } - 7 x - 18 = 0$ 
C)  $x ^ { 2 } - 18 x - 7 = 0$ 
D)  $x ^ { 2 } - 18 x + 7 = 0$ 
A)  $x ^ { 2 } + 7 x - 18 = 0$ 
B)  $x ^ { 2 } - 7 x - 18 = 0$ 
C)  $x ^ { 2 } - 18 x - 7 = 0$ 
D)  $x ^ { 2 } - 18 x + 7 = 0$

Question 3

Solve and graph the inequality. Give answer in interval notation.
-$$- 1 \leq \frac { x + 1 } { - 2 } \leq 3$$

Accepted Answer

A)  $[ - 7,1 ]$
  
B)  $( - 3,5 )$
  
C)  $[ - 5,3 ]$
  
D)  $( - 1,7 )$
  
A)  $[ - 7,1 ]$
  
B)  $( - 3,5 )$
  
C)  $[ - 5,3 ]$
  
D)  $( - 1,7 )$

Question 4

Write the number in standard form a + bi.
-$\frac { 8 - \sqrt { - 20 } } { 2 }$

Accepted Answer

A)  $4 - i \sqrt { 5 }$ 
B)  $4 - i \sqrt { 10 }$ 
C)  $4 + i \sqrt { 10 }$ 
D)  $4 - 2 i \sqrt { 5 }$ 
A)  $4 - i \sqrt { 5 }$ 
B)  $4 - i \sqrt { 10 }$ 
C)  $4 + i \sqrt { 10 }$ 
D)  $4 - 2 i \sqrt { 5 }$

Question 5

Solve the cubic equation using factoring and the quadratic formula.
-$$\mathrm { x } ^ { 2 } = - 18$$

Accepted Answer

A)  $\pm 9 \mathrm { i } \sqrt { 2 }$ 
B)  $\pm 3 i \sqrt { 2 }$ 
C)  $\pm 3 \sqrt { 2 }$ 
D)  $\pm 9 \sqrt { 2 }$ 
A)  $\pm 9 \mathrm { i } \sqrt { 2 }$ 
B)  $\pm 3 i \sqrt { 2 }$ 
C)  $\pm 3 \sqrt { 2 }$ 
D)  $\pm 9 \sqrt { 2 }$

Question 6

Graph the solution set.
-$$| 5 x + 4 | = | x + 9 |$$

Accepted Answer

A)  $\varnothing$ 
B)  $\left\{ \frac { 5 } { 4 } , - \frac { 13 } { 6 } \right\}$ 
C)  $\left\{ - \frac { 5 } { 4 } , \frac { 13 } { 6 } \right\}$ 
D)  $\left\{ \frac { 5 } { 4 } \right\}$ 
A)  $\varnothing$ 
B)  $\left\{ \frac { 5 } { 4 } , - \frac { 13 } { 6 } \right\}$ 
C)  $\left\{ - \frac { 5 } { 4 } , \frac { 13 } { 6 } \right\}$ 
D)  $\left\{ \frac { 5 } { 4 } \right\}$

Question 7

Solve the formula for the indicated variable.
-$\mathrm { A } = \mathrm { P } ( 1 + \mathrm { nr } )$, for $\mathrm { r }$

Accepted Answer

A)  $r = \frac { A } { n }$ 
B)  $r = \frac { P n } { A - P }$ 
C)  $\mathrm { r } = \frac { \mathrm { A } - \mathrm { P } } { \mathrm { Pn } }$ 
D)  $r = \frac { P - A } { P n }$ 
A)  $r = \frac { A } { n }$ 
B)  $r = \frac { P n } { A - P }$ 
C)  $\mathrm { r } = \frac { \mathrm { A } - \mathrm { P } } { \mathrm { Pn } }$ 
D)  $r = \frac { P - A } { P n }$

Question 8

Solve the equation by completing the square.
-$$x ^ { 2 } - 2 x - 24 = 0$$

Accepted Answer

A)  $\{ - 6,4 \}$ 
B)  $\{ 6 , - 4 \}$ 
C)  $\{ - 20 , - 4 \}$ 
D)  $\{ \pm 2 \mathrm { i } \sqrt { 6 } \}$ 
A)  $\{ - 6,4 \}$ 
B)  $\{ 6 , - 4 \}$ 
C)  $\{ - 20 , - 4 \}$ 
D)  $\{ \pm 2 \mathrm { i } \sqrt { 6 } \}$

Question 9

A lot is in the shape of a right triangle. The shorter leg measures 90 m. The hypotenuse is 30 m longer than the length of the longer leg. How long is the longer leg?

Accepted Answer

A)  180 m 
B)  150 m 
C)  120 m 
D)  90 m 
A)  180 m 
B)  150 m 
C)  120 m 
D)  90 m

Question 10

Find the sum or difference. Write the answer in standard form.
-$\mathrm { i } \sqrt { 5 } + 1 - ( 7 + 8 \mathrm { i } \sqrt { 5 } ) - ( 6 - \mathrm { i } \sqrt { 5 } )$

Accepted Answer

A)  $12 - 10 \mathrm { i } \sqrt { 5 }$ 
B)  $- 12 - 6 i \sqrt { 5 }$ 
C)  $- 12 + 6 i \sqrt { 5 }$ 
D)  $- 12 - 10 \mathrm { i } \sqrt { 5 }$ 
A)  $12 - 10 \mathrm { i } \sqrt { 5 }$ 
B)  $- 12 - 6 i \sqrt { 5 }$ 
C)  $- 12 + 6 i \sqrt { 5 }$ 
D)  $- 12 - 10 \mathrm { i } \sqrt { 5 }$

Question 11

Find the product. Write the answer in standard form.
-$7 \mathrm { i } ( 5 - 5 \mathrm { i } )$

Accepted Answer

A)  $35 \mathrm { i } - 35$ 
B)  $- 35 \mathrm { i } - 35 \mathrm { i } ^ { 2 }$ 
C)  $35 + 35 i$ 
D)  $35 \mathrm { i } + 35 \mathrm { i } ^ { 2 }$ 
A)  $35 \mathrm { i } - 35$ 
B)  $- 35 \mathrm { i } - 35 \mathrm { i } ^ { 2 }$ 
C)  $35 + 35 i$ 
D)  $35 \mathrm { i } + 35 \mathrm { i } ^ { 2 }$

Question 12

Decide whether or not the equations are equivalent.
-$\begin{array} { l } 
x = 4 - 3 x \
2 x = 4
\end{array}$

Accepted Answer

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

Question 13

Graph the solution set.
-$$| 2 x - 6 | = | x + 8 |$$

Accepted Answer

A)  $\left\{ 14 , - \frac { 2 } { 3 } \right\}$ 
B)  $\varnothing$ 
C)  $\{ 14 \}$ 
D)  $\left\{ - 14 , \frac { 2 } { 3 } \right\}$ 
A)  $\left\{ 14 , - \frac { 2 } { 3 } \right\}$ 
B)  $\varnothing$ 
C)  $\{ 14 \}$ 
D)  $\left\{ - 14 , \frac { 2 } { 3 } \right\}$

Question 14

Solve the equation by the square root property.
-$$( x - 14 ) ^ { 2 } = 81$$

Accepted Answer

A)  $\{ 5,23 \}$ 
B)  $\{ 23 \}$ 
C)  $\{ - 67 \}$ 
D)  $\{ - 5 , - 23 \}$ 
A)  $\{ 5,23 \}$ 
B)  $\{ 23 \}$ 
C)  $\{ - 67 \}$ 
D)  $\{ - 5 , - 23 \}$

Question 15

Write the number as the product of a real number and i.
-$\sqrt { - 44 }$

Accepted Answer

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

Question 16

Solve the equation for the indicated variable. Assume no denominator is 0.
-$\mathrm { M } = \pi \mathrm { r } ^ { 2 } \mathrm { hd }$, for $\mathrm { r }$

Accepted Answer

A)  $r = \pm \sqrt { \pi M h d }$ 
B)  $r = \frac { \pm \sqrt { \pi \mathrm { Mhd } } } { \mathrm { hd } }$ 
C)  $r = \frac { \pm \sqrt { \text { Mnd } } } { \pi h d }$ 
D)  $r = \frac { \pm \mathrm { M } \sqrt { \pi h d } } { \pi h d }$ 
A)  $r = \pm \sqrt { \pi M h d }$ 
B)  $r = \frac { \pm \sqrt { \pi \mathrm { Mhd } } } { \mathrm { hd } }$ 
C)  $r = \frac { \pm \sqrt { \text { Mnd } } } { \pi h d }$ 
D)  $r = \frac { \pm \mathrm { M } \sqrt { \pi h d } } { \pi h d }$

Question 17

Graph the solution set.
-$$\left| 2 x ^ { 3 } - 7 x ^ { 2 } - 9 x \right| = 0$$

Accepted Answer

A)  $\left\{ \frac { 2 } { 9 } , - 1 \right\}$ 
B)  $\left\{ \frac { 2 } { 9 } , 1,0 \right\}$ 
C)  $\left\{ \frac { 2 } { 9 } , 0 \right\}$ 
D)  $\left\{ \frac { 9 } { 2 } , - 1,0 \right\}$ 
A)  $\left\{ \frac { 2 } { 9 } , - 1 \right\}$ 
B)  $\left\{ \frac { 2 } { 9 } , 1,0 \right\}$ 
C)  $\left\{ \frac { 2 } { 9 } , 0 \right\}$ 
D)  $\left\{ \frac { 9 } { 2 } , - 1,0 \right\}$

Question 18

Solve and graph the inequality. Give answer in interval notation.
-$$11 > 2 x + 3 \geq 3$$

Accepted Answer

A)  $[ 0,4 ]$
  
B)  $( 0,4 )$
  
C)  $[ 0,4 )$
  
D)  $( 0,4 ]$
  
A)  $[ 0,4 ]$
  
B)  $( 0,4 )$
  
C)  $[ 0,4 )$
  
D)  $( 0,4 ]$

Question 19

Solve the equation by the square root property.
-$$( x + 1 ) ^ { 2 } = - 3$$

Accepted Answer

A)  $\{ - 1 \pm \sqrt { 3 } \}$ 
B)  $\{ 2,4 \}$ 
C)  $\{ - 1 \pm i \sqrt { 3 } \}$ 
D)  $\{ - 1 - \sqrt { 3 } \}$ 
A)  $\{ - 1 \pm \sqrt { 3 } \}$ 
B)  $\{ 2,4 \}$ 
C)  $\{ - 1 \pm i \sqrt { 3 } \}$ 
D)  $\{ - 1 - \sqrt { 3 } \}$

Question 20

Solve the problem.
-An airplane flies from Metro City to Gotham with a tailwind that increases its normal speed by 100 mph. On the return trip, the plane must fly against this wind, which decreases its normal speed by the same amount. The
Flight from Metro City takes 2.00 hours and the return trip takes 3.60 hours. How far is it from Metro City to
Gotham?

Accepted Answer

A)  1200 mi 
B)  1100 mi 
C)  900 mi 
D)  1020 mi 
A)  1200 mi 
B)  1100 mi 
C)  900 mi 
D)  1020 mi

Solve the equation using the quadratic formula. - $( x + 6 ) ( x - 1 ) = 5$

Find the values of a, b, and c for which the quadratic equation $a x ^ { 2 } + b x + c = 0$ 0 has the given numbers as solutions. Then use those values to write a quadratic equation. - $- 2,9$

Solve and graph the inequality. Give answer in interval notation. - $- 1 \leq \frac { x + 1 } { - 2 } \leq 3$ $Solve and graph the inequality. Give answer in interval notation. - - 1 \leq \frac { x + 1 } { - 2 } \leq 3$

Write the number in standard form a + bi. - $\frac { 8 - \sqrt { - 20 } } { 2 }$

Solve the cubic equation using factoring and the quadratic formula. - $\mathrm { x } ^ { 2 } = - 18$

Graph the solution set. - $| 5 x + 4 | = | x + 9 |$

Solve the formula for the indicated variable. - $\mathrm { A } = \mathrm { P } ( 1 + \mathrm { nr } )$ , for $\mathrm { r }$

Solve the equation by completing the square. - $x ^ { 2 } - 2 x - 24 = 0$

A lot is in the shape of a right triangle. The shorter leg measures 90 m. The hypotenuse is 30 m longer than the length of the longer leg. How long is the longer leg?

Find the sum or difference. Write the answer in standard form. - $\mathrm { i } \sqrt { 5 } + 1 - ( 7 + 8 \mathrm { i } \sqrt { 5 } ) - ( 6 - \mathrm { i } \sqrt { 5 } )$

Find the product. Write the answer in standard form. - $7 \mathrm { i } ( 5 - 5 \mathrm { i } )$

Decide whether or not the equations are equivalent. - x=4-3x 2x=4

Graph the solution set. - $| 2 x - 6 | = | x + 8 |$

Solve the equation by the square root property. - $( x - 14 ) ^ { 2 } = 81$

Write the number as the product of a real number and i. - $\sqrt { - 44 }$

Solve the equation for the indicated variable. Assume no denominator is 0. - $\mathrm { M } = \pi \mathrm { r } ^ { 2 } \mathrm { hd }$ , for $\mathrm { r }$

Graph the solution set. - $\left| 2 x ^ { 3 } - 7 x ^ { 2 } - 9 x \right| = 0$

Solve and graph the inequality. Give answer in interval notation. - $11 > 2 x + 3 \geq 3$ $Solve and graph the inequality. Give answer in interval notation. - 11 > 2 x + 3 \geq 3$

Solve the equation by the square root property. - $( x + 1 ) ^ { 2 } = - 3$

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

Solve the equation using the quadratic formula. - (x+6)(x−1)=5( x + 6 ) ( x - 1 ) = 5(x+6)(x−1)=5

Find the values of a, b, and c for which the quadratic equation ax2+bx+c=0a x ^ { 2 } + b x + c = 0ax2+bx+c=0 0 has the given numbers as solutions. Then use those values to write a quadratic equation. - −2,9- 2,9−2,9

Solve and graph the inequality. Give answer in interval notation. - −1≤x+1−2≤3- 1 \leq \frac { x + 1 } { - 2 } \leq 3−1≤−2x+1​≤3

Write the number in standard form a + bi. - 8−−202\frac { 8 - \sqrt { - 20 } } { 2 }28−−20​​

Solve the cubic equation using factoring and the quadratic formula. - x2=−18\mathrm { x } ^ { 2 } = - 18x2=−18

Graph the solution set. - ∣5x+4∣=∣x+9∣| 5 x + 4 | = | x + 9 |∣5x+4∣=∣x+9∣

Solve the formula for the indicated variable. - A=P(1+nr)\mathrm { A } = \mathrm { P } ( 1 + \mathrm { nr } )A=P(1+nr) , for r\mathrm { r }r

Solve the equation by completing the square. - x2−2x−24=0x ^ { 2 } - 2 x - 24 = 0x2−2x−24=0

A lot is in the shape of a right triangle. The shorter leg measures 90 m. The hypotenuse is 30 m longer than the length of the longer leg. How long is the longer leg?

Find the sum or difference. Write the answer in standard form. - i5+1−(7+8i5)−(6−i5)\mathrm { i } \sqrt { 5 } + 1 - ( 7 + 8 \mathrm { i } \sqrt { 5 } ) - ( 6 - \mathrm { i } \sqrt { 5 } )i5​+1−(7+8i5​)−(6−i5​)

Find the product. Write the answer in standard form. - 7i(5−5i)7 \mathrm { i } ( 5 - 5 \mathrm { i } )7i(5−5i)

Decide whether or not the equations are equivalent. - x=4-3x 2x=4

Graph the solution set. - ∣2x−6∣=∣x+8∣| 2 x - 6 | = | x + 8 |∣2x−6∣=∣x+8∣

Solve the equation by the square root property. - (x−14)2=81( x - 14 ) ^ { 2 } = 81(x−14)2=81

Write the number as the product of a real number and i. - −44\sqrt { - 44 }−44​

Solve the equation for the indicated variable. Assume no denominator is 0. - M=πr2hd\mathrm { M } = \pi \mathrm { r } ^ { 2 } \mathrm { hd }M=πr2hd , for r\mathrm { r }r

Graph the solution set. - ∣2x3−7x2−9x∣=0\left| 2 x ^ { 3 } - 7 x ^ { 2 } - 9 x \right| = 0​2x3−7x2−9x​=0

Solve and graph the inequality. Give answer in interval notation. - 11>2x+3≥311 > 2 x + 3 \geq 311>2x+3≥3

Solve the equation by the square root property. - (x+1)2=−3( x + 1 ) ^ { 2 } = - 3(x+1)2=−3

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

Solve the equation using the quadratic formula. - $( x + 6 ) ( x - 1 ) = 5$

Find the values of a, b, and c for which the quadratic equation $a x ^ { 2 } + b x + c = 0$ 0 has the given numbers as solutions. Then use those values to write a quadratic equation. - $- 2,9$

Solve and graph the inequality. Give answer in interval notation. - $- 1 \leq \frac { x + 1 } { - 2 } \leq 3$ $Solve and graph the inequality. Give answer in interval notation. - - 1 \leq \frac { x + 1 } { - 2 } \leq 3$

Write the number in standard form a + bi. - $\frac { 8 - \sqrt { - 20 } } { 2 }$

Solve the cubic equation using factoring and the quadratic formula. - $\mathrm { x } ^ { 2 } = - 18$

Graph the solution set. - $| 5 x + 4 | = | x + 9 |$

Solve the formula for the indicated variable. - $\mathrm { A } = \mathrm { P } ( 1 + \mathrm { nr } )$ , for $\mathrm { r }$

Solve the equation by completing the square. - $x ^ { 2 } - 2 x - 24 = 0$

Find the sum or difference. Write the answer in standard form. - $\mathrm { i } \sqrt { 5 } + 1 - ( 7 + 8 \mathrm { i } \sqrt { 5 } ) - ( 6 - \mathrm { i } \sqrt { 5 } )$

Find the product. Write the answer in standard form. - $7 \mathrm { i } ( 5 - 5 \mathrm { i } )$

Graph the solution set. - $| 2 x - 6 | = | x + 8 |$

Solve the equation by the square root property. - $( x - 14 ) ^ { 2 } = 81$

Write the number as the product of a real number and i. - $\sqrt { - 44 }$

Solve the equation for the indicated variable. Assume no denominator is 0. - $\mathrm { M } = \pi \mathrm { r } ^ { 2 } \mathrm { hd }$ , for $\mathrm { r }$

Graph the solution set. - $\left| 2 x ^ { 3 } - 7 x ^ { 2 } - 9 x \right| = 0$

Solve and graph the inequality. Give answer in interval notation. - $11 > 2 x + 3 \geq 3$ $Solve and graph the inequality. Give answer in interval notation. - 11 > 2 x + 3 \geq 3$

Solve the equation by the square root property. - $( x + 1 ) ^ { 2 } = - 3$