Question 1

Solve the equation by factoring.
-$$3 x ^ { 2 } + 7 x = 20$$

Accepted Answer

A)  $\left\{ \frac { 5 } { 3 } , - 4 \right\}$ 
B)  $\left\{ - \frac { 5 } { 3 } , - 4 \right\}$ 
C)  $\left\{ - \frac { 5 } { 3 } , 4 \right\}$ 
D)  $\left\{ \frac { 5 } { 3 } , 4 \right\}$ 
A)  $\left\{ \frac { 5 } { 3 } , - 4 \right\}$ 
B)  $\left\{ - \frac { 5 } { 3 } , - 4 \right\}$ 
C)  $\left\{ - \frac { 5 } { 3 } , 4 \right\}$ 
D)  $\left\{ \frac { 5 } { 3 } , 4 \right\}$

Question 2

Solve the equation.
-16x = -15 + 15x

Accepted Answer

A)  $\{ 0 \}$ 
B)  $\{ 15 \}$ 
C)  $\{ - 14 \}$ 
D)  $\{ - 15 \}$ 
A)  $\{ 0 \}$ 
B)  $\{ 15 \}$ 
C)  $\{ - 14 \}$ 
D)  $\{ - 15 \}$

Question 3

Perform the desired operation. Write the answer in the form a + bi.
-$$( 2 + 8 i ) ( 6 + 6 i )$$

Accepted Answer

A)  $48 \mathrm { i } ^ { 2 } + 60 \mathrm { i } + 12$ 
B)  $60 + 36 i$ 
C)  $- 36 + 60 \mathrm { i }$ 
D)  $- 36 - 60 \mathrm { i }$ 
A)  $48 \mathrm { i } ^ { 2 } + 60 \mathrm { i } + 12$ 
B)  $60 + 36 i$ 
C)  $- 36 + 60 \mathrm { i }$ 
D)  $- 36 - 60 \mathrm { i }$

Question 4

Find the real solutions, if any, of the equation. Use the quadratic formula.
-$16 x ^ { 2 } - 64 x + 64 = 0$

Accepted Answer

A)  no real solution 
B)  $\{ 2 , - 32 \}$ 
C)  $\{ - 2 \}$ 
D)  $\{ 2 \}$ 
A)  no real solution 
B)  $\{ 2 , - 32 \}$ 
C)  $\{ - 2 \}$ 
D)  $\{ 2 \}$

Question 5

Solve the equation.
-$$\frac { 2 x } { x ^ { 2 } - 1 } = \frac { 3 } { x ^ { 2 } - 1 } - \frac { 4 } { x + 1 }$$

Accepted Answer

A)  $\left\{ \frac { 1 } { 2 } \right\}$ 
B)  $\left\{ - \frac { 1 } { 8 } \right\}$ 
C)  $\left\{ - \frac { 1 } { 6 } \right\}$ 
D)  $\left\{ \frac { 7 } { 6 } \right\}$ 
A)  $\left\{ \frac { 1 } { 2 } \right\}$ 
B)  $\left\{ - \frac { 1 } { 8 } \right\}$ 
C)  $\left\{ - \frac { 1 } { 6 } \right\}$ 
D)  $\left\{ \frac { 7 } { 6 } \right\}$

Question 6

Find the real solutions, if any, of the equation. Use the quadratic formula.
-$$\mathrm { x } ^ { 2 } + \mathrm { x } + 2 = 0$$

Accepted Answer

A)  $\left\{ \frac { - 1 - \sqrt { 7 } } { 2 } , \frac { - 1 + \sqrt { 7 } } { 2 } \right\}$ 
B)  $\left\{ \frac { 1 - \sqrt { 7 } } { 2 } , \frac { 1 + \sqrt { 7 } } { 2 } \right\}$ 
C)  $\left\{ \frac { - 1 - \sqrt { 7 } } { 2 } , \frac { 1 + \sqrt { 7 } } { 2 } \right\}$ 
D)  no real solution 
A)  $\left\{ \frac { - 1 - \sqrt { 7 } } { 2 } , \frac { - 1 + \sqrt { 7 } } { 2 } \right\}$ 
B)  $\left\{ \frac { 1 - \sqrt { 7 } } { 2 } , \frac { 1 + \sqrt { 7 } } { 2 } \right\}$ 
C)  $\left\{ \frac { - 1 - \sqrt { 7 } } { 2 } , \frac { 1 + \sqrt { 7 } } { 2 } \right\}$ 
D)  no real solution

Question 7

Determine whether the equation is linear or nonlinear.
-$$x ^ { 2 } - 5 = 4$$

Accepted Answer

A) linear 
B) nonlinear 
A) linear 
B) nonlinear

Question 8

Find the product of the given complex number and its conjugate. Write the answer in the form a + bi.
-$\sqrt { 5 } + 3 \mathrm { i }$

Accepted Answer

A)  $5 + 9 i$ 
B)  2 
C)  $5 - 9 \mathrm { i }$ 
D)  14 
A)  $5 + 9 i$ 
B)  2 
C)  $5 - 9 \mathrm { i }$ 
D)  14

Question 9

Solve the inequality. Express your answer using interval notation.
-$$| 5 \mathrm { k } + 3 | + 6 > 10$$

Accepted Answer

A)  $\left( \frac { 1 } { 5 } , \infty \right)$ 
B)  $\left( - \frac { 7 } { 5 } , \frac { 1 } { 5 } \right)$ 
C)  $\left( - \infty , - \frac { 7 } { 5 } \right) \cup \left( \frac { 1 } { 5 } , \infty \right)$ 
D)  $\left( - \infty , - \frac { 7 } { 5 } \right] \cup \left[ \frac { 1 } { 5 } , \infty \right)$ 
A)  $\left( \frac { 1 } { 5 } , \infty \right)$ 
B)  $\left( - \frac { 7 } { 5 } , \frac { 1 } { 5 } \right)$ 
C)  $\left( - \infty , - \frac { 7 } { 5 } \right) \cup \left( \frac { 1 } { 5 } , \infty \right)$ 
D)  $\left( - \infty , - \frac { 7 } { 5 } \right] \cup \left[ \frac { 1 } { 5 } , \infty \right)$

Question 10

Write the expression in the standard form a + bi.
-$( 6 - 7 i ) + ( 3 + 3 i )$

Accepted Answer

A)  $9 + 4 i$ 
B)  $- 9 + 4 \mathrm { i }$ 
C)  $3 + 10 \mathrm { i }$ 
D)  $9 - 4 \mathrm { i }$ 
A)  $9 + 4 i$ 
B)  $- 9 + 4 \mathrm { i }$ 
C)  $3 + 10 \mathrm { i }$ 
D)  $9 - 4 \mathrm { i }$

Question 11

Solve the equation.
-4x + 2 = 2x - 16

Accepted Answer

A)  $\{ - 9 \}$ 
B)  $\{ - 8 \}$ 
C)  $\{ 9 \}$ 
D)  $\{ 8 \}$ 
A)  $\{ - 9 \}$ 
B)  $\{ - 8 \}$ 
C)  $\{ 9 \}$ 
D)  $\{ 8 \}$

Question 12

Solve the polynomial inequality. Express the solution in interval notation.
-$$x ^ { 2 } - 3 x - 10 \leq 0$$

Accepted Answer

A)  $( - \infty , - 2 ]$ 
B)  $[ - 2,5 ]$ 
C)  $( - \infty , - 2 ] \cup [ 5 , \infty )$ 
D)  $[ 5 , \infty )$ 
A)  $( - \infty , - 2 ]$ 
B)  $[ - 2,5 ]$ 
C)  $( - \infty , - 2 ] \cup [ 5 , \infty )$ 
D)  $[ 5 , \infty )$

Question 13

Determine whether the equation is linear or nonlinear.
-$$0.11 x + 24 = 0.29$$

Accepted Answer

A) linear 
B) nonlinear 
A) linear 
B) nonlinear

Question 14

Write the power of i as i, -1, -i, or 1.
-$$\mathrm { i } ^ { 15 }$$

Accepted Answer

A) -i 
B) 1 
C) i 
D) -1 
A) -i 
B) 1 
C) i 
D) -1

Question 15

Use the discriminant to determine the number and nature of the solutions to the quadratic equation. Do not solve the
equation.
-$$3 x ^ { 2 } - 3 x + 4 = 0$$

Accepted Answer

A) two nonreal solutions 
B) two real solutions 
C) exactly one real solution 
A) two nonreal solutions 
B) two real solutions 
C) exactly one real solution

Question 16

Find the real solutions, if any, of the equation. Use the quadratic formula.
-$$x ^ { 2 } + 8 x - 3 = 0$$

Accepted Answer

A)  $\{ 4 + \sqrt { 19 } \}$ 
B)  $\{ - 1 - \sqrt { 19 } , - 1 + \sqrt { 19 } \}$ 
C)  $\{ - 4 - \sqrt { 19 } , - 4 + \sqrt { 19 } \}$ 
D)  $\{ - 4 - 1 \sqrt { 19 } , - 4 + 1 \sqrt { 19 } \}$ 
A)  $\{ 4 + \sqrt { 19 } \}$ 
B)  $\{ - 1 - \sqrt { 19 } , - 1 + \sqrt { 19 } \}$ 
C)  $\{ - 4 - \sqrt { 19 } , - 4 + \sqrt { 19 } \}$ 
D)  $\{ - 4 - 1 \sqrt { 19 } , - 4 + 1 \sqrt { 19 } \}$

Question 17

Find the real solutions, if any, of the equation. Use the quadratic formula.
-$$4 x ^ { 2 } + 17 x - 15 = 0$$

Accepted Answer

A)  $\left\{ - \frac { 3 } { 4 } , - 5 \right\}$ 
B)  $\left\{ - \frac { 3 } { 4 } , 5 \right\}$ 
C)  $\left\{ \frac { 3 } { 4 } , - 5 \right\}$ 
D)  $\left\{ \frac { 3 } { 4 } , 5 \right\}$ 
A)  $\left\{ - \frac { 3 } { 4 } , - 5 \right\}$ 
B)  $\left\{ - \frac { 3 } { 4 } , 5 \right\}$ 
C)  $\left\{ \frac { 3 } { 4 } , - 5 \right\}$ 
D)  $\left\{ \frac { 3 } { 4 } , 5 \right\}$

Question 18

Solve the equation using the square root property.
-$$( x - 2 ) ^ { 2 } = 49$$

Accepted Answer

A)  $\{ 9 , - 5 \}$ 
B)  $\{ - 5 , - 9 \}$ 
C)  $\{ 51 \}$ 
D)  $\{ 7 , - 7 \}$ 
A)  $\{ 9 , - 5 \}$ 
B)  $\{ - 5 , - 9 \}$ 
C)  $\{ 51 \}$ 
D)  $\{ 7 , - 7 \}$

Question 19

Solve the linear inequality. Express the solution in set-builder notation.
-$$- 7 x - 3 > - 8 x + 6$$

Accepted Answer

A) $\{ x \mid x > 9 \}$ B) $\{ x \mid x > 3 \}$ C) $\{ x \mid x < 3 \}$ D) $\{ x \mid x < 9 \}$ A) $\{ x \mid x > 9 \}$ B) $\{ x \mid x > 3 \}$ C) $\{ x \mid x < 3 \}$ D) $\{ x \mid x < 9 \}$

Question 20

Solve the linear inequality. Express the solution in set-builder notation.
-$$- 7 x + 7 \leq - 8 x + 3$$

Accepted Answer

A) $\{ x \mid x > - 7 \}$ B) $\{ x \mid x < - 7 \}$ C) $\{ x \mid x \leq - 4 \}$ D) $\{ x \mid x \geq - 4 \}$ A) $\{ x \mid x > - 7 \}$ B) $\{ x \mid x < - 7 \}$ C) $\{ x \mid x \leq - 4 \}$ D) $\{ x \mid x \geq - 4 \}$

Solve the equation by factoring. - $3 x ^ { 2 } + 7 x = 20$

Solve the equation. -16x = -15 + 15x

Perform the desired operation. Write the answer in the form a + bi. - $( 2 + 8 i ) ( 6 + 6 i )$

Find the real solutions, if any, of the equation. Use the quadratic formula. - $16 x ^ { 2 } - 64 x + 64 = 0$

Solve the equation. - $\frac { 2 x } { x ^ { 2 } - 1 } = \frac { 3 } { x ^ { 2 } - 1 } - \frac { 4 } { x + 1 }$

Find the real solutions, if any, of the equation. Use the quadratic formula. - $\mathrm { x } ^ { 2 } + \mathrm { x } + 2 = 0$

Determine whether the equation is linear or nonlinear. - $x ^ { 2 } - 5 = 4$

Find the product of the given complex number and its conjugate. Write the answer in the form a + bi. - $\sqrt { 5 } + 3 \mathrm { i }$

Solve the inequality. Express your answer using interval notation. - $| 5 \mathrm { k } + 3 | + 6 > 10$

Write the expression in the standard form a + bi. - $( 6 - 7 i ) + ( 3 + 3 i )$

Solve the equation. -4x + 2 = 2x - 16

Solve the polynomial inequality. Express the solution in interval notation. - $x ^ { 2 } - 3 x - 10 \leq 0$

Determine whether the equation is linear or nonlinear. - $0.11 x + 24 = 0.29$

Write the power of i as i, -1, -i, or 1. - $\mathrm { i } ^ { 15 }$

Use the discriminant to determine the number and nature of the solutions to the quadratic equation. Do not solve the equation. - $3 x ^ { 2 } - 3 x + 4 = 0$

Find the real solutions, if any, of the equation. Use the quadratic formula. - $x ^ { 2 } + 8 x - 3 = 0$

Find the real solutions, if any, of the equation. Use the quadratic formula. - $4 x ^ { 2 } + 17 x - 15 = 0$

Solve the equation using the square root property. - $( x - 2 ) ^ { 2 } = 49$

Solve the linear inequality. Express the solution in set-builder notation. - $- 7 x - 3 > - 8 x + 6$

Solve the linear inequality. Express the solution in set-builder notation. - $- 7 x + 7 \leq - 8 x + 3$

The Rectangular Coordinate System, Lines, and Circles

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Exam 1: Equations, Inequalities, and Applications

Solve the equation by factoring. - 3x2+7x=203 x ^ { 2 } + 7 x = 203x2+7x=20

Solve the equation. -16x = -15 + 15x

Perform the desired operation. Write the answer in the form a + bi. - (2+8i)(6+6i)( 2 + 8 i ) ( 6 + 6 i )(2+8i)(6+6i)

Find the real solutions, if any, of the equation. Use the quadratic formula. - 16x2−64x+64=016 x ^ { 2 } - 64 x + 64 = 016x2−64x+64=0

Solve the equation. - 2xx2−1=3x2−1−4x+1\frac { 2 x } { x ^ { 2 } - 1 } = \frac { 3 } { x ^ { 2 } - 1 } - \frac { 4 } { x + 1 }x2−12x​=x2−13​−x+14​

Find the real solutions, if any, of the equation. Use the quadratic formula. - x2+x+2=0\mathrm { x } ^ { 2 } + \mathrm { x } + 2 = 0x2+x+2=0

Determine whether the equation is linear or nonlinear. - x2−5=4x ^ { 2 } - 5 = 4x2−5=4

Find the product of the given complex number and its conjugate. Write the answer in the form a + bi. - 5+3i\sqrt { 5 } + 3 \mathrm { i }5​+3i

Solve the inequality. Express your answer using interval notation. - ∣5k+3∣+6>10| 5 \mathrm { k } + 3 | + 6 > 10∣5k+3∣+6>10

Write the expression in the standard form a + bi. - (6−7i)+(3+3i)( 6 - 7 i ) + ( 3 + 3 i )(6−7i)+(3+3i)