Question 1

Solve the quadratic inequality. Write the solution set in interval notation.
-$$x ^ { 2 } - 2 x - 8 \leq 0$$

Accepted Answer

A)  $[ - 2,4 ]$ 
B)  $( - \infty , - 2 ] \cup [ 4 , \infty )$ 
C)  $( - \infty , - 2 ]$ 
D)  $[ 4 , \infty )$ 
A)  $[ - 2,4 ]$ 
B)  $( - \infty , - 2 ] \cup [ 4 , \infty )$ 
C)  $( - \infty , - 2 ]$ 
D)  $[ 4 , \infty )$

Question 2

Solve the problem.
-A ball is thrown downward from a window in a tall building. Its position at time $t$ in seconds is $s = 16 t ^ { 2 } + 32 t$, where $s$ is in feet. How long (to the nearest tenth) will it take the ball to fall 152 feet?

Accepted Answer

A)  $2.2 \mathrm { sec }$ 
B)  $2.0 \mathrm { sec }$ 
C)  $4.8 \mathrm { sec }$ 
D)  $3.1 \mathrm { sec }$ 
A)  $2.2 \mathrm { sec }$ 
B)  $2.0 \mathrm { sec }$ 
C)  $4.8 \mathrm { sec }$ 
D)  $3.1 \mathrm { sec }$

Question 3

Solve the equation by the square root property.
-$$( x - 15 ) ^ { 2 } = 64$$

Accepted Answer

A)  $\{ 23 \}$ 
B)  $\{ - 49 \}$ 
C)  $\{ 7,23 \}$ 
D)  $\{ - 7 , - 23 \}$ 
A)  $\{ 23 \}$ 
B)  $\{ - 49 \}$ 
C)  $\{ 7,23 \}$ 
D)  $\{ - 7 , - 23 \}$

Question 4

Solve the equation.
-$\sqrt [ 4 ] { \mathrm { x } ^ { 2 } - 13 } = 1$

Accepted Answer

A)  $\{ - \sqrt { 14 } , \sqrt { 14 } \}$ 
B)  $\{ \sqrt { 13 } \}$ 
C)  $\{ \sqrt { 14 } \}$ 
D)  $\{ - \sqrt { 13 } , \sqrt { 13 } \}$ 
A)  $\{ - \sqrt { 14 } , \sqrt { 14 } \}$ 
B)  $\{ \sqrt { 13 } \}$ 
C)  $\{ \sqrt { 14 } \}$ 
D)  $\{ - \sqrt { 13 } , \sqrt { 13 } \}$

Question 5

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex.
-$$v ^ { 2 } - 7 v + 7 = 0$$

Accepted Answer

A)  Two distinct irrational solutions 
B)  Two distinct nonreal complex solutions 
C)  Two distinct rational solutions 
D)  One rational solution (a double solution) 
A)  Two distinct irrational solutions 
B)  Two distinct nonreal complex solutions 
C)  Two distinct rational solutions 
D)  One rational solution (a double solution)

Question 6

Solve the equation.
-$$\left| \frac { 9 x - 3 } { 10 } \right| = 5$$

Accepted Answer

A)  $\left\{ \frac { 53 } { 9 } \right\}$ 
B)  $\left\{ \frac { 47 } { 5 } , - \frac { 53 } { 5 } \right\}$ 
C)  $\left\{ \frac { 8 } { 5 } , - \frac { 2 } { 5 } \right\}$ 
D)  $\left\{ \frac { 53 } { 9 } , - \frac { 47 } { 9 } \right\}$ 
A)  $\left\{ \frac { 53 } { 9 } \right\}$ 
B)  $\left\{ \frac { 47 } { 5 } , - \frac { 53 } { 5 } \right\}$ 
C)  $\left\{ \frac { 8 } { 5 } , - \frac { 2 } { 5 } \right\}$ 
D)  $\left\{ \frac { 53 } { 9 } , - \frac { 47 } { 9 } \right\}$

Question 7

Solve the problem.
-A water tank can be filled in 9 minutes and emptied in 10 minutes. If the drain is accidentally left open when the tank is being filled, how long does it take to fill the tank?

Accepted Answer

A)  $\frac { 90 } { 19 } \mathrm {~min}$ 
B)  $\frac { 1 } { 19 } \mathrm {~min}$ 
C)  $90 \mathrm {~min}$ 
D)  $\frac { 1 } { 90 } \mathrm {~min}$ 
A)  $\frac { 90 } { 19 } \mathrm {~min}$ 
B)  $\frac { 1 } { 19 } \mathrm {~min}$ 
C)  $90 \mathrm {~min}$ 
D)  $\frac { 1 } { 90 } \mathrm {~min}$

Question 8

Solve the problem.
-A toy company uses the linear model y = -2x + 597 to predict the decline in sales of a toy after it has been on the market more than one year. If x is the number of months after the first year and y
Is the number of toys sold in hundreds during that month, how many toys will be sold 9 months
After the first year?

Accepted Answer

A)  57,900 toys 
B)  61,500 toys 
C)  -118,500 toys 
D)  -29,400 toys 
A)  57,900 toys 
B)  61,500 toys 
C)  -118,500 toys 
D)  -29,400 toys

Question 9

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

Accepted Answer

A)  $\{ - 3 \}$ 
B)  $\{ 3 \}$ 
C)  $\left\{ 3 , \frac { 11 } { 9 } \right\}$ 
D)  $\varnothing$ 
A)  $\{ - 3 \}$ 
B)  $\{ 3 \}$ 
C)  $\left\{ 3 , \frac { 11 } { 9 } \right\}$ 
D)  $\varnothing$

Question 10

Find the product. Write the answer in standard form.
-$$4 \mathrm { i } ( 8 - 5 \mathrm { i } )$$

Accepted Answer

A)  $32 \mathrm { i } - 20$ 
B)  $32 i + 20 i ^ { 2 }$ 
C)  $- 32 \mathrm { i } - 20 \mathrm { i } ^ { 2 }$ 
D)  $20 + 32 \mathrm { i }$ 
A)  $32 \mathrm { i } - 20$ 
B)  $32 i + 20 i ^ { 2 }$ 
C)  $- 32 \mathrm { i } - 20 \mathrm { i } ^ { 2 }$ 
D)  $20 + 32 \mathrm { i }$

Question 11

Find the product. Write the answer in standard form.
-$$- 3 i ( 2 - 6 i ) ^ { 2 }$$

Accepted Answer

A)  $- 72 \mathrm { i } + 72 \mathrm { i } ^ { 2 } - 108 \mathrm { i } ^ { 3 }$ 
B)  $96 i$ 
C)  $- 72 + 96 i$ 
D)  $96 + 72 \mathrm { i }$ 
A)  $- 72 \mathrm { i } + 72 \mathrm { i } ^ { 2 } - 108 \mathrm { i } ^ { 3 }$ 
B)  $96 i$ 
C)  $- 72 + 96 i$ 
D)  $96 + 72 \mathrm { i }$

Question 12

Solve the equation using the quadratic formula.
-$$x ^ { 2 } - 14 x + 74 = 0$$

Accepted Answer

A)  $\{ 12,2 \}$ 
B)  $\{ - 7 \pm 5 \mathrm { i } \}$ 
C)  $\{ 7 \pm 5 i \}$ 
D)  $\{ 14 \pm 10 \mathrm { i } \}$ 
A)  $\{ 12,2 \}$ 
B)  $\{ - 7 \pm 5 \mathrm { i } \}$ 
C)  $\{ 7 \pm 5 i \}$ 
D)  $\{ 14 \pm 10 \mathrm { i } \}$

Question 13

Solve for y.
-$$y - 4 ( x + 9 ) = 8 + 2 y$$

Accepted Answer

A)  $y = - 4 x - 44$ 
B)  $y = - 4 x + 44$ 
C)  $y = 4 x + 28$ 
D)  $y = 4 x + 44$ 
A)  $y = - 4 x - 44$ 
B)  $y = - 4 x + 44$ 
C)  $y = 4 x + 28$ 
D)  $y = 4 x + 44$

Question 14

Answer the question.
-The mat around the picture shown measures x inches across. Which one of the following equations says that the area of the picture itself is 900 square inches?

Accepted Answer

A)  $( 45 - 2 x ) ( 30 - 2 x ) = 900$ 
B)  $2 ( 45 - 2 x ) + 2 ( 30 - 2 x ) = 900$ 
C)  $( 45 - x ) ( 30 - x ) = 900$ 
D)  $( 45 ) ( 30 ) - x ^ { 2 } = 900$ 
A)  $( 45 - 2 x ) ( 30 - 2 x ) = 900$ 
B)  $2 ( 45 - 2 x ) + 2 ( 30 - 2 x ) = 900$ 
C)  $( 45 - x ) ( 30 - x ) = 900$ 
D)  $( 45 ) ( 30 ) - x ^ { 2 } = 900$

Question 15

Solve the equation.
-$$\frac { - 5 x ^ { 2 } - 4 } { x - 4 } = \frac { - 15 x } { x - 4 } + 4$$

Accepted Answer

A)  $\left\{ - \frac { 4 } { 5 } , 3 \right\}$ 
B)  $\left\{ \frac { 4 } { 5 } , - 3 \right\}$ 
C)  $\{ 3 \}$ 
D)  $\left\{ \frac { - 5 \pm \sqrt { 145 } } { 3 } \right\}$ 
A)  $\left\{ - \frac { 4 } { 5 } , 3 \right\}$ 
B)  $\left\{ \frac { 4 } { 5 } , - 3 \right\}$ 
C)  $\{ 3 \}$ 
D)  $\left\{ \frac { - 5 \pm \sqrt { 145 } } { 3 } \right\}$

Question 16

Solve the equation.
-$$\frac { 1 } { x } + \frac { 2 } { 13 x } = - 3$$

Accepted Answer

A)  $\{ - 5 \}$ 
B)  $\{ - 1 \}$ 
C)  $\varnothing$ 
D)  $\left\{ - \frac { 5 } { 13 } \right\}$ 
A)  $\{ - 5 \}$ 
B)  $\{ - 1 \}$ 
C)  $\varnothing$ 
D)  $\left\{ - \frac { 5 } { 13 } \right\}$

Question 17

Solve the equation.
-$$1 + \frac { 1 } { x } = \frac { 6 } { x ^ { 2 } }$$

Accepted Answer

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

Question 18

Solve the equation by completing the square.
-$$8 x ^ { 2 } + 7 x = - 2$$

Accepted Answer

A)  $\left\{ \frac { - 7 \pm \sqrt { 15 } } { 16 } \right\}$ 
B)  $\left\{ \frac { 7 \pm \sqrt { 15 } } { 16 } \right\}$ 
C)  $\left\{ \frac { 7 } { 16 } \pm \frac { \sqrt { 15 } } { 16 } \mathrm { i } \right\}$ 
D)  $\left\{ - \frac { 7 } { 16 } \pm \frac { \sqrt { 15 } } { 16 } \mathrm { i } \right\}$ 
A)  $\left\{ \frac { - 7 \pm \sqrt { 15 } } { 16 } \right\}$ 
B)  $\left\{ \frac { 7 \pm \sqrt { 15 } } { 16 } \right\}$ 
C)  $\left\{ \frac { 7 } { 16 } \pm \frac { \sqrt { 15 } } { 16 } \mathrm { i } \right\}$ 
D)  $\left\{ - \frac { 7 } { 16 } \pm \frac { \sqrt { 15 } } { 16 } \mathrm { i } \right\}$

Question 19

Solve the problem.
-The average annual growth rate of a coral reef in inches satisfies the inequality $| x - 4.92 | \leq 2.24$. What range of growth corresponds to this inequality?

Accepted Answer

A)  $[ 2.68,14.32 ]$ 
B)  $[ 2.24,4.92 ]$ 
C)  $[ 2.68,7.16 ]$ 
D)  $[ 1.34,7.16 ]$ 
A)  $[ 2.68,14.32 ]$ 
B)  $[ 2.24,4.92 ]$ 
C)  $[ 2.68,7.16 ]$ 
D)  $[ 1.34,7.16 ]$

Question 20

Solve the equation.
-$x - 10 = 0$

Accepted Answer

A)  $\pm 10$ 
B)  10 
C)  $- 10$ 
D)  $\sqrt { 10 }$ 
A)  $\pm 10$ 
B)  10 
C)  $- 10$ 
D)  $\sqrt { 10 }$

Solve the quadratic inequality. Write the solution set in interval notation. - $x ^ { 2 } - 2 x - 8 \leq 0$

Solve the problem. -A ball is thrown downward from a window in a tall building. Its position at time $t$ in seconds is $s = 16 t ^ { 2 } + 32 t$ , where $s$ is in feet. How long (to the nearest tenth) will it take the ball to fall 152 feet?

Solve the equation by the square root property. - $( x - 15 ) ^ { 2 } = 64$

Solve the equation. - $\sqrt [ 4 ] { \mathrm { x } ^ { 2 } - 13 } = 1$

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. - $v ^ { 2 } - 7 v + 7 = 0$

Solve the equation. - $\left| \frac { 9 x - 3 } { 10 } \right| = 5$

Solve the problem. -A water tank can be filled in 9 minutes and emptied in 10 minutes. If the drain is accidentally left open when the tank is being filled, how long does it take to fill the tank?

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

Find the product. Write the answer in standard form. - $4 \mathrm { i } ( 8 - 5 \mathrm { i } )$

Find the product. Write the answer in standard form. - $- 3 i ( 2 - 6 i ) ^ { 2 }$

Solve the equation using the quadratic formula. - $x ^ { 2 } - 14 x + 74 = 0$

Solve for y. - $y - 4 ( x + 9 ) = 8 + 2 y$

Answer the question. -The mat around the picture shown measures x inches across. Which one of the following equations says that the area of the picture itself is 900 square inches?

Solve the equation. - $\frac { - 5 x ^ { 2 } - 4 } { x - 4 } = \frac { - 15 x } { x - 4 } + 4$

Solve the equation. - $\frac { 1 } { x } + \frac { 2 } { 13 x } = - 3$

Solve the equation. - $1 + \frac { 1 } { x } = \frac { 6 } { x ^ { 2 } }$

Solve the equation by completing the square. - $8 x ^ { 2 } + 7 x = - 2$

Solve the problem. -The average annual growth rate of a coral reef in inches satisfies the inequality $| x - 4.92 | \leq 2.24$ . What range of growth corresponds to this inequality?

Solve the equation. - $x - 10 = 0$

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Exam 1: Equations and Inequalities

Solve the quadratic inequality. Write the solution set in interval notation. - x2−2x−8≤0x ^ { 2 } - 2 x - 8 \leq 0x2−2x−8≤0

Solve the problem. -A ball is thrown downward from a window in a tall building. Its position at time ttt in seconds is s=16t2+32ts = 16 t ^ { 2 } + 32 ts=16t2+32t , where sss is in feet. How long (to the nearest tenth) will it take the ball to fall 152 feet?

Solve the equation by the square root property. - (x−15)2=64( x - 15 ) ^ { 2 } = 64(x−15)2=64

Solve the equation. - x2−134=1\sqrt [ 4 ] { \mathrm { x } ^ { 2 } - 13 } = 14x2−13​=1

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. - v2−7v+7=0v ^ { 2 } - 7 v + 7 = 0v2−7v+7=0

Solve the equation. - ∣9x−310∣=5\left| \frac { 9 x - 3 } { 10 } \right| = 5​109x−3​​=5