Question 1

Determine whether or not the equation is linear.
-$4 x ^ { 2 } + 5 x + 4 = 0$

Accepted Answer

A)  Linear 
B)  Not linear 
A)  Linear 
B)  Not linear

Question 2

Simplify the power of i.
-$\frac { 1 } { \mathrm { i } ^ { 41 } }$

Accepted Answer

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

Question 3

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\frac { 1 } { x - 3 } - \frac { 1 } { x + 8 } = 10$$

Accepted Answer

A)  $- \frac { 1 } { 8 } , \frac { 1 } { 3 }$ 
B)  $- 3,8$ 
C)  $- 8,3$ 
D)  $- \frac { 1 } { 3 } , \frac { 1 } { 8 }$ 
A)  $- \frac { 1 } { 8 } , \frac { 1 } { 3 }$ 
B)  $- 3,8$ 
C)  $- 8,3$ 
D)  $- \frac { 1 } { 3 } , \frac { 1 } { 8 }$

Question 4

Graph the solution set.
-$$| 2 x - 8 | = 7$$

Accepted Answer

A)  $\left\{ \frac { 1 } { 2 } , - \frac { 15 } { 2 } \right\}$ 
B)  $\left\{ \frac { 15 } { 2 } \right\}$ 
C)  $\left\{ - \frac { 1 } { 2 } , - \frac { 15 } { 2 } \right\}$ 
D)  $\left\{ \frac { 15 } { 2 } , \frac { 1 } { 2 } \right\}$ 
A)  $\left\{ \frac { 1 } { 2 } , - \frac { 15 } { 2 } \right\}$ 
B)  $\left\{ \frac { 15 } { 2 } \right\}$ 
C)  $\left\{ - \frac { 1 } { 2 } , - \frac { 15 } { 2 } \right\}$ 
D)  $\left\{ \frac { 15 } { 2 } , \frac { 1 } { 2 } \right\}$

Question 5

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\frac { 3 x + 6 } { 3 } - \frac { 4 x } { x - 3 } = x$$

Accepted Answer

A)  $\{ 1 \}$ 
B)  $\{ - 1 \}$ 
C)  $\left\{ - \frac { 3 } { 11 } \right\}$ 
D)  $\{ - 3 \rangle$ 
A)  $\{ 1 \}$ 
B)  $\{ - 1 \}$ 
C)  $\left\{ - \frac { 3 } { 11 } \right\}$ 
D)  $\{ - 3 \rangle$

Question 6

Solve the equation using the quadratic formula.
-$$2 x ^ { 2 } = - 8 x - 7$$

Accepted Answer

A)  $\left\{ \frac { - 8 \pm \sqrt { 2 } } { 2 } \right\}$ 
B)  $\left\{ \frac { - 4 \pm \sqrt { 2 } } { 4 } \right\}$ 
C)  $\left\{ \frac { - 4 \pm \sqrt { 30 } } { 2 } \right\}$ 
D)  $\left\{ \frac { - 4 \pm \sqrt { 2 } } { 2 } \right\}$ 
A)  $\left\{ \frac { - 8 \pm \sqrt { 2 } } { 2 } \right\}$ 
B)  $\left\{ \frac { - 4 \pm \sqrt { 2 } } { 4 } \right\}$ 
C)  $\left\{ \frac { - 4 \pm \sqrt { 30 } } { 2 } \right\}$ 
D)  $\left\{ \frac { - 4 \pm \sqrt { 2 } } { 2 } \right\}$

Question 7

Solve the equation by the zero-factor property.
-$$2 x ^ { 2 } = 21 x - 49$$

Accepted Answer

A)  $\left\{ - 7 , - \frac { 7 } { 2 } \right\}$ 
B)  $\left\{ \frac { 7 } { 2 } , 7 \right\}$ 
C)  $\left\{ - 7 , \frac { 7 } { 2 } \right\}$ 
D)  $\{ 7,14 \}$ 
A)  $\left\{ - 7 , - \frac { 7 } { 2 } \right\}$ 
B)  $\left\{ \frac { 7 } { 2 } , 7 \right\}$ 
C)  $\left\{ - 7 , \frac { 7 } { 2 } \right\}$ 
D)  $\{ 7,14 \}$

Question 8

If a rectangle is x feet long and y feet wide, which one of the following expressions is the length of its diagonal in terms of x and y?

Accepted Answer

A)  $x + y$ 
B)  $\sqrt { x + y }$ 
C)  $x ^ { 2 } + y ^ { 2 }$ 
D)  $\sqrt { x ^ { 2 } + y ^ { 2 } }$ 
A)  $x + y$ 
B)  $\sqrt { x + y }$ 
C)  $x ^ { 2 } + y ^ { 2 }$ 
D)  $\sqrt { x ^ { 2 } + y ^ { 2 } }$

Question 9

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

Accepted Answer

A)  54 
B)  $5 - 49 \mathrm { i }$ 
C)  $- 2$ 
D)  $5 + 49 i$ 
A)  54 
B)  $5 - 49 \mathrm { i }$ 
C)  $- 2$ 
D)  $5 + 49 i$

Question 10

Determine whether or not the equation is linear.
-$$5 [ - 5 x - 7 - 6 ( x + 1 ) ] = 2 x + 7$$

Accepted Answer

A)  $\left\{ - \frac { 72 } { 5 } \right\}$ 
B)  $\left\{ - \frac { 24 } { 19 } \right\}$ 
C)  $\left\{ - \frac { 2 } { 5 } \right\}$ 
D)  $\left\{ - \frac { 2 } { 57 } \right\}$ 
A)  $\left\{ - \frac { 72 } { 5 } \right\}$ 
B)  $\left\{ - \frac { 24 } { 19 } \right\}$ 
C)  $\left\{ - \frac { 2 } { 5 } \right\}$ 
D)  $\left\{ - \frac { 2 } { 57 } \right\}$

Question 11

A rock falls from a tower that is 208 feet high. As it is falling, its height is given by the formula $h = 208 - 16 t { } ^ { 2 }$. How many seconds (in tenths) will it take for the rock to hit the ground $( h = 0 )$ ?

Accepted Answer

A)  3.6 sec 
B)  13.9 sec 
C)  14.4 sec 
D)  2704 sec 
A)  3.6 sec 
B)  13.9 sec 
C)  14.4 sec 
D)  2704 sec

Question 12

Decide whether the statement is true or false.
-$1 \text { is a solution of } - 8 x + 9 x = 1 \text {. }$

Accepted Answer

A) True 
 B)False

Question 13

Solve the inequality. Write the solution set in interval notation.
-$$| 3 x - 8 | - 1 \geq 3$$

Accepted Answer

A)  $\varnothing$ 
B)  $\left[ \frac { 4 } { 3 } , 4 \right]$ 
C)  $\left( \infty , \frac { 4 } { 3 } \right] \cup [ 4 , \infty )$ 
D)  $[ 4 , \infty ]$ 
A)  $\varnothing$ 
B)  $\left[ \frac { 4 } { 3 } , 4 \right]$ 
C)  $\left( \infty , \frac { 4 } { 3 } \right] \cup [ 4 , \infty )$ 
D)  $[ 4 , \infty ]$

Question 14

Decide what values of the variable cannot possibly be solutions for the equation.
-$$x ^ { 1 / 2 } = 4 x ^ { 1 / 4 }$$

Accepted Answer

A)  $\{ 0,16 \}$ 
B)  $\varnothing$ 
C)  $\{ 0,4 \}$ 
D)  $\{ 0,256 \}$ 
A)  $\{ 0,16 \}$ 
B)  $\varnothing$ 
C)  $\{ 0,4 \}$ 
D)  $\{ 0,256 \}$

Question 15

Solve for y.
-Levi borrowed $6944 at 4% simple interest for 6 months. How much will the interest amount to? What is the total amount that Levi will have to pay back at the end of 6 months? Round answers to the nearest cent if
Necessary.

Accepted Answer

A)  $138.88; $7082.88 
B)  $140.05; $7084.05 
C)  $115.73; $7059.73 
D)  $162.03; $7106.03 
A)  $138.88; $7082.88 
B)  $140.05; $7084.05 
C)  $115.73; $7059.73 
D)  $162.03; $7106.03

Question 16

A rug is to fit in a room so that a border of even width is left on all four sides. If the room is 12 feet by 15 feet and the area of the rug is 108 square feet, how wide will the border be?

Accepted Answer

A)  2.2 ft 
B)  3 ft 
C)  1.5 ft 
D)  1 ft 
A)  2.2 ft 
B)  3 ft 
C)  1.5 ft 
D)  1 ft

Question 17

Decide what values of the variable cannot possibly be solutions for the equation.
-$\sqrt { 9 x - 3 } - \sqrt { 4 x + 5 } = 0$

Accepted Answer

A)  $\left\{ \frac { 5 } { 8 } \right\}$ 
B)  $\left\{ \frac { 2 } { 5 } \right\}$ 
C)  $\left\{ \frac { 8 } { 13 } \right\}$ 
D)  $\left\{ \frac { 8 } { 5 } \right\}$ 
A)  $\left\{ \frac { 5 } { 8 } \right\}$ 
B)  $\left\{ \frac { 2 } { 5 } \right\}$ 
C)  $\left\{ \frac { 8 } { 13 } \right\}$ 
D)  $\left\{ \frac { 8 } { 5 } \right\}$

Question 18

Solve the problem.
-Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 250 miles in the same time that Dana travels 230 miles. If Chuck's rate of travel is 4 mph more than Dana's, and they travel the same length of time, at
What speed does Chuck travel?

Accepted Answer

A)  50 mph 
B)  46 mph 
C)  45 mph 
D)  55 mph 
A)  50 mph 
B)  46 mph 
C)  45 mph 
D)  55 mph

Question 19

Solve the rational inequality. Write the solution set in interval notation.
-$$\frac { - 2 x + 5 } { 7 x ^ { 2 } + 4 } > 0$$

Accepted Answer

A)  $\left( - \frac { 5 } { 2 } , \infty \right)$ 
B)  $\left( - \infty , \frac { 5 } { 2 } \right)$ 
C)  $\left( - \infty , - \frac { 2 } { 5 } \right)$ 
D)  $( - \infty , 0 )$ 
A)  $\left( - \frac { 5 } { 2 } , \infty \right)$ 
B)  $\left( - \infty , \frac { 5 } { 2 } \right)$ 
C)  $\left( - \infty , - \frac { 2 } { 5 } \right)$ 
D)  $( - \infty , 0 )$

Question 20

Solve and graph the inequality. Give answer in interval notation.
-$$- 12 x + 1 \geq - 11 x + 7$$

Accepted Answer

A)  $( - 12 , \infty )$
  
B)  $[ 6 , \infty )$
  
C)  $( - \infty , - 6 ]$
  
D)  $( - \infty , - 12 ]$
  
A)  $( - 12 , \infty )$
  
B)  $[ 6 , \infty )$
  
C)  $( - \infty , - 6 ]$
  
D)  $( - \infty , - 12 ]$

Determine whether or not the equation is linear. - $4 x ^ { 2 } + 5 x + 4 = 0$

Simplify the power of i. - $\frac { 1 } { \mathrm { i } ^ { 41 } }$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { 1 } { x - 3 } - \frac { 1 } { x + 8 } = 10$

Graph the solution set. - $| 2 x - 8 | = 7$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { 3 x + 6 } { 3 } - \frac { 4 x } { x - 3 } = x$

Solve the equation using the quadratic formula. - $2 x ^ { 2 } = - 8 x - 7$

Solve the equation by the zero-factor property. - $2 x ^ { 2 } = 21 x - 49$

If a rectangle is x feet long and y feet wide, which one of the following expressions is the length of its diagonal in terms of x and y?

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

Determine whether or not the equation is linear. - $5 [ - 5 x - 7 - 6 ( x + 1 ) ] = 2 x + 7$

A rock falls from a tower that is 208 feet high. As it is falling, its height is given by the formula $h = 208 - 16 t { } ^ { 2 }$ . How many seconds (in tenths) will it take for the rock to hit the ground $( h = 0 )$ ?

Decide whether the statement is true or false. - $1 \text { is a solution of } - 8 x + 9 x = 1 \text {. }$

Solve the inequality. Write the solution set in interval notation. - $| 3 x - 8 | - 1 \geq 3$

Decide what values of the variable cannot possibly be solutions for the equation. - $x ^ { 1 / 2 } = 4 x ^ { 1 / 4 }$

Solve for y. -Levi borrowed $6944 at 4% simple interest for 6 months. How much will the interest amount to? What is the total amount that Levi will have to pay back at the end of 6 months? Round answers to the nearest cent if Necessary.

A rug is to fit in a room so that a border of even width is left on all four sides. If the room is 12 feet by 15 feet and the area of the rug is 108 square feet, how wide will the border be?

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt { 9 x - 3 } - \sqrt { 4 x + 5 } = 0$

Solve the problem. -Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 250 miles in the same time that Dana travels 230 miles. If Chuck's rate of travel is 4 mph more than Dana's, and they travel the same length of time, at What speed does Chuck travel?

Solve the rational inequality. Write the solution set in interval notation. - $\frac { - 2 x + 5 } { 7 x ^ { 2 } + 4 } > 0$

Solve and graph the inequality. Give answer in interval notation. - $- 12 x + 1 \geq - 11 x + 7$ $Solve and graph the inequality. Give answer in interval notation. - - 12 x + 1 \geq - 11 x + 7$

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

Determine whether or not the equation is linear. - 4x2+5x+4=04 x ^ { 2 } + 5 x + 4 = 04x2+5x+4=0

Simplify the power of i. - 1i41\frac { 1 } { \mathrm { i } ^ { 41 } }i411​

Decide what values of the variable cannot possibly be solutions for the equation. - 1x−3−1x+8=10\frac { 1 } { x - 3 } - \frac { 1 } { x + 8 } = 10x−31​−x+81​=10

Graph the solution set. - ∣2x−8∣=7| 2 x - 8 | = 7∣2x−8∣=7

Decide what values of the variable cannot possibly be solutions for the equation. - 3x+63−4xx−3=x\frac { 3 x + 6 } { 3 } - \frac { 4 x } { x - 3 } = x33x+6​−x−34x​=x

Solve the equation using the quadratic formula. - 2x2=−8x−72 x ^ { 2 } = - 8 x - 72x2=−8x−7

Solve the equation by the zero-factor property. - 2x2=21x−492 x ^ { 2 } = 21 x - 492x2=21x−49

If a rectangle is x feet long and y feet wide, which one of the following expressions is the length of its diagonal in terms of x and y?

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

Determine whether or not the equation is linear. - 5[−5x−7−6(x+1)]=2x+75 [ - 5 x - 7 - 6 ( x + 1 ) ] = 2 x + 75[−5x−7−6(x+1)]=2x+7

A rock falls from a tower that is 208 feet high. As it is falling, its height is given by the formula h=208−16t2h = 208 - 16 t { } ^ { 2 }h=208−16t2 . How many seconds (in tenths) will it take for the rock to hit the ground (h=0)( h = 0 )(h=0) ?

Decide whether the statement is true or false. - 1 is a solution of −8x+9x=1. 1 \text { is a solution of } - 8 x + 9 x = 1 \text {. }1 is a solution of −8x+9x=1.

Solve the inequality. Write the solution set in interval notation. - ∣3x−8∣−1≥3| 3 x - 8 | - 1 \geq 3∣3x−8∣−1≥3

Decide what values of the variable cannot possibly be solutions for the equation. - x1/2=4x1/4x ^ { 1 / 2 } = 4 x ^ { 1 / 4 }x1/2=4x1/4

Solve for y. -Levi borrowed $6944 at 4% simple interest for 6 months. How much will the interest amount to? What is the total amount that Levi will have to pay back at the end of 6 months? Round answers to the nearest cent if Necessary.

A rug is to fit in a room so that a border of even width is left on all four sides. If the room is 12 feet by 15 feet and the area of the rug is 108 square feet, how wide will the border be?

Decide what values of the variable cannot possibly be solutions for the equation. - 9x−3−4x+5=0\sqrt { 9 x - 3 } - \sqrt { 4 x + 5 } = 09x−3​−4x+5​=0

Solve the problem. -Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 250 miles in the same time that Dana travels 230 miles. If Chuck's rate of travel is 4 mph more than Dana's, and they travel the same length of time, at What speed does Chuck travel?

Solve the rational inequality. Write the solution set in interval notation. - −2x+57x2+4>0\frac { - 2 x + 5 } { 7 x ^ { 2 } + 4 } > 07x2+4−2x+5​>0

Solve and graph the inequality. Give answer in interval notation. - −12x+1≥−11x+7- 12 x + 1 \geq - 11 x + 7−12x+1≥−11x+7

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

Determine whether or not the equation is linear. - $4 x ^ { 2 } + 5 x + 4 = 0$

Simplify the power of i. - $\frac { 1 } { \mathrm { i } ^ { 41 } }$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { 1 } { x - 3 } - \frac { 1 } { x + 8 } = 10$

Graph the solution set. - $| 2 x - 8 | = 7$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { 3 x + 6 } { 3 } - \frac { 4 x } { x - 3 } = x$

Solve the equation using the quadratic formula. - $2 x ^ { 2 } = - 8 x - 7$

Solve the equation by the zero-factor property. - $2 x ^ { 2 } = 21 x - 49$

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

Determine whether or not the equation is linear. - $5 [ - 5 x - 7 - 6 ( x + 1 ) ] = 2 x + 7$

A rock falls from a tower that is 208 feet high. As it is falling, its height is given by the formula $h = 208 - 16 t { } ^ { 2 }$ . How many seconds (in tenths) will it take for the rock to hit the ground $( h = 0 )$ ?

Decide whether the statement is true or false. - $1 \text { is a solution of } - 8 x + 9 x = 1 \text {. }$

Solve the inequality. Write the solution set in interval notation. - $| 3 x - 8 | - 1 \geq 3$

Decide what values of the variable cannot possibly be solutions for the equation. - $x ^ { 1 / 2 } = 4 x ^ { 1 / 4 }$

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt { 9 x - 3 } - \sqrt { 4 x + 5 } = 0$

Solve the rational inequality. Write the solution set in interval notation. - $\frac { - 2 x + 5 } { 7 x ^ { 2 } + 4 } > 0$

Solve and graph the inequality. Give answer in interval notation. - $- 12 x + 1 \geq - 11 x + 7$ $Solve and graph the inequality. Give answer in interval notation. - - 12 x + 1 \geq - 11 x + 7$