Question 1

Write the number in standard form a + bi.
-$$\frac { - 5 + \sqrt { - 75 } } { 20 }$$

Accepted Answer

A)  $= \frac { 1 } { 4 } + \frac { 5 \sqrt { 3 } } { 4 } \mathrm { i }$ 
B)  $= \frac { 1 } { 4 } + \frac { 3 \sqrt { 5 } } { 4 } \mathrm { i }$ 
C)  $- \frac { 1 } { 4 } + \frac { \sqrt { 3 } } { 20 } \mathrm { i }$ 
D)  $- \frac { 1 } { 4 } + \frac { \sqrt { 3 } } { 4 } \mathrm { i }$ 
A)  $= \frac { 1 } { 4 } + \frac { 5 \sqrt { 3 } } { 4 } \mathrm { i }$ 
B)  $= \frac { 1 } { 4 } + \frac { 3 \sqrt { 5 } } { 4 } \mathrm { i }$ 
C)  $- \frac { 1 } { 4 } + \frac { \sqrt { 3 } } { 20 } \mathrm { i }$ 
D)  $- \frac { 1 } { 4 } + \frac { \sqrt { 3 } } { 4 } \mathrm { i }$

Question 2

Write the statement as an absolute value inequality.
-$x$ is within 10 units of 9

Accepted Answer

A)  $| x - 10 | < 9$ 
B)  $| x - 9 | < 10$ 
C)  $| x - 9 | \leq 10$ 
D)  $| 10 - x | < 9$ 
A)  $| x - 10 | < 9$ 
B)  $| x - 9 | < 10$ 
C)  $| x - 9 | \leq 10$ 
D)  $| 10 - x | < 9$

Question 3

Solve the problem.
-A person's emotional quotient (EQ) is found by multiplying emotional age by 100 and dividing by chronological age. Using this information, if a 5 yr old person has an EQ of 102 what is that person's emotional
Age?

Accepted Answer

A)  5 years old 
B)  4.9 years old 
C)  21.4 years old 
D)  5.1 years old 
A)  5 years old 
B)  4.9 years old 
C)  21.4 years old 
D)  5.1 years old

Question 4

Decide whether or not the equations are equivalent.
-$\begin{array} { l } 
2 x - 3 = 8 \
- 2 x - 3 = 8
\end{array}$

Accepted Answer

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

Question 5

Graph the solution set.
-$$| x | = 9$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 6

Solve the problem.
-A rectangular Persian carpet has a perimeter of 224 inches. The length of the carpet is 24 in. more than the width. What are the dimensions of the carpet?

Accepted Answer

A)  Width: 88 in.; length: 112 in. 
B)  Width: 68 in.; length: 92 in. 
C)  Width: 100 in.; length: 124 in. 
D)  Width: 44 in.; length: 68 in. 
A)  Width: 88 in.; length: 112 in. 
B)  Width: 68 in.; length: 92 in. 
C)  Width: 100 in.; length: 124 in. 
D)  Width: 44 in.; length: 68 in.

Question 7

Decide what values of the variable cannot possibly be solutions for the equation.
-$$( 2 x + 3 ) ^ { 1 / 2 } + ( 4 - x ) ^ { 1 / 2 } = 4$$

Accepted Answer

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

Question 8

Solve the problem.
-In the morning, May drove to an appointment at 50 mph. Her average speed on the return trip in the afternoon was 40 mph. The return trip took $\frac { 1 } { 8 }$ hour longer. How far did she travel to the appointment?

Accepted Answer

A)  20 mi 
B)  7.5 mi 
C)  0.5 mi 
D)  25 mi 
A)  20 mi 
B)  7.5 mi 
C)  0.5 mi 
D)  25 mi

Question 9

The sum of the squares of two consecutive integers is 61. Find the integers.

Accepted Answer

A)  $5 , - 6$ 
B)  5,6 or $- 5 , - 6$ 
C)  5,6 
D)  $- 5 , - 6$ 
A)  $5 , - 6$ 
B)  5,6 or $- 5 , - 6$ 
C)  5,6 
D)  $- 5 , - 6$

Question 10

Decide what values of the variable cannot possibly be solutions for the equation.
-$\sqrt [ 5 ] { 6 x + 7 } = 3$

Accepted Answer

A)  $\{ 243 \}$ 
B)  $\{ 236 \}$ 
C)  $\left\{ \frac { 81 } { 2 } \right\}$ 
D)  $\left\{ \frac { 118 } { 3 } \right\}$ 
A)  $\{ 243 \}$ 
B)  $\{ 236 \}$ 
C)  $\left\{ \frac { 81 } { 2 } \right\}$ 
D)  $\left\{ \frac { 118 } { 3 } \right\}$

Question 11

Graph the solution set.
-$$| 4 x + 1 | - 5 = - 13$$

Accepted Answer

A)  $\left\{ - \frac { 7 } { 4 } , - \frac { 9 } { 4 } \right\}$ 
B)  $\left\{ \frac { 7 } { 4 } , \frac { 9 } { 4 } \right\}$ 
C)  $\varnothing$ 
D)  $\left\{ - \frac { 9 } { 4 } \right\}$ 
A)  $\left\{ - \frac { 7 } { 4 } , - \frac { 9 } { 4 } \right\}$ 
B)  $\left\{ \frac { 7 } { 4 } , \frac { 9 } { 4 } \right\}$ 
C)  $\varnothing$ 
D)  $\left\{ - \frac { 9 } { 4 } \right\}$

Question 12

Write the inequality in interval notation.
-$- 2 < x < 1$

Accepted Answer

A)  $[ - 2,1 )$ 
B)  $[ - 2,1 ]$ 
C)  $( - 2,1 )$ 
D)  $( - 2,1 ]$ 
A)  $[ - 2,1 )$ 
B)  $[ - 2,1 ]$ 
C)  $( - 2,1 )$ 
D)  $( - 2,1 ]$

Question 13

Solve the inequality. Write the solution set in interval notation.
-$3 + \left| 1 - \frac { 1 } { 2 } x \right| \geq 5$

Accepted Answer

A)  $( - \infty , - 6 ] \cup [ 2 , \infty )$ 
B)  $( - \infty , - 2 ] \cup [ 6 , \infty )$ 
C)  $[ - 6,2 ]$ 
D)  $[ - 2,6 ]$ 
A)  $( - \infty , - 6 ] \cup [ 2 , \infty )$ 
B)  $( - \infty , - 2 ] \cup [ 6 , \infty )$ 
C)  $[ - 6,2 ]$ 
D)  $[ - 2,6 ]$

Question 14

A building needs a ramp to make it handicap accessible. By law, the ramp must run 10 inches horizontally for every 1 inch of rise. If the surface of the ramp is 52 inches long how far above the ground is the inclined end of
The ramp? Round to the nearest tenth of an inch.

Accepted Answer

A)  4.7 in. 
B)  5.2 in. 
C)  4.1 in. 
D)  17.3 in. 
A)  4.7 in. 
B)  5.2 in. 
C)  4.1 in. 
D)  17.3 in.

Question 15

Solve the problem.
-How much pure acid should be mixed with 6 gallons of a 50% acid solution in order to get an 80% acid solution?

Accepted Answer

A)  9 gal 
B)  24 gal 
C)  15 gal 
D)  3 gal 
A)  9 gal 
B)  24 gal 
C)  15 gal 
D)  3 gal

Question 16

Graph the solution set.
-$$| 4 x - 5 | = | x + 2 |$$

Accepted Answer

A)  $\left\{ \frac { 7 } { 3 } , \frac { 3 } { 5 } \right\}$ 
B)  $\left\{ - \frac { 7 } { 3 } , - 1 \right\}$ 
C)  $\varnothing$ 
D)  $\left\{ \frac { 7 } { 3 } , - 4 \right\}$ 
A)  $\left\{ \frac { 7 } { 3 } , \frac { 3 } { 5 } \right\}$ 
B)  $\left\{ - \frac { 7 } { 3 } , - 1 \right\}$ 
C)  $\varnothing$ 
D)  $\left\{ \frac { 7 } { 3 } , - 4 \right\}$

Question 17

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set.
-$$10 x - 48 = 5 ( 2 x - 11 )$$

Accepted Answer

A)  Contradiction; $\varnothing$ 
B)  Conditional; $\{ - 2 \}$ 
C)  Conditional; $\{ 2 \}$ 
D)  Identity; {all real numbers\} 
A)  Contradiction; $\varnothing$ 
B)  Conditional; $\{ - 2 \}$ 
C)  Conditional; $\{ 2 \}$ 
D)  Identity; {all real numbers\}

Question 18

Write the inequality in interval notation.
-

Accepted Answer

A)  $( 4 , \infty )$ 
B)  $( - \infty , \infty ]$ 
C)  $( - \infty , - 5 ]$ 
D)  $( - \infty , 4 )$ 
A)  $( 4 , \infty )$ 
B)  $( - \infty , \infty ]$ 
C)  $( - \infty , - 5 ]$ 
D)  $( - \infty , 4 )$

Question 19

Use these equations to convert between the two systems. $C = \frac { 5 } { 9 } ( F - 32 ) \quad F = \frac { 9 } { 5 } C + 32$ Round answer to the nearest tenth of a degree if necessary.
-$$C = 8 ^ { \circ }$$

Accepted Answer

A)  $\mathrm { F } = 72 ^ { \circ }$ 
B)  $\mathrm { F } = - 13.3 ^ { \circ }$ 
C)  $\mathrm { F } = 22.2 ^ { \circ }$ 
D)  $\mathrm { F } = 46.4 ^ { \circ }$ 
A)  $\mathrm { F } = 72 ^ { \circ }$ 
B)  $\mathrm { F } = - 13.3 ^ { \circ }$ 
C)  $\mathrm { F } = 22.2 ^ { \circ }$ 
D)  $\mathrm { F } = 46.4 ^ { \circ }$

Question 20

Solve the equation for the indicated variable. Assume no denominator is 0.
-$2 x ^ { 2 } - 4 x y + 3 y ^ { 2 } = 1$, for $y$

Accepted Answer

A)  $y = \frac { 2 x \pm 4 \sqrt { 3 - 2 x ^ { 2 } } } { 3 }$ 
B)  $y = \frac { 2 x \pm \sqrt { 6 - 4 x ^ { 2 } } } { 3 }$ 
C)  $y = \frac { 2 x \pm \sqrt { 3 - 2 x ^ { 2 } } } { 3 }$ 
D)  $y = \frac { 2 x \pm 2 \sqrt { 3 - 2 x ^ { 2 } } } { 3 }$ 
A)  $y = \frac { 2 x \pm 4 \sqrt { 3 - 2 x ^ { 2 } } } { 3 }$ 
B)  $y = \frac { 2 x \pm \sqrt { 6 - 4 x ^ { 2 } } } { 3 }$ 
C)  $y = \frac { 2 x \pm \sqrt { 3 - 2 x ^ { 2 } } } { 3 }$ 
D)  $y = \frac { 2 x \pm 2 \sqrt { 3 - 2 x ^ { 2 } } } { 3 }$

Write the number in standard form a + bi. - $\frac { - 5 + \sqrt { - 75 } } { 20 }$

Write the statement as an absolute value inequality. - $x$ is within 10 units of 9

Solve the problem. -A person's emotional quotient (EQ) is found by multiplying emotional age by 100 and dividing by chronological age. Using this information, if a 5 yr old person has an EQ of 102 what is that person's emotional Age?

Decide whether or not the equations are equivalent. - 2x-3=8 -2x-3=8

Graph the solution set. - $| x | = 9$

Solve the problem. -A rectangular Persian carpet has a perimeter of 224 inches. The length of the carpet is 24 in. more than the width. What are the dimensions of the carpet?

Decide what values of the variable cannot possibly be solutions for the equation. - $( 2 x + 3 ) ^ { 1 / 2 } + ( 4 - x ) ^ { 1 / 2 } = 4$

Solve the problem. -In the morning, May drove to an appointment at 50 mph. Her average speed on the return trip in the afternoon was 40 mph. The return trip took $\frac { 1 } { 8 }$ hour longer. How far did she travel to the appointment?

The sum of the squares of two consecutive integers is 61. Find the integers.

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt [ 5 ] { 6 x + 7 } = 3$

Graph the solution set. - $| 4 x + 1 | - 5 = - 13$

Write the inequality in interval notation. - $- 2 < x < 1$

Solve the inequality. Write the solution set in interval notation. - $3 + \left| 1 - \frac { 1 } { 2 } x \right| \geq 5$

A building needs a ramp to make it handicap accessible. By law, the ramp must run 10 inches horizontally for every 1 inch of rise. If the surface of the ramp is 52 inches long how far above the ground is the inclined end of The ramp? Round to the nearest tenth of an inch.

Solve the problem. -How much pure acid should be mixed with 6 gallons of a 50% acid solution in order to get an 80% acid solution?

Graph the solution set. - $| 4 x - 5 | = | x + 2 |$

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $10 x - 48 = 5 ( 2 x - 11 )$

Write the inequality in interval notation. -

Use these equations to convert between the two systems. $C = \frac { 5 } { 9 } ( F - 32 ) \quad F = \frac { 9 } { 5 } C + 32$ Round answer to the nearest tenth of a degree if necessary. - $C = 8 ^ { \circ }$

Solve the equation for the indicated variable. Assume no denominator is 0. - $2 x ^ { 2 } - 4 x y + 3 y ^ { 2 } = 1$ , for $y$

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

Write the number in standard form a + bi. - −5+−7520\frac { - 5 + \sqrt { - 75 } } { 20 }20−5+−75​​

Write the statement as an absolute value inequality. - xxx is within 10 units of 9

Solve the problem. -A person's emotional quotient (EQ) is found by multiplying emotional age by 100 and dividing by chronological age. Using this information, if a 5 yr old person has an EQ of 102 what is that person's emotional Age?

Decide whether or not the equations are equivalent. - 2x-3=8 -2x-3=8

Graph the solution set. - ∣x∣=9| x | = 9∣x∣=9

Solve the problem. -A rectangular Persian carpet has a perimeter of 224 inches. The length of the carpet is 24 in. more than the width. What are the dimensions of the carpet?

Decide what values of the variable cannot possibly be solutions for the equation. - (2x+3)1/2+(4−x)1/2=4( 2 x + 3 ) ^ { 1 / 2 } + ( 4 - x ) ^ { 1 / 2 } = 4(2x+3)1/2+(4−x)1/2=4

Solve the problem. -In the morning, May drove to an appointment at 50 mph. Her average speed on the return trip in the afternoon was 40 mph. The return trip took 18\frac { 1 } { 8 }81​ hour longer. How far did she travel to the appointment?

The sum of the squares of two consecutive integers is 61. Find the integers.

Decide what values of the variable cannot possibly be solutions for the equation. - 6x+75=3\sqrt [ 5 ] { 6 x + 7 } = 356x+7​=3

Graph the solution set. - ∣4x+1∣−5=−13| 4 x + 1 | - 5 = - 13∣4x+1∣−5=−13

Write the inequality in interval notation. - −2<x<1- 2 < x < 1−2<x<1

Solve the inequality. Write the solution set in interval notation. - 3+∣1−12x∣≥53 + \left| 1 - \frac { 1 } { 2 } x \right| \geq 53+​1−21​x​≥5

A building needs a ramp to make it handicap accessible. By law, the ramp must run 10 inches horizontally for every 1 inch of rise. If the surface of the ramp is 52 inches long how far above the ground is the inclined end of The ramp? Round to the nearest tenth of an inch.

Solve the problem. -How much pure acid should be mixed with 6 gallons of a 50% acid solution in order to get an 80% acid solution?

Graph the solution set. - ∣4x−5∣=∣x+2∣| 4 x - 5 | = | x + 2 |∣4x−5∣=∣x+2∣

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - 10x−48=5(2x−11)10 x - 48 = 5 ( 2 x - 11 )10x−48=5(2x−11)

Write the inequality in interval notation. -

Use these equations to convert between the two systems. C=59(F−32)F=95C+32C = \frac { 5 } { 9 } ( F - 32 ) \quad F = \frac { 9 } { 5 } C + 32C=95​(F−32)F=59​C+32 Round answer to the nearest tenth of a degree if necessary. - C=8∘C = 8 ^ { \circ }C=8∘

Solve the equation for the indicated variable. Assume no denominator is 0. - 2x2−4xy+3y2=12 x ^ { 2 } - 4 x y + 3 y ^ { 2 } = 12x2−4xy+3y2=1 , for yyy

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

Write the number in standard form a + bi. - $\frac { - 5 + \sqrt { - 75 } } { 20 }$

Write the statement as an absolute value inequality. - $x$ is within 10 units of 9

Graph the solution set. - $| x | = 9$

Decide what values of the variable cannot possibly be solutions for the equation. - $( 2 x + 3 ) ^ { 1 / 2 } + ( 4 - x ) ^ { 1 / 2 } = 4$

Solve the problem. -In the morning, May drove to an appointment at 50 mph. Her average speed on the return trip in the afternoon was 40 mph. The return trip took $\frac { 1 } { 8 }$ hour longer. How far did she travel to the appointment?

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt [ 5 ] { 6 x + 7 } = 3$

Graph the solution set. - $| 4 x + 1 | - 5 = - 13$

Write the inequality in interval notation. - $- 2 < x < 1$

Solve the inequality. Write the solution set in interval notation. - $3 + \left| 1 - \frac { 1 } { 2 } x \right| \geq 5$

Graph the solution set. - $| 4 x - 5 | = | x + 2 |$

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $10 x - 48 = 5 ( 2 x - 11 )$

Use these equations to convert between the two systems. $C = \frac { 5 } { 9 } ( F - 32 ) \quad F = \frac { 9 } { 5 } C + 32$ Round answer to the nearest tenth of a degree if necessary. - $C = 8 ^ { \circ }$

Solve the equation for the indicated variable. Assume no denominator is 0. - $2 x ^ { 2 } - 4 x y + 3 y ^ { 2 } = 1$ , for $y$