Question 1

Use interval notation to express the solution set of the inequality below. $| 3 x - 6 | \geq 3$

Accepted Answer

A)  $[ - 1,1 ]$ 
B)  $[ - 3 , - 1 ]$ 
C)  $[ 1,3 ]$ 
D)  $( - \infty , - 3 ] \cup [ - 1 , \infty )$ 
E)  $( - \infty , 1 ] \cup [ 3 , \infty )$ 
A)  $[ - 1,1 ]$ 
B)  $[ - 3 , - 1 ]$ 
C)  $[ 1,3 ]$ 
D)  $( - \infty , - 3 ] \cup [ - 1 , \infty )$ 
E)  $( - \infty , 1 ] \cup [ 3 , \infty )$ E

Question 2

Determine which of the following values of x is a solution to the equation $5 + \frac { 1 } { x + 4 } = 6$ .

Accepted Answer

A)  $x = - 3$ 
B)  $x = - \frac { 3 } { 5 }$ 
C)  $x = - 4$ 
D)  $x = 5$ 
E)  $x = 3$ 
A)  $x = - 3$ 
B)  $x = - \frac { 3 } { 5 }$ 
C)  $x = - 4$ 
D)  $x = 5$ 
E)  $x = 3$ A

Question 3

The price of a computer fell 10% this year. If the computer now costs $621, how much did it cost last year?

Accepted Answer

A) $700 
B) $650 
C) $690 
D) $700.0 
E) $660 
A) $700 
B) $650 
C) $690 
D) $700.0 
E) $660 C

Question 4

Find all solutions of $7 x + 57 = \frac { - 8 } { x }$ .

Accepted Answer

A)  $x = - \frac { 8 } { 7 } , - 8$ 
B)  $x = \frac { 7 } { 8 } , - 7$ 
C)  $x = - \frac { 1 } { 7 } , - 8$ 
D)  $x = - \frac { 7 } { 8 } , 8$ 
E)  $x = - \frac { 1 } { 8 } , - 7$ 
A)  $x = - \frac { 8 } { 7 } , - 8$ 
B)  $x = \frac { 7 } { 8 } , - 7$ 
C)  $x = - \frac { 1 } { 7 } , - 8$ 
D)  $x = - \frac { 7 } { 8 } , 8$ 
E)  $x = - \frac { 1 } { 8 } , - 7$

Question 5

Your weekly paycheck is 20% more than your coworker's. Your two paychecks total $1034. Find the amount of your paycheck.

Accepted Answer

A) $529 
B) $470 
C) $434 
D) $481 
E) $564 
A) $529 
B) $470 
C) $434 
D) $481 
E) $564

Question 6

You accept a new job with a starting salary of $36,000. You receive a 4.4% raise at the start of your second year, a 7.3% raise at the start of your third year, and a 9.3% raise at the start of your fourth year. Find your salary for the fourth year.

Accepted Answer

A) $44,078.10 
B) $43,214.60 
C) $43,732.70 
D) $44,423.50 
E) $44,768.90 
A) $44,078.10 
B) $43,214.60 
C) $43,732.70 
D) $44,423.50 
E) $44,768.90

Question 7

Find all solutions of $\left( x ^ { 2 } + 9 \right) ^ { 3 / 2 } = 125$ .

Accepted Answer

A)  $x = \pm 4$ 
B)  $x = \sqrt [ 3 ] { 9 }$ 
C)  $x = - 4$ 
D)  $x = 5$ 
E)  $x = \pm \sqrt [ 3 ] { 9 }$ 
A)  $x = \pm 4$ 
B)  $x = \sqrt [ 3 ] { 9 }$ 
C)  $x = - 4$ 
D)  $x = 5$ 
E)  $x = \pm \sqrt [ 3 ] { 9 }$

Question 8

Determine which of the following values of x is a solution to the equation $x ^ { 2 } + 9 x + 20 = 0$ .

Accepted Answer

A)  $x = 4 , x = - 5$ 
B)  $x = - 4$ 
C)  $x = - 4 , x = - 5$ 
D)  $x = - 4 , x = 5$ 
E)  $x = 5$ 
A)  $x = 4 , x = - 5$ 
B)  $x = - 4$ 
C)  $x = - 4 , x = - 5$ 
D)  $x = - 4 , x = 5$ 
E)  $x = 5$

Question 9

A square piece of cardboard is formed into a box by cutting out 2-inch squares from each of the corners and folding up the sides. If the volume of the box needs to be 112.5 cubic inches, what size square piece of cardboard is needed?

Accepted Answer

A) 14.5 inches by 14.5 inches 
B) 15.0 inches by 15.0 inches 
C) 5.5 inches by 5.5 inches 
D) 9.5 inches by 9.5 inches 
E) 11.5 inches by 11.5 inches 
A) 14.5 inches by 14.5 inches 
B) 15.0 inches by 15.0 inches 
C) 5.5 inches by 5.5 inches 
D) 9.5 inches by 9.5 inches 
E) 11.5 inches by 11.5 inches

Question 10

Match the inequality $| x | \geq 4$ with its graph.

Accepted Answer

A)    $~~~~~~~~-4~~~~~~~~~~4$ 
B)    $~~~~~~~~-4~~~~~~~~~~4$ 
C)    $~~~~~~~~-4~~~~~~~~~~4$ 
D)    $~~~~~~~~0~~~~~~~~~~4$ 
E)    $~~~~~~~~-4~~~~~~~~~~4$ 
A)    $~~~~~~~~-4~~~~~~~~~~4$ 
B)    $~~~~~~~~-4~~~~~~~~~~4$ 
C)    $~~~~~~~~-4~~~~~~~~~~4$ 
D)    $~~~~~~~~0~~~~~~~~~~4$ 
E)    $~~~~~~~~-4~~~~~~~~~~4$

Question 11

A professional painter can paint a kitchen in 10 hours. His apprentice can paint the same kitchen in 14 hours. If they worked together, how long would it take for them to paint the kitchen?

Accepted Answer

A) 12 
B)  $7 \frac { 23 } { 25 }$ 
C)  $15 \frac { 21 } { 25 }$ 
D) 4 
E)  $5 \frac { 5 } { 6 }$ 
A) 12 
B)  $7 \frac { 23 } { 25 }$ 
C)  $15 \frac { 21 } { 25 }$ 
D) 4 
E)  $5 \frac { 5 } { 6 }$

Question 12

The number of new privately-owned housing projects $H$ (in thousands) started from 2000 to 2005 can be modeled by $H = - 1993 + 204.9 t + \frac { 15,005 } { t },$ $10 \leq t \leq 15$ where $t$ represents the year, with $t = 10$ corresponding to 2000. Use the model to predict the year that about 1,700,000 new housing projects were started.

Accepted Answer

A) 2003 
B) 2002 
C) 2001 
D) 2004 
E) 2000 
A) 2003 
B) 2002 
C) 2001 
D) 2004 
E) 2000

Question 13

The relationship between the length of an adult's femur (thigh bone) and the height of the adult can be approximated by the linear equations $y = 0.432 x - 10.44$ Female $y = 0.449 x - 12.15$ Male where $y$ is the length of the femur in inches and x is the height of the adult in inches (see figure).   An anthropologist discovers a femur belonging to an adult human male. The bone is 12 inches long. Estimate the height of the male. Round to the nearest tenth of an inch.

Accepted Answer

A) 52.6 inches 
B) 54.4 inches 
C) 53.8 inches 
D) 55.0 inches 
E) 56.9 inches 
A) 52.6 inches 
B) 54.4 inches 
C) 53.8 inches 
D) 55.0 inches 
E) 56.9 inches

Question 14

Suppose a lunch consisting of a large hamburger, large fries and large soft drink at a fast food chain contains 1280 calories. A lunch consisting of a small hamburger, small fries and a small soft drink at the same fast food chain contains 740 calories. Find the percent change in calories from the smaller to the larger lunch. Round to the nearest hundredth of a percent.

Accepted Answer

A) 72.97% increase 
B) 42.19% increase 
C) 42.19% decrease 
D) 72.97% decrease 
E) 57.81% increase 
A) 72.97% increase 
B) 42.19% increase 
C) 42.19% decrease 
D) 72.97% decrease 
E) 57.81% increase

Question 15

Translate the following statement into an algebraic expression. $\text { "The speed of an automobile that travels } d \text { miles in } t \text { hours" }$

Accepted Answer

A)  $d t$ 
B)  $\frac { t } { d }$ 
C)  $d + t$ 
D)  $\frac { d } { t }$ 
E)  $\frac { d t } { t }$ 
A)  $d t$ 
B)  $\frac { t } { d }$ 
C)  $d + t$ 
D)  $\frac { d } { t }$ 
E)  $\frac { d t } { t }$

Question 16

Assume that air resistance is negligible, which implies that the position equation $s = - 16 t ^ { 2 } + v _ { 0 } t + s _ { 0 }$ is a reasonable model. A rock is dropped from the top of a 180-foot cliff that overlooks the ocean. How long will it take for the rock to hit the water? Round to the nearest hundredth of a second.

Accepted Answer

A) 7.30 seconds 
B) 3.35 seconds 
C) 5.99 seconds 
D) 4.67 seconds 
E) 11.25 seconds 
A) 7.30 seconds 
B) 3.35 seconds 
C) 5.99 seconds 
D) 4.67 seconds 
E) 11.25 seconds

Question 17

The height, h, in feet, of a baseball above the ground t seconds after it is hit is given by $h = - 16 t ^ { 2 } + 80 t + 2.5.$ Use this equation to determine the number of seconds, to the nearest tenth of a second, from the time the ball is hit until the ball hits the ground.

Accepted Answer

A) 4.7 s 
B) 4.8 s 
C) 4.9 s 
D) 5.0 s 
E) 5.1 s 
A) 4.7 s 
B) 4.8 s 
C) 4.9 s 
D) 5.0 s 
E) 5.1 s

Question 18

An investment adviser invested $\$ 120,000$ in two accounts. One investment earned 8% annual simple interest, and the other investment earned 10.5% annual simple interest. The amount of interest earned for 1 year was $\$ 10,850.$ How much was invested in each account?

Accepted Answer

A)  $\$ 97,500$ @ 8%; $\$ 22,500$ @ 10.5% 
B)  $\$ 77,500$ @ 8%; $\$ 42,500$ @ 10.5% 
C) $70,000 @ 8%; $50,000 @ 10.5% 
D)  $\$ 63,000$ @ 8%; $\$ 57,000$ @ 10.5% 
E)  $\$ 65,000$ @ 8%; $\$ 55,000$ @ 10.5% 
A)  $\$ 97,500$ @ 8%; $\$ 22,500$ @ 10.5% 
B)  $\$ 77,500$ @ 8%; $\$ 42,500$ @ 10.5% 
C) $70,000 @ 8%; $50,000 @ 10.5% 
D)  $\$ 63,000$ @ 8%; $\$ 57,000$ @ 10.5% 
E)  $\$ 65,000$ @ 8%; $\$ 55,000$ @ 10.5%

Question 19

Use the critical value method to solve each rational inequality. Write each solution set in interval notation. $\frac { x - 2 } { x + 9 } < 0$

Accepted Answer

A)  $( - 9,9 )$ 
B)  $( - 2,9 )$ 
C)  $( - 9 , - 2 )$ 
D)  $( - 9,2 )$ 
E)  $( 2,9 )$ 
A)  $( - 9,9 )$ 
B)  $( - 2,9 )$ 
C)  $( - 9 , - 2 )$ 
D)  $( - 9,2 )$ 
E)  $( 2,9 )$

Question 20

The projected public college enrollment $E$ (in thousands) in the United States from 2005 to 2015 can be modeled by $E = 180.3 t + 12,312,$ $5 \leq t \leq 15$ where $t$ represents the year, with $t = 5$ corresponding to 2005. Use the model to predict the year that public college enrollment will exceed 13,200,000.

Accepted Answer

A) 2008 
B) 2012 
C) 2013 
D) 2007 
E) 2005 
A) 2008 
B) 2012 
C) 2013 
D) 2007 
E) 2005

Use interval notation to express the solution set of the inequality below. $| 3 x - 6 | \geq 3$

Determine which of the following values of x is a solution to the equation $5 + \frac { 1 } { x + 4 } = 6$ .

The price of a computer fell 10% this year. If the computer now costs $621, how much did it cost last year?

Find all solutions of $7 x + 57 = \frac { - 8 } { x }$ .

Your weekly paycheck is 20% more than your coworker's. Your two paychecks total $1034. Find the amount of your paycheck.

You accept a new job with a starting salary of $36,000. You receive a 4.4% raise at the start of your second year, a 7.3% raise at the start of your third year, and a 9.3% raise at the start of your fourth year. Find your salary for the fourth year.

Find all solutions of $\left( x ^ { 2 } + 9 \right) ^ { 3 / 2 } = 125$ .

Determine which of the following values of x is a solution to the equation $x ^ { 2 } + 9 x + 20 = 0$ .

A square piece of cardboard is formed into a box by cutting out 2-inch squares from each of the corners and folding up the sides. If the volume of the box needs to be 112.5 cubic inches, what size square piece of cardboard is needed?

Match the inequality $| x | \geq 4$ with its graph.

A professional painter can paint a kitchen in 10 hours. His apprentice can paint the same kitchen in 14 hours. If they worked together, how long would it take for them to paint the kitchen?

Translate the following statement into an algebraic expression. $\text { "The speed of an automobile that travels } d \text { miles in } t \text { hours" }$

The height, h, in feet, of a baseball above the ground t seconds after it is hit is given by $h = - 16 t ^ { 2 } + 80 t + 2.5.$ Use this equation to determine the number of seconds, to the nearest tenth of a second, from the time the ball is hit until the ball hits the ground.

An investment adviser invested $\$ 120,000$ in two accounts. One investment earned 8% annual simple interest, and the other investment earned 10.5% annual simple interest. The amount of interest earned for 1 year was $\$ 10,850.$ How much was invested in each account?

Use the critical value method to solve each rational inequality. Write each solution set in interval notation. $\frac { x - 2 } { x + 9 } < 0$

Fundamental Concepts of Algebra

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants

Limits and Derivatives

Applications of the Derivative

Further Applications of the Derivative

Derivatives of Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions Web

Series and Taylor Polynomials Web

Probability Web

Filters

Exam 2: Equations and Inequalities

Use interval notation to express the solution set of the inequality below. ∣3x−6∣≥3| 3 x - 6 | \geq 3∣3x−6∣≥3

Determine which of the following values of x is a solution to the equation 5+1x+4=65 + \frac { 1 } { x + 4 } = 65+x+41​=6 .

The price of a computer fell 10% this year. If the computer now costs $621, how much did it cost last year?

Find all solutions of 7x+57=−8x7 x + 57 = \frac { - 8 } { x }7x+57=x−8​ .

Your weekly paycheck is 20% more than your coworker's. Your two paychecks total $1034. Find the amount of your paycheck.

You accept a new job with a starting salary of $36,000. You receive a 4.4% raise at the start of your second year, a 7.3% raise at the start of your third year, and a 9.3% raise at the start of your fourth year. Find your salary for the fourth year.

Find all solutions of (x2+9)3/2=125\left( x ^ { 2 } + 9 \right) ^ { 3 / 2 } = 125(x2+9)3/2=125 .

Determine which of the following values of x is a solution to the equation x2+9x+20=0x ^ { 2 } + 9 x + 20 = 0x2+9x+20=0 .

A square piece of cardboard is formed into a box by cutting out 2-inch squares from each of the corners and folding up the sides. If the volume of the box needs to be 112.5 cubic inches, what size square piece of cardboard is needed?

Match the inequality ∣x∣≥4| x | \geq 4∣x∣≥4 with its graph.

A professional painter can paint a kitchen in 10 hours. His apprentice can paint the same kitchen in 14 hours. If they worked together, how long would it take for them to paint the kitchen?

Translate the following statement into an algebraic expression. "The speed of an automobile that travels d miles in t hours" \text { "The speed of an automobile that travels } d \text { miles in } t \text { hours" } "The speed of an automobile that travels d miles in t hours"

An investment adviser invested $120,000\$ 120,000$120,000 in two accounts. One investment earned 8% annual simple interest, and the other investment earned 10.5% annual simple interest. The amount of interest earned for 1 year was $10,850.\$ 10,850.$10,850. How much was invested in each account?

Use the critical value method to solve each rational inequality. Write each solution set in interval notation. x−2x+9<0\frac { x - 2 } { x + 9 } < 0x+9x−2​<0

Fundamental Concepts of Algebra

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants

Limits and Derivatives

Applications of the Derivative

Further Applications of the Derivative

Derivatives of Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions Web

Series and Taylor Polynomials Web

Probability Web

Filters

Use interval notation to express the solution set of the inequality below. $| 3 x - 6 | \geq 3$

Determine which of the following values of x is a solution to the equation $5 + \frac { 1 } { x + 4 } = 6$ .

Find all solutions of $7 x + 57 = \frac { - 8 } { x }$ .

Find all solutions of $\left( x ^ { 2 } + 9 \right) ^ { 3 / 2 } = 125$ .

Determine which of the following values of x is a solution to the equation $x ^ { 2 } + 9 x + 20 = 0$ .

Match the inequality $| x | \geq 4$ with its graph.

Translate the following statement into an algebraic expression. $\text { "The speed of an automobile that travels } d \text { miles in } t \text { hours" }$

An investment adviser invested $\$ 120,000$ in two accounts. One investment earned 8% annual simple interest, and the other investment earned 10.5% annual simple interest. The amount of interest earned for 1 year was $\$ 10,850.$ How much was invested in each account?

Use the critical value method to solve each rational inequality. Write each solution set in interval notation. $\frac { x - 2 } { x + 9 } < 0$