Algebra 1 Name: ___________________________

Keystone Review Packet Date: _____________ Period: _______

KEYSTONE EXAM… Review Packet (Multiple Choice and CRQ)

Section 1: Equations and Inequalities

______ 1) One of the steps Jaime used to solve an equation is shown below.

−5(3𝑥 + 7) = 10−15𝑥 + (−35) = 10

Which statements describe the procedure Jamie used in this step and identify the property

that justifies the procedure?

A) Jamie added −5 and 3𝑥 to eliminate the parenthesis. This procedure is

justified by the associative property.

B) Jamie added −5 and 3𝑥 to eliminate the parenthesis. This procedure is

justified by the distributive property.

C) Jamie multiplied 3𝑥 and 7 by −5 to eliminate the parenthesis. This

procedure is justified by the associative property.

D) Jamie multiplied 3𝑥 and 7 by −5 to eliminate the parenthesis. This

procedure is justified by the distributive property.

______ 2) A theme park charges $52 for a day pass and $110 for a week pass. Last month, 4,432 day

passes were sold and 979 week passes were sold. Which is the closest estimate of the total

amount of money paid for the day and week passes for last month?

A) $300,000 B) $400,000

C) $500,000 D) $600,000

______ 3) A compound inequality is shown below. What is the solution of the compound inequality?

5 < 2 − 3𝑦 < 14

A) −4 > 𝑦 > −1 B) −4 < 𝑦 < −1

C) 1 > 𝑦 > 4 D) 1 < 𝑦 < 4

______ 4) Jenny has a job that pays her $8 per hour plus tips (t). Jenny worked for 4 hours on Monday

and made 65 in all. Which equation could be used to find t , the amount Jenny made in tips?

A) 65 = 4𝑡 + 8 B) 65 = 8𝑡 ÷ 4

C) 65 = 8𝑡 + 4 D) 65 = 8(4) + 𝑡

______ 5) The solution set of an inequality is graphed on the number line below. The graph shows the

solution set of which inequality?

A) −𝑥

9≥ −

1

3 B)

𝑥

9≤ −

1

3

C) −𝑥

9≤

1

3 D) −

𝑥

9≥

1

3

______ 6) A baseball team had $1000 to spend on supplies. The team spent $185 on a new bat. New

baseballs cost $4 each. The inequality 185 + 4𝑏 ≤ 1000 can be used to determine the

number of new baseballs (b) that the team can purchase. Which statement about the number

of new baseballs that can be purchased is true?

A) The team can purchase 204 new baseballs.

B) The minimum number of new baseballs that can be purchased is 185.

C) The maximum number of new baseballs that can be purchased is 185.

D) The team can purchase 185 new baseballs, but this number is neither the maximum or minimum.

______ 7) A person’s hair is 8 centimeters long. The equation below can be used to estimate the length

(𝐿), in centimeters (cm), that the person’s hair will be after 𝑤 weeks.

𝐿 =𝑤

4+ 8

Based on the equation, what will be the estimated length of the person’s hair after 10 weeks?

A) 4.5 cm B) 8 cm

C) 10 cm D) 10.5 cm

______8) Which is the graph of the solution of the inequality |2𝑥 − 1| ≥ 5 ?

A)

B)

C)

D)

______ 9) Dairy Queen is offering the principal of Lenape Middle School a choice between 2 plans on

ordering ice-cream cakes for each teacher’s birthday.

• Plan A costs $2,100 and includes 1 year of unlimited ice-cream cakes.

• Plan B costs $30 per ice-cream cake.

The principal wants to use the less expensive plan. She uses the inequality 2,100 < 30𝑐 to

decide which plan to choose based on the number of ice-cream cakes, 𝑐, she expects to need.

Based on the solution of the inequality, which statement about the principal’s choice of plan is

true?

A) The principal should choose Plan A only if she expects to need fewer than 70

ice-cream cakes in 1 year.

B) The principal can choose either plan and pay the same amount if she expects

to need more than 70 ice-cream cakes in 1 year.

C) The principal should choose Plan A only if she expects to need more than 70

ice-cream cakes in 1 year.

D) The principal can choose either plan and pay the same amount if she expects

to need fewer than 70 ice-cream cakes in 1 year.

______ 10) At the beginning of her mathematics class, Mrs. Reno gives a warm-up problem. She says, “I

am thinking of a number such that 6 less than the product of 7 and this number is 85.” Which

number is she thinking of?

A) 112

7 B) 13

C) 84 D) 637

______ 11) Jason decided that he will sell his stocks if their value per share (𝑥) goes below $5 or above

$15. Which compound inequality represents the values at which Jason will sell his stocks?

A) 𝑥 > $5 or 𝑥 < $15 B) 𝑥 < $5 or 𝑥 > $15

C) 𝑥 > $5 and 𝑥 < $15 D) 𝑥 < $5 and 𝑥 > $15

______ 12) Tim’s scores the first 5 times he played a video game are listed below.

4,526 4,599 4,672 4,745 4,818

Tim’s scores follow a pattern. Which expression can be used to determine his score after he

played the video game 𝑛 times?

A) 73𝑛 + 4,453 B) 73(𝑛 + 4,453)

C) 4,453𝑛 + 73 D) 4,526𝑛

______ 13) Ms. Bernard monitored the growth of a fish. The fish originally weighed 27 ounces. The fish

grew at a rate of 5 ounces per month. The equation below can be used to describe the weight,

in ounces, of the fish.

72 = 27 + 5𝑥

Ms. Bernard correctly determined that 𝑥 = 9. What does the solution of the equation mean?

A) The fish grew at a rate of 9 ounces per month for 72 months.

B) The fish grew at a rate of 72 ounces per month for 9 months.

C) It took 9 months for the fish to grow to a weight of 72 ounces.

D) It took 72 months for the fish to grow to a weight of 9 ounces.

______ 14) An inequality is shown below.

−4𝑥 − 2 > −2𝑥 − 9

Which graph shows the solution of the inequality?

A)

B)

C)

D)

______ 15) A ticket to a baseball game costs $20. Each soda sold at the game costs $5. Shawn may spend

no more than $50. He buys 1 ticket and 𝑥 sodas. Shawn represents this situation with the

inequality below.

5𝑥 + 20 ≤ 50

The solution of the inequality is 𝑥 ≤ 6. Which statement best describes the solution of the

inequality?

A) Shawn buys 6 or fewer sodas.

B) Shawn buys 6 or fewer tickets.

C) Shawn buys 1 tickets and 5 sodas.

D) Shawn has less than or equal to $6 remaining when he leaves the game.

______ 16) Rebecca and Tony are solving the equation 1

3(45𝑦 − 18) = 15(𝑦 + 1).

• Rebecca’s first step gives her 15𝑦 − 18 = 15𝑦 + 1.

• Tony’s first step gives him 15𝑦 − 6 = 15𝑦 + 15.

A) Rebecca uses the distributive property, resulting in a correct first step.

B) Rebecca uses the associative property, resulting in a correct first step.

C) Tony uses the distributive property, resulting in a correct first step.

D) Tony uses the associative property, resulting in a correct first step.

______ 17) C.B. West High School earned $5,100 in ticket sales for a play. The cost per ticket was $12. Let

t represent the number of tickets sold to the play. Which of the following equations could be

used to determine how many tickets were sold to the play?

A) 12 = 5,100𝑡 B) 12𝑡 = 5,100

C) 𝑡 = 5,100 − 12 D) 𝑡 = 5,100 ∙ 12

______ 18) Arya and her little sister Brynn set-up a lemonade stand. Their goal is to earn at least $80 for

the deluxe version of the video game Overwatch 7.

• The sisters charge $0.75 per cup of lemonade.

• They spent $35 on materials for the Lemonade at Wegman’s.

The inequality 0.75𝑥 − 35 ≥ 80 models this situation. Which best describes the meaning of 𝑥

in the inequality?

A) the profit made from 1 day of selling lemonade

B) the profit made from the sale of 154 cups of lemonade

C) the number of cups of lemonade that need to be sold in order to gain back the

money they spent on materials at Wegman’s

D) the number of cups of lemonade that need to be sold for the sisters to meet

their goal

______ 19) Old McDonald had a farm, and on his farm he had two different hot pepper plants. He

measured each plant every day. The Ghost Pepper plant was 1.5 inches tall when Old

McDonald began his measuring, and it grew 0.8 inches per day. The Carolina Reaper plant was

4 inches tall, and it grew 0.6 inches per day. On which day, were the hot pepper plants the

same height?

A) day 4 B) day 8

C) day 12 D) day 13

______ 20) A plain order of mac and cheese from The Perk takes 15 minutes to bake. At least 3 minutes

of baking time is required for each ounce of toppings added to the mac and cheese. The total

baking time for a specialty mac and cheese is at least 24 minutes and at most 33 minutes.

Which compound inequality shows the possible number of ounces of all the toppings, 𝑡, on a

specialty mac and cheese?

A) 3 ≤ 𝑡 ≤ 6 B) 9 ≤ 𝑡 ≤ 18

C) 14 ≤ 𝑡 ≤ 23 D) 24 ≤ 𝑡 ≤ 33

Section 2: Graphs and Functions

______ 21) Which graph shows y as a function of x ?

A) B)

C) D)

______ 22) The graph of a function is shown below. Which value is not in the range of the function?

A) 0 B) 3

C) 4 D) 5

______ 23) Little Debbie is baking brownies. The table below shows the relationship between the number

of batches of brownies she bakes and the number of cups of sugar she uses.

Number of Batches Number of Cups of Sugar

1 2

3

4

2 5

1

2

3 8

1

4

Based on the relationship shown in the table, how many more cups of sugar does Little Debbie

use to bake 15 batches of brownies than to bake 9 batches of brownies?

A) 6 B) 16.5

C) 24.75 D) 41.25

______ 24) A graph of a linear equation is shown below. Which equation describes the graph?

A) 𝑦 = 0.5𝑥 − 1.5 B) 𝑦 = 0.5𝑥 + 3

C) 𝑦 = 2𝑥 − 1.5 D) 𝑦 = 2𝑥 + 3

______ 25) A ball rolls down a ramp with a slope of 2

3. At one point the ball is 10 feet high, and at another

point the ball is 4 feet high, as shown in the diagram below.

What is the horizontal distance (𝑥) , in feet, the ball traveled as it rolled down the ramp from

10 feet high to 4 feet high?

A) 6 B) 9 C) 14 D) 15

______ 26) A juice machine dispenses the same amount of juice into a cup each time the machine is used.

The equation below describes the relationship between the number of cups (𝑥) into which

juice is dispensed and the gallons of juice (𝑦) remaining in the machine.

𝑥 + 12𝑦 = 180

How many gallons of juice are in the machine when it is full?

A) 12 B) 15 C) 168 D) 180

______ 27) What is the slope of the line that passes through the points (−6 , 1) and (4 , −4)?

A) −2 B) 2 C) 1

2 D) −

1

2

______ 28) A function of 𝑥 is graphed on the coordinate plane below. What is the slope of the graph?

A) 0

B) 1

5

C) 5

D) undefined

______ 29) Find the domain of the function represented in the graph.

A) The domain consists of input values from −5 to 3.

B) The domain consists of input values from −4 to 6.

C) The domain consists of input values from −5 to 6.

D) The domain consists of input values from −4 to 3.

______ 30) The travel path of a ferry heading from a mainland harbor toward an island jetty is graphed on

a coordinate grid. The graph is a straight line with a slope of 4

1 . If the mainland harbor is

located at point (2 , 1) , which graph represents the travel path of the ferry?

A) B)

C) D)

______ 31) Busy Bee Taxi charges a flat fee and a mileage charge. The total cost is modeled by the

function 𝑓(𝑥) = 3 + 2𝑥. Which statement represents the meaning of each part of the

function?

A) 𝑥 is the total cost, 𝑦 is the number of miles, $3 is the flat fee, and $2 is the

amount charged per mile.

B) 𝑥 is the total cost, 𝑦 is the number of miles, $2 is the flat fee, and $3 is the

amount charged per mile.

C) 𝑦 is the total cost, 𝑥 is the number of miles, $3 is the flat fee, and $2 is the

amount charged per mile.

D) 𝑦 is the total cost, 𝑥 is the number of miles, $2 is the flat fee, and $3 is the

amount charged per mile.

______ 32) For a science experiment, Corrine is adding hydrochloric acid to distilled water. The

relationship between the amount of hydrochloric acid, 𝑥, and the amount of distilled water, 𝑦,

is graphed below. Which inequality best represents this graph?

A) 2𝑦 − 3𝑥 < 0 B) 3𝑦 − 2𝑥 < 0

C) 2𝑦 − 3𝑥 > 0 D) 3𝑦 − 2𝑥 > 0

______ 33) An architect designed an outdoor staircase for a house. The relationship between the height of

the steps and the length of the tread is modeled by the equation 57𝑥 − 95𝑦 = 0. Which of the

following represents the slope of the equation?

A) 5

3 B)

3

2 C)

2

3 D)

3

5

______ 34) The set of ordered pairs shown below is a relation that is a function of 𝑥.

{(3 , 1) , (4 , 2), (5 , 3), (6 ,4)}

Which ordered pair could not be included in the set so that the relation remains a function of

𝑥?

A) (0 , 4) B) (1 , 6)

C) (3, 7) D) (−4 , 2)

______ 35) An economics teacher plotted the value of a stock on 11 different days during a 500-day

period and used line segments to connect them. In the graph below, the horizontal axis is

measured in days and the vertical axis is measured in dollars.

Based on the graph, which of the following best describes the range of the value of the stock

for this 500-day period?

A) 0 ≤ 𝑥 ≤ 500 B) 1 ≤ 𝑥 ≤ 500

C) 10 ≤ 𝑦 ≤ 60 D) 0 ≤ 𝑦 ≤ 80

______ 36) David is training for a marathon. He writes down the time and distance for each training run

and then records the data on a scatter plot. He has drawn a line of best fit on the scatter plot,

as shown below.

Which statement best expresses the meaning of the slope as a rate of change for this line of

best fit?

A) It represents the number of miles he will have to run to finish the marathon.

B) It represents the average speed, in miles per hour, of his training runs.

C) It represents the number of hours he will need to finish the marathon.

D) It represents the distances, in miles, that he ran while he was training.

______ 37) The set of ordered pairs shown below is a relation.

{(−8 , 5) , (1 , 6), (−3 , −3), (5 , 2)}

What is the domain of the function?

A) {−3 , 2 , 5 , 6}

B) {−8 , −3 , 1 , 5}

C) {all real numbers from −3 to 6}

D) {all real numbers from −8 to 5}

______ 38) Napoleon Dynamite ordered tater-tots from the new tater-tots station in the cafeteria. The

linear function below describes the total cost, 𝑦, of his order with 𝑥 amount of toppings.

𝑦 = 1.5𝑥 + 3.5.

The ordered pair (5 , 11) is a solution of the linear function. What does the solution

represent?

A) His order cost $5 for tots with 11 toppings.

B) His order cost $5 for tots with 5 toppings.

C) His order cost $11 for tots with 5 toppings.

D) His order cost $11 for tots with 11 toppings.

______ 39) What are the range values of the function 𝑔(𝑥) = −3𝑥2 + 5 for the domain values

{−2 , 0, 1} ?

A) {−31 , −4 , 5} B) {−7 , 2, 5}

C) {5 , 8, 17} D) {5, 14, 41}

______ 40) Which inequality is represented by the graph to the right?

A) 𝑦 < −2𝑥 − 4

B) 𝑦 ≥ −2𝑥 − 4

C) 𝑦 > −1

2𝑥 − 4

D) 𝑦 > −2𝑥 − 4

Section 3: Writing Linear Equations

______ 41) John recorded the weight of his dog Spot at different ages as shown in the scatter plot below.

Based on the line of best fit, what will be Spot’s weight after 18 months?

A) 27 pounds B) 32 pounds

C) 36 pounds D) 50 pounds

______ 42) The table below shows values of y as a function of x. Which linear equation below does not

describe the relationship between 𝑥 and 𝑦?

x y

2 10

6 25

14 55

26 100

34 130

A) 𝑦 = 3.75𝑥 + 2.5 B) 𝑦 − 55 = 3.75(𝑥 − 14)

C) 15𝑥 − 4𝑦 = −10 D) 𝑦 − 26 = 3.75(𝑥 − 100)

______ 43) The linear equation 𝑦 − 2 =3

2(𝑥 −

16

3) has …

A) a slope of 3

2 and y-intercept of −6.

B) a slope of −3

2 and y-intercept of 6.

C) a slope of 3 and y-intercept of −2.

D) a slope of 2 and y-intercept of 16

3.

______ 44) Which equation represents the line passing through the points (3 , 2) and (−9 , 6) ?

A) 𝑦 =1

3𝑥 − 3 B) 𝑦 = −

1

3𝑥 + 3

C) 𝑦 = 3𝑥 + 9 D) 𝑦 = −3𝑥 + 9

______ 45) Jeff’s restaurant sells hamburgers. The amount charged for a hamburger, h, is based on the

cost for a plain hamburger plus an additional charge for each topping, t, as shown in the

equation below.

ℎ = 0.60𝑡 + 5

What does the number 0.60 represent in the equation?

A) the number of toppings

B) the cost of a plain hamburger

C) the additional cost for each topping

D) the cost of a hamburger with 1 topping

______ 46) The scatter plot below shows the cost, y, of ground shipping packages from Harrisburg, PA, to

Minneapolis, MN, based on the package weight, 𝑥.

Which equation best describes the line of best fit?

A) 𝑦 = 0.37𝑥 + 1.57 B) 𝑦 = 0.37𝑥 + 10.11

C) 𝑦 = 0.68𝑥 + 2.32 D) 𝑦 = 0.68𝑥 + 6.61

______ 47) A pizza restaurant charges for pizzas and adds a delivery fee. The cost (𝑐), in dollars, to have

any number of pizzas (𝑝) delivered to a home is described by the function 𝑐 = 8𝑝 + 3. Which

statement is true?

A) The cost of 8 pizzas is $11.

B) The cost of 3 pizzas is $14.

C) Each pizza costs $8 and the delivery fee is $3.

D) Each pizza costs $3 and the delivery fee is $8.

______ 48) Which equation represents a line that is parallel to the line 𝑦 = −4𝑥 + 5 ?

A) 𝑦 = −4𝑥 + 3 B) 𝑦 = −1

4𝑥 + 5

C) 𝑦 = 4𝑥 + 5 D) 𝑦 =1

4𝑥 + 3

______ 49) Greg teaches martial arts. He charges a one-time processing fee. The total cost of the

classes are shown below. Let 𝑥 represent the number of classes and 𝑦 represent the cost of

classes. Based on this information, what will it cost to take 10 classes?

A) $123.00 B) $125.00

C) $128.00 D) $130.00

______ 50) What does the 𝑦-intercept represent in the context of the graph below?

A) You bought a new computer and it took

you 17 weeks to pay it off.

B) You bought a new computer for $850.

C) You paid $50 a week in order to pay off

the purchase of a new computer.

D) The place you bought the computer from

charges you $50 a week in interest until

the computer is paid off.

Number of Classes, x 1 2 3 4

Cost of Classes, y $15.00 $27.00 $39.00 $51.00

______ 51) The table below represents a function of 𝑥.

Which equation describes the function?

A) 𝑦 = 𝑥 − 12 B) 𝑦 = 2𝑥 + 5

C) 𝑦 = 4𝑥 − 9 D) 𝑦 = −4𝑥 + 13

______ 52) Liz earned $60.00 for working 8 hours this weekend. What is the total amount of money Liz

would earn for working 34 hours at the same rate of pay?

A) $255 B) $272

C) $315 D) $453

______ 53) Cowculators, the new math tutoring business in town, charges a yearly fee of $39.95.

Each hour they tutor a student, they charge $24.25. Which equation describes the

relationship between the number of hours of math tutoring a student received (𝑥) and the

total yearly cost (𝑦), in dollars, in one year?

A) 𝑦 = 24.25𝑥 B) 𝑦 = 64.2𝑥

C) 𝑦 = 24.25𝑥 + 39.95 D) 𝑦 = 39.95𝑥 + 24.25

______ 54) A 1,500-gallon tank contains 200 gallons of water. Water begins to run into the tank at a rate

of 75 gallons per hour. When will the tank be full but not overflowing?

A) 7 hours, 8 minutes B) 17 hours, 20 minutes

C) 20 hours D) 22 hours, 40 minutes

______ 55) In a technical drawing class, students are analyzing the side view of a house that has been

positioned on a coordinate grid, as shown below.

Which of the following equations best represents the line that contains 𝑃𝑄̅̅ ̅̅ ?

A) 𝑦 = −5

2𝑥 + 14.4 B) 𝑦 =

5

2𝑥 + 27

C) 𝑦 = −2

5𝑥 + 14.4 D) 𝑦 =

2

5𝑥 + 27

______ 56) The graph below shows the relationship between the number of minutes (𝑥) that have passed

since an airplane began its descent and the height above ground (𝑦), in feet, of the airplane.

Based on the graph, how long after it starts its descent will the airplane reach a height of

6,000 feet?

A) 30 minutes B) 40 minutes

C) 50 minutes D) 60 minutes

______ 57) Which of these is the equation of a line that passes through (−1 , 2) and has a slope of 1

3 in

point-slope form?

A) 𝑦 − 2 =1

3(𝑥 − 1) B) 𝑦 − 2 =

1

3(𝑥 + 1)

C) 𝑦 + 1 =1

3(𝑥 − 2) D) 𝑦 − 1 =

1

3(𝑥 + 2)

______ 58) The table shows the cost of a 12-inch pizza for different numbers of toppings. Which equation

gives 𝐶, the cost of pizza with 𝑡 toppings?

Pizza Pricing

Number of Toppings Cost of Pizza

0 $15.50 1 $17.35 2 $19.20 3 $21.05 4 $22.90

A) 𝐶 = 1.85𝑡 B) 𝐶 = 17.35𝑡

C) 𝐶 = 15.50 + 1.85𝑡 D) 𝐶 = 22.90 − 1.85𝑡

______ 59) According to the graph, which statement best describes the slope?

A) As the distance traveled increases by 20, the amount of gas in the tank

decreases by 3.

B) As the distance traveled decreases by 3, the amount of gas in the tank

increases by 20.

C) As the distance traveled increases by 30, the amount of gas in the tank

increases by 2.

D) As the distance traveled decreases by 20, the mount of gas in the tank

decreases by 3.

______ 60) Aki wants to buy a music player that costs $234 using only the money he earned from mowing

lawns. The table below shows the amount of money Aki earned as a function of the number of

lawns he mowed.

Based on the function shown in the table, what is the least number of lawns Aki will have to

mow to buy the music player?

A) 22 B) 30

C) 29 D) 31

Section 4: Systems of Linear Equations and Inequalities

______ 61) Jack bought 3 slices of cheese pizza and 4 slices of mushroom pizza for a total of $12.50. Grace

bought 3 slices of cheese pizza and 2 slices of mushroom pizza for a total cost of $8.50. What is

the cost of one slice of mushroom pizza?

A) $1.50 B) $2.00

C) $3.00 D) $3.50

______ 62) Jen burned 15 calories per minute running for x minutes and 10 calories per minute hiking

for y minutes. She spent a total of 60 minutes running and hiking and burned 700 calories.

Which statement best describes the solution to the system of equations?

A) Jen spent 40 minutes running and 20 minutes hiking.

B) Jen could not burn 700 calories in 60 minutes of running and hiking.

C) Jen spent 20 minutes running and 40 minutes hiking.

D) Jen burns an average of 25 calories per minute.

______ 63) Janet and Rich went to American Eagle and purchased new clothes. Janet purchased 3 t-shirts

for x dollars each and 1 sweatshirt for y dollars each and spent $89 on the clothes. Rich

purchased 2 t-shirts for x dollars each and 2 sweatshirts for y dollars each and spent $140. The

system of equations shown below represents this situation.

3𝑥 + 𝑦 = 894𝑥 + 2𝑦 = 140

Which statement is false?

A) A t-shirt costs $13 more than a sweatshirt.

B) Rich spent $12 more on t-shirts than sweatshirts.

C) Janet spent more money on t-shirts than sweatshirts.

D) Rich bought twice as many sweatshirts as Janet.

______ 64) The Bagel Barrel is testing two new specialty bagels for this year’s Chili Festival. It costs $0.15

to make the ghost-pepper everything bagel and $0.20 to make each buffalo blue cheese bagel.

The baker at Bagel Barrel wants to sell more than 250 of these specialty bagels on the day of

the festival but does not want to spend more than $50 making them. The system of

inequalities below describes the relationship between the number of ghost-pepper everything

bagels (𝑥) and the number of buffalo blue cheese bagels (𝑦) the baker could make for this

year’s Chili Festival. 𝑥 + 𝑦 > 250

. 15𝑥 + .20𝑦 ≤ 50

One solution of the system of inequalities is the ordered pair (96 , 171). Which statement

describes the meaning of the solution?

A) The Bagel Barrel will make $96 on ghost-pepper everything bagels and $171

on buffalo blue cheese bagels.

B) The Bagel Barrel will spend exactly $50 making 96 ghost-pepper everything

bagels and 171 buffalo blue cheese bagels.

C) The Bagel Barrel could make 96 ghost-pepper everything bagels and 171

buffalo blue cheese bagels.

D) The maximum number of ghost-pepper everything bagels that can be made is

96 and the maximum number of buffalo blue cheese bagels that can be made

is 171.

______ 65) Matt always leaves a tip of between 12% and 20% for the waiter when he goes out for dinner

at the restaurant Phi. This can be represented by the system of inequalities shown below,

where y is the amount of tip and x is the cost of dinner.

𝑦 > 0.12𝑥𝑦 < 0.2𝑥

Which of the following is a true statement?

A) When the cost of dinner, x, is $25 the amount of tip, y, must be between $3 and $6.

B) When the cost of dinner, x, is $40 the amount of tip, y, must be between $4.90 and $8.00

C) When the tip, y, is $7.50, the cost of dinner, x, must be between $37.00 and

$63.00.

D) When the tip, y is $1.80, the cost of dinner, x, must be between $9.00 and $15.

______ 66) Mario and Luigi are brothers. They are each saving money to buy Donkey Kong a special

birthday present. Mario has $35 in his piggy bank and plans to save $20 from his allowance

each month. Luigi has been saving his money a bit longer, so he has $80 in his bank account.

Luigi plans to save $15 per month from his part-time job at Dunkin’ Donuts. After how many

months, 𝑥, will they both have the same amount saved up, 𝑦, and how much money will each

brother contribute to Donkey Kong’s birthday gift?

A) After 9 months, each brother will contribute $315 towards Donkey Kong’s gift.

B) After 9 months, each brother will contribute $215 towards Donkey Kong’s gift.

C) After 5 months, each brother will contribute $175 towards Donkey Kong’s gift.

D) After 5 months, each brother will contribute $575 towards Donkey Kong’s gift.

______ 67) Which system of equations is represented by the graph below?

A) 𝑥 − 2𝑦 = 6𝑥 + 𝑦 = 3

B) 𝑦 = 𝑥 + 3

𝑦 = −1

2𝑥 + 3

C) 𝑦 = 𝑥 − 3

𝑦 =1

2𝑥 + 3

D) 𝑥 + 2𝑦 = 6𝑥 − 𝑦 = 3

______ 68) Tommy paid $17.50 to buy 6 youth tickets and 1 adult ticket to a school carnival. Susan paid

$22.50 to buy 3 youth tickets and 3 adult tickets at the carnival. What was the price of an

adult ticket?

A) $2.00 B) $2.90

C) $5.50 D) $7.50

______ 69) Russ bought 3 medium and 2 large hoagies from Wawa for a total of $29.95. Stacey bought 4

medium hoagies and 1 large hoagie, also from Wawa, for a total of $28.45 . Which statement

shows the cost of each medium and large hoagie from Wawa?

A) Each medium hoagie costs $5.69 and each large hoagie costs $6.89.

B) Each medium hoagie costs $5.69 and each large hoagie costs $6.39.

C) Each medium hoagie costs $5.39 and each large hoagie costs $6.89.

D) Each medium hoagie costs $ 5.39 and each large hoagie costs $6.39

______ 70) In the system of equations below, 𝑏, and 𝑐 represent the price per pound, in dollars, of beef

and chicken, respectively, 𝑥 weeks after July 1 during last summer. What was the price per

pound of beef when it was equal to the price per pound of chicken?

𝑏 = 2.35 + 0.25𝑥𝑐 = 1.75 + 0.40𝑥

A) $2.60 B) $2.85

C) $2.95 D) $3.35

______ 71) A cell phone producer distributes boxes of units to retail stores. A unit is either a cell phone or

an accessory, and each box can have up to 24 units composed of 𝑐 cellphones and 𝑎

accessories. In addition, each box must have at least as many cell phones as accessories. Which

of the following systems of inequalities best models the situation described above?

A) 𝑎 + 𝑐 ≥ 24

𝑎 ≤ 𝑐 B)

𝑎 + 𝑐 ≥ 24𝑐 ≤ 𝑎

C) 𝑎 + 𝑐 ≤ 24

𝑎 ≤ 𝑐 D)

𝑎 + 𝑐 ≤ 24𝑐 ≤ 𝑎

______ 72) Which system of inequalities is represented by the graph?

A) 𝑦 > −𝑥 − 3𝑦 < −𝑥 + 3

B) 𝑦 ≤ −𝑥 − 3𝑦 ≥ −𝑥 + 3

C) 𝑦 < −𝑥 − 3𝑦 > −𝑥 + 3

D) 𝑦 ≥ −𝑥 − 3𝑦 ≤ −𝑥 + 3

______ 73) Mr. Carter is mapping the boundaries of a park on a coordinate grid. The park’s headquarters

are located at the origin. The equations shown below represent two boundaries of the park.

𝑦 = 2𝑥 − 52𝑥 + 4𝑦 = 12

The park’s entrance is located at the intersection of these two boundaries. Which coordinate

grid correctly shows the two boundaries and the park’s entrance?

A) B)

C) D)

______ 74) Which system describes the following situation: The sum of two numbers is 20. The difference

between three times the larger and twice the smaller is 40.

A) 𝑥 + 𝑦 = 20

3𝑥 + 2𝑦 = 40 B)

𝑥 − 𝑦 = 203𝑥 − 2𝑦 = 40

C) 𝑥 + 𝑦 = 20

3𝑥 − 2𝑦 = 40 D)

𝑥 − 𝑦 = 203𝑥 + 2𝑦 = 40

______ 75) A group of friends will buy at most 8 snacks at a movie theater and spend no more than $42.

They will pay $4 for each box of candy and $7 for each bag of popcorn. The system of

inequalities graphed below represents this information. Which combination of boxes of candy

and bags of popcorn could the group buy?

A) 2 boxes of candy and 6 bags of popcorn

B) 3 boxes of candy and 4 bags of popcorn

C) 5 boxes of candy and 4 bags of popcorn

D) 8 boxes of candy and 1 bag of popcorn

______ 76) A coffee shop creates a custom blend of coffee using two types of coffee.

• There are 100 pounds of the blend.

• Brazilian coffee costs $9.00 per pound.

• Peruvian coffee costs $15.00 per pound.

• The custom blend costs $13.50 per pound.

How many pounds of Peruvian coffee are in the custom blend?

A) 25 pounds B) 75 pounds

C) 247.5 pounds D) 147.75 pounds

______ 77) Which of the following is true for the system of inequalities shown below?

𝑦 < −2

𝑦 > 3𝑥 + 5

A) The graph of the system is located in Quadrants I , II, and III.

B) The graph of the system is located in Quadrant II only.

C) The graph of the system is located in Quadrant III only.

D) The graph of the system is located in Quadrants IV only.

______ 78) Juan answered all 50 questions on a test. He earned 3 points for each question he answered

correctly. He lost 1 point for each question he answered incorrectly. His final test score was

102 points. The system of equations below describes the relationship between the number of

questions he answered correctly (𝑥) and the number of questions he answered incorrectly

(𝑦).

𝑥 + 𝑦 = 50

3𝑥 − 𝑦 = 102

Part of the solution of the system of equations is 𝑥 = 38. What does this value represent?

A) The number of questions Juan answered correctly.

B) The number of questions Juan answered incorrectly.

C) The number of points Juan lost from questions he answered incorrectly.

D) The number of points Juan earned from questions he answered correctly.

______ 79) Which system of inequalities is graphed at the right?

A) 𝑥 + 𝑦 > −5

−2𝑥 + 𝑦 ≥ 3 B)

𝑥 + 𝑦 > −5−2𝑥 + 𝑦 < 3

C) 𝑥 + 𝑦 > −5

−2𝑥 + 𝑦 ≤ 3 D)

𝑥 + 𝑦 > −5−2𝑥 + 𝑦 > 3

______ 80) At the Gap, 5 pairs of jeans and 2 sweatshirts costs $166, while 3 pairs of jeans and 4

sweatshirts costs $164. Which system of linear equations models this situation?

A) 16445

16623

sj

sj B)

16443

16625

sj

sj

C) 16425

16643

sj

sj D)

16434

16652

sj

sj

Section 5: Statistics and Data Analysis

______ 81) The daily high temperature in degrees Fahrenheit in Allentown, PA, for a period of 10 days is

shown below.

76 80 89 96 98 100 98 91 89 82

Which statement correctly describes the data?

A) The median value is 98.

B) The interquartile range is 16.

C) The lower quartile value is 76.

D) The upper quartile value is 96.

______ 82) A math teacher measures the time it takes each student in a class to complete a quiz. The first

quartile value of the teacher’s data is 22 minutes. The third quartile value is 30 minutes.

Which statement must be true?

A) About 25% of the students completed the quiz in 30 minutes or less.

B) Exactly 50% of students completed the quiz in 26 minutes or less.

C) Exactly 25% of students completed the quiz in exactly 22 minutes.

D) About 50% of students completed the quiz in 30 minutes or more.

______ 83) Lily asked 200 students to select their favorite sport and then recorded the results in the bar

graph below.

Lily will ask another 80 students to select their favorite sport. Based on the information in the

bar graph, how many more students of the next 80 asked will select basketball rather than

football as their favorite sport?

A) 10 B) 20

C) 25 D) 30

______ 84) The points scored by a football team are shown in the stem-and-leaf plot below. What was

the median number of points scored by the football team?

A) 24 B) 27

C) 28 D) 32

______ 85) Jake worked part-time at a restaurant. The amount of money Jake earned for each of six weeks

is shown.

$40 , $80 , $38 , $40 , $32 , $65

Jake then earned $25 for working a seventh week. How were the mean and median affected?

A) The mean decreased and the median remained the same.

B) The median decreased and the mean remained the same.

C) The median and the mean both remained the same.

D) The mean and the median both decreased.

______ 86) Marcie heated a beaker of water in science class. The scatter plot below shows the

temperature (𝑦), in degrees Celsius (℃), of the water based on the number of minutes (𝑥)

she heated the water.

Which equation describes the line of best fit for the temperature

of the water based on the number of minutes Marcie heated the

water?

A) 𝑦 = 5.3𝑥 + 12

B) 𝑦 = 5.3𝑥 + 23

C) 𝑦 = −5.3𝑥 + 23

D) 𝑦 = −5.3𝑥 + 50

______ 87) Which is most likely the equation of the line of best fit for the set of data points?

A) 𝑦 =5

2𝑥 + 6 B) 𝑦 =

2

5𝑥 + 6

C) 𝑦 = −2

5𝑥 + 6 D) 𝑦 = −

5

2𝑥 + 6

______ 88) Javier’s score on a science test is equal to the upper quartile value of all the scores on the test.

Based on this information, which statement about Javier’s score is most likely to be true?

A) Javier’s score is 75.

B) Javier’s score is greater than 75 other scores.

C) Javier’s score is the same as 75% of all the scores.

D) Javier’s score is greater than 75% of all the scores.

______ 89) The circle graph below shows the percent of the total number of students enrolled in a high

school who are in each grade.

There are currently 448 freshman enrolled in the high school. About 75% of the seniors

enrolled in the high school will attend college next year. Which is most likely the number of

seniors currently enrolled in the high school who will attend college next year?

A) 167 B) 288

C) 336 D) 384

______ 90) Four violin students recorded the number of days they practiced violin each month for a year.

Which stem-and-leaf plot has mode and median values that are equal?

A) B)

C) D)

______ 91) The scatter plot below shows the arm spans and heights of 20 people in Dorian’s class.

Based on the line of best fit, which is most likely the height of a person with an arm span of

200 cm?

A) 188 cm B) 192 cm

C) 197 cm D) 205 cm

______ 92) The box-and-whisker plot below represents the number of cookies eaten by a contestant in an

eating competition.

Based on the box-and-whisker plot, which statement about the number of cookies eaten by

each contestant is most likely true?

A) One-half of the contestants ate 8 cookies.

B) One-fourth of the contestants ate between 8 and 22 cookies.

C) All of the contestants ate more than 6 cookies.

D) One-half of the contestants ate between 22 and 25 cookies.

______ 93) Four members of the Ladak family attend an event where door prizes are given. If 52 people

total attend the event, and each person has an equal chance of winning a door prize, what is

the probability that someone from the Ladak family will win a door prize?

A) 1

13 B)

1

4

C) 4

13 D)

2

5

______ 94) The bar graph below shows the average number of minutes Ryder spends each week

participating in four activities.

Based on the information shown in the bar graph, which value is most likely the difference

between the number of minutes Ryder will spend playing sports the next 4 weeks and the

number of minutes Ryder will spend social networking the next 4 weeks.

A) 56 B) 168

C) 224 D) 295

______ 95) Sally needs a green pen. Her backpack has 7 green pens, 12 black pens, 9 blue pens, 6 red

pens, and 4 purple pens. If she picks a pen out of her backpack without looking, what is the

probability that it will be green?

A) 7

38 B)

9

38

C) 6

19 D)

31

38

______ 96) A grocery store employee opens a delivery box of ice-cream. There are 25 containers of

vanilla, 15 containers of mint chocolate chip, 12 containers of peanut butter ripple, 10

containers of cookie dough, and 13 containers of pistachio. The employee randomly selects 3

containers from the box to place in the freezer first. Which expression could be used to

determine the probability that the employee selects 3 containers of mint chocolate chip in a

row?

A) 15

75∙

15

74∙

15

73 B)

15

75∙

14

74∙

13

73

C) 15

75∙

14

75∙

13

75 D)

15

75∙

15

75∙

15

75

______ 97) Einstein asked 6 of his friends how many math worksheets they did during their summer

vacation. Einstein determined the following measures about the number of math worksheets

by the 6 friends.

• Mean: 11

• Median: 9

• Range: 23

The 3 friends who did the most math worksheets over the summer did 24, 15, and 20

worksheets. How many worksheets were done by each of the other 3 friends?

A) 1, 2, 3 B) 1, 3, 3

C) 1, 3, 4 D) 1, 4, 5

______ 98) The range of the weights, in pounds, of all the pumpkins in the Kohler Farm pumpkin patch is

75. Which statement about the weights of the pumpkins is most likely true?

A) Exactly 50% of the pumpkins in the patch weigh within 75 pounds of each

other.

B) The heaviest pumpkin in the patch weighs 75 pounds.

C) There is a pumpkin in the patch that weighs 75 pounds more than another

pumpkin in the patch.

D) Exactly 50% of the pumpkins in the patch weigh less than 37.5 pounds.

______ 99) The data 5 , 6 , 7 , 8 , 9 , 9 , 9 , 10 , 12 , 14, 17 , 17 , 18 , 19 , 19 represents the number of hours

spend on the Internet in a week by students in a mathematics class. Which box-and-whisker

plot and inter-quartile range represents the data?

A) IQR = 9 B) IQR = 9

C) IQR = 8 D) IQR = 9

______ 100) John left his home and walked 3 blocks to his school, as shown in the graph below. What is one

possible interpretation of the section of the graph from point 𝐵 to point 𝐶?

A) John arrived at school and stayed throughout the day.

B) John waited before crossing a busy street.

C) John returned home to get his math homework.

D) John reached the top of a hill and began walking on level ground.

Section 6: Exponents and Polynomials

______ 101) Simplify: 2(2√4)−2

A) 1

8 B)

1

4

C) 16 D) 32

______ 102) A polynomial expression is shown below.

(𝑚𝑥3 + 3)(2𝑥2 + 5𝑥 + 2) − (8𝑥5 + 20𝑥4)

The expression is simplified to 8𝑥3 + 6𝑥2 + 15𝑥 + 6. What is the value of 𝑚?

A) −8 B) −4

C) 4 D) 8

______ 103) Simplify: (5𝑥2 + 3𝑥 − 7) − (−𝑥2 + 8𝑥 − 2)

A) 4𝑥2 + 11𝑥 − 5 B) 4𝑥2 + 11𝑥 − 9

C) 6𝑥2 − 5𝑥 − 9 D) 6𝑥2 − 5𝑥 − 5

______ 104) Which of the following value of 𝑏 will make (3𝑎 − 𝑏)2 simplify to 9𝑎2 − 30𝑎 + 25?

A) 𝑏 = −30 B) 𝑏 = −5

C) 𝑏 = 5 D) 𝑏 = 30

______ 105) Find the value of 𝑥 that makes 54𝑥+2

52𝑥 = 524 true.

A) 11

3 B)

11

4

C) 11 D) 13

______ 106) When 3𝑔2 − 4𝑔 + 2 is subtracted from 7𝑔2 + 5𝑔 − 1 , the difference is _______________ .

A) −4𝑔2 − 9𝑔 + 3 B) 4𝑔2 + 𝑔 + 1

C) 4𝑔2 + 9𝑔 − 3 D) 10𝑔2 + 𝑔 + 1

______ 107) The length of each side of a square wooden box, in inches, is represented by the expression

8𝑚2. The volume of the box, in cubic inches, is (8𝑚2)3. Which simplified expression

represents the volume of the box?

A) 8𝑚6 B) 24𝑚5

C) 512𝑚5 D) 512𝑚6

______ 108) A farmer has a rectangular field that measures 100 feet by 150 feet. He plans to increase the

area of the field by 20%. He will do this by increasing the length and width by the same

amount, 𝑥. Which equation represents the area of the new field?

A) (100 + 2𝑥)(150 + 𝑥) = 18,000

B) 2(100 + 𝑥) + 2(150 + 𝑥) = 15,000

C) (100 + 𝑥)(150 + 𝑥) = 18,000

D) (100 + 𝑥)(150 + 𝑥) = 15,000

______ 109) Which trinomial is equivalent to (3𝑥 − 2)(𝑥 + 4) ?

A) 3𝑥2 + 10𝑥 + 8 B) 3𝑥2 + 10𝑥 − 8

C) 3𝑥2 − 10𝑥 − 8 D) 3𝑥2 − 10𝑥 + 8

______ 110) A greenhouse that specializes in growing bell peppers is divided into sections. The number of

plants in each section depends on the number of sprinklers in that section. In a section with 𝑥

sprinklers, there are 3𝑥(𝑥 + 3) red bell peppers plants and (𝑥 + 4)2 yellow bell pepper

plants. Which simplified expression represents the total number of red and yellow bell pepper

plants in a section with 𝑥 sprinklers?

A) 3𝑥2 + 17𝑥 + 16 B) 4𝑥2 + 17𝑥 + 16

C) 3𝑥4 + 17𝑥2 + 16 D) 4𝑥4 + 17𝑥2 + 16

______ 111) Which equation correctly shows that (𝑥4)2 = 𝑥8 ?

A) (𝑥4)2 = (𝑥4)(𝑥2) = 𝑥8

B) (𝑥4)2 = 2(4𝑥) = 8𝑥 = 𝑥8

C) (𝑥4)2 = 2(𝑥4) = 𝑥4 + 𝑥4 = 𝑥8

D) (𝑥4)2 = (𝑥4)(𝑥4) = 𝑥 ∙ 𝑥 ∙ 𝑥 ∙ 𝑥 ∙ 𝑥 ∙ 𝑥 ∙ 𝑥 ∙ 𝑥 = 𝑥8

______ 112) Which expression is equivalent to the perimeter of the shaded portion of the rectangle?

A) 2𝑥 + 10 B) 2𝑥 + 12

C) 4𝑥 + 14 D) 8𝑥 + 28

______ 113) Dawn simplified the expression (𝑎3𝑏−6)(𝑎2𝑏2). Her final answer was in the form 𝑎𝑚

𝑏𝑛 . If she

simplified the expression correctly, what is the value of 𝑛?

A) 5 B) 6

C) 4 D) 8

______ 114) If the exponential expression (4𝑥𝑚𝑦2)3 ∙ 2𝑥4𝑦𝑛 simplifies to 128𝑥22𝑦10, what do the values

of 𝑚 and 𝑛 have to be?

A) 𝑚 = 15 , 𝑛 = 4 B) 𝑚 = 9 , 𝑛 = 2

C) 𝑚 = 6 , 𝑛 = 4 D) 𝑚 = 15 , 𝑛 = 5

______ 115) When the following two binomials are multiplied, the result is 20𝑤2 + 41𝑤 − 9. What does

the value of 𝑧 have to be to obtain this result?

(5𝑤 − 1)(𝑧𝑤 + 9)

A) 𝑧 = 4

B) 𝑧 = −8

C) 𝑧 = 8 D) 𝑧 = −4

______ 116) Which is an equivalent form for all values of 𝑥, 𝑦, and 𝑧 for which the expression is defined?

3𝑥6𝑦2𝑧9

12𝑥3𝑦4𝑧3

A) 𝑥2𝑧

4𝑦2 B) 𝑥3𝑧6

4𝑦2

C) 4𝑥2𝑧3

𝑦2 D) 4𝑥3𝑧6

𝑦2

______ 117) The polynomial expression (4𝑐3 − 3𝑑𝑐2 + 6) − (7𝑐3 + 4𝑐2 − 6) simplifies completely to

−3𝑐3 + 25𝑐2 + 12. For this to happen, what is the value of 𝑑?

A) 𝑑 = −7 B) 𝑑 = 7

C) 𝑑 = −92

3 D) 𝑑 = 9

2

3

______ 118) Simplify: 10𝑥5𝑦3

2𝑥6𝑦

A) 5𝑥𝑦2 B) 5𝑦2

𝑥

C) 5𝑥

𝑦2 D) 𝑥

5𝑦2

______ 119) What is the standard form of the product (3𝑥 − 1)(5𝑥 + 3)?

A) 15𝑥2 + 2𝑥 − 3 B) 15𝑥2 + 2𝑥 + 3

C) 15𝑥2 − 4𝑥 − 3 D) 15𝑥2 + 4𝑥 − 3

______ 120) Simplify: (5𝑥3 + 𝑥 − 1) − (𝑥2 + 𝑥 + 3)

A) 5𝑥3 − 𝑥2 − 4 B) 5𝑥3 + 𝑥2 + 2𝑥 + 2

C) 4𝑥3 + 2𝑥 + 2 D) 4𝑥3 − 𝑥2 − 4

Section 7: Factoring and Solving by Factoring.

______ 121) Which is a factor of the trinomial 𝑥2 − 2𝑥 − 15 ?

A) (𝑥 − 13) B) (𝑥 − 5)

C) (𝑥 + 5) D) (𝑥 + 13)

______ 122) When factored completely, which is a factor of 12𝑎𝑥2 − 3𝑎 ?

A) 12𝑎 B) 4𝑥2 + 1

C) 3𝑎 D) 4𝑥 − 1

______ 123) If (𝑥 − 4) is a factor of 𝑥2 − 𝑥 − 𝑤 = 0 , then the value of 𝑤 is ________ .

A) 12 B) −12

C) 3 D) −3

______ 124) Factored, the expression 16𝑥2 − 25𝑦2 is equivalent to ____________________ .

A) (4𝑥 − 5𝑦)(4𝑥 + 5𝑦) B) (4𝑥 − 5𝑦)(4𝑥 − 5𝑦)

C) (8𝑥 − 5𝑦)(8𝑥 + 5𝑦) D) (8𝑥 − 5𝑦)(8𝑥 − 5𝑦)

______ 125) Factored completely, the expression 2𝑥2 + 10𝑥 − 12 is equivalent to _________________ .

A) 2(𝑥 − 6)(𝑥 + 1) B) 2(𝑥 + 6)(𝑥 − 1)

C) 2(𝑥 + 2)(𝑥 + 3) D) 2(𝑥 − 2)(𝑥 − 3)

______ 126) A rectangle has an area of 24 square units. The width is 5 units less than the length. What is

the length, in units, of the rectangle?

A) 6 B) 3

C) 8 D) 19

______ 127) The greatest common factor (GCF) of 2 monomials is 4𝑥𝑦3. One of the monomials is 8𝑥2𝑦4.

Which could be the other monomial?

A) 4𝑥𝑦 B) 8𝑥𝑦3

C) 12𝑥3𝑦 D) 20𝑥𝑦3

______ 128) Jennie solved the equation shown below by factoring.

𝑥2 + 2𝑥 − 8 = 0

Which of the following shows a step in solving the equation shown?

A) (𝑥 + 2)(𝑥 + 4) = 0 B) (𝑥 + 2)(𝑥 − 4) = 0

C) (𝑥 − 2)(𝑥 + 4) = 0 D) (𝑥 − 2)(𝑥 − 4) = 0

______ 129) When the polynomial 3𝑣4 + 27𝑣2 is factored completely, which of the following is a correct

factor?

A) 𝑣 + 3 B) 𝑣 − 3

C) 3𝑣 D) 𝑣2 + 9

______ 130) When factored completely, which is a factor of 7𝑥3 − 7𝑥2 − 140𝑥 ?

A) 7𝑥 + 28 B) 𝑥 − 4

C) 𝑥 − 5 D) 𝑥 + 5

______ 131) Which values of 𝑥 make the quadratic 𝑥2 + 𝑥 − 12 = 0 true?

A) {−6 , 2} B) {−4 , 3}

C) {−3 , 4} D) {−2 , 6}

______ 132) Which of the following is a solution to 2𝑏2 + 2𝑏 − 12 = 0 ?

A) −12 B) −3

C) −2 D) 0

______ 133) Solve: 𝑥2 − 𝑥 = 0

A) 𝑥 = 0 B) 𝑥 = 1

C) 𝑥 = {0 , 1} D) 𝑥 = {−1 , 0}

______ 134) Which of the following is a factor of 𝑥2 − 2𝑥 − 24 ?

A) (𝑥 − 6) B) (𝑥 + 6)

C) (𝑥 − 4) D) (𝑥 + 8)

______ 135) Factor completely: 4𝑥2 − 𝑥 − 14

A) (4𝑥 + 7)(𝑥 − 2) B) (2𝑥 − 7)(2𝑥 + 2)

C) (4𝑥 − 7)(𝑥 + 2) D) (2𝑥 + 7)(2𝑥 − 2)

______ 136) A rectangular sheet of paper has an area of 55 square inches. Its dimensions are (𝑥 + 2)

inches by (𝑥 + 8) inches. What are the dimensions of the sheet of paper?

A) 5 inches by 11 inches B) 6 inches by 11 inches

C) 5 inches by 12 inches D) 5 inches by 10 inches

______ 137) The length of a rectangular window is 5 feet more than it its width, 𝑤. The area of the window

is 36 square feet. Which equation could be used to find the dimensions of the window?

A) 𝑤2 + 5𝑤 + 36 = 0 B) 𝑤2 − 5𝑤 + 36 = 0

C) 𝑤2 − 5𝑤 − 36 = 0 D) 𝑤2 + 5𝑤 − 36 = 0

______ 138) The greatest common factor (GCF) of 𝑎5𝑏𝑛 and 𝑎3𝑛𝑏5 is 𝑎5𝑏3. What is the value of 𝑛?

A) 𝑛 = 2 B) 𝑛 = 3

C) 𝑛 = 4 D) 𝑛 = 5

______ 139) Suppose 𝑥2 − 6𝑥 + 𝑐 = (𝑥 + 𝑚)(𝑥 + 𝑛) where 𝑐, 𝑚, 𝑛, are integers. Which of the following

are possible values of 𝑚 and 𝑛?

A) 𝑚 = −2 and 𝑛 = −3 B) 𝑚 = −1 and 𝑛 = −5

C) Both A and C D) None of these

______ 140) Suppose 𝑥2 + 4𝑥 + 𝑐 = (𝑥 + 𝑚)(𝑥 + 𝑛) where 𝑐, 𝑚, 𝑛, are integers. Which of the following

are NOT possible values of m and n?

A) 𝑚 = 2 and 𝑛 = 2 B) 𝑚 = −1 and 𝑛 = 5

C) 𝑚 = −2 and 𝑛 = −2 D) 𝑚 = 1 and 𝑛 = 3

Section 8: Rational Expressions

______ 141) Simplify: −3𝑥3+9𝑥2+30𝑥

−3𝑥3−18𝑥2−24𝑥 ; 𝑥 ≠ {−4 , −2, 0}

A) −1

2𝑥2 −

5

4𝑥 B) 𝑥3 −

1

2𝑥2 −

5

4𝑥

C) 𝑥−5

𝑥+4 D)

𝑥+5

𝑥−4

______ 142) Simplify the rational expression below completely.

𝑥2 − 9

(𝑥 + 3)2 ; 𝑥 ≠ −3

A) 𝑥−3

𝑥+3 B) 𝑥 − 3

C) 𝑥+3

𝑥−3 D)

𝑥2−9

(𝑥+3)2

______ 143) Simplify the rational expression 𝑞2+11𝑞+24

𝑞2−5𝑞−24 and state any restrictions on the variable.

A) 𝑞+8

𝑞−8 ; 𝑞 ≠ {−8 , −3} B)

𝑞+8

𝑞−8 ; 𝑞 ≠ {−3 , 8}

C) −(𝑞+8)

𝑞−8 ; 𝑞 ≠ 8 D)

−(𝑞+8)

𝑞−8 ; 𝑞 ≠ {−3 , 8}

______ 144) Two monomials are shown below.

9𝑎3𝑏 12𝑎2𝑏4

What is the least common multiple (LCM) of these monomials?

A) 36𝑎2𝑏 B) 36𝑎3𝑏4

C) 108𝑎2𝑏 D) 108𝑎3𝑏4

______ 145) Over the summer you mow lawns as a part-time job. You average 2 lawns every 45 minutes.

You work 6 hours each day. At this rate, how many lawns can you mow in one day?

A) 4 lawns B) 8 lawns

C) 12 lawns D) 16 lawns

______ 146) Which value of 𝑥 makes the expression 𝑥+4

𝑥−3 undefined?

A) −4 B) −3

C) 3 D) 0

______ 147) Which expression represents 2𝑥2−12𝑥

𝑥−6 ; 𝑥 ≠ 6 in simplest form?

A) 0 B) 2𝑥

C) 4𝑥 D) 2𝑥 + 2

______ 148) Simplify: −𝑥3−4𝑥2+12𝑥

−𝑥3−8𝑥2−12𝑥 ; 𝑥 ≠ {−6 , −2, 0}

A) 1

2𝑥2 − 𝑥 B) 𝑥3 +

1

2𝑥2 − 𝑥

C) 𝑥−2

𝑥+2 D)

𝑥+2

𝑥−2

______ 149) Tammy made similar models of a building, with dimensions, in inches, as shown in the diagram

below.

What is the value, in inches, of 𝑥?

A) 3 B) 4

C) 5 D) 6

______ 150) Charlie needs to simplify the expression below before he substitutes values for 𝑥 and 𝑦.

𝑥18𝑦12+𝑥9𝑦8

𝑥3𝑦4

If 𝑥 ≠ 0 and 𝑦 ≠ 0, which of the following is a simplified version of the expression above?

A) 𝑥9𝑦5 B) 𝑥24𝑦16

C) 𝑥6𝑦3 + 𝑥3𝑦2 D) 𝑥15𝑦8 + 𝑥6𝑦4

______ 151) Simplify: (𝑥−7)2

𝑥(𝑥−4)−21 ; 𝑥 ≠ {−3 , 7}

A) −14 B) 7𝑥+7

2𝑥−3

C) 1

𝑥+3 D)

𝑥−7

𝑥+3

______ 152) Simplify the rational expression below and state the values that make the domain undefined.

𝑝(𝑝 − 4) − 32

𝑝 + 4

A) −𝑝 + 8 ; 𝑝 ≠ −4 B) −𝑝 − 8 ; 𝑝 ≠ 4

C) 𝑝 − 8 ; 𝑝 ≠ −4 D) 𝑝 + 8 ; 𝑝 ≠ 4

______ 153) Simplify: −2𝑥2+32𝑥−126

−2𝑥2+12𝑥+14 ; 𝑥 ≠ {−1 , 7}

A) 𝑥2 +8

3𝑥 − 9 B) −9

C) 𝑥−9

𝑥+1 D)

𝑥+9

𝑥−1

______ 154) Two monomials are shown below.

5𝑥7𝑦3 20𝑥9𝑦4

What is the least common multiple (LCM) of these monomials?

A) 20𝑥7𝑦3 B) 5𝑥9𝑦4

C) 100𝑥9𝑦4 D) 20𝑥9𝑦4

______ 155) Simplify: −2𝑦2−11𝑦−5

−𝑦2−6𝑦−5 ; 𝑦 ≠ {−5 , −1}

A) 2 B) 𝑦+1

2𝑦+5

C) 2𝑦+1

𝑦+1 D)

2𝑦+11

𝑦+6

______ 156) Simplify: −𝑥2(𝑥−16)−64𝑥

−𝑥3+4𝑥(𝑥+8) ; 𝑥 ≠ {−4, 0, 8}

A) 𝑥+8

𝑥−4 B)

𝑥−8

𝑥+4

C) 𝑥3 + 4𝑥2 − 2𝑥 D) 4𝑥2 − 2𝑥

______ 157) Two monomials are shown below.

36𝑥𝑦2𝑧4 20𝑥3𝑦3𝑧2

What is the least common multiple (LCM) of these monomials?

A) 4𝑥𝑦2𝑧2 B) 180𝑥𝑦2𝑧2

C) 4𝑥3𝑦3𝑧4 D) 180𝑥3𝑦3𝑧4

______ 158) Simplify: 2𝑚6−6𝑚4−4𝑚2

2𝑚2

A) 2𝑚3 − 6𝑚2 − 4 B) 𝑚4 − 4𝑚2 − 2

C) 𝑚4 − 3𝑚2 − 2 D) 𝑚3 − 3𝑚2 − 2𝑚

______ 159) There are 0.5 milligrams of iron in a 3.5 ounce serving of cod. How much iron is in 5 ounces of

cod?

A) 1.4 mg B) 0.7 mg

C) 0.4 mg D) 1.7 mg

______ 160) It is recommended that there be at least 13.8 square feet of ground space in a

garden for every newly planed shrub. The garden is rectangular and measures 32.2 feet long

and 18 feet wide. Find the maximum number of shrubs the garden can accommodate.

A) 3 shrubs B) 13 shrubs

C) 42 shrubs D) 193 shrubs

Section 9: Radicals

______ 161) An expression is shown below.

2√51𝑥

Which value of 𝑥 makes the expression equivalent to 10√51 ?

A) 5 B) 25

C) 50 D) 100

______ 162) Saying that 4 < √𝑥 < 9 is equivalent to saying what about 𝑥?

A) 0 < 𝑥 < 65 B) 2 < 𝑥 < 3

C) 4 < 𝑥 < 9 D) 16 < 𝑥 < 81

______ 163) Simplify: √250

A) 5√10 B) 10√5

C) 25√10 D) 50√2

______ 164) When 𝑥 = 3, which expression can be completely simplified to 6√3 ?

A) 2√6𝑥 B) 2√3𝑥

C) 3√6𝑥 D) 2√9𝑥

______ 165) A list of real numbers is shown below.

4√5 √48 (3√3)2

(√3)3

List the real numbers shown from least to greatest.

A) (√3)3

, √48 , (3√3)2

, 4√5

B) (√3)3

, √48 , 4√5 , (3√3)2

C) (3√3)2

, 4√5 , √48 , (√3)3

D) (3√3)2

, (√3)3

, 4√5 , √48

______ 166) Keeli simplified the expression √864 for a homework assignment. If Keeli simplified the

expression correctly, which of the following is her answer?

A) 12√6 B) 144√3

C) 12√3 D) 144√6

______ 167) The value of 𝑑 is a real number such that 0.4 ≤ 𝑑 ≤ √0.5. A list of expressions is shown below.

√𝑑3 √𝑑4 2√𝑑2 𝑑2√𝑑

List the expressions from least to greatest for all possible values of 𝑑.

A) 𝑑2√𝑑 , √𝑑4 , √𝑑3 , 2√𝑑2

B) √𝑑4 , √𝑑3 , 2√𝑑2 , 𝑑2√𝑑

C) 2√𝑑2 , 𝑑2√𝑑 , √𝑑4 , √𝑑3

D) √𝑑3 , √𝑑4 , 2√𝑑2 , 𝑑2√𝑑

______ 168) Four expressions are shown below.

√𝑥2 𝑥3 2

𝑥

𝑥

3

Which inequality comparing two of the expressions is true when 0.2 ≤ 𝑥 ≤ 0.6.

A) 𝑥3 >2

𝑥 B) 𝑥 >

2

𝑥

C) 𝑥

3> 𝑥3 D) √𝑥2 > 𝑥

______ 169) Five expressions are shown below.

−√25 √7 1

2√32 𝜋√81 √24

Which expressions are irrational?

A) √7 ,1

2√32 , 𝜋√81 , √24 B) √7 , 𝜋√81

C) All of the expressions D) None

______ 170) Simplify: 1

3(3√3)

−2

A) −27 B) 27

C) −3 D) 1

81

______ 171) Simplify the radical √240 completely.

A) 4√15 B) 16√15

C) 2√60 D) 4√60

______ 172) Solve: 4 + √𝑦 − 3 = 11

A) 52 B) 46

C) 14 D) 10

______ 173) Which value is an irrational number greater than √72 ?

A) √48 B) √81

C) √108 D) √144

______ 174) Simplify the radical expression 5√3𝑥 completely if 𝑥 = 6.

A) 15√2 B) 15√18

C) 3√10 D) 6√5

______ 175) An expression is shown below.

3√18𝑥

Which value of 𝑥 makes the expression equivalent to 18√2 ?

A) 4 B) 6

C) 9 D) 36

______ 176) The formula 𝑆 = 5.5√𝑐𝑙 is used to find the speed of a vehicle, 𝑆, in miles per hour, given the

coefficient of friction, 𝑐, between the road surface and the tires, and the length, 𝑙, of the skid

mark, measured in feet. Find the speed of the vehicle when the coefficient of friction is 0.75

and the skid mark is 140 feet long.

A) 25.7 mph B) 56.4 mph

C) 57.8 mph D) 65.3 mph

______ 177) Simplify: 1

2(−√64) ÷ (2√5)2 ∙ √25

A) −1 B) −1

5

C) 5 D) −5

______ 178) Simplify: 1

7(√49 ÷ 23) + 34 ÷ |−9|

A) 91

8 B) 8

1

9

C) 111

24 D) −8

7

8

______ 179) Suppose: 4√83𝑥

Which value of 𝑥 makes the expression above equivalent to 32√83 ?

A) 1,024 B) 64

C) 256 D) 8

______ 180) If 𝑥 = 16, order the four statements below from least to greatest.

𝑥√𝑥 2𝑥√𝑥2 𝑥

4√4𝑥

𝑥2

𝑥

A) 𝑥2

𝑥 , 𝑥√𝑥 ,

𝑥

4√4𝑥 , 2𝑥√𝑥2

B) 𝑥2

𝑥 , 𝑥√𝑥 , 2𝑥√𝑥2 ,

𝑥

4√4𝑥

C) 𝑥2

𝑥 ,

𝑥

4√4𝑥 , 𝑥√𝑥 , 2𝑥√𝑥2

D) 2𝑥√𝑥2 , 𝑥√𝑥 ,𝑥

4√4𝑥 ,

𝑥2

𝑥

Section 10: Constructed-Response Questions (CRQ)

181) The scatter plot shows the attendance and final grades of students in a class.

A) What is the final grade of the student who missed 8 classes?

B) Does the data show a positive correlation, a negative correlation, or no relationship? Explain.

C) Write an equation of the line of best fit in slope-intercept form.

D) Use your equation from part C to predict the final grade of the student who missed 12 classes.

Show your work.

182) A large washtub already contains 6 gallons of water. A faucet is turned on and continues to fill the

washtub at a rate of 1

2 gallon per minute.

A) How many total gallons of water will be in the washtub when the faucet has been on for 5

minutes?

B) When the faucet has been on for 𝑥 minutes, there will be 𝑦 gallons of water in the washtub.

Write a linear equation to model the number of gallons of water (𝑦) in the washtub 𝑥 minutes

after the faucet has been turned on.

C) Using your equation from part B, determine the number of minutes from when the faucet is

turned on until there are exactly 233

4 gallons of water in the washtub.

D) A second washtub already contains 2 gallons of water. A larger faucet is used to fill this

washtub at a rate of 11

2 times the rate of the first faucet. If both faucets are turned on at the

same time, determine the number of minutes until both washtubs contain the same number

of gallons of water.

183) The table shows the height 𝑦 (in meters) of a rising hot air balloon after 𝑥 seconds.

A) Write a linear equation in slope-intercept form that represents the data in the table.

B) What is the height of the balloon after 10 seconds?

C) The equation 𝑦 = −2𝑥 + 24 gives the height 𝑦 (in meters) of another hot air balloon that

begins descending at the same time. Graph this equation and the equation from Exercise 1 on

the same coordinate plane. Use a scale of 2 on both the x-axis and the y-axis.

D) When are the balloons at the same height? Justify your answer algebraically or graphically.

184) The list below shows the number of PJ Masks episodes Arya watched on each of six consecutive days.

4 , 11 , 1 , 5 , 13, 11

A) What are the median and mode number of episodes Arya watched?

B) Arya found the range of episodes watched to be 12 episodes. Explain why the range does not

describe a typical number of episodes she watches.

C) How many episodes does Arya need to watch on day seven to have a mean of 9. Show or

explain all your work.

185) Rolando drives at least 40 miles but less than 60 miles each week.

A) Graph the compound inequality representing all of the possible distances Rolando could drive for 8 weeks.

B) Explain why you chose to use the symbols you used for the endpoints of the compound

inequality in part A.

C) Rolando buys at least 8.5 but no more than 11 gallons of gas each week. The price of gas has ranged from $2.40 to $2.65 per gallon each week. Write an inequality to model all the possible amounts of money (𝑚) Rolando spends on gas each week. Show or explain all your work.

186) You and your friend are training for the cross country team. The graph shows your two-mile times 𝑡 (in

minutes) as a function of the number of weeks 𝑤 you have trained. The table shows your friend’s two-

mile times 𝑡 (in minutes) as a function of the number of weeks 𝑤 your friend has trained.

A) Who had a faster time before you began training?

B) Who had a faster time after 10 weeks of training?

C) Whose time is decreasing faster?

D) Write the equation of the line, in slope-intercept form, that represents your two-mile times.

E) If the pattern continues, after what week will you and your friend have the same two-mile

time?

187) The table shows the percent of battery life (in decimal form) remaining in a toy helicopter since you

started flying it.

A) Write a linear function in slope-intercept form that relates the battery life 𝑏 to the number 𝑚

of minutes you fly the helicopter.

B) Interpret the slope and 𝑦-intercept.

slope =

𝑦-intercept =

C) Why must the slope be negative in the context of this scenario? Explain.

D) You fly the helicopter until the battery runs out. How long did you fly the helicopter?

188) Students must design and create a structure that will store an egg and prevent it from breaking when

dropped from a height of 30 feet. The graph shows the height 𝑦 (in feet) of a structure 𝑥 seconds after

it was dropped with an egg inside.

A) On what part of the domain is the graph nonlinear? Explain your reasoning.

B) On what part of the domain is the graph linear? Explain your reasoning.

C) At what rate does the structure fall after the parachute fills with air?

D) Find the equation, in slope-intercept form, for the linear part of the graph showing the height

𝑦 (in feet) of a structure after filling with air 𝑥 seconds after it was dropped with an egg inside.

E) What does the 𝑥-intercept represent in this situation? Explain your reasoning.

189) You invited 17 people to your house for a party. You want to spend a $50 gift card completely on the

items shown. You also want to have exactly two servings of food for each person.

A) Define your variables.

x =

y =

B) Write a system of linear equations that represents this situation.

Equation 1:

Equation 2:

C) Solve the system of linear equations from part B.

D) How many pizzas should you buy? How many bags of wings should you buy?

Pizzas:

Bags of Wings:

E) The price of a bag of wings increases to $7.50. Now how many of each item should you buy?

190) The graph shows a school cafeteria’s profit 𝑃 for selling 𝑥 lunches on pizza day.

A) Find the slope of the line in the graph above.

B) Write an equation of the line in slope-intercept form of profit, 𝑃 , (in

dollars) in terms of number of lunchs sold, 𝑥.

C) Find and interpret the 𝑥-intercept.

𝑥-intercept =

Interpretation:

D) Find and interpret the 𝑦-intercept.

𝑦-intercept =

Interpretation:

E) What is the profit for selling 100 lunches on pizza day?

F) How many lunches need to be sold on pizza day for the school cafeteria to

make a profit of $270?

191) A bank charges $3 each time you use an out-of-network ATM. At the beginning of the month, you have

$1500 in your bank account. You withdraw $60 from your bank account each time you use an out-of-

network ATM.

A) Write an equation in slope-intercept form that represents the balance in your account 𝑦 after

you use an out-of-network ATM 𝑥 times.

B) Explain why the slope must be negative from part A.

C) How many times can you withdraw from an out-of-network ATM before you run out of

money?

D) What is your balance if you withdraw 17 times from an out-of-network ATM?

192) At a balloon popping competition, competitors get 8 points for every red balloon they pop and 3

points for every blue balloon they pop. Each round of the competition lasts 1 minute.

A) Gina wrote the following system of linear equations.

𝑥 + 𝑦 = 413𝑥 + 8𝑦 = 183

What does the 𝑦-variable represent in Gina’s system of linear equations?

B) How many points did Gina score during the competition popping blue balloons?

C) A second competitor, Ashleigh, popped 29 balloons and scored a total of 137 points.

Write a system of two linear equations to represent Ashleigh’s performance. Let 𝑥 and 𝑦 have

the same representation as they did in Gina’s system of linear equations in part A.

Equation 1:

Equation 2:

D) A third competitor, Nancy, wrote a system of linear equations to represent her performance of

scoring 112 points. She solved the system of linear equations and found that the solution was

(8, 16).

Explain how you know that Nancy made a mistake in solving her system of equations.

193) Mrs. Sampson opens a 500-piece bag of candy. Students start consuming the candy at a rate of 30

pieces per day.

A) Let 𝑥 = the number of school days since the bag of candy was opened. Let 𝑦 = the number of

pieces of candy remaining. Write a linear function using 𝑓(𝑥) for this situation.

B) Using your function from part A, evaluate 𝑓(10).

C) Explain the real-world meaning of the number that you got in part B.

D) On a certain day, there are 320 pieces of candy remaining. How many days have passed since

the package of candy was opened? Show your work.

E) When your function from part A is graphed, what will the slope and 𝑦-intercept be? Then

interpret the slope and 𝑦-intercept with regard to this scenario.

Slope =

Interpretation:

𝑦-intercept =

Interpretation:

194) At a state fair, there is a game where you throw a ball at a pyramid of cans. If you knock over all of the

cans, you win a prize. The cost is 3 throws for $1, but if you buy a special wristband when you enter

the fair, you can get 6 throws for $1. The wristband costs $10.

A) If 𝑥 = the number of throws and 𝐶 = cost, write two cost equations for the game in terms of

the number of throws purchased, one without a wristband and one with.

Without Wristband:

With Wristband:

B) Using a scale of 10 on both axes, graph the cost equations from part A on the graph below. Be

sure to label each axis.

C) Find and interpret the point of intersection.

Point of Intersection:

Interpretation:

D) When does it make sense to buy the wristband?

195) A large bucket that is full of water has a small leak on the bottom. The bucket loses water at a rate of

0.5 gallons per minute. After 6 minutes, the bucket contains exactly 9 gallons of water.

A) How many gallons of water were initially in the bucket?

B) Write an equation in point-slope form to model the number of gallons (𝑦) of water after 𝑥

minutes.

C) How many minutes does it take for the bucket to lose 7.5 gallons of water?

D) What is the total number of minutes it will take for the bucket to be completely empty?

196) A clothing manufacturer has 1,000 yards of cotton to make shirts and pajamas. A shirt requires 1 yard

of fabric and a pair of pajamas requires 2 yards of fabric. It takes 2 hours to make a shirt and 3 hours

to make the pajamas. There are at most 1,800 hours available to make the clothing.

A) Let 𝑥 = the number of shirts and let 𝑦 = the number of pajamas. Explain why 𝑥 ≥ 0 and 𝑦 ≥ 0

act as constraints to this problem.

B) Write a system of two linear inequalities that model this situation.

Inequality 1:

Inequality 2:

C) Graph the inequalities from part B and shade the solution set. Use a scale of 50 on both axes.

D) Explain, either graphically or algebraically, why the ordered pair (850, 50) is not a solution to

the system of linear inequalities.

197) Jasmine created a painting on a rectangular sheet of paper with a width of √10 feet and a length of

√32 , as shown in the diagram below.

A) Find the exact area of the painting, in simplified form. Show each step.

B) When Jasmine’s painting was unveiled, the school made a smaller version of the painting to

advertise the event. The replica’s length and width were half the size of the original painting.

Find the exact area of the replica, in simplified form. Show each step.

C) Determine by what factor the area of the replica decreased when compared to the area of the

mural. Show each step.

198) City officials are putting a garden around a memorial site as shown in the diagram below.

A) Determine the area of the memorial site in terms of 𝑥. Write your answer in simplified

polynomial form and include units.

B) The outside edges of the garden form a rectangle whose length and width are proportional to

the sides of the memorial site, increased by a scale factor of 3. What is the difference between

the perimeter of the garden and the perimeter of the memorial site? Write your answer in

simplified polynomial form and include units.

C) Determine the area of the garden in terms of 𝑥. Write your answer in simplified polynomial

form and include units.

199) A new home security company is planning to open a technical support center to answer customer

phone calls and e-mails. The company plans to purchase a large building with an open floor plan to

house cubicles where operators will sit while they work. There are two options for cubicles: a small

cubicle that can house one operator and a larger cubicle that can house two operators. The company

knows it wants at least 15 cubicles. However, because of rising costs of employee benefits, the

company wants to hire at most 20 operators.

A) This information can be modeled with a system of linear inequalities. When 𝑥 is the number of

small cubicles built and 𝑦 is the number of large cubicles built. Two of the inequalities that act

as restrictions concerning this situation are 𝑥 ≥ 0 and 𝑦 ≥ 0. Explain why these two

inequalities serve as restrictions on the system of inequalities.

B) Write two more inequalities to complete the system.

Inequality 1:

Inequality 2:

C) Graph the solution set for the system of inequalities from part B. Label each axis and use a

scale of 2 on both axes.

D) The first location the company finds is smaller than it would like. The space will only hold 10

cubicles total. If the company still wants to employ up to 20 operators, is it possible in this

space to have the maximum number of cubicles and operators with a combination of both

small and large cubicles? Explain your answer mathematically.

200) Albert sells baseball programs at a stadium. The function 𝑚(𝑥) = 2.50𝑥 represents the total amount

of money collected, in dollars, for selling 𝑥 baseball programs.

A) Fill in the table with the amounts of money collected for selling baseball programs.

B) The cost, in dollars, to print up 𝑥 programs for each game is represented by the function

𝑐(𝑥) = 0.50𝑥 + 40. On the grid below, draw a line that contains the coordinate points of the

cost to print up 𝑥 programs for each game.

C) In addition to his hourly wage, Albert earns a bonus when the amount of money collected is

greater than the cost to print the total number of programs he sold. His bonus is equal to 1

2 of

the difference between the amount of money collected, 𝑚(𝑥) = 2.50𝑥 and

𝑐(𝑥) = 0.50𝑥 + 40. How much money does Albert earn as a bonus when he sells 309 baseball

programs? Show all of your work.