Ms. Jones is taking the Drama Club on a field trip to see the musical Phantom of the Opera. The school treasurer asked Ms. Jones for the group’s total ticket cost. He wrote the following cost function for the school treasurer: Total Cost = 53 (40 + 4) Which of the following statements best describes this cost function?

Tickets cost $53 each, and there are 40 students and 4 teachers going on the field trip.

A total of 53 people, which included 40 students and 4 teachers, will attend the field trip.

The bus fits 53 people, including 40 students and 4 teachers.

The school will buy 53 tickets for the musical. Tickets cost $40 for each student and $4 for each teacher.

A shoe store is having a sale in which all tennis shoes are $25. The sales tax is 7%. If Dan buys n tennis shoes during this sale, the total cost of his purchase will be 25n + 0.07(25n). Interpret the meaning of 0.07(25n) in this context.

The expression 0.07(25n) represents the total tax on Dan’s purchases.

Last weekend, Cindy purchased two tops, a pair of pants, and a skirt in her favorite store. The equation T = 1.075x can be used to calculate her total cost where x represents the pretax subtotal cost of her purchase. In the equation T = 1.075x, what does the number “1” represent? Explain using the context of Cindy’s situation. In the equation T = 1.075x, what does the number “0.075” represent? Explain using the context of Cindy’s situation.

1 represents 100% or the cost of Cindy's purchase before tax is added. The number 0.075 represents the tax rate, 7.5% and when multiplied to x, the result is the tax dollar amount.

What is the difference between a rational and irrational number?

A rational number can be written as a ratio of two integers whereas an irrational number cannot.

An irrational number is a non-terminating/non-repeating decimal whereas a rational number is a terminating or repeating decimal.

If a, b, c, and d are integers. Then a/b + c/d will:

Always produce a rational number.

Sometimes produce a rational number.

Never produce a rational number.

Describe the difference between a rational and an irrational number. Give a general explanation and an example of each.

Rational numbers can be written as terminating or repeating decimals and Irrational numbers cannot.

Rational numbers can be written as fractions where irrational numbers cannot.

Explain why the product of a non-zero rational number and an irrational number is irrational.

Multiplication does not change the irrational number. Multiplication serves to make the irrational number bigger.

The homecoming committee bought 500 plastic souvenir footballs to sell at the homecoming game to raise money for a local charity. The profit (in dollars), p, from the sale of s footballs can be represented by the following equation. p = 5s – 128 Since the homecoming committee bought only 500 footballs, they can sell no more than this. Represents this constraint with an inequality.

0 ≤ s ≤ 500 0\le s\le500 0 ≤ s ≤ 5 0 0

0 ≥ s ≥ 500 0\ge s\ge500 0 ≥ s ≥ 5 0 0

The homecoming committee bought 500 plastic souvenir footballs to sell at the homecoming game to raise money for a local charity. The profit (in dollars), p, from the sale of s footballs can be represented by the following equation. p = 5s – 128 Is it possible for the profit to be exactly $1500? Show your work and justify your answer.

No, the number of footballs which must be sold to bring in $1500 is not possible. The number to sell is 325.6

Yes, the number of footballs which must be sold to bring in $1500 is possible. The number to sell is 325

There is not enough information

The homecoming committee bought 500 plastic souvenir footballs to sell at the homecoming game to raise money for a local charity. The profit (in dollars), p, from the sale of s footballs can be represented by the following equation. p = 5s – 128 Is it possible for the profit to be at least $2400? Show your work and justify your answer.

No, the number of footballs which must be sold to bring in $2400 is not possible. The number to sell is more than 500.

Yes, the number of footballs which must be sold to bring in $2400 is possible. The number to sell is less than 500.

There is not enough information

Cassie knows the height and the required volume of a cone-shaped vase she’s designing. Which formula can she use to determine the radius of the vase?

r = 3 V π h r=\sqrt{\frac{3V}{\pi h}} r = π h 3 V <path d="M424,2478c-1.3,-0.7,-38.5,-172,-111.5,-514c-73, -342,-109.8,-513.3,-110.5,-514c0,-2,-10.7,14.3,-32,49c-4.7,7.3,-9.8,15.7,-15.5, 25c-5.7,9.3,-9.8,16,-12.5,20s-5,7,-5,7c-4,-3.3,-8.3,-7.7,-13,-13s-13,-13,-13, -13s76,-122,76,-122s77,-121,77,-121s209,968,209,968c0,-2,84.7,-361.7,254,-1079 c169.3,-717.3,254.7,-1077.7,256,-1081c4,-6.7,10,-10,18,-10H400000v40H1014.6 s-87.3,378.7,-272.6,1166c-185.3,787.3,-279.3,1182.3,-282,1185c-2,6,-10,9,-24,9 c-8,0,-12,-0.7,-12,-2z M1001 80H400000v40H1014z">

r = V 3 π h r=\sqrt{\frac{V}{3\pi h}} r = 3 π h V <path d="M424,2478c-1.3,-0.7,-38.5,-172,-111.5,-514c-73, -342,-109.8,-513.3,-110.5,-514c0,-2,-10.7,14.3,-32,49c-4.7,7.3,-9.8,15.7,-15.5, 25c-5.7,9.3,-9.8,16,-12.5,20s-5,7,-5,7c-4,-3.3,-8.3,-7.7,-13,-13s-13,-13,-13, -13s76,-122,76,-122s77,-121,77,-121s209,968,209,968c0,-2,84.7,-361.7,254,-1079 c169.3,-717.3,254.7,-1077.7,256,-1081c4,-6.7,10,-10,18,-10H400000v40H1014.6 s-87.3,378.7,-272.6,1166c-185.3,787.3,-279.3,1182.3,-282,1185c-2,6,-10,9,-24,9 c-8,0,-12,-0.7,-12,-2z M1001 80H400000v40H1014z">

r = 3 V π h r=\frac{\sqrt{3V}}{\pi h} r = π h 3 V <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

r = ± 3 V π h r=\pm\sqrt{\frac{3V}{\pi h}} r = ± π h 3 V <path d="M424,2478c-1.3,-0.7,-38.5,-172,-111.5,-514c-73, -342,-109.8,-513.3,-110.5,-514c0,-2,-10.7,14.3,-32,49c-4.7,7.3,-9.8,15.7,-15.5, 25c-5.7,9.3,-9.8,16,-12.5,20s-5,7,-5,7c-4,-3.3,-8.3,-7.7,-13,-13s-13,-13,-13, -13s76,-122,76,-122s77,-121,77,-121s209,968,209,968c0,-2,84.7,-361.7,254,-1079 c169.3,-717.3,254.7,-1077.7,256,-1081c4,-6.7,10,-10,18,-10H400000v40H1014.6 s-87.3,378.7,-272.6,1166c-185.3,787.3,-279.3,1182.3,-282,1185c-2,6,-10,9,-24,9 c-8,0,-12,-0.7,-12,-2z M1001 80H400000v40H1014z">

Solve the following equation for x, in terms of a and b. ax = 15 + bx

x = 15 a − b x=\frac{15}{a-b} x = a − b 1 5

x = 15 − ( a − b ) x=15-\left(a-b\right) x = 1 5 − ( a − b )

x = 15 + ( a − b ) x=15+\left(a-b\right) x = 1 5 + ( a − b )

x = a − b 15 x=\frac{a-b}{15} x = 1 5 a − b

Solve each formula for the indicated variable. Show all of your work. Solve for x: y = mx + b Solve for d: k = 5(d – 6) Check all that apply.

x = y − b m x=\frac{y-b}{m} x = m y − b

d = k 5 + 6 d=\frac{k}{5}+6 d = 5 k + 6

x = y + b m x=\frac{y+b}{m} x = m y + b

d = k + 6 5 d=\frac{k+6}{5} d = 5 k + 6

Solve the formula for the indicated variable. Show all of your work. Solve for y 2 y_2 y 2 : m = y 2 − y 1 x 2 − x 1 m=\frac{y_2-y_1}{x_2-x_1} m = x 2 − x 1 y 2 − y 1

y 2 = m ( x 2 − x 1 ) + y 1 y_2=m\left(x_2-x_1\right)+y_1 y 2 = m ( x 2 − x 1 ) + y 1

y 2 = m + y 1 x 2 − x 1 y_2=\frac{m+y_1}{x_2-x_1} y 2 = x 2 − x 1 m + y 1

y 2 = m x 2 − x 1 + y 1 y_2=\frac{m}{x_2-x_1}+y_1 y 2 = x 2 − x 1 m + y 1

y 2 = m ( x 2 + x 1 ) − y 1 y_2=m\left(x_2+x_1\right)-y_1 y 2 = m ( x 2 + x 1 ) − y 1

What two properties are used in the following solution to 5x – 7 = 23? 5x – 7 = 23 5x – 7 + 7 = 23 + 7 5x = 30 5x/5 = 30/5 x = 6

Addition Property of Equality and Division Property of Equality

Subtraction Property of Equality and Addition Property of Equality

Multiplication Property of Equality and Distributive Property

Subtractions Property of Equality and Zero Product Property

Which of the following properties would not be used to justify any of the steps below?

Subtraction Property of Equality

Multiplication Property of Equality

Zoey is solving the equation 7x + 3(x – 2) = 14. Her first step is shown as 7x + 3x – 6 = 14. Which statement best describes Zoey’s work in her first step.

She distributed 3 to the terms in the parentheses.

She combined the terms 3 and x.

She combined like terms by adding them together.

She removed parentheses in order to isolate the variable.

A student solved the equation 3x + 2 = 9 – x as shown below. Assume there is a value of x that satisfies the equation. Provide the definition, property, or theorem that justifies each step of the solution process. 3x + 2 = 9 – x (1) 4x + 2 = 9 Justification: (2) 4x = 7 Justification: (3) x=7/4 Justification:

Addition Property of Equality, Subtraction Property of Equality, Division Property of Equality

Addition Property, Subtraction Property, Division Property

Let a, b, and c be constants, and let x be a variable. Which of the following is equivalent to a(x + b) < c when a < 0?

x > c a − b x>\frac{c}{a}-b x > a c − b

x < c − b a x<\frac{c-b}{a} x < a c − b

x > c − b a x>\frac{c-b}{a} x > a c − b

x < c a − b x<\frac{c}{a}-b x < a c − b

Gabriel has already read 200 pages of his 530-page summer reading book. If he reads at an average rate of 55 pages per hour, how long will he need to finish the book? Write and solve an equation to find the answer. Show your work.

(530 - 200) / 55 = time, 330/55 = 6 hours

EOC Practice #1

Quiz

•

Mathematics

•

9th - 12th Grade

•

Practice Problem

•

Hard

•

CCSS

HSA.CED.A.4, HSA-SSE.A.1A, HSA.REI.A.1

+18

Standards-aligned

Araceli Miranda

Used 18+ times

FREE Resource

39 questions

Show all answers

FILL IN THE BLANK QUESTION

15 mins • 1 pt

John designs computer labs for a community college. The
college has 115 computers and receives 26 additional
computers each year. What expression can Sue use to
determine the number of computers the college will
have in n years?

Answer explanation

Start with 115 computers.
Receive 26 additional each year.
n = number of years
26n + 115

Tags

CCSS.6.EE.B.6

FILL IN THE BLANK QUESTION

15 mins • 1 pt

Kaye want to make trail mix made up of almonds, walnuts, and raisins. She wants to mix one part almonds, three parts walnuts, and four parts raisins. Almonds cost $10 per pound, walnuts cost $12 per pound, and raisins cost $6 per pound.
Kaye has $25 to spend on the trail mix. Determine how many pounds of trail mix she can make.

Answer explanation

Let x = pounds of an ingredient
1 almonds: 3 walnuts: 4 raisins
1:3:4
1x + 3x + 4x = 8x pounds of mix
10(x) + 12(3x) + 6(4x) = 25
70x = 25
x = 25/70 = 5/14
8(5/14) = 2 6/7
Kaye can make 2 6/7 lbs of trail mix.

Tags

CCSS.6.RP.A.3B

FILL IN THE BLANK QUESTION

15 mins • 1 pt

A rectangular garden measuring 15 meter by 12 meters is to have a walkway installed around it with a width of x meters, as shown in the diagram below. Together, the walkway and the garden have an area of 378 square meters. Write an equation (using factors) that can be used to find x, the width of the walkway.

Answer explanation

x = width of walkway
One side of the garden including walkway = 2x+12
Other side of the garden including walkway = 2x +15
Area is 378
Length x Width = Area
(2x + 12)(2x +15) = 378

FILL IN THE BLANK QUESTION

15 mins • 1 pt

An animal shelter spends $3.45 per day to care for each cat and $6.50 per day to care for each dog. Pat noticed that the shelter spent $92.20 caring for cats and dogs on Wednesday. Pat said that there might have been 8 cats and 14 dogs at the shelter on Wednesday. Are Pat’s numbers possible? Create an equation to represent the possible number of cats and dogs that could have been at the shelter on Wednesday and use it to justify you answer.

Answer explanation

c = cats d = dogs
$3.45 to care for cats $6.50 to care for dogs
Total spent = $92.20
3.45c + 6.50d = 92.20
3.45(8) + 6.50(14) = 92.20
118.60 ≠ 92.20
It is not possible for there to have been 8 cats and 14 dogs at the shelter Wednesday.

Tags

CCSS.8.EE.C.7B

FILL IN THE BLANK QUESTION

15 mins • 1 pt

The Freshman Spirit Club took a trip to the state fair. There were 59 Students and 6 chaperones, and the total admission cost for the groups was $508. Student tickets cost $2 more than chaperone tickets.
Write and solve an equation to find the cost of a student ticket. Show your work and explain the meaning of your variable.

Answer explanation

Students = 59 Chaperones = 6
Total Admission = $508
Student Tickets = $2 + Chaperone Tickets
Let c = Chaperone Tickets
508 = 6c + 59(2 + c)
Chaperone tickets = $6
Therefore student tickets cost $8

Tags

CCSS.HSA.CED.A.1

FILL IN THE BLANK QUESTION

15 mins • 1 pt

A number n is divided by 9 is 3. What is the remainder when 3n + 5 is divided by 9?

Answer explanation

n/9=3, so therefore n=27
Substitute n for 27:
3(27)+5
Solve and then divide by 9 and the remainder is:
3(27) + 5 = 86
86÷9= 9 r 5
So the remainder is 5.

Tags

CCSS.7.EE.A.1

FILL IN THE BLANK QUESTION

15 mins • 1 pt

A company uses two different-sized trucks to deliver sand. The first truck can transport x cubic yards, and the second y cubic yards. The first truck makes S trips to a job site, while the second makes T trips. What quantities do the following expressions represent in terms of the problem’s context?
xS + yT

Answer explanation

1st truck transports x cubic yards and makes S trips.
2nd truck transports y cubic yards and makes T trips.
xS is the total amount delivered by the 1st truck
yT is the total amount delivered by the 2nd truck
So xS + yT is the total amount delivered by both trucks

Tags

CCSS.HSA-SSE.A.1A

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EOC Practice #1

39 questions

John designs computer labs for a community college. Thecollege has 115 computers and receives 26 additionalcomputers each year. What expression can Sue use todetermine the number of computers the college willhave in n years?

Start with 115 computers.Receive 26 additional each year.n = number of years26n + 115

Let x = pounds of an ingredient1 almonds: 3 walnuts: 4 raisins1:3:41x + 3x + 4x = 8x pounds of mix10(x) + 12(3x) + 6(4x) = 2570x = 25x = 25/70 = 5/148(5/14) = 2 6/7 Kaye can make 2 6/7 lbs of trail mix.

x = width of walkwayOne side of the garden including walkway = 2x+12Other side of the garden including walkway = 2x +15Area is 378Length x Width = Area(2x + 12)(2x +15) = 378

c = cats d = dogs$3.45 to care for cats $6.50 to care for dogsTotal spent = $92.203.45c + 6.50d = 92.203.45(8) + 6.50(14) = 92.20118.60 ≠ 92.20It is not possible for there to have been 8 cats and 14 dogs at the shelter Wednesday.

Students = 59 Chaperones = 6Total Admission = $508Student Tickets = $2 + Chaperone TicketsLet c = Chaperone Tickets508 = 6c + 59(2 + c)Chaperone tickets = $6Therefore student tickets cost $8

A number n is divided by 9 is 3. What is the remainder when 3n + 5 is divided by 9?

n/9=3, so therefore n=27Substitute n for 27:3(27)+5Solve and then divide by 9 and the remainder is:3(27) + 5 = 8686÷9= 9 r 5So the remainder is 5.

1st truck transports x cubic yards and makes S trips.2nd truck transports y cubic yards and makes T trips.xS is the total amount delivered by the 1st truckyT is the total amount delivered by the 2nd truckSo xS + yT is the total amount delivered by both trucks

40 represents the amount of students4 represent the amount of teachersThe total people attending is 44.The 53 represents the amount of cost for the tickets. So 53(44) = $2,332 which represents the total amount for the tickets.

A shoe store is having a sale in which all tennis shoes are $25. The sales tax is 7%. If Dan buys n tennis shoes during this sale, the total cost of his purchase will be 25n + 0.07(25n). Interpret the meaning of 0.07(25n) in this context.

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John designs computer labs for a community college. The
college has 115 computers and receives 26 additional
computers each year. What expression can Sue use to
determine the number of computers the college will
have in n years?

Start with 115 computers.
Receive 26 additional each year.
n = number of years
26n + 115

Let x = pounds of an ingredient
1 almonds: 3 walnuts: 4 raisins
1:3:4
1x + 3x + 4x = 8x pounds of mix
10(x) + 12(3x) + 6(4x) = 25
70x = 25
x = 25/70 = 5/14
8(5/14) = 2 6/7
Kaye can make 2 6/7 lbs of trail mix.

x = width of walkway
One side of the garden including walkway = 2x+12
Other side of the garden including walkway = 2x +15
Area is 378
Length x Width = Area
(2x + 12)(2x +15) = 378

c = cats d = dogs
$3.45 to care for cats $6.50 to care for dogs
Total spent = $92.20
3.45c + 6.50d = 92.20
3.45(8) + 6.50(14) = 92.20
118.60 ≠ 92.20
It is not possible for there to have been 8 cats and 14 dogs at the shelter Wednesday.

Students = 59 Chaperones = 6
Total Admission = $508
Student Tickets = $2 + Chaperone Tickets
Let c = Chaperone Tickets
508 = 6c + 59(2 + c)
Chaperone tickets = $6
Therefore student tickets cost $8

n/9=3, so therefore n=27
Substitute n for 27:
3(27)+5
Solve and then divide by 9 and the remainder is:
3(27) + 5 = 86
86÷9= 9 r 5
So the remainder is 5.

1st truck transports x cubic yards and makes S trips.
2nd truck transports y cubic yards and makes T trips.
xS is the total amount delivered by the 1st truck
yT is the total amount delivered by the 2nd truck
So xS + yT is the total amount delivered by both trucks

40 represents the amount of students
4 represent the amount of teachers
The total people attending is 44.
The 53 represents the amount of cost for the tickets.
So 53(44) = $2,332 which represents the total amount for the tickets.