Level Up: BenchMark 3 Review

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100

A penny is dropped from the roof of a tower that is 408 meters in height. The penny falls at a constant speed of 17 meters per second.

Which equation represents the height of the penny from the bottom of the tower? Let h represent the height of the penny in meters, and let t represent the number of seconds since the penny was dropped.

A. h= 17 + 408t

B. h= -17 - 408t

C. h= 17t - 408

D. h= -17t + 408

D. -17t + 408

100

Monika is in charge of ordering pens for an upcoming convention. Pens come in boxes of 6 and boxes of 8. Monika needs at least 720 pens. Which inequality describes this situation?

x = number of boxes of 6 pens

y = number of boxes of 8 pens

A. 6x + 8y >= 720

B. 8x + 6y >= 720

C. 6x + 8y <= 720

D. 8x + 6y <= 720

A. 6x + 8y >= 720

100

One solution for the equation has an x-value that is five times its y-value. What is that solution?

A. (3, 15)

B. (4, 8)

C. (15, 3)

D. (20, 40)

C. (15, 3)

100

What number can be added to both sides to create a perfect square when completing the square for

0 = x^2 - 4x + 7

A. -11

B. -3

C. 4

D. 7

C. 4

200

Melissa needs to earn at least $500 during the summer months. She babysits for $12 per hour and teaches swimming for $20 per hour. Due to her summer school class, she can only work 30 hours or less per week.

Which set of inequalities model this situation?

A. 20b +125 >= 500

b + s <= 30

B. 12b + 20s < 500

b + s >=30

C. 12b + 20s >=500

b + s <= 30

D. 20b +2s >=500

b + s =30

12b + 20s >=500

b + s <= 30

200

Iona sells pies and cakes. She sells pies for $8 and cakes for $11. Her goal is to sell a total of 200 cakes and pies next month. If p is the number of pies Iona sells and c is the number of cakes she sells, which of the following linear equations correctly models Iona's goal?

A. p + c = 200

B. p - c = 200

C. 8p + 11c = 200

D. 11p + 9c = 200

A. p + c = 200

200

Dennis has a maximum of $80 that he can spend on books. He wants to buy a combination of nonfiction books which cost $12 each and fiction books which cost $8 each. To evaluate his decision, Dennis makes a graph with the number of nonfiction books bought on the x-axis and the number of fiction books bought on the y-axis. He graphs a linear equation that models the fact that he has $80 to spend.

Which two ordered pairs represent points on the line that Dennis graphs?

A. (4, 5)

B. (4, 4)

C. (5, 4)

D. (7, 2)

E. (2, 7)

B. (4, 4)

E. (2, 7)

200

Marshall solves the equation

x^2 +14x = -22

by completing the square. Which answer correctly shows the equation in the form

(x + p )^2 = q

Choose the correct answer.

(x + 7)^2 = -27

(x+7)^2 = -22

(x+7)^2 = 27

(x+7)^2= 49

(x+7)^2 =27

300

Hannah brings $20 to her school's Field Day. The entrance fee to the field is $5.00 and each game on the field costs $1.50. Hannah decides to write and solve inequality to determine the greatest number of games she can play.

Let x represent the number of games Hannah plays. Which inequality represents her situation?

A. 1.50 + 5x<=20

B. 1.50x + 5 >=20

C. 1.50 + 5x >= 20

D. 1.50x + 5 <= 20

300

An arrow is shot at an upward velocity of 288 feet per second from a platform that is raised 4 feet off the ground. Use the vertical motion model -16t^2+vt+c where h is the ending height of the arrow, t is the time in seconds, v is the arrow's velocity, and c is the initial height, in feet, of the arrow. How long will it take the arrow to reach its maximum height and what is that maximum height? (Disregard any extra height added by the person firing the arrow.) At ___________ seconds, the arrow will reach its maximum height of ___________ feet.

At ____9_____ seconds, the arrow will reach its maximum height of ___1300____ feet.

300

The volume of a sphere, S, is at least one-third the volume of a cone, C. The volume of the cone is no more than 150 cubic centimeters. Which system of inequalities below represents this problem?

300

Solve for x.

2x^2-26x+84=0

A. x = { -7,6}

B. x={-15.679, 2.679}

C. x= {6,7}

D. x has no real solutions

C. x = {6, 7}

400

Amiya has $725 in savings. She plans to save an additional $25 per month. What is the number of additional months Amy will need to save money in order to have exactly $1000?

A. 11

B. 29

C. 40

D. 69

A. 11

400

At the county fair, Marie pays an entry fee of $5 and an additional $2 per ride. Let be the number of rides Marie pays for and let be the total cost of her trip to the fair. If the linear equation relating and in this problem were graphed on the coordinate axis below, which of the following points would the line pass? Select all of the ordered pairs that would lie on the graph.

A. (1,7)

C. (5,15)

E. (9,23)

400

Which of the following situations can be modeled by the inequality below?

60x < 50(x+3)

A. Damon drives at 60 miles per hour for a certain amount of time. Lily drives at 50 miles per hour for 3 hours more than Damon. Damon drives farther than Lily.

B. Damon drives at 60 miles per hour for a certain amount of time. Lily drives at 50 miles per hour for 3 hours more than Damon. Lily drives farther than Damon.

C. Damon drives at 50 miles per hour for a certain amount of time. Lily drives at 60 miles per hour for 3 hours more than Damon. Damon drives farther than Lily.

D. Damon drives at 50 miles per hour for a certain amount of time. Lily drives at 60 miles per hour for 3 hours more than Damon. Lily drives farther than Damon.

B. Damon drives at 60 miles per hour for a certain amount of time. Lily drives at 50 miles per hour for 3 hours more than Damon. Lily drives farther than Damon.

400

Sakr is attempting to solve the quadratic equation x^2+10x-3=0 by completing the square.

Which of the following equation is an equivalent form of Sakr's equation?

A. (x+5)^2=7

B. (x+5)^2=13

C. (x+5)^2=22

D. (x+5)^2=28

(x+5)^2=28

500

Which of the following represents the statement below?

Five times a number x is 3 more than x.

A. 5x = x + 3

B. 5x > x + 3

C. 5x + 3 = x

D. 5x + 3 > x

A. 5x = x + 3

500

Nick deposited $500 in a bank that gives him 5% interest compounded annually. Which equation can be used to find the total amount, in T dollars, in Nick’s account after x years?

A. T=500+5X

B. T=500+1.05^x

C. T=500(0.95)^x

D. T=500(1.05)^x

500

Dennis has a maximum of $80 that he can spend on books. He wants to buy at least 8 books. He wants to buy a combination of nonfiction books which costs $12 each and fiction books which costs $8 each. Let n be the number of nonfiction books Dennis buys and f be the number of fiction books he buys.

Which system of linear inequalities model Dennis's situation?

A. n + f <= 8

12n + 8f >= 80

B. n + f >= 8

12n + 8f <= 80

C. 12n + 8f <= 80

n + f >= 80

D. 12n + 8f >= 8

n + f <= 80

B. n + f >= 8

12n + 8f <= 80

500

Steve is using the completing the square method to solve a quadratic equation. His first 2 steps are shown.

Given: 2x^2 +32x+16=0

Step 1: x^2+16x+8=0

Step 2: x^2+16x=-8

Write numbers in each blank to correctly complete the square in step 3.

Step 3: x²+ 16x + _____ = _____

x²+ 16x + 64 = 56