name: algebra 2 400 date: midterm review application problems #1 · date: _____ midterm review –...

Name: _________________ Algebra 2 400 Date: __________________ Midterm Review – Application Problems #1

1) Mr. McGivney wants to build a bonsai garden in his apartment. The garden will be 20 feet long and 10

feet wide. Surrounding his garden will be a x-foot wide walkway so Mr. McGivney can tend to his bonsai

tree.

a) Write the length and the width of the (entire) region as a function of x.

L =

W =

b) Write the area of the (entire) region as a function of x.

c) Predict the area of the (entire) region if the walkway is 2, 4, or 6 feet wide (3 separate answers)

d) Mr. McGivney can’t fit a garden that’s bigger than 250 square feet in his apartment. How wide should

the walkway be?

e) Graph your area function over a reasonable domain. Include any intercepts.


2) Based on data collected from cinemas in our nation, there exists a linear relationship between the

average number of previews viewed (p) and the total gross of a film viewed in theatres in millions (d).

When a preview is seen 12 times on average, the gross of the movie is $200 million. When a preview was

seen an average of 3 times, the gross is $101 million.

a) Identify the variables

Independent:

Dependent:

b) Find the rate of change, both the number and the units

c) Write an equation that models this data in each indicated form:

Point-slope:

Slope-intercept:

Standard:

d) Suppose a film grosses $420 million. About how many previews were seen?

e) Sketch a graph of your function, including any intercepts.


3) Tammy is a secret agent working for the North Korean government. One day, she gets in her car to go

destroy an intelligence document that she does not want Mr. President to see. But, on the way, Tom sees

her, and having seen her on a “Wanted” poster, and being the great American he is, he opens fire on her

car. One bullet hits her gas tank and after 1 minute there are 18 gallons left in her tank. After 2 minutes

there are 16.2 gallons left, and after 3 minutes there are 15.3 gallons left. Assume the situation can be

modeled quadratically.

a) Write an equation expressing gallons left in her tank in terms of time.

b) How many gallons were in her tank when Tom first opened fire?

c) According to this model, when will the gas tank be empty?

d) Sketch a graph of your function over a reasonable domain, including any intercepts.


h(t) = -½gt² + v0t + h0 (g = 9.8m/sec2 or g = 32ft/sec2 )

4) Jack Sparrow is trying to escape capture. He decided that his best route to get away would be to climb to

the highest point of the boat and then jump into the water. Once Jack jumps into the water he is 105 above

the water and jumps at an upward velocity of 10 feet per second.

a) Write the quadratic equation that best represents the given scenario

b) How many seconds will it take for Jack to hit the water?

c) What will Jack’s distance from the water be after 3 seconds?

d) What is the max height that Jack will reach when he jumps off the boat?

e) How long will it take for Jack to reach his max height?

f) Graph the equation. Make sure to have both solid and dotted lines when appropriate.


1) Mr. McGivney wants to build a bonsai garden in his one-bedroom apartment. The garden will be 20

feet long and 10 feet wide. Surrounding his garden will be a x-foot wide walkway so Mr. McGivney can

tend to his bonsai tree.

a) Write the length and the width of the (entire) region as a function of x.

L =

W =

b) Write the area of the (entire) region as a function of x.

c) Predict the area of the (entire) region if the walkway is 2, 4, or 6 feet wide (3 separate answers)

d) Mr. McGivney can’t fit a garden that’s bigger than 250 square feet in his apartment How wide should

the walkway be?

e) Graph your area function over a reasonable domain. Include any intercepts.


2) Based on data that world-famous movie critic Anthony Dushku collected from cinemas in our nation,

there exists a linear relationship between the average number of previews viewed (p) and the total gross of

a film viewed in theatres in millions (d). When a preview is seen 12 times on average, the gross of the

movie is $200 million. When a preview was seen an average of 3 times, the gross is $101 million.

a) Identify the variables

Independent:

Dependent:

b) Find the rate of change, both the number and the units

c) Write an equation that models this data in each indicated form:

Point-slope:

Slope-intercept:

Standard:

d) Suppose a film grosses $420 million. About how many previews were seen?

e) Sketch a graph of your function, including any intercepts.


3) Tammy is a secret agent working for the North Korean government. One day, she gets in her car to go

destroy an intelligence document that she does not want Mr. President to see. But, on the way, Tom sees

her, and having seen her on a “Wanted” poster, and being the great American he is, he opens fire on her

car. One bullet hits her gas tank and after 1 minute there are 18 gallons left in her tank. After 2 minutes

there are 16.2 gallons left, and after 3 minutes there are 15.3 gallons left. Assume the situation can be

modeled quadratically.

a) Write an equation expressing gallons left in her tank in terms of time.

b) How many gallons were in her tank when Tom first opened fire?

c) According to this model, when will the gas tank be empty?

d) Sketch a graph of your function over a reasonable domain, including any intercepts.


h(t) = -½gt² + v0t + h0 (g = 9.8m/sec2 or g = 32ft/sec2 )

4) Jack Sparrow is trying to escape capture. He decided that his best route to get away would be to climb to

the highest point of the boat and then jump into the water. Once Jack jumps into the water he is 105 above

the water and jumps at an upward velocity of 10 feet per second.

a) Write the quadratic equation that best represents the given scenario

b) How many seconds will it take for Jack to hit the water?

c) What will Jack’s distance from the water be after 3 seconds?

d) What is the max height that Jack will reach when he jumps off the boat?

e) How long will it take for Jack to reach his max height?

f) Graph the equation. Make sure to have both solid and dotted lines when appropriate.

name: algebra 2 400 date: midterm review application problems #1 · date: _____ midterm review –...

Documents