Math III Review [578574]
Student
Class
Date
Read the following and answer the questions below:
The Ferris Wheel
The Ferris Wheel
“School’s out!” Ryan shouted gleefully to his older sister, Claire, as he barged through the front door of his house and slung his backpack on the floor. They attended the local high school, where Ryan had been a freshman and Claire a junior. Summer vacation had finally begun.
Ryan and Claire had even more reason to celebrate because the family vacation their parents had planned to Chicago, Illinois, was now only two days away. Claire had wanted to visit Chicago ever since her friend Marco returned from a visit there; she still remembers how he ranted and raved about all there was to see and do in the “Windy City.”
Ryan and Claire had been doing research online about the numerous sights to see and all the exciting things they should do on their visit. Claire was very interested in seeing the downtown area with its prominent buildings and skyscrapers, many having been designed by important architects. But both Ryan and Claire were most excited about finally getting to go to Navy Pier, an amusement park located on Lake Michigan that includes a musical carousel, indoor mall, great food, and the famous Ferris wheel.

“Hey, Ryan, did you know that the Navy Pier Ferris wheel is 150 feet high?” Claire said in amazement. “According to this information, that’s as tall as a 13-story building.”
“You aren’t going to ride the Ferris wheel. You will be too frightened once you see how high it really is,” Ryan teased.
“Oh, be quiet, Ryan! I won’t be too scared, especially since we will all be together—that is, as long as you promise not to rock the carriage when we get to the top. This website says that it has 40 carriages, or gondolas, that you sit in, and each one will seat up to 6 people. Therefore, we will all definitely be able to fit in one.”
Claire went on to read that during the 7-minute ride, she would be able to see most of downtown. In fact, from the top of the Ferris wheel, on a clear day, one could see 50 miles in all directions.
“Look! It says you can see the entire downtown area when you get to the top.”
“That’s great, Claire. But the only sight I want to see is my eating a Chicago-style hot dog with fries and a funnel cake.” Ryan laughed at his joke, but Claire was too busy studying the website to even look away and roll her eyes at his absurd comment, which would have been her normal reaction.
Claire loved to learn about how things were built, all the way from the inception of the idea drafted on paper to the actual building of the structure, which is why she planned to study architecture in college. She found the subject fascinating and read as much as she could about the Ferris wheel, wanting to know when, why, and how it came about.
Claire discovered that the Ferris wheel was invented by George Washington Ferris back in the 1890s. The first Ferris wheel was 25 stories high and was made entirely of steel. It had a diameter of 250 feet and was supported by 2 towers, each 140 feet high. There were 36 enclosed carriages that could hold slightly more than 1,400 passengers at any given time. The ride itself lasted for 10 minutes, circling 2 full revolutions around; the first revolution was slower than the second so that passengers could be loaded into the carriages.

It debuted at the World’s Columbian Exposition, which is more commonly known as the 1893 Chicago World’s Fair. George Ferris wanted the attendees of the fair to marvel at his innovative invention and forget about the Eiffel Tower, which had been revealed four years earlier at the Paris International Exposition. Though the wheel was popular at first, it soon lost its superstar appeal and was dismantled and eventually sold as scrap metal.
Claire looked up from her computer. She was more excited than ever, knowing that soon she would experience all of the sites she had read about. There was only one thing left to do: pack.
1. / Read “The Ferris Wheel” and answer the question.
Claire and Ryan’s carriage on the Navy Pier Ferris wheel travels 205 feet counterclockwise from the loading point before they can get a clear view of the city. How many radians, rounded to the nearest hundredth, does the carriage rotate to reach this point?
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FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf
2. / Read “The Ferris Wheel” and answer the question.
Explain how the unit circle in the coordinate plane relates to the rotation of the Navy Pier Ferris wheel. How does this comparison enable the extension of trigonometric functions to all real numbers?
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FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf
3. / What is the simplified form of the expression
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4. / If what is the value of
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5. / Which expression is equivalent to (3x2–5x+4)+(2x2–7)?
A. / 5x2 – 5x – 3
B. / 5x2 – 5x – 11
C. / 6x2 – 5x – 3
D. / 5x4 – 5x – 3
6. / Whichexpression is equivalent to
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7. / What are thezeros of the polynomial function
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8. / Which function has a remainder of 3 when divided by
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9. / Which polynomial has exactly 2 positive x-intercepts?
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10. / Which graph best represents the function
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11. / Let the function What are all the x-intercepts for the graph of
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12. / A polynomial can be expressedso that What is the value of a?
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13. / Part A:
Prove the identity for the cube of a binomial:

Part B:
Explain the change in the formula when the binomial indicates addition rather than subtraction.
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14. / For this task, assume that a and b are both positive and a is greater than b.
Part A.Use the diagram below toprove the polynomial identity , when a is the length of thelargest, outer square, and b is the length of the white square. Justify your reasoning.

Part B.Draw adiagramthat can be used to provethe polynomial identity Use the diagram to prove the polynomial identity and justify your reasoning.
Part C. Use polynomial division to prove the polynomial identity Explain why polynomial division can be used to prove this polynomial identity. Can the same method be used to prove the polynomial identity Explain why or why not.
Part D. There is also a geometric way of proving the difference of cubes polynomial identity. Use the three-dimensional figures below to construct an argument as to why for and

Part E. Draw the figures that can help prove for and Use the figures to construct an argument as to why for the given values of a and b.
Part F. Could a similar geometric method be used to prove Explain why or why not.
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15. / Which polynomial identity can be proved using the polynomial division given below?

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16. / The distributive property is used to prove which of the given identities shown below are true?



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A. / I and II only
B. / I and III only
C. / II and III only
D. / I, II, and III
17. / Which of these expressions is equivalent to
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18. / Given: If what is the value of
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19. / A computer repairman charges $50 to come to a home or office, plus $30 per hour of work. During one week, he visits 12 homes or offices earning $1,800. How many hours did the repairman work?
A. / 22 hours
B. / 40 hours
C. / 42 hours
D. / 58 hours
20. / A high school is hosting a basketball tournament. Their goal is to raise at least $1,500.00. Students can buy tickets for $3.00 and non-students for $5.00. The seating capacity for the gym is 400 people. Which could represent the number of each type of ticket sold to meet the high school’s goal and not exceed the capacity of the gym?
A. / 100 student, 200 non-student
B. / 125 student, 175 non-student
C. / 150 student, 350 non-student
D. / 170 student, 229 non-student
21. / Alma invests $300 in an account that compounds interest annually. After 2 years, the balance of the account is $329.49. To the nearest tenth of a percent, what is the rate of interest on the account?
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A. / 6.9%
B. / 5.4%
C. / 4.8%
D. / 4.4%
22. / Trevor is making two types of bracelets.
·  Each Type P bracelet needs 12 inches of leather and 3 inches of string.
·  Each Type Q bracelet needs 4 inches of leather and 18 inches of string.
·  Trevor has 5 yards of leather and 6 yards of string.
·  x equals the number of Type P bracelets Trevor makes.
·  y equals the number of Type Q bracelets Trevor makes.
Which system of equations models the constraints on the number of bracelets Trevor can make?
A. / 12x + 4y ≤ 180
3x + 18y ≤ 216
x ≥ 0
y ≥ 0
B. / 12x + 3y ≤ 180
4x + 18y ≤ 216
x ≥ 0
y ≥ 0
C. / 12x + 4y ≤ 5
3x + 18y ≤ 6
x ≥ 0
y ≥ 0
D. / 12x + 3y ≤ 5
4x + 18y ≤ 6
x ≥ 0
y ≥ 0
23. / The escape velocity, v,with which a body should be projected so that it overcomes the gravitational pull of the Earth is given as where g is the acceleration due to gravity on the Earth and R is the radius of the Earth.
Part A. Find the formula that can be used to calculate the acceleration due to gravity on the Earth, given the escape velocity and the radius of the Earth.
Part B. Find the formula that can be used to calculate the radius of the Earth, given the acceleration due to gravity and the escape velocity.
Use words, numbers, and/or pictures to show your work.
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FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf
24. / The sum of three consecutive integers is 51. What is the value of the largest integer?
A. / 16
B. / 17
C. / 18
D. / 19
25. / Jacob stated that he solved the equation using the addition and multiplication property of equality. Which statement is true?
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A. / Jacob added to both sides and multiplied both sides by
B. / Jacob added to both sides and multiplied both sides by
C. / Jacob added to both sides and multiplied both sides by
D. / Jacob added to both sides and multiplied both sides by
26. / The equationcan be used to convert temperature from degrees Fahrenheit to degrees Celsius Which of these couldbe the first step insolving the equation for
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27. / Which value is asolution to the equation
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28. / Consider this equation.

Part A. Solve the equation for x,showing all steps andboth resulting values of x.
Part B. Do both values of x represent solutions to the equation? Explain your answer.
Use words, numbers, and/or pictures to show your work.
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29. / For what value ofp is the expression equivalent tothe expression
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30. / Write and solve the equations for the situations listed below. Choose the most efficient method to solve each equation and show your work.
Part A.A drawing room is in the shape of a square and has an area of 144 square feet. Write an equation to determine the side, s, of the room length.
Part B.There isa table with a widthof 3feet less than its length and an area of 10 square feet. Write and solve an equation to determine the length and width of the table.
Part C. A sofa has a length that is 3 feet more than twice its width. If the sofa occupies an area of 18 square feet, write and solve an equation to determine the approximate dimensions of the sofa.
Part D. Arectangular plotof land is to befenced in using 100 feet of fencing. If you want the maximum area to be fenced in, whatwould be the dimensions of the plot of land that is fenced?
Use words, numbers, and/or pictures to show your work.
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31. / Susan has a vegetable garden on a rectangular piece of property. Last year, she dividedher garden into threesquare sections:
In thesouth section, she planted beans.
In the middle section, she planted carrots.
In the north section, she planted cabbage.
This year, Susan makes two changes to her garden:
First, she uses some of the area of the cabbage section for a tool shed. She builds the tool shed along the north end of the property. The tool shed goes all the way across the north end of the property and measures 2 yards from front to back. After subtracting the area taken up by the tool shed, the area of Susan's three vegetable plots is 133 square yards.
Second, she decides to surround hergardenwith a fence to keep thevegetables safe from animals. She will need to fence all four sides of thegarden. The tool shed will be outside of the fence.