Math III Review [578574] - WordPress.com · Web viewClara’s college fund can be modeled by the function f(x) = 500x + 2,500, where x is the number of years since 1998. Michelle’s

Math III Review [578574]StudentClassDate

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.

Math III Review Page 1/170

“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?

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?

3. What is the simplified form of the expression

A.

B.

C.

D.

4. If what is the value of


A.

B.

C.

D.

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.Which expression is equivalent to

A.

B.


C.

D.

7. What are the zeros of the polynomial function

A.

B.

C.

D.

8. Which function has a remainder of 3 when divided by

A.

B.

C.

D.


9. Which polynomial has exactly 2 positive x-intercepts?

A.

B.

C.

D.

10. Which graph best represents the function

A.


B.

C.


D.

11. Let the function What are all the x-intercepts for the graph of

A.

B.

C.

D.

12. A polynomial can be expressed so that What is the value of a?


A.

B.

C.

D.

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.

14.

For this task, assume that a and b are both positive and a is greater than b.Part A. Use the diagram below to prove the polynomial identity ,

when a is the length of the largest, outer square, and b is the length of the white square. Justify your reasoning.


Part B. Draw a diagram that can be used to prove the 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.

15. Which polynomial identity can be proved using the polynomial division given below?

A.

B.

C.


D.

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

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

A.


B.

C.

D.

18.

Given: If what is the value of

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?

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 ≤ 1803x + 18y ≤ 216x ≥ 0y ≥ 0

B. 12x + 3y ≤ 1804x + 18y ≤ 216x ≥ 0y ≥ 0

C. 12x + 4y ≤ 53x + 18y ≤ 6x ≥ 0y ≥ 0

D. 12x + 3y ≤ 54x + 18y ≤ 6x ≥ 0y ≥ 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.

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?

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 equation can be used to convert temperature from degrees Fahrenheit to degrees Celsius Which of these could be the first step in solving the equation for

A.

B.

C.

D.

27.Which value is a solution to the equation

A.

B.


C.

D.

28. Consider this equation.

Part A. Solve the equation for x, showing all steps and both 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.

29. For what value of p is the expression equivalent to the expression

A.

B.

C.

D.


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 is a table with a width of 3 feet 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. A rectangular plot of land is to be fenced in using 100 feet of fencing. If you want the maximum area to be fenced in, what would be the dimensions of the plot of land that is fenced?


31. Susan has a vegetable garden on a rectangular piece of property. Last year, she divided her garden into three square sections:In the south 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 her garden with a fence to keep the vegetables safe from animals. She will need to fence all four sides of the garden. The tool shed will be outside of the fence.


Part A. Draw a picture to represent Susan's vegetable garden, the fence, and the tool shed. Label each part of the picture.Part B. Write an expression for the area that Susan will use this year to plant vegetables, in terms of x, the length of the short edge of her property. Set that expression equal to 133.Part C. Solve the equation from Part B using two methods:Use the method of completing the square to change the equation into the form where p and q are real numbers. Solve for x. Show your work.Use the quadratic formula. Solve for x. Show your work.What is the length of the short side of the garden?Part D. Determine how many yards of fencing Susan will need.

32. If quadratic equation is rewritten in the form of what are the values of p and q?

A.

B.

C.

D.

33. Which choice is an ordered pair that, for every real number k,


represents a point that lies on the graph of 30x – 5y = 10?

A. (k + 2, 6k + 10)

B. (k + 4, 6k + 20)

C. (3k, 18k + 2)

D. (5k, 30k + 2)

34.

If a point is on the graph of the equation and also on the graph of what is the value of b?

A.

B.

C.

D.

35. Who Will Catch Up When?


Three friends are packing gift boxes to be handed out at the high school dance. Each box has ten sections to be filled. They each pack the boxes at different rates.

Part A. The tables below show Kelsey’s and Andrew’s progress. The variable t stands for the time that has passed since their starting time at 10:00 a.m. Andrew had already packed 4 boxes the day before.

Fill in the tables, assuming that each person packs the boxes at a constant rate.

Part B. Let the number of boxes Kelsey packs be represented by k(t) and the number Andrew packs by a(t). Using the information from the tables, write the functions for k(t) and a(t). Interpret each function in terms of the context it represents.

Kelsey:

Andrew:

In terms of k(t) and a(t), what equation can be solved to find the time at which both Kelsey and Andrew have packed the same number of boxes? Explain.

Part C. Graph and label the functions k(t) and a(t) on the same coordinate grid below.


What is the solution of the equation that was written in part B that could be used to find the time at which Kelsey and Andrew have packed the same number of boxes? Explain how you can find the solution on the graph and then verify your answer by solving the equation algebraically.

Part D. The third friend, James, starts out packing the boxes very quickly but then slows down. His approximate progress can be modeled by the square root equation below, where t stands for the time that has passed since their starting time at 10:00 a.m.

Fill in the table to show James’s progress. Round the values to the nearest 0.1 box.

Part E. Sketch a graph of the function j(t) on the coordinate grid above, where k(t) and a(t) are already graphed. Write the equation that could be used to find the time at which

Kelsey and James have packed the same number of


boxes. Approximate the solution or solutions to this equation using the graph.

Write the equation that could be used to find the time at which Andrew and James have packed the same number of boxes. Approximate the solution or solutions to this equation using the graph.

36. If f(x) = 5(2)x and g(x) = –2x + 46, for what positive value of x does f(x) = g(x)?

A. 3

B. 5

C. 40

D. 46

37. Two functions are shown below.f(x) = 2x + 2

g(x) = –2x + 6For what value of x does f(x) = g(x)?

A. 1

B. 2

C. 4


D. 6

38. What is the maximum number of intersections an exponential function can have with a linear function?

A. 0

B. 1

C. 2

D. 3

39. Let Find all real values of x such that

40.Which expression is equivalent to where k is an even number?

A.

B.


C.

D.

41. The expression for the amount of money earned on a savings account compounded quarterly is given by the expression where represents the principal and is the time in years since the principal was invested. Which expression is the equivalent form of the given expression and shows the amount earned when the interest is compounded half-yearly?

A.

B.

C.

D.

42. Jesse and Shaun are comparing investment products to see who has the better investment rate for their money. The interest on the money Jesse invested in Product X is compounded annually. The value of the investment after n years can be found using the formula where is the intial amount of money invested.The interest on the money Shaun invested in Product Y is compounded monthly. The value of the investment after m months can be found using the formula where is the intial amount of money invested.


Part A. Rewrite Jesse's formula to find the approximate equivalent monthly interest rate. Show your work.Part B. Which product offers the best return on an investment? Use the interest rates to justify your answer.

43. An athlete is training to run a marathon. She plans to run 2 miles the first week. She increases the distance by 8% each week. Which function models how far she will run in the nth week?

A.

B.

C.

D.

44. Cindy invested $2,800. The function V(t) = 2,800(1.025)t models the value of Cindy’s investment after y months. The function S(t) = 10t models the amount of money that Cindy has saved in a safe at her house after t months. Which function C(t) models the combined value of the investment and money in the safe?

A. C(t) =2,810(1.025)t

B. C(t) = 2,800(1.025)11t


C. C(t) =(2,800 + 10t)(1.025)t

D. C(t) =2,800(1.025)t + 10t

45. A plane is at a height of 30,000 feet above the ground when it begins to descend at a rate of 1,500 feet per minute. If and write a recursive formula that can be used to determine the height of the plane above the ground after n number of minutes.

46. The ingredients for a particular kind of European chocolates cost $12 per box. The foil wrappers cost $0.05 per piece of chocolate. The box has x pieces of chocolates in it. Which function represents the total cost per piece of chocolate?

A.

B.

C.

D.

47. Which recursive formula models the sequence shown below?–3, 1, 5, 9, . . .


A. NEXT = NOW + 4

B. NEXT = NOW – 4

C. NEXT = 4 • NOW

D. NEXT = 4 • NOW + 7

48. At the beginning of the school year, Jason’s dad gave him $50 to put into his lunch account. Jason spends $2 each day on his lunch. Which recursive formula models the amount of money that Jason has in his account?

A. NEXT = NOW + 2

B. NEXT = NOW – 2

C. NEXT = 50 – 2 • NOW

D. NEXT = 52 – 2 • NOW

49. If and which equation represents the explicit formula for the sequence?

A.


B.

C.

D.

50. The first term of an arithmetic sequence is 3. The nth term of the sequence is found by using the formula Which other formula could be used to find the nth term?

A.

B.

C.

D.

51. Which transformation occurs to the graph of f(x) = x to produce the graph of g(x) = x + 2?

A. down 2 units

B. up 2 units

C. left 2 units


D. right 2 units

52. If the graph of is translated 2 units right and 4 units down, which of these functions describes the transformed graph?

A.

B.

C.

D.

53. The function f(x) = 6x was replaced with f(x) + k resulting in the function shown in the table below.

x y0 101 152 453 225

What is the value of k?

A. 7


B. 8

C. 9

D. 10

54. The function f(x) = x – 2 was translated down 6 units, resulting in the function g(x). Which function represents g(x)?

A. g(x) = 6x – 2

B. g(x) = 2x – 8

C. g(x) = x – 8

D. g(x) = x + 4

55. A function is defined as where

Part A. Write a function that represents the inverse of the function

Part B. How do the domain and range of compare with the domain and range of the inverse function



56. The table below shows the attempts made by four students to find the

inverse of the function

Which student correctly found the inverse of the function?

A. Danie

l

B. Jean

C. Scott

D. Sophia

57. The function h(t) = 200 – 16t represents the height of a ball dropped from 200 feet. How far had the ball traveled after falling for 11 seconds?

A. 16 feet


B. 24 feet

C. 176 feet

D. 200 feet

58. The function f(t)=12,000(1.075)t models the value of an investment t years from now. What is the meaning of the value of f(5)?

A. the value of the investment 5 years ago

B. the value of the investment in 5 years

C. the initial value of the investment

D. the interest rate the investment earns

59. The table below shows the cost for a toy company to produce different amounts of toys.

Toys Produced Cost 1,000 $122,000 3,000 $26,000 5,000 $10,000 7,000 $74,000


Assuming a quadratic relationship, about how many toys should the company produce to minimize costs?

A. 1,000

B. 4,000

C. 5,000

D. 6,000

60. The table below shows the distance Chris is located from his school at different times.

Time (minutes)

Distance (miles)

0 20 3 18 6 16 9 14

12 12 15 10

Assuming a linear relationship, how long will it take Chris to get to school?

A. 20 minutes

B. 24 minutes

C. 27 minutes


D. 30 minutes

61. Jimmy threw a baseball in the air from the roof of his house. The path followed by the baseball can be modeled by the function

where t represents the time in seconds after the ball was thrown and represents its height, in feet, from the ground. Part A. How high is the roof from the ground? How many seconds did it take for the ball to hit the ground after it was thrown off the roof? Part B. Jimmy wanted to throw the ball at a maximum height of 120 feet. Did Jimmy's baseball reach this height after it was thrown? Explain your answer. Use words, numbers, and/or pictures to show your work.

62. Which function has the following features? symmetry over the y-axis increasing for all y-intercept of 0

A.

B.

C.


D.

63. Part A. Emma’s cell phone plan charges $0.20 for each text message. The function represents the cost of the total number of text messages Emma sends and receives. If x represents the total number of messages, what is the domain of the function

Part B. How will the domain of the function change if Emma puts a limit of $25 on her monthly texting bill?

Part C. The dollar amount of Emma’s prepaid call balance decreases by r for each second of a call. The call balance left is modeled by the function

where b is the initial balance in dollars and s is the number of seconds. What is the domain of the function

Part D. Emma changes her call plan from prepaid to pay-as-you-go. The

function represents the total bill she pays after a month,

where A is the fixed monthly fees and is the amount in dollars charged for each second of calls she made. What is the reasonable domain of the function in terms of the given context?

64. The table below shows the population of a state during different years.

Year (x) Population (y) 2004 8,500,000 2006 8,900,000 2007 9,000,000 2008 9,200,000 2010 9,500,000

What is the approximaterelative domain of the line of best fit


for the data?

A. x > 0

B. x > 1650

C. x > 1952

D. x > 2004

65. Function has a minimum value of and a maximum value of 8. Which graph most likely represents function

A.


B.

C.


D.

66. Which graph represents the function

A.


B.

C.


D.

67. Which is the graph of 3x – 2y = 4?

A.


B.

C.


D.

68. Graphing

Part A. Consider the functions and What are the domain and range of each function?

Part B. What are the x-intercepts and y-intercepts (if any) on On

Part C. Where are the functions increasing or decreasing?

Part D. What are the maximum points (if any) on and

Part E. Sketch graphs of the functions and


Part F. How are the graphs of the two functions in part A related? How do you see these relationships in the equations?

Part G. Sketch graphs of the functions and Explain how you determined the coordinates of key points.


Part H. How are the graphs of the three functions in part G related? How do you see these relationships in the equations?

69. The height in feet, a kangaroo reaches seconds after it has jumped in the air is modeled by the quadratic function Which equation shows the correctly factored version of the function and the number of seconds it takes for the kangaroo to return to the ground?

A. 8 seconds

B. 1.5 seconds

C. 8 seconds

D. 1.5 seconds


70. The function f(x) = 19,000(0.89)x models the value of a boat x years after its purchase. Which statement correctly describes the value of the boat?

A. The value is decreasing by 11% per year.

B. The value is decreasing by 89% per year.

C. The value is increasing by 11% per year.

D. The value is increasing by 89% per year.

71. Genevieve deposited $400 into her bank account. The equation can be used to calculate the value of her money after t years. What is the annual interest rate she is earning on her deposit?

A. 0.07%

B. 1.07%

C. 7%

D. 107%

72. The function f(x) = 2,500(0.97)x models the value of an investment after x months. Which statement is true about the value of the investment?


A. The value of the investment increases by 3% each month.

B. The value of the investment decreases by 3% each month.

C. The value of the investment increases by 97% each month.

D. The value of the investment decreases by 97% each month.

73. Joseph compared the function f(x) = 3x2 + 2x – 1 to the quadratic function that fits the values shown in the table below.

x g(x) 0 –11 82 233 444 71

Which statement is true about the two functions?

A. The functions have the same y-intercepts.

B. The functions have the same x-intercepts.

C. The functions have the same vertex.

D. The functions have the same axis of symmetry.


74. Austin and Janda threw grappling hooks into the air. The function gives the height, in feet, of Austin’s hook x seconds

after he threw it. The graph below shows the height, in feet, of Janda’s hook x seconds after she threw it.

If both of them threw the grappling hooks at the same time, which of these statements is true?

A. Austin’s hook hit the ground first.

B. Austin’s hook reached its maximum height first.

C. Austin’s hook reached a greater maximum height.

D. Austin threw the hook from a greater initial height.

75. Two functions are shown below.


f(x) = 1.02x + 100 g(x) = 50(1.02)x

What is the smallest positive integer in which the value of g(x) exceeds the value of f(x)?

A. 60

B. 59

C. 55

D. 50

76. Ronald invests $1000 at a simple interest rate of 10% for 4 years. His best friend Rudy invests the same amount of money, but earns 10% interest compounded annually for 4 years. Part ACreate a table to show the amount of Rudy's investment after each year. Calculate the amount of Ronald's investment after 4 years.Part BBased on the amounts they made, which friend made the better investment? Explain.

77. Clara’s and Michelle’s parents started saving for college in 1998. Clara’s college fund can be modeled by the function f(x) =

500x + 2,500, where x is the number of years since 1998. Michelle’s college fund can be modeled by the function g(x)


= 2,500(1.1)x, where x is the number of years since 1998.

About what year will Michelle’s college fund first exceed Clara’s college fund?

A. 2013

B. 2015

C. 2017

D. 2019

78. Which table shows the function that increases at the fastest rate?

A.

B.


C.

D.

79. For what value of x is it true that

A.

B.

C.

D.


80. The bacteria in a certain Petri dish grow at a rate modeled by where represents the number of bacteria in the dish and t represents the time in minutes since the introduction of the bacteria. Which equation can be used to determine how many minutes will pass before there are 68 bacteria in the dish, if the dish started with a single bacterium?

A.minute

s

B.minute

s

C.minute

s

D.minute

s

81.What is the solution to the equation

A.

B.


C.

D.

82. What is the solution to the equation

A.

B.

C.

D.

83. Circle P, shown below, has a radius of 1 unit.


Which of these equations correctly identifies the relationship between angle QPR, in radians, and the length, a, of arc QR?

A.

B.

C.

D.

84. Let and be two values such that but

Express in terms of .

85. In the right triangle pictured below, the measure of angle A, in radians, is The side adjacent to angle A measures 6 cm and the side opposite

measures 5 cm.


Which of the following values is closest to

A.

B.

C.

D.

86.Toni claims that the cosine of is equal to the cosine of .Which equation could be used to justify Toni's claim?

A.

B.


C. for any integer k

D. for any integer k

87. Which function best represents a sine curve that repeats every 12 units and has a maximum of 42 and a minimum of 4?

A.

B.

C.

D.

88. George’s height above the ground as he rides a Ferris wheel ranges from 4 meters to 30 meters. If it takes 200 seconds to complete one revolution, which sine function represents his height, from the ground as a function of time,

A.

B.


C.

D.

89. A Ferris wheel with a diameter of 40 feet completes 2 revolutions in one minute. The center of the wheel is 30 feet above the ground. If a person taking a ride starts at the lowest point, which trigonometric function can be used to model the rider’s height h(t) above the ground after t seconds? (Consider the height of the rider negligible).

A.

B.

C.

D.

90. Nan draws the swinging end of a pendulum 10 centimeters to the left of its rest position and releases it to swing. She wants to model the horizontal displacement of the pendulum, d, as a function of time, t, where at the point of release. Which function family is best for Nan to use and why?

A. , because


B. , because is an extremum

C. , because

D. , because is an extremum

91.What is the value of if and Write your answer in simplest form.

92. Point P is a point on the unit circle.

Part A. Use the Pythagorean theorem and the diagram above to prove the trigonometric identity

Part B. If use the identity to find



93. Based on the diagram below, how can the Pythagorean identity be shown?

A.

B.

C.

D.


94. Let p represent a point on the unit circle, in the second quadrant. The line including p and the origin has a slope of -2. What is the x-value of p?

A.

B.

C.

D.

95. Similarity in CirclesGeometric similarity is an extremely useful concept. Similar figures are alike except for their size; their corresponding angles are congruent, and their corresponding parts are proportional. On the coordinate plane, one figure can be mapped to the other by a series of transformations.

Part A. Consider these two equilateral triangles. Are they similar? How do you know? Write a proportion showing the relationship of their sides.


Part B. Are any two squares similar? Tell how you know.

Remember that the measure of each angle of a regular polygon is

where n is the number of sides. Can you make a general statement about the similarity of two regular polygons (n-gons) with the same number of sides? Explain your answer. Part C. As the number of sides of a regular polygon increases, what figure does it begin to look like?

What is a reasonable conclusion about the similarity of figures of this kind of different sizes? Part D. Consider these two circles on the coordinate plane. What is the radius of circle A? Of circle B? Write the ratio. Write the ratios for the diameters and circumferences of the two circles. Are the circles proportional?


Part E. You can also prove that two figures are similar by showing that a series of transformations will map one figure to the other. What is the equation for circle A?

Part F. What series of transformations will map circle A to circle B? Write the equation for circle B. Are these two circles similar?

Part G. Any two circles can be centered at the origin through translations. If both circles are centered at the origin, what one transformation will map one to the other, proving their similarity? If the equation of one circle is and the radius of the other circle is f times the radius of the first, what is the equation of the second circle?

What is the equation of the second circle if the center is NOT In either case, no matter what the size or position of the

circles, are all circles similar?

96. Which statement best explains why all circles are similar?

A. All circles have exactly one center

point.

B. The diameter of all circles is twice the length of the radius.


C. All circles can be mapped onto any other circle using only

translations.

D. All circles can be mapped onto any other circle using a translation

and dilation.

97. Which property of quadrilaterals inscribed in a circle can be used to find the value of x in the figure below?

A. The difference between an opposite pair of angles is 180°.

B. The difference between an opposite pair of angles is 0°.

C. The sum of an opposite pair of angles is 180°.

D. The sum of an opposite pair of angles is 360°.

98. In the figure given below, is a diameter of the circle with center O.


If what is

A. 60°

B. 70°

C. 80°

D. 110°

99. In the figure below, are radii of the circle with center O.

Given that what is


A. 20°

B. 35°

C. 40°

D. 80°

100. In the figure shown below, and are radii of the circle with center If what is

A. 56°

B. 62°

C.

D. 124°


101. Points A, B, C, and D lie on circle E as shown in the figure below.

Which statement must be true about the figure?

A.

B.

C.

D.

102. The figure shown below is a circle.


Which statement must be true?

A.

B.

C.

D.

103. Amy is designing a piece of jewelry to sell in her craft store. She begins with the triangular piece of silver, as shown below.

Part A. Amy wants to add a circular piece of gold that will be inscribed inside the triangular piece of silver. Use a compass and straightedge to


show how she can add the circular piece to the triangle above. Explain the steps you used to perform the construction. Part B. She needs to know the radius of the inscribed circle so that she can calculate the circumference and area of the circular gold piece she needs to make for the jewelry. Given that the silver triangle is a right triangle with side lengths a, b, and c, find the equation Amy can use to determine the radius of the circle, r. Explain your answer and draw a diagram or use your construction in part A to support your reasoning. Part C. Amy then decides to inscribe another similar silver triangle inside a circular piece of copper so that each vertex of the triangle touches the edge of the copper circle. Use a compass and straightedge to construct her design below. Explain the steps you used to perform the construction.

Part D. A couple of months ago, Amy designed a piece of jewelry with a gold quadrilateral inscribed on a circular piece of silver. She found the sketch of her design in her desk drawer, as shown below.


Now Amy wants to produce an identical piece of jewelry but needs to know the exact angle measures for the gold quadrilateral. What geometric property about quadrilaterals can Amy use to find the measures of the angles of her jewelry design? Use a paragraph proof to justify your response. Part E. What are the measures of the three missing angles in Amy’s sketch of the piece of jewelry in part D? Explain how you know.

104. Quadrilateral is inscribed in circle E. Angle is a central angle, and angle is an inscribed angle.


Which statement about the angles in this figure must be true?

A.

B.

C.

D.

105. In the given image, and the angles are measured in radians. Which of these must be true?


A.

B.

C.

D.

106. Part AUsing the circle below, set up a proportion to determine the length, m, of arc HI. Use for the central angle of a complete circle and for the circumference of the circle where r is the radius. Solve for m.

Part B The circle below has a central angle which measures 2.1 radians and a diameter of 3 inches. Find the length, in inches, of arc HJ.


107. In circle C below, is measured in radians.

Which expression can be used to find the area of the shaded sector?

A.

B.

C.

D.


108. Ashley is studying circle O, shown below.

She wrote the steps below.

What did Ashley derive?

A. that all circles are similar

B. the formula for arc length

C. the formula for the area of a sector of a circle

D. that a central angle has the same measure as the arc it subtends

109. Which of these correctly defines a ray?

A. a part of a line with exactly two end points


B. a straight path that extends endlessly in both directions

C. a circular path such that every point on the path is equidistant from

its center

D. a part of a line that begins at a particular point and extends

endlessly in one direction

110. The distance between points A and P is the same as the distance between points B and P. If P does not lie on a line joining the points A and B, which of these conclusions are true?

I. All the points on will be equidistant from point P.

II. The angles and are congruent.

III. and form

IV. and form arc APB.

A. I and III

B. II and IV

C. II and III

D. I and IV


111. What is a definition of a line that is parallel to

A. a coplanar line that bisects

B. a coplanar line that does not intersect

C. a coplanar line that intersects at a right angle

D. a coplanar line that intersects but not at a right angle

112. Chris draws an image of two lines that lie in the same plane and are equidistant at all points. Which of these describes the image drawn by Chris?

A. an

angle

B. parallel

lines

C. intersecting

lines

D. perpendicular

lines


113. A proof of the Alternate Interior Angles Theorem, using parallel lines a and b with transversal m, is shown below.

Which property is used in step 4?

A. reflexive

property

B. transitive

property

C. associative propert

y

D. commutative

property

114. Two parallel lines are cut by a transversal x and a transversal y so that x and y intersect at point Q as shown.


Wong constructs the following argument:

Angle a is [missing reason 1] and therefore congruent to one angle in the triangle formed by lines m, x, and y.

Angles b and c are [missing reason 2] and therefore congruent to two other angles in the triangle.

The sum of the three angles in a triangle is 180 degrees. Therefore .

What are the missing reasons in Wong’s argument?

A. Reason 1: an alternating exterior angle with one angle in the triangleReason 2: vertical angles with the other two angles in the triangle

B. Reason 1: an alternating exterior angle with one angle in the triangleReason 2: complementary angles with the other two angles in


the triangle

C. Reason 1: a corresponding angle with one angle in the triangleReason 2: vertical angles with the other two angles in the triangle

D. Reason 1: a corresponding angle with one angle in the triangleReason 2: complementary angles with the other two angles in the triangle

115. John draws with as the perpendicular bisector of such that and are congruent to each other.

Which statement can John use this figure to prove?

A. Every isosceles triangle is a right triangle.

B. The base angles of any triangle are congruent.


C. The points on the perpendicular bisector of a side of a triangle are

equidistant from all of the vertices of the triangle.

D. The points on the perpendicular bisector of a side of a triangle are

equidistant from the vertices of the side it bisects.

116. Part A. In the figure below, Based on facts about corresponding angles and vertical angles, write a paragraph proof to show that the measures of angles 1 and 8 are equal.

Part B. If it had not already been determined that in this figure, would the information that be enough to verify that p is in fact parallel to q? Justify your answer using relevant theorems about lines and angles.


117. John writes the proof below to show that the sum of the angles in a triangle is equal to 180º.


Which of these reasons would John NOT need to use in his proof?

A. The sum of the angles on one side of a straight line is 180º.

B. If a statement about a is true and the statement formed by replacing a with b is also true.

C. When two parallel lines are cut by a transversal, the resulting

alternate interior angles are congruent.

D. When two parallel lines are cut by a transversal, the resulting

alternate exterior angles are congruent.

118. In triangle and Which of these can be proved using the triangle sum theorem?

A.


B.

C.

D.

119. In isosceles triangle Roshni’s teacher asked different students to draw different segments in triangle Roshni drew a median from vertex R to point T on side as shown below.

The teacher asked the students to trade papers with a partner and identify which type of segment their partner had drawn. Roshni’s partner, Jose, looked at her drawing and told her he thought that she had drawn an altitude.

Part A. Is an altitude, median, neither, or both? Explain using a paragraph proof.

Part B. Is a perpendicular bisector of Explain using the definition of perpendicular bisector and your answer to part A.


Part C. Does bisect Explain using a two-column proof as shown below.

Part D. If Roshni draws a median from to S, is the median also an altitude? Why or why not? How does this compare to the result in part A? Use words, numbers, and/or pictures to show your work.

120. In


Given the information above, which statement can be proved to be true?

A. Triangle is isosceles.

B. is perpendicular to

C. The length of is half the length of

D. Triangle is congruent to triangle

121. A proof of the base angle theorem is shown.


Which statements correctly complete the proof?

A.

B.

C.


D.

122. The statements of a two-column proof are listed below.

What should the corresponding reasons be?

A. 1. Given; 2. Definition of congruency; 3. Definition of congruency; 4.

SAS theorem; 5. CPCTC

B. 1. Given; 2. Definition of congruency; 3. Reflexive property; 4.

Hypotenuse-leg theorem; 5. CPCTC

C. 1. Given; 2. Definition of perpendicular lines; 3. Definition of

congruency; 4. SAS theorem; 5. CPCTC

D. 1. Given; 2. Definition of perpendicular lines; 3. Reflexive property;


4. Hypotenuse-leg theorem; 5. CPCTC

123. Properties of Parallelograms In this task, you will be proving and comparing properties of certain types of parallelograms. Figure below is a parallelogram. Extending the sides and drawing other lines in the parallelogram can be helpful when proving the properties of parallelograms.

Part A. Mark all the angles in the figure that are congruent to Choose three pairs of these angles and explain how you know they are congruent.

Part B. are both perpendicular to Based on properties


of parallelograms, how do you know How do you know

Part C. Use the facts from parts A and B in a paragraph proof to prove that the opposite sides of parallelogram are congruent.

Part D. In the figure below, parallelogram has diagonals that intersect at point E. Use the properties of triangles and parallel lines in the two-column proof template below to show that the diagonals of the parallelogram bisect each other.

Part E. Figure is a parallelogram with diagonals intersecting at point Z. If what can be determined about parallelogram Use a paragraph proof to explain your answer. Add labels and/or marks to the figure below to support your proof.


Part F. Use the two-column proof template and rhombus shown below to prove that the diagonals of a rhombus bisect its angles.

Part G. Compare the properties of parallelograms. Fill in the chart to show whether a property is always, sometimes, or never true for each type of parallelogram listed.


124.

The figure below shows the parallelogram ABCD with segments AC and BD as diagonals.

Which of these correctly proves that the diagonals of a parallelogram bisect each other?


A.

B.

C.


D.

125.

Consider the quadrilateral with vertices

Part A. One way to prove that the quadrilateral is a parallelogram is to show that the diagonals bisect each other. Explain two other different methods that can be used to prove that the quadrilateral is a parallelogram.Part B. Explain how Part A illustrates the claim that the diagonals of a parallelogram bisect each other.

126.

Quadrilateral MATH includes the points M(2,-4) and A(5,-2).Part A: Find coordinates for T and H such that quadrilateral MATH is a rectangle.Part B: Prove that the resulting quadrilateral is a rectangle.


127.

An architect is designing a new city park. She draws a scale model that includes plans for different park features.

Part A. The architect includes a triangular playground in her design of the park. In her scale model, the playground is in the shape of an isosceles triangle with a 112° angle and two legs that measure 1.5 inches. Use a protractor and a ruler to create the scale model of the playground. Explain the steps you used to complete the construction. Part B. A sprinkler will be placed in one area of the park. The region to be watered by the sprinkler is shown below.

Use a compass and a straightedge to bisect the angle of the region the sprinkler will water. Explain the steps you used to complete the construction. Part C. The architect’s plans for the park include a brick wall with a flower garden in front of it, as shown by the diagram below.


The flower garden will be divided into two equal halves with different types of flowers planted in each half. What geometric construction can be used to divide the garden into two equal halves? Perform the construction on the diagram above and explain the steps you used to complete the construction. Part D. A walking trail is planned to form a straight path between the parking lot and the athletic fields at the opposite end of the park, as shown below.

The architect wants to design a bicycle route that goes through point X and is parallel to the walking trail. Construct and label the bicycle route on the diagram above. Explain the steps you used to complete the construction. Part E. The architect wants to make another path for joggers. The new


path will intersect the walking trail and bicycle route and run perpendicular to both. Use the diagram in part D to construct the jogging path. Explain the steps you used to complete the construction.

128.

Line m and point P are shown in the diagram.

Which method would not be used to construct a line through point P that is parallel to line m?

A. Draw a transversal through point P intersecting line m. Construct a pair of


congruent corresponding angles.

B. Draw a transversal through point P intersecting line m. Construct a pair of congruent alternate interior angles.


C. Construct a line l through point P that is perpendicular to line m. Construct a line, k, through point P that is parallel to line l.

D. Construct a line


l through point P that is perpendicular to line m. Construct a line, k, through point P that is perpendicular to line l.

129. The figure below shows

Part A. Construct the same length as using a compass and a


straightedge. Explain how you know the line segments are the same length.

Part B. Use a compass and straightedge to construct the perpendicular bisector of Explain how you know the line segment you constructed is a perpendicular bisector.


130. Amanda is constructing a line parallel to the line segment through point

P. So far, she has taken the steps shown below.

The first arc is the same distance from G as the second is from P. Part A. What further steps does she need to take to complete the construction? Part B. Sketch an example of what the completed construction would look like. Use words, numbers, and/or pictures to show your work.

13 April wants to construct quadrilateral congruent to the


1. quadrilateral shown below using only a compass and a straightedge.

Part A. Her first step is to copy the base of the quadrilateral. Draw and explain the steps April should use to construct congruent to

Part B. Next, April needs to copy Draw and explain the steps she should use to construct an angle congruent to along with the vertex at point Part C. What are the next two steps that April needs to perform in order to successfully continue her construction? Draw and explain the steps she needs to take. Part D. Complete April’s construction of quadrilateral Draw and explain the steps she needs to take to finish her copied figure. Use words, numbers, and/or pictures to show your work.

132.

Correct Constructions


Rajon is using a compass and a straightedge, along with his knowledge of the characteristics of lines, angles, and triangles, to draw figures according to certain specifications.

Part A. First, he has to draw the perpendicular bisector of segment He starts by opening the compass so that the opening is greater than half the length of the segment. He puts the point of the compass on one end of the segment and draws an arc, as shown. What are the next steps to drawing the bisector?

Part B. Use the tools to complete the drawing. Label the points where the arcs intersect and and label the midpoint of point Part C. Construct triangles and and use them to explain how you know that the segment you have made is a bisector of

Part D. Now, Rajon will draw a line parallel to line that passes through point shown below. Explain how he can use a compass and a straightedge to achieve this.


Part E. Draw the required line and explain how you know it is parallel to the original line. Label points as necessary. Part F. Finally, Rajon will bisect the angle below. Explain how he can use a compass and a straightedge to bisect the angle.

Part G. Explain how you know that the two angles formed by the bisector are congruent.

133.

The equation shown below represents a circle. Which statement describes the key features of the circle that can be determined from the equation?

A. The circle has a cent


er at

and radius of 2 units.

B. The circle has a center at


C. The circle has a


center at


D. The circle has a center at


134. What is the equation of the circle that has a center at and a radius

of 4 units?


A.

B.

C.

D.

135.

What is the center and the radius of a circle given by the equation

A.

B.

C.

D.

136.

In the standard xy-coordinate plane, the horizontal line intersects the circle

at two points, and


Part A: Complete the square to determine the standard form of the equation of the circle:

Part B: Find a value for such that the distance from to is 10. Show your work or explain your reasoning.

137.

A circle with a radius of 3 units has its center at the origin. Which equation gives any point on the circle?

A.

B.

C.

D.

138.

A circle with its diameter is shown on the coordinate grid below.


Which equation represents the circle given above?

A.

B.

C.

D.

139.

Given that a certain parabola has a focus at and a directrix at answer the following questions.

Part A. What are the coordinates of the vertex of the parabola? Show your work.

Part B. Does the parabola open up, down, left, or right? Explain your answer using the locations of the focus and vertex.


Part C. Derive the equation that represents this parabola. Show your work and explain your steps.

Part D. Sketch a graph of this parabola on the coordinate plane below. Label the vertex of the parabola as well as the focus and directrix.


140.

What is the vertex of a parabola with focus and directrix

A.

B.

C.

D.


141.

What is the equation of a parabola with a focus of and a directrix that goes through a point that is ten units directly above the focus?

A.

B.

C.

D.

142.

What is the equation of a parabola with a focus of and a directrix of

143.

Katie is using graph paper to sketch a design for a flat wooden bench that will have a rectangular seat. The front and side views that Katie sketched are shown below.


If Katie uses a scale on the graph paper in which each box represents a 6-inch by 6-inch square, what are the dimensions of the seat of the bench Katie is designing?

A. 2 feet long by 2.5 feet deep

B. 5 feet long by 2 feet deep

C. 5.5 feet long by 2.5 feet de


ep

D. 10 feet long by 5 feet deep

144.

Pet Fence Dana is planning to build an enclosure in her yard so that her dogs can play in a secure area. She is planning to use fencing that comes in rigid 6-foot-long sections. She cannot bend the individual sections, but she can join them at any angle to form different polygons. Dana has enough money to buy 24 sections of fencing, including one with a gate. Dana plans to use all 24 sections of fencing when building the enclosure for her dogs. Part A. Dana first considers making a rectangular enclosure. In the table below, list all possible ways Dana could use the fencing to make an enclosure that has an area of at least 900 square feet. What is the greatest rectangular area Dana could enclose with the 24 sections of fencing? Explain your answer.


Part B. Dana decides to sketch models of the rectangular enclosures. She uses tick-marks to show each section of fencing on the models, and she labels what will be the actual length and width of the enclosures. If represents two pieces of fencing placed next to each other, use a ruler or graph paper to sketch models of all of the possible enclosures that have an area of at least 1,000 square feet. Label the models with what will be the actual lengths and widths of the enclosures. How does the area of each enclosure, in square feet, relate to the area of each enclosure in fence section by fence section? Use the models you drew to help explain your answer. Part C. Dana is also considering making the enclosure in the shape of a regular hexagon. Use a ruler or graph paper to sketch a model of a regular hexagon with tick-marks to show how many fence sections would be needed for each side. Include the length of each side, in feet. Then, divide the hexagon into sections so that you can compute its area in square feet. Show how you chose to divide the hexagon and show your work for computing the area. When appropriate, leave side lengths in radical form. For your final answer, round the area to the nearest square foot. Part D. Dana’s sister suggested she make the enclosure in the shape of a regular octagon. Use a ruler or graph paper to sketch a model of a regular octagon with tick-marks to show how many fence sections would be needed for each side. Include the length of each side, in feet. Then, divide


the octagon into sections so that you can compute its area in square feet, and sketch your divisions on your model. Show your work and label the lengths you used in your calculations. When appropriate, leave side lengths in radical form. For your final answer, round the area to the nearest square foot. Part E. If Dana uses all 24 pieces of fencing as the sides of the enclosure, how could Dana construct the enclosure in order to maximize the area? Describe the configuration and explain your answer.

145.

Build a Corner Cupboard

You are taking an interest in carpentry and want to design a corner cupboard for books and knickknacks. A corner cupboard, or cabinet, is shaped like a triangular prism and fits into the corner of a room. You use geometric methods to work out the specifications for the cabinet.

Part A. Given the space you have available, you are thinking that the cabinet should come out 18 inches (in.) from the corner along each wall. How wide will it be across the front? Show your work, and give your answer to the nearest inch.

Part B. The back corner of the cabinet measures What is the measure


of the two other angles of the cabinet?

How deep will the cabinet be, from the back corner to the center front of the cabinet? Show your work, and give your answer to the nearest inch.

Part C. You would like the cabinet to be 6 feet tall. At the bottom, there will be 1 shelf enclosed by doors that are 2 feet high. There will be an open shelf at the level of the top of the doors, 3 other evenly spaced shelves, and then the top of the cabinet. You will have to buy extra wood to allow for waste when you cut it, but what is the minimum amount of wood you need for the sides, shelves, and top excluding the doors? Show your work, and give your answer to the nearest square foot.

Part D. What is the area of each shelf in square inches? What is the total volume of the cabinet in cubic feet? Give your answer to the nearest cubic foot. Show your work.

Part E. With triangular shelves, not all of the area is always usable space. You have a set of books you want to put on one of the shelves, with

bookends at either end. Each book is 9 in. high, 6 in. wide, and in. thick. If you put the books in a row across the shelf, with the spine of each book at the edge of the shelf, what is the maximum number of books you can put in the row? Draw a sketch, show your work, and explain your answer.

Part F. You are thinking about making a small 3-in. rail for the top shelf, as shown in darker gray below.

Show how you could cut a piece of wood like the one below to make the rail with the least waste possible. Label lengths and angles. What is the minimum length of wood that you would need?


146.

Sandy is designing cartons to hold cans of beans. The cartons are in the shape of a rectangular prism, and the cans are cylinders measuring 6.858 centimeters (cm) in diameter and 10.16 cm tall. The carton must be able to hold 30 cans on one layer and have a length no greater than 50 cm. Due to restrictions on the machine that creates the cartons, Sandy first completes her calculations and then rounds her results up to the next 0.25 cm.

Part ADetermine the dimensions for the base of the carton that would best accommodate 30 cans with the least amount of space left over. Show and explain your work.

Part BUsing the dimensions found for part A, determine the amount of area NOT covered by the cans on the base level. Show your work. Round your answer to the nearest hundredth.

Part CThe material for the cans weighs 0.0055 ounces per square centimeter. How many ounces does each can weigh? Round your answer to the nearest hundredth.

147.

is obtained by dilating by a factor of 2, then translating it 5 units to the left. If which statement must be correct?

A. Since translation preserves sid


e lengths, the corresponding side

B. Since translation preserves side lengths, the corresponding side


C. Since dilation results in proportional side lengths, the corresponding side

D. Since dilation results in


proportional side lengths, the corresponding side

148.

Triangles and shown below, are similar.


Which series of transformations best takes to

A. reflection over the y-axis, dilation by a factor


of 0.75, and rotation about point F by 90° counter-clockwise

B. reflection over the y-axis, dilation by


a factor of 0.5, and rotation about point F by 45° counter-clockwise

C. translation 16 units to the right,


dilation by a factor of 0.75, and rotation about point F by 90° counter-clockwise

D. translation 16 units to


the right, dilation by a factor of 0.5, and rotation about point F by 45° counter-clockwise

149.

Given:


Which of the following statements cannot be proven true or false for all cases?

A.

B.

C.

D.

150. In the diagram below, and the dimensions are in meters.

What is the length of

A. 34.4


meters

B. 40 meters

C. 43.2 meters

D. 45 meters

151.

Use the given image to answer part A and part B.


Part A. What transformation(s) does undergo to produce Be as specific as possible. Part B. What is true about the corresponding angles of these triangles? Is this true for all triangles of this type? Explain.


152.

In the figure below, is the result of a dilation of with point B as the center of dilation.

Which statement best uses this information to explain why the AA criterion can be used to prove


A. A dilation takes a line not passing through the center of dilation to a parallel line, so

Because they


are corresponding angles on parallel lines,

and

B. A dilation takes a line not passing through the


center of dilation to a parallel line, so

Because they are corresponding angles on parallel lines,

and


C. By the reflexive property,

A dilation results in line segments that are proportional in the


scale factor of the dilation. Therefore,

D. By the reflexive property,

A dilation results in line segm


ents that are proportional in the scale factor of the dilation. Therefore,

153.

Ms. Morales showed her geometry students the figure below and told them that She asked them to use this information to prove that divides and proportionally.


Hannah used the midpoint formula to show that and

Jaden used the slope formula to prove that and have equal slopes.

Omar used the distance formula to show that Which student or students used a formula that will help them prove the relationship?

A. Jaden only

B. Omar only


C. Hannah and Omar only

D. Hannah, Jaden, and Omar

154. In the given


What is the value of x?

A. 12

in.

B. 16

in.

C. 20

in.

D. 30

in.

155. Which expression is equivalent to the expression

A.

B.

C.

D.

156. Which number is equivalent to the complex number


A.

B.

C.

D.

157. Use the expression to answer the questions below.

Part A. If and what will be the real and imaginary part of the above expression?

Part B. If and write the above expression in simplest complex form.


158.

Which of these correctly defines the complex number i?

A.

B.

C.


D.

159. Which expression is equivalent to

A.

B.

C.

D.

160. Which expression is equivalent to

A.

B.

C.

D.

161.

Use to answer the following questions.

What is Give answer in form.


Define in form such that is a real number.


162.

What is the value of

A.

B.

C.

D.

163. What are the solutions of the equation

A.

B.

C.

D.


164. Which equation has as two of its solutions?

A.

B.

C.

D.

165. Which of these are the solutions of the equation

A.

B.

C.

D.

166. Which shows a solution of


A.

B.

C.

D.

167. The equation can be used to determine the kinetic energy of an

object, where m is the mass, in kilograms, and v is the velocity, in meters per second. What are the units of kinetic energy?

A.

B.

C.

D.


168.

A recipe for cookies needs 6 tablespoons of butter per batch. Logan is making 6 batches of cookies for a bake sale. How much butter will Logan need? (Note: 4 tablespoons = cup)

A. 2 cups plus 4 tablespoons

B. 2 cups plus 8 tablespoons

C. 9 tables


poons

D. 36 cups

169.

John leaves his house for the local community center. He walks a distance of 3 miles from his house in 45 minutes before stopping at a store to pick up a bottle of water. From there, he walks to the community center, which is 5 miles away from the store, in 1 hour. What is John’s approximate average speed, in miles per minute, for the entire time he is walking?

A. 0.0

67

B. 0.0

76

C. 0.0

83

D. 0.1

50

170.

Paul is a carpenter. He designs doors that are different sizes and shapes. His prices are dependent on the size of the door he designs. Part A. Paul wants to advertise his prices on a flyer. If he measures the dimensions of the door in feet to calculate the surface area, what units


should he use to represent the cost? Part B. A customer calls and asks Paul what his prices would be if he measured the door in yards instead of feet. The equation describes the cost, c, Paul charges per unit of area, a, when measuring the dimensions of the door in feet. Write an equation to show the cost if Paul wee to measure the dimensions of the door in yards. Use words, numbers, and/or pictures to show your work.

171.

Which expression results in an irrational number when simplified?

A.

B.

C.

D.

172.

Is the expression shown below rational?

A. Yes,


because the sum of two irrational numbers is rational

B. No, because the sum of two irrational nu


mbers is irrational

C. Yes, because the sum of a rational number and an irrational number is rational


D. No, because the sum of a rational number and an irrational number is irrational

173.

The host of a television news program wants to predict the voters' preferred candidate in the upcoming election. Which of the following sampling processes would be the least subject to bias?


A. The host sets up a booth at the local shopping mall and asks shoppers to participate in a survey.


B. The host asks viewers to call in, text, or visit the show's website to participate in the survey.

C. The ho


st requires each of the show's employees to have four of their neighbors participate in the survey.

D. The


host acquires a list of all citizens who voted in the last election and selects every 100th voter on the list to pa


rticipate in the survey.

174.

As senior class president, Grace wants to help the cafeteria provide more lunch items that the students like to eat. She designs a survey that assesses the favorite foods of students. After school one day, on her way to catch her bus, Grace administers the survey to 50 students waiting at the bus loop where buses meet to take students home.Part AWill the results of this survey represent a random sample, a convenience sample, or a self-selected sample? Explain why.Part BWhich sampling method would be the best method in this situation? Explain why.

175.

Which characteristic in a statistical study is necessary in order for conclusions to be drawn regarding the whole population, based on the sample population?

A. The sample must be


randomly selected.

B. The sample must not be randomly selected.

C. The population size must meet a mi


nimum number requirement, based on the sample size.

D. The population size must meet a maximum nu


mber requirement, based on the sample size.

176.

A teacher assigned students to determine the number of red cars in the student parking lot.

Student 1 looked at all the cars in the student parking lot and recorded the number of red cars.

Student 2 looked at the first 10 cars entering the student parking lot, counted the number of them that were red, and calculated the percent. The student multiplied this percent times the number of parking spaces in the parking lot to estimate the total number of red cars.

Compare the methods used by the two students. Include the words random, sample, and population in your comparison.

177.

An excerpt from a voting report is shown below. Use the information in the table to answer the questions below.


Part A. The report lists a number and a percentage for each of the categories. Why should we take into consideration the voting percentages instead of simply looking at the number of people who vote within each category?

Part B. Suppose a politician claims that more young citizens ages 18 to 24 vote than older citizens ages 75 and older. Do the data support this claim? Why or why not?


Part C. Overall, what are some trends that you see in the type of people who vote? Who votes most frequently? Who votes less frequently?


178.

A sports-and-exercise shop sampled its customer base one weekend and asked 35 customers their age:24, 24, 24, 24, 24, 24, 25, 25, 26, 26, 26, 26, 26, 26, 26, 26, 27, 27, 27, 28, 28, 28, 28, 28, 29, 29, 30, 30, 31, 33, 33, 33, 36, 45, 46Which interval estimate of the population mean has a margin of error of 1.7 ?

A.

B.

C.


D.

179.

James wants to find out whether polyurethane swimsuits help swimmers swim faster. To investigate, he chose seven volunteers from his swim team to participate in an experiment. On two consecutive Sundays, he had each volunteer swim 50 meters. On one Sunday, each swimmer wore a polyurethane swimsuit, and on the other Sunday, each swimmer wore an ordinary swimsuit. The times he recorded are listed below.

He then ran a simulation using a computer program to figure out what differences in means could be expected to occur simply due to random chance. Which statement best explains what James can conclude based on the results of the simulation?

A. James can conclude that polyurethane


swimsuits help swimmers swim faster if the mean difference of the simulation is close to the experimental


mean difference.

B. James can conclude that polyurethane swimsuits help swimmers swim faster if the me


an difference of the simulation is less than the experimental mean difference.

C. James can conclude


that polyurethane swimsuits help swimmers swim faster if the mean difference of the simulation is greater th


an the experimental mean difference.

D. James can conclude that polyurethane swimsuits do not help


swimmers swim faster if the mean difference is equal to the experimental mean difference.

180.

A survey was conducted where 150 high school students were asked the average amount of time they spent doing household chores in one week. The data collected resulted in a mean time of 180.5 minutes with a standard deviation of 5.5 minutes. Which of these represents a 95%


confidence interval for the mean weekly hours spent doing household chores of all high school students?

A. 171.5–189.5

B. 175–186

C. 178.25–182.75

D. 179.62–181.38

181.

In a college math class, 500 students took a final exam. The final exam results showed students had an average score of 65.3% with a standard deviation of 5.2%. The scores on the final exam followed a normal distribution curve with population percentages as shown below.


How many students scored above 54.9% but below 70.5%?

A. 78

B. 82

C. 34

1

D. 40

9

182.

A factory manufactures light bulbs and then packs them in boxes to be shipped to its customers. Before each shipment, boxes are randomly chosen and the bulbs inside are inspected. The number of bulbs found to be defective in each box can be normally distributed. The mean number of defective bulbs in each box is 12 with a standard deviation of 2.


Use the normal curve shown above to answer the questions. Let represent the mean and represent the standard deviation.

Part A. If any one box among the sample of inspected boxes chosen has a total of 9 defective bulbs, what percentage of the sample boxes will have more defective bulbs than this box? Explain what this means in terms of the given context.

Part B. If there are 60 boxes that contain between 12 and 15 defective bulbs, how many total boxes were inspected?


183.

A book editor was proofreading a draft of a novel. She found that the number of errors on each page of the book was normally distributed, with the mean number of errors on a page as 8 and a standard deviation of 1. If 82 pages had between 7 and 9 errors, what was the approximate total number of pages in the book?


A. 56 pages

B. 68 pages

C. 120 pages

D. 202 pages


184.

The distributions below represent the batting averages of the players on two baseball teams, A and B.

Which of these is true based on the graph?

I. The mean batting average for team A is less than the mean batting average for team B.II. The standard deviation for team A is less than the standard deviation for team B.

A. I only

B. II only

C. both I and II

D. nei


ther I nor II


Documents

Math III Review [578574] - WordPress.com · Web viewClara’s college fund can be modeled by the function f(x) = 500x + 2,500, where x is the number of years since 1998. Michelle’s