Math 3 Final Review Schoolnet.pdf

TEST NAME:Math 3 Final Review

TEST ID:382677

GRADE:09 12

SUBJECT:Mathematics

TEST CATEGORY:School Assessment

Math 3 Final Review of 72

Student:

Class:

Date:

Read the passage 'The Ferris Wheel' and answer the question below:

The Ferris Wheel

The Ferris Wheel

“School’s out!” Ryan shouted gleefully to his older sister, Claire, as he bargedthrough the front door of his house and slung his backpack on the floor. Theyattended the local high school, where Ryan had been a freshman and Claire ajunior. Summer vacation had finally begun.

Ryan and Claire had even more reason to celebrate because the family vacationtheir parents had planned to Chicago, Illinois, was now only two days away. Clairehad wanted to visit Chicago ever since her friend Marco returned from a visitthere; she still remembers how he ranted and raved about all there was to seeand do in the “Windy City.”

Ryan and Claire had been doing research online about the numerous sights to seeand all the exciting things they should do on their visit. Claire was very interestedin seeing the downtown area with its prominent buildings and skyscrapers, manyhaving been designed by important architects. But both Ryan and Claire weremost excited about finally getting to go to Navy Pier, an amusement park locatedon Lake Michigan that includes a musical carousel, indoor mall, great food, andthe famous Ferris wheel.

“Hey, Ryan, did you know that the Navy Pier Ferris wheel is 150 feet high?” Clairesaid in amazement. “According to this information, that’s as tall as a 13storybuilding.”

“You aren’t going to ride the Ferris wheel. You will be too frightened once you seehow 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 eachone will seat up to 6 people. Therefore, we will all definitely be able to fit inone.”


Claire went on to read that during the 7minute ride, she would be able to seemost of downtown. In fact, from the top of the Ferris wheel, on a clear day, onecould 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 Chicagostylehot dog with fries and a funnel cake.” Ryan laughed at his joke, but Claire was toobusy studying the website to even look away and roll her eyes at his absurdcomment, which would have been her normal reaction.

Claire loved to learn about how things were built, all the way from the inceptionof the idea drafted on paper to the actual building of the structure, which is whyshe planned to study architecture in college. She found the subject fascinatingand 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 Ferrisback in the 1890s. The first Ferris wheel was 25 stories high and was madeentirely 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 morethan 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 secondso that passengers could be loaded into the carriages.

It debuted at the World’s Columbian Exposition, which is more commonly knownas the 1893 Chicago World’s Fair. George Ferris wanted the attendees of the fairto marvel at his innovative invention and forget about the Eiffel Tower, which hadbeen revealed four years earlier at the Paris International Exposition. Though thewheel was popular at first, it soon lost its superstar appeal and was dismantledand eventually sold as scrap metal.


Claire looked up from her computer. She was more excited than ever, knowing thatsoon she would experience all of the sites she had read about. There was onlyone thing left to do: pack.

1. Read “The Ferris Wheel” and answer the question.

A sketch of the first Ferris wheel invented by George Ferris was drawnusing the unit circle as the model for the sketch. What is the arc length,in radians, on the sketch of the Ferris wheel that represents the arclength of feet on the actual Ferris wheel?

A.

B.

C.

D.

Read the passage 'Flagstone Pathways' and answer the question below:

Flagstone Pathways

Flagstone Pathways

Bill’s Landscaping is a local company that offers several services for families inthe area, such as planning and building gardens; constructing pathways in yards,gardens, and pools; and maintaining landscaped areas.

Bill’s Landscaping would like to be sure that the price it is charging per squarefoot of flagstone pathway is competitive in the local landscaping market andyields the maximum profit. Currently, the company charges $18 per square foot ofpathway laid. At this price, it brings in about 2,400 square feet of pathway workfrom customers each month.

However, the owners are thinking of decreasing the price charged per square footto be more competitive. Using information about the local landscaping market,they have determined that for every $1 decrease in price per square foot, theamount of work brought in by customer requests for flagstone pathways willincrease by 200 square feet monthly.

The Johnsons, a family living in the area, are considering hiring a company to helpthem build a garden. The garden will be rectangular in shape and will besurrounded by a stone pathway of uniform width throughout.

The Johnsons have heard that Bill’s Landscaping is the most reliable companyaround but can be expensive at times. They must take this into considerationwhen determining the width (overall area) of the pathway. Mr. Johnson thinks thatthe walkable portion of the pathway should be at least 2 feet (ft) in width. Mrs.Johnson would like to have a decorative border around the pathway that willincrease the width slightly. The diagram below shows the Johnsons’ vision for the


garden, where x represents the width of the decorative border that Mrs. Johnsonwould like to have.

The Johnsons are not the only family in the community that is hiring a landscapingcompany to help with constructing garden pathways. Recently, there has been alot of interest in stone pathways, particularly using flagstone, in garden andbackyard areas. Flagstone is a flat stone slab that comes in several differentnatural colors and is often irregularly shaped, although it can also be square orrectangular. The stone is used to make naturallooking pathways in backyards andother landscaping projects. The picture below shows a typical flagstone pathway.

The Johnsons have heard about the possible decrease in prices at Bill’sLandscaping. They hope that this reduction in prices will allow them to hire Bill’s


to construct a flagstone pathway around their garden and still have enough intheir budget to include a decorative border.

2. Read “Flagstone Pathways” and answer the question.

A customer at Bill’s Landscaping Company wants to spend a maximum of$4,200 to put in a straight flagstone pathway that is rectangular in shapealong one side of a plot of land. Based on the current pricing at Bill’sLandscaping Company, which expression represents the maximum widthof the pathway that can be built?

A.

B.

C.

D.

Read the passage 'Pollution Research' and answer the question below:

Pollution Research

Pollution Research

In her environmental science class, Kaylie has been learning about air pollution.The teacher told the class that pollution occurs when chemicals and particles arereleased into the air we breathe. These pollutants can be very harmful to peopleand other living organisms in the environment.

Several natural processes release pollutants. Most pollution is caused by humanactivities that release hazardous chemicals into the air through their exhaust:when cars run and burn gasoline, when factories use coal for fuel, or even whengas stoves are used to cook food. These chemicals, when exposed to sunlight, canreact with other substances to form smog, which is the haze that is often seensurrounding large cities. Air pollution and smog are harmful to people’s health andto the environment. They have been known to aggravate asthma and respiratorydisease as well as to cause acid rain.

Kaylie is interested in learning more about what causes air pollution and what shecan do to minimize it. She has noticed that the city she lives in has areas withmore smog than others. She would like to know what chemicals are present in theair in this city. She goes to the local climate research center to get moreinformation.

At the research center, scientists inform Kaylie that the main source of pollutionin the area is car exhaust from commuters traveling in and out of the city everyday. Car exhaust produces a chemical known as nitrogen dioxide that can absorblight and eventually create pollutants. The scientists tell Kaylie that whennitrogen dioxide breaks down, it forms particles of oxygen that are different fromthe oxygen we breathe. These oxygen particles combine with other substances in


the air to form pollutants. Kaylie realizes that when the nitrogen dioxide from carexhaust breaks down and decreases in amount, this means that oxygen particles,and therefore pollutants, are being formed and are increasing in amount.

The scientists at the research center have been doing pollution experiments intheir laboratories. They have been comparing the amount of nitrogen dioxide thatbreaks down with the amount of oxygen particles formed. They do this bymeasuring the concentrations of these substances over short periods to see howthey change. Concentrations are determined by finding the amount of a substanceper unit volume. In this case, the scientists measured concentration inmicrograms per cubic meter They let Kaylie look at the results from a

recent investigation.

These results show how the concentration of nitrogen dioxide and oxygen particleschanged in relation to one another over a period of 20 minutes. After looking atthe results, Kaylie is convinced that nitrogen dioxide is harmful to theenvironment. She will remember her trip to the research center the next time sheneeds to go somewhere. Maybe she will try walking or riding her bike more often!

* Micrograms are very small units that are a fraction of a gram, so

3. Read "Pollution Research" and answer the question.

Which units would be used to measure the rate of change inconcentration over time for either substance shown in the table in thepassage?

A.

B.

C.

D.


4. The expression 5x + 2x + 3 represents the area of a square. The area ofa rectangle is represented by 2x + 3x + 1. Which expression representsthe combined area of the square and rectangle?

A. 7x + 5x + 4

B. 3x x + 2

C. 7x + 5x + 4

D. 3x x + 2

5. Which expression is equivalent to (3x – 5x + 4) + (2x – 7)?

A. 5x – 5x – 3

B. 5x – 5x – 11

C. 6x – 5x – 3

D. 5x – 5x – 3

6. A triangle has side lengths of inches and inches. If theperimeter of the triangle is inches, which expression representsthe length, in inches, of the third side of the triangle?

A.

B.

C.

D.

7. What is the remainder when is divided by

A.

B.

C.

D.

22

4 2

4 2

2

2

2 2

2

2

2

4


8. Which statement best justifies whether is a factor of the

polynomial

A. It is a factor of p(x) because

B. It is a factor of p(x) because

C. It is not a factor of p(x) because

D. It is not a factor of p(x) because

9. At which points does the graph of the polynomial

intersect the xaxis?

A.

B.

C.

D.

10. Which graph best represents the function

A.


B.

C.

D.


11. Four functions are listed below.

Which two functions, when graphed, have the same number of xintercepts?

A. f(x) and g(x)

B. g(x) and h(x)

C. h(x) and k(x)

D. k(x) and f(x)

12. Which of these best exemplifies a sketch of the graph of the polynomialfunction ?

A.

B.


C.

D.


13. Which function best represents the graph below?

A.

B.

C.

D.

14. A farmer has a corn field with an area of square feet and a wheat

field with an area of How many more square feet is the wheat

field compared to the corn field, in terms of x and y?


15. The figure below contains two circles, both with a center at point O.

The formula for the area of the shaded region is Based on

polynomial identities, what is another expression that represents thearea of the shaded region?

A.

B.

C.

D.

16. Simplify.

A.

B.

C.

D.


17.Which of these expressions is equivalent to

A.

B.

C.

D.

18.Which of these is equivalent to the expression if and

A.

B.

C.

D.

19. Alma invests $300 in an account that compounds interest annually. After2 years, the balance of the account is $329.49. To the nearest tenth of apercent, what is the rate of interest on the account?

A. 6.9%

B. 5.4%

C. 4.8%

D. 4.4%


20. A rectangle has a perimeter of 52 inches. The length of the rectangle is 4inches more than its width. What is the length of the rectangle?

A. 11 inches

B. 13 inches

C. 15 inches

D. 19 inches

21. Marcus wants to exchange his American dollars to pesos before leaving on atrip to Mexico. A bank offers 13 pesos for each American dollar. The bankcharges a service fee of $2.50 to exchange the money. Which equationmodels the number of pesos, y, that Marcus will receive for x American dollarsafter the service fee?

A.

B.

C.

D.

22. The function is a linear function of x:

. for all x and for all constant b

As well, f(x, y) is a linear function of y:

for all y and for all constant a.

The following values are known:

What is

A. 9

B. 42

C. 54

D. 66


23. Nick deposited $500 in a bank that gives him 5% interest compoundedannually. Which equation can be used to find the total amount, in Tdollars, in Nick’s account after x years?

A.

B.

C.

D.

24. A box manufacturing company compared the volume of several rectangular boxes with the same lengths andwidths but varying heights as shown in the table.

Which equation can be used to find the volume, v, for one of these boxes with a height of h?

A.

B.

C.

D.

25. Jane invested $755 in an account that earns interest at a rate of 8.5%,compounded annually. Which equation can be used to determine thevalue, v (in dollars), of Jane’s investment after t years?

A. v = 755 + 1.085t

B. v = 755(1.085t)

C. v = 755(1.085)

D. v = [755(1.850)]

t

t


26. Karen is making bird houses, x, and dog houses, y, to earn money. Shefound that her feasible region intersected at the points (9, 20), (0, 16),and (11, 0). She knows that she will lose $1 on each bird house, but willmake $5 on each dog house that she sells. How many dog houses willKaren need to sell to maximize her profit?

A. 91

B. 80

C. 20

D. 16

27. The Student Council is having a talent show.

They plan to sell no more than 500 student tickets and no more than300 general admission tickets. It costs $0.50 per ticket to advertise the show to the students and $1per ticket to advertise the show to the general public. The advertising budget is, at most, $400 for the show. Student Council makes $6 profit for a student ticket and $9 profit for ageneral admission ticket.

What is the maximum profit that the Student Council can expect from theshow?

A. $4,350

B. $3,900

C. $3,000

D. $2,750

28. What equation is equivalent to 24 = ax + 4y – 10, when solving for y?

A.

B.

C.

D.


29. Which formula represents the equation , when solved for y?

A.

B.

C.

D.


30. Michaela is learning to solve algebraic equations by applying themathematical properties of equality. She had to solve the equation

Michaela wrote down the steps she took to solve theequation below.

Steps taken to solve the equation

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

Step 6:

Step 7:

Step 8:

Step 9:

Why does the equation found at step 4 preserve the equality asserted bythe equation found at step 3?

A. The sum of a number and its additive inverse is 0.

B. The product of a number and its multiplicative inverse is 1.

C. The equality of numbers will not change when a constant is added toone side of an equation and the additive inverse of the constant isadded to the other side of the equation.

D. The equality of numbers will not change when one side of anequation is multiplied by a constant and the other side of theequation is multiplied by the multiplicative inverse of the constant.


31.Which value is a solution to the equation

A.

B.

C.

D.

32. What are the solutions to the equation below?

A.

B.

C.

D.

33. Which point lies on the graph of y = 3x – 15?

A. ( 3, 21)

B. ( 1, 15)

C. (14, 27)

D. (16, 30)

– –

– –


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. Two functions are shown below.

f(x) = 2(3)g(x) = 4x + 2

What is the difference in the yvalues of the two unique points wheref(x) = g(x)?

A. 0

B. 2

C. 4

D. 6

36. Two functions are shown below.

f(x) = 0.5(2)g(x) = 5x – 12

Which is a point of intersection where f(x) = g(x)?

A. (8, 4)

B. (6, 44)

C. (4, 8)

D. (3, 3)

x

x


37. Which statement is true about the equation given

and

A. It has two solutions at

B. It has two solutions at

C. It has four solutions at .

D. It has four solutions at

38. George is filling a swimming pool with volume V cubic units. He observedthat at time the volume of the pool filled is and that at time onefourth of the pool was left to be filled. What does the expression

represent?

A. the volume of the pool left to be filled

B. the volume of the pool filled until time

C. the volume of water filled in time

D. the volume of water filled in time

39. Which variable in the function is responsible for the

vertical translation of the graph?

A. a

B. h

C. k

D. x


40.If can be rewritten as where and what

are the values of b and c?

A.

B.

C.

D.

41. Which expression is equivalent to

A.

B.

C.

D.

42. What are the zeros of the function defined by x – 5x – 24?

A. 8, 3

B. 8, 3

C. 3, 8

D. 3, 8

43. The population of a colony of bacteria is growing at 6.2% per day. Thisgrowth can be modeled by the expression where represents the

initial population and t is the time in days. What expression is theequivalent for the approximate perhour growth rate of the population?

A.

B.

C.

D.

2

– –

–

–


44. The Sanchez family wants to go on a vacation in August, and they beginsaving in December. The Sanchez family expects the vacation to cost$1,700. Each month they will deposit 5% more than the previous month.In December, they deposit $100. How much will the Sanchez family havesaved for their vacation after 9 months?

A. $147.75

B. $1,102.66

C. $2,864.73

D. $6,000.00

45. Jessie deposited $6,000 in a savings account. The amount in the accountafter 1, 2, and 3 years is shown below.

$6,240, $6,480, $6,720, ...

Which expression represents the total amount in her account at the endof t years?

A.

B.

C.

D.

46. The function C(x) = 200 + 3.3x models the cost for a company to producex units of a product. The function R(x) = 25x models the revenue thecompany earns if they sell x units of the product. Which function, P(x),models the profit the company earns if they sell x units of the product?(Profit = Revenue – Cost)

A. P(x) = 28.3x – 200

B. P(x) = 21.7x – 200

C. P(x) = 200 – 21.7x

D.P(x) = 28.3x + 200


47. The number of cows a farmer has can be modeled by an arithmeticsequence. The 2nd, 5th and 7th terms in that sequence are 30, 39, and45, respectively. How many cows did the farmer begin with?

A. 21

B. 24

C. 27

D. 30

48. Which context best matches the recursive equation NEXT = NOW + 5?

A. the population of sea bass in 5 year’s time

B. the speed of a bike traveling at 5 miles per hour

C. the number of students at a basketball game, increasing by 5students every minute

D. the time it takes a person to run a marathon, decreasing by 5minutes each marathon

49. Marcus dropped a ball from a height of 400 cm. The sequence belowshows the height of the ball, in cm, during its first four bounces.

240, 144, 86.4, 51.84, ...

Which formula could be used to determine the height of the ball after nbounces?A. h(n) = 400(0.60)

B. h(n) = 400(0.60)

C. h(n) = 240(0.60)

D. h(n) = 240(0.60)

n

(n – 1)

n

(n – 1)


50. The function below describes an arithmetic sequence, where A(n) is thenth term and n is the term number.

A(n) = 6 + 3(n – 1)

Which table best fits the sequence?

A.

n 1 2 3 4

A(n) 6 12 15 18

B.

n 1 1.5 2 2.5

A(n) 6 7.5 9 10.5

C.

n 2 3 4 5

A(n) 6 9 12 15

D.

n 2 3 4 5

A(n) 9 12 15 18

51. A sequence is shown below.

Which recursive formula models the sequence?

A.

B.

C.

D.


52. The function f(x) = x – 3 was replaced with f(x) + 2 resulting in thefunction g(x). What is the yintercept of g(x)?

A. (0, 1)

B. (0, 5)

C. (0, 2)

D. (0, 5)

53. The graph of the function f(x) and the transformed functionare shown below.

Which values are the best estimates for the values of a and k?

A. and

B. and

C. and

D. and

–

–


54. Which expression represents the inverse of

A.

B.

C.

D.

55. Which relation is the inverse of the function

A.

B.

C.

D.

56. A car company uses the function g(x) = 25,400(0.88) to predict thevalue of a car x years from now. What will be the approximate value ofthe car 6 years from now?

A. $7,113

B. $11,796

C. $18,288

D. $22,352

57. An Internet company uses the function f(x) = 6.052(1.378) to predictthe number of subscribers (in millions) x years after2000. Approximately what is the predicted number of Internetsubscribers the company will have in 2019?

A. 442 million

B. 1 billion 943 million

C. 2 billion 677 million

D. 3 billion 689 million

x

x


58. The amount of profit a company makes from selling video games for xdollars is modeled by the function P(x) = x + 100x + 350,000. To thenearest dollar, what price gives the maximum profit?

A. $40.00

B. $45.00

C. $50.00

D. $55.00

59. Jim borrowed $850 to purchase a stereo system for his car. He has beenmaking payments each week for the last four weeks. The chart belowshows the history of his loan balance.

In the linear function that models these data, x represents the week andy represents the balance of the loan. What is the slope of the function?

A.

B.

C.

D.

– 2


60. Shane is filling a barrel with water. The table below shows the amount ofwater in the barrel after different amounts of time.

Time (seconds)

Amount of Water (cubic inches)

1 25 2 32 3 39 4 46

Assuming Shane filled the barrel at a constant rate, how much water wasinitially in the barrel?

A. 18 cubic inches

B. 16 cubic inches

C. 14 cubic inches

D. 12 cubic inches

61. A high school baseball team is having a fundraiser at a restaurant. Thefunction f(x) = 4x models the amount of money that the restaurant willdonate to the team if x customers purchase dinner. The restaurantagrees to donate a maximum of $500 to the team. What is the mostappropriate domain of the function?

A. all nonnegative integers ≤ 4

B. all nonnegative integers ≤ 125

C. all nonnegative integers ≤ 500

D. all nonnegative integers

62. A company uses the function f(x) = 20x – 500 to calculate profit or loss,where x is the number of products sold. What is the most appropriatedomain of the function?

A. all integers

B. all real numbers

C. all whole numbers

D. all rational numbers

63. Which graph represents a linear function with a slope of and a yintercept of


A.

B.

C.

D.


D.

64. Which is an equation of the function graphed below?

A. y = 2 + 3

B. y = 2 – 3

C. y = 3 + 2

D. y = 3 – 2

x – 1

x + 1

x – 1

x + 1


65.

Graph the function on the coordinate plane below.

66. Which equation best models the function graphed below?

A. y = x – 6x – 8

B. y = x + 6x – 8

C. y = x + 6x + 8

D. y = x + 6x + 8

2

– 2

– 2

2


67. Which graph correctly represents the zeros and end behavior of the function?

A.

B.

C.

D.


68. Amy deposited $2500 into a savings account. The value of theaccount after t years is given by the equation shown below.

Which of these statements about the growth rate of the savingsaccount is true?

A. It is growing at an annual rate of 1.8% compounded quarterly.

B. It is growing at an annual rate of 1.8% compounded yearly.

C. It is growing at an annual rate of 7.2% compounded quarterly.

D. It is growing at an annual rate of 7.2% compounded yearly.

69. Two functions are shown.

In which quadrant does each function's minimum occur?

A. f(x): Quadrant I

g(x): Quadrant II

B. f(x): Quadrant I

g(x): Quadrant IV

C. f(x): Quadrant II

g(x): Quadrant I

D. f(x): Quadrant IV

g(x): Quadrant III


70. Which of these correctly transforms into vertex form and

identifies the vertex?

A. with the vertex at

B. with the vertex at

C. with the vertex at

D. with the vertex at

71. The height in feet, a kangaroo reaches seconds after it has jumpedin the air is modeled by the quadratic function Which

equation shows the correctly factored version of the function andthe 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

72. Suppose the equation h(t) = t + 5t + 14 models the height of a ballthrown into the air off the bleachers. Which statement about the flight ofthe ball is true?

A. The ball starts from a height of 19 feet.

B. The ball takes 5 seconds before it hits the ground.

C. The ball takes 14 seconds before it hits the ground.

D. The ball reaches a maximum height of 20.25 feet.

– 2


73. 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’shook x seconds after she threw it.

If both of them threw the grappling hooks at the same time, which ofthese 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.

74. Angela earns $8 for every hour she works at her job. The amount ofmoney Kelly earns at her job is modeled by the function f(x) = 15t,where t represents hours worked. Angela and Kelly both worked 38 hourslast week. Which statement accurately describes the amount of moneyAngela and Kelly earned last week?

A. Angela made $38 more than Kelly.

B. Kelly made $266 more than Angela.

C. Angela made $304 more than Kelly.

D. Kelly made $570 more than Angela.


75. Two functions are shown in the table below.

x f(x) g(x) 0 100 5 1 102 10 2 104 20 3 106 40

Which statement is true about the two functions when x = 5?

A. The value of f(x) exceeds the value of g(x) by 20.

B. The value of g(x) exceeds the value of f(x) by 20.

C. The value of f(x) exceeds the value of g(x) by 50.

D. The value of g(x) exceeds the value of f(x) by 50.

76. The number of female nurses in a country can be predicted using thefunction f(t)=7,300 + 25t, where t is the number of years since 2000.The number of male nurses can be predicted using the function m(t) =2,500(1.02) , where t is the number of years since 2000. About howmany years will it take before the number of male nurses is expected toexceed the number of female nurses?

A. 60

B. 65

C. 70

D. 75

77. For what value of x is it true that

A.

B.

C.

D.

t


78.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

79. A Ferris wheel with a diameter of 40 feet completes 2 revolutions in oneminute. The center of the wheel is 30 feet above the ground. If a persontaking a ride starts at the lowest point, which trigonometric function canbe used to model the rider’s height h(t) above the ground after tseconds? (Consider the height of the rider negligible).

A.

B.

C.

D.

80. George’s height above the ground as he rides a Ferris wheel ranges from4 meters to 30 meters. If it takes 200 seconds to complete onerevolution, which sine function represents his height, from the

ground as a function of time,

A.

B.

C.

D.


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

A.

B.

C.

D.

80. Let p represent a point on the unit circle, in the second quadrant. Theline including p and the origin has a slope of 2. What is the xvalue ofp?

A.

B.

C.

D.

83. 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 onlytranslations.

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


82. In the given figure, is tangent to circle M at point B.

If find the length of

A. 9

B. 11

C. 15

D. 17

83. 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°

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


Part A. Amy wants to add a circular piece of gold that will be inscribedinside the triangular piece of silver. Use a compass and straightedge toshow how she can add the circular piece to the triangle above. Explainthe steps you used to perform the construction.

Part B. She needs to know the radius of the inscribed circle so that shecan calculate the circumference and area of the circular gold piece sheneeds to make for the jewelry. Given that the silver triangle is a righttriangle with side lengths a, b, and c, find the equation Amy can use todetermine the radius of the circle, r. Explain your answer and draw adiagram or use your construction in part A to support your reasoning.

Part C. Amy then decides to inscribe another similar silver triangle insidea circular piece of copper so that each vertex of the triangle touches theedge of the copper circle. Use a compass and straightedge toconstruct her design below. Explain the steps you used to perform theconstruction.

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


Now Amy wants to produce an identical piece of jewelry but needs toknow the exact angle measures for the gold quadrilateral. Whatgeometric property about quadrilaterals can Amy use to find themeasures of the angles of her jewelry design? Use a paragraph proof tojustify your response.

Part E. What are the measures of the three missing angles in Amy’ssketch of the piece of jewelry in part D? Explain how you know.

85. If is the radian measure of a central angle of a circle and r is the radiusof the circle, which is the correct derivation of the area, A, of the sectorbounded by the sides of the central angle and the arc it subtends?

A.

B.

C.

D.


86. Jessica is using the image below to derive a formula for arc length.

If x is measured in radians, which procedure explains how Jessica couldcorrectly derive arc length?

A. Set the ratio of s to the circumference proportional to the ratio of x to

B. Set the ratio of s to the circumference proportional to the ratio of x to360.

C. Set the ratio of s to r proportional to the ratio of x to

D. Set the ratio of s to r proportional to the ratio of x to 360.

87. What is a definition of a circle?

A. the set of all points in a plane equidistant from a line

B. the set of all points in a plane equidistant from a point

C. the set of all points in a plane equidistant from 2 points

D. the set of all points in a plane equidistant from the endpoints of a line segment

88. Which of these is defined as a part of a line that is bounded by two endpoints?

A. ray

B. angle

C. point

D. line segment


89. Two parallel lines are cut by a transversal x and a transversal y so that xand 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 thetriangle formed by lines m, x, and y.

Angles b and c are [missing reason 2] and therefore congruent to twoother 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 thetriangle

Reason 2: vertical angles with the other two angles in the triangle

B. Reason 1: an alternating exterior angle with one angle in thetriangle

Reason 2: complementary angles with the other two angles in thetriangle

C. Reason 1: a corresponding angle with one angle in the triangle

Reason 2: vertical angles with the other two angles in the triangle

D. Reason 1: a corresponding angle with one angle in the triangle

Reason 2: complementary angles with the other two angles in thetriangle


90. A proof of the Vertical Angles Theorem is shown below.

Which is the correct reason used in step 4?

A. addition property

B. substitution property

C. definition of supplementary angles

D. definition of complementary angles

91. Elizabeth wants to prove the triangle angle sum theorem. Which stepscould be part of her proof?

A. Construct an altitude of one side, and then use corresponding partsof congruent triangles.

B. Construct a line perpendicular to two sides of the triangle, and thenuse the linear pair postulate.

C. Construct a line passing through a vertex and parallel to the base ofthe triangle, and then use alternate interior angles.

D. Construct a line passing through two sides of the triangle and parallelto the base of the triangle, and then use corresponding angles.


92. In the diagram, line l is parallel to line m . When proving that the sum of the measures of the angles of a triangleis 180°, it is stated that because

Why is this true?

A. and because alternate interior angles are supplementary if lines are

parallel.

B. and because alternate interior angles are congruent if lines are parallel.

C. and because corresponding angles are congruent if lines are parallel.

D. and because sameside interior angles are congruent if lines are parallel.

93. Which of these properties is enough to prove that a given parallelogramis also a rectangle?

A. The diagonals bisect each other.

B. The opposite angles are equal.

C. The opposite sides are equal.

D. The diagonals are congruent.


94. James has written the first four statements and reasons of a proof. Hiswork is shown below.

Which of these could be statement 5 in the proof?

A.

B.

C.

D.


97. 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 correspondingangles.

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

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


98. 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 theconstruction?

Part B. Sketch an example of what the completed construction would looklike.

Use words, numbers, and/or pictures to show your work.

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

radius of 4 units?

A.

B.

C.

D.


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

Which equation represents the circle given above?

A.

B.

C.

D.

99. Which equation of a parabola has a graph with a focus located on the xaxis at and a directrix of

A.

B.

C.

D.


102. What is the vertex of a parabola with focus and directrix

A.

B.

C.

D.

103. The equation of a parabola is What is the focus of the

parabola?

A.

B.

C.

D.


104. Margaret is using a cardboard model to design a flowerpot. To createthis flowerpot model, she cut the tops off of two congruent squarepyramids that each had a height of 40 inches and a base length of 15inches. She used the bottom half of one pyramid and the bottom onefifth of the other pyramid and then attached the bases as shown.

Margaret would like to use this model to determine how much pottingsoil a flowerpot this size and shape would hold. Which expressionrepresents the volume of the flowerpot?

A.

B.

C.

D.


102. Mr.Williams drew on a coordinate grid and asked his students todetermine the transformations that will result in a transformed figure

such that is similar but NOT congruent to Twostudent responses are shown below.

Student 1: Reflect across the yaxis and then dilate it by a scalefactor of 1 with the center of dilation at the origin.

Student 2: Dilate by a scale factor of 2 and the center of dilationat the origin and then reflect it across the xaxis.

Which statement is true?

A. Neither student 1 nor student 2, because dilations and reflectionspreserve both side lengths and angle measures.

B. Both student 1 and student 2, because dilations and reflectionspreserve angle measures but not side lengths.

C. Only student 2, because dilations preserve angle measures and sidelengths are proportional.

D. Only student 1, because this dilation preserves angle measures andside lengths.


103. Noah has drawn two triangles and on the coordinateplane as shown below.

Which statement is the best explanation of the relationship betweenthese triangles?

A. The given triangles are similar because they can be mapped ontoeach other by a series of reflections, translations, and dilations.

B. The given triangles are similar because they can be mapped ontoeach other by a series of reflections, translations, and rotations.

C. The given triangles are not similar because they cannot be mappedonto each other by a series of reflections, translations, anddilations.

D. The given triangles are not similar because they cannot be mappedonto each other by a series of reflections, translations, androtations.


104. Hector looks at two polygons that have the same number of sides.Based on his observation, he makes a claim:

"If all the angles of the first polygon are congruent to the correspondingangles of the second polygon, then the two polygons must be similarfigures."

Which of the following conditions must be true in order for Hector'sclaim to be accurate?

A. The first polygon is a triangle.

B. The first polygon is equiangular.

C. The polygons are both convex.

D. The sides must be straight segments.

108. Martin dilated and then reflected it to produce

Which statement must be true?

A.

B.

C.

D.


109. Consider the given figure.

What information about this figure would be used as a step in a proofof the Pythagorean theorem?

A. showing that

B. showing that

C. showing that

D. showing that is the perpendicular bisector of

110. Jamelia is trying to prove that for the figure below, She is given

the information that and lists the first five statements of her

proof.


What are the correct remaining statements in Jamelia’s proof?

A.

B.

C.

D.


107. In the given triangle,

Which of these statements can be proved?

I.

II.

III.

A. I only

B. II only

C. I and III only

D. II and III only


108. In the figure below,

What is the measure of

A. 19.7°

B. 24.4°

C. 79.5°

D. 93.6°

113. In the figure below, determine the perimeter of

A. 39 units

B. 55 units

C. 66 units

D. 82 units

114. Which expression is equivalent to the expression

A.

B.

C.

D.


111. Which of these expressions is equivalent to

A.

B.

C.

D.

112. Use to answer the following questions.

What is Give answer in form.

Define in form such that is a real number.

Use words, numbers, and/or pictures to show your work.

113. Which expression is equivalent to

A.

B.

C.

D.

114. Consider the equation

Part A. Find the value of the discriminant. Show your work.

Part B. Based on the value of the discriminant found in part A, howmany real roots does have?

Part C. Use the quadratic formula to find the values of x when Show each step.

115. Use the quadratic equation to answer Parts A, B, and C.

Part A: Explain how the degree of the quadratic is connected to thenumber of complexvalued roots.

Part B: Find the discriminant and use this to determine whether theroots are realvalued or not.

Part C: Solve the equation.


116. Alex needs to buy 11 yards of fabric. A store sells fabric by the meter.Approximately how many meters of fabric does Alex need to buy?(Note: 1 inch ≈ 2.54 cm)

A. 10 m

B. 9 m

C. 8 m

D. 4 m

117. Jessica and Greg both ran in a race. Jessica’s average speed was 11.73feet per second. Greg’s average speed was 7.32 miles per hour. Whichstatement is true? (Note: 1 mile = 5,280 feet)

A. Jessica’s average speed was greater than Greg’s by about 1 foot persecond.

B. Jessica’s average speed was greater than Greg’s by about 3 feet persecond.

C. Greg’s average speed was greater than Jessica’s by about 1 foot persecond.

D. Greg’s average speed was greater than Jessica’s by about 3 feet persecond.

118. Brittany’s dog ran 432 inches in 3 seconds. What was the dog’s averagespeed in yards per minute?

A. 2,160 yards per minute

B. 720 yards per minute

C. 240 yards per minute

D. 86.4 yards per minute


119. The volume of a cylindrical water tank can be found using the expressionBh, where B represents the area of the base of the water tank, in squarefeet, and h represents the height of the water tank, in feet. Whichexpression could be used to convert the volume of the tank to cubicinches?

A. 20736Bh

B. 1728Bh

C. 144Bh

D. 12Bh

124. The dimensions of a rectangular piece of cardboard are 15.2167centimeters (cm) and 10.6879 cm. Which of these is the most accuratearea of the piece of cardboard?

A.

B.

C.

D.

125. The Smith family is installing wood floors in a rectangular room that is feet wide and feet in length.

The wood floor they selected is sold in bundles of 20 square feet. They will also purchase extra flooring

for emergency repairs. Based on the information provided, what is the appropriate unit of measure and quantityof wood flooring they should order?

A. 231 square feet

B. 242 square feet

C. 12 bundles

D. 13 bundles

126. If P and S are rational numbers and R and Q are irrational numbers,which of these statements is true?

A. The product of R and Q is always an irrational number.

B. The product of P and S is always a rational number.

C. The sum of R and Q is always an irrational number.

D. The sum of P and Q is always a rational number.


127. For a given rectangle, the perimeter is a rational number and the area isan irrational number. What must be true about the length and the widthof this rectangle?

A. The length is a rational number and the width is an irrationalnumber.

B. The length is an irrational number and the width is a rationalnumber.

C. Both the length and the width are irrational numbers.

D. Both the length and the width are rational numbers.

128. Which expression results in an irrational number when simplified?

A.

B.

C.

D.

122. If p and q are nonzero rational numbers, and s and t are irrationalnumbers, which statement is possibly true?

A. The product is irrational.

B. The product is rational.

C. The quotient is irrational.

D. The quotient is rational.


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

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

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

C. The host requires each of the show's employees to have four of theirneighbors participate in the survey.

D. The host acquires a list of all citizens who voted in the last electionand selects every 100th voter on the list to participate in the survey.

128. A basketball coach wants to know if extra freethrow practice time willimprove his players' accuracy in making free throws.

Design and describe an experiment the coach could conduct to assessthe impact of extra freethrow practice time on the players' accuracyin making free throws. Explain all the factors you considered indetermining the best design for the experiment and why you believethat your experiment satisfies those requirements.

Explain how an observational study differs from an experiment.

129. A scientist studied the growth of bacteria under two differenttemperature conditions. First, the scientist recorded the growth rate ofthe bacteria at room temperature. Then the scientist placed an identicalsample into a container that was heated to 20 degrees above roomtemperature and recorded the growth rate. Which of these statements iscorrect?

A. This situation represents an experiment because the scientist didnot change a study variable for either group.

B. This situation represents an experiment because the scientistchanged a study variable for one group but not the other.

C. This situation represents an observational study because thescientist did not change a study variable for either group.

D. This situation represents an observational study because thescientist changed a study variable for one group but not the other.


126. A survey was conducted where 150 high school students were asked theaverage amount of time they spent doing household chores in one week.The data collected resulted in a mean time of 180.5 minutes with astandard deviation of 5.5 minutes. Which of these represents a 95%confidence interval for the mean weekly hours spent doing householdchores of all high school students?

A. 171.5–189.5

B. 175–186

C. 178.25–182.75

D. 179.62–181.38

127. A survey of 640 people reports that 458 are willing to contribute to acharity. What is the margin of error for this survey in order toachieve a 95% confidence level in the estimate of the portion ofthe population willing to contribute to a charity?

A. 0.009

B. 0.018

C. 0.035

D. 0.041


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

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

A. James can conclude that polyurethane swimsuits help swimmersswim faster if the mean difference of the simulation is close to theexperimental mean difference.

B. James can conclude that polyurethane swimsuits help swimmersswim faster if the mean difference of the simulation is less than theexperimental mean difference.

C. James can conclude that polyurethane swimsuits help swimmersswim faster if the mean difference of the simulation is greater thanthe experimental mean difference.

D. James can conclude that polyurethane swimsuits do not helpswimmers swim faster if the mean difference is equal to theexperimental mean difference.


133. The local water company completed a study of a new water treatmentprocedure. The bellshaped curves represent the distributions forboth the new treatment (solid) and the control group (dotted). Themean values are indicated with vertical dashed lines and are equalamong the following cases. In which case does the new treatment showthe greatest effect?

A.

B.

C.

D.


129. An experiment was designed to study whether the consumption ofcaffeine has an impact on pulse rates. In the experiment the pulse rateof 20 volunteers was measured. Then a random sample of 10volunteers consumed a caffeinated beverage while the other10 consumed decaffeinated beverages. Their pulse rates were measuredagain after 15 minutes. The change in the pulse rate is shown.

Group with caffeine: 4, 3, –1, 5, 2, 3, 4, –1, 2, 5

Group without caffeine: 6, –1, 0, 2, 1, –2, –3, 4, 1, 2

The researcher then ran a simulation using a computer program to figureout what differences in means could be expected to occur simply due torandom chance. The simulation, based on 1000 trials, resulted in amean difference of 0.1 favoring the group with caffeine, with a varianceof 2.5. Based on the results of the experiment and simulation, is thereconvincing evidence that a caffeinated beverage has an impact on pulserates?

A. Yes, because the mean difference of the data is not within astandard deviation of the simulated mean difference.

B. No, because the mean difference of the data is not within a standarddeviation of the simulated mean difference.

C. Yes, because the mean difference of the data is within a standarddeviation of the simulated mean difference.

D. No, because the mean difference of the data is within a standarddeviation of the simulated mean difference.

130. One piece of information that is determined from census data is a“Center of Population.” If all residents of the United States had identicalweight and were placed on a flat, weightless, and rigid map of theUnited States, the center would be the place on the map where the mapwould balance perfectly. Based on the 2010 Census, the National MeanCenter of Population was near Plato, Missouri.

A report claims that the center has had a "southerly drift" over time.

Part A. Describe the type of data that would support this finding, andgive a specific example.

Part B. Describe the type of data that would neither support nordisprove this finding, and give a specific example.


131. Fred and Evelyn are measuring the number of color bands on a localspecies of caterpillar. Fred collects 30 caterpillars, finds that they havean average of 6.2 color bands, and releases them back into thepopulation. Simultaneously, Evelyn collects 40 caterpillars from thesame population, finds that they have an average of 10.2 color bands,and releases them back into the population.

Which evaluation of this situation is best supported?

A. Although uncommon, this variation could result from randomizedsampling.

B. The results are not comparable because Evelyn's sample is largerthan Fred's.

C. The variation in results requires a population standard deviation ofat least 2.0.

D. The variation in results indicates that at least one sample must bestrongly biased.

132. The ages of the employees of a company are normally distributed, withthe mean age being 32 years and a standard deviation of 2 years. Whichpercentage of the employees are likely to be more than 33 years old?

A. 15.9%

B. 19.1%

C. 30.9%

D. 69.1%


131. A book editor was proofreading a draft of a novel. She found that thenumber 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 deviationof 1. If 82 pages had between 7 and 9 errors, what was the approximatetotal number of pages in the book?

A. 56 pages

B. 68 pages

C. 120 pages

D. 202 pages


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