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North Thurston Public SchoolsALGEBRA 1EOC Exit Exam Review PacketName:Teacher:Period:
BIG IDEA of the Week #1:Finding Slope and π-InterceptFind the slope and π¦-intercept for each line, whether as an equation or as two points the line passes through:8i.(6, 20) and (13, 14)ii.π¦ π₯ 33iii.3π₯ 4π¦ 0iv.(15, 8) and (5, 19)v.π¦ 6π₯ 2vi.(0, 7) and ( 17, 8)vii.π¦ 3π₯ 1ix.(18, 1) and ( 4, 2)2viii.x.4π₯ π¦ 3π₯ π¦ 5
1. Ingrid is training for an upcoming race. To practice, each day she runs a total of 3 miles. As of today, she has run atotal of 12 miles. Let π¦ represent the total number of miles she has run and π₯ represent days (with π₯ 0representing today). If she continues to run the same amount each day, which graph best models her trainingroutine:βA.βB.βC.2. Select all coordinate pairswhich represent a solution tothe function graphed at )3. The state of New York had a population of approximately 300,000 people in the year 1800. The population ofNew York was predicted to increase by 1.58% per year. If the percent increase in population is correct, whatwould the population of New York be in the year 2015?
4. Let π(π₯) 0.25(8)π₯ , select all of the equations below which represent solutions of π(π₯):βA.π(0) 0βB.π(1) 2βC.π(2) 4βπ(3) 128D.5. Select all of the following expressions that are equivalent to 3(π₯ 2) (π₯ 3)π₯:βA.βB. 5π₯ 6 3π₯ (π₯ 3)π₯ 6βC.π₯ 2 6π₯ 6βπ₯ 2 6π₯ 2D.6. Ms. Stevens gave a 30 question quiz to her Algebra 1class. After grading the quizzes, her students receivedthe following scores:15, 16, 30, 28, 22, 24, 25, 25, 26, 17, 20, 22, 25, 25a) Create a box plot of the quiz scores:b) Would you describe the box plot as symmetric orskewed? Why?c) Based on your answers above, find the value for anappropriate measure of center and spread for thequiz scores:7. The explicit formula for an arithmetic sequence can be expressed by: ππ π1 (π 1)π. Select all of thefollowing equations which are equivalent to the explicit formula for an arithmetic sequence:ππ π1ππ π1βA.βB.π π 1 π 1πβC.βD.ππ π1 ππ ππ1 (π 1)π ππ8. Consider the functiongraphed to the right, overwhich intervals is thefunction increasing andnegative:βA.( , 1)βB.( 2, 4)βC.(1, 4)βD.(1, )
9. Create a system of two linear equations such that (2, 3) represents the solution to one of the equations, but notthe other, and such that (4, 2) represents the solution to the system:π₯ 410. Solve: 2 4π₯ 6:βA.βC.16710π₯ 3π₯ βB.βD.11. Austin works for a company that sells garden gnomes. The gnomes comein two different sizes: small (which weigh 4 pounds each) and large(which weigh 7 pounds each). Austin ships the garden gnomes tocustomers in a box that can hold no more than 60 pounds. Brian asksAustin to send him 3 large gnomes and as many small gnomes as he canfit in one box before it exceed the weight limit. How many small gnomeswill Austin ship to Brian?83π₯ 7π₯ βA.6 small gnomesβB.7 small gnomesβC.9 small gnomesβD.10 small gnomes12. For each equation below, state the property (Associative, Commutative, or Distributive) that allows us to state thatthe expression on the left of the equation is equivalent to the expression on the right:a) (πππ (π π)) πππ πππ ((π π) πππ)b) πππ ((π π) πππ) πππ π π πππc) πππ π π πππ π πππ π πππd) π πππ π πππ π(1 ππ) π(1 ππ)e) π(1 ππ) π(1 ππ) (π π)(1 ππ)f)(π π)(1 ππ) (π π)(ππ 1)g) (π π)(ππ 1) (π π)(ππ 1)h) (π π)(ππ 1) (ππ 1)(π π)i)(ππ 1)(π π) πππ π πππ πj)πππ π πππ π πππ π πππ πk) πππ π πππ π πππ π π πππl)πππ π π πππ (πππ (π π)) πππ
13. The function π(π₯) is shownin the graph at right. Thefunction π(π₯) is atransformation of theparent function π(π₯) π₯ 2 .Based on the graph, whichfunction represent π(π₯) interms of π(π₯):βA.π(π₯) π(π₯ 4) 2βB.π(π₯) π(π₯ 2) 4βC.π(π₯) π(π₯ 4) 2βD.π(π₯) π(π₯ 2) 414. The dimensions of a rectangle are such that the length is equal to 2 more than a number, and the width is equalto 3 less than twice a number. The area of the rectangle is equal to 12 square units. Select all of the followingequations which represent the area of the rectangle:(2π₯ 3)(π₯ 2) 12βA.βB.2π₯ 2 π₯ 18β2π₯ 2 π₯ 6 12C.βD.(π₯ 2)(2π₯ 3) 1215. For each of the following sequences, state whether the sequence is arithmetic or geometric, then write theexplicit form of the sequence:a) 6, 2, 2, 6, 10, b) 3, 6, 12, 24, 48, 1c) 512, 64, 8, 1, 8 , d) 17, 20, 23, 26, 29,
BIG IDEA of the Week #2:Solving EquationsSolve each of the equations below for π₯, be sure to check your solution:i.π₯ 8 8ii. 133 7π₯iii. 7 3π₯ 8 6iv. 135 5(3π₯ 3)v. 34 3(π₯ 8) 7(6π₯ 7)vi.6 4π₯ 4 2π₯vii.6π₯ 6 4π₯ 6 2π₯ix. 3(6 4π₯) (π₯ 2) 2viii.x. 5(1 5π₯) 6π₯ 24 128 4π₯ 2( 6 8π₯)
16. The quadratic functionπ(π₯) is graphed at right.Select all of the followingstatements about π(π₯)which are true:βA.The vertex at (0,0) is aminimumβB.The vertex at (0,0) is amaximumβC.The vertex at (4, 4)is a minimumβD.The vertex at (4, 4)is a maximum17. Assume π(π₯) π(π₯). If π(π₯) π₯ 2 4π₯ 4, select all of the following functions which could represent π(π₯):βA.π(π₯) (π₯ 2)(π₯ 2)βB.π(π₯) π₯ 2 8π₯βC.π(π₯) π₯(π₯ 4) 4βD.π(π₯) (π₯ 2)218. After several days of dry weather, it started to rain at a constant rate of 2 centimeters per hour at 5:00am. Itcontinued at this rate until 7:00am, when it started raining at a constant rate of 1.5 centimeters per hour, andcontinued raining at that rate for the next four hours. From 11:00am to 2:00pm, no rain fell. Starting at 2:00pmthe rain fell at a constant rate of 3 cm per hour. The rain fell at that rate for two hours, and then there was nomore rain for the remainder of the day:a) When had a total of 13 centimeters of rain accumulated for that day?b) On that day, how much total rain had accumulated by 9:00am?19. Janna decided to take a job babysitting on the weekends. She is paid 40 for each day that she babysits, plus anadditional 2 per hour. Let π¦ represent the total amount of money she earns per day babysitting, and π₯ representthe number of hours she spends babysitting on a given day. The graph below shows the total amount of moneyshe would earn based on the number of hours she spent babysitting:ββHow much money would Janna earn for babysitting 7.5 hours?A.β 15.00C. 55.00βB. 47.50D. 62.50
20. What is the value of the function π(π₯) 3 4π₯ when π₯ 2βA.π(2) 5ββC.π(2) 13βB.π(2) 8D.π(2) 1621. For each of the following quadratic equations, state the number of real solutions:a) π₯ 2 4 5π₯ 40b) π₯ 2 1 8π₯ 8c) π₯ 2 10π₯ 4 2π₯ 20d) π₯ 2 12 6π₯22. Select what would be the most appropriate method to measure center and variability for the following data:10, 90, 21, 91, 32, 92, 43, 93, 54, 94, 65, 95, 76, 96, 87, 97, 98, 99βA.Center: MeanβB.Center: MeanVariability: Interquartile RangeVariability: Standard DeviationβC.Center: MedianβD.Center: MedianVariability: Interquartile RangeVariability: Standard Deviation23. Select all of the systems of linear equations and/or inequalities that have more than one solution:π¦ 3π₯ 6π¦ 4π₯ 8βA.βB.6π₯ 2π¦ 12π¦ 4π₯ 2 6π₯ 3π¦ 6π¦ 0.5π₯ 3βC.βD.π¦ 2π₯ 1π¦ 0.5π₯ 224. Completely factor the following quadratic expressions:a) 2π₯ 2 7π₯ 4b) 6π₯ 2 13π₯ 6c) 2π₯ 2 8π₯ 8d) 6π₯ 2 12π₯ 625. Which of the following represents the solution set for the equation 2π₯ 2 30 98{ , 3, 2, 1, 0, 1, 2, 3, }βA.βB.βC.{8}βD.{ 8, 8}{64}
26. A scientist is studying a certain colony of fungus. After several months of study, she has determined that thepopulation of the fungi can be modeled by the following function, π(π) 4(3)π , where π represents time indays, and π(π) represents the total amount of fungi in the colony after π days. Which of the following statementsbest describes the population of the fungus colony:βA.Starting with 3 fungi, the population addsβB.Starting with 3 fungi, the population4% more fungi each dayquadruples each dayβC.Starting with 4 fungi, the population growsβD.Starting with 4 fungi, the populationby 3 more fungi each dayincreases by a factor of 3 each day27. Jon decide to conduct a survey of all the students in 8 randomly selected high school math classrooms. Jon wascurious to see if there were any differences between female and male students as to what their favorite type ofpet was (as such, each respondent could only choose one type of pet as their favorite). Each respondent wasasked to give their gender and select their favorite type of pet: βCat,β βDog,β βOther,β or βNone.β As Jon drovehome for the day, he realized that he left all of the surveys on top of his car and they were lost. Luckily, Jon hadwritten down some of the information about the survey participants: 270 total students took the survey, of which152 were female. Among females, 60 replied βCatsβ were there favorite, and 20 responded βOther.β Amongmales, 98 replied βDogsβ were there favorite, and 8 responded βNone.β Additionally, 28 total respondents statedβOtherβ was there favorite, and 18 selected βNone.βa) Complete the two-way frequency table below using Jonβs information:TotalTotalb) Garfield claims that cats must be everyoneβs favorite pet because βCatsβ were preferred three times as much asβOtherβ by female respondents. Do you agree or disagree with Garfield? Why?c) Odie claims that dogs are clearly everyoneβs favorite pet, but doesnβt give any reason why. State whether youagree or disagree with Odie and justify your answer by using data from the table.28. The following system ofinequalities is shown inthe graph at right:1π¦ π₯ 22π¦ 4π₯ 7Select all of thecoordinate points whichrepresent a solution tothis system:βA.(0, 2)βB.(1, 3)βC.(2, 1)βD.(4, 0)
29. Tobin and his friends are planning on renting a car for the weekend. The car rental company only charges an initialfee of 100 to rent the vehicle, plus 25 for each person who will be in the vehicle (the driver and all passengersare each expected to pay 25). Tobin and his friends plan on splitting the cost of the rental car equally betweenthem. Let π represent the cost per person, and let π represent the number of people in the vehicle. Whichequation best models this situation:100βA.βB.π 25π 100π 25π25βC.βD.π 125ππ 100π30. Solve each equation for π₯, be sure to check your answer:11a) 4 (8 4(π₯ 2)) 7 (7π₯ 14)b)π₯π₯ 2π₯ 1 π₯ 2c) 3(π₯ 2) π₯ 2 2π₯ 6
BIG IDEA of the Week #3:Solving InequalitiesSolve each inequality for π₯, then create an appropriate number line and graph the solution:i.16 π₯ 28ii.π₯ 1 12iii.v. 3π₯ 1 55iv.2 π₯15320vi.π₯ 12 7viii.42 10π₯ 8π₯ 20vii.π₯5 7 10ix.π₯2 0 or 7 π₯ 12x. 17 π₯ 5 14
31. The table at rightrepresents arelation of orderedpairs. What changesneed to be made tothe table so that itwould represent afunction:π₯π¦ 14 2901 2110βA.Arrange the π₯-coordinates indescending orderβB.Replace all negative π₯coordinates with positive valuesβC.Replace ( 2, 1) with (2, 1)βD.Replace (1, 0) with ( 1, 0)32. Select all of the graphs below which show a system of two equations with exactly 2 solutionsβA.βB.βC.βD.
33. The data in the table belowcompares waist circumference (ininches) to height (in inches) in adults:WaistCircumference (in)Height (in)40383836424448327064726266707860a) Use the data to make a scatterploton the graph at right (be sure to labelyour axes):b) Based on your scatterplot, would thebest fit function for this data belinear, exponential, or quadratic?Why?34. Select all of the following functions which represent a parabola that would open downward when graphed:βA.βB.π(π₯) 4(π₯ 2)π(π₯) 2(π₯ 6)2 1βC.π(π₯) ( 3π₯ 2)( 2π₯ 1)βD.π(π₯) 3π₯ 2 3π₯ 635. A virologist was studying a new species of virus. There were 20 virus in the petri dish at the beginning of thestudy, and after several days it became apparent that the population quadrupled each day. Let π‘ represent time indays, and π£(π‘) represent the total population on day π‘. Which of the following best represents the domain:βA.βB.π‘ is an integer multiple of 4π£(π‘) 20βC.π£(π‘) is a positive integer greater than orequal to 20βD.π‘ 036. Barry, Garry, and Larry are hanging out in the park playing soccer. Barry kicks the ball up in the air as hard as hecan, and it follows a path modeled by π(π‘) 0.25π₯(2π₯ 24), where π‘ represents time in seconds, and π(π‘)represents the height of Barryβs ball in feet after π‘ seconds. Not to be outdone, Garry grabs the ball and kicks it ashard as he can, and it follows a path modeled by π(π‘) 0.5(π₯ 6)2 18, where π‘ represents time in seconds,and π(π‘) represents the height of Garryβs ball in feet after π‘ seconds. As soon as the ball lands Garry yells, βMyball went so much higher than yours Barry!β Barry retorts, βWell, my ball stayed in the air way longer than yours!βLarry turns to them and says, βYouβre both wrong!βa) Who do you agree with, Barry, Garry, or Larry?b) Explain your thinking, and be sure to use the functions π(π‘) and π(π‘) as part of your explanation:
37. Select which property is illustrated by the equation: (π₯ 2 π¦)(π₯) (π₯ 3 π₯π¦)βA.Associative PropertyβB.βC.Distributive Property38. Select which of the following statements bestdescribes the function represent in the table at right:βA.Since the values of the π₯-coordinateincrease by 2, the function is linearβC.Since the values of the π₯-coordinateincrease by 2, when the value of π(π₯)triples, the function has a slope of 3 2βD.π₯π(π₯)βB.βD.Commutative PropertyTransitive Property024681392781Since both π₯ and π(π₯) are increasing, thisis a quadratic function, representing aparabola opening upwardSince the value of π(π₯) triples each timethe value of the π₯-coordinate increases by2, it is an exponential function39. Hugo has just won the January lottery! Before he can collect his winnings, he has to choose if he would rather getall of his money under Plan A, βThe Lump Sum Plan,β or Plan B, βThe Exponential Payment Plan.β If Hugo choosesPlan A, he will be given one check for 750,000,000 on Day 1 and receive no additional money. If Hugo choosesPlan B, he will be given a check for 1 on Day 1, a check for 2 on Day 2, a check for 4 on Day 3, a check for 8on Day 4, and so on, for all 31 days in January. Hugo knows he want to make as much money as possible, but hecanβt figure out which plan to choose, so he asks you for help. Hugo knows you are a bright mathematician, but heis also a skeptical individual and will need you to include some mathematics (equations, graphs, tables, etc.) inyour justification before he is convinced you are right.a) If Hugo wants to make as much money as possible, should he choose Plan A or Plan B?b) Justify your choice to Hugo mathematically:40. Which values of π₯ make the following equation true: 2π₯ 2 8π₯ 24βA.βB.π₯ 6, 2π₯ 4, 0π₯ 4, 2π₯ 2, 6βC.βD.41. Roseanne works for a salad dressing manufacturer. In order for the salad dressing to be ready to ship out tostores, each bottle must be filled to at least 85% of capacity but less than 98% capacity. Let π represent thepercentage of capacity of each salad dressing bottle. Choose the correct interval which represents a saladdressing bottle ready to ship:βA.π 85 or π 98βB.π 85 or π 98βC.85 π 98βD.85 π 98
42. Completely factor each expression:a) π₯ 2 π₯ 6b) 2π₯ 2 7π₯ 6c) π₯ 2 12π₯ 20d) π₯ 2 7π₯ 1243. Roger runs his own landscaping company. To determine how much to charge each client, Roger uses the functionπ(β) 100(. 5)β 200, where π(β) represents the total cost (in dollars) for β hours of work per day. Select allof the following values a client could expect to owe Roger for one day of work, if he uses the function π(β) toarrive at the cost for his services:βA.βB. 75 150βC. 175β44. In general, a person who is exposed to 100,000 millirems of radioactivitywill experience negative impacts to their health. Bananas (along withcarrots, red meat, lima beans and several other foods) are naturallyradioactive (the average person is exposed to about 30 millirems eachyear through the food we eat). An average banana exposes you to justunder 0.01 millirems. Let π represent the number of bananas anindividual consumes each year. Select all intervals which would keep anindividual below 100,000 millirems of exposure from bananas.45. State the domain and range of each of the following functions:a) π(π₯) 6π₯ 4b) π(π₯) 2(3)π₯c) β(π₯) π₯ 2 4d) π(π₯) π₯ 1 2 250D.βA.π 0βB.π 1,000,000,000βC.100 π 1,000,000βD.1,000 π 10,000
BIG IDEA of the Week #4:FactoringCompletely factor each expression:i. 48π5 42π 3ii.5π₯ 2 35π₯π¦iii.30π5 18π4 48π3 24π2iv.π₯ 4 7π₯ 3 18π₯ 2v.27π₯ 3 π¦ 3 15π₯π¦ 2 3π₯π¦vi.π₯ 2 3π₯π¦vii. 7π2 39π 20ix. 6π₯ 3 π§ 15π₯ 3 π§ 4 π¦ 18π₯ 4 π§ 2 π¦ 18π₯ 5 π§ 2viii.x.27π₯ 2 π¦ 4 9π₯ 5 π§45π2 45π 200
46. Let π(π₯) and π(π₯) both be linear functions: π(π₯) hasa slope of 3 and a π¦-intercept of (0, 9), and π(π₯) isrepresented in the table at right. Choose the correctinterval for which both functions have a positiveoutput:βA. π₯ βπ₯ 2 or π₯ 3C.π₯π(π₯) 3 10 2 8 1 60 4βB.π₯ 2βD.2 π₯ 347. Belle just purchased a new painting. The dimensions of her painting are21 inches long by 26 inches high. Belle wants to purchase a frame for hernew painting. In order to hang the painting where she wants it, the totalarea of the artwork (painting and frame) must be less than 750 squareinches. Let π‘ represent the thickness of the frame in inches. Choose thecorrect interval for π‘ which represents all possible thicknesses of theframe which meets Belleβs requirement for total area:βA.0 π‘ 2βB.0 π‘ 4βC.0 π‘ 4βD.0 π‘ 71 248. Rewrite each quadratic function in vertex form:a) π(π₯) π₯ 2 6π₯ 2b) π(π₯) π₯ 2 12π₯ 30c) β(π₯) π₯ 2 4π₯ 4d) π(π₯) π₯ 2 4π₯ 449. Determine all of the π₯- and π¦-intercepts for the function π(π₯) π₯ 2 2π₯ 8βA.(0, 8), (2, 0), and ( 4, 0)βB.( 4, 0), (2, 0), and (0, 8)βC.(0, 4), (0, 2), and (8, 0)βD.(0, 2), (0, 4), and (8, 0)50. A system of linearequations consists of twofunctions: π(π₯) is shownin the graph at right, andπ(π₯) 4π₯ 5βA.(0, 10)βB.(2.5, 5)βC.(5, 0)Choose the coordinatepair which represents thesolution to the system ofequations:βD.(7.5, 5)
51. Let π(π₯) π₯ 2 4π₯. Evaluate π(π₯) for the given input, simplify if possible:a) π(2) b) π( 3) c) π(π) d) π(π π) 52. Shirlee, Kay, Elma, and Fiona decided to buy a new television for their apartment, but not everyone contributedthe same amount of money to purchase the television. Each person paid an average of 187.50. If Shirlee paid 190, Kay paid 210, and Elma paid 150, how much did Fiona pay for the television:βA.βB. 170.00 187.50βC. 200.00βD. 550.0053. Claudio is the coach of the Lilβ Kickers Elementary School Soccer Team. Each game Claudio brings orange slices forhis players to enjoy during halftime. Claudio uses the function π (π) 5π 20 to determine how many orangeslices he needs to bring to each game. Let π (π) represent the total number of orange slices brought to the game,and π represent the number of players present at the game. What is the best interpretation of Claudioβs function:βA.Claudio brings 20 oranges, cut into 5βB.Claudio brings 5 slices per player, and 20equal slicesadditional slicesβC.Claudio brings 25 slices total, to be sharedβD.Claudio brings 20 slices per player, and 5equally among all the playersadditional slices54. Solve each inequality for π₯ and graph the solution on the number line:a) 1 3π₯ 2 22b) π₯ 3 1 or 4π₯ 24c) 5π₯ 30 15 and π₯ 2 1
55. A local coffee company, Netherlanders Sisters, is trying to determine how much it costs to run a coffee stand forone day. The daily cost to pay employees can be represented by 15π₯, the daily cost for ingredients/supplies canbe represented by 10π₯ 25, and the daily cost to rent the coffee stand is 200
agree or disagree with Odie and justify your answer by using data from the table. 28. The following system of inequalities is shown in the graph at right: R 1 2 2 4 7 Select all of the coordinate points which represent a solution to this system: β A. (0,2) β B. (1,3) β C. (2,1) β D. (4,0)
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