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New York Regents Algebra I (Common Core) June 2015 Exam

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ALGEBRA I (COMMON CORE) The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA I (Common Core) Wednesday, June 17, 2015 1:15 to 4:15 p.m., only Student Name:________________________________________________________ School Name: ______________________________________________________________ The possession or use of any communications device is strictly prohibited when taking this examination. If you have or use any communications device, no matter how briefly, your examination will be invalidated and no score will be calculated for you. Print your name and the name of your school on the lines above. A separate answer sheet for Part I has been provided to you. Follow the instructions from the proctor for completing the student information on your answer sheet. This examination has four parts, with a total of 37 questions. You must answer all questions in this examination. Record your answers to the Part I multiple-choice questions on the separate answer sheet. Write your answers to the questions in Parts II, III, and IV directly in this booklet. All work should be written in pen, except graphs and drawings, which should be done in pencil. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. The formulas that you may need to answer some questions in this examination are found at the end of the examination. This sheet is perforated so you may remove it from this booklet. Scrap paper is not permitted for any part of this examination, but you may use the blank spaces in this booklet as scrap paper. A perforated sheet of scrap graph paper is provided at the end of this booklet for any question for which graphing may be helpful but is not required. You may remove this sheet from this booklet. Any work done on this sheet of scrap graph paper will not be scored. When you have completed the examination, you must sign the statement printed at the end of the answer sheet, indicating that you had no unlawful knowledge of the questions or answers prior to the examination and that you have neither given nor received assistance in answering any of the questions during the examination. Your answer sheet cannot be accepted if you fail to sign this declaration. Notice A graphing calculator and a straightedge (ruler) must be available for you to use while taking this examination. DO NOT OPEN THIS EXAMINATION BOOKLET UNTIL THE SIGNAL IS GIVEN. ALGEBRA I (COMMON CORE) Part I Answer all 24 questions in this part. Each correct answer will receive 2 credits. No partial credit will be allowed. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. For each statement or question, choose the word or expression that, of those given, best completes the statement or answers the question. Record your answers on your separate answer sheet. [48] 1 The cost of airing a commercial on television is modeled by the function C(n) 110n 900, where n is the number of times the commercial is aired. Based on this model, which statement is true? (1) The commercial costs $0 to produce and $110 per airing up to $900. (2) The commercial costs $110 to produce and $900 each time it is aired. (3) The commercial costs $900 to produce and $110 each time it is aired. (4) The commercial costs $1010 to produce and can air an unlimited number of times. Speed (miles per hour) 2 The graph below represents a jogger s speed during her 20-minute jog around her neighborhood. 8 6 4 2 0 0 2 4 6 8 10 12 14 Time (in minutes) 16 18 20 Which statement best describes what the jogger was doing during the 9 12 minute interval of her jog? (1) She was standing still. (2) She was increasing her speed. (3) She was decreasing her speed. (4) She was jogging at a constant rate. Algebra I (Common Core) June 15 [2] Use this space for computations. x4 9y2, 3 If the area of a rectangle is expressed as then the product of the length and the width of the rectangle could be expressed as (1) (x 3y)(x 3y) (3) (x2 3y)(x2 3y) (2) (x2 3y)(x2 3y) Use this space for computations. (4) (x4 y)(x 9y) 4 Which table represents a function? x 2 4 2 4 x 3 5 7 9 f(x) 3 5 7 9 f(x) 2 4 2 4 (1) (3) x 0 1 0 1 x 0 1 1 0 f(x) 0 1 1 0 f(x) 0 1 0 1 (2) (4) 5 Which inequality is represented in the graph below? y 5 4 3 2 1 5 4 3 2 1 0 1 1 2 3 4 5 x 2 3 4 5 (1) y 3x 4 (3) y 4x 3 (2) y 3x 4 (4) y 4x 3 Algebra I (Common Core) June 15 [3] [OVER] 6 Mo s farm stand sold a total of 165 pounds of apples and peaches. She sold apples for $1.75 per pound and peaches for $2.50 per pound. If she made $337.50, how many pounds of peaches did she sell? (1) 11 (3) 65 (2) 18 (4) 100 5 4 3 2 1 Division Division 7 Morgan can start wrestling at age 5 in Division 1. He remains in that division until his next odd birthday when he is required to move up to the next division level. Which graph correctly represents this information? 5 7 9 11 Age 13 5 4 3 2 1 15 5 7 9 11 Age 5 4 3 2 1 5 7 9 11 Age 15 13 15 (3) Division Division (1) 13 13 15 5 4 3 2 1 5 7 9 11 Age (2) Algebra I (Common Core) June 15 (4) [4] Use this space for computations. Use this space for computations. 8 Which statement is not always true? (1) The sum of two rational numbers is rational. (2) The product of two irrational numbers is rational. (3) The sum of a rational number and an irrational number is irrational. (4) The product of a nonzero rational number and an irrational number is irrational. 9 The graph of the function f (x) x 4 is shown below. f(x) x The domain of the function is (1) { x | x 0} (3) { x | x 4} (2) { x | x 0} (4) { x | x 4} 10 What are the zeros of the function f(x) x2 13x 30? (1) 10 and 3 (3) 15 and 2 (2) 10 and 3 (4) 15 and 2 Algebra I (Common Core) June 15 [5] [OVER] 11 Joey enlarged a 3-inch by 5-inch photograph on a copy machine. He enlarged it four times. The table below shows the area of the photograph after each enlargement. Enlargement 0 1 2 3 4 Area (square inches) 15 18.8 23.4 29.3 36.6 What is the average rate of change of the area from the original photograph to the fourth enlargement, to the nearest tenth? (1) 4.3 (3) 5.4 (2) 4.5 (4) 6.0 12 Which equation(s) represent the graph below? I y (x 2)(x2 4 x 12) II y (x 3)(x2 x 2) III y (x 1)(x2 5 x 6) y 8 7 6 5 4 3 2 1 5 4 3 2 1 1 2 3 4 1 2 x 3 4 5 (1) I, only (3) I and II (2) II, only (4) II and III Algebra I (Common Core) June 15 [6] Use this space for computations. 13 A laboratory technician studied the population growth of a colony of bacteria. He recorded the number of bacteria every other day, as shown in the partial table below. t (time, in days) 0 2 4 f(t) (bacteria) 25 15,625 Use this space for computations. 9,765,625 Which function would accurately model the technician s data? (1) f(t) 25 t (2) f(t) 25 (3) f(t) 25t t 1 (4) f(t) 25(t 1) 14 Which quadratic function has the largest maximum? h(x) (3 x)(2 x) k(x) 5x2 12x 4 (1) (3) g(x) x f(x) 1 3 0 5 1 9 2 9 3 5 4 3 1 x 1 (2) (4) 15 If f(x) 3 x and g(x) 2x 5, at which value of x is f(x) g(x)? (1) 1 (3) 3 (2) 2 (4) 4 Algebra I (Common Core) June 15 [7] [OVER] 16 Beverly did a study this past spring using data she collected from a cafeteria. She recorded data weekly for ice cream sales and soda sales. Beverly found the line of best fit and the correlation coefficient, as shown in the diagram below. Cans of Soda Sold Beverly s Cafeteria Study r .96 Ice Cream Bars Sold Given this information, which statement(s) can correctly be concluded? I. Eating more ice cream causes a person to become thirsty. II. Drinking more soda causes a person to become hungry. III. There is a strong correlation between ice cream sales and soda sales. (1) I, only (3) I and III (2) III, only (4) II and III 17 The function V(t) 1350(1.017)t represents the value V(t), in dollars, of a comic book t years after its purchase. The yearly rate of appreciation of the comic book is (1) 17% (3) 1.017% (2) 1.7% (4) 0.017% Algebra I (Common Core) June 15 [8] Use this space for computations. 18 When directed to solve a quadratic equation by completing the ( 5 square, Sam arrived at the equation x __ 2 ) 2 Use this space for computations. __ . Which equation 13 4 could have been the original equation given to Sam? (1) x2 5x 7 0 (3) x2 5x 7 0 (2) x2 5x 3 0 (4) x2 5x 3 0 19 The distance a free falling object has traveled can be modeled by the 1 2 equation d __ at , where a is acceleration due to gravity and t is 2 the amount of time the object has fallen. What is t in terms of a and d? (d) (1) t da 2 (3) t da (2) t 2d a 2 (4) t 2d (a) 2 20 The table below shows the annual salaries for the 24 members of a professional sports team in terms of millions of dollars. 0.5 0.5 0.6 0.7 0.75 0.8 1.0 1.0 1.1 1.25 1.3 1.4 1.4 1.8 2.5 3.7 3.8 4 4.2 4.6 5.1 6 6.3 7.2 The team signs an additional player to a contract worth 10 million dollars per year. Which statement about the median and mean is true? (1) Both will increase. (2) Only the median will increase. (3) Only the mean will increase. (4) Neither will change. Algebra I (Common Core) June 15 [9] [OVER] 21 A student is asked to solve the equation 4(3x The student s solution to the problem starts as 1)2 17 83. 4(3x 1)2 100 (3x 1)2 25 A correct next step in the solution of the problem is (1) 3x 1 5 (3) 9x2 1 25 (2) 3x 1 25 (4) 9x2 6x 1 5 22 A pattern of blocks is shown below. Term 1 Term 2 Term 3 Term 4 If the pattern of blocks continues, which formula(s) could be used to determine the number of blocks in the nth term? I an n 4 II a1 2 an an 1 4 III an 4n 2 (1) I and II (3) II and III (2) I and III (4) III, only Algebra I (Common Core) June 15 [10] Use this space for computations. 23 What are the solutions to the equation x2 8x 24? (1) x 4 2 10 (3) x 4 2 2 (2) x 4 2 10 Use this space for computations. (4) x 4 2 2 24 Natasha is planning a school celebration and wants to have live music and food for everyone who attends. She has found a band that will charge her $750 and a caterer who will provide snacks and drinks for $2.25 per person. If her goal is to keep the average cost per person between $2.75 and $3.25, how many people, p, must attend? (1) 225 p 325 (3) 500 p 1000 (2) 325 p 750 (4) 750 p 1500 Algebra I (Common Core) June 15 [11] [OVER] Part II Answer all 8 questions in this part. Each correct answer will receive 2 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. [16] 25 Graph the function y |x 3| on the set of axes below. y x Explain how the graph of y |x 3| has changed from the related graph y |x|. Algebra I (Common Core) June 15 [12] 26 Alex is selling tickets to a school play. An adult ticket costs $6.50 and a student ticket costs $4.00. Alex sells x adult tickets and 12 student tickets. Write a function, f(x), to represent how much money Alex collected from selling tickets. Algebra I (Common Core) June 15 [13] [OVER] 27 John and Sarah are each saving money for a car. The total amount of money John will save is given by the function f(x) 60 5x. The total amount of money Sarah will save is given by the function g(x) x2 46. After how many weeks, x, will they have the same amount of money saved? Explain how you arrived at your answer. Algebra I (Common Core) June 15 [14] 1 2 28 If the difference (3x2 2x 5) (x2 3x 2) is multiplied by __ x , what is the result, 2 written in standard form? Algebra I (Common Core) June 15 [15] [OVER] 29 Dylan invested $600 in a savings account at a 1.6% annual interest rate. He made no deposits or withdrawals on the account for 2 years. The interest was compounded annually. Find, to the nearest cent, the balance in the account after 2 years. Algebra I (Common Core) June 15 [16] 30 Determine the smallest integer that makes 3x 7 5x 15 true. Algebra I (Common Core) June 15 [17] [OVER] 31 The residual plots from two different sets of bivariate data are graphed below. 0.6 0.4 0.2 0 0.2 2 4 6 0.4 0.6 8 10 12 5 4 3 2 1 0 1 2 3 Graph A 2 4 6 8 10 12 Graph B Explain, using evidence from graph A and graph B, which graph indicates that the model for the data is a good fit. Algebra I (Common Core) June 15 [18] 32 A landscaper is creating a rectangular flower bed such that the width is half of the length. The area of the flower bed is 34 square feet. Write and solve an equation to determine the width of the flower bed, to the nearest tenth of a foot. Algebra I (Common Core) June 15 [19] [OVER] Part III Answer all 4 questions in this part. Each correct answer will receive 4 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. [16] 33 Albert says that the two systems of equations shown below have the same solutions. First System Second System 8x 9y 48 8x 9y 48 12x 5y 21 8.5y 51 Determine and state whether you agree with Albert. Justify your answer. Algebra I (Common Core) June 15 [20] 34 The equation to determine the weekly earnings of an employee at The Hamburger Shack is given by w(x), where x is the number of hours worked. w(x) 10x, 0 x 40 { 15( x 40) 400, x 40 Determine the difference in salary, in dollars, for an employee who works 52 hours versus one who works 38 hours. Determine the number of hours an employee must work in order to earn $445. Explain how you arrived at this answer. Algebra I (Common Core) June 15 [21] [OVER] 35 An on-line electronics store must sell at least $2500 worth of printers and computers per day. Each printer costs $50 and each computer costs $500. The store can ship a maximum of 15 items per day. Number of Computers On the set of axes below, graph a system of inequalities that models these constraints. Number of Printers Determine a combination of printers and computers that would allow the electronics store to meet all of the constraints. Explain how you obtained your answer. Algebra I (Common Core) June 15 [22] 36 An application developer released a new app to be downloaded. The table below gives the number of downloads for the first four weeks after the launch of the app. Number of Weeks Number of Downloads 1 2 3 4 120 180 270 405 Write an exponential equation that models these data. Use this model to predict how many downloads the developer would expect in the 26th week if this trend continues. Round your answer to the nearest download. Would it be reasonable to use this model to predict the number of downloads past one year? Explain your reasoning. Algebra I (Common Core) June 15 [23] [OVER] Part IV Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. A correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be written in pencil. [6] 37 A football player attempts to kick a football over a goal post. The path of the football can be 1 2 2 ___ modeled by the function h(x) 225 x __ x, where x is the horizontal distance from the kick, 3 and h(x) is the height of the football above the ground, when both are measured in feet. On the set of axes below, graph the function y h(x) over the interval 0 x 150. y x Determine the vertex of y h(x). Interpret the meaning of this vertex in the context of the problem. The goal post is 10 feet high and 45 yards away from the kick. Will the ball be high enough to pass over the goal post? Justify your answer. Algebra I (Common Core) June 15 [24] FOR TEACHERS ONLY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA I (Common Core) Wednesday, June 17, 2015 1:15 to 4:15 p.m., only SCORING KEY AND RATING GUIDE Mechanics of Rating The following procedures are to be followed for scoring student answer papers for the Regents Examination in Algebra I (Common Core). More detailed information about scoring is provided in the publication Information Booklet for Scoring The Regents Examination in Algebra I (Common Core). Do not attempt to correct the student s work by making insertions or changes of any kind. In scoring the constructed-response questions, use check marks to indicate student errors. Unless otherwise specified, mathematically correct variations in the answers will be allowed. Units need not be given when the wording of the questions allows such omissions. Each student s answer paper is to be scored by a minimum of three mathematics teachers. No one teacher is to score more than approximately one-third of the constructedresponse questions on a student s paper. Teachers may not score their own students answer papers. On the student s separate answer sheet, for each question, record the number of credits earned and the teacher s assigned rater/scorer letter. Schools are not permitted to rescore any of the open-ended questions on this exam after each question has been rated once, regardless of the final exam score. Schools are required to ensure that the raw scores have been added correctly and that the resulting scale score has been determined accurately. Raters should record the student s scores for all questions and the total raw score on the student s separate answer sheet. Then the student s total raw score should be converted to a scale score by using the conversion chart that will be posted on the Department s web site at: http://www.p12.nysed.gov/assessment/ by Wednesday, June 17, 2015. Because scale scores corresponding to raw scores in the conversion chart may change from one administration to another, it is crucial that, for each administration, the conversion chart provided for that administration be used to determine the student s final score. The student s scale score should be entered in the box provided on the student s separate answer sheet. The scale score is the student s final examination score. If the student s responses for the multiple-choice questions are being hand scored prior to being scanned, the scorer must be careful not to make any marks on the answer sheet except to record the scores in the designated score boxes. Marks elsewhere on the answer sheet will interfere with the accuracy of the scanning. Part I Allow a total of 48 credits, 2 credits for each of the following. (1) . . . . . 3 . . . . . (9) . . . . . 4 . . . . . (17) . . . . . 2 . . . . . (2) . . . . . 4 . . . . . (10) . . . . . 4 . . . . . (18) . . . . . 4 . . . . . (3) . . . . . 2 . . . . . (11) . . . . . 3 . . . . . (19) . . . . . 2 . . . . . (4) . . . . . 3 . . . . . (12) . . . . . 2 . . . . . (20) . . . . . 3 . . . . . (5) . . . . . 1 . . . . . (13) . . . . . 2 . . . . . (21) . . . . . 1 . . . . . (6) . . . . . 3 . . . . . (14) . . . . . 3 . . . . . (22) . . . . . 3 . . . . . (7) . . . . . 1 . . . . . (15) . . . . . 1 . . . . . (23) . . . . . 1 . . . . . (8) . . . . . 2 . . . . . (16) . . . . . 2 . . . . . (24) . . . . . 4 . . . . . Updated information regarding the rating of this examination may be posted on the New York State Education Department s web site during the rating period. Check this web site at: http://www.p12.nysed.gov/assessment/ and select the link Scoring Information for any recently posted information regarding this examination. This site should be checked before the rating process for this examination begins and several times throughout the Regents Examination period. The Department is providing supplemental scoring guidance, the Model Response Set, for the Regents Examination in Algebra I (Common Core). This guidance is recommended to be part of the scorer training. Schools are encouraged to incorporate the Model Response Sets into the scorer training or to use them as additional information during scoring. While not reflective of all scenarios, the model responses selected for the Model Response Set illustrate how less common student responses to constructed-response questions may be scored. The Model Response Set will be available on the Department s web site at http://www.nysedregents.org/algebraone/. Algebra I (Common Core) Rating Guide June 15 [2] Question 25 25 Graph the function y |x 3| on the set of axes below. Explain how the graph of y |x 3| has changed from the related graph y |x|. Score 2: The student has a complete and correct response. Algebra I (Common Core) June 15 [2] Question 26 26 Alex is selling tickets to a school play. An adult ticket costs $6.50 and a student ticket costs $4.00. Alex sells x adult tickets and 12 student tickets. Write a function, f(x), to represent how much money Alex collected from selling tickets. Score 2: The student has a complete and correct response. Algebra I (Common Core) June 15 [7] Question 27 27 John and Sarah are each saving money for a car. The total amount of money John will save is given by the function f(x) 60 5x. The total amount of money Sarah will save is given by the function g(x) x2 46. After how many weeks, x, will they have the same amount of money saved? Explain how you arrived at your answer. Score 2: The student has a complete and correct response. Algebra I (Common Core) June 15 [12] Question 28 1 2 x , what is the result, 28 If the difference (3x2 2x 5) (x2 3x 2) is multiplied by __ 2 written in standard form? Score 2: The student has a complete and correct response. Algebra I (Common Core) June 15 [17] Question 29 29 Dylan invested $600 in a savings account at a 1.6% annual interest rate. He made no deposits or withdrawals on the account for 2 years. The interest was compounded annually. Find, to the nearest cent, the balance in the account after 2 years. Score 2: The student has a complete and correct response. Algebra I (Common Core) June 15 [23] Question 30 30 Determine the smallest integer that makes 3x 7 5x 15 true. Score 2: The student has a complete and correct response. Algebra I (Common Core) June 15 [29] Question 31 31 The residual plots from two different sets of bivariate data are graphed below. 0.6 0.4 0.2 0 2 4 6 0.2 0.4 0.6 8 10 12 5 4 3 2 1 0 1 2 3 2 Graph A 4 6 8 10 12 Graph B Explain, using evidence from graph A and graph B, which graph indicates that the model for the data is a good fit. Score 2: The student has a complete and correct response. Algebra I (Common Core) June 15 [32] Question 32 32 A landscaper is creating a rectangular flower bed such that the width is half of the length. The area of the flower bed is 34 square feet. Write and solve an equation to determine the width of the flower bed, to the nearest tenth of a foot. Score 2: The student has a complete and correct response. Algebra I (Common Core) June 15 [37] Question 33 33 Albert says that the two systems of equations shown below have the same solutions. First System Second System 8x 9y 48 8x 9y 48 12x 5y 21 8.5y 51 Determine and state whether you agree with Albert. Justify your answer. Score 4: The student has a complete and correct response. Algebra I (Common Core) June 15 [43] Question 34 34 The equation to determine the weekly earnings of an employee at The Hamburger Shack is given by w(x), where x is the number of hours worked. w(x) x, 0 x 40 { 10 15(x 40) 400, x 40 Determine the difference in salary, in dollars, for an employee who works 52 hours versus one who works 38 hours. Determine the number of hours an employee must work in order to earn $445. Explain how you arrived at this answer. Score 4: The student has a complete and correct response. Algebra I (Common Core) June 15 [52] Question 35 35 An on-line electronics store must sell at least $2500 worth of printers and computers per day. Each printer costs $50 and each computer costs $500. The store can ship a maximum of 15 items per day. On the set of axes below, graph a system of inequalities that models these constraints. Determine a combination of printers and computers that would allow the electronics store to meet all of the constraints. Explain how you obtained your answer. Score 4: The student has a complete and correct response. Algebra I (Common Core) June 15 [58] Question 36 36 An application developer released a new app to be downloaded. The table below gives the number of downloads for the first four weeks after the launch of the app. Number of Weeks Number of Downloads 1 2 3 4 120 180 270 405 Write an exponential equation that models these data. Use this model to predict how many downloads the developer would expect in the 26th week if this trend continues. Round your answer to the nearest download. Would it be reasonable to use this model to predict the number of downloads past one year? Explain your reasoning. Score 4: The student has a complete and correct response. Algebra I (Common Core) June 15 [65] Question 37 37 A football player attempts to kick a football over a goal post. The path of the football can be 1 2 2 ___ x __ x, where x is the horizontal distance from the kick, modeled by the function h(x) 225 3 and h(x) is the height of the football above the ground, when both are measured in feet. On the set of axes below, graph the function y h(x) over the interval 0 x 150. Determine the vertex of y h(x). Interpret the meaning of this vertex in the context of the problem. The goal post is 10 feet high and 45 yards away from the kick. Will the ball be high enough to pass over the goal post? Justify your answer. Score 6: The student has a complete and correct response. Algebra I (Common Core) June 15 [74]

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