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New York Regents Algebra I (Common Core) January 2016 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) Thursday, January 28, 2016 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 In the function f(x) (x when x is 2)2 4, the minimum value occurs (1) 2 (3) 4 (2) 2 (4) 4 2 The graph below was created by an employee at a gas station. Gas Sales 50 Cost of Gas (in dollars) 45 40 35 30 25 20 15 10 5 0 2 4 6 8 10 12 14 16 18 20 Number of Gallons Which statement can be justified by using the graph? (1) If 10 gallons of gas was purchased, $35 was paid. (2) For every gallon of gas purchased, $3.75 was paid. (3) For every 2 gallons of gas purchased, $5.00 was paid. (4) If zero gallons of gas were purchased, zero miles were driven. Algebra I (Common Core) Jan. 16 [2] Use this space for computations. 119.67(0.61)x 3 For a recently released movie, the function y models the revenue earned, y, in millions of dollars each week, x, for several weeks after its release. Use this space for computations. Based on the equation, how much more money, in millions of dollars, was earned in revenue for week 3 than for week 5? (1) 37.27 (3) 17.06 (2) 27.16 (4) 10.11 4 Given the following expressions: I. 5 8 3 5 II. 1 2 2 III. IV. ( 5) ( 5) 3 ( 49) Which expression(s) result in an irrational number? (1) II, only (3) I, III, IV (2) III, only (4) II, III, IV 5 Which inequality is represented by the graph below? y x (1) y 2x 3 (3) y 3x 2 (2) y 2x 3 (4) y 3x 2 Algebra I (Common Core) Jan. 16 [3] [OVER] 6 Michael borrows money from his uncle, who is charging him simple interest using the formula I Prt. To figure out what the interest rate, r, is, Michael rearranges the formula to find r. His new formula is r equals (1) I P (3) I (2) P I (4) Pt t t Pt I 7 Which equation is equivalent to y 34 x(x 12)? (1) y (x 17)(x 2) (3) y (x 6)2 2 (2) y (x 17)(x 2) (4) y (x 6)2 2 8 The equation A 1300(1.02)7 is being used to calculate the amount of money in a savings account. What does 1.02 represent in this equation? (1) 0.02% decay (3) 2% decay (2) 0.02% growth (4) 2% growth 9 The zeros of the function f(x) 2x2 4x 6 are (1) 3 and 1 (3) 3 and 1 (2) 3 and 1 (4) 3 and 1 10 When (2x 3)2 is subtracted from 5x2, the result is (1) x2 12x 9 (3) x2 12x 9 (2) x2 12x 9 (4) x2 12x 9 Algebra I (Common Core) Jan. 16 [4] Use this space for computations. 11 Joe has a rectangular patio that measures 10 feet by 12 feet. He wants to increase the area by 50% and plans to increase each dimension by equal lengths, x. Which equation could be used to determine x? (1) (10 x)(12 x) 120 (3) (15 x)(18 x) 180 (2) (10 x)(12 x) 180 Use this space for computations. (4) (15)(18) 120 x2 12 When factored completely, x3 13x2 30x is (1) x(x 3)(x 10) (3) x(x 2)(x 15) (2) x(x 3)(x 10) (4) x(x 2)(x 15) 13 The table below shows the cost of mailing a postcard in different years. During which time interval did the cost increase at the greatest average rate? Year 1898 1971 1985 2006 2012 Cost ( ) 1 6 14 24 35 (1) 1898 1971 (3) 1985 2006 (2) 1971 1985 (4) 2006 2012 14 When solving the equation x2 8x 7 0 by completing the square, which equation is a step in the process? (1) (x 4)2 9 (3) (x 8)2 9 (2) (x 4)2 23 (4) (x 8)2 23 15 A construction company uses the function f(p), where p is the number of people working on a project, to model the amount of money it spends to complete a project. A reasonable domain for this function would be (1) positive integers (2) positive real numbers (3) both positive and negative integers (4) both positive and negative real numbers Algebra I (Common Core) Jan. 16 [5] [OVER] Use this space for computations. 16 Which function is shown in the table below? x 2 1 0 1 2 3 f(x) 1 9 1 3 1 3 9 27 (1) f(x) 3x (3) f(x) x3 (2) f(x) x 3 (4) f(x) 3x 1 17 Given the functions h(x) x 3 and j(x) |x|, which value of x 2 makes h(x) j(x)? (1) 2 (3) 3 (2) 2 (4) 6 18 Which recursively defined function represents the sequence 3, 7, 15, 31, ? (1) f(1) 3, f(n 1) 2 f(n) 3 (2) f(1) 3, f(n 1) 2 f(n) 1 (3) f(1) 3, f(n 1) 2f(n) 1 (4) f(1) 3, f(n 1) 3f(n) 2 19 The range of the function defined as y 5x is (1) y 0 (3) y 0 (2) y 0 (4) y 0 Algebra I (Common Core) Jan. 16 [6] Use this space for computations. 20 The graph of y f(x) is shown below. y x What is the graph of y f(x 1) 2? y y x x (1) (3) y y x x (2) Algebra I (Common Core) Jan. 16 (4) [7] [OVER] 21 Which pair of equations could not be used to solve the following equations for x and y? 4x 2y 22 2x 2y 8 (1) 4x 2y 22 2x 2y 8 (3) 12x 6y 66 6x 6y 24 (2) 4x 2y 22 4x 4y 16 (4) 8x 4y 44 8x 8y 8 22 The graph representing a function is shown below. y x Which function has a minimum that is less than the one shown in the graph? (1) y x2 6x 7 (3) y x2 2x 10 (2) y |x 3| 6 (4) y |x 8| 2 Algebra I (Common Core) Jan. 16 [8] Use this space for computations. Use this space for computations. 23 Grisham is considering the three situations below. I. For the first 28 days, a sunflower grows at a rate of 3.5 cm per day. II. The value of a car depreciates at a rate of 15% per year after it is purchased. III. The amount of bacteria in a culture triples every two days during an experiment. Which of the statements describes a situation with an equal difference over an equal interval? (1) I, only (3) I and III (2) II, only (4) II and III 24 After performing analyses on a set of data, Jackie examined the scatter plot of the residual values for each analysis. Which scatter plot indicates the best linear fit for the data? y y x x (1) (3) y y x (2) Algebra I (Common Core) Jan. 16 x (4) [9] [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 The function, t(x), is shown in the table below. x t(x) 3 10 1 7.5 1 5 3 2.5 5 0 Determine whether t(x) is linear or exponential. Explain your answer. Algebra I (Common Core) Jan. 16 [10] 26 Marcel claims that the graph below represents a function. y 4 3 2 1 4 3 2 1 1 1 2 3 4 x 2 3 4 State whether Marcel is correct. Justify your answer. Algebra I (Common Core) Jan. 16 [11] [OVER] 27 Solve the equation for y. (y 3)2 4y 12 Algebra I (Common Core) Jan. 16 [12] 28 The graph below shows the variation in the average temperature of Earth s surface from 1950 2000, according to one source. Variation of Earth s Surface Temperature Over 50 Years Average Variation in Temperature ( C) 0.4 0.3 0.2 0.1 0 0.1 0.2 0.3 0.4 2000 1995 1990 1985 1980 1975 1970 1965 1960 1955 1950 Year During which years did the temperature variation change the most per unit time? Explain how you determined your answer. Algebra I (Common Core) Jan. 16 [13] [OVER] 29 The cost of belonging to a gym can be modeled by C(m) 50m 79.50, where C(m) is the total cost for m months of membership. State the meaning of the slope and y-intercept of this function with respect to the costs associated with the gym membership. Algebra I (Common Core) Jan. 16 [14] 30 A statistics class surveyed some students during one lunch period to obtain opinions about television programming preferences. The results of the survey are summarized in the table below. Programming Preferences Comedy Drama Male 70 35 Female 48 42 Based on the sample, predict how many of the school s 351 males would prefer comedy. Justify your answer. Algebra I (Common Core) Jan. 16 [15] [OVER] 31 Given that a b, solve for x in terms of a and b: b(x 3) ax 7b Algebra I (Common Core) Jan. 16 [16] 32 Jacob and Jessica are studying the spread of dandelions. Jacob discovers that the growth over t weeks can be defined by the function f(t) (8) 2 t. Jessica finds that the growth function over t weeks is g(t) 2 t 3. Calculate the number of dandelions that Jacob and Jessica will each have after 5 weeks. Based on the growth from both functions, explain the relationship between f(t) and g(t). Algebra I (Common Core) Jan. 16 [17] [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 Let h(t) 16t2 64t 80 represent the height of an object above the ground after t seconds. Determine the number of seconds it takes to achieve its maximum height. Justify your answer. State the time interval, in seconds, during which the height of the object decreases. Explain your reasoning. Algebra I (Common Core) Jan. 16 [18] 34 Fred s teacher gave the class the quadratic function f(x) 4x2 16x 9. a) State two different methods Fred could use to solve the equation f(x) 0. b) Using one of the methods stated in part a, solve f(x) 0 for x, to the nearest tenth. Algebra I (Common Core) Jan. 16 [19] [OVER] 35 Erica, the manager at Stellarbeans, collected data on the daily high temperature and revenue from coffee sales. Data from nine days this past fall are shown in the table below. Day 1 High Temperature, t Coffee Sales, f(t) Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Day 9 54 50 62 67 70 58 52 46 48 $2900 $3080 $2500 $2380 $2200 $2700 $3000 $3620 $3720 State the linear regression function, f(t), that estimates the day s coffee sales with a high temperature of t. Round all values to the nearest integer. State the correlation coefficient, r, of the data to the nearest hundredth. Does r indicate a strong linear relationship between the variables? Explain your reasoning. Algebra I (Common Core) Jan. 16 [20] 36 A contractor has 48 meters of fencing that he is going to use as the perimeter of a rectangular garden. The length of one side of the garden is represented by x, and the area of the garden is 108 square meters. Determine, algebraically, the dimensions of the garden in meters. Algebra I (Common Core) Jan. 16 [21] [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 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 done in pencil. [6] 37 The Reel Good Cinema is conducting a mathematical study. In its theater, there are 200 seats. Adult tickets cost $12.50 and child tickets cost $6.25. The cinema s goal is to sell at least $1500 worth of tickets for the theater. Write a system of linear inequalities that can be used to find the possible combinations of adult tickets, x, and child tickets, y, that would satisfy the cinema s goal. Graph the solution to this system of inequalities on the set of axes on the next page. Label the solution with an S. Marta claims that selling 30 adult tickets and 80 child tickets will result in meeting the cinema s goal. Explain whether she is correct or incorrect, based on the graph drawn. Algebra I (Common Core) Jan. 16 [22] y 250 240 230 220 210 200 190 180 170 160 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 x 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 Algebra I (Common Core) Jan. 16 [23] FOR TEACHERS ONLY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA I (Common Core) Thursday, January 28, 2016 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 Thursday, January 28, 2016. 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) . . . . . 2 . . . . . (9) . . . . . 1 . . . . . (17) . . . . . 1 . . . . . (2) . . . . . 2 . . . . . (10) . . . . . 3 . . . . . (18) . . . . . 3 . . . . . (3) . . . . . 3 . . . . . (11) . . . . . 2 . . . . . (19) . . . . . 2 . . . . . (4) . . . . . 1 . . . . . (12) . . . . . 3 . . . . . (20) . . . . . 1 . . . . . (5) . . . . . 2 . . . . . (13) . . . . . 4 . . . . . (21) . . . . . 4 . . . . . (6) . . . . . 3 . . . . . (14) . . . . . 2 . . . . . (22) . . . . . 3 . . . . . (7) . . . . . 4 . . . . . (15) . . . . . 1 . . . . . (23) . . . . . 1 . . . . . (8) . . . . . 4 . . . . . (16) . . . . . 4 . . . . . (24) . . . . . 3 . . . . . 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 Jan. 16 [2] Question 25 25 The function, t(x), is shown in the table below. x t(x) 3 10 1 7.5 1 5 3 2.5 5 0 Determine whether t(x) is linear or exponential. Explain your answer. Score 2: The student has a complete and correct response. Algebra I (Common Core) Jan. 16 [2] Question 26 26 Marcel claims that the graph below represents a function. y 4 3 2 1 1 4 3 2 1 1 2 3 4 2 3 4 State whether Marcel is correct. Justify your answer. Score 2: The student has a complete and correct response. Algebra I (Common Core) Jan. 16 [7] x Question 27 27 Solve the equation for y. (y 3)2 4y 12 Score 2: The student has a complete and correct response. Algebra I (Common Core) Jan. 16 [12] Question 28 28 The graph below shows the variation in the average temperature of Earth s surface from 1950 2000, according to one source. Variation of Earth s Surface Variation of Earth s Surface Temperature Over 50 Years Temperature Over 50 Years Average Variation in Temperature e ( C) ( C) 0.4 0.4 0.3 0.3 0.2 0.1 0 0.1 0.2 0.3 0.4 2000 1995 1990 1985 1980 1975 1970 1965 1960 1955 1950 Year During which years did the temperature variation change the most per unit time? Explain how you determined your answer. Score 2: The student has a complete and correct response. Algebra I (Common Core) Jan. 16 [19] Question 29 29 The cost of belonging to a gym can be modeled by C(m) 50m 79.50, where C(m) is the total cost for m months of membership. State the meaning of the slope and y-intercept of this function with respect to the costs associated with the gym membership. Score 2: The student has a complete and correct response. Algebra I (Common Core) Jan. 16 [24] Question 30 30 A statistics class surveyed some students during one lunch period to obtain opinions about television programming preferences. The results of the survey are summarized in the table below. Programming Preferences Comedy Drama Male 70 35 Female 48 42 Based on the sample, predict how many of the school s 351 males would prefer comedy. Justify your answer. Score 2: The student has a complete and correct response. Algebra I (Common Core) Jan. 16 [28] Question 31 31 Given that a b, solve for x in terms of a and b: b(x 3) ax 7b Score 2: The student has a complete and correct response. Algebra I (Common Core) Jan. 16 [32] Question 32 32 Jacob and Jessica are studying the spread of dandelions. Jacob discovers that the growth over t weeks can be defined by the function f(t) (8) 2 t. Jessica finds that the growth function over t weeks is g(t) 2 t 3. Calculate the number of dandelions that Jacob and Jessica will each have after 5 weeks. Based on the growth from both functions, explain the relationship between f(t) and g(t). Score 2: The student has a complete and correct response. Algebra I (Common Core) Jan. 16 [37] Question 33 33 Let h(t) 16t2 64t 80 represent the height of an object above the ground after t seconds. Determine the number of seconds it takes to achieve its maximum height. Justify your answer. State the time interval, in seconds, during which the height of the object decreases. Explain your reasoning. Score 4: The student has a complete and correct response. Algebra I (Common Core) Jan. 16 [42] Question 34 34 Fred s teacher gave the class the quadratic function f(x) 4x2 16x 9. a) State two different methods Fred could use to solve the equation f(x) 0. b) Using one of the methods stated in part a, solve f(x) 0 for x, to the nearest tenth. Score 4: The student has a complete and correct response. Algebra I (Common Core) Jan. 16 [53] Question 35 35 Erica, the manager at Stellarbeans, collected data on the daily high temperature and revenue from coffee sales. Data from nine days this past fall are shown in the table below. Day 1 High Temperature, t Coffee Sales, f(t) Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Day 9 54 50 62 67 70 58 52 46 48 $2900 $3080 $2500 $2380 $2200 $2700 $3000 $3620 $3720 State the linear regression function, f(t), that estimates the day s coffee sales with a high temperature of t. Round all values to the nearest integer. State the correlation coefficient, r, of the data to the nearest hundredth. Does r indicate a strong linear relationship between the variables? Explain your reasoning. Score 4: The student has a complete and correct response. Algebra I (Common Core) Jan. 16 [65] Question 36 36 A contractor has 48 meters of fencing that he is going to use as the perimeter of a rectangular garden. The length of one side of the garden is represented by x, and the area of the garden is 108 square meters. Determine, algebraically, the dimensions of the garden in meters. Score 4: The student has a complete and correct response. Algebra I (Common Core) Jan. 16 [73] Question 37 37 The Reel Good Cinema is conducting a mathematical study. In its theater, there are 200 seats. Adult tickets cost $12.50 and child tickets cost $6.25. The cinema s goal is to sell at least $1500 worth of tickets for the theater. Write a system of linear inequalities that can be used to find the possible combinations of adult tickets, x, and child tickets, y, that would satisfy the cinema s goal. Graph the solution to this system of inequalities on the set of axes on the next page. Label the solution with an S. Marta claims that selling 30 adult tickets and 80 child tickets will result in meeting the cinema s goal. Explain whether she is correct or incorrect, based on the graph drawn. Score 6: The student has a complete and correct response. Algebra I (Common Core) Jan. 16 [83] Question 37 Algebra I (Common Core) Jan. 16 [84]

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