ALGEBRA I COMMON CORE The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION algebra I Common Core Wednesday August 17 2016 8 30 to 11 30 a 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 for 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 graph below shows the distance in miles m hiked from a camp in h hours 6 Miles m 5 4 3 2 1 0 1 2 4 3 Hours h 5 6 Which hourly interval had the greatest rate of change 1 hour 0 to hour 1 3 hour 2 to hour 3 2 hour 1 to hour 2 4 hour 3 to hour 4 2 The solution of an equation with two variables x and y is 1 the set of all x values that make y 5 0 2 the set of all y values that make x 5 0 3 the set of all ordered pairs x y that make the equation true 4 the set of all ordered pairs x y where the graph of the equation crosses the y axis 3 Which statistic can not be determined from a box plot representing the scores on a math test in Mrs DeRidder s algebra class 1 the lowest score 2 the median score 3 the highest score 4 the score that occurs most frequently Algebra I Common Core Aug 16 2 Use this space for computations

4 Which chart could represent the function f x 5 22x 1 6 x f x x f x 0 6 0 8 2 10 2 10 4 14 4 12 6 18 6 14 1 Use this space for computations 3 x f x x f x 0 4 0 6 2 6 2 2 4 8 4 2 6 10 6 6 2 4 5 If f n 5 n 2 1 2 1 3n which statement is true 1 f 3 5 22 3 f 22 5 215 2 f 22 5 3 4 f 215 5 22 6 The table below shows 6 students overall averages and their averages in their math class Overall Student Average 92 98 84 80 75 82 Math Class Average 91 95 85 85 75 78 If a linear model is applied to these data which statement best describes the correlation coefficient 1 It is close to 21 3 It is close to 0 2 It is close to 1 4 It is close to 0 5 Algebra I Common Core Aug 16 3 OVER

Use this space for computations 7 What is the solution to 2h 1 8 3h 2 6 1 h 14 3 h 14 2 h 14 4 h 14 5 5 8 Which expression is equivalent to 36x2 2 100 1 4 3x 2 5 3x 2 5 3 2 9x 2 25 9x 2 25 2 4 3x 1 5 3x 2 5 4 2 9x 1 25 9x 2 25 9 Patricia is trying to compare the average rainfall of New York to that of Arizona A comparison between these two states for the months of July through September would be best measured in 1 feet per hour 3 inches per month 2 inches per hour 4 feet per month 10 Which function defines the sequence 26 210 214 218 where f 6 5 226 1 f x 5 24x 2 2 3 f x 5 2x 1 32 2 f x 5 4x 2 2 4 f x 5 x 2 26 11 Which function has the greatest y intercept 1 f x 5 3x 2 2x 1 3y 5 12 3 the line that has a slope of 2 and passes through 1 24 f x 4 x Algebra I Common Core Aug 16 4

Use this space for computations 12 What is the product of 2x 1 3 and 4x2 2 5x 1 6 1 8x3 2 2x2 1 3x 1 18 3 8x3 1 2x2 2 3x 1 18 2 8x3 2 2x2 2 3x 1 18 4 8x3 1 2x2 1 3x 1 18 13 The height of a rocket at selected times is shown in the table below Time sec 0 1 2 3 4 5 6 7 Height ft 180 260 308 324 308 260 180 68 Based on these data which statement is not a valid conclusion 1 The rocket was launched from a height of 180 feet 2 The maximum height of the rocket occurred 3 seconds after launch 3 The rocket was in the air approximately 6 seconds before hitting the ground 4 The rocket was above 300 feet for approximately 2 seconds 14 A parking garage charges a base rate of 3 50 for up to 2 hours and an hourly rate for each additional hour The sign below gives the prices for up to 5 hours of parking Parking Rates 2 hours 3 50 3 hours 9 00 4 hours 14 50 5 hours 20 00 Which linear equation can be used to find x the additional hourly parking rate 1 9 00 1 3x 5 20 00 3 2x 1 3 50 5 14 50 2 9 00 1 3 50x 5 20 00 4 2x 1 9 00 5 14 50 Algebra I Common Core Aug 16 5 OVER

Use this space for computations 15 Which function has a constant rate of change equal to 23 y x y 0 2 1 5 2 8 3 11 x 1 3 1 5 2 2 3 5 4 4 2 2y 6x 10 4 16 Kendal bought x boxes of cookies to bring to a party Each box contains 12 cookies She decides to keep two boxes for herself She brings 60 cookies to the party Which equation can be used to find the number of boxes x Kendal bought 1 2x 2 12 5 60 3 12x 2 24 5 60 2 12x 2 2 5 60 4 24 2 12x 5 60 17 The table below shows the temperature T m of a cup of hot chocolate that is allowed to chill over several minutes m Time m minutes 0 2 4 6 8 Temperature T m F 150 108 78 56 41 Which expression best fits the data for T m 1 150 0 85 m 3 150 0 85 m 2 1 2 150 1 15 m 4 150 1 15 m 2 1 Algebra I Common Core Aug 16 6

18 As x increases beyond 25 which function will have the largest value 1 f x 5 1 5x 3 h x 5 1 5x2 2 g x 5 1 5x 1 3 4 k x 5 1 5x3 1 1 5x2 Use this space for computations 19 What are the solutions to the equation 3x2 1 10x 5 8 1 2 and 24 3 3 4 and 22 3 4 2 4 and 2 3 2 2 2 and 4 3 20 An online company lets you download songs for 0 99 each after you have paid a 5 membership fee Which domain would be most appropriate to calculate the cost to download songs 1 rational numbers greater than zero 2 whole numbers greater than or equal to one 3 integers less than or equal to zero 4 whole numbers less than or equal to one 21 The function f x 5 3x2 1 12x 1 11 can be written in vertex form as 1 f x 5 3x 1 6 2 2 25 3 f x 5 3 x 1 2 2 2 1 2 f x 5 3 x 1 6 2 2 25 4 f x 5 3 x 1 2 2 1 7 22 A system of equations is given below x 1 2y 5 5 2x 1 y 5 4 Which system of equations does not have the same solution 1 3x 1 6y 5 15 3 x 1 2y 5 5 2x 1 y 5 4 6x 1 3y 5 12 2 4x 1 8y 5 20 4 x 1 2y 5 5 2x 1 y 5 4 4x 1 2y 5 12 Algebra I Common Core Aug 16 7 OVER

23 Based on the graph below which expression is a possible factorization of p x p x x 1 1 x 1 3 x 2 2 x 2 4 3 x 1 3 x 2 5 x 2 2 x 2 4 2 x 2 3 x 1 2 x 1 4 4 x 2 3 x 1 5 x 1 2 x 1 4 24 Milton has his money invested in a stock portfolio The value v x of his portfolio can be modeled with the function v x 5 30 000 0 78 x where x is the number of years since he made his investment Which statement describes the rate of change of the value of his portfolio 1 It decreases 78 per year 2 It decreases 22 per year 3 It increases 78 per year 4 It increases 22 per year Algebra I Common Core Aug 16 8 Use this space for computations

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 5 2 x 1 3 on the set of axes below y x Algebra I Common Core Aug 16 9 OVER

26 Richard is asked to transform the graph of b x below b x x The graph of b x is transformed using the equation h x 5 b x 2 2 2 3 Describe how the graph of b x changed to form the graph of h x Algebra I Common Core Aug 16 10

27 Consider the pattern of squares shown below Which type of model linear or exponential should be used to determine how many squares are in the nth pattern Explain your answer 28 When multiplying polynomials for a math assignment Pat found the product to be 24x 1 8x2 2 2x3 1 5 He then had to state the leading coefficient of this polynomial Pat wrote down 24 Do you agree with Pat s answer Explain your reasoning Algebra I Common Core Aug 16 11 OVER

29 Is the sum of 3 2 and 4 2 rational or irrational Explain your answer 30 The graph below shows two functions f x and g x State all the values of x for which f x 5 g x y g x f x x Algebra I Common Core Aug 16 12

31 Find the zeros of f x 5 x 2 3 2 2 49 algebraically 32 Solve the equation below for x in terms of a 4 ax 1 3 2 3ax 5 25 1 3a Algebra I Common Core Aug 16 13 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 The data table below shows the median diameter of grains of sand and the slope of the beach for 9 naturally occurring ocean beaches Median Diameter of Grains of Sand in Millimeters x 0 17 0 19 0 22 0 235 0 235 0 3 0 35 0 42 0 85 Slope of Beach in Degrees y 0 63 0 7 0 82 0 88 1 5 4 4 7 3 11 3 1 15 Write the linear regression equation for this set of data rounding all values to the nearest thousandth Using this equation predict the slope of a beach to the nearest tenth of a degree on a beach with grains of sand having a median diameter of 0 65 mm Algebra I Common Core Aug 16 14

34 Shawn incorrectly graphed the inequality 2x 2 2y 8 as shown below y x Explain Shawn s mistake Graph the inequality correctly on the set of axes below y x Algebra I Common Core Aug 16 15 OVER

35 A drama club is selling tickets to the spring musical The auditorium holds 200 people Tickets cost 12 at the door and 8 50 if purchased in advance The drama club has a goal of selling at least 1000 worth of tickets to Saturday s show Write a system of inequalities that can be used to model this scenario If 50 tickets are sold in advance what is the minimum number of tickets that must be sold at the door so that the club meets its goal Justify your answer Algebra I Common Core Aug 16 16

36 Janice is asked to solve 0 5 64x2 1 16x 2 3 She begins the problem by writing the following steps Line 1 Line 2 Line 3 0 5 64x2 1 16x 2 3 0 5 B2 1 2B 2 3 0 5 B 1 3 B 2 1 Use Janice s procedure to solve the equation for x Explain the method Janice used to solve the quadratic equation Algebra I Common Core Aug 16 17 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 For a class picnic two teachers went to the same store to purchase drinks One teacher purchased 18 juice boxes and 32 bottles of water and spent 19 92 The other teacher purchased 14 juice boxes and 26 bottles of water and spent 15 76 Write a system of equations to represent the costs of a juice box j and a bottle of water w Kara said that the juice boxes might have cost 52 cents each and that the bottles of water might have cost 33 cents each Use your system of equations to justify that Kara s prices are not possible Question 37 is continued on the next page Algebra I Common Core Aug 16 18

Solve your system of equations to determine the actual cost in dollars of each juice box and each bottle of water Algebra I Common Core Aug 16 19 OVER

Tear Here Tear Here Scrap Graph Paper this sheet will not be scored

Scrap Graph Paper this sheet will not be scored Tear Here Tear Here

1 inch 2 54 centimeters 1 meter 39 37 inches 1 mile 5280 feet 1 mile 1760 yards 1 mile 1 609 kilometers 1 kilometer 0 62 mile 1 pound 16 ounces 1 pound 0 454 kilogram 1 kilogram 2 2 pounds 1 ton 2000 pounds 1 cup 8 fluid ounces 1 pint 2 cups 1 quart 2 pints 1 gallon 4 quarts 1 gallon 3 785 liters 1 liter 0 264 gallon 1 liter 1000 cubic centimeters Pythagorean Theorem a2 b2 c2 A bh Quadratic Formula x Circle A r 2 Arithmetic Sequence an a1 n 1 d Circle C d or C 2 r Geometric Sequence a n a 1r n 1 General Prisms V Bh Geometric Series Sn Cylinder V r 2h Radians 1 radian 180 degrees Sphere V 4 3 r 3 Degrees 1 degree radians 180 Cone V 1 2 r h 3 Exponential Growth Decay A A0ek t t0 B0 Pyramid V 1 Bh 3 Triangle A Parallelogram 1 bh 2 Tear Here Tear Here High School Math Reference Sheet Algebra I Common Core Aug 16 23 b b2 4ac 2a a1 a1r n 1 r where r 1

ALGEBRA I COMMON CORE Tear Here Tear Here Printed on Recycled Paper ALGEBRA I COMMON CORE