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integrated algebra the university of the state of new york regents high school examination integrated algebra wednesday august 17 2011 8:30 to 11:30 a.m only student name school name 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 39 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 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 the use of any communications device is strictly prohibited when taking this examination if you use any communications device no matter how briefly your examination will be invalidated and no score will be calculated for you do not open this examination booklet until the signal is given integrated algebra

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part i answer all 30 questions in this part each correct answer will receive 2 credits no partial credit will be allowed for each question write on the separate answer sheet the numeral preceding the word or expression that best completes the statement or answers the question [60 use this space for computations 1 the number of calories burned while jogging varies directly with the number of minutes spent jogging if george burns 150 calories by jogging for 20 minutes how many calories does he burn by jogging for 30 minutes 1 100 2 180 3 200 4 225 2 the scatter plot below represents the relationship between the number of peanuts a student eats and the student s bowling score 300 bowling score 250 200 150 100 50 0 10 20 30 40 50 60 number of peanuts eaten which conclusion about the scatter plot is valid 1 there is almost no relationship between eating peanuts and bowling score 2 students who eat more peanuts have higher bowling scores 3 students who eat more peanuts have lower bowling scores 4 no bowlers eat peanuts integrated algebra ­ august 11 [2]

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3 if the universal set is {pennies nickels dimes quarters what is the complement of the set {nickels 1 2 {pennies quarters 3 {pennies dimes quarters 4 {pennies nickels dimes quarters use this space for computations 4 which situation does not describe a causal relationship 1 the higher the volume on a radio the louder the sound will be 2 the faster a student types a research paper the more pages the paper will have 3 the shorter the distance driven the less gasoline that will be used 4 the slower the pace of a runner the longer it will take the runner to finish the race 5 a cylinder has a diameter of 10 inches and a height of 2.3 inches what is the volume of this cylinder to the nearest tenth of a cubic inch 1 72.3 2 83.1 3 180.6 4 722.6 integrated algebra ­ august 11 [3 [over]

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6 based on the box-and-whisker plot below which statement is false use this space for computations 0 1 2 3 4 5 6 7 8 9 10 11 12 13 1 the median is 7 2 the range is 12 3 the first quartile is 4 4 the third quartile is 11 7 the ninth grade class at a local high school needs to purchase a park permit for $250.00 for their upcoming class picnic each ninth grader attending the picnic pays $0.75 each guest pays $1.25 if 200 ninth graders attend the picnic which inequality can be used to determine the number of guests x needed to cover the cost of the permit 1 0.75x 1.25 200 250.00 2 0.75x 1.25 200 250.00 3 0.75 200 1.25x 250.00 4 0.75 200 1.25x 250.00 8 which equation represents the line that passes through the point 1,5 and has a slope of -2 1 y -2x 7 2 y -2x 11 3 y 2x 9 4 y 2x 3 9 what is the solution of the system of equations 2x 5y 11 and -2x 3y -9 1 3 1 2 1,3 3 3 1 4 3,1 integrated algebra ­ august 11 [4]

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10 which algebraic expression represents 15 less than x divided by 9 x 1 15 9 x 3 15 9 use this space for computations 2 9x 15 4 15 9x 11 what are the vertex and the axis of symmetry of the parabola shown in the graph below y x 1 vertex 1,6 axis of symmetry y 1 2 vertex 1,6 axis of symmetry x 1 3 vertex 6,1 axis of symmetry y 1 4 vertex 6,1 axis of symmetry x 1 integrated algebra ­ august 11 [5 [over]

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12 the diagram below shows right triangle abc a 13 use this space for computations 5 c 12 b which ratio represents the tangent of abc 5 1 13 12 5 2 12 3 13 5 12 4 13 what is the value of the expression -3x 2 y 4x when x -4 and y 2 1 -112 2 -80 3 80 4 272 14 which expression is equivalent to -3xx 4 2xx 3 1 -x2 1 2 -x2 18x 3 -5x2 6x 4 -5x2 6x integrated algebra ­ august 11 [6]

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15 the data in the table below are graphed and the slope is examined x 0.5 1 1.5 2 2.5 use this space for computations y 9.0 8.75 8.5 8.25 8.0 the rate of change represented in this table can be described as 1 negative 2 positive 3 undefined 4 zero 16 the length of a rectangle is 3 inches more than its width the area of the rectangle is 40 square inches what is the length in inches of the rectangle 1 5 2 8 3 8.5 4 11.5 17 in interval notation the set of all real numbers greater than -6 and less than or equal to 14 is represented by 1 6 14 2 6 14 3 6 14 4 6 14 18 which equation represents a quadratic function 1 y x 2 2 y x 2 3 y x 2 4 y 2 x integrated algebra ­ august 11 [7 [over]

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19 ben has four more than twice as many cds as jake if they have a total of 31 cds how many cds does jake have 1 9 2 13 3 14 4 22 use this space for computations 20 what are the roots of the equation x 2 5x 6 0 1 1 and -6 2 2 and 3 3 -1 and 6 4 -2 and -3 21 what is the solution of the inequality -6x 17 8x 25 1 x 3 2 x 3 3 x -3 4 x -3 22 which set of data can be classified as qualitative 1 scores of students in an algebra class 2 ages of students in a biology class 3 numbers of students in history classes 4 eye colors of students in an economics class integrated algebra ­ august 11 [8]

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23 jack wants to replace the flooring in his rectangular kitchen he calculates the area of the floor to be 12.8 square meters the actual area of the floor is 13.5 square meters what is the relative error in calculating the area of the floor to the nearest thousandth 1 0.051 2 0.052 3 0.054 4 0.055 use this space for computations 24 the current student population of the brentwood student center is 2,000 the enrollment at the center increases at a rate of 4 each year to the nearest whole number what will the student population be closest to in 3 years 1 2,240 2 2,250 3 5,488 4 6,240 25 maria has a set of 10 index cards labeled with the digits 0 through 9 she puts them in a bag and selects one at random the outcome that is most likely to occur is selecting 1 an odd number 2 a prime number 3 a number that is at most 5 4 a number that is divisible by 3 26 a right triangle contains a 38° angle whose adjacent side measures 10 centimeters what is the length of the hypotenuse to the nearest hundredth of a centimeter 1 7.88 2 12.69 3 12.80 4 16.24 integrated algebra ­ august 11 [9 [over]

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27 which ordered pair is in the solution set of the system of inequalities shown in the graph below y use this space for computations x 1 2 1 2 2,2 3 2 4 4 2 2 integrated algebra ­ august 11 [10]

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28 a garden is in the shape of an isosceles trapezoid and a semicircle as shown in the diagram below a fence will be put around the perimeter of the entire garden 8m 7m 12 m use this space for computations which expression represents the length of fencing in meters that will be needed 1 22 6 2 22 12 3 15 6 4 15 12 29 which expression represents 36x2 100y6 factored completely 1 29x 25y3 9x 25y3 2 43x 5y3 3x 5y3 3 6x 10y3 6x 10y3 4 18x 50y3 18x 50y3 x 2x 30 what is the quotient of divided by 2 x+4 x 16 2 1 x-4 2 x2 3 2 x 16 2 x-4 4 2x2 2 x-4 integrated algebra ­ august 11 [11 [over]

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part ii answer all 3 questions in this part each correct answer will receive 2 credits clearly indicate the necessary steps including appropriate formula substitutions diagrams graphs charts etc 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 [6 31 solve for c in terms of a and b bc ac ab integrated algebra ­ august 11 [12]

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32 ms hopkins recorded her students final exam scores in the frequency table below interval 61­70 71­80 81­90 91­100 tally frequency 5 4 9 6 on the grid below construct a frequency histogram based on the table integrated algebra ­ august 11 [13 [over]

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33 mrs chen owns two pieces of property the areas of the properties are 77,120 square feet and 33,500 square feet 43,560 square feet 1 acre find the total number of acres mrs chen owns to the nearest hundredth of an acre integrated algebra ­ august 11 [14]

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part iii answer all 3 questions in this part each correct answer will receive 3 credits clearly indicate the necessary steps including appropriate formula substitutions diagrams graphs charts etc 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 [9 34 on the set of axes below graph and label the equations y x and y 3x for the interval -3 x 3 y x explain how changing the coefficient of the absolute value from 1 to 3 affects the graph integrated algebra ­ august 11 [15 [over]

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