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integrated algebra the university of the state of new york regents high school examination integrated algebra wednesday august 18 2010 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 then turn to the last page of this booklet which is the answer sheet for part i fold the last page along the perforations and slowly and carefully tear off the answer sheet then fill in the heading of your answer sheet this examination has four parts with a total of 39 questions you must answer all questions in this examination write 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 school store did a study comparing the cost of a sweatshirt with the number of sweatshirts sold the price was changed several times and the numbers of sweatshirts sold were recorded the data are shown in the table below cost of sweatshirt number sold $10 9 $25 6 $15 15 $20 11 $5 14 which scatter plot represents the data y number sold 20 15 10 5 5 10 15 20 25 y number sold 20 15 10 5 5 10 15 20 25 x x cost of sweatshirt in dollars cost of sweatshirt in dollars 1 y cost of sweatshirt in dollars 15 10 5 5 10 15 20 25 3 y cost of sweatshirt in dollars 20 15 10 5 5 10 15 20 25 20 x x number sold number sold 2 4 integrated algebra ­ august 10 [2]

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2 what is the solution of 32m 1 4m 7 1 m 5 2 m 5 3 m 4 4 m 4 use this space for computations 3 which set represents the intersection of sets a b and c shown in the diagram below a 3 1 4 7 9 2 5 6 8 b c 1 {3 4 5 6 7 2 {2 3 {2 3 4 5 6 7 4 {1 2 3 4 5 6 7 8 9 integrated algebra ­ august 10 [3 [over]

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4 the end of a dog s leash is attached to the top of a 5-foot-tall fence post as shown in the diagram below the dog is 7 feet away from the base of the fence post use this space for computations 5 ft leash 7 ft dog how long is the leash to the nearest tenth of a foot 1 4.9 2 8.6 3 9.0 4 12.0 5 what is the slope of the line passing through the points a and b as shown on the graph below yabx 1 -3 1 2 3 3 3 1 4 3 integrated algebra ­ august 10 [4]

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6 the quotient of 9.2 × notation is 1 4,000 2 40,000 106 and 2.3 × 102 expressed in scientific use this space for computations 3 4 × 103 4 4 × 104 7 in a recent town election 1,860 people voted for either candidate a or candidate b for the position of supervisor if candidate a received 55 of the votes how many votes did candidate b receive 1 186 2 837 3 1,023 4 1,805 8 which expression is equivalent to 121 x2 1 x 11 x 11 2 x 11 x 11 3 11 x 11 x 4 11 x 11 x 9 given u {1 2 3 4 5 6 7 8 b {2 3 5 6 set b is a subset of set u what is the complement of set b 1 2 {2 3 5 6 3 {1 4 7 8 4 {1 2 3 4 5 6 7 8 integrated algebra ­ august 10 [5 [over]

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10 which graph can be used to find the solution of the following system of equations y x2 2x 3 2y 2x 10 y y use this space for computations x x 1 y 3 y x x 2 4 integrated algebra ­ august 10 [6]

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11 the width of a rectangle is 3 less than twice the length x if the area of the rectangle is 43 square feet which equation can be used to find the length in feet 1 2xx 3 43 2 x3 2x 43 3 2x 22x 3 43 4 x2x 3 43 use this space for computations 2x 3 2 12 which value of x is the solution of x-4 3 1 1 4 1 2 4 3 -4 4 4 13 what is the perimeter of a regular pentagon with a side whose length is x 4 1 x2 16 2 4x 16 3 5x 4 4 5x 20 14 which equation represents a line parallel to the y-axis 1 x y 2 x 4 3 y 4 4 y x 4 integrated algebra ­ august 10 [7 [over]

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15 the diagram below shows the graph of y y -x2 c use this space for computations x which diagram shows the graph of y x2 c yyxx 1 y 3 y x x 2 4 integrated algebra ­ august 10 [8]

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16 which point lies on the line whose equation is 2x 3y 9 1 1 3 2 1 3 3 0 3 4 0 3 use this space for computations 17 which phrase best describes the relationship between the number of miles driven and the amount of gasoline used 1 causal but not correlated 2 correlated but not causal 3 both correlated and causal 4 neither correlated nor causal 18 the height y of a ball tossed into the air can be represented by the equation y -x2 10x 3 where x is the elapsed time what is the equation of the axis of symmetry of this parabola 1 y 5 2 y -5 3 x 5 4 x -5 19 in the diagram below math is a rectangle gb 4.6 mh 6 and ht 15 mgabht what is the area of polygon mbath 1 34.5 2 55.5 3 90.0 4 124.5 integrated algebra ­ august 10 [9 [over]

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20 this year john played in 10 baseball games in these games he had hit the ball 2 3 0 1 3 2 4 0 2 and 3 times in the first 10 games he plays next year john wants to increase his average mean hits per game by 0.5 what is the total number of hits john needs over the first 10 games next year to achieve his goal 1 5 2 2 3 20 4 25 use this space for computations 21 what is the value of the y-coordinate of the solution to the system of equations 2x y 8 and x 3y -3 1 -2 2 2 3 3 4 -3 22 which set-builder notation describes 3 -2 -1 0 1 2 1 {x -3 x 2 where x is an integer 2 {x -3 x 2 where x is an integer 3 {x -3 x 2 where x is an integer 4 {x -3 x 2 where x is an integer integrated algebra ­ august 10 [10]

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23 corinne calculated the area of a paper plate to be 50.27 square inches if the actual area of the plate is 55.42 square inches what is the relative error in calculating the area to the nearest thousandth 1 0.092 2 0.093 3 0.102 4 0.103 use this space for computations 3 24 the probability that it will snow on sunday is the probability 5 3 that it will snow on both sunday and monday is what is the 10 probability that it will snow on monday if it snowed on sunday 9 1 50 1 3 2 9 4 10 2 2 integrated algebra ­ august 10 [11 [over]

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25 which graph represents an exponential equation y use this space for computations y x x 1 y 3 y x x 2 4 integrated algebra ­ august 10 [12]

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26 right triangle abc has legs of 8 and 15 and a hypotenuse of 17 as shown in the diagram below a use this space for computations 8 17 c 15 b the value of the tangent of b is 1 0.4706 2 0.5333 3 0.8824 4 1.8750 2+x x-2 27 what is expressed in simplest form 5x 5x 1 0 2 2 5 4 3 5x 2x 4 4 5x integrated algebra ­ august 10 [13 [over]

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28 how many different four-letter arrangements are possible with the letters g a r d e n if each letter may be used only once 1 15 2 24 3 360 4 720 use this space for computations 29 what is an equation of the line that passes through the points 1,3 and 8,5 2 1 y 1 x 3 7 7 2 2 y 5 x 8 2 3 y 1 x 3 7 7 2 4 y 5 x 8 30 an example of an algebraic expression is 1 x 2 2 y x 2 3 y x 2 4 y x2 2x integrated algebra ­ august 10 [14]

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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 [6 45a4b3 90a3b 31 express in simplest form 2 15a b integrated algebra ­ august 10 [15 [over]

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