The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA. Student Name: School Name:

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1 INTEGRATED ALGEBRA The Universit of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA Wednesda, August 18, :30 to 11:30 a.m., onl Student Name: School Name: Print our name and the name of our 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, slowl and carefull, tear off the answer sheet. Then fill in the heading of our answer sheet. This eamination has four parts, with a total of 39 questions. You must answer all questions in this eamination. Write our answers to the Part I multiple-choice questions on the separate answer sheet. Write our answers to the questions in Parts II, III, and IV directl in this booklet. All work should be written in pen, ecept graphs and drawings, which should be done in pencil. Clearl indicate the necessar steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. The formulas that ou ma need to answer some questions in this eamination are found at the end of the eamination. This sheet is perforated so ou ma remove it from this booklet. Scrap paper is not permitted for an part of this eamination, but ou ma 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 an question for which graphing ma be helpful but is not required. You ma remove this sheet from this booklet. An work done on this sheet of scrap graph paper will not be scored. When ou have completed the eamination, ou must sign the statement printed at the end of the answer sheet, indicating that ou had no unlawful knowledge of the questions or answers prior to the eamination and that ou have neither given nor received assistance in answering an of the questions during the eamination. Your answer sheet cannot be accepted if ou fail to sign this declaration. Notice A graphing calculator and a straightedge (ruler) must be available for ou to use while taking this eamination. The use of an communications device is strictl prohibited when taking this eamination. If ou use an communications device, no matter how briefl, our eamination will be invalidated and no score will be calculated for ou. DO NOT OPEN THIS EXAMINATION BOOKLET UNTIL THE SIGNAL IS GIVEN. INTEGRATED ALGEBRA

2 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 epression that best completes the statement or answers the question. [60] 1 The school store did a stud 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. Use this space for computations. Cost of Sweatshirt $10 $25 $15 $20 $5 Number Sold Which scatter plot represents the data? Number Sold Cost of Sweatshirt (in dollars) Number Sold Cost of Sweatshirt (in dollars) (1) (3) Cost of Sweatshirt (in dollars) Number Sold Cost of Sweatshirt (in dollars) Number Sold (2) (4) Integrated Algebra August 10 [2]

3 2 What is the solution of 3(2m 1) 4m + 7? (1) m 5 (3) m 4 (2) m 5 (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 B C (1) {3, 4, 5, 6, 7} (3) {2, 3, 4, 5, 6, 7} (2) {2} (4) {1, 2, 3, 4, 5, 6, 7, 8, 9} Integrated Algebra August 10 [3] [OVER]

4 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 awa 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 (3) 9.0 (2) 8.6 (4) What is the slope of the line passing through the points A and B, as shown on the graph below? A B (1) 3 (3) 3 (2) 1 3 (4) 1 3 Integrated Algebra August 10 [4]

5 6 The quotient of ( ) and ( ) epressed in scientific notation is (1) 4,000 (3) (2) 40,000 (4) Use this space for computations. 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 man votes did candidate B receive? (1) 186 (3) 1,023 (2) 837 (4) 1,805 8 Which epression is equivalent to 121 2? (1) ( 11)( 11) (3) (11 )(11 + ) (2) ( + 11)( 11) (4) (11 )(11 ) 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) { } (3) {1, 4, 7, 8} (2) {2, 3, 5, 6} (4) {1, 2, 3, 4, 5, 6, 7, 8} Integrated Algebra August 10 [5] [OVER]

6 10 Which graph can be used to find the solution of the following sstem of equations? = = 10 Use this space for computations. (1) (3) (2) (4) Integrated Algebra August 10 [6]

7 11 The width of a rectangle is 3 less than twice the length,. If the area of the rectangle is 43 square feet, which equation can be used to find the length, in feet? (1) 2( 3) = 43 (3) 2 + 2(2 3) = 43 (2) (3 2) = 43 (4) (2 3) = 43 Use this space for computations. 12 Which value of is the solution of = 2 3? (1) 1 4 (2) 1 4 (3) 4 (4) 4 13 What is the perimeter of a regular pentagon with a side whose length is + 4? (1) (3) (2) (4) Which equation represents a line parallel to the -ais? (1) = (3) = 4 (2) = 4 (4) = + 4 Integrated Algebra August 10 [7] [OVER]

8 15 The diagram below shows the graph of = 2 c. Use this space for computations. Which diagram shows the graph of = 2 c? (1) (3) (2) (4) Integrated Algebra August 10 [8]

9 16 Which point lies on the line whose equation is 2 3 = 9? (1) ( 1, 3) (3) (0, 3) (2) ( 1, 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,, of a ball tossed into the air can be represented b the equation = , where is the elapsed time. What is the equation of the ais of smmetr of this parabola? (1) = 5 (3) = 5 (2) = 5 (4) = 5 19 In the diagram below, MATH is a rectangle, GB = 4.6, MH = 6, and HT = 15. M G A H B T What is the area of polgon MBATH? (1) 34.5 (3) 90.0 (2) 55.5 (4) Integrated Algebra August 10 [9] [OVER]

10 20 This ear, John plaed 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 plas net ear, John wants to increase his average (mean) hits per game b 0.5. What is the total number of hits John needs over the first 10 games net ear to achieve his goal? (1) 5 (3) 20 (2) 2 (4) 25 Use this space for computations. 21 What is the value of the -coordinate of the solution to the sstem of equations 2 + = 8 and 3 = 3? (1) 2 (3) 3 (2) 2 (4) 3 22 Which set-builder notation describes { 3, 2, 1, 0, 1, 2}? (1) { 3 < 2, where is an integer} (2) { 3 < 2, where is an integer} (3) { 3 < < 2, where is an integer} (4) { 3 2, where is an integer} Integrated Algebra August 10 [10]

11 23 Corinne calculated the area of a paper plate to be square inches. If the actual area of the plate is square inches, what is the relative error in calculating the area, to the nearest thousandth? (1) (3) (2) (4) Use this space for computations. 24 The probabilit that it will snow on Sunda is 3. The probabilit 5 that it will snow on both Sunda and Monda is 3. What is the 10 probabilit that it will snow on Monda, if it snowed on Sunda? (1) 9 50 (3) 1 2 (2) 2 (4) 9 10 Integrated Algebra August 10 [11] [OVER]

12 25 Which graph represents an eponential equation? Use this space for computations. (1) (3) (2) (4) Integrated Algebra August 10 [12]

13 26 Right triangle ABC has legs of 8 and 15 and a hpotenuse of 17, as shown in the diagram below. Use this space for computations. A 8 17 C 15 B The value of the tangent of B is (1) (3) (2) (4) What is epressed in simplest form? 5 (1) 0 (3) 4 5 (2) 2 5 (4) Integrated Algebra August 10 [13] [OVER]

14 28 How man different four-letter arrangements are possible with the letters G, A, R, D, E, N if each letter ma be used onl once? (1) 15 (3) 360 (2) 24 (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)? (1) + 1 = 2 7 ( + 3) (3) 1 = 2 ( + 3) 7 (2) 5 = 2 7 ( 8) (4) + 5 = 2 ( 8) 7 30 An eample of an algebraic epression is (1) + 2 (3) < + 2 (2) = + 2 (4) = Integrated Algebra August 10 [14]

15 Part II Answer all 3 questions in this part. Each correct answer will receive 2 credits. Clearl indicate the necessar 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 onl 1 credit. [6] 31 Epress in simplest form: 45 a 4 b 3 90 a 3 b 15 a 2 b Integrated Algebra August 10 [15] [OVER]

16 32 Joseph tped a 1,200-word essa in 25 minutes. At this rate, determine how man words he can tpe in 45 minutes. 33 Epress 3 48 in simplest radical form. Integrated Algebra August 10 [16]

17 Part III Answer all 3 questions in this part. Each correct answer will receive 3 credits. Clearl indicate the necessar 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 onl 1 credit. [9] 34 The number of songs fifteen students have on their MP3 plaers is: 120, 124, 132, 145, 200, 255, 260, 292, 308, 314, 342, 407, 421, 435, 452 State the values of the minimum, 1st quartile, median, 3rd quartile, and maimum. Using these values, construct a bo-and-whisker plot using an appropriate scale on the line below. Integrated Algebra August 10 [17] [OVER]

18 35 Find the volume, in cubic centimeters, and the surface area, in square centimeters, of the rectangular prism shown below. 4 cm 10 cm 2 cm Integrated Algebra August 10 [18]

19 36 Find the roots of the equation 2 = algebraicall. Integrated Algebra August 10 [19] [OVER]

20 Part IV Answer all 3 questions in this part. Each correct answer will receive 4 credits. Clearl indicate the necessar 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 onl 1 credit. [12] 37 On the set of aes below, solve the following sstem of inequalities graphicall. < State the coordinates of a point in the solution set. Integrated Algebra August 10 [20]

21 38 Each of the hats shown below has colored marbles placed inside. Hat A contains five green marbles and four red marbles. Hat B contains si blue marbles and five red marbles. Hat C contains five green marbles and five blue marbles. Hat A Hat B Hat C If a student were to randoml pick one marble from each of these three hats, determine from which hat the student would most likel pick a green marble. Justif our answer. Determine the fewest number of marbles, if an, and the color of these marbles that could be added to each hat so that the probabilit of picking a green marble will be one-half in each of the three hats. Integrated Algebra August 10 [21] [OVER]

22 39 A hot-air balloon is tied to the ground with two taut (straight) ropes, as shown in the diagram below. One rope is directl under the balloon and makes a right angle with the ground. The other rope forms an angle of 50 with the ground. Hot-air balloon 110 feet Ground 50 Determine the height, to the nearest foot, of the balloon directl above the ground. Determine the distance, to the nearest foot, on the ground between the two ropes. Integrated Algebra August 10 [22]

23 Reference Sheet Tear Here sin A = opposite hpotenuse Trigonometric Ratios cos A = tan A = adjacent hpotenuse opposite adjacent 1 Area trapezoid A = h(b b 2 ) Volume clinder V = πr 2 h Surface Area rectangular prism SA = 2lw + 2hw + 2lh clinder SA = 2πr 2 + 2πrh Coordinate Geometr Δ m = Δ = Tear Here Integrated Algebra August 10 [23]

24 Tear Here Tear Here

25 Scrap Graph Paper This sheet will not be scored. Tear Here Tear Here

26 Scrap Graph Paper This sheet will not be scored. Tear Here Tear Here

27 The Universit of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA Tear Here Wednesda, August 18, :30 to 11:30 a.m., onl ANSWER SHEET Student Se: Male Female Grade Teacher School Your answers to Part I should be recorded on this answer sheet. Part I Answer all 30 questions in this part Your answers for Parts II, III, and IV should be written in the test booklet. The declaration below must be signed when ou have completed the eamination. Tear Here I do hereb affirm, at the close of this eamination, that I had no unlawful knowledge of the questions or answers prior to the eamination and that I have neither given nor received assistance in answering an of the questions during the eamination. Signature Integrated Algebra August 10 [27]

28 INTEGRATED ALGEBRA Question INTEGRATED ALGEBRA Maimum Credit Part I Part II Part III Part IV Credits Earned Rater s/scorer s Initials Rater s/scorer s Name (minimum of three) Tear Here 39 4 Maimum Total 87 Total Raw Score Checked b Scale Score (from conversion chart) Tear Here Integrated Algebra August 10 [28] Printed on Reccled Paper INTEGRATED ALGEBRA