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New York Regents Integrated Algebra August 2010

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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 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] 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 $25 $15 $20 $5 9 6 15 11 14 Which scatter plot represents the data? y 20 15 10 5 5 10 15 20 25 x Number Sold Number Sold y 20 15 10 5 5 10 15 20 25 Cost of Sweatshirt (in dollars) Cost of Sweatshirt (in dollars) (1) (3) y 20 15 10 5 5 10 15 20 25 Number Sold x Cost of Sweatshirt (in dollars) y Cost of Sweatshirt (in dollars) x 20 15 10 5 5 10 15 20 25 Number Sold (2) Integrated Algebra August 10 (4) [2] x Use this space for computations. Use this space for computations. 2 What is the solution of 3(2m 1) 4m + 7? (1) m 5 (3) m 4 (2) m 5 (4) m 4 3 Which set represents the intersection of sets A, B, and C shown in the diagram below? A B 3 8 1 2 4 7 5 6 9 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 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. Leash 5 ft Dog 7 ft How long is the leash, to the nearest tenth of a foot? (1) 4.9 (3) 9.0 (2) 8.6 (4) 12.0 5 What is the slope of the line passing through the points A and B, as shown on the graph below? y A B x (1) 3 (3) 3 1 (2) __ 3 1 (4) __ Integrated Algebra August 10 3 [4] Use this space for computations. 6 The quotient of (9.2 notation is 106) and (2.3 102) (1) 4,000 (3) 4 103 (2) 40,000 expressed in scientific Use this space for computations. (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 (3) 1,023 (2) 837 (4) 1,805 8 Which expression is equivalent to 121 x2 ? (1) (x 11)(x 11) (3) (11 x)(11 + x) (2) (x + 11)(x 11) (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) { } (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] 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 x x (1) (3) y y x (2) Integrated Algebra August 10 x (4) [6] Use this space for computations. 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) 2x(x 3) = 43 (3) 2x + 2(2x 3) = 43 (2) x(3 2x) = 43 Use this space for computations. (4) x(2x 3) = 43 2x 3 2 12 Which value of x is the solution of ______ = __ ? x 4 1 (1) __ 4 (3) 4 1 (2) __ 3 (4) 4 4 13 What is the perimeter of a regular pentagon with a side whose length is x + 4? (1) x2 + 16 (3) 5x + 4 (2) 4x + 16 (4) 5x + 20 14 Which equation represents a line parallel to the y-axis? (1) x = y (3) y = 4 (2) x = 4 (4) y = x + 4 Integrated Algebra August 10 [7] [OVER] 15 The diagram below shows the graph of y = x2 Use this space for computations. c. y x Which diagram shows the graph of y = x2 c? y y x x (1) (3) y y x (2) Integrated Algebra August 10 x (4) [8] 16 Which point lies on the line whose equation is 2x 3y = 9? (1) ( 1, 3) (3) (0, 3) (2) ( 1, 3) Use this space for computations. (4) (0, 3) 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 (3) x = 5 (2) y = 5 (4) x = 5 19 In the diagram below, MATH is a rectangle, GB = 4.6, MH = 6, and HT = 15. M A G B H T What is the area of polygon MBATH? (1) 34.5 (3) 90.0 (2) 55.5 (4) 124.5 Integrated Algebra August 10 [9] [OVER] 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 (3) 20 (2) 2 (4) 25 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 (3) 3 (2) 2 (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] Use this space for computations. 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 (3) 0.102 (2) 0.093 Use this space for computations. (4) 0.103 3 24 The probability that it will snow on Sunday is __ . The probability 5 __ that it will snow on both Sunday and Monday is _3 . What is the 10 probability that it will snow on Monday, if it snowed on Sunday? __ (1) _9 1 (3) __ (2) 2 __ (4) _9 50 Integrated Algebra August 10 2 10 [11] [OVER] Use this space for computations. 25 Which graph represents an exponential equation? y y x x (1) (3) y y x x (2) Integrated Algebra August 10 (4) [12] 26 Right triangle ABC has legs of 8 and 15 and a hypotenuse of 17, as shown in the diagram below. Use this space for computations. A 17 8 C B 15 The value of the tangent of B is (1) 0.4706 (3) 0.8824 (2) 0.5333 (4) 1.8750 2+x x 2 27 What is _____ _____ expressed in simplest form? 5x 5x (1) 0 4 (3) __ 2 (2) __ 2x + 4 (4) ______ 5 Integrated Algebra August 10 5x 5x [13] [OVER] 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 (3) 360 (2) 24 (4) 720 29 What is an equation of the line that passes through the points (1,3) and (8,5)? 2 (1) y + 1 = __ (x + 3) 2 (3) y 1 = __ (x + 3) 2 (2) y 5 = __ (x 8) 2 (4) y + 5 = __ (x 8) 7 7 7 7 30 An example of an algebraic expression is (1) x + 2 (3) y < x + 2 (2) y = x + 2 (4) y = x2 + 2x Integrated Algebra August 10 [14] Use this space for computations. 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] 32 Joseph typed a 1,200-word essay in 25 minutes. At this rate, determine how many words he can type in 45 minutes. ___ 33 Express 3 48 in simplest radical form. Integrated Algebra August 10 [16] 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. [9] 34 The number of songs fifteen students have on their MP3 players 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 maximum. Using these values, construct a box-and-whisker plot using an appropriate scale on the line below. Integrated Algebra August 10 [17] [OVER] 35 Find the volume, in cubic centimeters, and the surface area, in square centimeters, of the rectangular prism shown below. 4 cm 2 cm 10 cm Integrated Algebra August 10 [18] 36 Find the roots of the equation x2 = 30 13x algebraically. Integrated Algebra August 10 [19] [OVER] Part IV Answer all 3 questions in this part. Each correct answer will receive 4 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. [12] 37 On the set of axes below, solve the following system of inequalities graphically. y < 2x + 1 1 y __ x + 4 3 State the coordinates of a point in the solution set. y x Integrated Algebra August 10 [20] 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 six 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 randomly pick one marble from each of these three hats, determine from which hat the student would most likely pick a green marble. Justify your answer. Determine the fewest number of marbles, if any, and the color of these marbles that could be added to each hat so that the probability of picking a green marble will be one-half in each of the three hats. Integrated Algebra August 10 [21] [OVER] 39 A hot-air balloon is tied to the ground with two taut (straight) ropes, as shown in the diagram below. One rope is directly 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 50 Ground Determine the height, to the nearest foot, of the balloon directly above the ground. Determine the distance, to the nearest foot, on the ground between the two ropes. Integrated Algebra August 10 [22] Tear Here Reference Sheet sin A = cos A = adjacent hypotenuse tan A = Trigonometric Ratios opposite hypotenuse opposite adjacent Area trapezoid Volume cylinder 1 A = h ( b 1 + b 2) 2 V = r 2h rectangular prism SA = 2lw + 2hw + 2lh Surface Area cylinder y y y m = x = x2 x1 2 1 Tear Here Coordinate Geometry Integrated Algebra August 10 SA = 2 r2 + 2 rh [23] Tear Here Tear Here 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 The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION Tear Here INTEGRATED ALGEBRA Wednesday, August 18, 2010 8:30 to 11:30 a.m., only ANSWER SHEET Student . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sex: 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. 1 ................ 9 ................ 17 . . . . . . . . . . . . . . . . 25 . . . . . . . . . . . . . . . . 2 ................ 10 . . . . . . . . . . . . . . . . 18 . . . . . . . . . . . . . . . . 26 . . . . . . . . . . . . . . . . 3 ................ 11 . . . . . . . . . . . . . . . . 19 . . . . . . . . . . . . . . . . 27 . . . . . . . . . . . . . . . . 4 ................ 12 . . . . . . . . . . . . . . . . 20 . . . . . . . . . . . . . . . . 28 . . . . . . . . . . . . . . . . 5 ................ 13 . . . . . . . . . . . . . . . . 21 . . . . . . . . . . . . . . . . 29 . . . . . . . . . . . . . . . . 6 ................ 14 . . . . . . . . . . . . . . . . 22 . . . . . . . . . . . . . . . . 30 . . . . . . . . . . . . . . . . 7 ................ 15 . . . . . . . . . . . . . . . . 23 . . . . . . . . . . . . . . . . 8 ................ 16 . . . . . . . . . . . . . . . . 24 . . . . . . . . . . . . . . . . Your answers for Parts II, III, and IV should be written in the test booklet. Tear Here The declaration below must be signed when you have completed the examination. I do hereby affirm, at the close of this examination, that I had no unlawful knowledge of the questions or answers prior to the examination and that I have neither given nor received assistance in answering any of the questions during the examination. Signature Integrated Algebra August 10 [27] INTEGRATED ALGEBRA Rater s/Scorer s Name (minimum of three) INTEGRATED ALGEBRA Maximum Credit Part I 1 30 60 Part II 31 2 32 2 33 2 34 3 35 3 36 3 37 4 38 4 39 4 Maximum Total 87 Part IV Rater s/Scorer s Initials Total Raw Score Part III Credits Earned Checked by Tear Here Question Scale Score (from conversion chart) Tear Here Printed on Recycled Paper [28] INTEGRATED ALGEBRA Integrated Algebra August 10 FOR TEACHERS ONLY 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 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 Integrated Algebra. More detailed information about scoring is provided in the publication Information Booklet for Scoring the Regents Examinations in Mathematics. Use only red ink or red pencil in rating Regents papers. Do not attempt to correct the student s work by making insertions or changes of any kind. 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. On the back of the student s detachable answer sheet, raters must enter their initials in the boxes next to the questions they have scored and also write their name in the box under the heading Rater s/Scorer s Name. Raters should record the student s scores for all questions and the total raw score on the student s detachable 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 http://www.emsc.nysed.gov/osa/ o n Wednesday, August 18, 2010. The student s scale score should be entered in the box provided on the student s detachable answer sheet. The scale score is the student s final examination score. INTEGRATED ALGEBRA continued Part I Allow a total of 60 credits, 2 credits for each of the following. Allow credit if the student has written the correct answer instead of the numeral 1, 2, 3, or 4. (1) 3 (9) 3 (17) 3 (25) 4 (2) 1 (10) 1 (18) 3 (26) 2 (3) 2 (11) 4 (19) 2 (27) 3 (4) 2 (12) 2 (20) 4 (28) 3 (5) 2 (13) 4 (21) 2 (29) 2 (6) 4 (14) 2 (22) 4 (30) 1 (7) 2 (15) 1 (23) 2 (8) 3 (16) 4 (24) 3 [2] INTEGRATED ALGEBRA continued 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 http://www.emsc.nysed.gov/osa/ and select the link Examination 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. General Rules for Applying Mathematics Rubrics General Principles for Rating The rubrics for the constructed-response questions on the Regents Examination in Integrated Algebra are designed to provide a systematic, consistent method for awarding credit. The rubrics are not to be considered all-inclusive; it is impossible to anticipate all the different methods that students might use to solve a given problem. Each response must be rated carefully using the teacher s professional judgment and knowledge of mathematics; all calculations must be checked. The specific rubrics for each question must be applied consistently to all responses. In cases that are not specifically addressed in the rubrics, raters must follow the general rating guidelines in the publication Information Booklet for Scoring the Regents Examinations in Mathematics, use their own professional judgment, confer with other mathematics teachers, and/or contact the consultants at the State Education Department for guidance. During each Regents examination administration period, rating questions may be referred directly to the Education Department. The contact numbers are sent to all schools before each administration period. II. Full-Credit Responses A full-credit response provides a complete and correct answer to all parts of the question. Sufficient work is shown to enable the rater to determine how the student arrived at the correct answer. When the rubric for the full-credit response includes one or more examples of an acceptable method for solving the question (usually introduced by the phrase such as ), it does not mean that there are no additional acceptable methods of arriving at the correct answer. Unless otherwise specified, mathematically correct alternative solutions should be awarded credit. The only exceptions are those questions that specify the type of solution that must be used; e.g., an algebraic solution or a graphic solution. A correct solution using a method other than the one specified is awarded half the credit of a correct solution using the specified method. III. Appropriate Work Full-Credit Responses: The directions in the examination booklet for all the constructed-response questions state: Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. The student has the responsibility of providing the correct answer and showing how that answer was obtained. The student must construct the response; the teacher should not have to search through a group of seemingly random calculations scribbled on the student paper to ascertain what method the student may have used. Responses With Errors: Rubrics that state Appropriate work is shown, but are intended to be used with solutions that show an essentially complete response to the question but contain certain types of errors, whether computational, rounding, graphing, or conceptual. If the response is incomplete; i.e., an equation is written but not solved or an equation is solved but not all of the parts of the question are answered, appropriate work has not been shown. Other rubrics address incomplete responses. IV. Multiple Errors Computational Errors, Graphing Errors, and Rounding Errors: Each of these types of errors results in a 1-credit deduction. Any combination of two of these types of errors results in a 2-credit deduction. No more than 2 credits should be deducted for such mechanical errors in any response. The teacher must carefully review the student s work to determine what errors were made and what type of errors they were. Conceptual Errors: A conceptual error involves a more serious lack of knowledge or procedure. Examples of conceptual errors include using the incorrect formula for the area of a figure, choosing the incorrect trigonometric function, or multiplying the exponents instead of adding them when multiplying terms with exponents. A response with one conceptual error can receive no more than half credit. If a response shows repeated occurrences of the same conceptual error, the student should not be penalized twice. If the same conceptual error is repeated in responses to other questions, credit should be deducted in each response. If a response shows two (or more) different major conceptual errors, it should be considered completely incorrect and receive no credit. If a response shows one conceptual error and one computational, graphing, or rounding error, the teacher must award credit that takes into account both errors; i.e., awarding half credit for the conceptual error and deducting 1 credit for each mechanical error (maximum of two deductions for mechanical errors). I. [3] [OVER] INTEGRATED ALGEBRA continued Part II For each question, use the specific criteria to award a maximum of two credits. Unless otherwise specified, mathematically correct alternative solutions should be awarded appropriate credit. (31) [2] 3a 2b 2 6a or an equivalent simplified expression, and appropriate work is shown. [1] Appropriate work is shown, but one computational, factoring, or simplification error is made. or [1] Appropriate work is shown, but one conceptual error is made. or [1] 3a 2b 2 6a or an equivalent simplified expression, but no work is shown. [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. (32) [2] 2,160, and appropriate work is shown. [1] Appropriate work is shown, but one computational error is made. or [1] Appropriate work is shown, but one conceptual error is made. or [1] 1200 x = or an equivalent equation, but no further correct work is shown. 25 45 or [1] Appropriate work is shown to find a rate of 48 words per minute, but no further correct work is shown. or [1] 2,160, but no work is shown. [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. [4] INTEGRATED ALGEBRA continued (33) [2] 12 3 , and appropriate work is shown. [1] Appropriate work is shown, but one computational error is made. or [1] Appropriate work is shown, but one conceptual error is made. or [1] Appropriate work is shown, but the answer is not expressed in simplest radical form. or [1] 12 3 , but no work is shown. [0] The answer is expressed as a decimal, and no work is shown. or [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. [5] [OVER] INTEGRATED ALGEBRA continued Part III For each question, use the specific criteria to award a maximum of three credits. Unless otherwise specified, mathematically correct alternative solutions should be awarded appropriate credit. (34) [3] Minimum = 120, first quartile = 145, median = 292, third quartile = 407, and maximum = 452 are indicated, and a correct box-and-whisker plot with an appropriate scale is drawn. [2] Five correct values are indicated, but one graphing error is made, such as using an inappropriate scale. or [2] Four correct values are indicated, and an appropriate box-and-whisker plot is drawn. [1] Five correct values are indicated, but two or more graphing errors are made. or [1] Appropriate work is shown, but one conceptual error is made. or [1] Two or three correct values are indicated, and an appropriate box-and-whisker plot is drawn. or [1] Five correct values are indicated, but no box-and-whisker plot is drawn. [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. [6] INTEGRATED ALGEBRA continued (35) [3] Volume = 80 and surface area = 136, and appropriate work is shown. [2] Appropriate work is shown, but one computational error is made. or [2] Appropriate work is shown to find 80 and 136, but the values are not labeled or are labeled incorrectly. or [2] Appropriate work is shown to find surface area = 136, but no further correct work is shown. [1] Appropriate work is shown, but two or more computational errors are made. or [1] Appropriate work is shown, but one conceptual error is made. or [1] Appropriate work is shown to find volume = 80, but no further correct work is shown. or [1] Volume = 80 and surface area = 136, but no work is shown. [0] Volume = 80 or surface area = 136, but no work is shown. or [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. [7] [OVER] INTEGRATED ALGEBRA continued (36) [3] 15 and 2, and appropriate algebraic work is shown. [2] Appropriate work is shown, but one computational or factoring error is made. or [2] Appropriate work is shown to find (x + 15)(x 2) = 0, but no further correct work is shown. [1] Appropriate work is shown, but two or more computational or factoring errors are made. or [1] Appropriate work is shown, but one conceptual error is made. or [1] 15 and 2, but a method other than algebraic is used. or [1] A correct quadratic equation in standard form (set equal to zero) is written, but no further correct work is shown. or [1] 15 and 2, but no work is shown. [0] 15 or 2, but no work is shown, or a method other than algebraic is used. or [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. [8] INTEGRATED ALGEBRA continued Part IV For each question, use the specific criteria to award a maximum of four credits. Unless otherwise specified, mathematically correct alternative solutions should be awarded appropriate credit. (37) [4] Both inequalities are graphed and shaded correctly, and at least one inequality is labeled, and the coordinates of a point in the solution set are stated. [3] Appropriate work is shown, but one graphing error is made, such as drawing a dashed line instead of a solid line or shading incorrectly, but an appropriate point in the solution set is stated. or [3] Both inequalities are graphed and shaded correctly, and a point in the solution set is stated, but the graphs are not labeled or are labeled incorrectly. or [3] Both inequalities are graphed and shaded correctly, and at least one inequality is labeled, but no point in the solution set is stated. [2] Appropriate work is shown, but two or more graphing errors are made, but an appropriate point in the solution set is stated. or [2] Appropriate work is shown, but one conceptual error is made, such as graphing 1 x + 4 , but an appropriate point in the solution set is the lines y = 2 x + 1 and y = 3 stated. or [2] Both inequalities are graphed and shaded correctly, but neither is labeled or they are labeled incorrectly, and no point in the solution set is stated. or [2] One inequality is graphed, labeled, and shaded correctly, but no further correct work is shown. [1] Appropriate work is shown, but one conceptual error and one graphing error are made, but an appropriate point in the solution set is stated. or [1] Both inequalities are graphed incorrectly, but at least one inequality is labeled, and an appropriate point in the solution set is stated. or [9] [OVER] INTEGRATED ALGEBRA continued 1 x + 4 are graphed appropriately, and at least 3 one line is labeled, but no further correct work is shown. [1] The lines y = 2 x + 1 and y = or [1] The coordinates of a point in the solution set are stated and shown to be correct by substituting in both inequalities, but no graphs are drawn. [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. [10] INTEGRATED ALGEBRA continued (38) [4] Hat A and an appropriate justification is given, and 1 color that is not green in hat A, 11 green in hat B, and none in hat C, and appropriate work is shown. [3] Appropriate work is shown, but one computational error is made, but an appropriate justification is given. or [3] Appropriate work is shown, but no justification or an incorrect justification is given. or [3] Hat A and an appropriate justification is given, but only the correct number of marbles for hat A and hat C is found, and no further correct work is shown. or [3] Hat A and an appropriate justification is given, but a method described to create 1 P(G) = in each hat involves both addition and subtraction. 2 [2] Appropriate work is shown, but two or more computational errors are made, but an appropriate justification is given. or [2] Appropriate work is shown, but one conceptual error is made, but an appropriate justification is given. or [2] Hat A and an appropriate justification is given, but no further correct work is shown. or [2] One color that is not green in hat A, 11 green in hat B, and none in hat C, but no further correct work is shown. [1] Appropriate work is shown, but one conceptual error and one computational error are made, but an appropriate justification is given. or [1] Hat A, and 1 color that is not green in hat A and 11 green in hat B, but no work and no justification are shown. [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. [11] [OVER] INTEGRATED ALGEBRA continued (39) [4] 84 and 71, and appropriate work is shown. [3] Appropriate work is shown, but one computational or rounding error is made. [2] Appropriate work is shown, but two or more computational or rounding errors are made. or [2] Appropriate work is shown, but one conceptual error is made, such as using an incorrect trigonometric function. or [2] Correct trigonometric equations are written, but no further correct work is shown. or [2] Appropriate work is shown to find 84 or 71, but no further correct work is shown. [1] Appropriate work is shown, but one conceptual error and one computational or rounding error are made. or [1] One correct trigonometric equation is written, but no further correct work is shown. or [1] 84 and 71, but no work is shown. [0] 84 or 71, but no work is shown. or [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. [12] INTEGRATED ALGEBRA concluded Map to Core Curriculum Content Strands Item Numbers Number Sense and Operations 6, 7, 28, 33 Algebra 2, 3, 4, 5, 8, 9, 11, 12, 13, 14, 16, 18, 21, 22, 26, 27, 29, 30, 31, 36, 39 Geometry 10, 15, 19, 25, 35, 37 Measurement 23, 32 Statistics and Probability 1, 17, 20, 24, 34, 38 Regents Examination in Integrated Algebra August 2010 Chart for Converting Total Test Raw Scores to Final Examination Scores (Scale Scores) The Chart for Determining the Final Examination Score for the August 2010 Regents Examination in Integrated Algebra will be posted on the Department s web site http://www.emsc.nysed.gov/osa/ on Wednesday, August 18, 2010. Conversion charts provided for previous administrations of the Integrated Algebra examination must NOT be used to determine students final scores for this administration. Online Submission of Teacher Evaluations of the Test to the Department Suggestions and feedback from teachers provide an important contribution to the test development process. The Department provides an online evaluation form for State assessments. It contains spaces for teachers to respond to several specific questions and to make suggestions. Instructions for completing the evaluation form are as follows: 1. Go to http://www.emsc.nysed.gov/osa/teacher/evaluation.html 2 . Select the test title. 3. Complete the required demographic fields. 4. Complete each evaluation question and provide comments in the space provided. 5. Click the SUBMIT button at the bottom of the page to submit the completed form. [13]

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Additional Info : Scoring key: page 29
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