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New York Regents Integrated Algebra August 2008

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INTEGRATED ALGEBRA The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA Wednesday, August 13, 2008 8:30 to 11:30 a.m., only Print Your Name: Print Your School s Name: Print your name and the name of your school in the boxes 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. 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. All work should be written in pen, except graphs and drawings, which should be done in pencil. 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. 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. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. 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 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 Which value of p is the solution of 5p 1 = 2p + 20? 19 (1) (3) 3 7 19 (2) 3 (4) 7 2 The statement 2 + 0 = 2 is an example of the use of which property of real numbers? (1) associative (3) additive inverse (2) additive identity (4) distributive 3 Mrs. Smith wrote Eight less than three times a number is greater than fifteen on the board. If x represents the number, which inequality is a correct translation of this statement? (1) 3x 8 > 15 (3) 8 3x > 15 (2) 3x 8 < 15 (4) 8 3x < 15 Integrated Algebra Aug. 08 [2] Use this space for computations. 4 Which statement is true about the data set 3, 4, 5, 6, 7, 7, 10? (1) mean = mode (3) mean = median (2) mean > mode Use this space for computations. (4) mean < median 5 Which value of x is in the solution set of the inequality 4x + 2 > 10? (1) 2 (3) 3 (2) 2 (4) 4 6 Factored completely, the expression 2x2 + 10x 12 is equivalent to (1) 2(x 6)(x + 1) (3) 2(x + 2)(x + 3) (2) 2(x + 6)(x 1) (4) 2(x 2)(x 3) Integrated Algebra Aug. 08 [3] [OVER] 7 The gas tank in a car holds a total of 16 gallons of gas. The car travels 75 miles on 4 gallons of gas. If the gas tank is full at the beginning of a trip, which graph represents the rate of change in the amount of gas in the tank? y Gas in Tank (gallons) 16 14 12 10 8 6 4 2 30 60 90 120 150 180 210 240 270 300 0 x 16 14 12 10 8 6 4 2 0 30 60 90 120 150 180 210 240 270 300 Gas in Tank (gallons) y Distance (miles) Distance (miles) (1) (3) 16 14 12 10 8 6 4 2 x 16 14 12 10 8 6 4 2 0 30 60 90 120 150 180 210 240 270 300 Gas in Tank (gallons) y 30 60 90 120 150 180 210 240 270 300 Gas in Tank (gallons) y 0 x Distance (miles) Distance (miles) (2) (4) 8 If 3ax + b = c, then x equals (1) c b + 3a (2) c + b 3a Integrated Algebra Aug. 08 c b 3a (4) b3a c (3) [4] x Use this space for computations. 9 The length of the hypotenuse of a right triangle is 34 inches and the length of one of its legs is 16 inches. What is the length, in inches, of the other leg of this right triangle? (1) 16 (3) 25 (2) 18 Use this space for computations. (4) 30 10 Which equation represents a line parallel to the x-axis? 1 (1) x = 5 (3) x = 3 y (2) y = 10 (4) y = 5x + 17 11 Sam and Odel have been selling frozen pizzas for a class fundraiser. Sam has sold half as many pizzas as Odel. Together they have sold a total of 126 pizzas. How many pizzas did Sam sell? (1) 21 (3) 63 (2) 42 (4) 84 12 Which ordered pair is in the solution set of the system of equations y = x + 1 and y = x2 + 5x + 6? (1) ( 5, 1) (3) (5, 4) (2) ( 5,6) (4) (5,2) Integrated Algebra Aug. 08 [5] [OVER] 13 A swim team member performs a dive from a 14-foot-high springboard. The parabola below shows the path of her dive. y 24 Height (feet) 20 16 12 8 4 0 2 4 6 8 x 10 Distance from Springboard (feet) Which equation represents the axis of symmetry? (1) x = 3 (3) x = 23 (2) y = 3 (4) y = 23 14 Nicole s aerobics class exercises to fast-paced music. If the rate of the music is 120 beats per minute, how many beats would there be in a class that is 0.75 hour long? (1) 90 (3) 5,400 (2) 160 (4) 7,200 Integrated Algebra Aug. 08 [6] Use this space for computations. 15 Luis is going to paint a basketball court on his driveway, as shown in the diagram below. This basketball court consists of a rectangle and a semicircle. Use this space for computations. 8 ft 10 ft Which expression represents the area of this basketball court, in square feet? (1) 80 (3) 80 + 16 (2) 80 + 8 (4) 80 + 64 16 John is going to line up his four golf trophies on a shelf in his bedroom. How many different possible arrangements can he make? (1) 24 (3) 10 (2) 16 (4) 4 Integrated Algebra Aug. 08 [7] [OVER] 17 A rectangle has an area of 24 square units. The width is 5 units less than the length. What is the length, in units, of the rectangle? (1) 6 (3) 3 (2) 8 (4) 19 18 What is the value of the third quartile shown on the box-and-whisker plot below? 0 3 6 (1) 6 12 (3) 10 (2) 8.5 9 (4) 12 19 When 3g2 4g + 2 is subtracted from 7g2 + 5g 1, the difference is (1) 4g2 9g + 3 (3) 4g2 + 9g 3 (2) 4g2 + g + 1 (4) 10g2 + g + 1 20 Which value of x is the solution of 2x + 1 = 7x - 2 ? 53 15 3 (1) __ 5 (3) 3 31 (2) ___ 26 (4) 7 Integrated Algebra Aug. 08 [8] Use this space for computations. 21 Which expression represents 5 (1) x (2) -5 x 25x - 125 in simplest form? x 2 - 25 25 (3) x-5 25 (4) x+5 Use this space for computations. 22 Which equation most closely represents the line of best fit for the scatter plot below? Money Earned from Babysitting Money (dollars) y 12 11 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12 x Babysitting Time (hours) (1) y = x 3 (3) y = 2 x + 4 2 (2) y = 3 x + 1 3 (4) y = 2 x + 1 23 In a linear equation, the independent variable increases at a constant rate while the dependent variable decreases at a constant rate. The slope of this line is (1) zero (3) positive (2) negative (4) undefined Integrated Algebra Aug. 08 [9] [OVER] 24 Which equation could be used to find the measure of one acute angle in the right triangle shown below? A 5 C B 4 4 (1) sin A = 5 5 (3) cos B = 4 5 (2) tan A = 4 4 (4) tan B = 5 25 Which ordered pair is in the solution set of the following system of inequalities? y< 1 x+4 2 y x + 1 (1) ( 5,3) (3) (3, 5) (2) (0,4) (4) (4,0) x2 - 1 4x 26 What is the product of x - 1 and 3x + 3 expressed in simplest form? 4x (1) 3 (3) 4x 2 3 (x + 1 ) 4x 2 3 (4) 4 (x + 1) 3 (2) Integrated Algebra Aug. 08 [10] Use this space for computations. Use this space for computations. 23 27 Which expression is equivalent to (3x ) ? (1) 9x5 (3) 27x5 (2) 9x6 (4) 27x6 28 Ryan estimates the measurement of the volume of a popcorn container to be 282 cubic inches. The actual volume of the popcorn container is 289 cubic inches. What is the relative error of Ryan s measurement to the nearest thousandth? (1) 0.024 (3) 0.096 (2) 0.025 (4) 1.025 29 In the diagram of ABC shown below, BC = 10 and AB = 16. B C A To the nearest tenth of a degree, what is the measure of the largest acute angle in the triangle? (1) 32.0 (3) 51.3 (2) 38.7 (4) 90.0 Integrated Algebra Aug. 08 [11] [OVER] 30 The faces of a cube are numbered from 1 to 6. If the cube is tossed once, what is the probability that a prime number or a number divisible by 2 is obtained? 6 (1) __ 6 5 (2) __ 6 Integrated Algebra Aug. 08 4 (3) __ 6 1 (4) __ 6 [12] Use this space for computations. Part II Answer all 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] 31 In a game of ice hockey, the hockey puck took 0.8 second to travel 89 feet to the goal line. Determine the average speed of the puck in feet per second. Integrated Algebra Aug. 08 [13] [OVER] 32 Brianna is using the two spinners shown below to play her new board game. She spins the arrow on each spinner once. Brianna uses the first spinner to determine how many spaces to move. She uses the second spinner to determine whether her move from the first spinner will be forward or backward. 1 2 Backward 4 Forward 3 Find the probability that Brianna will move fewer than four spaces and backward. Integrated Algebra Aug. 08 [14] 33 Twelve players make up a high school basketball team. The team jerseys are numbered 1 through 12. The players wearing the jerseys numbered 3, 6, 7, 8, and 11 are the only players who start a game. Using set notation, list the complement of this subset. Integrated Algebra Aug. 08 [15] [OVER] Part III Answer all 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 Express the product of 3 20 (2 5 7) in simplest radical form. Integrated Algebra Aug. 08 [16] 35 On the set of axes below, draw the graph of y = 2 x over the interval -1 # x # 3. Will this graph ever intersect the x-axis? Justify your answer. y x Integrated Algebra Aug. 08 [17] [OVER] 36 Write an equation that represents the line that passes through the points (5,4) and ( 5,0). Integrated Algebra Aug. 08 [18] Part IV Answer all 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 The cost of 3 markers and 2 pencils is $1.80. The cost of 4 markers and 6 pencils is $2.90. What is the cost of each item? Include appropriate units in your answer. Integrated Algebra Aug. 08 [19] [OVER] 38 Twenty students were surveyed about the number of days they played outside in one week. The results of this survey are shown below. {6, 5, 4, 3, 0, 7, 1, 5, 4, 4, 3, 2, 2, 3, 2, 4, 3, 4, 0, 7} Complete the frequency table below for these data. Number of Days Outside Interval Tally Frequency 0 1 2 3 4 5 6 7 Complete the cumulative frequency table below using these data. Number of Days Outside Interval Cumulative Frequency 0 1 0 3 0 5 0 7 This question continues on the next page. Integrated Algebra Aug. 08 [20] Question 38 continued On the grid below, create a cumulative frequency histogram based on the table you made on the previous page. Integrated Algebra Aug. 08 [21] [OVER] 39 On the set of axes below, solve the following system of equations graphically and state the coordinates of all points in the solution set. y = x2 + 4x 5 y=x 1 y x Integrated Algebra Aug. 08 [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 Tear Here cylinder Coordinate Geometry Integrated Algebra Aug. 08 SA = 2 r2 + 2 rh y y2 y1 m = x = x x 2 1 [23] Tear Here Tear Here Integrated Algebra Aug. 08 [24] 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 13, 2008 8:30 to 11:30 a.m., only ANSWER SHEET Male Female Student . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sex: 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 should 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 Aug. 08 [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 Scaled Score (from conversion chart) Tear Here [28] INTEGRATED ALGEBRA Integrated Algebra Aug. 08 FOR TEACHERS ONLY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA Wednesday, August 13, 2008 8:30 to 11:30 a.m., only SCORING KEY 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 Examination in Integrated Algebra. 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 scaled score by using the conversion chart that will be posted on the Department s web site http://www.emsc.nysed.gov/osa/ on Wednesday, August 13, 2008. The student s scaled score should be entered in the box provided on the student s detachable answer sheet. The scaled 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) 4 (9) 4 (17) 2 (25) 4 (2) 2 (10) 2 (18) 3 (26) 1 (3) 1 (11) 2 (19) 3 (27) 4 (4) 3 (12) 2 (20) 4 (28) 1 (5) 4 (13) 1 (21) 4 (29) 3 (6) 2 (14) 3 (22) 4 (30) 2 (7) 2 (15) 2 (23) 2 (8) 3 (16) 1 (24) 1 [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. I. 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 Examination in Integrated Algebra, 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, 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). [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) 1 [2] 111.25 or 111 4 , and appropriate work is shown. [1] Appropriate work is shown, but the answer is rounded. or [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] 111.25, 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] 3 8 or 0.375, and appropriate work is shown. [1] Appropriate work is shown, but the answer is rounded. or [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] 3 8, 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] {1, 2, 4, 5, 9, 10, 12} or {x | x = 1, 2, 4, 5, 9, 10, 12} [1] 1, 2, 4, 5, 9, 10, 12, but set notation is not used. or [1] Set notation is used and at least five correct numbers (but not the entire set) are written. [0] Set notation is used, but fewer than five correct numbers are written. or [0] {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} 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] 60 42 5 , and appropriate work is shown. [2] Appropriate work is shown, but one computational error is made. or [2] Appropriate work is shown, but only one term is expressed in simplest radical form. [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, but the answer is expressed as a decimal. or [1] The distributive property is correctly applied, yielding 6 100 21 20 , but no further correct work is shown. or [1] 60 42 5 , 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. [6] INTEGRATED ALGEBRA continued (35) [3] A correct graph is drawn over the given interval, the function is identified as one that will not intersect the x-axis, and an appropriate justification is given. [2] Appropriate work is shown, but one graphing error is made, but an appropriate answer and justification are given. or [2] A correct graph is drawn over the given interval, but no further correct work is shown. [1] Appropriate work is shown, but two or more graphing errors are made, but an appropriate answer and justification are given. or [1] Appropriate work is shown, but one conceptual error is made, but an appropriate answer and justification are given. [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. (36) 2 2 [3] y 4 = 5 (x 5) or y = 5 x + 2 or an equivalent equation, and appropriate work is shown. [2] Appropriate work is shown, but one computational error is made. or [2] Appropriate work is shown to find the slope and y-intercept, but an equation is not written or is written incorrectly. [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 the slope or y-intercept, but an equation is not written or is written incorrectly. or 2 2 [1] y 4 = 5 (x 5) or y = 5 x + 2, 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. [7] [OVER] 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] A marker = $.50 or 50 and a pencil = $.15 or 15 , and appropriate work is shown, such as solving a system of equations algebraically or by trial and error with at least three trials and appropriate checks. [3] Appropriate work is shown, but one computational error is made. or [3] Appropriate work is shown, but only the cost of a marker or a pencil is found, but appropriate units are written. or [3] Appropriate work is shown, but the correct answers are not labeled or are labeled incorrectly, but appropriate units are written. or [3] Appropriate work is shown, and the answers are labeled correctly, but the units are written incorrectly, such as a marker = .50 . [2] Appropriate work is shown, but two or more computational errors are made. or [2] Appropriate work is shown, but one conceptual error is made. or [2] Appropriate work is shown, but the answers are not labeled or are labeled incorrectly, and the units are not written or are written incorrectly. or [2] An incorrect system of equations is written, but two appropriate answers are found and labeled, and appropriate units are written. or [2] The trial-and-error method is used to find the correct answers, but only two trials and appropriate checks are shown. or [2] The trial-and-error method is attempted and at least six systematic trials and appropriate checks are shown, but no answers are found. [1] Appropriate work is shown, but one conceptual error and one computational error are made. or [1] A correct system of equations is written, but no further correct work is shown. or [8] INTEGRATED ALGEBRA continued [1] The trial-and-error method is used to find the correct answers, but only one trial with an appropriate check is shown. or [1] A marker = $.50 or 50 and a pencil = $.15 or 15 , but no work is shown. [0] One correct equation is written, but no further correct work is shown. or [0] Either the correct price of a marker or a pencil is stated, but no work is shown. or [0] The correct prices of the marker and pencil are found, but no work is shown, and the answers are not labeled or are labeled incorrectly. or [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. [9] [OVER] INTEGRATED ALGEBRA continued (38) [4] The tables are completed correctly, and a correct cumulative frequency histogram is drawn and labeled. [3] The tables are completed correctly, but one graphing error is made on the cumulative frequency histogram. or [3] The tables are completed with one error, but an appropriate cumulative frequency histogram is drawn and labeled. or [3] The tables are completed correctly and a correct cumulative frequency histogram is drawn, but the histogram is not labeled or is labeled incorrectly. [2] The tables are completed with two errors, but an appropriate cumulative frequency histogram is drawn and labeled. or [2] Appropriate work is shown, but one conceptual error is made, such as drawing a frequency histogram or a cumulative frequency bar graph. or [2] The tables are completed correctly, but no further correct work is shown. [1] Appropriate work is shown, but one conceptual error and one graphing or labeling error are made on the cumulative frequency histogram. or [1] The frequency table is completed correctly, but no further correct 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. [10] INTEGRATED ALGEBRA continued (39) [4] Appropriate graphs are drawn, and (1,0) and ( 4, 5) are stated. [3] Appropriate work is shown, but one graphing error is made, but appropriate solutions are stated. or [3] Both graphs are drawn correctly, but only one solution is stated. [2] Appropriate work is shown, but two or more graphing errors are made, but appropriate solutions are stated. or [2] Appropriate work is shown, but one conceptual error is made, such as graphing a line instead of a parabola, but appropriate solutions are stated. or [2] Both graphs are drawn correctly, but no solutions are stated. or [2] (1,0) and ( 4, 5) are found as the points of intersection, but a method other than graphic is used. [1] The system is solved algebraically for only the x values, y values, or the coordinates of one point. or [1] Appropriate work is shown, but one graphing error and one conceptual error are made. or [1] One graph is drawn correctly, but no further correct work is shown. or [1] (1,0) and ( 4, 5) are stated, but no work is shown. [0] (1,0) or ( 4, 5) is stated, 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. [11] [OVER] INTEGRATED ALGEBRA concluded Map to Learning Standards Key Ideas Item Numbers Number Sense and Operations 2, 16, 34 Algebra 1, 3, 5, 6, 8, 9, 10, 11, 12, 17, 19, 20, 21, 23, 24, 25, 26, 27, 29, 33, 36, 37 Geometry 7, 13, 15, 35, 39 Measurement 14, 28, 31 Probability and Statistics 4, 18, 22, 30, 32, 38 Regents Examination in Integrated Algebra August 2008 Chart for Converting Total Test Raw Scores to Final Examination Scores (Scaled Scores) The Chart for Determining the Final Examination Score for the August 2008 Regents Examination in Integrated Algebra will be posted on the Department s web site http://www.emsc.nysed.gov/osa/ on Wednesday, August 13, 2008. Conversion charts provided for previous administrations of the Integrated Algebra examination must NOT be used to determine students final scores for this administration. Submitting 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. 2. 3. 4. 5. Go to www.emsc.nysed.gov/osa/exameval. Select the test title. Complete the required demographic fields. Complete each evaluation question and provide comments in the space provided. Click the SUBMIT button at the bottom of the page to submit the completed form. [12]

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Additional Info : Refer end of paper for Scoring Key (page 29)
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