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New York Regents Korean Integrated Algebra January 2009

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KOREAN EDITION INTEGRATED ALGEBRA THURSDAY, JANUARY 29, 2009 1:15 P.M. to 4:15 P.M., ONLY INTEGRATED ALGEBRA The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION 2009 1 29 1 15 - 4 15 : : . 1 . , . . . . , . , . II, III, IV , . , . , 39 . . , I . II, III, IV . , , , . , . . : ( ) . , . . . INTEGRATED ALGEBRA I . 2 . . [60] 1 , 15 (C) . , (F) . 15 C ? (1) 9 (2) 35 (3) 59 (4) 85 2 6 24 ? (1) 144 (2) 30 (3) 18 (4) 4 3 1 6 . , ? (1) (2) (3) (4) 6 4 Integrated Algebra Jan. 09 [2] . 4 7 19 . 29 50 . ? (1) 150 (2) 271 . (3) 421 (4) 692 5 . ? (1) (3) (2) (4) ? 6 (1) 1 (2) 5 Integrated Algebra Jan. 09 (3) 6 (4) 14 [3] [ ] 7 60 , 74 , 82 , 87 , 87 , 94 . ? (1) < < (3) < < (2) < < (4) < < 8 64 . , . r t ? (1) t = 64(r)0.5 (2) t = 64( 0.5)r (3) t = 64(1.5)r (4) t = 64(0.5)r 9 9x2 100 ? (1) (9x 10)(x + 10) (2) (3x 10)(3x + 10) (3) (3x 100)(3x 1) (4) (9x 100)(x + 1) 10 (3, 3) ( 3, 3) ? (1) y = 3 (2) x = 3 Integrated Algebra Jan. 09 (3) y = 3 (4) x = y [4] . 11 P = 2l + 2w , w ? (1) (3) (2) . (4) 12 , x ? (1) 12 (2) 14 (3) 21 (4) 28 13 (2,5) (7,3) ? (1) (3) (2) (4) Integrated Algebra Jan. 09 [5] [ ] 14 x 10x + 21 = 0 ? 2 (1) 1 21 (2) 5 5 (3) 3 7 (4) 3 7 15 1 35 . , x ? (1) 0.05(x + 6) + 0.10x = 1.35 (2) 0.05x + 0.10(x + 6) = 1.35 (3) 0.05 + 0.10(6x) = 1.35 (4) 0.15(x + 6) = 1.35 16 ? (1) y = 3 (2) x = 3 Integrated Algebra Jan. 09 (3) y = 25 (4) x = 25 [6] . 17 ? . (1) (2) (3) (4) 18 x ? (1) 8 (3) (2) (4) 8 19 UPC . U ? (1) (3) (2) (4) Integrated Algebra Jan. 09 [7] [ ] 20 ? (1) (2) (3) (4) 21 ? (1) (3) (2) (4) 22 y = x2 x 20 y = 3x 15? ? (1) ( 5, 30) (2) ( 1, 18) (3) (0,5) (4) (5, 1) 23 . ? (1) 10 (2) 25 (3) 50 (4) 75 Integrated Algebra Jan. 09 [8] . 24 w 7 . ? (1) 3w 4 (2) 3w 7 (3) 3w2 4w (4) 3w2 7w 25 x ? (1) 0 3 (2) 3 3 . (3) 3 (4) 3 26 y = 3 2x ? (1) 4x + 2y = 5 (2) 2x + 4y = 1 Integrated Algebra Jan. 09 (3) y = 3 4x (4) y = 4x 2 [9] [ ] 27 8.4 108 4.2 103 ? (1) 2.0 105 (2) 12.6 1011 (3) 35.28 1011 (4) 3.528 1012 28 . , . , ? (1) (3) (2) (4) Integrated Algebra Jan. 09 [10] . 29 . . . ? (1) 600 . (2) 400 . (3) 300 600 . (4) 300 400 . 30 ? (1) (3) (2) (4) Integrated Algebra Jan. 09 [11] [ ] II . 2 , , , . , 1 . [6] 31 . , . ? Integrated Algebra Jan. 09 [12] 32 : Integrated Algebra Jan. 09 [13] [ ] 33 . h d . , 40 . Integrated Algebra Jan. 09 [14] III . 3 . , , , . , 1 . [9] 34 . 36 42 . 36.5 42.5 . . . . . Integrated Algebra Jan. 09 [15] [ ] 35 : Integrated Algebra Jan. 09 [16] 36 . 342 cm3 , 6 cm . ( ) . 36 cm , . . Integrated Algebra Jan. 09 [17] [ ] IV . 4 . , , , . , 1 . [12] 37 : 3x + 2y = 4 4x + 3y = 7 [ .] Integrated Algebra Jan. 09 [18] 38 , , . Integrated Algebra Jan. 09 [19] [ ] 39 , , , . . ? . . . . Integrated Algebra Jan. 09 [20] Integrated Algebra Jan. 09 [23] [ ] Integrated Algebra Jan. 09 [24] The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION 2009 1 29 1 15 - 4 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I . I 30 . 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 . . . . . . . . . . . . . . . . . II, III IV . . . Integrated Algebra Jan. 09 [27] INTEGRATED ALGEBRA Rater s/Scorer s Name (minimum of three) INTEGRATED ALGEBRA Maximum Credit Part I 1 30 60 Part II 2 32 Part III 2 34 3 35 3 36 Part IV Checked by 2 33 Rater s/Scorer s Initials Total Raw Score 31 Credits Earned Question 3 37 4 38 4 39 4 Maximum Total 87 Scaled Score (from conversion chart) [28] INTEGRATED ALGEBRA Integrated Algebra Jan. 09 FOR TEACHERS ONLY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA Thursday, January 29, 2009 1:15 to 4:15 p.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 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/ o n Thursday, January 29, 2009. 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) 3 (9) 2 (17) 3 (25) 2 (2) 4 (10) 3 (18) 1 (26) 1 (3) 4 (11) 2 (19) 2 (27) 4 (4) 1 (12) 3 (20) 3 (28) 1 (5) 1 (13) 2 (21) 2 (29) 4 (6) 3 (14) 3 (22) 2 (30) 4 (7) 4 (15) 2 (23) 1 (8) 4 (16) 2 (24) 4 [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 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). 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] 50, and appropriate work is shown. [1] Appropriate work is shown, but one computational or rounding error is made. or [1] Appropriate work is shown, but one conceptual error is made. or [1] 50, 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] 3k 2 m6 or an equivalent answer, and appropriate work is shown. 4 [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] 3k 2 m6 , but no work is shown. 4 [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] d = 6.25h or an equivalent equation and 250, 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] A correct equation is written, but no further correct work is shown. or [1] Appropriate work is shown to find 250, but the equation is missing or is incorrect. [0] 250, 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. [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] 1,512 and 1,551.25 and 0.025, and appropriate work is shown. [2] Appropriate work is shown, but one computational or rounding error is made. [1] Appropriate work is shown, but two or more computational or rounding errors are made. or [1] Appropriate work is shown, but one conceptual error is made, such as dividing by 1,512. or [1] Appropriate work is shown to find 1,512 and 1,551.25, but no further correct work is shown. or [1] 1,512 and 1,551.25 and 0.025, but no work is shown. [0] 1,512 or 1,551.25 or 0.025, 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. (35) [3] 3 3 or , and appropriate work is shown. 4( x 2) 4x 8 [2] Appropriate work is shown, but one computational, factoring, or simplification error is made. [1] Appropriate work is shown, but two or more computational, factoring, or simplification errors are made. or [1] Appropriate work is shown, but one conceptual error is made. or [1] 3 3 or , but no work is shown. 4( x 2) 4x 8 [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 (36) [3] 38 or an equivalent answer in terms of , and 2, and appropriate work is shown, and an appropriate explanation is given. [2] Appropriate work is shown, but one computational or rounding error is made, but an appropriate explanation is given. or [2] Appropriate work is shown and an appropriate explanation is given, but the correct height of the can is expressed as a decimal. or [2] 38 and 2, and appropriate work is shown, but an appropriate explanation is not given. [1] Appropriate work is shown, but two or more computational or rounding errors are made, but an appropriate explanation is given. or [1] Appropriate work is shown, but one conceptual error is made, but an appropriate explanation is given. or [1] [0] 38 38 and 2, but no work is shown. or 2, 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 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] ( 2,5) or x = 2 and y = 5, and appropriate algebraic work is shown. [3] Appropriate algebraic work is shown, but one computational error is made, but appropriate values are found for x and y. or [3] x = 2 or y = 5, and appropriate algebraic work is shown. [2] Appropriate algebraic work is shown, but two or more computational errors are made, but appropriate values are found for x and y. or [2] Appropriate algebraic work is shown, but one conceptual error is made. or [2] ( 2,5) or x = 2 and y = 5, but a method other than an algebraic method is used. [1] Appropriate algebraic work is shown, but one conceptual error and one computational error are made. or [1] The trial-and-error method is used to find the correct solution, but fewer than three trials and appropriate checks are shown. or [1] x = 2 or y = 5, but a method other than an algebraic method is used. or [1] ( 2,5) or x = 2 and y = 5, but no work is shown. [0] x = 2 or y = 5, 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. [8] INTEGRATED ALGEBRA continued (38) [4] Both inequalities are graphed and shaded correctly, and at least one is labeled, and a point in the solution set is identified. [3] Appropriate work is shown, but one graphing error is made, such as drawing a solid line for x > 2 or shading incorrectly, but an appropriate point in the solution set is identified. or [3] Both inequalities are graphed and shaded correctly, and a point in the solution set is identified correctly, but the graphs are not labeled or are labeled incorrectly. or [3] Both inequalities are graphed and shaded correctly, and at least one is labeled, but no point in the solution set is identified. [2] Appropriate work is shown, but two or more graphing errors are made, but an appropriate point in the solution set is identified. or [2] Appropriate work is shown, but one conceptual error is made, such as graphing the lines x = 2 and y = 2x 6 and identifying the point of intersection. or [2] One of the inequalities is graphed and shaded correctly, and at least one is labeled, 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 identified. or [1] Both inequalities are graphed incorrectly, but an appropriate point in the solution set is identified. or [1] The lines x = 2 and y = 2x 6 are graphed correctly, and at least one is labeled, but no further correct work is shown. or [1] A point in the solution set is identified and shown to be correct by checking 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. [9] [OVER] INTEGRATED ALGEBRA continued (39) [4] A correct tree diagram or sample space is given, and 18 total meals, 12 meals without juice, and 6 meals with chicken nuggets. [3] A correct tree diagram or sample space is given, but either 18, 12, or 6 is missing or is incorrect. or [3] The fundamental counting principle is used to find 18 total meals, 12 meals without juice, and 6 meals with chicken nuggets, but no tree diagram or sample space is given. or [3] An incorrect tree diagram or sample space is given, but an appropriate number of meals is found for all three categories. [2] A correct tree diagram or sample space is given, but an appropriate number of meals is found for only one category. or [2] An incorrect tree diagram or sample space is given, but an appropriate number of meals is found for only two categories. [1] A correct tree diagram or sample space is given, but no number of meals is found correctly. or [1] An incorrect tree diagram or sample space is given, but an appropriate number of meals is found for only one category. or [1] 18 total meals, 12 meals without juice, and 6 meals with chicken nuggets, but no work is shown. [0] 18 total meals or 12 meals without juice or 6 meals with chicken nuggets, 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. [10] INTEGRATED ALGEBRA concluded Map to Learning Standards Key Ideas Item Numbers Number Sense and Operations 20, 27, 33 Algebra 4, 6, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 21, 22, 24, 25, 26, 32, 35, 37 Geometry 5, 16, 30, 31, 36, 38 Measurement 1, 2, 34 Probability and Statistics 3, 7, 23, 28, 29, 39 Regents Examination in Integrated Algebra January 2009 Chart for Converting Total Test Raw Scores to Final Examination Scores (Scaled Scores) The Chart for Determining the Final Examination Score for the January 2009 Regents Examination in Integrated Algebra will be posted on the Department s web site http://www.emsc.nysed.gov/osa/ on Thursday, January 29, 2009. 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. Go to www.emsc.nysed.gov/osa/exameval. 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. [11] [12]

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Additional Info : Refer : Formulas (page 23) and Scoring Key (page 29)
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