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New York Regents Korean Integrated Algebra June 2010

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INTEGRATED ALGEBRA The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION KOREAN EDITION INTEGRATED ALGEBRA FRIDAY, JUNE 18, 2010 1:15 P.M. to 4:15 P.M., ONLY 2010 6 18 , 1 15 - 4 15 : ____________________________________________________________ : _________________________________________________________________ . I . . . , 39 . . I . II, III IV . , . , , , . . . . . . . . . ( ) . , . , . . INTEGRATED ALGEBRA KOREAN EDITION I 30 . 2 . . [60] . 1 : U = {S, O, P, H, I, A} B = {A, I, O} B U , B ? (1) {O, P, S} (3) {A, H, P} (2) {I, P, S} (4) {H, P, S} 2 , , , , ? (1) 10 (3) 15 (2) 13 (4) 30 3 4x3 + 6x2 + 2x 3 3x3 + 3x2 5x 5 ? (1) 7x3 + 3x2 3x 8 (3) 7x3 + 9x2 3x 8 (2) 7x3 + 3x2 + 7x + 2 (4) 7x6 + 9x4 3x2 8 Integrated Algebra June 10 Korean Edition [2] . 4 (3,5) ( 2,2) ? (1) 1 5 (2) 3 5 (3) 5 3 (4) 5 5 ? y x (1) : (1, 4); : x = 1 (2) : (1, 4); : x = 4 (3) : ( 4,1); : x = 1 (4) : ( 4,1); : x = 4 Integrated Algebra June 10 Korean Edition [3] [ ] 6 11 , , , . , 40 . . 15 13 12 , ? 1 3 3 (2) 5 (1) 3 8 5 (4) 8 (3) 7 (1,3) ? (1) x + 2y = 5 (3) 2x + y = 5 (2) x 2y = 5 (4) 2x y = 5 8 72 3 2 ? (1) 5 2 (3) 3 2 (2) 3 6 (4) Integrated Algebra June 10 Korean Edition 6 [4] . 9 ABC B = 90 , AC = 50, AB = 48, BC = 14 . A ? (1) 14 50 (2) 14 48 . (3) 48 50 (4) 48 14 10 ? y x (1) (1, 4) (3) (5,3) (2) ( 5,7) (4) ( 7, 2) Integrated Algebra June 10 Korean Edition [5] [ ] . 11 ? (1) ( ) ( ) 39 50 48 70 60 90 (2) 15 300 20 400 25 500 70 12 80 15 90 6 (3) (4) ( ) ( 40 80 50 120 55 ) 150 12 c + 3d = 8 c = 4d 6 ? (1) c = 14, d = 2 (3) c = 2, d = 2 (2) c = 2, d = 2 (4) c = 14, d = 2 Integrated Algebra June 10 Korean Edition [6] . 13 ? y y x x (1) (3) y y x x (2) (4) (1) 0 x 2 x ? x2 9 (3) 3 (2) 2 (4) 9 14 Integrated Algebra June 10 Korean Edition [7] [ ] 15 y = 2x 7 y kx = 7 k ? (1) 2 (3) 7 (2) 2 (4) 7 1 (n 3) ? 2 (1) n 3 16 (2) 3 n (3) n 3 (4) n 3 17 12 . . 1 2 3 4 5 6 7 8 9 10 11 12 20 35 32 45 58 46 28 23 31 79 65 62 2 ? (1) 29.5 (3) 40 (2) 30.5 (4) 60 Integrated Algebra June 10 Korean Edition [8] . . 14a2 c8 18 7a3 c2 ? 2c 4 a (1) 2ac4 (3) (2) 2ac6 6 (4) 2c a 19 x + x+1 = x x ? 3 2 (1) 1 (3) 3 (2) 1 (4) 3 20 36 , . ? (1) 9 (3) 3 (2) 6 (4) 4 21 5 12 ? (1) [5, 12) (3) (5, 12) (2) (5, 12] (4) [5, 12] Integrated Algebra June 10 Korean Edition [9] [ ] 22 400 . . 16 25 150 26 35 129 36 45 33 46 55 57 56 65 31 ? (1) 16 . (2) . (3) . (4) . 12 23 v = 2 at . a v t ? 2v (1) a = t 2v (2) a = 2 t v (3) a = t (4) a = v2 2t Integrated Algebra June 10 Korean Edition [10] . 24 x + 7 2x + 4 (1) x + 12 2x + 4 (2) 3x + 12 2x + 4 . 2x + 5 ? 2x + 4 (3) x + 12 4x + 8 (4) 3x + 12 4x + 8 1 25 150 1 . 2 ? (1) 6 (3) 100 (2) 60 (4) 6,000 26 ABSOLUTE , ? (1) 56 (3) 168 (2) 112 (4) 336 27 3x2 3x 18 ? (1) 3(x2 x 6) (3) (3x 9)(x + 2) (2) 3(x 3)(x + 2) (4) (3x + 6)(x 3) Integrated Algebra June 10 Korean Edition [11] [ ] 28 y 2x ? (1) 1 (3) 3 (2) 2 (4) 4 29 . 6 cm 5 cm ? (1) 39.4 (3) 48.8 (2) 44.1 (4) 58.3 x 30 $15,000 x y , y = 15000(1.2) 3 . 6 ( ) ? (1) $6,600 (3) $21,600 (2) $10,799 (4) $25,799 Integrated Algebra June 10 Korean Edition [12] . II 3 . 2 . , , , . 1 . [6] 31 600 . 592 . . Integrated Algebra June 10 Korean Edition [13] [ ] 32 : 6(a 7) . Integrated Algebra June 10 Korean Edition [14] 33 30 . , 50 . 50 30 . Integrated Algebra June 10 Korean Edition [15] [ ] III 3 . 3 . , , , . 1 . [9] 34 : A = {18, 6, 3, 12} 2 3 x + 3 < 2x 7 A . Integrated Algebra June 10 Korean Edition [16] 35 . y = |x| y= 1x 2 x y = |x| . y x Integrated Algebra June 10 Korean Edition [17] [ ] 36 . 18 $20,000 . 12 P . t( ) P( ) 1 2 3 4 5 6 7 8 9 10 11 12 3.0 2.5 4.0 5.0 6.5 5.5 7.0 6.0 7.5 7.0 9.0 9.5 P 20 18 16 14 12 10 8 6 4 2 0 2 4 6 8 10 12 14 16 18 20 t (line of best fit) . (line of best fit) , 18 . . Integrated Algebra June 10 Korean Edition [18] IV 3 . 4 . , , , . 1 . [12] 37 : Integrated Algebra June 10 Korean Edition [19] x 2 + 9x + 14 3x + 6 x 2 49 x 2 + x 56 [ ] ( ) 38 . 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2 0 41 50 41 60 41 70 41 80 41 90 41 100 ? 70 ? . . Integrated Algebra June 10 Korean Edition [20] 39 x y . y = x2 4x + 12 y = 2x + 4 y x Integrated Algebra June 10 Korean Edition [21] [ ] sin A = cos A = tan A = A = 1 h ( b 1 + b 2) 2 V = r 2h SA = 2lw + 2hw + 2lh SA = 2 r2 + 2 rh y y y m = x = x 2 x 1 2 1 Integrated Algebra June 10 Korean Edition [23] - . - . The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION 2010 6 18 , 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 June 10 Korean Edition [27] INTEGRATED ALGEBRA KOREAN EDITION 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 Part IV Maximum Total Rater s/Scorer s Initials Total Raw Score Part III Credits Earned Checked by Question 87 Scale Score (from conversion chart) [28] INTEGRATED ALGEBRA KOREAN EDITION Integrated Algebra June 10 Korean Edition FOR TEACHERS ONLY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA Friday, June 18, 2010 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 Examinations in Integrated Algebra and Geometry . 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 Friday, June 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) 4 (9) 2 (17) 3 (25) 4 (2) 4 (10) 1 (18) 4 (26) 4 (3) 3 (11) 3 (19) 3 (27) 2 (4) 2 (12) 3 (20) 1 (28) 4 (5) 1 (13) 4 (21) 1 (29) 2 (6) 3 (14) 3 (22) 4 (30) 1 (7) 3 (15) 2 (23) 2 (8) 3 (16) 4 (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. 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 Integrated Algebra and Geometry, 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] 0.014, 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, such as dividing by 600. or [1] Appropriate work is shown, but the answer is expressed as a percent. or [1] 0.014, 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] 6a + 42 , and the distributive property is stated. [1] 6a + 42 , but the property is not stated. or [1] The distributive property is stated, but the operation is not performed. [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] 37, 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, such as using an incorrect trigonometric function. or [1] A correct trigonometric equation is written, but no further correct work is shown. or [1] 37, 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. [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] 12 , and appropriate work is shown, such as solving the inequality or substituting each value into the inequality and indicating its truth value. [2] Appropriate work is shown, but one computational error is made. or [2] The inequality is solved correctly for x, but the required solution is not stated or is stated 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] 12 , 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] Both equations are graphed correctly and at least one of the graphs is labeled, and an appropriate explanation is given, such as the graph becomes wider. [2] Both equations are graphed correctly and at least one of the graphs is labeled, but no explanation or an incorrect explanation is given. or [2] One equation is graphed and labeled correctly, and an appropriate explanation is given. [1] Appropriate work is shown, but one conceptual error is made. or [1] One equation is graphed and labeled correctly, but no further correct work is shown. or [1] An appropriate explanation is given, 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. [7] [OVER] INTEGRATED ALGEBRA continued (36) [3] An appropriate line of best fit is drawn, and No, and an appropriate justification is written. [2] An appropriate line of best fit is drawn, and No, but no justification or an incorrect justification is written. or [2] The line of best fit is not drawn or is drawn incorrectly, but an appropriate prediction is stated, and an appropriate justification is written. [1] An appropriate line of best fit is drawn, but no further correct work is shown. [0] No, 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 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] x +8 , and appropriate work is shown. 3 [3] Appropriate work is shown, but one computational, factoring, or simplification error is made. [2] Appropriate work is shown, but two or more computational, factoring, or simplification errors are made. or [2] Appropriate work is shown, but one conceptual error is made, such as not multiplying by the reciprocal. or [2] The expression is correctly written as a product and all numerators and denominators are factored correctly, but no further correct work is shown. [1] Appropriate work is shown, but one conceptual error and one computational, factoring, or simplification error are made. or [1] All numerators and denominators are factored correctly, but no further correct work is shown. or [1] x +8 , but no work is shown. 3 [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] 30 students total are in the class, 20 students scored higher than 70, 71 80 is the interval containing the median, and 81 90 and 91 100 are the intervals containing the same frequency. [3] Three of the four solutions are correct. [2] Two of the four solutions are correct. [1] One of the four solutions is correct. [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] Both equations are graphed correctly, and (2,0) and ( 4,12) are stated. [3] Appropriate work is shown, but one computational or graphing error is made. or [3] Both equations are graphed correctly, but only one correct point of intersection is stated. [2] Appropriate work is shown, but two or more computational or graphing errors are made. or [2] Appropriate work is shown, but one conceptual error is made. or [2] Both equations are graphed correctly, but the points of the intersection are not stated or are stated incorrectly. or [2] (2,0) and ( 4,12), but a method other than graphic is used. [1] Appropriate work is shown, but one conceptual error and one computational or graphing error are made. or [1] One of the equations is graphed correctly, but no further correct work is shown. or [1] (2,0) and ( 4,12) are stated, but no work is shown. [0] (2,0) or ( 4,12) are 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 Core Curriculum Content Strands Item Numbers Number Sense and Operations 2, 8, 26, 32 Algebra 1, 3, 4, 7, 9, 10, 12, 14, 15, 16, 18, 19, 20, 21, 23, 24, 27, 30, 33, 34, 37 Geometry 5, 13, 28, 29, 35, 39 Measurement 25, 31 Statistics and Probability 6, 11, 17, 22, 36, 38 Regents Examination in Integrated Algebra June 2010 Chart for Converting Total Test Raw Scores to Final Examination Scores (Scale Scores) The Chart for Determining the Final Examination Score for the June 2010 Regents Examination in Integrated Algebra will be posted on the Department s web site http://www.emsc.nysed.gov/osa/ on Friday, June 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 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. [12]

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