FOR TEACHERS ONLY. The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA 2/TRIGONOMETRY

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1 FOR TEACHERS ONLY The University of the State of New Yk REGENTS HIGH SCHOOL EXAMINATION ALGEBRA 2/TRIGONOMETRY Friday, January 29, :15 a.m. to 12:15 p.m., only SCORING KEY AND RATING GUIDE Mechanics of Rating The following procedures are to be followed f scing student answer papers f the Regents Examination in Algebra 2/Trigonometry. Me detailed infmation about scing is provided in the publication Infmation Booklet f Scing the Regents Examinations in Mathematics. Do not attempt to crect the student s wk by making insertions changes of any kind. In scing the open-ended questions, use check marks to indicate student errs. Unless otherwise specified, mathematically crect variations in the answers will be allowed. Units need not be given when the wding of the questions allows such omissions. Each student s answer paper is to be sced by a minimum of three mathematics teachers. No one teacher is to sce me than approximately one-third of the open-ended questions on a student s paper. Teachers may not sce their own students answer papers. On the student s separate answer sheet, f each question, recd the number of credits earned and the teacher s assigned rater/scer letter. Schools are not permitted to resce any of the open-ended questions on this exam after each question has been rated once, regardless of the final exam sce. Schools are required to ensure that the raw sces have been added crectly and that the resulting scale sce has been determined accurately. Raters should recd the student s sces f all questions and the total raw sce on the student s separate answer sheet. Then the student s total raw sce should be converted to a scale sce by using the conversion chart that will be posted on the Department s web site at: on Friday, January 29, Because scale sces cresponding to raw sces in the conversion chart may change from one administration to another, it is crucial that, f each administration, the conversion chart provided f that administration be used to determine the student s final sce. The student s scale sce should be entered in the box provided on the student s separate answer sheet. The scale sce is the student s final examination sce.

2 If the student s responses f the multiple-choice questions are being hand sced pri to being scanned, the scer must be careful not to make any marks on the answer sheet except to recd the sces in the designated sce boxes. Marks elsewhere on the answer sheet will interfere with the accuracy of the scanning. Part I Allow a total of 54 credits, 2 credits f each of the following. (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (24) (25) (26) (27) Updated infmation regarding the rating of this examination may be posted on the New Yk State Education Department s web site during the rating period. Check this web site at: and select the link Scing Infmation f any recently posted infmation regarding this examination. This site should be checked befe the rating process f this examination begins and several times throughout the Regents Examination period. Beginning in June 2013, the Department is providing supplemental scing guidance, the Sample Response Set, f the Regents Examination in Algebra 2/Trigonometry. This guidance is not required as part of the scer training. It is at the school s discretion to incpate it into the scer training to use it as supplemental infmation during scing. While not reflective of all scenarios, the sample student responses selected f the Sample Response Set illustrate how less common student responses to open-ended questions may be sced. The Sample Response Set will be available on the Department s web site at: Algebra 2/Trigonometry Rating Guide Jan. 16 [2]

3 General Rules f Applying Mathematics Rubrics I. General Principles f Rating The rubrics f the constructed-response questions on the Regents Examination in Algebra 2/Trigonometry are designed to provide a systematic, consistent method f 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 f 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 Infmation Booklet f Scing the Regents Examinations in Mathematics, use their own professional judgment, confer with other mathematics teachers, and/ contact the State Education Department f 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 befe each administration period. II. Full-Credit Responses A full-credit response provides a complete and crect answer to all parts of the question. Sufficient wk is shown to enable the rater to determine how the student arrived at the crect answer. When the rubric f the full-credit response includes one me examples of an acceptable method f 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 crect answer. Unless otherwise specified, mathematically crect 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 a graphic solution. A crect solution using a method other than the one specified is awarded half the credit of a crect solution using the specified method. III. Appropriate Wk Full-Credit Responses: The directions in the examination booklet f all the constructed-response questions state: Clearly indicate the necessary steps, including appropriate fmula substitutions, diagrams, graphs, charts, etc. The student has the responsibility of providing the crect 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 Errs: Rubrics that state Appropriate wk is shown, but are intended to be used with solutions that show an essentially complete response to the question but contain certain types of errs, whether computational, rounding, graphing, conceptual. If the response is incomplete; i.e., an equation is written but not solved an equation is solved but not all of the parts of the question are answered, appropriate wk has not been shown. Other rubrics address incomplete responses. IV. Multiple Errs Computational Errs, Graphing Errs, and Rounding Errs: Each of these types of errs results in a 1-credit deduction. Any combination of two of these types of errs results in a 2-credit deduction. No me than 2 credits should be deducted f such mechanical errs in any response. The teacher must carefully review the student s wk to determine what errs were made and what type of errs they were. Conceptual Errs: A conceptual err involves a me serious lack of knowledge procedure. Examples of conceptual errs include using the increct fmula f the area of a figure, choosing the increct trigonometric function, multiplying the exponents instead of adding them when multiplying terms with exponents. If a response shows repeated occurrences of the same conceptual err, the student should not be penalized twice. If the same conceptual err is repeated in responses to other questions, credit should be deducted in each response. F 4- and 6-credit questions, if a response shows one conceptual err and one computational, graphing, rounding err, the teacher must award credit that takes into account both errs. Refer to the rubric f specific scing guidelines. Algebra 2/Trigonometry Rating Guide Jan. 16 [3]

4 Part II F each question, use the specific criteria to award a maximum of 2 credits. Unless otherwise specified, mathematically crect alternative solutions should be awarded appropriate credit. (28) [2] 7.5, and crect algebraic wk is shown. [1] Appropriate wk is shown, but one computational err is made. [1] Appropriate wk is shown, but one conceptual err is made. [1] 7.5, but a method other than algebraic is used. [1] 7.5, but no wk is shown. [0] A zero response is completely increct, irrelevant, incoherent is a crect response that was obtained by an obviously increct procedure. (29) [2] (x 2 2)(x 3), and crect wk is shown. [1] Appropriate wk is shown, but one facting err is made. [1] Appropriate wk is shown, but one conceptual err is made. [1] x 2 (x 3) 2(x 3), but no further crect wk is shown. [1] (x 2 2)(x 3), but no wk is shown. [0] A zero response is completely increct, irrelevant, incoherent is a crect response that was obtained by an obviously increct procedure. Algebra 2/Trigonometry Rating Guide Jan. 16 [4]

5 (30) [2] _ and crect algebraic wk is shown. [1] Appropriate wk is shown, but one computational rounding err is made. [1] Appropriate wk is shown, but one conceptual err is made. [1] [1] 1 3, but a method other than algebraic is used. 1 3, but no wk is shown. [0] A zero response is completely increct, irrelevant, incoherent is a crect response that was obtained by an obviously increct procedure. (31) [2] 1,663,200, and crect wk is shown. [1] Appropriate wk is shown, but one computational err is made. [1] Appropriate wk is shown, but one conceptual err is made. [1] 11! 322!!! is written, but no further crect wk is shown. [1] 1,663,200, but no wk is shown. [0] 39,916,800 is found, but no further crect wk is shown. [0] A zero response is completely increct, irrelevant, incoherent is a crect response that was obtained by an obviously increct procedure. (32) [2] 2.27, and crect wk is shown. [1] Appropriate wk is shown, but one computational rounding err is made. [1] Appropriate wk is shown, but one conceptual err is made. [1] 2.27, but no wk is shown. Algebra 2/Trigonometry Rating Guide Jan. 16 [5] [0] A zero response is completely increct, irrelevant, incoherent is a crect response that was obtained by an obviously increct procedure.

6 (33) [2] 194, and crect wk is shown. [1] Appropriate wk is shown, but one computational rounding err is made. [1] Appropriate wk is shown, but one conceptual err is made. [1] A crect substitution into the area fmula is made, but no further crect wk is shown. [1] 194, but no wk is shown. [0] 125 is found, but no further crect wk is shown. [0] A zero response is completely increct, irrelevant, incoherent is a crect response that was obtained by an obviously increct procedure. (34) [2] Crect wk is shown to prove the identity. [1] Appropriate wk is shown, but one substitution simplification err is made. [1] Appropriate wk is shown, but one conceptual err is made. [1] All trigonometric functions are written in terms of sin θ and cos θ, but no further crect wk is shown. [0] A zero response is completely increct, irrelevant, incoherent is a crect response that was obtained by an obviously increct procedure. (35) [2] 2 3 x x2 7 9 x 2, and crect wk is shown. 9 [1] Appropriate wk is shown, but one computational err is made. [1] Appropriate wk is shown, but one conceptual err is made. [1] 2 3 x x2 7 9 x 2, but no wk is shown. 9 [0] A zero response is completely increct, irrelevant, incoherent is a crect response that was obtained by an obviously increct procedure. Algebra 2/Trigonometry Rating Guide Jan. 16 [6]

7 Part III F each question, use the specific criteria to award a maximum of 4 credits. Unless otherwise specified, mathematically crect alternative solutions should be awarded appropriate credit. (36) [4] 5 33, and crect wk is shown using completing the square. [3] Appropriate wk is shown, but one computational err is made. [3] Appropriate wk is shown, but only one root is stated. [3] Appropriate wk is shown to find x 5 33, but no further crect wk is shown. [2] Appropriate wk is shown, but two me computational errs are made. [2] Appropriate wk is shown, but one conceptual err is made. [2] Appropriate wk is shown to find (x 5) 2 33, but no further crect wk is shown. [2] 5 33, but the quadratic fmula is used. [1] Appropriate wk is shown, but one conceptual err and one computational err are made. [1] x 2 10x is written, but no further crect wk is shown. [1] 5 33, but no wk is shown. [0] A zero response is completely increct, irrelevant, incoherent is a crect response that was obtained by an obviously increct procedure. Algebra 2/Trigonometry Rating Guide Jan. 16 [7]

8 (37) [4] y 2.19(3.23) x and 4.5, and crect algebraic wk is shown. [3] Appropriate wk is shown, but one computational rounding err is made. [3] The expression 2.19(3.23) x is written and 4.5, and appropriate wk is shown. [3] An increct exponential regression equation is written and solved appropriately. [3] y 2.19(3.23) x and 4.5, but a method other than algebraic is used no wk is shown. [2] Appropriate wk is shown, but two me computational rounding errs are made. [2] Appropriate wk is shown, but one conceptual err is made. [2] y 2.19(3.23) x, but no further crect wk is shown. [2] The expression 2.19(3.23) x is written and 4.5, but no wk is shown. [1] Appropriate wk is shown, but one conceptual err and one computational rounding err are made. [1] An increct exponential equation is written, but no further crect wk is shown. [1] A regression equation other than exponential is written and solved appropriately. [1] The expression 2.19(3.23) x is written, but no further crect wk is shown. [1] 4.5, but no wk is shown. [0] A zero response is completely increct, irrelevant, incoherent is a crect response that was obtained by an obviously increct procedure. Algebra 2/Trigonometry Rating Guide Jan. 16 [8]

9 (38) [4] 0, 120, 240, and crect algebraic wk is shown. [3] Appropriate wk is shown, but one computational facting err is made. [3] Appropriate wk is shown to find two of the crect values. [2] Appropriate wk is shown, but two me computational facting errs are made. [2] Appropriate wk is shown, but one conceptual err is made. [2] Appropriate wk is shown to find (2cos x 1)(cos x 1) 0, but no further crect wk is shown. [2] A crect substitution is made into the quadratic fmula, but no further crect wk is shown. [2] 0, 120, and 240, but a method other than algebraic is used. [1] Appropriate wk is shown, but one conceptual err and one computational facting err are made. [1] 2cos 2 x cos x 1 0 is written, but no further crect wk is shown. [1] 0, 120, 240, but no wk is shown. [0] A zero response is completely increct, irrelevant, incoherent is a crect response that was obtained by an obviously increct procedure. Algebra 2/Trigonometry Rating Guide Jan. 16 [9]

10 Part IV F this question, use the specific criteria to award a maximum of 6 credits. Unless otherwise specified, mathematically crect alternative solutions should be awarded appropriate credit. (39) [6] 43.3 and 11.7, and crect wk is shown. [5] Appropriate wk is shown, but one computational rounding err is made. [5] Appropriate wk is shown to find 11.7 and BG 16. [4] Appropriate wk is shown, but two computational rounding errs are made. [4] Appropriate wk is shown, but one conceptual err is made. [4] Appropriate wk is shown to find 11.7, but no further crect wk is shown. [3] Appropriate wk is shown, but three me computational rounding errs are made. [3] Appropriate wk is shown, but one conceptual err and one computational rounding err are made. [3] Appropriate wk is shown to find m C and/ m D and BG 16, but no further crect wk is shown. [2] Appropriate wk is shown, but one conceptual err and two me computational rounding errs are made. [2] Appropriate wk is shown, but two conceptual errs are made. [2] Appropriate wk is shown to find 43.3, but no further crect wk is shown. [2] Appropriate wk is shown to find m C and/ m D, but no further crect wk is shown. [2] 43.3 and 11.7, but no wk is shown. Algebra 2/Trigonometry Rating Guide Jan. 16 [10]

11 [1] BG 16, but no further crect wk is shown. [1] 43.3 and 11.7, but no wk is shown. [0] A zero response is completely increct, irrelevant, incoherent is a crect response that was obtained by an obviously increct procedure. Algebra 2/Trigonometry Rating Guide Jan. 16 [11]

12 Map to Ce Curriculum Content Strands Item Numbers Number Sense and Operations 17, 20, 26, 35 Algebra 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 15, 18, 19, 21, 22, 23, 24, 25, 27, 28, 29, 30, 33, 34, 36, 38, 39 Measurement 32 Statistics and Probability 1, 5, 14, 16, 31, 37 Regents Examination in Algebra 2/Trigonometry January 2016 Chart f Converting Total Test Raw Sces to Final Examination Sces (Scale Sces) The Chart f Determining the Final Examination Sce f the January 2016 Regents Examination in Algebra 2/Trigonometry will be posted on the Department s web site at: on Friday, January 29, Conversion charts provided f previous administrations of the Regents Examination in Algebra 2/Trigonometry must NOT be used to determine students final sces f this administration. Online Submission of Teacher Evaluations of the Test to the Department Suggestions and feedback from teachers provide an imptant contribution to the test development process. The Department provides an online evaluation fm f State assessments. It contains spaces f teachers to respond to several specific questions and to make suggestions. Instructions f completing the evaluation fm are as follows: 1. Go to 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 fm. Algebra 2/Trigonometry Rating Guide Jan. 16 [12]