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New York Regents Algebra 2 / Trigonometry June 2010

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ALGEBRA 2/TRIGONOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA 2/TRIGONOMETRY Tuesday, June 15, 2010 9:15 a.m. to 12:15 p.m., only Student Name: ______________________________________________________________ School Name: _______________________________________________________________ Print your name and the name of your school on the lines above. This examination has four parts, with a total of 39 questions. You must answer all questions in this examination. Record your answers to the Part I multiple-choice questions, using a No. 2 pencil, on the separate answer sheet provided to you. Write your answers to the questions in Parts II, III, and IV directly in this test booklet. All work for Parts II, III, and IV should be written in pen, except graphs and drawings, which should be done in pencil. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. The formulas that you may need to answer some questions in this examination are found at the end of the examination. This sheet is perforated so you may remove it from this booklet. Scrap paper is not permitted for any part of this examination, but you may use the blank spaces in this booklet as scrap paper. A perforated sheet of scrap graph paper is provided at the end of this booklet for any question for which graphing may be helpful but is not required. You may remove this sheet from this booklet. Any work done on this sheet of scrap graph paper will not be scored. When you have completed the examination, you must sign the statement printed at the end of the answer sheet, indicating that you had no unlawful knowledge of the questions or answers prior to the examination and that you have neither given nor received assistance in answering any of the questions during the examination. Your answer sheet cannot be accepted if you fail to sign this declaration. Notice A graphing calculator and a straightedge (ruler) must be available for you to use while taking this examination. The use of any communications device is strictly prohibited when taking this examination. If you use any communications device, no matter how briefly, your examination will be invalidated and no score will be calculated for you. DO NOT OPEN THIS EXAMINATION BOOKLET UNTIL THE SIGNAL IS GIVEN. ALGEBRA 2/TRIGONOMETRY Part I Answer all 27 questions in this part. Each correct answer will receive 2 credits. No partial credit will be allowed. For each question, record your answer, using a No. 2 pencil, on the separate answer sheet provided to you. [54] 1 What is the common difference of the arithmetic sequence 5, 8, 11, 14? 8 (1) __ (3) 3 (2) 3 (4) 9 5 2 What is the number of degrees in an angle whose radian measure 11 is ____? 12 (1) 150 (3) 330 (2) 165 (4) 518 2 a 3 If a = 3 and b = 2, what is the value of the expression ____ ? 3 b 9 (1) __ 8 (2) 1 Algebra 2/Trigonometry June 10 8 (3) __ 9 8 (4) __ 9 [2] Use this space for computations. 4 Four points on the graph of the function f(x) are shown below. Use this space for computations. {(0,1), (1,2), (2,4), (3,8)} Which equation represents f(x)? (1) f(x) = 2 x (3) f(x) = x + 1 (2) f(x) = 2x (4) f(x) = log 2 x 5 The graph of y = f(x) is shown below. y 20 10 10 5 5 10 x 10 20 Which set lists all the real solutions of f(x) = 0? (1) { 3, 2} (3) { 3, 0, 2} (2) { 2, 3} (4) { 2, 0, 3} Algebra 2/Trigonometry June 10 [3] [OVER] Use this space for computations. _____ 6 In simplest form, 300 is equivalent to ___ __ (1) 3i 10 (3) 10i 3 (2) 5i 12 (4) 12i 5 __ ___ 7 Twenty different cameras will be assigned to several boxes. Three cameras will be randomly selected and assigned to box A. Which expression can be used to calculate the number of ways that three cameras can be assigned to box A? (1) 20! (3) 20C3 20! (2) ___ (4) 20 P3 3! 8 Factored completely, the expression 12x4 + 10x3 12x2 is equivalent to (1) x2(4x + 6)(3x 2) (3) 2x2(2x 3)(3x + 2) (2) 2(2x2 + 3x)(3x2 2x) (4) 2x2(2x + 3)(3x 2) 9 The solutions of the equation y2 3y = 9 are __ 3 3i 3 (1) _______ 2 __ 3 3i 5 (2) _______ 2 Algebra 2/Trigonometry June 10 __ 3 3 5 (3) _________ 2 __ 3 3 5 (4) _______ 2 [4] 10 The expression 2 log x (3 log y + log z) is equivalent to 2 __ (3) log _2x __ (1) log _x3 3yz yz 2 2xz (4) log ___ xz (2) log ___ 3 3y y 11 The expression ( x2 1 ) (1) 3 2 __ 3 is equivalent to _ (x2 1)2 1 __ (2) _________ 3 (x2 Use this space for computations. ________ (3) (x2 1)3 1 ________ (4) _________ (x2 1)3 1)2 __ __ + 5 3 12 Which expression is equivalent to ______ ? 3 5 __ 14 + 5 3 (1) ________ 11 __ 17 + 5 3 (2) ________ 11 __ 14 + 5 3 (3) ________ 14 __ 17 + 5 3 (4) ________ 14 13 Which relation is not a function? (1) (x 2)2 + y2 = 4 (3) x + y = 4 (2) x2 + 4x + y = 4 (4) xy = 4 Algebra 2/Trigonometry June 10 [5] [OVER] Use this space for computations. 2 14 If A is acute and tan A = __, then 3 2 (1) cot A = __ 2 (3) cot(90 A) = __ 3 1 (2) cot A = __ 3 3 1 (4) cot(90 A) = __ 3 2 + 4x 15 The solution set of 4x = 2 6 is (1) {1, 3} (3) { 1, 3} (2) { 1, 3} (4) {1, 3} 16 The equation x2 + y2 2x + 6y + 3 = 0 is equivalent to (1) (x 1)2 + (y + 3)2 = 3 (2) (x 1)2 + (y + 3)2 = 7 (3) (x + 1)2 + (y + 3)2 = 7 (4) (x + 1)2 + (y + 3)2 = 10 Algebra 2/Trigonometry June 10 [6] 17 Which graph best represents the inequality y + 6 y x2 x? Use this space for computations. y x x (1) (3) y y x x (2) (4) _____ 18 The solution set of the equation x + 3 = 3 x is (1) {1} (3) {1, 6} (2) {0} (4) {2, 3} Algebra 2/Trigonometry June 10 [7] [OVER] 19 The product of i7 and i5 Use this space for computations. is equivalent to (1) 1 (3) i (2) 1 (4) i 20 Which equation is represented by the graph below? y 1 0 2 3 2 2 x 1 (1) y = cot x (3) y = sec x (2) y = csc x (4) y = tan x 21 Which value of r represents data with a strong negative linear correlation between two variables? (1) 1.07 (3) 0.14 (2) 0.89 (4) 0.92 Algebra 2/Trigonometry June 10 [8] 22 The function f(x) = tan x is defined in such a way that function. What can be the domain of f(x)? (1) {x 0 x } (3) x __ < x < __ 2 2 (2) {x 0 x 2 } 3 (4) x __ < x < ___ 2 2 { { f 1(x) is a Use this space for computations. } } 23 In the diagram below of right triangle KTW, KW = 6, KT = 5, and m KTW = 90. W 6 T 5 K What is the measure of K, to the nearest minute? (1) 33 33' (3) 33 55' (2) 33 34' (4) 33 56' 24 The expression cos2 cos 2 is equivalent to (1) sin2 (3) cos2 + 1 (2) sin2 (4) cos2 1 Algebra 2/Trigonometry June 10 [9] [OVER] 25 Mrs. Hill asked her students to express the sum 1 + 3 + 5 + 7 + 9 + . . . + 39 using sigma notation. Four different student answers were given. Which student answer is correct? 20 (1) (2k 1) 37 (3) (k + 2) k=1 40 (2) k = 1 39 (k 1) k=2 (4) (2k 1) k=1 26 What is the formula for the nth term of the sequence 54, 18, 6, . . .? (3) = 6( 1 ) 3 1 (1) an = 6 __ (2) an n __ n 1 (3) = 54( 1 ) 3 1 (3) an = 54 __ (4) an n __ n 1 ( ) 1 27 What is the period of the function y = __ sin _x_ ? 2 3 1 (1) __ 2 (3) __ 1 (2) __ (4) 6 2 3 Algebra 2/Trigonometry June 10 3 [10] Use this space for computations. Part II Answer all 8 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. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. [16] 28 Use the discriminant to determine all values of k that would result in the equation x2 kx + 4 = 0 having equal roots. Algebra 2/Trigonometry June 10 [11] [OVER] 29 The scores of one class on the Unit 2 mathematics test are shown in the table below. Unit 2 Mathematics Test Test Score Frequency 96 1 92 2 84 5 80 3 76 6 72 3 68 2 Find the population standard deviation of these scores, to the nearest tenth. Algebra 2/Trigonometry June 10 [12] 30 Find the sum and product of the roots of the equation 5x2 + 11x 3 = 0. Algebra 2/Trigonometry June 10 [13] [OVER] (2) x 1 31 The graph of the equation y = __ has an asymptote. On the grid below, sketch the graph of (2) x 1 y = __ and write the equation of this asymptote. y x Algebra 2/Trigonometry June 10 [14] ___ ____ 32 Express 5 3x3 2 27x3 in simplest radical form. Algebra 2/Trigonometry June 10 [15] [OVER] 33 On the unit circle shown in the diagram below, sketch an angle, in standard position, whose degree measure is 240 and find the exact value of sin 240 . y (1,0) Algebra 2/Trigonometry June 10 [16] x 34 Two sides of a parallelogram are 24 feet and 30 feet. The measure of the angle between these sides is 57 . Find the area of the parallelogram, to the nearest square foot. Algebra 2/Trigonometry June 10 [17] [OVER] 1 4 __ __ ______ 35 Express in simplest form: _2 d 1 __ + _3 __ d Algebra 2/Trigonometry June 10 2d [18] Part III Answer all 3 questions in this part. Each correct answer will receive 4 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. [12] 36 The members of a men s club have a choice of wearing black or red vests to their club meetings. A study done over a period of many years determined that the percentage of black vests worn is 60%. If there are 10 men at a club meeting on a given night, what is the probability, to the nearest thousandth, that at least 8 of the vests worn will be black? Algebra 2/Trigonometry June 10 [19] [OVER] 37 Find all values of in the interval 0 < 360 that satisfy the equation sin 2 = sin . Algebra 2/Trigonometry June 10 [20] 38 The letters of any word can be rearranged. Carol believes that the number of different 9-letter arrangements of the word TENNESSEE is greater than the number of different 7-letter arrangements of the word VERMONT. Is she correct? Justify your answer. Algebra 2/Trigonometry June 10 [21] [OVER] Part IV Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. A correct numerical answer with no work shown will receive only 1 credit. The answer should be written in pen. [6] 39 In a triangle, two sides that measure 6 cm and 10 cm form an angle that measures 80 . Find, to the nearest degree, the measure of the smallest angle in the triangle. Algebra 2/Trigonometry June 10 [22] 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 Tear Here Reference Sheet Area of a Triangle 1 K _ ab sin C 2 Functions of the Sum of Two Angles sin (A + B) cos (A + B) tan (A + B) Law of Cosines a2 b 2 + c 2 2 bc cos A Functions of the Double Angle sin A cos B + cos A sin B cos A cos B sin A sin B _tan A + tan B __________ 1 tan A tan B sin 2A cos 2A cos 2A cos 2A 2 sin A cos A cos2 A sin2 A 2 cos2 A 1 1 2 sin2 A _2 tan A ______ Functions of the Difference of Two Angles tan 2A sin (A B) cos (A B) Functions of the Half Angle tan (A B) sin A cos B cos A sin B cos A cos B + sin A sin B tan A tan B ____________ 1 + tan A tan B Law of Sines b a ____ ____ sin A sin B _________ 1 sin _ A 2 1 cos _ A c ____ 2 sin C 1 tan _ A 2 Sum of a Finite Arithmetic Series n(a1 + an) Sn _______ 2 + nC1an 1b1 + nC2an 2b2 + ... + nCna0bn 0nCr an rbr r= Tear Here (a + b)n nb0 nC0a n Algebra 2/Trigonometry June 10 1 ______ _ cos A 2 _________ 1 ______ _ + cos A 2 _________ 1 cos A _______ 1 + cos A Sum of a Finite Geometric Series a 1(1 r n) _______ Sn 1 r Binomial Theorem (a + b)n 1 tan2 A [27] ALGEBRA 2/TRIGONOMETRY Tear Here Tear Here Printed on Recycled Paper ALGEBRA 2/TRIGONOMETRY FOR TEACHERS ONLY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA 2/TRIGONOMETRY Tuesday, June 15, 2010 9:15 a.m. to 12:15 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 Algebra 2/Trigonometry. More detailed information about scoring is provided in the publication Information Booklet for Scoring the Regents Examination in Algebra 2/Trigonometry. Use only a No. 2 pencil in rating the Regents Examination in Algebra 2/Trigonometry. Do not attempt to correct the student s work by making insertions or changes of any kind. Scoring overlays have been included in the package of scoring materials and must be used to score Part I, the multiple-choice section. When scoring the examination: cut out the rectangular space on the bottom of the scoring overlay to record the total Part I score do not punch holes in the scoring overlay do not make any marks on the answer sheet, other than in the spaces provided for recording scores do not machine scan the answer sheets. Marking up or scanning these answer sheets will interfere with the score collection. 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 write their name in the box under the heading Rater s/Scorer s Name, and also bubble in the circle under Rater s/Scorer s Code Letter that corresponds to their name. Raters should record the student s scores for all questions and the total raw score on the student s answer sheet. Make a careful record to be retained in the school of the total raw score earned by each student. The State Education Department will provide a recordkeeping form for this purpose as part of the detailed directions for administering and scoring the June 2010 Regents Examination in Algebra 2/Trigonometry. The conversion chart for the Regents Examination in Algebra 2/Trigonometry will be posted on the Department s web site http://www.emsc.nysed.gov/osa/ no later than Rating Day, Thursday, June 24, 2010. ALGEBRA 2/TRIGONOMETRY continued Part I Allow a total of 54 credits, 2 credits for each of the following: (1) 3 (8) 4 (15) 3 (22) 3 (2) 2 (9) 4 (16) 2 (23) 1 (3) 3 (10) 1 (17) 1 (24) 1 (4) 1 (11) 2 (18) 1 (25) 1 (5) 4 (12) 1 (19) 1 (26) 4 (6) 3 (13) 1 (20) 3 (27) 4 (7) (14) 3 (21) 2 3 [2] ALGEBRA 2/TRIGONOMETRY 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 Algebra 2/Trigonometry 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 Algebra 2/Trigonometry, use their own professional judgment, confer with other mathematics teachers, and/or contact the consultants at the State Education Department for guidance. During each Regents examination administration period, rating questions may be referred directly to the Education Department. The contact numbers are sent to all schools before each administration period. II. Full-Credit Responses A full-credit response provides a complete and correct answer to all parts of the question. Sufficient work is shown to enable the rater to determine how the student arrived at the correct answer. When the rubric for the full-credit response includes one or more examples of an acceptable method for solving the question (usually introduced by the phrase such as ), it does not mean that there are no additional acceptable methods of arriving at the correct answer. Unless otherwise specified, mathematically correct alternative solutions should be awarded credit. The only exceptions are those questions that specify the type of solution that must be used; e.g., an algebraic solution or a graphic solution. A correct solution using a method other than the one specified is awarded half the credit of a correct solution using the specified method. III. Appropriate Work Full-Credit Responses: The directions in the examination booklet for all the constructed-response questions state: Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. The student has the responsibility of providing the correct answer and showing how that answer was obtained. The student must construct the response; the teacher should not have to search through a group of seemingly random calculations scribbled on the student paper to ascertain what method the student may have used. Responses With Errors: Rubrics that state Appropriate work is shown, but are intended to be used with solutions that show an essentially complete response to the question but contain certain types of errors, whether computational, rounding, graphing, or conceptual. If the response is incomplete; i.e., an equation is written but not solved or an equation is solved but not all of the parts of the question are answered, appropriate work has not been shown. Other rubrics address incomplete responses. IV. Multiple Errors Computational Errors, Graphing Errors, and Rounding Errors: Each of these types of errors results in a 1-credit deduction. Any combination of two of these types of errors results in a 2-credit deduction. No more than 2 credits should be deducted for such mechanical errors in any response. The teacher must carefully review the student s work to determine what errors were made and what type of errors they were. Conceptual Errors: A conceptual error involves a more serious lack of knowledge or procedure. Examples of conceptual errors include using the incorrect formula for the area of a figure, choosing the incorrect trigonometric function, or multiplying the exponents instead of adding them when multiplying terms with exponents. A response with one conceptual error can receive no more than half credit. If a response shows repeated occurrences of the same conceptual error, the student should not be penalized twice. If the same conceptual error is repeated in responses to other questions, credit should be deducted in each response. If a response shows two (or more) different major conceptual errors, it should be considered completely incorrect and receive no credit. If a response shows one conceptual error and one computational, graphing, or rounding error, the teacher must award credit that takes into account both errors; i.e., awarding half credit for the conceptual error and deducting 1 credit for each mechanical error (maximum of two deductions for mechanical errors). [3] [OVER] ALGEBRA 2/TRIGONOMETRY 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. (28) [2] 4 and 4, and appropriate work using the discriminant is shown. [1] Appropriate work is shown, but one computational error is made. or [1] Appropriate work is shown, but one conceptual error is made. or [1] Appropriate work is shown, but only one value of k is found. or 2 [1] k 4(1)(4) = 0 or an equivalent equation, but no further correct work is shown. or [1] 4 and 4, but a method other than the discriminant is used. or [1] 4 and 4, but no work is shown. [0] 4 or 4, 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. (29) [2] 7.4 [1] One rounding error is made. or [1] One conceptual error is made, such as stating 7.5, the sample standard deviation. [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. [4] ALGEBRA 2/TRIGONOMETRY continued (30) 11 3 and product = or an equivalent answer, and appropriate work is 5 5 shown, such as stating the formulas. [2] Sum = [1] Appropriate work is shown, but one computational error is made. or [1] Appropriate work is shown, but one conceptual error is made. or [1] Appropriate work is shown, but the answers are not labeled or are labeled incorrectly. or [1] Appropriate work is shown to find sum = 11 3 or product = , but no further 5 5 correct work is shown. or [1] Sum = [0] 11 3 and product = , but no work is shown. 5 5 11 3 and , but no work is shown. 5 5 or [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. (31) [2] A correct graph is drawn, and y = 0. [1] Appropriate work is shown, but one computational or graphing error is made. or [1] Appropriate work is shown, but one conceptual error is made. or [1] A correct graph is drawn, and x-axis is stated as the asymptote. or [1] A correct graph is drawn, but no further correct work is shown. or [1] y = 0, 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] ALGEBRA 2/TRIGONOMETRY continued (32) [2] x 3x , 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, such as not expressing the answer in simplest radical form. or [1] x 3x , 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. (33) [2] An angle in standard position is drawn correctly and 3 . 2 [1] Appropriate work is shown, but one computational or graphing error is made. or [1] Appropriate work is shown, but one conceptual error is made, such as stating the value of sin 240 to be 0.866. or [1] An angle in standard position is drawn correctly, but no further correct work is shown. or [1] 3 , but no work is shown. 2 [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. [6] ALGEBRA 2/TRIGONOMETRY continued (34) [2] 604, 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] 604, but no work is shown. [0] Appropriate work is shown to find 720, but no further 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) [2] d 8 , and appropriate work is shown. 5 [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] d 8 , but no work is shown. 5 [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] ALGEBRA 2/TRIGONOMETRY continued Part III 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. (36) [4] 0.167, and appropriate work is shown. [3] Appropriate work is shown, but one computational or rounding error is made. [2] Appropriate work is shown, but two or more computational or rounding errors are made. or [2] Appropriate work is shown, but one conceptual error is made, such as finding at most 8 black vests. or 8 2 9 1 [2] A correct expression, such as 10C8(0.6) (0.4) + 10C9(0.6) (0.4) + 10 0 10C10(0.6) (0.4) , is written, but no further correct work is shown. [1] Appropriate work is shown, but one conceptual error and one computational or rounding error are made. or [1] The probability for exactly eight times is calculated correctly. or [1] 0.167, 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. [8] ALGEBRA 2/TRIGONOMETRY continued (37) [4] 0, 60, 180, and 300, and appropriate work is shown. [3] Appropriate work is shown, but one computational, factoring, or substitution error is made. or [3] Appropriate work is shown, but only three of the four correct solutions are found. [2] Appropriate work is shown, but two or more computational, factoring, or substitution errors are made. or [2] Appropriate work is shown, but one conceptual error is made. or [2] Appropriate work is shown, but only two of the four correct solutions are found. or [2] Appropriate work is shown, and sin = 0 and 2 cos 1 = 0 is written, but no further correct work is shown. [1] Appropriate work is shown, but one conceptual error and one computational, factoring, or substitution error are made. or [1] Appropriate work is shown, and sin (2 cos 1) = 0 is written, but no further correct work is shown. or [1] 0, 60, 180, and 300, but no work is shown. [0] A correct substitution is made for sin 2 , but no further correct work is shown. or [0] 0 or 60 or 180 or 300, 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. [9] [OVER] ALGEBRA 2/TRIGONOMETRY continued (38) [4] No, and an appropriate justification is given, such as comparing 7! for Vermont 9! to for Tennessee. 4!2!2! [3] Appropriate work is shown, but one computational error is made, but an appropriate justification is given. or [3] Appropriate work is shown to find 5,040 and 3,780, but No is not stated. [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 to find 3,780, but no further correct work is shown. [1] Appropriate work is shown, but one conceptual error and one computational error are made. or [1] Appropriate work is shown to find 5,040, but no further correct work is shown. or [1] 5,040 and 3,780 and No, but no work is shown. [0] 5,040 and 3,780, 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] ALGEBRA 2/TRIGONOMETRY continued Part IV For this question, use the specific criteria to award a maximum of six credits. Unless otherwise specified, mathematically correct alternative solutions should be awarded appropriate credit. (39) [6] 33, and appropriate work is shown. [5] Appropriate work is shown, but one computational or rounding error is made. [4] Appropriate work is shown, but two computational or rounding errors are made. or [4] Appropriate work is shown, but one conceptual error is made. [3] Appropriate work is shown, but three or more computational or rounding errors are made. or [3] Appropriate work is shown, but one conceptual error and one computational or rounding error are made. or [3] Appropriate work is shown to find the third side, but no further correct work is shown. [2] Appropriate work is shown, but one conceptual error and two or more computational or rounding errors are made. or [2] Appropriate work is shown, but two conceptual errors are made. or 10 6 6 10 [2] Incorrectly uses the proportion or to find the = = sin 80 sin x sin 80 sin x smallest angle. [1] Appropriate work is shown, but two conceptual errors and one computational or rounding error are made. or [1] A correct substitution is made into the Law of Cosines, but no further correct work is shown. or [1] 33, 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. [11] [OVER] ALGEBRA 2/TRIGONOMETRY concluded Map to Core Curriculum Content Strand Item Numbers Number Sense and Operations 6, 12, 19, 32 Algebra 1, 3, 4, 5, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 20, 22, 23, 24, 25, 26, 27, 28, 30, 31, 33, 34, 35, 37, 39 Measurement 2 Statistics and Probability 7, 21, 29, 36, 38 Regents Examination in Algebra 2/Trigonometry 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 Algebra 2/Trigonometry will be posted on the Department s web site http://www.emsc.nysed.gov/osa/ no later than Rating Day, Thursday, June 24, 2010. 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 http://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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