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New York Regents Algebra 2 / Trigonometry June 2011

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ALGEBRA 2/TRIGONOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA 2/TRIGONOMETRY Tuesday, June 21, 2011 1:15 to 4:15 p.m., only Student Name: ______________________________________________________________ School Name: _______________________________________________________________ Print your name and the name of your school on the lines above. Then turn to the last page of this booklet, which is the answer sheet for Part I. Fold the last page along the perforations and, slowly and carefully, tear off the answer sheet. Then fill in the heading of your answer sheet. This examination has four parts, with a total of 39 questions. You must answer all questions in this examination. Write your answers to the Part I multiple-choice questions on the separate answer sheet. Write your answers to the questions in Parts II, III, and IV directly in this booklet. All work 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, write on the separate answer sheet the numeral preceding the word or expression that best completes the statement or answers the question. [54] 1 A doctor wants to test the effectiveness of a new drug on her patients. She separates her sample of patients into two groups and administers the drug to only one of these groups. She then compares the results. Which type of study best describes this situation? (1) census (3) observation (2) survey (4) controlled experiment _____ 2 If f(x) = _2 x , what is the value of f( 10)? x 16 5 (1) __ 2 __ (3) _5 __ (2) _5 42 __ (4) _5 58 18 3 An auditorium has 21 rows of seats. The first row has 18 seats, and each succeeding row has two more seats than the previous row. How many seats are in the auditorium? (1) 540 (3) 760 (2) 567 (4) 798 Algebra 2/Trigonometry June 11 [2] Use this space for computations. 4 Expressed as a function of a positive acute angle, cos ( 305 ) is equal to (1) cos 55 (3) sin 55 (2) cos 55 Use this space for computations. (4) sin 55 5 The value of x in the equation 42x + 5 = 83x is (1) 1 (3) 5 (2) 2 (4) 10 6 What is the value of x in the equation log 5 x = 4? (1) 1.16 (3) 625 (2) 20 (4) 1,024 4 _ 7 The expression 16x2y7 is equivalent to 17 __ __ 17 __ __ (1) 2x 2 y 4 (3) 4x 2 y 4 (2) 2x8y28 (4) 4x8y28 Algebra 2/Trigonometry June 11 [3] [OVER] Use this space for computations. 8 Which equation is represented by the graph below? y x (1) y = 5x (3) y = 5 x (2) y = 0.5x (4) y = 0.5 x __ ___ 9 What is the fifteenth term of the geometric sequence 5 , 10 , __ 2 5 , . . . ? __ __ (1) 128 5 (3) 16384 5 (2) 128 10 (4) 16384 10 ___ Algebra 2/Trigonometry June 11 ___ [4] 10 In ABC, a = 15, b = 14, and c = 13, as shown in the diagram below. What is the m C, to the nearest degree? Use this space for computations. B 13 A 15 C 14 (1) 53 (3) 67 (2) 59 (4) 127 11 What is the period of the function f( ) = 2cos 3 ? (1) 3 (3) ___ 2 (2) ___ (4) 2 3 2 12 What is the range of f(x) = (x + 4)2 + 7? (1) y 4 (3) y = 7 (2) y 4 (4) y 7 Algebra 2/Trigonometry June 11 [5] [OVER] 13 Ms. Bell s mathematics class consists of 4 sophomores, 10 juniors, and 5 seniors. How many different ways can Ms. Bell create a fourmember committee of juniors if each junior has an equal chance of being selected? (1) 210 (3) 5,040 (2) 3,876 (4) 93,024 14 Which graph represents a relation that is not a function? y y x x (1) (3) y y x (2) Algebra 2/Trigonometry June 11 x (4) [6] Use this space for computations. 15 The value of tan 126 43 to the nearest ten-thousandth is (1) 1.3407 (3) 1.3548 (2) 1.3408 Use this space for computations. (4) 1.3549 4 ___ 16 The expression _______ is equivalent to ___ 5 13 ___ 4 ___ 13 (1) _________ 5 + 13 (3) _______ 3 5 13 13 ___ ___ 4(5 13 ) (2) _________ 4(5 + 13 ) (4) _________ 38 38 17 Akeem invests $25,000 in an account that pays 4.75% annual interest compounded continuously. Using the formula A = Pert, where A = the amount in the account after t years, P = principal invested, and r = the annual interest rate, how many years, to the nearest tenth, will it take for Akeem s investment to triple? (1) 10.0 (3) 23.1 (2) 14.6 (4) 24.0 5 18 The value of the expression (1) 38 (2) 12 Algebra 2/Trigonometry June 11 ( r 2 + r) is r=3 (3) 26 (4) 62 [7] [OVER] 19 Which graph shows y = Use this space for computations. cos 1 x? y y 2 2 3 2 3 2 2 2 x 1 x 1 1 1 (1) (3) y y 2 2 3 2 3 2 2 2 x 1 1 (2) Algebra 2/Trigonometry June 11 x 1 1 (4) [8] Use this space for computations. _ C 3 A2B 20 If r = ____ , then log r can be represented by 1 1 (1) __ log A + __ log B log C 6 3 (2) 3(log A2 + log B log C) 1 (3) __ log(A2 + B) C 3 1 1 2 (4) __ log A + __ log B __ log C 3 3 3 _______ 21 The solution set of 3x + 16 = x + 2 is (1) { 3, 4} (3) {3} (2) { 4, 3} (4) { 4} 22 Brian correctly used a method of completing the square to solve the equation x2 + 7x 11 = 0. Brian s first step was to rewrite the equation as x2 + 7x = 11. He then added a number to both sides of the equation. Which number did he add? 7 (1) __ 49 (3) ___ 49 (2) ___ (4) 49 2 4 Algebra 2/Trigonometry June 11 2 [9] [OVER] Use this space for computations. s n2 + cos2 23 The expression _i__________ is equivalent to 1 sin2 (1) cos2 (3) sec2 (2) sin2 (4) csc2 24 The number of minutes students took to complete a quiz is summarized in the table below. Minutes Number of Students 14 15 16 17 18 19 20 5 3 x 5 2 10 1 If the mean number of minutes was 17, which equation could be used to calculate the value of x? 119 + x (1) 17 = _______ x 446 + x (3) 17 = _______ 119 + 16x (2) 17 = ________ x 446 + 16x (4) 17 = ________ 26 + x 26 + x 25 What is the radian measure of the smaller angle formed by the hands of a clock at 7 o clock? (1) __ 5 (3) ___ 2 (2) ___ 7 (4) ___ 2 3 Algebra 2/Trigonometry June 11 6 6 [10] 26 What is the coefficient of the fourth term in the expansion of (a 4b)9? (1) 5,376 (3) 336 (2) 336 Use this space for computations. (4) 5,376 27 Samantha constructs the scatter plot below from a set of data. y 100 80 60 40 20 0 2 4 6 8 10 x Based on her scatter plot, which regression model would be most appropriate? (1) exponential (3) logarithmic (2) linear (4) power Algebra 2/Trigonometry June 11 [11] [OVER] 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] (2 )( ) 3 1 1 28 Express the product of __y2 __y and 12y + __ as a trinomial. Algebra 2/Trigonometry June 11 3 5 [12] 29 In a study of 82 video game players, the researchers found that the ages of these players were normally distributed, with a mean age of 17 years and a standard deviation of 3 years. Determine if there were 15 video game players in this study over the age of 20. Justify your answer. Algebra 2/Trigonometry June 11 [13] [OVER] 30 Write a quadratic equation such that the sum of its roots is 6 and the product of its roots is 27. 31 Evaluate e xlny when x = 3 and y = 2. Algebra 2/Trigonometry June 11 [14] 32 If f(x) = x2 6, find f 1(x). Algebra 2/Trigonometry June 11 [15] [OVER] 33 Factor the expression 12 t8 75 t4 completely. Algebra 2/Trigonometry June 11 [16] 3x 4y5 34 Simplify the expression _________ and write the answer using only positive exponents. 3 7 2 (2x y Algebra 2/Trigonometry June 11 ) [17] [OVER] 35 If f(x) = x2 6 and g(x) = 2x 1, determine the value of (g f)( 3). Algebra 2/Trigonometry June 11 [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 Express as a single fraction the exact value of sin 75 . Algebra 2/Trigonometry June 11 [19] [OVER] 37 Solve the inequality 3 6 x < 15 for x. Graph the solution on the line below. Algebra 2/Trigonometry June 11 [20] 1 38 The probability that a professional baseball player will get a hit is __. Calculate the exact probability 3 that he will get at least 3 hits in 5 attempts. Algebra 2/Trigonometry June 11 [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 Solve the following system of equations algebraically: 5=y x 4 x2 = 17x + y + 4 Algebra 2/Trigonometry June 11 [22] 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) 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 Cosines a2 b 2 + c 2 2 bc cos A Functions of the Double Angle 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 1 tan2 A _________ 1 sin _ A 2 1 ______ _ cos A 2 _________ Law of Sines a b ____ ____ sin A sin B c ____ Binomial Theorem nb0 nC0a n 0nCr an rbr r= Algebra 2/Trigonometry June 11 1 ______ _ + cos A 2 _________ 1 tan _ A 2 1 cos A _______ 1 + cos A Sum of a Finite Geometric Series a 1(1 r n) _______ Sn 1 r + nC1an 1b1 + nC2an 2b2 + ... + nCna0bn Tear Here (a + b)n 2 sin C Sum of a Finite Arithmetic Series n(a1 + an) Sn _______ 2 (a + b)n 1 cos _ A Tear Here Tear Here Tear Here Tear Here Scrap Graph Paper This sheet will not be scored. Scrap Graph Paper This sheet will not be scored. Tear Here Tear Here The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION Tear Here ALGEBRA 2/TRIGONOMETRY Tuesday, June 21, 2011 1:15 to 4:15 p.m., only ANSWER SHEET Student . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sex: Male Female Grade . . . . . . Teacher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . School . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Your answers to Part I should be recorded on this answer sheet. Part I Answer all 27 questions in this part. 1 ................ 8 ................ 15 . . . . . . . . . . . . . . . . 22 . . . . . . . . . . . . . . . . 2 ................ 9 ................ 16 . . . . . . . . . . . . . . . . 23 . . . . . . . . . . . . . . . . 3 ................ 10 . . . . . . . . . . . . . . . . 17 . . . . . . . . . . . . . . . . 24 . . . . . . . . . . . . . . . . 4 ................ 11 . . . . . . . . . . . . . . . . 18 . . . . . . . . . . . . . . . . 25 . . . . . . . . . . . . . . . . 5 ................ 12 . . . . . . . . . . . . . . . . 19 . . . . . . . . . . . . . . . . 26 . . . . . . . . . . . . . . . . 6 ................ 13 . . . . . . . . . . . . . . . . 20 . . . . . . . . . . . . . . . . 27 . . . . . . . . . . . . . . . . 7 ................ 14 . . . . . . . . . . . . . . . . 21 . . . . . . . . . . . . . . . . Your answers for Parts II, III, and IV should be written in the test booklet. Tear Here The declaration below must be signed when you have completed the examination. I do hereby affirm, at the close of this examination, that I had no unlawful knowledge of the questions or answers prior to the examination and that I have neither given nor received assistance in answering any of the questions during the examination. Signature Algebra 2/Trigonometry June 11 ALGEBRA 2/TRIGONOMETRY Rater s/Scorer s Name (minimum of three) ALGEBRA 2/TRIGONOMETRY Maximum Credit Part I 1 27 54 Part II 28 2 29 2 30 2 31 2 32 2 33 2 34 2 35 2 36 4 37 4 38 4 39 6 Maximum Total 88 Part IV Rater s/Scorer s Initials Total Raw Score Part III Credits Earned Checked by Tear Here Question Scale Score (from conversion chart) Tear Here Printed on Recycled Paper ALGEBRA 2/TRIGONOMETRY Algebra 2/Trigonometry June 11 FOR TEACHERS ONLY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA 2/TRIGONOMETRY Tuesday, June 21, 2011 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 Algebra 2/Trigonometry. More detailed information about scoring is provided in the publication Information Booklet for Scoring the Regents Examinations in Mathematics. 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. No one teacher is to score more than approximately one-third of the open-ended questions on a student s paper. 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. Beginning in June 2011, schools are no longer permitted to rescore any of the open-ended questions on this exam after each question has been rated once, regardless of the final exam score. Schools are required to ensure that the raw scores have been added correctly and that the resulting scale score has been determined accurately. R aters 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 at: http://www.p12.nysed.gov/apda/ o n Tuesday, June 21, 2011. Because scale scores corresponding to raw scores in the conversion chart may change from one examination to another, it is crucial that for each administration, the conversion chart provided for that administration be used to determine the student s final score. 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. Part I Allow a total of 54 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 (8) 2 (15) 2 (22) 2 (2) 2 (9) 1 (16) 1 or 3* (23) 3 (3) 4 (10) 1 (17) 3 (24) 4 (4) 2 (11) 2 (18) 1 (25) 3 (5) 2 (12) 4 (19) 3 (26) 1 (6) 3 (13) 1 (20) 4 (27) 3 (7) 1 (14) 3 (21) 3 * Allow credit for 1 or 3 as an acceptable response for question 16. Algebra 2/Trigonometry Rating Guide June 11 [2] 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.p12.nysed.gov/apda/ and select the link 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 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 Examinations in Mathematics, 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). I. Algebra 2/Trigonometry Rating Guide June 11 [3] 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] 6 y 3 37 2 1 y y or an equivalent trinomial, and appropriate work is 10 5 shown. [1] Appropriate work is shown, but one computational or simplification error is made. or [1] Appropriate work is shown, but one conceptual error is made. or [1] 6 y 3 37 2 1 y y , but no work is shown. 10 5 [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] No, and an appropriate justification is given. [1] Appropriate work is shown, but one computational error is made. or [1] Appropriate work is shown, but one conceptual error is made. [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. Algebra 2/Trigonometry Rating Guide June 11 [4] (30) [2] x2 6x 27 = 0 or an equivalent equation. [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] The expression x2 6x 27 is written. or [1] The equation y = x2 6x 27 is written. [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] 8, and appropriate work is shown, such as a substitution for x and y. [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] 8, but no work is shown. [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. Algebra 2/Trigonometry Rating Guide June 11 [5] (32) [2] x + 6 , 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 writing with the radical. or [1] x + 6 , 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] 3t 4 (2t 2 + 5)(2t 2 5), or 3t 4 (2 t 2 + 5)( 2 t 5 )( 2 t + 5 ) , and appropriate work is shown. [1] Appropriate work is shown, but one factoring error is made. or [1] Appropriate work is shown, but one conceptual error is made. or [1] 3t 4 (2t 2 + 5)(2t 2 5), but no work is shown. [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. Algebra 2/Trigonometry Rating Guide June 11 [6] (34) [2] 12 x 2 y9 , and appropriate work is shown. [1] Appropriate work is shown, but one computational or simplification error is made. or [1] Appropriate work is shown, but one conceptual error is made. or [1] Appropriate work is shown, but the answer is expressed as 12 x 2 y 9 . or [1] 12 x 2 y9 , 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. (35) [2] 7, 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 finding (f o g)( 3). or [1] 7, 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. Algebra 2/Trigonometry Rating Guide June 11 [7] 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] 2+ 6 4 or 3 1+ 2 if the half-angle formula is used, and appropriate 2 work is shown. [3] Appropriate work is shown, but one computational or substitution error is made. [2] Appropriate work is shown, but two or more computational or substitution errors are made. or [2] Appropriate work is shown, but one conceptual error is made. [1] Appropriate work is shown, but one conceptual error and one computational or substitution error are made. or [1] sin 30 cos 45 + cos 30 sin 45 or 1 cos150 is written, but no further 2 correct work is shown. or [1] 2+ 6 4 , but no work is shown. [0] 0.9659258263, 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. Algebra 2/Trigonometry Rating Guide June 11 [8] (37) [4] x < 1 or x > 11 or an equivalent interval notation, and a correct graph is drawn, and appropriate work is shown. [3] Appropriate work is shown, but one computational or graphing error is made. or [3] Appropriate work is shown, but the answer is not expressed as a disjunction. [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] Appropriate work is shown to find and graph x > 11, but no further correct work is shown. [1] Appropriate work is shown, but one conceptual error and one computational or graphing error are made. or [1] Appropriate work is shown to find and graph x < 1, but no further correct work is shown. or [1] x < 1 or x > 11 , 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. Algebra 2/Trigonometry Rating Guide June 11 [9] (38) [4] 51 243 or an equivalent fraction, and appropriate work is shown. [3] Appropriate work is shown, but one computational error is made. or [3] Appropriate work is shown to find 40 243 , 10 243 , and 1 243 , but the values are not added. or [3] Appropriate work is shown, but the answer is expressed as a decimal. [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, such as finding the probability of at most 3 hits. or 3 2 4 1 5 1 2 1 2 1 2 [2] A correct expression, such as 5 C3 + 5 C4 + 5 C5 3 3 3 3 3 3 is written, 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 40 243 , the probability of exactly 3 hits, but no further correct work is shown. or [1] 51 243 , 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. Algebra 2/Trigonometry Rating Guide June 11 [10] 0 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) 9 1 1 11 [6] , and , or an equivalent answer, and appropriate algebraic 2 2 2 2 work is shown. [5] Appropriate work is shown, but one computational, substitution, or factoring error is made. or [5] Appropriate work is shown, but only one correct solution is found or only the x- or the y-values are found correctly. [4] Appropriate work is shown, but two computational, substitution, or factoring errors are made. or [4] Appropriate work is shown to find (2 x 1)(2 x + 9) = 0 or (2 y 11)(2 y 1) = 0 , but no further correct work is shown. or [4] A correct substitution is made into the quadratic formula, but no further correct work is shown. [3] Appropriate work is shown, but three or more computational, substitution, or factoring errors are made. or [3] Appropriate work is shown, but one conceptual error is made. or [3] A correct quadratic equation in standard form is written, but no further correct work is shown. or 9 1 1 11 [3] , and , or an equivalent answer, but a method other than 2 2 2 2 algebraic is used. [2] Appropriate work is shown, but one conceptual error and one computational, substitution, or factoring error are made. [1] Appropriate work is shown, but one conceptual error and two or more computational, substitution, or factoring errors are made. or Algebra 2/Trigonometry Rating Guide June 11 [11] [1] A correct equation in one variable is written, but no further correct work is shown. or 9 1 1 11 [1] , and , , but no work is shown. 2 2 2 2 [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. Algebra 2/Trigonometry Rating Guide June 11 [12] Map to Core Curriculum Content Strand Item Numbers Number Sense and Operations 16, 18, 28 Algebra 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 17, 19, 20, 21, 22, 23, 26, 30, 31, 32, 33, 34, 35, 36, 37, 39 Measurement 25 Statistics and Probability 1, 13, 24, 27, 29, 38 Regents Examination in Algebra 2/Trigonometry June 2011 Chart for Converting Total Test Raw Scores to Final Examination Scores (Scale Scores) The Chart for Determining the Final Examination Score for the June 2011 Regents Examination in Algebra 2/Trigonometry will be posted on the Department s web site at: http://www.p12.nysed.gov/apda/ on Tuesday, June 21, 2011. Conversion charts provided for previous administrations of the Algebra 2/ Trigonometry 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 http://www.forms2.nysed.gov/emsc/osa/exameval/reexameval.cfm. 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. Algebra 2/Trigonometry Rating Guide June 11 [13]

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Additional Info : Scoring Key on page 29
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