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New York Regents Algebra 2 / Trigonometry June 2012

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ALGEBRA 2/TRIGONOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA 2/TRIGONOMETRY Tuesday, June 19, 2012 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. A separate answer sheet for Part I has been provided to you. Follow the instructions from the proctor for completing the student information on 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] ( ) ( Use this space for computations. ) 3 2 3 2 2 2 __ __ __ 1 What is the product of __ 5 x 4 y and 5 x 4 y ? 4 2 9 4 __ (1) __ 25 x 16 y 2 2 __ 3 4 (3) __ 5x 4y 9 2 4 __ (2) __ 25 x 16 y 4 (4) __ 5x 2 What is the domain of the function shown below? y x (1) 1 x 6 (3) 2 x 5 (2) 1 y 6 (4) 2 y 5 Algebra 2/Trigonometry June 12 [2] 3 What is the solution set for 2 cos 1 0 in the interval 0 360 ? (1) {30 , 150 } (3) {30 , 330 } (2) {60 , 120 } Use this space for computations. (4) {60 , 300 } 4 The expression 3 64a16 is equivalent to (1) 8a4 (3) 4a5 3 a (2) 8a8 (4) 4a 3 a5 5 Which summation represents 5 7 9 11 43? 43 (1) n 24 (3) n 5 20 (2) (2 n 3) n 1 Algebra 2/Trigonometry June 12 (2 n 3) n 4 23 (4) (3n 4) n 3 [3] [OVER] 6 If m 50, which diagram represents drawn in standard position? y y x (1) ( 3) y x y x x ( 4) (2) ( ) 1 7 If log b x 3 log b p 2 log b t __ 2 log b r , then the value of x is (1) p3 (3) t2r 1 (2) p3 t 2 r 2 (4) p3 t 2 r p3 t2 r 9 8 Which equation has roots with the sum equal to __ 4 and the product 3 equal to __ 4? (1) 4x2 9x 3 0 (3) 4x2 9x 3 0 (2) 4x2 9x 3 0 (4) 4x2 9x 3 0 Algebra 2/Trigonometry June 12 [4] Use this space for computations. 4x 5 9 Which graph represents the solution set of ______ 1? | 5 4 3 2 1 0 1 2 3 4 2 3 4 5 1 2 3 4 5 1 2 3 4 | 5 1 3 Use this space for computations. 5 (1) 5 4 3 2 1 0 (2) 5 4 3 2 1 0 (3) 5 4 3 2 1 0 (4) 10 Which expression is equivalent to x 1y4 3x 5y 1 (1) x 4 y5 3 (3) 3x4y5 (2) x 5y4 3 (4) ? Algebra 2/Trigonometry June 12 y4 3x5 [5] [OVER] Use this space for computations. 11 Which graph represents the function log 2 x y? y y (1,0) (1,0) x (1) ( 3) y x y (0,2) (2,0) x x ( 4) (2) 12 A circle is drawn to represent a pizza with a 12 inch diameter. The circle is cut into eight congruent pieces. What is the length of the outer edge of any one piece of this circle? 3 (1) ___ 4 3 (3) ___ 2 (2) (4) 3 Algebra 2/Trigonometry June 12 [6] 13 What is the solution set for the equation (1) {4} (3) {4, 5} (2) { 5} 5x 29 x 3 ? Use this space for computations. (4) { 5, 4} 14 When factored completely, x3 3x2 4x 12 equals (1) (x 2)(x 2)(x 3) (2) (x 2)(x 2)(x 3) (3) (x2 4)(x 3) (4) (x2 4)(x 3) 6 x 15 What is the middle term in the expansion of __ 2y ? (2 (1) 20x3y3 (3) 20x3y3 __ x4y2 (2) 15 4 ) __ x4y2 (4) 15 4 Algebra 2/Trigonometry June 12 [7] [OVER] 16 Which expression is equivalent to (n m p)(x), given m(x) sin x, n(x) 3x, and p(x) x2? (1) sin (3x)2 (3) sin2 (3x) (2) 3 sin x2 (4) 3 sin2 x 17 The value of csc 138 23 rounded to four decimal places is (1) 1.3376 (3) 1.5012 (2) 1.3408 (4) 1.5057 18 Which function is one-to-one? (1) k(x) x2 2 3 (2) g(x) x 2 (3) f(x) |x| 2 (4) j(x) x4 2 19 The conjugate of the complex expression 5x 4i is (1) 5x 4i (3) 5x 4i (2) 5x 4i (4) 5x 4i 1 20 What is a positive value of tan __ 2 x, when sin x 0.8? (1) 0.5 (3) 0.33 (2) 0.4 (4) 0.25 Algebra 2/Trigonometry June 12 [8] Use this space for computations. 21 The table below displays the results of a survey regarding the number of pets each student in a class has. The average number of pets per student in this class is 2. Number of Pets 0 1 2 3 4 5 Number of Students 4 6 10 0 k Use this space for computations. 2 What is the value of k for this table? (1) 9 (3) 8 (2) 2 (4) 4 22 How many negative solutions to the equation 2x3 4x2 3x 1 0 exist? (1) 1 (3) 3 (2) 2 (4) 0 23 A study finds that 80% of the local high school students text while doing homework. Ten students are selected at random from the local high school. Which expression would be part of the process used to determine the probability that, at most, 7 of the 10 students text while doing homework? 6 4 4 __ 1 (__ 5) (5) 4 1 __ C (__ 5) (5) (1) 10C6 (2) 10 10 7 7 Algebra 2/Trigonometry June 12 10 7 3 __ __ (10 ) (10 ) 7 __ 3 __ C (10 ) (10 ) (3) 10C8 (4) 10 9 2 1 9 [9] [OVER] 24 In which interval of f(x) cos(x) is the inverse also a function? __ (1) __ (3) 0 x 2 x 2 3 x ___ (4) __ 2 2 x __ (2) __ 2 2 25 As shown in the table below, a person s target heart rate during exercise changes as the person gets older. Age (years) Target Heart Rate (beats per minute) 20 135 25 132 30 129 35 125 40 122 45 119 50 115 Which value represents the linear correlation coefficient, rounded to the nearest thousandth, between a person s age, in years, and that person s target heart rate, in beats per minute? (1) 0.999 (3) 0.998 (2) 0.664 (4) 1.503 Algebra 2/Trigonometry June 12 [10] Use this space for computations. 26 In MNP, m 6 and n 10. Two distinct triangles can be constructed if the measure of angle M is (1) 35 (3) 45 (2) 40 Use this space for computations. (4) 50 27 If order does not matter, which selection of students would produce the most possible committees? (1) 5 out of 15 (3) 20 out of 25 (2) 5 out of 25 (4) 15 out of 25 Algebra 2/Trigonometry June 12 [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] 28 Determine the value of n in simplest form: i13 i18 i31 n 0 Algebra 2/Trigonometry June 12 [12] 29 The formula for continuously compounded interest is A Pert, where A is the amount of money in the account, P is the initial investment, r is the interest rate, and t is the time in years. Using the formula, determine, to the nearest dollar, the amount in the account after 8 years if $750 is invested at an annual rate of 3%. Algebra 2/Trigonometry June 12 [13] [OVER] 30 Express cos (sec cos ), in terms of sin . Algebra 2/Trigonometry June 12 [14] 31 A cup of soup is left on a countertop to cool. The table below gives the temperatures, in degrees Fahrenheit, of the soup recorded over a 10-minute period. Time in Minutes (x) Temperature in F (y) 0 2 4 6 8 10 180.2 165.8 146.3 135.4 127.7 110.5 Write an exponential regression equation for the data, rounding all values to the nearest thousandth. 32 Find, to the nearest tenth, the radian measure of 216 . Algebra 2/Trigonometry June 12 [15] [OVER] 33 Find the third term in the recursive sequence ak 1 2ak 1, where a1 3. Algebra 2/Trigonometry June 12 [16] 34 The two sides and included angle of a parallelogram are 18, 22, and 60 . Find its exact area in simplest form. Algebra 2/Trigonometry June 12 [17] [OVER] 35 Write an equation for the graph of the trigonometric function shown below. y 1 0 1 Algebra 2/Trigonometry June 12 2 [18] x 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] 4 x2 2 36 Express in simplest form: x 7 x 12 2x 4 x 3 Algebra 2/Trigonometry June 12 [19] [OVER] 37 During a particular month, a local company surveyed all its employees to determine their travel times to work, in minutes. The data for all 15 employees are shown below. 25 45 52 55 59 30 40 35 8 65 25 40 29 37 55 Determine the number of employees whose travel time is within one standard deviation of the mean. Algebra 2/Trigonometry June 12 [20] 38 The measures of the angles between the resultant and two applied forces are 60 and 45 , and the magnitude of the resultant is 27 pounds. Find, to the nearest pound, the magnitude of each applied force. Algebra 2/Trigonometry June 12 [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 algebraically for all values of x: 81 Algebra 2/Trigonometry June 12 x3 2 x2 27 [22] 5x 3 Reference Sheet Functions of the Double Angle sin (A + B) sin A cos B + cos A sin B cos (A + B) cos A cos B sin A sin B tan A + tan B tan (A + B) ___________ 1 tan A tan B sin 2A 2 sin A cos A cos 2A cos2 A sin2 A cos 2A 2 cos2 A 1 cos 2A 1 2 sin2 A Functions of the Difference of Two Angles Tear Here Area of a Triangle 1 ab sin C K _ 2 Functions of the Sum of Two Angles 2 tan A tan 2A _______ 1 tan2 A Law of Cosines a 2 b 2 + c 2 2bc cos A sin (A B) sin A cos B cos A sin B cos (A B) cos A cos B + sin A sin B tan A tan B tan (A B) ____________ 1 + tan A tan B Functions of the Half Angle _________ 1 A q sin _ 2 1 cos A _______ 2 _________ Law of Sines c b ____ a ____ ____ sin A sin B sin C + cos A 1 _______ A q 1 cos _ 2 2 _________ 1 cos A 1 tan _ A q _______ 2 1 + cos A Sum of a Finite Arithmetic Series n(a1 + an) Sn _______ 2 Sum of a Finite Geometric Series a 1(1 r n) _______ Sn 1 r Binomial Theorem (a + b)n nC0anb0 + nC1an 1b1 + nC2an 2b2 + ... + nCna0bn n (a + b)n n rbr nCr a r=0 /PSNBM $VSWF 4UBOEBSE %FWJBUJPO Tear Here m m m m Algebra 2/Trigonometry June 12 m m 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 ALGEBRA 2/TRIGONOMETRY Printed on Recycled Paper ALGEBRA 2/TRIGONOMETRY Algebra 2/Trigonometry June 12 FOR TEACHERS ONLY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA 2/TRIGONOMETRY Tuesday, June 19, 2012 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. Do not attempt to correct the student s work by making insertions or changes of any kind. In scoring the open-ended questions, use check marks to indicate student errors. If the student s responses for the multiple-choice questions are being hand scored prior to being scanned, the scorer must be careful not to make any stray marks on the answer sheet that might later interfere with the accuracy of the scanning. 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 student s separate answer sheet, for each question, record the number of credits earned and the teacher s assigned rater/scorer letter. Schools are not 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. Raters should record the student s scores for all questions and the total raw score on the student s separate 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/ on Tuesday, June 19, 2012. Because scale scores corresponding to raw scores in the conversion chart may change from one administration 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 separate 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) . . . . . 1 . . . . . (8) . . . . . 3 . . . . . (15) . . . . . 3 . . . . . (22) . . . . . 4 . . . . . (2) . . . . . 1 . . . . . (9) . . . . . 3 . . . . . (16) . . . . . 2 . . . . . (23) . . . . . 1 . . . . . (3) . . . . . 4 . . . . . (10) . . . . . 1 . . . . . (17) . . . . . 4 . . . . . (24) . . . . . 3 . . . . . (4) . . . . . 3 . . . . . (11) . . . . . 1 . . . . . (18) . . . . . 2 . . . . . (25) . . . . . 1 . . . . . (5) . . . . . 2 . . . . . (12) . . . . . 3 . . . . . (19) . . . . . 3 . . . . . (26) . . . . . 1 . . . . . (6) . . . . . 4 . . . . . (13) . . . . . 1 . . . . . (20) . . . . . 1 . . . . . (27) . . . . . 4 . . . . . (7) . . . . . 4 . . . . . (14) . . . . . 2 . . . . . (21) . . . . . 4 . . . . . Algebra 2/Trigonometry Rating Guide June 12 [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 at: 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 I. 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 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). Algebra 2/Trigonometry Rating Guide June 12 [3] Part II For each question, use the specific criteria to award a maximum of 2 credits. Unless otherwise specified, mathematically correct alternative solutions should be awarded appropriate credit. (28) [2] 1, and appropriate work is shown. [1] Appropriate work is shown, but one computational error is made. or [1] Appropriate work is shown, but one conceptual error is made. or [1] Appropriate work is shown, but the answer is not expressed in simplest form. or [1] 1, 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. (29) [2] 953, 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] 953, 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 12 [4] (30) [2] sin2 , and appropriate work is shown. [1] Appropriate work is shown, but one substitution or simplification error is made. or [1] Appropriate work is shown, but one conceptual error is made. or [1] cos sec cos2 or cos 1 cos cos or 1 cos2 is written, but no further correct work is shown. or [1] sin2 , 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. (31) [2] y 180.377(0.954)x [1] Appropriate work is shown, but one rounding error is made. or [1] Appropriate work is shown, but one conceptual error is made, such as using the wrong regression equation. or x [1] The expression 180.377(0.954) is written. or [1] An incorrect exponential regression equation 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. Algebra 2/Trigonometry Rating Guide June 12 [5] (32) [2] 3.8, 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] Appropriate work is shown to find 1.2 , but no further correct work is shown. or [1] 3.8, 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. (33) [2] 9, and appropriate work is shown. [1] Appropriate work is shown, but one computational error is made. or [1] Appropriate work is shown, but one conceptual error is made. or [1] 9, 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. (34) [2] 198 3 , and appropriate work is shown. [1] Appropriate work is shown, but one computational error is made. or [1] Appropriate work is shown, but one conceptual error is made. or [1] Appropriate work is shown, but the answer is expressed as a decimal. or [1] Appropriate work is shown to find 396 sin 60, but no further correct work is shown. or [1] 198 3 , 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 12 [6] (35) [2] y 3 sin 2x, or an equivalent equation is written. [1] One computational error is made, but an appropriate equation is written. or [1] One conceptual error is made, but an appropriate equation is written. or [1] Amplitude 3 and frequency 2 are found. or [1] The expression 3 sin 2x 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. Algebra 2/Trigonometry Rating Guide June 12 [7] Part III For each question, use the specific criteria to award a maximum of 4 credits. Unless otherwise specified, mathematically correct alternative solutions should be awarded appropriate credit. (36) [4] (x 2) or x 2 or an equivalent simplified answer, and appropriate 2(x 4) 2x 8 work is shown. [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 factoring out the 1. [1] Appropriate work is shown, but one conceptual error and one computational, factoring, or simplification error are made. or [1] (x 2) , but no work is shown. 2(x 4) [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. (37) [4] 8, and appropriate work is shown. [3] Appropriate work is shown, but one computational error is made. or [3] 25.1 x 54.9 or an equivalent expression is written, but no further correct work is shown. [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 using 15.4, the sample standard deviation. or [2] 14.9, but no further correct work is shown. [1] Appropriate work is shown, but one conceptual error and one computational error are 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 12 [8] (38) [4] 24 and 20, and appropriate work is shown. [3] Appropriate work is shown, but one computational or rounding error is made. or [3] Appropriate work is shown to find either 24 or 20, but no further correct work is shown. [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. or [2] A correct substitution is made into the Law of Sines, 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] A correctly labeled diagram is drawn, but no further correct work is shown. or [1] 24 and 20, 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 12 [9] Part IV For this question, use the specific criteria to award a maximum of 6 credits. Unless otherwise specified, mathematically correct alternative solutions should be awarded appropriate credit. (39) [6] 5 , 0, and 1 , and appropriate algebraic work is shown. 2 2 [5] Appropriate work is shown, but one computational or factoring error is made. [4] Appropriate work is shown, but two computational or factoring errors are made. or [4] Appropriate work is shown to find x(2x 5)(2x 1) 0, but no further correct work is shown. or [4] Appropriate work is shown to find x 0, and 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 or factoring errors are made. or [3] Appropriate work is shown, but one conceptual error is made. or ( ) [3] Appropriate work is shown to find x 4x 2 8x 5 0 , but no further correct work is shown. or [3] 5 , 0, and 1 , but a method other than algebraic is used. 2 2 Algebra 2/Trigonometry Rating Guide June 12 [10] [2] Appropriate work is shown, but one conceptual error and one computational or factoring error are made. or [2] Appropriate work is shown to find 4x 3 8x 2 5x or an equivalent equation, but no further correct work is shown. [1] Appropriate work is shown, but one conceptual error and two or more computational or factoring errors are made. or [1] 34(x 3 + 2x 2 ) 3 5x 3 3 is written, but no further correct work is shown. or [1] 5 , 0, and 1 , but no work is shown. 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 12 [11] Map to Core Curriculum Content Strands Item Numbers Number Sense and Operations 1, 19, 28 Algebra 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 13, 14, 15, 16, 17, 18, 20, 22, 24, 26, 29, 30, 33, 34, 35, 36, 38, 39 Measurement 32 Statistics and Probability 21, 23, 25, 27, 31, 37 Regents Examination in Algebra 2/Trigonometry June 2012 Chart for Converting Total Test Raw Scores to Final Examination Scores (Scale Scores) The Chart for Determining the Final Examination Score for the June 2012 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 19, 2012. 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 12 [12]

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