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New York Regents Algebra 2 / Trigonometry January 2012

36 pages, 39 questions, 11 questions with responses, 11 total responses,    0    0
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ALGEBRA 2/TRIGONOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA 2/TRIGONOMETRY Wednesday, January 25, 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. 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 The yearbook staff has designed a survey to learn student opinions on how the yearbook could be improved for this year. If they want to distribute this survey to 100 students and obtain the most reliable data, they should survey (1) every third student sent to the office (2) every third student to enter the library (3) every third student to enter the gym for the basketball game (4) every third student arriving at school in the morning 2 What is the sum of the first 19 terms of the sequence 3, 10, 17, 24, 31, ? (1) 1188 (3) 1254 (2) 1197 (4) 1292 3 Which expression, when rounded to three decimal places, is equal to 1.155? () () 5 (1) sec ___ 6 (3) sin (2) tan(49 20 ) (4) csc( 118 ) 4 If f(x) 4x x2 and g(x) 3 ___ 5 () 1 1 __ , then (f g) __ is equal to 2 x 4 (1) __ 7 7 (3) __ 2 (2) (4) 4 2 Algebra 2/Trigonometry January 12 [2] Use this space for computations. 5 A population of rabbits doubles every 60 days according to the t formula P Use this space for computations. 10(2) 60 , where P is the population of rabbits on day t. What is the value of t when the population is 320? (1) 240 (3) 660 (2) 300 (4) 960 6 What is the product of ( x 4 ) )( 1 ? 3 x 1 and 4 3 x2 (1) __ 8 1 __ 9 x2 (3) __ 8 x __ 6 1 __ 9 x2 (2) __ 16 1 __ 9 x2 (4) __ 16 x __ 6 1 __ 9 7 Which is a graph of y cot x? y y 1 1 2 1 x 2 1 (1) (3) y x y 1 1 1 2 (2) Algebra 2/Trigonometry January 12 x 1 2 x (4) [3] [OVER] Use this space for computations. 8 Which expression always equals 1? (1) cos2 x sin2 x (3) cos x sin x (2) cos2 x sin2 x (4) cos x sin x 9 What are the sum and product of the roots of the equation 6x2 4x 12 0? 2 __ ; product 2 3 2 __ ; product 2 3 2 2; product __ 3 2 __ 2; product 3 (1) sum (2) sum (3) sum (4) sum 10 Given ABC with a 9, b triangle can be drawn? 10, and m B 70, what type of (1) an acute triangle, only (2) an obtuse triangle, only (3) both an acute triangle and an obtuse triangle (4) neither an acute triangle nor an obtuse triangle 11 When x 1 1 is divided by x 1, the quotient equals (1) 1 (3) x 1 (2) __ x (4) Algebra 2/Trigonometry January 12 1 __ x [4] 12 If the amount of time students work in any given week is normally distributed with a mean of 10 hours per week and a standard deviation of 2 hours, what is the probability a student works between 8 and 11 hours per week? (1) 34.1% (3) 53.2% (2) 38.2% Use this space for computations. (4) 68.2% 1 13 What is the conjugate of __ 2 (1) 1 __ 2 1 (2) __ 2 3 __ i 2 3 __ i 2 3 __ i? 2 3 (3) __ 2 (4) 1 __ 2 1 __ i 2 3 __ i 2 14 Given angle A in Quadrant I with sin A Quadrant II with cos B 33 (1) __ 65 (2) 33 __ 65 12 __ and angle B in 13 3 __ , what is the value of cos (A 5 B)? 63 (3) __ 65 (4) 63 __ 65 15 Which expression represents the third term in the expansion of (2x4 y)3? (1) y3 (3) 6x4y2 (2) 6 x 4y 2 (4) 2x4y2 Algebra 2/Trigonometry January 12 [5] [OVER] 16 What is the solution set of the equation 3x5 (1) {0, 2} (3) {0, (2) {0, 2, 3} (4) { 2, 2, 48x 0? 2i} 2i} 17 A sequence has the following terms: a1 4, a2 10, a3 25, a4 Which formula represents the nth term in this sequence? (1) an 4 (2) an 4 2.5(n (3) an 2.5n 1) Use this space for computations. 4(2.5)n (4) an 4(2.5)n 62.5. 1 18 In parallelogram BFLO, OL 3.8, LF 7.4, and m O ___ If diagonal BL is drawn, what is the area of BLF? (1) 11.4 (3) 22.7 (2) 14.1 126. (4) 28.1 19 Which statement about the graph of the equation y e x is not true? (1) It is asymptotic to the x-axis. (2) The domain is the set of all real numbers. (3) It lies in Quadrants I and II. (4) It passes through the point (e,1). 20 What is the number of degrees in an angle whose measure is 2 radians? 360 (1) ___ (3) 360 (2) ___ 360 (4) 90 Algebra 2/Trigonometry January 12 [6] 21 A spinner is divided into eight equal sections. Five sections are red and three are green. If the spinner is spun three times, what is the probability that it lands on red exactly twice? 25 (1) __ 64 75 (3) ___ 512 45 (2) ___ 512 Use this space for computations. 225 (4) ___ 512 22 What is the range of f(x) |x 3| 2? (1) {x | x 3} (3) {x | x real numbers} (2) {y| y 2} (4) {y| y real numbers} 23 Which calculator output shows the strongest linear relationship between x and y? (1) Lin Reg y a bx a 59.026 b 6.767 r .8643 (3) Lin Reg y a bx a 2.45 b .95 r .6022 (2) Lin Reg y a bx a .7 b 24.2 r .8361 (4) Lin Reg y a bx a 2.9 b 24.1 r .8924 24 If log x2 log 2a equivalent to log 3a, then log x expressed in terms of log a is 1 (1) __ log 5a 2 1 (2) __ log 6 2 (3) log 6 log a Algebra 2/Trigonometry January 12 log a (4) log 6 2 log a [7] [OVER] Use this space for computations. 25 Which function is one-to-one? (1) f(x) |x| (3) f(x) x2 (2) f(x) 2x (4) f(x) sin x 26 If p varies inversely as q, and p 3 of p when q __ ? 5 10 when q (1) 25 (3) 9 (2) 15 3 __ , what is the value 2 (4) 4 27 Which equation is graphed in the diagram below? y (15,8) 8 6 4 2 x 3 6 9 12 15 18 21 24 27 30 (1) y (2) y 3 cos ___ x 30 () 3 cos(___ x) 15 8 (3) y 5 (4) y Algebra 2/Trigonometry January 12 3 cos ___ x 30 () 3 cos(___ x) 15 [8] 8 5 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 Find the solution of the inequality x2 Algebra 2/Trigonometry January 12 4x 5, algebraically. [9] [OVER] 29 Solve algebraically for x: 4 3 30 Evaluate: ( n4 2x 5 1 n) n1 Algebra 2/Trigonometry January 12 [10] 31 Express in simplest form: 3 a 6 b9 64 32 A blood bank needs twenty people to help with a blood drive. Twenty-five people have volunteered. Find how many different groups of twenty can be formed from the twenty-five volunteers. Algebra 2/Trigonometry January 12 [11] [OVER] 33 On the axes below, for 2 x 2x 2, graph y 1 3. y x Algebra 2/Trigonometry January 12 [12] 34 Write an equation of the circle shown in the diagram below. y ( 8,4) ( 5,2) x Algebra 2/Trigonometry January 12 [13] [OVER] 35 Express the exact value of csc 60 , with a rational denominator. Algebra 2/Trigonometry January 12 [14] 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 diagram below shows the plans for a cell phone tower. A guy wire attached to the top of the tower makes an angle of 65 degrees with the ground. From a point on the ground 100 feet from the end of the guy wire, the angle of elevation to the top of the tower is 32 degrees. Find the height of the tower, to the nearest foot. Wire 32 Tower 65 100 ft Algebra 2/Trigonometry January 12 [15] [OVER] 37 If log 4 x 2.5 and log y 125 Algebra 2/Trigonometry January 12 x 3 __ , find the numerical value of __ , in simplest form. y 2 [16] 38 A population of single-celled organisms was grown in a Petri dish over a period of 16 hours. The number of organisms at a given time is recorded in the table below. Time, hrs (x) Number of Organisms ( y) 0 25 2 36 4 52 6 68 8 85 10 104 12 142 16 260 Determine the exponential regression equation model for these data, rounding all values to the nearest ten-thousandth. Using this equation, predict the number of single-celled organisms, to the nearest whole number, at the end of the 18th hour. Algebra 2/Trigonometry January 12 [17] [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 Perform the indicated operations and simplify completely: x3 Algebra 2/Trigonometry January 12 3x2 x2 6x 4x 18 2x 4 x4 3x3 [18] x2 2x 16 8 x 2 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 b a ____ ____ sin A sin B c ____ Binomial Theorem n b0 0nCr an rbr r= Algebra 2/Trigonometry January 12 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 nC0a 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 ALGEBRA 2/TRIGONOMETRY Tear Here Wednesday, January 25, 2012 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. The declaration below must be signed when you have completed the examination. Tear Here 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 January 12 ALGEBRA 2/TRIGONOMETRY Rater s/Scorer s Name (minimum of three) Question 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 Tear Here ALGEBRA 2/TRIGONOMETRY 88 Part IV Rater s/Scorer s Initials Total Raw Score Part III Credits Earned Checked by Scale Score (from conversion chart) Tear Here Printed on Recycled Paper ALGEBRA 2/TRIGONOMETRY Algebra 2/Trigonometry January 12 FOR TEACHERS ONLY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA 2/TRIGONOMETRY Wednesday, January 25, 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 rating the open-ended questions, you may make check marks in the exam booklet to indicate student errors. If the students were given scannable answer sheets for the multiplechoice questions, 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 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. 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. 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 Wednesday, January 25, 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 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) . . . . . 3 . . . . . (22) . . . . . 2 . . . . . (2) . . . . . 3 . . . . . (9) . . . . . 2 . . . . . (16) . . . . . 3 . . . . . (23) . . . . . 4 . . . . . (3) . . . . . 1 . . . . . (10) . . . . . 1 . . . . . (17) . . . . . 4 . . . . . (24) . . . . . 2 . . . . . (4) . . . . . 4 . . . . . (11) . . . . . 2 . . . . . (18) . . . . . 1 . . . . . (25) . . . . . 2 . . . . . (5) . . . . . 2 . . . . . (12) . . . . . 3 . . . . . (19) . . . . . 4 . . . . . (26) . . . . . 1 . . . . . (6) . . . . . 2 . . . . . (13) . . . . . 2 . . . . . (20) . . . . . 1 . . . . . (27) . . . . . 4 . . . . . (7) . . . . . 3 . . . . . (14) . . . . . 1 . . . . . (21) . . . . . 4 . . . . . Algebra 2/Trigonometry Rating Guide January 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 January 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] x 1 or x 5 , or an equivalent interval notation, and appropriate algebraic work is shown. [1] Appropriate work is shown, but one computational or factoring error is made. or [1] Appropriate work is shown, but one conceptual error is made, such as not representing the solution as a disjunction. or [1] Appropriate work is shown, but only one correct inequality is found. or [1] x 1 or x 5 , but a method other than algebraic is used. or [1] x 1 or x 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. (29) [2] 7, and appropriate algebraic 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] 7, but a method other than an algebraic method is used. 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 January 12 [4] (30) [2] 104, 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] 104, 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] a 2 b3 4 [1] One computational or simplification error is made. or [1] One conceptual error is made. [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 January 12 [5] (32) [2] 53,130, 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 evaluating 25P20. or [1] C20 or an equivalent expression, but no further correct work is shown. 25 or [1] 53,130, but no work is shown. [0] P is stated, but no further work is shown. 25 20 or [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] A correct graph is drawn. [1] One graphing error is made. or [1] One conceptual error is made. [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 January 12 [6] (34) [2] (x 5)2 (y 2)2 13, 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 to find the radius, but no further work is shown. or [1] (x 5) 2 (y 2) 2 13, 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] 23 , and appropriate work is shown. 3 [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 with a rational denominator. or [1] 23 , but no work is shown. 3 [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. Algebra 2/Trigonometry Rating Guide January 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] 88, 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. or [2] The hypotenuse of one of the right triangles is found correctly, 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] 88, but no work is shown. [0] The obtuse triangle is treated as a right triangle. 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 January 12 [8] (37) [4] 800, and appropriate work is shown. [3] Appropriate work is shown, but one computational or simplification error is made. or [3] Appropriate work is shown to find both x and y, but no further correct work is shown. [2] Appropriate work is shown, but two or more computational or simplification errors are made. or [2] Appropriate work is shown, but one conceptual error is made. or [2] Appropriate work is shown to find y, but no further correct work is shown. [1] Appropriate work is shown, but one conceptual error and one computational or simplification error are made. or [1] Appropriate work is shown to find x, but no further correct work is shown. or [1] 800, 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 January 12 [9] (38) [4] y 27.2025(1.1509)x and 341, and appropriate work is shown. [3] Appropriate work is shown, but one computational or rounding error is made. or [3] The expression 27.2025(1.1509)x is written and 341, and appropriate work is shown. or [3] y 27.2025(1.1509)x and 341, but no 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 x [2] The expression 27.2025(1.1509) is written and 341, but no work is shown. or [2] y 27.2025(1.1509)x, but no further correct work is shown. or [2] An incorrect regression equation of equal difficulty is solved appropriately for the number of single-celled organisms. [1] Appropriate work is shown, but one conceptual error and one computational or rounding error are made. or [1] The expression 27.2025(1.1509)x is written, but no further correct work is shown. or [1] 341, 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 January 12 [10] 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] 2 ( x2 x 6) 4 or 2 x2 x 12 4 , and appropriate work is shown. [5] Appropriate work is shown, but one computational, factoring, or simplification error is made. [4] Appropriate work is shown, but two computational, factoring, or simplification errors are made. or [4] ( x2 6)( x 3) 2( x 2) ( x 4)( x 4) or an equivalently factored 3 x( x 4) x ( x 3) ( x 4)( x 2) expression, but no further correct work is shown. [3] Appropriate work is shown, but three or more computational, factoring, or simplification errors are made. or [3] Appropriate work is shown, but one conceptual error is made. [2] Appropriate work is shown, but one conceptual error and one computational, factoring, or simplification error are made. [1] Appropriate work is shown, but one conceptual error and two or more computational, factoring, or simplification errors are made. or [1] 2 ( x2 x 4 6) or 2 x2 x 12 4 , 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 January 12 [11] Map to Core Curriculum Content Strands Item Numbers Number Sense and Operations 6, 13, 30 Algebra 2, 3, 4, 5, 7, 8, 9, 10, 11, 14, 15, 16, 17, 18, 19, 22, 24, 25, 26, 27, 28, 29, 31, 33, 34, 35, 36, 37, 39 Measurement 20 Statistics and Probability 1, 12, 21, 23, 32, 38 Regents Examination in Algebra 2/Trigonometry January 2012 Chart for Converting Total Test Raw Scores to Final Examination Scores (Scale Scores) The Chart for Determining the Final Examination Score for the January 2012 Regents Examination in Algebra 2/Trigonometry will be posted on the Department s web site at: http://www.p12.nysed.gov/apda/ on Wednesday, January 25, 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 January 12 [12]

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