ALGEBRA 2/TRIGONOMETRY

Transcription

1 ALGEBRA 2/TRIGONOMETRY The University of the State of New Yk REGENTS HIGH SCHOOL EXAMINATION ALGEBRA 2/TRIGONOMETRY Tuesday, January 28, :15 to 4:15 p.m., only Student Name: School Name: The possession use of any communications device is strictly prohibited when taking this examination. If you have use any communications device, no matter how briefly, your examination will be invalidated and no sce will be calculated f you. Print your name and the name of your school on the lines above. A separate answer sheet f Part I has been provided to you. Follow the instructions from the proct f completing the student infmation on your answer sheet. This examination has four parts, with a total of 39 questions. You must answer all questions in this examination. Recd 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 wk should be written in pen, except f graphs and drawings, which should be done in pencil. Clearly indicate the necessary steps, including appropriate fmula substitutions, diagrams, graphs, charts, etc. The fmulas that you may need to answer some questions in this examination are found at the end of the examination. This sheet is perfated so you may remove it from this booklet. Scrap paper is not permitted f any part of this examination, but you may use the blank spaces in this booklet as scrap paper. A perfated sheet of scrap graph paper is provided at the end of this booklet f any question f which graphing may be helpful but is not required. You may remove this sheet from this booklet. Any wk done on this sheet of scrap graph paper will not be sced. 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 answers pri to the examination and that you have neither given n 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 calculat and a straightedge (ruler) must be available f you to use while taking this examination. DO NOT OPEN THIS EXAMINATION BOOKLET UNTIL THE SIGNAL IS GIVEN. ALGEBRA 2/TRIGONOMETRY

2 Part I Answer all 27 questions in this part. Each crect answer will receive 2 credits. F each statement question, choose the wd expression that, of those given, best completes the statement answers the question. Recd your answers on your separate answer sheet. [54] 1 What is the common difference in the sequence 2a 1, 4a 4, 6a 7, 8a 10,...? (1) 2a 3 (3) 2a 5 (2) 2a 3 (4) 2a 5 Use this space f computations. 2 Which expression is equivalent to 3 x 2 1 ( )? 1 1 (1) (3) 2 2 3x 9x (2) 3x 2 (4) 9x 2 3 If g(x) 1 x 8 and h(x) 1 x 2, what is the value of 2 2 g(h( 8))? (1) 0 (3) 5 (2) 9 (4) The expression 7 11 is equivalent to (1) 7 11 (3) (2) 7 11 (4) Algebra 2/Trigonometry January 14 [2]

3 b a c 5 The expression is equivalent to b d c c 1 (1) (3) d 1 ac cd b b Use this space f computations. a b (2) (4) d b ac cd A school cafeteria has five different lunch periods. The cafeteria staff wants to find out which items on the menu are most popular, so they give every student in the first lunch period a list of questions to answer in der to collect data to represent the school. Which type of study does this represent? (1) observation (3) population survey (2) controlled experiment (4) sample survey 7 Which relation is both one-to-one and onto? r m h s r m h s (1) (3) r m h s r m h s (2) (4) Algebra 2/Trigonometry January 14 [3] [OVER]

4 8 Max solves a quadratic equation by completing the square. He shows a crect step: Use this space f computations. (x 2) 2 9 What are the solutions to his equation? (1) 2 3i (3) 3 2i (2) 2 3i (4) 3 2i 9 Which expression represents the total number of different 11-letter arrangements that can be made using the letters in the wd MATHEMATICS? (1) 11! 3! (3) (2) 11! 2! 2! 2! (4) 11! 8! 11! 2! 2! 2! 10 If $5000 is invested at a rate of 3% interest compounded quarterly, what is the value of the investment in 5 years? (Use the fmula A P r ( 1 nt n ), where A is the amount accrued, P is the principal, r is the interest rate, n is the number of times per year the money is compounded, and t is the length of time, in years.) (1) $ (3) $ (2) $ (4) $ The roots of the equation 2x 2 4 9x are (1) real, rational, and equal (2) real, rational, and unequal (3) real, irrational, and unequal (4) imaginary Algebra 2/Trigonometry January 14 [4]

5 12 If d varies inversely as t, and d 20 when t 2, what is the value of t when d 5? (1) 8 (3) 8 (2) 2 (4) 2 Use this space f computations. 13 If sin A 7 and A terminates in Quadrant IV, tan A equals 25 (1) 7 25 (3) (2) 7 24 (4) Which expression is equivalent to ( a n) n 1 (1) 2a 2 17 (3) 2a 2 10a 17 (2) 4a 2 30 (4) 4a 2 20a ? 15 What are the codinates of the center of a circle whose equation is x 2 y 2 16x 6y 53 0? (1) ( 8, 3) (3) (8, 3) (2) ( 8,3) (4) (8,3) Algebra 2/Trigonometry January 14 [5] [OVER]

6 16 F y 3, what are the domain and range? x 4 (1) {x x 4} and {y y 0} (3) {x x 4} and {y y 0} (2) {x x 4} and {y y 0} (4) {x x 4} and {y y 0} Use this space f computations. 17 A math club has 30 boys and 20 girls. Which expression represents the total number of different 5-member teams, consisting of 3 boys and 2 girls, that can be fmed? (1) 30 P 3 20 P 2 (3) 30 P 3 20 P 2 (2) 30 C 3 20 C 2 (4) 30 C 3 20 C 2 18 What is the product of the roots of x 2 4x k 0 if one of the roots is 7? (1) 21 (3) 21 (2) 11 (4) In DEF, d 5, e 8, and m D 32. How many distinct triangles can be drawn given these measurements? (1) 1 (3) 3 (2) 2 (4) 0 20 Liz has applied to a college that requires students to sce in the top 6.7% on the mathematics ption of an aptitude test. The sces on the test are approximately nmally distributed with a mean sce of 576 and a standard deviation of 104. What is the minimum sce Liz must earn to meet this requirement? (1) 680 (3) 740 (2) 732 (4) 784 Algebra 2/Trigonometry January 14 [6]

7 3 2 3 ( )( 4 ) 21 The expression 27x 16x is equivalent to Use this space f computations. 2 3 (1) 12x 2 (3) 6x 2x 2 3 (2) 12x 2x (4) 6x Which sketch shows the inverse of y a x, where a 1? y y 1 x 1 x (1) (3) y y 1 x 1 x (2) (4) Algebra 2/Trigonometry January 14 [7] [OVER]

8 2 x 9x The expression (2 x) is equivalent to 2 x 121 (1) x 11 (3) 11 x 1 1 (2) x 11 (4) 11 x Use this space f computations. 24 Which graph represents the solution set of x 16 x 2 7? (1) 0 5 (2) 0 5 (3) 0 5 (4) 0 5 Algebra 2/Trigonometry January 14 [8]

9 25 Which equation represents a graph that has a period of 4π? Use this space f computations. (1) y 3 sin 1 2 x (3) y 3 sin 1 4 x (2) y 3 sin 2x (4) y 3 sin 4x 26 The expression x 2 (x 2) (x 2) is equivalent to (1) x 2 (3) x 3 2x 2 x 2 (2) x 2 1 (4) (x 1)(x 1)(x 2) 27 Approximately how many degrees does five radians equal? π (1) 286 (3) 36 (2) 900 (4) 5π Algebra 2/Trigonometry January 14 [9] [OVER]

10 Part II Answer all 8 questions in this part. Each crect answer will receive 2 credits. Clearly indicate the necessary steps, including appropriate fmula substitutions, diagrams, graphs, charts, etc. F all questions in this part, a crect numerical answer with no wk shown will receive only 1 credit. All answers should be written in pen, except f graphs and drawings, which should be done in pencil. [16] 28 Show that sec θ sin θ cot θ 1 is an identity. 29 Find, to the nearest tenth of a square foot, the area of a rhombus that has a side of 6 feet and an angle of 50. Algebra 2/Trigonometry January 14 [10]

11 30 The following is a list of the individual points sced by all twelve members of the Webster High School basketball team at a recent game: Find the interquartile range f this set of data. 31 Determine algebraically the x-codinate of all points where the graphs of xy 10 and y x 3 intersect. Algebra 2/Trigonometry January 14 [11] [OVER]

12 32 Solve 4x 5 13 algebraically f x. 33 Express 4xi 5yi 8 6xi 3 2yi 4 in simplest a bi fm. Algebra 2/Trigonometry January 14 [12]

13 34 In an arithmetic sequence, a 4 19 and a Determine a fmula f a n, the n th term of this sequence. Algebra 2/Trigonometry January 14 [13] [OVER]

14 35 Circle O shown below has a radius of 12 centimeters. To the nearest tenth of a centimeter, determine the length of the arc, x, subtended by an angle of x 12 cm O Algebra 2/Trigonometry January 14 [14]

15 Part III Answer all 3 questions in this part. Each crect answer will receive 4 credits. Clearly indicate the necessary steps, including appropriate fmula substitutions, diagrams, graphs, charts, etc. F all questions in this part, a crect numerical answer with no wk shown will receive only 1 credit. All answers should be written in pen, except f graphs and drawings, which should be done in pencil. [12] 36 Solve algebraically f all exact values of x in the interval 0 x 2π: 2 sin 2 x 5 sin x 3 Algebra 2/Trigonometry January 14 [15] [OVER]

16 37 Because Sam s backyard gets very little sunlight, the probability that a geranium planted there will flower is Sam planted five geraniums. Determine the probability, to the nearest thousandth, that at least four geraniums will flower. Algebra 2/Trigonometry January 14 [16]

17 38 Two sides of a parallelogram measure 27 cm and 32 cm. The included angle measures 48. Find the length of the longer diagonal of the parallelogram, to the nearest centimeter. Algebra 2/Trigonometry January 14 [17] [OVER]

18 Part IV Answer the question in this part. A crect answer will receive 6 credits. Clearly indicate the necessary steps, including appropriate fmula substitutions, diagrams, graphs, charts, etc. A crect numerical answer with no wk shown will receive only 1 credit. The answer should be written in pen. [6] 39 Solve algebraically f all values of x: log (x 3) (2x 3) log (x 3) (x 5) 2 Algebra 2/Trigonometry January 14 [18]

19 Tear Here Tear Here Reference Sheet Area of a Triangle Law of Cosines K _ 1 ab sin C a 2 b 2 + c 2 2bc cos A 2 Functions of the Sum of Two Angles Functions of the Double Angle sin (A + B) sin A cos B + cos A sin B sin 2A 2 sin A cos A cos (A + B) cos A cos B sin A sin B cos 2A cos 2 A sin 2 A tan A + tan B cos 2A 2 cos tan (A + B) 2 A 1 1 tan A tan B cos 2A 1 2 sin 2 A Functions of the Difference of Two Angles tan 2A 2 tan A 1 tan 2 A sin (A B) sin A cos B cos A sin B cos (A B) cos A cos B + sin A sin B Functions of the Half Angle tan A tan B tan (A B) 1 + tan A tan B sin _ 1 2 A 1 cos A 2 Law of Sines a sin A b sin B c cos _ 1 2 A 1 + cos A 2 sin C tan _ 1 Sum of a Finite Arithmetic Series 2 A 1 cos A 1 + cos A S n n(a 1 + a n ) Sum of a Finite Geometric Series 2 S n a 1(1 r n ) Binomial Theem 1 r (a + b) n n C 0 a n b 0 + n C 1 a n 1 b 1 + n C 2 a n 2 b n C n a 0 b n n (a + b) n nc r a n r b r r = 0 Algebra 2/Trigonometry January 14 [19]

20 Tear Here Tear Here

21 Tear Here Tear Here Scrap Graph Paper This sheet will not be sced.

22 Scrap Graph Paper This sheet will not be sced. Tear Here Tear Here

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24 ALGEBRA 2/TRIGONOMETRY Printed on Recycled Paper ALGEBRA 2/TRIGONOMETRY

25 FOR TEACHERS ONLY The University of the State of New Yk REGENTS HIGH SCHOOL EXAMINATION ALGEBRA 2/TRIGONOMETRY Tuesday, January 28, :15 to 4:15 p.m., only SCORING KEY AND RATING GUIDE Mechanics of Rating The following procedures are to be followed f scing student answer papers f the Regents Examination in Algebra 2/Trigonometry. Me detailed infmation about scing is provided in the publication Infmation Booklet f Scing the Regents Examinations in Mathematics. Do not attempt to crect the student s wk by making insertions changes of any kind. In scing the open-ended questions, use check marks to indicate student errs. Unless otherwise specified, mathematically crect variations in the answers will be allowed. Units need not be given when the wding of the questions allows such omissions. Each student s answer paper is to be sced by a minimum of three mathematics teachers. No one teacher is to sce me than approximately one-third of the open-ended questions on a student s paper. Teachers may not sce their own students answer papers. On the student s separate answer sheet, f each question, recd the number of credits earned and the teacher s assigned rater/scer letter. Schools are not permitted to resce any of the open-ended questions on this exam after each question has been rated once, regardless of the final exam sce. Schools are required to ensure that the raw sces have been added crectly and that the resulting scale sce has been determined accurately. Raters should recd the student s sces f all questions and the total raw sce on the student s separate answer sheet. Then the student s total raw sce should be converted to a scale sce by using the conversion chart that will be posted on the Department s web site at: on Tuesday, January 28, Because scale sces cresponding to raw sces in the conversion chart may change from one administration to another, it is crucial that, f each administration, the conversion chart provided f that administration be used to determine the student s final sce. The student s scale sce should be entered in the box provided on the student s separate answer sheet. The scale sce is the student s final examination sce.

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

27 General Rules f Applying Mathematics Rubrics I. General Principles f Rating The rubrics f the constructed-response questions on the Regents Examination in Algebra 2/Trigonometry are designed to provide a systematic, consistent method f awarding credit. The rubrics are not to be considered all-inclusive; it is impossible to anticipate all the different methods that students might use to solve a given problem. Each response must be rated carefully using the teacher s professional judgment and knowledge of mathematics; all calculations must be checked. The specific rubrics f each question must be applied consistently to all responses. In cases that are not specifically addressed in the rubrics, raters must follow the general rating guidelines in the publication Infmation Booklet f Scing the Regents Examinations in Mathematics, use their own professional judgment, confer with other mathematics teachers, and/ contact the State Education Department f guidance. During each Regents Examination administration period, rating questions may be referred directly to the Education Department. The contact numbers are sent to all schools befe each administration period. II. Full-Credit Responses A full-credit response provides a complete and crect answer to all parts of the question. Sufficient wk is shown to enable the rater to determine how the student arrived at the crect answer. When the rubric f the full-credit response includes one me examples of an acceptable method f solving the question (usually introduced by the phrase such as ), it does not mean that there are no additional acceptable methods of arriving at the crect answer. Unless otherwise specified, mathematically crect alternative solutions should be awarded credit. The only exceptions are those questions that specify the type of solution that must be used; e.g., an algebraic solution a graphic solution. A crect solution using a method other than the one specified is awarded half the credit of a crect solution using the specified method. III. Appropriate Wk Full-Credit Responses: The directions in the examination booklet f all the constructed-response questions state: Clearly indicate the necessary steps, including appropriate fmula substitutions, diagrams, graphs, charts, etc. The student has the responsibility of providing the crect answer and showing how that answer was obtained. The student must construct the response; the teacher should not have to search through a group of seemingly random calculations scribbled on the student paper to ascertain what method the student may have used. Responses With Errs: Rubrics that state Appropriate wk is shown, but are intended to be used with solutions that show an essentially complete response to the question but contain certain types of errs, whether computational, rounding, graphing, conceptual. If the response is incomplete; i.e., an equation is written but not solved an equation is solved but not all of the parts of the question are answered, appropriate wk has not been shown. Other rubrics address incomplete responses. IV. Multiple Errs Computational Errs, Graphing Errs, and Rounding Errs: Each of these types of errs results in a 1-credit deduction. Any combination of two of these types of errs results in a 2-credit deduction. No me than 2 credits should be deducted f such mechanical errs in any response. The teacher must carefully review the student s wk to determine what errs were made and what type of errs they were. Conceptual Errs: A conceptual err involves a me serious lack of knowledge procedure. Examples of conceptual errs include using the increct fmula f the area of a figure, choosing the increct trigonometric function, multiplying the exponents instead of adding them when multiplying terms with exponents. A response with one conceptual err can receive no me than half credit. If a response shows repeated occurrences of the same conceptual err, the student should not be penalized twice. If the same conceptual err is repeated in responses to other questions, credit should be deducted in each response. If a response shows two ( me) different maj conceptual errs, it should be considered completely increct and receive no credit. If a response shows one conceptual err and one computational, graphing, rounding err, the teacher must award credit that takes into account both errs; i.e., awarding half credit f the conceptual err and deducting 1 credit f each mechanical err (maximum of two deductions f mechanical errs). Algebra 2/Trigonometry Rating Guide January 14 [3]

28 Part II F each question, use the specific criteria to award a maximum of 2 credits. Unless otherwise specified, mathematically crect alternative solutions should be awarded appropriate credit. (28) [2] Crect wk is shown to prove the identity. [1] Appropriate wk is shown, but one substitution simplification err is made. [1] Appropriate wk is shown, but one conceptual err is made. [1] All trigonometric functions are crectly written in terms of sin θ and cos θ, but no further crect wk is shown. [0] A zero response is completely increct, irrelevant, incoherent is a crect response that was obtained by an obviously increct procedure. (29) [2] 27.6, and crect wk is shown. [1] Appropriate wk is shown, but one computational rounding err is made. [1] Appropriate wk is shown, but one conceptual err is made. [1] 27.6, but no wk is shown. [0] A zero response is completely increct, irrelevant, incoherent is a crect response that was obtained by an obviously increct procedure. Algebra 2/Trigonometry Rating Guide January 14 [4]

29 (30) [2] 7, and crect wk is shown. [1] Appropriate wk is shown, but one computational err is made. [1] Appropriate wk is shown, but one conceptual err is made, such as expressing the interquartile range as [1] 7, but no wk is shown. [0] A zero response is completely increct, irrelevant, incoherent is a crect response that was obtained by an obviously increct procedure. (31) [2] 2 and 5, and crect algebraic wk is shown. [1] Appropriate wk is shown, but one computational facting err is made. [1] Appropriate wk is shown, but one conceptual err is made. [1] Crect wk is shown to find either 2 5, but no further crect wk is shown. [1] x 2 3x 10 0 is written, but no further crect wk is shown. [1] 2 and 5, but a method other than algebraic is used. [1] 2 and 5, but no wk is shown. [0] A zero response is completely increct, irrelevant, incoherent is a crect response that was obtained by an obviously increct procedure. Algebra 2/Trigonometry Rating Guide January 14 [5]

30 (32) [2] 2 x 4.5 an equivalent interval notation, and crect algebraic wk is shown. [1] Appropriate wk is shown, but one computational err is made. [1] Appropriate wk is shown, but one conceptual err is made. [1] Appropriate wk is shown, but the answer is not represented as a conjunction. [1] 2 x 4.5, but a method other than algebraic is used. [1] 2 x 4.5, but no wk is shown. [0] A zero response is completely increct, irrelevant, incoherent is a crect response that was obtained by an obviously increct procedure. (33) [2] 7y 2xi, and crect wk is shown. [1] Appropriate wk is shown, but one computational simplification err is made. [1] Appropriate wk is shown, but one conceptual err is made. [1] Appropriate wk is shown, but the answer is not expressed in a bi fm. [1] 7y 2xi, but no wk is shown. [0] A zero response is completely increct, irrelevant, incoherent is a crect response that was obtained by an obviously increct procedure. Algebra 2/Trigonometry Rating Guide January 14 [6]

31 (34) [2] a n 7 (n 1)4 an equivalent equation, and crect wk is shown. [1] Appropriate wk is shown, but one computational err is made. [1] Appropriate wk is shown, but one conceptual err is made. [1] The expression 7 (n 1)4 an equivalent expression is written, and appropriate wk is shown. [1] Crect wk is shown to find the common difference, 4, and the first term, 7. No further crect wk is shown. [1] a n 7 (n 1)4, but no wk is shown. [0] The expression 7 (n 1)4 is written, but no wk is shown. [0] A zero response is completely increct, irrelevant, incoherent is a crect response that was obtained by an obviously increct procedure. (35) [2] 17.6, and crect wk is shown. [1] Appropriate wk is shown, but one computational rounding err is made. [1] Appropriate wk is shown, but one conceptual err is made. [1] 17.6, but no wk is shown. [0] A zero response is completely increct, irrelevant, incoherent is a crect response that was obtained by an obviously increct procedure. Algebra 2/Trigonometry Rating Guide January 14 [7]

32 Part III F each question, use the specific criteria to award a maximum of 4 credits. Unless otherwise specified, mathematically crect alternative solutions should be awarded appropriate credit. π π (36) [4] and 5, and crect algebraic wk is shown. 6 6 [3] Appropriate wk is shown, but one computational facting err is made. π π [3] Crect wk is shown to find 5, but no further crect wk is shown. 6 6 [3] 30 and 150, and crect algebraic wk is shown. [2] Appropriate wk is shown, but two me computational facting errs are made. [2] Appropriate wk is shown, but one conceptual err is made. [2] Crect wk is shown to find sin x crect wk is shown. 1 2 and sin x 3, but no further π π [2] and 5, but a method other than algebraic is used. 6 6 [1] Appropriate wk is shown, but one conceptual err and one computational facting err are made. [1] (2 sin x 1)(sin x 3) 0 is written, but no further crect wk is shown. [1] A crect substitution is made into the quadratic fmula, but no further crect wk is shown. π π [1] and 5, but no wk is shown. 6 6 [0] 30 and 150, but no wk is shown. [0] A zero response is completely increct, irrelevant, incoherent is a crect response that was obtained by an obviously increct procedure. Algebra 2/Trigonometry Rating Guide January 14 [8]

33 (37) [4] 0.024, and crect wk is shown. [3] Appropriate wk is shown, but one computational rounding err is made. [2] Appropriate wk is shown, but two me computational rounding errs are made. [2] Appropriate wk is shown, but one conceptual err is made. [2] 5 C 4 (0.28) 4 (0.72) 5 C 5 (0.28) 5 (0.72) 0 an equivalent expression is written, but no further crect wk is shown. [2] Appropriate wk is shown to find 0.022, exactly four out of five flowers, but no further crect wk is shown. [1] Appropriate wk is shown, but one conceptual err and one computational rounding err are made. [1] 0.024, but no wk is shown. [0] A zero response is completely increct, irrelevant, incoherent is a crect response that was obtained by an obviously increct procedure. Algebra 2/Trigonometry Rating Guide January 14 [9]

34 (38) [4] 54, and crect wk is shown. [3] Appropriate wk is shown, but one computational rounding err is made. [2] Appropriate wk is shown, but two me computational rounding errs are made. [2] Appropriate wk is shown, but one conceptual err is made, such as finding 24, the shter diagonal. [2] A crect substitution is made into the Law of Cosines, but no further crect wk is shown. [1] Appropriate wk is shown, but one conceptual err and one computational rounding err are made. [1] A crectly labeled diagram (including the longer diagonal) is drawn, but no further crect wk is shown. [1] 54, but no wk is shown. [0] A zero response is completely increct, irrelevant, incoherent is a crect response that was obtained by an obviously increct procedure. Algebra 2/Trigonometry Rating Guide January 14 [10]

35 Part IV F this question, use the specific criteria to award a maximum of 6 credits. Unless otherwise specified, mathematically crect alternative solutions should be awarded appropriate credit. (39) [6] 1, and crect algebraic wk is shown. [5] Appropriate wk is shown, but one computational facting err is made. [5] Crect wk is shown, but 6 is not rejected. [4] Appropriate wk is shown, but two computational facting errs are made. [4] Crect wk is shown to find (x 1)(x 6) 0, but no further crect wk is shown. [3] Appropriate wk is shown, but three me computational facting errs are made. [3] Appropriate wk is shown, but one conceptual err is made. [3] Crect wk is shown to find x 2 7x 6 0, but no further crect wk is shown. [3] 1, but a method other than algebraic is used. [2] Appropriate wk is shown, but one conceptual err and one computational facting err are made. [2] Crect wk is shown to find (2x 3)(x 5) (x 3) 2, but no further crect wk is shown. [1] Appropriate wk is shown, but one conceptual err and two me computational facting errs are made. [1] 1, but no wk is shown. [1] log (x 3) [(2x 3)(x 5)] 2 is written, but no further crect wk is shown. [0] A zero response is completely increct, irrelevant, incoherent is a crect response that was obtained by an obviously increct procedure. Algebra 2/Trigonometry Rating Guide January 14 [11]

36 Map to Ce Curriculum Content Strands Item Numbers Number Sense and Operations 4, 14, 21, 33 Algebra 1, 2, 3, 5, 7, 8, 10, 11, 12, 13, 15, 16, 18, 19, 22, 23, 24, 25, 26, 28, 29, 31, 32, 34, 35, 36, 38, 39 Measurement 27 Statistics and Probability 6, 9, 17, 20, 30, 37 Regents Examination in Algebra 2/Trigonometry January 2014 Chart f Converting Total Test Raw Sces to Final Examination Sces (Scale Sces) The Chart f Determining the Final Examination Sce f the January 2014 Regents Examination in Algebra 2/Trigonometry will be posted on the Department s web site at: on Tuesday, January 28, Conversion charts provided f previous administrations of the Regents Examination in Algebra 2/Trigonometry must NOT be used to determine students final sces f this administration. Online Submission of Teacher Evaluations of the Test to the Department Suggestions and feedback from teachers provide an imptant contribution to the test development process. The Department provides an online evaluation fm f State assessments. It contains spaces f teachers to respond to several specific questions and to make suggestions. Instructions f completing the evaluation fm are as follows: 1. Go to 2. Select the test title. 3. Complete the required demographic fields. 4. Complete each evaluation question and provide comments in the space provided. 5. Click the SUBMIT button at the bottom of the page to submit the completed fm. Algebra 2/Trigonometry Rating Guide January 14 [12]

37 The University of the State of New Yk REGENTS HIGH SCHOOL EXAMINATION ALGEBRA 2/ TRIGONOMETRY Tuesday, January 28, :15 4:15 p.m. SAMPLE RESPONSE SET Table of Contents Question Question Question Question Question Question Question Question Question Question Question Question

38 Question Show that sec θ sin θ cot θ 1 is an identity. Sce 2: The student has a complete and crect response. Algebra 2/Trigonometry Jan. 14 [2]

39 Question Show that sec θ sin θ cot θ 1 is an identity. Sce 1: The student made a substitution err by replacing 1 tan θ with sin θ cos θ. Algebra 2/Trigonometry Jan. 14 [3]

40 Question Show that sec θ sin θ cot θ 1 is an identity. Sce 0: The student made multiple errs when substituting f sec θ and sin θ. Algebra 2/Trigonometry Jan. 14 [4]

41 Question Find, to the nearest tenth of a square foot, the area of a rhombus that has a side of 6 feet and an angle of 50. Sce 2: The student has a complete and crect response. Algebra 2/Trigonometry Jan. 14 [5]

42 Question Find, to the nearest tenth of a square foot, the area of a rhombus that has a side of 6 feet and an angle of 50. Sce 1: The student stated the wrong units. Algebra 2/Trigonometry Jan. 14 [6]

43 Question Find, to the nearest tenth of a square foot, the area of a rhombus that has a side of 6 feet and an angle of 50. Sce 1: The student made a conceptual err by not doubling the area of the triangle. Algebra 2/Trigonometry Jan. 14 [7]

44 Question Find, to the nearest tenth of a square foot, the area of a rhombus that has a side of 6 feet and an angle of 50. Sce 0: The student made multiple conceptual errs, including the use of the Pythagean Theem and the increct use of the Law of Sines. Algebra 2/Trigonometry Jan. 14 [8]

45 Question The following is a list of the individual points sced by all twelve members of the Webster High School basketball team at a recent game: Find the interquartile range f this set of data. Sce 2: The student has a complete and crect response. Algebra 2/Trigonometry Jan. 14 [9]

46 Question The following is a list of the individual points sced by all twelve members of the Webster High School basketball team at a recent game: Find the interquartile range f this set of data. Sce 1: The student made a conceptual err by expressing the interquartile range as an interval. Algebra 2/Trigonometry Jan. 14 [10]

47 Question The following is a list of the individual points sced by all twelve members of the Webster High School basketball team at a recent game: Find the interquartile range f this set of data. Sce 0: The student made two conceptual errs. The quartiles were found increctly and the interquartile range was expressed as a set. Algebra 2/Trigonometry Jan. 14 [11]

48 Question Determine algebraically the x-codinate of all points where the graphs of xy 10 and y x 3 intersect. Sce 2: The student has a complete and crect response. Algebra 2/Trigonometry Jan. 14 [12]

49 Question Determine algebraically the x-codinate of all points where the graphs of xy 10 and y x 3 intersect. Sce 2: The student has a complete and crect response, with crect wk beyond the solutions. Algebra 2/Trigonometry Jan. 14 [13]

50 Question Determine algebraically the x-codinate of all points where the graphs of xy 10 and y x 3 intersect. Sce 1: The student crectly solved the system of equations graphically. Algebra 2/Trigonometry Jan. 14 [14]

51 Question Determine algebraically the x-codinate of all points where the graphs of xy 10 and y x 3 intersect. Sce 0: The student crectly solved f y 10 x, but no further crect wk is shown. The x-codinate that the student wrote is increct. Algebra 2/Trigonometry Jan. 14 [15]

52 Question Solve 4x 5 13 algebraically f x. Sce 2: The student has a complete and crect response. Algebra 2/Trigonometry Jan. 14 [16]

53 Question Solve 4x 5 13 algebraically f x. Sce 2: The student has a complete and crect response. Algebra 2/Trigonometry Jan. 14 [17]

54 Question Solve 4x 5 13 algebraically f x. Sce 1: The student crectly solved the absolute value inequality as an absolute value equation. This is considered a conceptual err. Algebra 2/Trigonometry Jan. 14 [18]

55 Question Solve 4x 5 13 algebraically f x. Sce 1: The answer is not expressed as a conjunction. Algebra 2/Trigonometry Jan. 14 [19]

56 Question Solve 4x 5 13 algebraically f x. Sce 0: The student made me than one conceptual err. Algebra 2/Trigonometry Jan. 14 [20]

57 Question Express 4xi 5yi 8 6xi 3 2yi 4 in simplest a bi fm. Sce 2: The student has a complete and crect response. Algebra 2/Trigonometry Jan. 14 [21]

58 Question Express 4xi 5yi 8 6xi 3 2yi 4 in simplest a bi fm. Sce 1: The student did not express the answer in simplest fm. The 1 should have been simplified to i. Algebra 2/Trigonometry Jan. 14 [22]

59 Question Express 4xi 5yi 8 6xi 3 2yi 4 in simplest a bi fm. Sce 1: The student did not write the solution in a bi fm. Algebra 2/Trigonometry Jan. 14 [23]

60 Question Express 4xi 5yi 8 6xi 3 2yi 4 in simplest a bi fm. Sce 0: The student made one conceptual err in replacing i and did not put the answer in a bi fm. Algebra 2/Trigonometry Jan. 14 [24]

61 Question In an arithmetic sequence, a 4 19 and a Determine a fmula f a n, the n th term of this sequence. Sce 2: The student has a complete and crect response. Algebra 2/Trigonometry Jan. 14 [25]

62 Question In an arithmetic sequence, a 4 19 and a Determine a fmula f a n, the n th term of this sequence. Sce 1: The student found the first term, 7, and the common difference of 4. No further crect wk is shown. Algebra 2/Trigonometry Jan. 14 [26]

63 Question In an arithmetic sequence, a 4 19 and a Determine a fmula f a n, the n th term of this sequence. Sce 0: The student response is completely incoherent. Algebra 2/Trigonometry Jan. 14 [27]

64 Question Circle O shown below has a radius of 12 centimeters. To the nearest tenth of a centimeter, determine the length of the arc, x, subtended by an angle of x 12 cm O Sce 2: The student has a complete and crect response. Algebra 2/Trigonometry Jan. 14 [28]

65 Question Circle O shown below has a radius of 12 centimeters. To the nearest tenth of a centimeter, determine the length of the arc, x, subtended by an angle of x 12 cm O Sce 1: The student made a conceptual err by using the area of a circle rather than the circumference. Algebra 2/Trigonometry Jan. 14 [29]

66 Question Circle O shown below has a radius of 12 centimeters. To the nearest tenth of a centimeter, determine the length of the arc, x, subtended by an angle of x 12 cm O Sce 0: The student response is completely incoherent. Algebra 2/Trigonometry Jan. 14 [30]

67 Question Solve algebraically f all exact values of x in the interval 0 x 2π: 2 sin 2 x 5 sin x 3 Sce 4: The student has a complete and crect response. Algebra 2/Trigonometry Jan. 14 [31]

68 Question Solve algebraically f all exact values of x in the interval 0 x 2π: 2 sin 2 x 5 sin x 3 Sce 4: The student has a complete and crect response. Algebra 2/Trigonometry Jan. 14 [32]

69 Question Solve algebraically f all exact values of x in the interval 0 x 2π: 2 sin 2 x 5 sin x 3 Sce 3: The student made a facting err. Algebra 2/Trigonometry Jan. 14 [33]

70 Question Solve algebraically f all exact values of x in the interval 0 x 2π: 2 sin 2 x 5 sin x 3 Sce 2: The student crectly found sin x 0.5 and sin x 3. Algebra 2/Trigonometry Jan. 14 [34]

71 Question Solve algebraically f all exact values of x in the interval 0 x 2π: 2 sin 2 x 5 sin x 3 Sce 1: A crect substitution into the quadratic fmula is made, but no further crect wk is shown. Algebra 2/Trigonometry Jan. 14 [35]

72 Question Solve algebraically f all exact values of x in the interval 0 x 2π: 2 sin 2 x 5 sin x 3 Sce 0: The student made me than one conceptual err. Algebra 2/Trigonometry Jan. 14 [36]

73 Question Because Sam s backyard gets very little sunlight, the probability that a geranium planted there will flower is Sam planted five geraniums. Determine the probability, to the nearest thousandth, that at least four geraniums will flower. Sce 4: The student has a complete and crect response. Algebra 2/Trigonometry Jan. 14 [37]

74 Question Because Sam s backyard gets very little sunlight, the probability that a geranium planted there will flower is Sam planted five geraniums. Determine the probability, to the nearest thousandth, that at least four geraniums will flower. Sce 4: The student has a complete and crect response. Algebra 2/Trigonometry Jan. 14 [38]

75 Question Because Sam s backyard gets very little sunlight, the probability that a geranium planted there will flower is Sam planted five geraniums. Determine the probability, to the nearest thousandth, that at least four geraniums will flower. Sce 4: The student has a complete and crect response. The answer of 2.4% is mathematically equivalent to Algebra 2/Trigonometry Jan. 14 [39]

76 Question Because Sam s backyard gets very little sunlight, the probability that a geranium planted there will flower is Sam planted five geraniums. Determine the probability, to the nearest thousandth, that at least four geraniums will flower. Sce 3: The student made one rounding err. Algebra 2/Trigonometry Jan. 14 [40]

77 Question Because Sam s backyard gets very little sunlight, the probability that a geranium planted there will flower is Sam planted five geraniums. Determine the probability, to the nearest thousandth, that at least four geraniums will flower. Sce 2: The student made one rounding err and expressed the answer as a percent. Algebra 2/Trigonometry Jan. 14 [41]

78 Question Because Sam s backyard gets very little sunlight, the probability that a geranium planted there will flower is Sam planted five geraniums. Determine the probability, to the nearest thousandth, that at least four geraniums will flower. Sce 1: The student found a crect probability f exactly four out of five, and did not round to the nearest thousandth. Algebra 2/Trigonometry Jan. 14 [42]

79 Question Because Sam s backyard gets very little sunlight, the probability that a geranium planted there will flower is Sam planted five geraniums. Determine the probability, to the nearest thousandth, that at least four geraniums will flower. Sce 0: The student made two conceptual errs. Increct exponents were written, and then the student subtracted this answer from 1. Algebra 2/Trigonometry Jan. 14 [43]

80 Question Two sides of a parallelogram measure 27 cm and 32 cm. The included angle measures 48. Find the length of the longer diagonal of the parallelogram, to the nearest centimeter. Sce 4: The student has a complete and crect response. Algebra 2/Trigonometry Jan. 14 [44]

81 Question Two sides of a parallelogram measure 27 cm and 32 cm. The included angle measures 48. Find the length of the longer diagonal of the parallelogram, to the nearest centimeter. Sce 3: The student made one computational err by using radian mode. Algebra 2/Trigonometry Jan. 14 [45]

82 Question Two sides of a parallelogram measure 27 cm and 32 cm. The included angle measures 48. Find the length of the longer diagonal of the parallelogram, to the nearest centimeter. Sce 2: The student made a crect substitution into the Law of Cosines. Algebra 2/Trigonometry Jan. 14 [46]

83 Question Two sides of a parallelogram measure 27 cm and 32 cm. The included angle measures 48. Find the length of the longer diagonal of the parallelogram, to the nearest centimeter. Sce 1: The student drew a crectly labeled diagram. The remainder of the wk shown is increct. Algebra 2/Trigonometry Jan. 14 [47]

84 Question Two sides of a parallelogram measure 27 cm and 32 cm. The included angle measures 48. Find the length of the longer diagonal of the parallelogram, to the nearest centimeter. Sce 0: The student made two conceptual errs by finding the shter diagonal and combining terms increctly. There was also one rounding err. Algebra 2/Trigonometry Jan. 14 [48]

85 Question Solve algebraically f all values of x: log (x 3) (2x 3) log (x 3) (x 5) 2 Sce 6: The student has a complete and crect response. Algebra 2/Trigonometry Jan. 14 [49]

86 Question Solve algebraically f all values of x: log (x 3) (2x 3) log (x 3) (x 5) 2 Sce 5: The student did not reject 6. Algebra 2/Trigonometry Jan. 14 [50]

87 Question Solve algebraically f all values of x: log (x 3) (2x 3) log (x 3) (x 5) 2 Sce 4: The student made one computational err when squaring x 3. The student also made an err in not discarding the imaginary solutions. Algebra 2/Trigonometry Jan. 14 [51]

88 Question Solve algebraically f all values of x: log (x 3) (2x 3) log (x 3) (x 5) 2 Sce 3: The student made a conceptual err by canceling the logs. Algebra 2/Trigonometry Jan. 14 [52]

89 Question Solve algebraically f all values of x: log (x 3) (2x 3) log (x 3) (x 5) 2 Sce 2: The student made a conceptual err by adding the binomials. The student did not discard the solution outside the domain. Algebra 2/Trigonometry Jan. 14 [53]

90 Question Solve algebraically f all values of x: log (x 3) (2x 3) log (x 3) (x 5) 2 Sce 1: The student crectly wrote log (x 3) (2x 3)(x 5) 2. The remainder of the wk was increct. Algebra 2/Trigonometry Jan. 14 [54]

91 Question Solve algebraically f all values of x: log (x 3) (2x 3) log (x 3) (x 5) 2 Sce 0: The student made multiple errs in attempting to solve the log equation. Algebra 2/Trigonometry Jan. 14 [55]

92 The State Education Department / The University of the State of New Yk Regents Examination in Algebra 2/Trigonometry January 2014 Chart f Converting Total Test Raw Sces to Final Examination Sces (Scale Sces) Raw Scale Raw Scale Raw Scale Raw Scale Sce Sce Sce Sce Sce Sce Sce Sce To determine the student s final examination sce, find the student s total test raw sce in the column labeled Raw Sce and then locate the scale sce that cresponds to that raw sce. The scale sce is the student s final examination sce. Enter this sce in the space labeled Scale Sce on the student s answer sheet. Schools are not permitted to resce any of the open-ended questions on this exam after each question has been rated once, regardless of the final exam sce. Schools are required to ensure that the raw sces have been added crectly and that the resulting scale sce has been determined accurately. Because scale sces cresponding to raw sces in the conversion chart change from one administration to another, it is crucial that f each administration the conversion chart provided f that administration be used to determine the student s final sce. The chart above is usable only f this administration of the Regents Examination in Algebra 2/Trigonometry. Algebra 2/Trigonometry Conversion Chart - Jan. '14 1 of 1