ALGEBRA 2/TRIGONOMETRY

Transcription

1 ALGEBRA /TRIGONOMETRY The University of the State of New Yk REGENTS HIGH SCHOOL EXAMINATION ALGEBRA /TRIGONOMETRY Tuesday, June 1, 011 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 f Part I. Fold the last page along the perfations 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 wk should be written in pen, except 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. 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 sce will be calculated f you. DO NOT OPEN THIS EXAMINATION BOOKLET UNTIL THE SIGNAL IS GIVEN. ALGEBRA /TRIGONOMETRY

2 Part I Answer all 7 questions in this part. Each crect answer will receive credits. No partial credit will be allowed. F each question, write on the separate answer sheet the numeral preceding the wd expression that best completes the statement answers the question. [54] 1 A doct wants to test the effectiveness of a new drug on her patients. She separates her sample of patients into two groups and administers the drug to only one of these groups. She then compares the results. Which type of study best describes this situation? (1) census (3) observation () survey (4) controlled experiment Use this space f computations. If f(x) = x x, what is the value of f( 10)? 16 (1) 5 () 5 4 (3) 5 58 (4) An auditium has 1 rows of seats. The first row has 18 seats, and each succeeding row has two me seats than the previous row. How many seats are in the auditium? (1) 540 (3) 760 () 567 (4) 798 Algebra /Trigonometry June 11 []

3 4 Expressed as a function of a positive acute angle, cos ( 305 ) is equal to (1) cos 55 (3) sin 55 () cos 55 (4) sin 55 Use this space f computations. 5 The value of x in the equation 4 x + 5 = 8 3x is (1) 1 (3) 5 () (4) 10 6 What is the value of x in the equation log 5 x = 4? (1) 1.16 (3) 65 () 0 (4) 1,04 7 The expression 4 _ 16x y 7 is equivalent to (1) x 1 y 7 4 (3) 4x 1 y 7 4 () x 8 y 8 (4) 4x 8 y 8 Algebra /Trigonometry June 11 [3] [OVER]

4 8 Which equation is represented by the graph below? Use this space f computations. y x (1) y = 5 x (3) y = 5 x () y = 0.5 x (4) y = 0.5 x 9 What is the fifteenth term of the geometric sequence 5, 10, 5,...? (1) 18 5 (3) () (4) Algebra /Trigonometry June 11 [4]

5 10 In ABC, a = 15, b = 14, and c = 13, as shown in the diagram below. What is the m C, to the nearest degree? Use this space f computations. B A 14 C (1) 53 (3) 67 () 59 (4) What is the period of the function f(θ) = cos 3θ? (1) π (3) 3π () π 3 (4) π 1 What is the range of f(x) = (x + 4) + 7? (1) y 4 (3) y = 7 () y 4 (4) y 7 Algebra /Trigonometry June 11 [5] [OVER]

6 13 Ms. Bell s mathematics class consists of 4 sophomes, 10 junis, and 5 senis. How many different ways can Ms. Bell create a fourmember committee of junis if each juni has an equal chance of being selected? (1) 10 (3) 5,040 () 3,876 (4) 93,04 Use this space f computations. 14 Which graph represents a relation that is not a function? y y x x (1) (3) y y x x () (4) Algebra /Trigonometry June 11 [6]

7 15 The value of tan to the nearest ten-thousandth is (1) (3) () (4) Use this space f computations. 16 The expression 4 5 is equivalent to 13 (1) (3) (5 13 ) () 4(5 + (4) 13 ) Akeem invests $5,000 in an account that pays 4.75% annual interest compounded continuously. Using the fmula A = Pe rt, where A = the amount in the account after t years, P = principal invested, and r = the annual interest rate, how many years, to the nearest tenth, will it take f Akeem s investment to triple? (1) 10.0 (3) 3.1 () 14.6 (4) The value of the expression ( r + r) is 5 r=3 (1) 38 (3) 6 () 1 (4) 6 Algebra /Trigonometry June 11 [7] [OVER]

8 19 Which graph shows y = cos 1 x? Use this space f computations. y y π π 3π 3π π π π π 1 1 x 1 1 x (1) (3) y y π π 3π 3π π π π π 1 1 x 1 1 x () (4) Algebra /Trigonometry June 11 [8]

9 0 If r = 3 A B, then log r can be represented by C Use this space f computations. (1) 1 6 log A log B log C () 3(log A + log B log C) (3) 1 3 log(a + B) C (4) 3 log A log B 1 3 log C 1 The solution set of 3x + 16 = x + is (1) { 3, 4} (3) {3} () { 4, 3} (4) { 4} Brian crectly used a method of completing the square to solve the equation x + 7x 11 = 0. Brian s first step was to rewrite the equation as x + 7x = 11. He then added a number to both sides of the equation. Which number did he add? (1) 7 () 49 4 (3) 49 (4) 49 Algebra /Trigonometry June 11 [9] [OVER]

10 3 The expression sin θ + co s θ 1 sin is equivalent to θ (1) cos θ (3) sec θ () sin θ (4) csc θ Use this space f computations. 4 The number of minutes students took to complete a quiz is summarized in the table below. Minutes Number of Students 5 3 x If the mean number of minutes was 17, which equation could be used to calculate the value of x? (1) 17 = x x () 17 = x x (3) 17 = x 6 + x (4) 17 = x 6 + x 5 What is the radian measure of the smaller angle fmed by the hands of a clock at 7 o clock? (1) π () π 3 (3) 5π 6 (4) 7π 6 Algebra /Trigonometry June 11 [10]

11 6 What is the coefficient of the fourth term in the expansion of (a 4b) 9? (1) 5,376 (3) 336 () 336 (4) 5,376 Use this space f computations. 7 Samantha constructs the scatter plot below from a set of data. 100 y x Based on her scatter plot, which regression model would be most appropriate? (1) exponential (3) logarithmic () linear (4) power Algebra /Trigonometry June 11 [11] [OVER]

12 Part II Answer all 8 questions in this part. Each crect answer will receive 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] 8 Express the product of ( 1 y 1 3 y ) and ( 1y + 3 as a trinomial. 5) Algebra /Trigonometry June 11 [1]

13 9 In a study of 8 video game players, the researchers found that the ages of these players were nmally distributed, with a mean age of 17 years and a standard deviation of 3 years. Determine if there were 15 video game players in this study over the age of 0. Justify your answer. Algebra /Trigonometry June 11 [13] [OVER]

14 30 Write a quadratic equation such that the sum of its roots is 6 and the product of its roots is Evaluate e xlny when x = 3 and y =. Algebra /Trigonometry June 11 [14]

15 3 If f(x) = x 6, find f 1 (x). Algebra /Trigonometry June 11 [15] [OVER]

16 33 Fact the expression 1t 8 75t 4 completely. Algebra /Trigonometry June 11 [16]

17 3x 34 Simplify the expression 4 y 5 ( x 3 y 7 and write the answer using only positive exponents. ) Algebra /Trigonometry June 11 [17] [OVER]

18 35 If f(x) = x 6 and g(x) = x 1, determine the value of (g f)( 3). Algebra /Trigonometry June 11 [18]

19 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. [1] 36 Express as a single fraction the exact value of sin 75. Algebra /Trigonometry June 11 [19] [OVER]

20 37 Solve the inequality 3 6 x < 15 f x. Graph the solution on the line below. Algebra /Trigonometry June 11 [0]

21 38 The probability that a professional baseball player will get a hit is 1. Calculate the exact probability 3 that he will get at least 3 hits in 5 attempts. Algebra /Trigonometry June 11 [1] [OVER]

22 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 the following system of equations algebraically: 5 = y x 4x = 17x + y + 4 Algebra /Trigonometry June 11 []

23 Tear Here Reference Sheet Area of a Triangle Law of Cosines K _ 1 ab sin C a b + c bc cos A Functions of the Sum of Two Angles Functions of the Double Angle sin (A + B) sin A cos B + cos A sin B sin A sin A cos A cos (A + B) cos A cos B sin A sin B cos A cos A sin A tan A + tan B cos A cos tan (A + B) A 1 1 tan A tan B cos A 1 sin A Functions of the Difference of Two Angles tan A tan A 1 tan 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_ A 1 cos A Law of Sines a sin A b sin B c cos 1_ A 1 + cos A sin C tan 1_ Sum of a Finite Arithmetic Series A 1 cos A 1 + cos A n(a 1 + a n ) S n Sum of a Finite Geometric Series a 1 (1 r n ) S 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 a n b n C n a 0 b n n (a + b) n nc r a n r b r r = 0 Tear Here Algebra /Trigonometry June 11

24 Tear Here Tear Here

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

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

27 The University of the State of New Yk REGENTS HIGH SCHOOL EXAMINATION ALGEBRA /TRIGONOMETRY Tear Here Tuesday, June 1, 011 1:15 to 4:15 p.m., only ANSWER SHEET Student Sex: Male Female Grade Teacher School Your answers to Part I should be recded on this answer sheet. Part I Answer all 7 questions in this part Your answers f 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 answers pri to the examination and that I have neither given n received assistance in answering any of the questions during the examination. Signature Algebra /Trigonometry June 11

28 ALGEBRA /TRIGONOMETRY Question ALGEBRA /TRIGONOMETRY Maximum Credit Part I Part II Part III Part IV 39 6 Maximum 88 Total Credits Earned Total Raw Sce Rater s/scer s Initials Checked by Scale Sce (from conversion chart) Rater s/scer s Name (minimum of three) Tear Here Tear Here Algebra /Trigonometry June 11 Printed on Recycled Paper ALGEBRA /TRIGONOMETRY

29 FOR TEACHERS ONLY The University of the State of New Yk REGENTS HIGH SCHOOL EXAMINATION ALGEBRA /TRIGONOMETRY Tuesday, June 1, 011 1:15 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 /Trigonometry. Me detailed infmation about scing is provided in the publication Infmation Booklet f Scing the Regents Examinations in Mathematics. Use only red ink red pencil in rating Regents papers. Do not attempt to crect the student s wk by making insertions changes of any kind. 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. On the back of the student s detachable answer sheet, raters must enter their initials in the boxes next to the questions they have sced and also write their name in the box under the heading Rater s/scer s Name. Beginning in June 011, schools are no longer 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 detachable 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, June 1, 011. Because scale sces cresponding to raw sces in the conversion chart may change from one examination 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 detachable answer sheet. The scale sce is the student s final examination sce.

30 Part I Allow a total of 54 credits, credits f each of the following. Allow credit if the student has written the crect answer instead of the numeral 1,, 3, 4. (1) 4 (8) (15) () () (9) 1 (16) 1 3* (3) 3 (3) 4 (10) 1 (17) 3 (4) 4 (4) (11) (18) 1 (5) 3 (5) (1) 4 (19) 3 (6) 1 (6) 3 (13) 1 (0) 4 (7) 3 (7) 1 (14) 3 (1) 3 *Allow credit f 1 3 as an acceptable response f question 16. Algebra /Trigonometry Rating Guide June 11 []

31 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 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. General Rules f Applying Mathematics Rubrics I. General Principles f Rating The rubrics f the constructed-response questions on the Regents Examination in Algebra /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 consultants at 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 -credit deduction. No me than 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 /Trigonometry Rating Guide June 11 [3]

32 Part II F each question, use the specific criteria to award a maximum of two credits. Unless otherwise specified, mathematically crect alternative solutions should be awarded appropriate credit (8) [] 6y y y an equivalent trinomial, and appropriate wk is 10 5 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] y y y, 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. (9) [] No, and an appropriate justification is given. [1] Appropriate wk is shown, but one computational err is made. [1] Appropriate wk is shown, but one conceptual err is made. [0] No, 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 /Trigonometry Rating Guide June 11 [4]

33 (30) [] x 6x 7 = 0 an equivalent equation. [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 x 6x 7 is written. [1] The equation y = x 6x 7 is written. [0] A zero response is completely increct, irrelevant, incoherent is a crect response that was obtained by an obviously increct procedure. (31) [] 8, and appropriate wk is shown, such as a substitution f x and y. [1] Appropriate wk is shown, but one computational err is made. [1] Appropriate wk is shown, but one conceptual err is made. [1] 8, 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 /Trigonometry Rating Guide June 11 [5]

34 (3) [] ± x + 6, and appropriate 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 not writing ± with the radical. [1] ± x + 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. 4 (33) [] 3 t (t + 5)(t 5), 3t 4 (t + 5)( t 5)( t + 5), and appropriate wk is shown. [1] Appropriate wk is shown, but one facting err is made. [1] Appropriate wk is shown, but one conceptual err is made. 4 [1] 3 t (t + 5)(t 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 /Trigonometry Rating Guide June 11 [6]

35 (34) [] 1x y 9, and appropriate 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 expressed as [1] 1x y 9, but no wk is shown. 9 1x y. [0] A zero response is completely increct, irrelevant, incoherent is a crect response that was obtained by an obviously increct procedure. (35) [] 7, and appropriate 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 finding (fo g)( 3). [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. Algebra /Trigonometry Rating Guide June 11 [7]

36 Part III F each question, use the specific criteria to award a maximum of four credits. Unless otherwise specified, mathematically crect alternative solutions should be awarded appropriate credit. (36) [4] wk is shown. if the half-angle fmula is used, and appropriate [3] Appropriate wk is shown, but one computational substitution err is made. [] Appropriate wk is shown, but two me computational substitution errs are made. [] Appropriate wk is shown, but one conceptual err is made. [1] Appropriate wk is shown, but one conceptual err and one computational substitution err are made. [1] sin 30 cos 45 + cos 30 sin 45 crect wk is shown. 1 cos150 is written, but no further [1] + 6 4, but no wk is shown. [0] , 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 /Trigonometry Rating Guide June 11 [8]

37 (37) [4] x < 1 x > 11 an equivalent interval notation, and a crect graph is drawn, and appropriate wk is shown. [3] Appropriate wk is shown, but one computational graphing err is made. [3] Appropriate wk is shown, but the answer is not expressed as a disjunction. [] Appropriate wk is shown, but two me computational graphing errs are made. [] Appropriate wk is shown, but one conceptual err is made. [] Appropriate wk is shown to find and graph x > 11, but no further crect wk is shown. [1] Appropriate wk is shown, but one conceptual err and one computational graphing err are made. [1] Appropriate wk is shown to find and graph x < 1, but no further crect wk is shown. [1] x < 1 x > 11, 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 /Trigonometry Rating Guide June 11 [9]

38 (38) [4] 51 an equivalent fraction, and appropriate wk is shown. 43 [3] Appropriate wk is shown, but one computational err is made. [3] Appropriate wk is shown to find 40 43, 10 43, and 1, but the values are 43 not added. [3] Appropriate wk is shown, but the answer is expressed as a decimal. [] Appropriate wk is shown, but two me computational errs are made. [] Appropriate wk is shown, but one conceptual err is made, such as finding the probability of at most 3 hits [] A crect expression, such as 5C3 5C C is written, but no further crect wk is shown. [1] Appropriate wk is shown, but one conceptual err and one computational err are made. [1] Appropriate wk is shown to find 40, the probability of exactly 3 hits, 43 but no further crect wk is shown. [1] 51, but no wk is shown. 43 [0] A zero response is completely increct, irrelevant, incoherent is a crect response that was obtained by an obviously increct procedure. Algebra /Trigonometry Rating Guide June 11 [10]

39 Part IV F this question, use the specific criteria to award a maximum of six credits. Unless otherwise specified, mathematically crect alternative solutions should be awarded appropriate credit. (39) [6] 9 1, and 1 11, wk is shown. an equivalent answer, and appropriate algebraic [5] Appropriate wk is shown, but one computational, substitution, facting err is made. [5] Appropriate wk is shown, but only one crect solution is found only the x- the y-values are found crectly. [4] Appropriate wk is shown, but two computational, substitution, facting errs are made. [4] Appropriate wk is shown to find (x 1)(x+ 9) = 0 (y 11)(y 1) = 0, but no further crect wk is shown. [4] A crect substitution is made into the quadratic fmula, but no further crect wk is shown. [3] Appropriate wk is shown, but three me computational, substitution, facting errs are made. [3] Appropriate wk is shown, but one conceptual err is made. [3] A crect quadratic equation in standard fm is written, but no further crect wk is shown [3], and, algebraic is used. an equivalent answer, but a method other than [] Appropriate wk is shown, but one conceptual err and one computational, substitution, facting err are made. [1] Appropriate wk is shown, but one conceptual err and two me computational, substitution, facting errs are made. Algebra /Trigonometry Rating Guide June 11 [11]

40 [1] A crect equation in one variable is written, but no further crect wk is shown. [1] 9 1, and 1 11,, 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 /Trigonometry Rating Guide June 11 [1]

41 Map to Ce Curriculum Content Strand Item Numbers Number Sense and Operations 16, 18, 8, 3, 4, 5, 6, 7, 8, 9, 10, 11, 1, 14, 15, Algebra 17, 19, 0, 1,, 3, 6, 30, 31, 3, 33, 34, 35, 36, 37, 39 Measurement 5 Statistics and Probability 1, 13, 4, 7, 9, 38 Regents Examination in Algebra /Trigonometry June 011 Chart f Converting Total Test Raw Sces to Final Examination Sces (Scale Sces) The Chart f Determining the Final Examination Sce f the June 011 Regents Examination in Algebra /Trigonometry will be posted on the Department s web site at: on Tuesday, June 1, 011. Conversion charts provided f previous administrations of the Algebra / Trigonometry examination 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 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 /Trigonometry Rating Guide June 11 [13]

42 The University of the State of New Yk THE STATE EDUCATION DEPARTMENT Office of Assessment Policy, Development and Administration Albany, New Yk 134 Scing Clarification f Teachers Regents Examination in Algebra /Trigonometry Tuesday, June 1, 011, 1:15 p.m. Because of variations in the use of f 1 notation throughout New Yk State, a revised rubric f Question 3 has been provided. Please resce all students responses to Question 3 using the revised rubric below. (3) [] ± x + 6, and appropriate wk is shown. [] Either x + 6 x + 6, and appropriate wk is shown. [] An explanation stating that the iginal function is not one-to-one and therefe there is no inverse function. [1] Appropriate wk is shown, but one computational err is made. [1] Appropriate wk is shown, but one conceptual err is made. [1] ± x + 6 x + 6 x + 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. We apologize f any inconvenience this may have caused you and your students, and we thank you f your continued cooperation. Please photocopy this notice and give a copy of it to each teacher scing the June 011 Regents Examination in Algebra /Trigonometry.

43 Regents Examination in Algebra /Trigonometry June 011 Chart f Converting Total Test Raw Sces to Final Examination Sces (Scale Sces) Raw Sce Scale Sce Raw Sce Scale Sce Raw Sce Scale Sce Raw Sce Scale 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. Beginning in June 011, schools are no longer 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 /Trigonometry.