NYSTP_HS_IntroAlgebra_2013Jun

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA Wednesday, June 12, 2013 — 1:15 to 4:15 p.m., only Student Name:________________________________________________________ School Name: ______________________________________________________________ Print your name and the name of your school on the lines above. A separate answer sheet for Part I has been provided to you. Follow the instructions from the proctor for completing the student information on your answer sheet. This examination has four parts, with a total of 39 questions. You must answer all questions in this examination. Record 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. INTEGRATED ALGEBRA DO NOT OPEN THIS EXAMINATION BOOKLET UNTIL THE SIGNAL IS GIVEN. Notice… A graphing calculator and a straightedge (ruler) must be available for you to use while taking this examination. INTEGRATED ALGEBRA The possession or use of any communications device is strictly prohibited when taking this examination. If you have or use any communications device, no matter how briefly, your examination will be invalidated and no score will be calculated for you. Part I Answer all 30 questions in this part. Each correct answer will receive 2 credits. Record your answers on your separate answer sheet. [60] Use this space for computations.1 Which expression represents “5 less than twice x”? (1) 2x – 5 (3) 2(5 – x) (2) 5 – 2x (4) 2(x – 5) 2 Gabriella has 20 quarters, 15 dimes, 7 nickels, and 8 pennies in a jar. After taking 6 quarters out of the jar, what will be the probability of Gabriella randomly selecting a quarter from the coins left in the jar? (1) 14__44 (3) 14__ 50 (2) 30__44 (4) 20__ 50 3 Based on the line of best fit drawn below, which value could be expected for the data in June 2015? (1) 230 (3) 480 (2) 310 (4) 540 ��� ��� ��� ��� ��� ��� �� ���� �� ���� �� ���� �� ���� ���� �� �� � � Integrated Algebra – June ’13 [2] Use this space for computations.4 If the point (5,k) lies on the line represented by the equation 2x � y � 9, the value of k is (1) 1 (3) �1 (2) 2 (4) �2 5 A soda container holds 5 1__2 gallons of soda. How many ounces of soda does this container hold? (1) 44 (3) 640 (2) 176 (4) 704 6 The roots of a quadratic equation can be found using the graph below. What are the roots of this equation? (1) �4, only (3) �1 and 4 (2) �4 and �1 (4) �4, �1, and 4 � 1 quart = 32 ounces 1 gallon = 4 quarts Integrated Algebra – June ’13 [3] [OVER] Use this space for computations.7 If the area of a rectangle is represented by x2 � 8x � 15 and its length is represented by x � 5, which expression represents the width of the rectangle? (1) x � 3 (3) x2 � 6x � 5 (2) x � 3 (4) x2 � 7x � 10 8 Which set of data describes a situation that would be classified as qualitative? (1) the colors of the birds at the city zoo (2) the shoe size of the zookeepers at the city zoo (3) the heights of the giraffes at the city zoo (4) the weights of the monkeys at the city zoo 9 The value of the expression 6! � 5!(3!)_____ 4! � 10 is (1) 50 (3) 740 (2) 102 (4) 750 10 Which interval notation represents �3 � x � 3? (1) [�3, 3] (3) [�3, 3) (2) (�3, 3] (4) (�3, 3) 11 The solutions of x2 � 16x � 28 are (1) �2 and �14 (3) �4 and �7 (2) 2 and 14 (4) 4 and 7 Integrated Algebra – June ’13 [4] Use this space for computations.12 If the expression (2ya)4 is equivalent to 16y8, what is the value of a? (1) 12 (3) 32 (2) 2 (4) 4 13 Which table shows bivariate data? Time Spent Studying (hr) Test Grade (%) 1 65 2 72 3 83 4 85 5 92 Age (yr) Frequency 14 12 15 21 16 14 17 19 18 15 Day Temperature (degrees F) Monday 63 Tuesday 58 Wednesday 72 Thursday 74 Friday 78 Type of Car Average Gas Mileage (mpg) van 25 SUV 23 luxury 26 compact 28 pickup 22 (1) (3) (2) (4) Integrated Algebra – June ’13 [5] [OVER] Use this space for computations.14 The box-and-whisker plot below represents the results of test scores in a math class. What do the scores 65, 85, and 100 represent? (1) Q1, median, Q3 (2) Q1, Q3, maximum (3) median, Q1, maximum (4) minimum, median, maximum 15 The expression x � 3_____ x � 2 is undefined when the value of x is (1) �2, only (3) 3, only (2) �2 and 3 (4) �3 and 2 16 If rx � st � r, which expression represents x? (1) (3) (2) (4) 17 What is the solution of the equation x � 2_____ 2 � 4__ x ? (1) 1 and �8 (2) 2 and �4 (3) �1 and 8 (4) �2 and 4 � �� �� �� �� ��� r st r � r r st� r r st� r st r � Integrated Algebra – June ’13 [6] Use this space for computations.18 Which type of function is graphed below? (1) linear (3) exponential (2) quadratic (4) absolute value 19 What is the slope of the line represented by the equation 4x � 3y � 12? (1) 4__3 (3) � 3__ 4 (2) 3__4 (4) � 4__ 3 � Integrated Algebra – June ’13 [7] [OVER] Use this space for computations.20 The diagram below shows the graph of which inequality? (1) y � x � 1 (3) y � x � 1 (2) y � x � 1 (4) y � x � 1 21 Carol plans to sell twice as many magazine subscriptions as Jennifer. If Carol and Jennifer need to sell at least 90 subscriptions in all, which inequality could be used to determine how many subscriptions, x, Jennifer needs to sell? (1) x � 45 (3) 2x � x � 90 (2) 2x � 90 (4) 2x � x � 90 22 When 2x2 � 3x � 2 is subtracted from 4x2 � 5x � 2, the result is (1) 2x2 � 2x (3) �2x2 � 8x � 4 (2) �2x2 � 2x (4) 2x2 � 8x � 4 23 Which expression represents the number of hours in w weeks and d days? (1) 7w � 12d (3) 168w � 24d (2) 84w � 24d (4) 168w � 60d Integrated Algebra – June ’13 [8] Use this space for computations.24 Given: R � {1, 2, 3, 4} A � {0, 2, 4, 6} P � {1, 3, 5, 7} What is R � P? (1) {0, 1, 2, 3, 4, 5, 6, 7} (3) {1, 3} (2) {1, 2, 3, 4, 5, 7} (4) {2, 4} 25 Which equation could be used to find the measure of angle D in the right triangle shown in the diagram below? (1) cos D � 12___ 13 (3) sin D � 5___ 13 (2) cos D � 13___ 12 (4) sin D � 12___ 13 26 If the roots of a quadratic equation are �2 and 3, the equation can be written as (1) (x � 2)(x � 3) � 0 (3) (x � 2)(x � 3) � 0 (2) (x � 2)(x � 3) � 0 (4) (x � 2)(x � 3) � 0 27 Which equation represents a line that is parallel to the y-axis and passes through the point (4,3)? (1) x � 3 (3) y � 3 (2) x � 4 (4) y � 4 � � �� �� �� Integrated Algebra – June ’13 [9] [OVER] Integrated Algebra – June ’13 [10] 28 There are 18 students in a class. Each day, the teacher randomly selects three students to assist in a game: a leader, a recorder, and a timekeeper. In how many possible ways can the jobs be assigned? (1) 306 (3) 4896 (2) 816 (4) 5832 29 In triangle RST, angle R is a right angle. If TR � 6 and TS � 8, what is the length of RS—? (1) 10 (3) 2√ _ 7 (2) 2 (4) 7√ _ 2 30 How many solutions are there for the following system of equations? y � x2 � 5x � 3 y � x � 6 (1) 1 (3) 3 (2) 2 (4) 0 Use this space for computations. 31 Solve the inequality �5(x � 7) � 15 algebraically for x. Integrated Algebra – June ’13 [11] [OVER] Part II Answer all 3 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. [6] 32 Oatmeal is packaged in a cylindrical container, as shown in the diagram below. The diameter of the container is 13 centimeters and its height is 24 centimeters. Determine, in terms of π, the volume of the cylinder, in cubic centimeters. ����� ����� � ���� Integrated Algebra – June ’13 [12] 33 The distance from Earth to Mars is 136,000,000 miles. A spaceship travels at 31,000 miles per hour. Determine, to the nearest day, how long it will take the spaceship to reach Mars. Integrated Algebra – June ’13 [13] [OVER] 34 The menu for the high school cafeteria is shown below. Determine the number of possible meals consisting of a main course, a vegetable, a dessert, and a beverage that can be selected from the menu. Determine how many of these meals will include chicken tenders. If a student chooses pizza, corn or carrots, a dessert, and a beverage from the menu, determine the number of possible meals that can be selected. �������� ���� ����� � ������ !��" #���$# ���� �"��$������ ��� �%�� ����������� ����%�� ��&���� #� �����&� %� �� �%%$�� ����������� � ��&$ ' ��� �%��&� �!���� �� �������� ���� ���� ������ �������� Integrated Algebra – June ’13 [14] Part III Answer all 3 questions in this part. Each correct answer will receive 3 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. [9] 35 A man standing on level ground is 1000 feet away from the base of a 350-foot-tall building. Find, to the nearest degree, the measure of the angle of elevation to the top of the building from the point on the ground where the man is standing. Integrated Algebra – June ’13 [15] [OVER] 36 Express √ __ 25 � 2√ _ 3 � √ __ 27 � 2√ _ 9 in simplest radical form. Integrated Algebra – June ’13 [16] 37 Solve algebraically: 2___ 3x � 4__ x � 7_____ x � 1 [Only an algebraic solution can receive full credit.] Integrated Algebra – June ’13 [17] [OVER] Part IV 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] 38 A jar contains five red marbles and three green marbles. A marble is drawn at random and not replaced. A second marble is then drawn from the jar. Find the probability that the first marble is red and the second marble is green. Find the probability that both marbles are red. Find the probability that both marbles are the same color. Integrated Algebra – June ’13 [18] Integrated Algebra – June ’13 [19] 39 In the diagram below of rectangle AFEB and a semicircle with diameter CD—, AB � 5 inches, AB � BC � DE � FE, and CD � 6 inches. Find the area of the shaded region, to the nearest hundredth of a square inch. ( �) � * � Te ar H er e Te ar H er e Scrap Graph Paper — This sheet will not be scored. Scrap Graph Paper — This sheet will not be scored. Tear H ere Tear H ere Integrated Algebra – June ’13 [23] Te ar H er e Te ar H er e Trigonometric Ratios sin A = opposite hypotenuse tan A = opposite adjacent cos A = adjacent hypotenuse Area trapezoid A = –h(b1 + b2)12 Volume cylinder V = πr2h Surface Area rectangular prism SA = 2lw + 2hw + 2lh cylinder SA = 2πr2 + 2πrh Coordinate Geometry 𝚫y 𝚫x y2 – y1 x2 – x1=m = Reference Sheet Tear H ere Tear H ere INTEGRATED ALGEBRA INTEGRATED ALGEBRA Printed on Recycled Paper FOR TEACHERS ONLY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA Wednesday, June 12, 2013 — 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 Integrated Algebra. More detailed information about scoring is provided in the publication Information Booklet for Scoring the Regents Examinations in Mathematics. Do not attempt to correct the student’s work by making insertions or changes of any kind. In scoring the open-ended questions, use check marks to indicate student errors. 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. Teachers may not score their own students’ answer papers. On the student’s separate answer sheet, for each question, record the number of credits earned and the teacher’s assigned rater/scorer letter. Schools are not permitted to rescore any of the open-ended questions on this exam after each question has been rated once, regardless of the final exam score. Schools are required to ensure that the raw scores have been added correctly and that the resulting scale score has been determined accurately. Raters should record the student’s scores for all questions and the total raw score on the student’s separate answer sheet. Then the student’s total raw score should be converted to a scale score by using the conversion chart that will be posted on the Department’s web site at: http://www.p12.nysed.gov/assessment/ on Wednesday, June 12, 2013. Because scale scores corresponding to raw scores in the conversion chart may change from one administration to another, it is crucial that, for each administration, the conversion chart provided for that administration be used to determine the student’s final score. The student’s scale score should be entered in the box provided on the student’s separate answer sheet. The scale score is the student’s final examination score. Integrated Algebra Rating Guide – June ’13 [2] If the student’s responses for the multiple-choice questions are being hand scored prior to being scanned, the scorer must be careful not to make any marks on the answer sheet except to record the scores in the designated score boxes. Marks elsewhere on the answer sheet will interfere with the accuracy of the scanning. Part I Allow a total of 60 credits, 2 credits for each of the following. (1) . . . . . 1 . . . . . (2) . . . . . 1 . . . . . (3) . . . . . 3 . . . . . (4) . . . . . 3 . . . . . (5) . . . . . 4 . . . . . (6) . . . . . 3 . . . . . (7) . . . . . 1 . . . . . (8) . . . . . 1 . . . . . (9) . . . . . 3 . . . . . (10) . . . . . 1 . . . . . (11) . . . . . 2 . . . . . (12) . . . . . 2 . . . . . (13) . . . . . 3 . . . . . (14) . . . . . 2 . . . . . (15) . . . . . 1 . . . . . (16) . . . . . 1 . . . . . (17) . . . . . 2 . . . . . (18) . . . . . 3 . . . . . (19) . . . . . 4 . . . . . (20) . . . . . 4 . . . . . (21) . . . . . 4 . . . . . (22) . . . . . 1 . . . . . (23) . . . . . 3 . . . . . (24) . . . . . 3 . . . . . (25) . . . . . 4 . . . . . (26) . . . . . 2 . . . . . (27) . . . . . 2 . . . . . (28) . . . . . 3 . . . . . (29) . . . . . 3 . . . . . (30) . . . . . 1 . . . . . 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/assessment/ 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. Beginning in January 2013, the Department is providing supplemental scoring guidance, the “Sample Response Set,” for the Regents Examination in Integrated Algebra. This guidance is not required as part of the scorer training. It is at the school’s discretion to incorporate it into the scorer training or to use it as supplemental information during scoring. While not reflective of all scenarios, the sample student responses selected for the Sample Response Set illustrate how less common student responses to open-ended questions may be scored. The Sample Response Set will be available on the Department’s web site at http://www.p12.nysed.gov/assessment/scoring/home-hs.html. Integrated Algebra Rating Guide – June ’13 [3] General Rules for Applying Mathematics Rubrics I. General Principles for Rating The rubrics for the constructed-response questions on the Regents Examination in Integrated Algebra 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 ob