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New York Regents Integrated Algebra January 2009

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INTEGRATED ALGEBRA The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION Integrated algebra Thursday, January 29, 2009 1:15 to 4:15 p.m., only Print Your Name: Print Your School s Name: Print your name and the name of your school in the boxes above. Then turn to the last page of this booklet, which is the answer sheet for Part I. Fold the last page along the perforations and, slowly and carefully, tear off the answer sheet. Then fill in the heading of your answer sheet. 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. All work should be written in pen, except graphs and drawings, which should be done in pencil. 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. 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. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. When you have completed the examination, you must sign the statement printed at the end of the answer sheet, indicating that you had no unlawful knowledge of the questions or answers prior to the examination and that you have neither given nor received assistance in answering any of the questions during the examination. Your answer sheet cannot be accepted if you fail to sign this declaration. Notice A graphing calculator and a straightedge (ruler) must be available for you to use while taking this examination. The use of any communications device is strictly prohibited when taking this examination. If you use any communications device, no matter how briefly, your examination will be invalidated and no score will be calculated for you. DO NOT OPEN THIS EXAMINATION BOOKLET UNTIL THE SIGNAL IS GIVEN. INTEGRATED ALGEBRA Part I Answer all questions in this part. Each correct answer will receive 2 credits. No partial credit will be allowed. For each question, write on the separate answer sheet the numeral preceding the word or expression that best completes the statement or answers the question. [60] 1 On a certain day in Toronto, Canada, the temperature was 9 15 Celsius (C). Using the formula F = C + 32 , Peter converts 5 this temperature to degrees Fahrenheit (F). Which temperature represents 15 C in degrees Fahrenheit? (1) 9 (3) 59 (2) 35 (4) 85 2 What is the speed, in meters per second, of a paper airplane that flies 24 meters in 6 seconds? (1) 144 (3) 18 (2) 30 (4) 4 3 The faces of a cube are numbered from 1 to 6. If the cube is rolled once, which outcome is least likely to occur? (1) rolling an odd number (2) rolling an even number (3) rolling a number less than 6 (4) rolling a number greater than 4 Integrated Algebra Jan. 09 [2] Use this space for computations. 4 Tamara has a cell phone plan that charges $0.07 per minute plus a monthly fee of $19.00. She budgets $29.50 per month for total cell phone expenses without taxes. What is the maximum number of minutes Tamara could use her phone each month in order to stay within her budget? (1) 150 (3) 421 (2) 271 Use this space for computations. (4) 692 0 Temperature 200 180 160 140 120 100 80 60 40 20 1 2 3 4 5 6 (degrees Fahrenheit) Temperature (degrees Fahrenheit) 5 Antwaan leaves a cup of hot chocolate on the counter in his kitchen. Which graph is the best representation of the change in temperature of his hot chocolate over time? 200 180 160 140 120 100 80 60 40 20 0 1 2 3 4 5 (3) 0 Temperature 200 180 160 140 120 100 80 60 40 20 1 2 3 4 5 6 (degrees Fahrenheit) Temperature Time (minutes) (1) (degrees Fahrenheit) Time (minutes) 6 200 180 160 140 120 100 80 60 40 20 0 1 2 3 4 5 Time (minutes) (2) 6 Time (minutes) (4) 6 What is the solution of k+4 k+9 = 2 3? (1) 1 (3) 6 (2) 5 (4) 14 Integrated Algebra Jan. 09 [3] [OVER] 7 Alex earned scores of 60, 74, 82, 87, 87, and 94 on his first six algebra tests. What is the relationship between the measures of central tendency of these scores? (1) median < mode < mean (3) mode < median < mean (2) mean < mode < median (4) mean < median < mode 8 The New York Volleyball Association invited 64 teams to compete in a tournament. After each round, half of the teams were eliminated. Which equation represents the number of teams, t, that remained in the tournament after r rounds? (1) t = 64(r)0.5 (3) t = 64(1.5)r (2) t = 64( 0.5)r (4) t = 64(0.5)r 9 The expression 9x2 100 is equivalent to (1) (9x 10)(x + 10) (3) (3x 100)(3x 1) (2) (3x 10)(3x + 10) (4) (9x 100)(x + 1) 10 What is an equation of the line that passes through the points (3, 3) and ( 3, 3)? (1) y = 3 (3) y = 3 (2) x = 3 (4) x = y Integrated Algebra Jan. 09 [4] Use this space for computations. 11 If the formula for the perimeter of a rectangle is P = 2l + 2w, then w can be expressed as 2l P 2 P 2l (2) w = 2 Use this space for computations. P l 2 P 2w (4) w = 2l (1) w = (3) w = 12 In the right triangle shown in the diagram below, what is the value of x to the nearest whole number? x 30 24 (1) 12 (3) 21 (2) 14 (4) 28 13 What is the slope of the line that passes through the points (2,5) and (7,3)? 5 8 (1) 2 (3) 9 2 9 (2) 5 (4) 8 Integrated Algebra Jan. 09 [5] [OVER] Use this space for computations. 2 14 What are the roots of the equation x 10x + 21 = 0? (1) 1 and 21 (3) 3 and 7 (2) 5 and 5 (4) 3 and 7 15 Rhonda has $1.35 in nickels and dimes in her pocket. If she has six more dimes than nickels, which equation can be used to determine x, the number of nickels she has? (1) 0.05(x + 6) + 0.10x = 1.35 (2) 0.05x + 0.10(x + 6) = 1.35 (3) 0.05 + 0.10(6x) = 1.35 (4) 0.15(x + 6) = 1.35 16 Which equation represents the axis of symmetry of the graph of the parabola below? y 25 5 x 5 25 (1) y = 3 (3) y = 25 (2) x = 3 (4) x = 25 Integrated Algebra Jan. 09 [6] 17 The set "1, 2, 3, 4 , is equivalent to The (1) # x ; 1 1 x 1 4,where x is a whole number (2) # x ; 0 1 x 1 4,where x is a whole number (3) # x ; 0 1 x # 4,where x is a whole number (4) # x ; 1 1 x # 4,where x is a whole number - Use this space for computations. 2 26 18 What is the value of x in the equation x - 3 = x ? 1 (1) 8 (3) 8 1 (2) 8 (4) 8 19 The diagram below shows right triangle UPC. U 8 C 17 15 P Which ratio represents the sine of U? 15 8 (1) 8 (3) 15 15 8 (2) (4) 17 17 Integrated Algebra Jan. 09 [7] [OVER] 20 What is 72 expressed in simplest radical form? (1) 2 18 (3) 6 2 (2) 3 8 (4) 8 3 6 2 21 What is 5x 3x in simplest form? 8 4 (1) (3) 2 15x 15x 8 4 (2) (4) 2x 15x 22 Which ordered pair is a solution of the system of equations y = x2 x 20 and y = 3x 15? (1) ( 5, 30) (3) (0,5) (2) ( 1, 18) (4) (5, 1) 23 A survey is being conducted to determine which types of television programs people watch. Which survey and location combination would likely contain the most bias? (1) surveying 10 people who work in a sporting goods store (2) surveying the first 25 people who enter a grocery store (3) randomly surveying 50 people during the day in a mall (4) randomly surveying 75 people during the day in a clothing store Integrated Algebra Jan. 09 [8] Use this space for computations. 24 The length of a rectangular room is 7 less than three times the width, w, of the room. Which expression represents the area of the room? (1) 3w 4 (3) 3w2 4w (2) 3w 7 Use this space for computations. (4) 3w2 7w (1) 0 or 3 x is undefined when the value of x is x -9 (3) 3, only (2) 3 or 3 (4) 3, only 25 The function y = 2 26 Which equation represents a line that is parallel to the line y = 3 2x? (1) 4x + 2y = 5 (3) y = 3 4x (2) 2x + 4y = 1 (4) y = 4x 2 Integrated Algebra Jan. 09 [9] [OVER] 27 What is the product of 8.4 108 and 4.2 103 written in scientific notation? (1) 2.0 105 (3) 35.28 1011 (2) 12.6 1011 (4) 3.528 1012 28 Keisha is playing a game using a wheel divided into eight equal sectors, as shown in the diagram below. Each time the spinner lands on orange, she will win a prize. Brown White Green Orange Yellow Brown Brown White If Keisha spins this wheel twice, what is the probability she will win a prize on both spins? 1 (1) 64 1 (2) 56 Integrated Algebra Jan. 09 1 (3) 16 1 (4) 4 [10] Use this space for computations. 29 A movie theater recorded the number of tickets sold daily for a popular movie during the month of June. The box-and-whisker plot shown below represents the data for the number of tickets sold, in hundreds. 0 1 2 3 4 5 6 7 8 9 Use this space for computations. 10 Which conclusion can be made using this plot? (1) The second quartile is 600. (2) The mean of the attendance is 400. (3) The range of the attendance is 300 to 600. (4) Twenty-five percent of the attendance is between 300 and 400. 30 Which graph represents a function? y y x x (1) (3) y y x x (2) Integrated Algebra Jan. 09 (4) [11] [OVER] Part II Answer all 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. [6] 31 A window is made up of a single piece of glass in the shape of a semicircle and a rectangle, as shown in the diagram below. Tess is decorating for a party and wants to put a string of lights all the way around the outside edge of the window. Window 12 ft 10 ft To the nearest foot, what is the length of the string of lights that Tess will need to decorate the window? Integrated Algebra Jan. 09 [12] 32 Simplify: 27k 5 m8 ^ 4k 3 h ^ 9m 2 h Integrated Algebra Jan. 09 [13] [OVER] 33 The table below represents the number of hours a student worked and the amount of money the student earned. Number of Hours ( h) Dollars Earned (d) 8 $50.00 15 $93.75 19 $118.75 30 $187.50 Write an equation that represents the number of dollars, d, earned in terms of the number of hours, h, worked. Using this equation, determine the number of dollars the student would earn for working 40 hours. Integrated Algebra Jan. 09 [14] Part III Answer all 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. [9] 34 Sarah measures her rectangular bedroom window for a new shade. Her measurements are 36 inches by 42 inches. The actual measurements of the window are 36.5 inches and 42.5 inches. Using the measurements that Sarah took, determine the number of square inches in the area of the window. Determine the number of square inches in the actual area of the window. Determine the relative error in calculating the area. Express your answer as a decimal to the nearest thousandth. Integrated Algebra Jan. 09 [15] [OVER] 35 Perform the indicated operation and simplify: Integrated Algebra Jan. 09 3x + 6 x2 - 4 ' x+3 4x + 12 [16] 36 A soup can is in the shape of a cylinder. The can has a volume of 342 cm3 and a diameter of 6 cm. Express the height of the can in terms of . Determine the maximum number of soup cans that can be stacked on their base between two shelves if the distance between the shelves is exactly 36 cm. Explain your answer. Integrated Algebra Jan. 09 [17] [OVER] Part IV Answer all 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. [12] 37 Solve the following system of equations algebraically: 3x + 2y = 4 4x + 3y = 7 [Only an algebraic solution can receive full credit.] Integrated Algebra Jan. 09 [18] 38 On the set of axes below, graph the following system of inequalities and state the coordinates of a point in the solution set. 2x - y $ 6 x22 y x Integrated Algebra Jan. 09 [19] [OVER] 39 A restaurant sells kids meals consisting of one main course, one side dish, and one drink, as shown in the table below. Kids Meal Choices Main Course Side Dish Drink hamburger French fries milk chicken nuggets applesauce juice turkey sandwich soda Draw a tree diagram or list the sample space showing all possible kids meals. How many different kids meals can a person order? Jos does not drink juice. Determine the number of different kids meals that do not include juice. Jos s sister will eat only chicken nuggets for her main course. Determine the number of different kids meals that include chicken nuggets. Integrated Algebra Jan. 09 [20] Tear Here Reference Sheet sin A = cos A = adjacent hypotenuse tan A = Trigonometric Ratios opposite hypotenuse opposite adjacent Area trapezoid Volume cylinder 1 A = h ( b 1 + b 2) 2 V = r 2h rectangular prism SA = 2lw + 2hw + 2lh Surface Area Tear Here cylinder Coordinate Geometry Integrated Algebra Jan. 09 SA = 2 r2 + 2 rh y y y m = x = x 2 x 1 2 1 [23] Tear Here Tear Here Integrated Algebra Jan. 09 [24] Tear Here Tear Here Scrap Graph Paper This sheet will not be scored. Scrap Graph Paper This sheet will not be scored. Tear Here Tear Here The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION Tear Here Integrated algebra Thursday, January 29, 2009 1:15 to 4:15 p.m., only ANSWER SHEET Student . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sex: Male Female Grade . . . . . . . . Teacher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . School . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Your answers to Part I should be recorded on this answer sheet. Part I Answer all 30 questions in this part. 1 ................ 9 ................ 17 . . . . . . . . . . . . . . . . 25 . . . . . . . . . . . . . . . . 2 ................ 10 . . . . . . . . . . . . . . . . 18 . . . . . . . . . . . . . . . . 26 . . . . . . . . . . . . . . . . 3 ................ 11 . . . . . . . . . . . . . . . . 19 . . . . . . . . . . . . . . . . 27 . . . . . . . . . . . . . . . . 4 ................ 12 . . . . . . . . . . . . . . . . 20 . . . . . . . . . . . . . . . . 28 . . . . . . . . . . . . . . . . 5 ................ 13 . . . . . . . . . . . . . . . . 21 . . . . . . . . . . . . . . . . 29 . . . . . . . . . . . . . . . . 6 ................ 14 . . . . . . . . . . . . . . . . 22 . . . . . . . . . . . . . . . . 30 . . . . . . . . . . . . . . . . 7 ................ 15 . . . . . . . . . . . . . . . . 23 . . . . . . . . . . . . . . . . 8 ................ 16 . . . . . . . . . . . . . . . . 24 . . . . . . . . . . . . . . . . Your answers for Parts II, III, and IV should be written in the test booklet. Tear Here The declaration below should be signed when you have completed the examination. I do hereby affirm, at the close of this examination, that I had no unlawful knowledge of the questions or answers prior to the examination and that I have neither given nor received assistance in answering any of the questions during the examination. Signature Integrated Algebra Jan. 09 [27] INTEGRATED ALGEBRA rater s/Scorer s name (minimum of three) Integrated algebra Maximum Credit Part I 1 30 60 Part II 31 2 32 2 33 2 34 3 35 3 36 3 37 4 38 4 39 4 Maximum total 87 Part IV rater s/Scorer s Initials total raw Score Part III Credits earned Checked by Tear Here Question Scaled Score (from conversion chart) Tear Here [28] INTEGRATED ALGEBRA Integrated Algebra Jan. 09 FOR TEACHERS ONLY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA Thursday, January 29, 2009 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 Examination in Integrated Algebra. Use only red ink or red pencil in rating Regents papers. Do not attempt to correct the student s work by making insertions or changes of any kind. 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. On the back of the student s detachable answer sheet, raters must enter their initials in the boxes next to the questions they have scored and also write their name in the box under the heading Rater s/Scorer s Name. Raters should record the student s scores for all questions and the total raw score on the student s detachable answer sheet. Then the student s total raw score should be converted to a scaled score by using the conversion chart that will be posted on the Department s web site http://www.emsc.nysed.gov/osa/ o n Thursday, January 29, 2009. The student s scaled score should be entered in the box provided on the student s detachable answer sheet. The scaled score is the student s final examination score. INTEGRATED ALGEBRA continued Part I Allow a total of 60 credits, 2 credits for each of the following. Allow credit if the student has written the correct answer instead of the numeral 1, 2, 3, or 4. (1) 3 (9) 2 (17) 3 (25) 2 (2) 4 (10) 3 (18) 1 (26) 1 (3) 4 (11) 2 (19) 2 (27) 4 (4) 1 (12) 3 (20) 3 (28) 1 (5) 1 (13) 2 (21) 2 (29) 4 (6) 3 (14) 3 (22) 2 (30) 4 (7) 4 (15) 2 (23) 1 (8) 4 (16) 2 (24) 4 [2] INTEGRATED ALGEBRA continued 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 http://www.emsc.nysed.gov/osa/ and select the link Examination Scoring Information for any recently posted information regarding this examination. This site should be checked before the rating process for this examination begins and several times throughout the Regents examination period. General Rules for Applying Mathematics Rubrics 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 Examination in Integrated Algebra, use their own professional judgment, confer with other mathematics teachers, and/or contact the consultants at 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, charts, etc. The student has the responsibility of providing the correct answer and showing how that answer was obtained. The student must construct the response; the teacher should not have to search through a group of seemingly random calculations scribbled on the student paper to ascertain what method the student may have used. Responses With Errors: Rubrics that state Appropriate work is shown, but are intended to be used with solutions that show an essentially complete response to the question but contain certain types of errors, whether computational, rounding, graphing, or conceptual. If the response is incomplete; i.e., an equation is written but not solved or an equation is solved but not all of the parts of the question are answered, appropriate work has not been shown. Other rubrics address incomplete responses. IV. Multiple Errors Computational Errors, Graphing Errors, and Rounding Errors: Each of these types of errors results in a 1-credit deduction. Any combination of two of these types of errors results in a 2-credit deduction. No more than 2 credits should be deducted for such mechanical errors in any response. The teacher must carefully review the student s work to determine what errors were made and what type of errors they were. Conceptual Errors: A conceptual error involves a more serious lack of knowledge or procedure. Examples of conceptual errors include using the incorrect formula for the area of a figure, choosing the incorrect trigonometric function, or multiplying the exponents instead of adding them when multiplying terms with exponents. A response with one conceptual error can receive no more than half credit. If a response shows repeated occurrences of the same conceptual error, the student should not be penalized twice. If the same conceptual error is repeated in responses to other questions, credit should be deducted in each response. If a response shows two (or more) different major conceptual errors, it should be considered completely incorrect and receive no credit. If a response shows one conceptual error and one computational, graphing, or rounding error, the teacher must award credit that takes into account both errors; i.e., awarding half credit for the conceptual error and deducting 1 credit for each mechanical error (maximum of two deductions for mechanical errors). I. [3] [OVER] INTEGRATED ALGEBRA continued Part II For each question, use the specific criteria to award a maximum of two credits. Unless otherwise specified, mathematically correct alternative solutions should be awarded appropriate credit. (31) [2] 50, and appropriate work is shown. [1] Appropriate work is shown, but one computational or rounding error is made. or [1] Appropriate work is shown, but one conceptual error is made. or [1] 50, but no work is shown. [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. (32) [2] 3k 2 m6 or an equivalent answer, and appropriate work is shown. 4 [1] Appropriate work is shown, but one computational error is made. or [1] Appropriate work is shown, but one conceptual error is made. or [1] 3k 2 m6 , but no work is shown. 4 [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. [4] INTEGRATED ALGEBRA continued (33) [2] d = 6.25h or an equivalent equation and 250, and appropriate work is shown. [1] Appropriate work is shown, but one computational error is made. or [1] Appropriate work is shown, but one conceptual error is made. or [1] A correct equation is written, but no further correct work is shown. or [1] Appropriate work is shown to find 250, but the equation is missing or is incorrect. [0] 250, but no work is shown. or [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. [5] [OVER] INTEGRATED ALGEBRA continued Part III For each question, use the specific criteria to award a maximum of three credits. Unless otherwise specified, mathematically correct alternative solutions should be awarded appropriate credit. (34) [3] 1,512 and 1,551.25 and 0.025, and appropriate work is shown. [2] Appropriate work is shown, but one computational or rounding error is made. [1] Appropriate work is shown, but two or more computational or rounding errors are made. or [1] Appropriate work is shown, but one conceptual error is made, such as dividing by 1,512. or [1] Appropriate work is shown to find 1,512 and 1,551.25, but no further correct work is shown. or [1] 1,512 and 1,551.25 and 0.025, but no work is shown. [0] 1,512 or 1,551.25 or 0.025, but no work is shown. or [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. (35) [3] 3 3 or , and appropriate work is shown. 4( x 2) 4x 8 [2] Appropriate work is shown, but one computational, factoring, or simplification error is made. [1] Appropriate work is shown, but two or more computational, factoring, or simplification errors are made. or [1] Appropriate work is shown, but one conceptual error is made. or [1] 3 3 or , but no work is shown. 4( x 2) 4x 8 [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. [6] INTEGRATED ALGEBRA continued (36) [3] 38 or an equivalent answer in terms of , and 2, and appropriate work is shown, and an appropriate explanation is given. [2] Appropriate work is shown, but one computational or rounding error is made, but an appropriate explanation is given. or [2] Appropriate work is shown and an appropriate explanation is given, but the correct height of the can is expressed as a decimal. or [2] 38 and 2, and appropriate work is shown, but an appropriate explanation is not given. [1] Appropriate work is shown, but two or more computational or rounding errors are made, but an appropriate explanation is given. or [1] Appropriate work is shown, but one conceptual error is made, but an appropriate explanation is given. or [1] [0] 38 38 and 2, but no work is shown. or 2, but no work is shown. or [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. [7] [OVER] INTEGRATED ALGEBRA continued Part IV For each question, use the specific criteria to award a maximum of four credits. Unless otherwise specified, mathematically correct alternative solutions should be awarded appropriate credit. (37) [4] ( 2,5) or x = 2 and y = 5, and appropriate algebraic work is shown. [3] Appropriate algebraic work is shown, but one computational error is made, but appropriate values are found for x and y. or [3] x = 2 or y = 5, and appropriate algebraic work is shown. [2] Appropriate algebraic work is shown, but two or more computational errors are made, but appropriate values are found for x and y. or [2] Appropriate algebraic work is shown, but one conceptual error is made. or [2] ( 2,5) or x = 2 and y = 5, but a method other than an algebraic method is used. [1] Appropriate algebraic work is shown, but one conceptual error and one computational error are made. or [1] The trial-and-error method is used to find the correct solution, but fewer than three trials and appropriate checks are shown. or [1] x = 2 or y = 5, but a method other than an algebraic method is used. or [1] ( 2,5) or x = 2 and y = 5, but no work is shown. [0] x = 2 or y = 5, but no work is shown. or [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. [8] INTEGRATED ALGEBRA continued (38) [4] Both inequalities are graphed and shaded correctly, and at least one is labeled, and a point in the solution set is identified. [3] Appropriate work is shown, but one graphing error is made, such as drawing a solid line for x > 2 or shading incorrectly, but an appropriate point in the solution set is identified. or [3] Both inequalities are graphed and shaded correctly, and a point in the solution set is identified correctly, but the graphs are not labeled or are labeled incorrectly. or [3] Both inequalities are graphed and shaded correctly, and at least one is labeled, but no point in the solution set is identified. [2] Appropriate work is shown, but two or more graphing errors are made, but an appropriate point in the solution set is identified. or [2] Appropriate work is shown, but one conceptual error is made, such as graphing the lines x = 2 and y = 2x 6 and identifying the point of intersection. or [2] One of the inequalities is graphed and shaded correctly, and at least one is labeled, but no further correct work is shown. [1] Appropriate work is shown, but one conceptual error and one graphing error are made, but an appropriate point in the solution set is identified. or [1] Both inequalities are graphed incorrectly, but an appropriate point in the solution set is identified. or [1] The lines x = 2 and y = 2x 6 are graphed correctly, and at least one is labeled, but no further correct work is shown. or [1] A point in the solution set is identified and shown to be correct by checking in both inequalities, but no graphs are drawn. [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. [9] [OVER] INTEGRATED ALGEBRA continued (39) [4] A correct tree diagram or sample space is given, and 18 total meals, 12 meals without juice, and 6 meals with chicken nuggets. [3] A correct tree diagram or sample space is given, but either 18, 12, or 6 is missing or is incorrect. or [3] The fundamental counting principle is used to find 18 total meals, 12 meals without juice, and 6 meals with chicken nuggets, but no tree diagram or sample space is given. or [3] An incorrect tree diagram or sample space is given, but an appropriate number of meals is found for all three categories. [2] A correct tree diagram or sample space is given, but an appropriate number of meals is found for only one category. or [2] An incorrect tree diagram or sample space is given, but an appropriate number of meals is found for only two categories. [1] A correct tree diagram or sample space is given, but no number of meals is found correctly. or [1] An incorrect tree diagram or sample space is given, but an appropriate number of meals is found for only one category. or [1] 18 total meals, 12 meals without juice, and 6 meals with chicken nuggets, but no work is shown. [0] 18 total meals or 12 meals without juice or 6 meals with chicken nuggets, but no work is shown. or [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. [10] INTEGRATED ALGEBRA concluded Map to Learning Standards Key Ideas Item Numbers Number Sense and Operations 20, 27, 33 Algebra 4, 6, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 21, 22, 24, 25, 26, 32, 35, 37 Geometry 5, 16, 30, 31, 36, 38 Measurement 1, 2, 34 Probability and Statistics 3, 7, 23, 28, 29, 39 Regents Examination in Integrated Algebra January 2009 Chart for Converting Total Test Raw Scores to Final Examination Scores (Scaled Scores) The Chart for Determining the Final Examination Score for the January 2009 Regents Examination in Integrated Algebra will be posted on the Department s web site http://www.emsc.nysed.gov/osa/ on Thursday, January 29, 2009. Conversion charts provided for previous administrations of the Integrated Algebra examination must NOT be used to determine students final scores for this administration. Submitting Teacher Evaluations of the Test to the Department Suggestions and feedback from teachers provide an important contribution to the test development process. The Department provides an online evaluation form for State assessments. It contains spaces for teachers to respond to several specific questions and to make suggestions. Instructions for completing the evaluation form are as follows: 1. Go to www.emsc.nysed.gov/osa/exameval. 2. Select the test title. 3. Complete the required demographic fields. 4. Complete each evaluation question and provide comments in the space provided. 5. Click the SUBMIT button at the bottom of the page to submit the completed form. [11] [12]

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Additional Info : Refer end of paper for Scoring Key (page 29)
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