# The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA. Tuesday, January 22, :15 a.m. SAMPLE RESPONSE SET

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1 The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA Tuesday, January 22, :15 a.m. SAMPLE RESPONSE SET Table of Contents Practice Papers Question Practice Papers Question Practice Papers Question Practice Papers Question Practice Papers Question Practice Papers Question Practice Papers Question Practice Papers Question Practice Papers Question Revisions have been made to pages 5, 6, 26, 29, and 46. Please print and replace these pages. Thank you for your cooperation.

2 Practice Papers Question Express 4 75 in simplest radical form. Score: 2 The student has a complete and correct response. The student shows a breakdown of 75 in this work. Integrated Algebra Jan. 13 [2]

3 Practice Papers Question Express 4 75 in simplest radical form. Score: 2 The student has a complete and correct response. It is not necessary for the student to show that 25 = 5. Integrated Algebra Jan. 13 [3]

4 Practice Papers Question Express 4 75 in simplest radical form. Score: 1 The student makes one conceptual error by writing 25 as 5 5. Integrated Algebra Jan. 13 [4]

5 Practice Papers Question Express 4 75 in simplest radical form. Score: 1 The student makes one conceptual error by adding 4 and 5 instead of multiplying them. Integrated Algebra Jan. 13 [5]

6 Practice Papers Question Express 4 75 in simplest radical form. Score: 0 The student makes two conceptual errors by writing 3 = 3 and 25 = 5. Integrated Algebra Jan. 13 [6]

7 Practice Papers Question Express 4 75 in simplest radical form. Score: 0 The student writes the answer as a decimal. Integrated Algebra Jan. 13 [7]

8 Practice Papers Question Factor completely: 5x 3 20x 2 60x Score: 2 The student has a complete and correct response. Integrated Algebra Jan. 13 [8]

9 Practice Papers Question Factor completely: 5x 3 20x 2 60x Score: 2 The student has a complete and correct response. The student factors the trinomial by grouping. Integrated Algebra Jan. 13 [9]

10 Practice Papers Question Factor completely: 5x 3 20x 2 60x Score: 1 The student takes out the greatest common factor, but no further correct work is shown. Integrated Algebra Jan. 13 [10]

11 Practice Papers Question Factor completely: 5x 3 20x 2 60x Score: 1 The student takes out the greatest common factor correctly, but then attempts to solve for roots. Integrated Algebra Jan. 13 [11]

12 Practice Papers Question Factor completely: 5x 3 20x 2 60x Score: 1 The student takes out greatest factor correctly, but then makes a factoring error. Integrated Algebra Jan. 13 [12]

13 Practice Papers Question Factor completely: 5x 3 20x 2 60x Score: 0 The student makes an error in taking out the greatest common factor and makes an error in factoring the trinomial. Integrated Algebra Jan. 13 [13]

14 Practice Papers Question Factor completely: 5x 3 20x 2 60x Score: 0 No correct work is shown. Integrated Algebra Jan. 13 [14]

15 Practice Papers Question On the set of axes below, graph y 2 x 3. Include the interval 7 x 1. Score: 2 The student has a complete and correct response. Integrated Algebra Jan. 13 [15]

16 Practice Papers Question On the set of axes below, graph y 2 x 3. Include the interval 7 x 1. Score: 2 The student has a complete and correct response. Since a table of values is given, it is not necessary to deduct credit for lines that are not straight. Integrated Algebra Jan. 13 [16]

17 Practice Papers Question On the set of axes below, graph y 2 x 3. Include the interval 7 x 1. Score: 1 The student makes a conceptual error by taking the absolute value of each number in the absolute value symbol instead of combining them first. Integrated Algebra Jan. 13 [17]

18 Practice Papers Question On the set of axes below, graph y 2 x 3. Include the interval 7 x 1. Score: 1 The student makes a conceptual error by treating the absolute value symbol as parentheses. Integrated Algebra Jan. 13 [18]

19 Practice Papers Question On the set of axes below, graph y 2 x 3. Include the interval 7 x 1. Score: 1 The student makes one conceptual error. The student uses an incorrect interval in the table, but calculates those points correctly. Integrated Algebra Jan. 13 [19]

20 Practice Papers Question On the set of axes below, graph y 2 x 3. Include the interval 7 x 1. Score: 0 The student makes two conceptual errors. Integrated Algebra Jan. 13 [20]

21 Practice Papers Question In a game, a player must spin each spinner shown in the diagram below once C B A Spinner 1 Spinner 2 Draw a tree diagram or list a sample space showing all possible outcomes. Determine the number of outcomes that consist of a prime number and a letter in the word CAT. Score: 3 The student has a complete and correct response. Integrated Algebra Jan. 13 [21]

22 Practice Papers Question In a game, a player must spin each spinner shown in the diagram below once C B A Spinner 1 Spinner 2 Draw a tree diagram or list a sample space showing all possible outcomes. Determine the number of outcomes that consist of a prime number and a letter in the word CAT. Score: 3 The student has a complete and correct response. Integrated Algebra Jan. 13 [22]

23 Practice Papers Question In a game, a player must spin each spinner shown in the diagram below once C B A Spinner 1 Spinner 2 Draw a tree diagram or list a sample space showing all possible outcomes. Determine the number of outcomes that consist of a prime number and a letter in the word CAT. Score: 2 The student has a correct tree diagram, but the number of outcomes is incorrect. Integrated Algebra Jan. 13 [23]

24 Practice Papers Question In a game, a player must spin each spinner shown in the diagram below once C B A Spinner 1 Spinner 2 Draw a tree diagram or list a sample space showing all possible outcomes. Determine the number of outcomes that consist of a prime number and a letter in the word CAT. Score: 2 Although sloppy, the student s tree diagram is correct, but no further correct work is shown. Integrated Algebra Jan. 13 [24]

25 Practice Papers Question In a game, a player must spin each spinner shown in the diagram below once C B A Spinner 1 Spinner 2 Draw a tree diagram or list a sample space showing all possible outcomes. Determine the number of outcomes that consist of a prime number and a letter in the word CAT. Score: 2 The student has a correct sample space with no further correct work. Integrated Algebra Jan. 13 [25]

26 Practice Papers Question In a game, a player must spin each spinner shown in the diagram below once C B A Spinner 1 Spinner 2 Draw a tree diagram or list a sample space showing all possible outcomes. Determine the number of outcomes that consist of a prime number and a letter in the word CAT. Score: 1 The student has a partially correct sample space (9A, 9B, and 9C are missing), but no further correct work is shown. Integrated Algebra Jan. 13 [26]

27 Practice Papers Question In a game, a player must spin each spinner shown in the diagram below once C B A Spinner 1 Spinner 2 Draw a tree diagram or list a sample space showing all possible outcomes. Determine the number of outcomes that consist of a prime number and a letter in the word CAT. Score: 1 The student shows appropriate work to find 6. Integrated Algebra Jan. 13 [27]

28 Practice Papers Question In a game, a player must spin each spinner shown in the diagram below once C B A Spinner 1 Spinner 2 Draw a tree diagram or list a sample space showing all possible outcomes. Determine the number of outcomes that consist of a prime number and a letter in the word CAT. Score: 0 The student has an incorrect tree diagram and incorrect work to find 6. Integrated Algebra Jan. 13 [28]

29 Practice Papers Question In a game, a player must spin each spinner shown in the diagram below once C B A Spinner 1 Spinner 2 Draw a tree diagram or list a sample space showing all possible outcomes. Determine the number of outcomes that consist of a prime number and a letter in the word CAT. Score: 0 The student has no correct tree diagram and no correct work to find the answer. Integrated Algebra Jan. 13 [29]

30 Practice Papers Question The cost of three notebooks and four pencils is \$8.50. The cost of five notebooks and eight pencils is \$ Determine the cost of one notebook and the cost of one pencil. [Only an algebraic solution can receive full credit.] Score: 3 The student has a complete and correct response. Integrated Algebra Jan. 13 [30]

31 Practice Papers Question The cost of three notebooks and four pencils is \$8.50. The cost of five notebooks and eight pencils is \$ Determine the cost of one notebook and the cost of one pencil. [Only an algebraic solution can receive full credit.] Score: 3 The student has a complete and correct response. Integrated Algebra Jan. 13 [31]

32 Practice Papers Question The cost of three notebooks and four pencils is \$8.50. The cost of five notebooks and eight pencils is \$ Determine the cost of one notebook and the cost of one pencil. [Only an algebraic solution can receive full credit.] Score: 2 The student shows correct work to find only the cost of a notebook. Integrated Algebra Jan. 13 [32]

33 Practice Papers Question The cost of three notebooks and four pencils is \$8.50. The cost of five notebooks and eight pencils is \$ Determine the cost of one notebook and the cost of one pencil. [Only an algebraic solution can receive full credit.] Score: 2 The student shows correct work to find only the cost of a pencil. Integrated Algebra Jan. 13 [33]

34 Practice Papers Question The cost of three notebooks and four pencils is \$8.50. The cost of five notebooks and eight pencils is \$ Determine the cost of one notebook and the cost of one pencil. [Only an algebraic solution can receive full credit.] Score: 1 The student makes two computational errors. Integrated Algebra Jan. 13 [34]

35 Practice Papers Question The cost of three notebooks and four pencils is \$8.50. The cost of five notebooks and eight pencils is \$ Determine the cost of one notebook and the cost of one pencil. [Only an algebraic solution can receive full credit.] Score: 1 The student writes a correct system of equations, but no further correct work is shown. Integrated Algebra Jan. 13 [35]

36 Practice Papers Question The cost of three notebooks and four pencils is \$8.50. The cost of five notebooks and eight pencils is \$ Determine the cost of one notebook and the cost of one pencil. [Only an algebraic solution can receive full credit.] Score: 0 No correct work is shown. Integrated Algebra Jan. 13 [36]

37 Practice Papers Question Wendy measures the floor in her rectangular bedroom for new carpeting. Her measurements are 24 feet by 14 feet. The actual measurements are 24.2 feet by 14.1 feet. Determine the relative error in calculating the area of her bedroom. Express your answer as a decimal to the nearest thousandth. Score: 3 The student has a complete and correct response. Integrated Algebra Jan. 13 [37]

38 Practice Papers Question Wendy measures the floor in her rectangular bedroom for new carpeting. Her measurements are 24 feet by 14 feet. The actual measurements are 24.2 feet by 14.1 feet. Determine the relative error in calculating the area of her bedroom. Express your answer as a decimal to the nearest thousandth. Score: 3 The student has a complete and correct response. Integrated Algebra Jan. 13 [38]

39 Practice Papers Question Wendy measures the floor in her rectangular bedroom for new carpeting. Her measurements are 24 feet by 14 feet. The actual measurements are 24.2 feet by 14.1 feet. Determine the relative error in calculating the area of her bedroom. Express your answer as a decimal to the nearest thousandth. Score: 2 The student makes a rounding error. Integrated Algebra Jan. 13 [39]

40 Practice Papers Question Wendy measures the floor in her rectangular bedroom for new carpeting. Her measurements are 24 feet by 14 feet. The actual measurements are 24.2 feet by 14.1 feet. Determine the relative error in calculating the area of her bedroom. Express your answer as a decimal to the nearest thousandth. Score: 2 The student does not express the answer as a decimal to the nearest thousandth. Integrated Algebra Jan. 13 [40]

41 Practice Papers Question Wendy measures the floor in her rectangular bedroom for new carpeting. Her measurements are 24 feet by 14 feet. The actual measurements are 24.2 feet by 14.1 feet. Determine the relative error in calculating the area of her bedroom. Express your answer as a decimal to the nearest thousandth. Score: 1 The student makes a conceptual error in writing the fraction. Integrated Algebra Jan. 13 [41]

42 Practice Papers Question Wendy measures the floor in her rectangular bedroom for new carpeting. Her measurements are 24 feet by 14 feet. The actual measurements are 24.2 feet by 14.1 feet. Determine the relative error in calculating the area of her bedroom. Express your answer as a decimal to the nearest thousandth. Score: 1 The student makes multiple rounding errors. Integrated Algebra Jan. 13 [42]

43 Practice Papers Question Wendy measures the floor in her rectangular bedroom for new carpeting. Her measurements are 24 feet by 14 feet. The actual measurements are 24.2 feet by 14.1 feet. Determine the relative error in calculating the area of her bedroom. Express your answer as a decimal to the nearest thousandth. Score: 0 The student finds only one area correctly. Integrated Algebra Jan. 13 [43]

44 Practice Papers Question Wendy measures the floor in her rectangular bedroom for new carpeting. Her measurements are 24 feet by 14 feet. The actual measurements are 24.2 feet by 14.1 feet. Determine the relative error in calculating the area of her bedroom. Express your answer as a decimal to the nearest thousandth. Score: 0 The student obtains a correct answer by a completely incorrect method. Integrated Algebra Jan. 13 [44]

45 Practice Papers Question Using the line provided, construct a box-and-whisker plot for the 12 scores below. 26, 32, 19, 65, 57, 16, 28, 42, 40, 21, 38, 10 Determine the number of scores that lie above the 75th percentile. Score: 4 The student has a correct response. The five statistics are correct and the box-and-whisker plot is correct. The student lists the three scores above the 75th percentile. Integrated Algebra Jan. 13 [45]

46 Practice Papers Question Using the line provided, construct a box-and-whisker plot for the 12 scores below. Determine the number of scores that lie above the 75th percentile. Score: 3 The student s scale is incorrect. Integrated Algebra Jan. 13 [46]

47 Practice Papers Question Using the line provided, construct a box-and-whisker plot for the 12 scores below. 26, 32, 19, 65, 57, 16, 28, 42, 40, 21, 38, 10 Determine the number of scores that lie above the 75th percentile. Score: 3 The student constructs a correct box-and-whisker plot, but states an incorrect number of scores. Integrated Algebra Jan. 13 [47]

48 Practice Papers Question Using the line provided, construct a box-and-whisker plot for the 12 scores below. Determine the number of scores that lie above the 75th percentile. Score: 3 The student makes a computational error in finding the 3rd quartile, but the rest of the work is appropriate based upon the error. Integrated Algebra Jan. 13 [48]

49 Practice Papers Question Using the line provided, construct a box-and-whisker plot for the 12 scores below. 26, 32, 19, 65, 57, 16, 28, 42, 40, 21, 38, 10 Determine the number of scores that lie above the 75th percentile. Score: 2 The student makes two or more graphing errors (max and min are missing and the number line passes through the box), but an appropriate number is stated. Integrated Algebra Jan. 13 [49]

50 Practice Papers Question Using the line provided, construct a box-and-whisker plot for the 12 scores below. Determine the number of scores that lie above the 75th percentile. Score: 2 The student does not draw in the line to indicate the median and incorrectly graphs 65 on the number line. Integrated Algebra Jan. 13 [50]

51 Practice Papers Question Using the line provided, construct a box-and-whisker plot for the 12 scores below. 26, 32, 19, 65, 57, 16, 28, 42, 40, 21, 38, 10 Determine the number of scores that lie above the 75th percentile. Score: 1 The student finds the five statistical measures correctly, but no further correct work is shown. Integrated Algebra Jan. 13 [51]

52 Practice Papers Question Using the line provided, construct a box-and-whisker plot for the 12 scores below. Determine the number of scores that lie above the 75th percentile. Score: 1 The student finds the first and third quartile incorrectly and has an incorrect scale on the number line, but an appropriate number of scores is found. Integrated Algebra Jan. 13 [52]

53 Practice Papers Question Using the line provided, construct a box-and-whisker plot for the 12 scores below. Determine the number of scores that lie above the 75th percentile. Score: 1 The student identifies the five statistical measures correctly but makes a conceptual error in making the graph, and the number of scores is incorrect. Integrated Algebra Jan. 13 [53]

54 Practice Papers Question Using the line provided, construct a box-and-whisker plot for the 12 scores below. Determine the number of scores that lie above the 75th percentile. Score: 0 No correct work is shown. Integrated Algebra Jan. 13 [54]

55 Practice Papers Question A metal pipe is used to hold up a 9-foot fence, as shown in the diagram below. The pipe makes an angle of 48 with the ground. Determine, to the nearest foot, how far the bottom of the pipe is from the base of the fence. Determine, to the nearest foot, the length of the metal pipe. Score: 4 The student uses trigonometric function/formula to find the solution and the Pythagoras Theorem to find the other. Integrated Algebra Jan. 13 [55]

56 Practice Papers Question A metal pipe is used to hold up a 9-foot fence, as shown in the diagram below. The pipe makes an angle of 48 with the ground. Determine, to the nearest foot, how far the bottom of the pipe is from the base of the fence. Determine, to the nearest foot, the length of the metal pipe. Score: 3 The student writes a correct equation for the first part, but rounds the tangent to the nearest integer. The solutions are appropriate based on this error. Integrated Algebra Jan. 13 [56]

57 Practice Papers Question A metal pipe is used to hold up a 9-foot fence, as shown in the diagram below. The pipe makes an angle of 48 with the ground. Determine, to the nearest foot, how far the bottom of the pipe is from the base of the fence. Determine, to the nearest foot, the length of the metal pipe. Score: 3 The student makes a computational error in finding the third angle of the triangle. The solutions are appropriate based on this error. Integrated Algebra Jan. 13 [57]

58 Practice Papers Question A metal pipe is used to hold up a 9-foot fence, as shown in the diagram below. The pipe makes an angle of 48 with the ground. Determine, to the nearest foot, how far the bottom of the pipe is from the base of the fence. Determine, to the nearest foot, the length of the metal pipe. Score: 2 The student writes a correct formula in each part but makes errors in the solution of the equations in each part. Integrated Algebra Jan. 13 [58]

59 Practice Papers Question A metal pipe is used to hold up a 9-foot fence, as shown in the diagram below. The pipe makes an angle of 48 with the ground. Determine, to the nearest foot, how far the bottom of the pipe is from the base of the fence. Determine, to the nearest foot, the length of the metal pipe. Score: 2 The student s work in the first part is completely incorrect, but the student uses a correct method in the second part to find an appropriate solution. Integrated Algebra Jan. 13 [59]

60 Practice Papers Question A metal pipe is used to hold up a 9-foot fence, as shown in the diagram below. The pipe makes an angle of 48 with the ground. Determine, to the nearest foot, how far the bottom of the pipe is from the base of the fence. Determine, to the nearest foot, the length of the metal pipe. Score: 1 The student writes one correct trigonometric equation for the first part, but no further correct work is shown. Integrated Algebra Jan. 13 [60]

61 Practice Papers Question A metal pipe is used to hold up a 9-foot fence, as shown in the diagram below. The pipe makes an angle of 48 with the ground. Determine, to the nearest foot, how far the bottom of the pipe is from the base of the fence. Determine, to the nearest foot, the length of the metal pipe. Score: 1 The student has one correct equation. Integrated Algebra Jan. 13 [61]

62 Practice Papers Question A metal pipe is used to hold up a 9-foot fence, as shown in the diagram below. The pipe makes an angle of 48 with the ground. Determine, to the nearest foot, how far the bottom of the pipe is from the base of the fence. Determine, to the nearest foot, the length of the metal pipe. Score: 1 In the first part, the student indicates that tan 48 = 9 x. Integrated Algebra Jan. 13 [62]

63 Practice Papers Question A metal pipe is used to hold up a 9-foot fence, as shown in the diagram below. The pipe makes an angle of 48 with the ground. Determine, to the nearest foot, how far the bottom of the pipe is from the base of the fence. Determine, to the nearest foot, the length of the metal pipe. Score: 0 The students work is incorrect. In order to receive 1 point, the student would need both correct answers with no work. Integrated Algebra Jan. 13 [63]

64 Practice Papers Question On the set of axes below, graph the following system of equations. y 2x x 2 4 y x 4 Using the graph, determine and state the coordinates of all points in the solution set for the system of equations. Score: 4 The student has a complete and correct response. Integrated Algebra Jan. 13 [64]

65 Practice Papers Question On the set of axes below, graph the following system of equations. y 2x x 2 4 y x 4 Using the graph, determine and state the coordinates of all points in the solution set for the system of equations. Score: 4 The student has a complete and correct response. Integrated Algebra Jan. 13 [65]

66 Practice Papers Question On the set of axes below, graph the following system of equations. y 2x x 2 4 y x 4 Using the graph, determine and state the coordinates of all points in the solution set for the system of equations. Score: 3 The student graphs both equations correctly, but only states one solution. Integrated Algebra Jan. 13 [66]

67 Practice Papers Question On the set of axes below, graph the following system of equations. y 2x x 2 4 y x 4 Using the graph, determine and state the coordinates of all points in the solution set for the system of equations. Score: 2 The student makes an error graphing the parabola and only states one solution correctly. Integrated Algebra Jan. 13 [67]

68 Practice Papers Question On the set of axes below, graph the following system of equations. y 2x x 2 4 y x 4 Using the graph, determine and state the coordinates of all points in the solution set for the system of equations. Score: 2 The student makes a conceptual error when graphing the parabola, but appropriate solutions are found. Integrated Algebra Jan. 13 [68]

69 Practice Papers Question On the set of axes below, graph the following system of equations. y 2x x 2 4 y x 4 Using the graph, determine and state the coordinates of all points in the solution set for the system of equations. Score: 2 The student graphs both equations correctly, but the solutions are not stated. Integrated Algebra Jan. 13 [69]

70 Practice Papers Question On the set of axes below, graph the following system of equations. y 2x x 2 4 y x 4 Using the graph, determine and state the coordinates of all points in the solution set for the system of equations. Score: 1 The student graphs one equation correctly. Integrated Algebra Jan. 13 [70]

71 Practice Papers Question On the set of axes below, graph the following system of equations. y 2x x 2 4 y x 4 Using the graph, determine and state the coordinates of all points in the solution set for the system of equations. Score: 1 The student graphs the parabola correctly. Integrated Algebra Jan. 13 [71]

72 Practice Papers Question On the set of axes below, graph the following system of equations. y 2x x 2 4 y x 4 Using the graph, determine and state the coordinates of all points in the solution set for the system of equations. Score: 0 No correct work is shown. Integrated Algebra Jan. 13 [72]

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA. Tuesday, January 22, 2013 9:15 a.m. to 12:15 p.m.

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