# ALGEBRA I (Common Core)

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1 The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA I (Common Core) Wednesday, August 13, :30 a.m. MODEL RESPONSE SET Table of Contents Question Question Question Question Question Question Question Question Question Question Question Question Question

2 Question In the equation x 2 10x 24 (x a)(x b), b is an integer. Find algebraically all possible values of b. Score 2: The student has a complete and correct response. Algebra I (Common Core) Aug. 14 [2]

3 Question In the equation x 2 10x 24 (x a)(x b), b is an integer. Find algebraically all possible values of b. Score 1: The student made one error by not stating all possible values of b. Algebra I (Common Core) Aug. 14 [3]

4 Question In the equation x 2 10x 24 (x a)(x b), b is an integer. Find algebraically all possible values of b. Score 1: The student used a method other than algebraic to find possible b values. Algebra I (Common Core) Aug. 14 [4]

5 Question In the equation x 2 10x 24 (x a)(x b), b is an integer. Find algebraically all possible values of b. Score 0: The student s response contains at least two different errors. Algebra I (Common Core) Aug. 14 [5]

6 Question Rhonda deposited \$3000 in an account in the Merrick National Bank, earning 4.2% interest, compounded annually. She made no deposits or withdrawals. Write an equation that can be used to find B, her account balance after t years. Score 2: The student has a complete and correct response. Algebra I (Common Core) Aug. 14 [6]

7 Question Rhonda deposited \$3000 in an account in the Merrick National Bank, earning 4.2% interest, compounded annually. She made no deposits or withdrawals. Write an equation that can be used to find B, her account balance after t years. Score 2: The student has a complete and correct response. Algebra I (Common Core) Aug. 14 [7]

8 Question Rhonda deposited \$3000 in an account in the Merrick National Bank, earning 4.2% interest, compounded annually. She made no deposits or withdrawals. Write an equation that can be used to find B, her account balance after t years. Score 1: The student made an error by not writing an equation. Algebra I (Common Core) Aug. 14 [8]

9 Question Rhonda deposited \$3000 in an account in the Merrick National Bank, earning 4.2% interest, compounded annually. She made no deposits or withdrawals. Write an equation that can be used to find B, her account balance after t years. Score 1: The student did not write an equation in terms of B and t. Algebra I (Common Core) Aug. 14 [9]

10 Question Rhonda deposited \$3000 in an account in the Merrick National Bank, earning 4.2% interest, compounded annually. She made no deposits or withdrawals. Write an equation that can be used to find B, her account balance after t years. Score 1: The student made an error by not including the 1 in the growth factor. Algebra I (Common Core) Aug. 14 [10]

11 Question Rhonda deposited \$3000 in an account in the Merrick National Bank, earning 4.2% interest, compounded annually. She made no deposits or withdrawals. Write an equation that can be used to find B, her account balance after t years. Score 0: The student made two errors by not including (1 r) and changing 4.2% to Algebra I (Common Core) Aug. 14 [11]

12 Question Guy and Jim work at a furniture store. Guy is paid \$185 per week plus 3% of his total sales in dollars, x, which can be represented by g(x) x. Jim is paid \$275 per week plus 2.5% of his total sales in dollars, x, which can be represented by f(x) x. Determine the value of x, in dollars, that will make their weekly pay the same. Score 2: The student has a complete and correct response. Algebra I (Common Core) Aug. 14 [12]

13 Question Guy and Jim work at a furniture store. Guy is paid \$185 per week plus 3% of his total sales in dollars, x, which can be represented by g(x) x. Jim is paid \$275 per week plus 2.5% of his total sales in dollars, x, which can be represented by f(x) x. Determine the value of x, in dollars, that will make their weekly pay the same. Score 2: The student has a complete and correct response. Algebra I (Common Core) Aug. 14 [13]

14 Question Guy and Jim work at a furniture store. Guy is paid \$185 per week plus 3% of his total sales in dollars, x, which can be represented by g(x) x. Jim is paid \$275 per week plus 2.5% of his total sales in dollars, x, which can be represented by f(x) x. Determine the value of x, in dollars, that will make their weekly pay the same. Score 1: The student made one error when dividing by Algebra I (Common Core) Aug. 14 [14]

15 Question Guy and Jim work at a furniture store. Guy is paid \$185 per week plus 3% of his total sales in dollars, x, which can be represented by g(x) x. Jim is paid \$275 per week plus 2.5% of his total sales in dollars, x, which can be represented by f(x) x. Determine the value of x, in dollars, that will make their weekly pay the same. Score 0: The student set the expressions equal, but showed no further correct work. Algebra I (Common Core) Aug. 14 [15]

16 Question Guy and Jim work at a furniture store. Guy is paid \$185 per week plus 3% of his total sales in dollars, x, which can be represented by g(x) x. Jim is paid \$275 per week plus 2.5% of his total sales in dollars, x, which can be represented by f(x) x. Determine the value of x, in dollars, that will make their weekly pay the same. Score 0: The student has a completely incorrect response. Algebra I (Common Core) Aug. 14 [16]

17 Question Express the product of 2x 2 7x 10 and x 5 in standard form. Score 2: The student has a complete and correct response. Algebra I (Common Core) Aug. 14 [17]

18 Question Express the product of 2x 2 7x 10 and x 5 in standard form. Score 2: The student has a complete and correct response. Algebra I (Common Core) Aug. 14 [18]

19 Question Express the product of 2x 2 7x 10 and x 5 in standard form. Score 1: The student made one error when multiplying 2x 2 and x. Algebra I (Common Core) Aug. 14 [19]

20 Question Express the product of 2x 2 7x 10 and x 5 in standard form. Score 1: The student did not express the product in standard form. Algebra I (Common Core) Aug. 14 [20]

21 Question Express the product of 2x 2 7x 10 and x 5 in standard form. Score 0: The student made multiple errors. Algebra I (Common Core) Aug. 14 [21]

22 Question Let f be the function represented by the graph below. y x Let g be a function such that g(x) 1 2 x2 4x 3. Determine which function has the larger maximum value. Justify your answer. Score 2: The student has a complete and correct response. Algebra I (Common Core) Aug. 14 [22]

23 Question Let f be the function represented by the graph below. y x Let g be a function such that g(x) 1 2 x2 4x 3. Determine which function has the larger maximum value. Justify your answer. Score 2: The student has a complete and correct response. Algebra I (Common Core) Aug. 14 [23]

24 Question Let f be the function represented by the graph below. y x Let g be a function such that g(x) 1 2 x2 4x 3. Determine which function has the larger maximum value. Justify your answer. Score 1: The student wrote an insufficient justification. Algebra I (Common Core) Aug. 14 [24]

25 Question Let f be the function represented by the graph below. y x Let g be a function such that g(x) 1 2 x2 4x 3. Determine which function has the larger maximum value. Justify your answer. Score 0: The student only found the maximum value of one function. Algebra I (Common Core) Aug. 14 [25]

26 Question Let f be the function represented by the graph below. y x Let g be a function such that g(x) 1 2 x2 4x 3. Determine which function has the larger maximum value. Justify your answer. Score 0: The student stated g(x), but gave no justification. Algebra I (Common Core) Aug. 14 [26]

27 Question Solve the inequality below to determine and state the smallest possible value for x in the solution set. Score 2: The student has a complete and correct response. Algebra I (Common Core) Aug. 14 [27]

28 Question Solve the inequality below to determine and state the smallest possible value for x in the solution set. 3(x 3) 5x 3 Score 2: The student has a complete and correct response. Algebra I (Common Core) Aug. 14 [28]

29 Question Solve the inequality below to determine and state the smallest possible value for x in the solution set. 3(x 3) 5x 3 Score 1: The student did not state 6 as the smallest possible value. Algebra I (Common Core) Aug. 14 [29]

30 Question Solve the inequality below to determine and state the smallest possible value for x in the solution set. 3(x 3) 5x 3 Score 1: The student made one computational error when distributing 3. Algebra I (Common Core) Aug. 14 [30]

31 Question Solve the inequality below to determine and state the smallest possible value for x in the solution set. 3(x 3) 5x 3 Score 0: The student made an error when solving the inequality and did not state that there is no smallest value of x possible. Algebra I (Common Core) Aug. 14 [31]

32 Question The table below represents the residuals for a line of best fit. x Residual Plot these residuals on the set of axes below. Residual Using the plot, assess the fit of the line for these residuals and justify your answer. Score 2: The student has a complete and correct response. Algebra I (Common Core) Aug. 14 [32]

33 Question The table below represents the residuals for a line of best fit. x Residual Plot these residuals on the set of axes below. Residual Using the plot, assess the fit of the line for these residuals and justify your answer. Score 1: The student drew a correct plot, but did not assess the fit of the line. Algebra I (Common Core) Aug. 14 [33]

34 Question The table below represents the residuals for a line of best fit. x Residual Plot these residuals on the set of axes below. Residual Using the plot, assess the fit of the line for these residuals and justify your answer. Score 1: The student drew a correct plot and correctly characterized the fit, but gave no justification. Algebra I (Common Core) Aug. 14 [34]

35 Question The table below represents the residuals for a line of best fit. x Residual Plot these residuals on the set of axes below. Residual Using the plot, assess the fit of the line for these residuals and justify your answer. Score 1: The student plotted the residuals correctly, but showed no further correct work. Algebra I (Common Core) Aug. 14 [35]

36 Question The table below represents the residuals for a line of best fit. x Residual Plot these residuals on the set of axes below. Residual Using the plot, assess the fit of the line for these residuals and justify your answer. Score 0: The student drew an incorrect plot and wrote an incorrect justification. Algebra I (Common Core) Aug. 14 [36]

37 Question A student was given the equation x 2 6x 13 0 to solve by completing the square. The first step that was written is shown below. x 2 6x 13 The next step in the student s process was x 2 6x c 13 c. State the value of c that creates a perfect square trinomial. Explain how the value of c is determined. Score 2: The student has a complete and correct response. Algebra I (Common Core) Aug. 14 [37]

38 Question A student was given the equation x 2 6x 13 0 to solve by completing the square. The first step that was written is shown below. x 2 6x 13 The next step in the student s process was x 2 6x c 13 c. State the value of c that creates a perfect square trinomial. Explain how the value of c is determined. Score 2: The student has a complete and correct response. Algebra I (Common Core) Aug. 14 [38]

39 Question A student was given the equation x 2 6x 13 0 to solve by completing the square. The first step that was written is shown below. x 2 6x 13 The next step in the student s process was x 2 6x c 13 c. State the value of c that creates a perfect square trinomial. Explain how the value of c is determined. Score 1: The student found c 9, but wrote an incorrect explanation. Algebra I (Common Core) Aug. 14 [39]

40 Question A student was given the equation x 2 6x 13 0 to solve by completing the square. The first step that was written is shown below. x 2 6x 13 The next step in the student s process was x 2 6x c 13 c. State the value of c that creates a perfect square trinomial. Explain how the value of c is determined. Score 0: The student wrote an irrelevant response. Algebra I (Common Core) Aug. 14 [40]

41 Question On the axes below, graph f(x) 3x. If g(x) f(x) 2, how is the graph of f(x) translated to form the graph of g(x)? If h(x) f(x 4), how is the graph of f(x) translated to form the graph of h(x)? Score 4: The student has a complete and correct response. Algebra I (Common Core) Aug. 14 [41]

42 Question On the axes below, graph f(x) 3x. y x If g(x) f(x) 2, how is the graph of f(x) translated to form the graph of g(x)? If h(x) f(x 4), how is the graph of f(x) translated to form the graph of h(x)? Score 4: The student has a complete and correct response. Algebra I (Common Core) Aug. 14 [42]

43 Question On the axes below, graph f(x) 3x. If g(x) f(x) 2, how is the graph of f(x) translated to form the graph of g(x)? If h(x) f(x 4), how is the graph of f(x) translated to form the graph of h(x)? Score 3: The student drew a correct graph, but only included a correct description for one relationship. Algebra I (Common Core) Aug. 14 [43]

44 Question On the axes below, graph f(x) 3x. If g(x) f(x) 2, how is the graph of f(x) translated to form the graph of g(x)? If h(x) f(x 4), how is the graph of f(x) translated to form the graph of h(x)? Score 2: The student did not show a complete graph for f(x) (the graph must have either arrows or extend to the edge of the grid) and did not include a correct relationship describing how h(x) is related to f(x). Algebra I (Common Core) Aug. 14 [44]

45 Question On the axes below, graph f(x) 3x. If g(x) f(x) 2, how is the graph of f(x) translated to form the graph of g(x)? If h(x) f(x 4), how is the graph of f(x) translated to form the graph of h(x)? Score 2: The student drew a correct graph, but did not state the direction of the translations. Algebra I (Common Core) Aug. 14 [45]

46 Question On the axes below, graph f(x) 3x. If g(x) f(x) 2, how is the graph of f(x) translated to form the graph of g(x)? If h(x) f(x 4), how is the graph of f(x) translated to form the graph of h(x)? Score 1: The student did not draw a complete graph for f(x) and did not describe how g(x) and h(x) are related to f(x). Algebra I (Common Core) Aug. 14 [46]

47 Question On the axes below, graph f(x) 3x. If g(x) f(x) 2, how is the graph of f(x) translated to form the graph of g(x)? If h(x) f(x 4), how is the graph of f(x) translated to form the graph of h(x)? Score 0: The student did not show sufficient work. Algebra I (Common Core) Aug. 14 [47]

48 Question The formula for the area of a trapezoid is A 1 2 h(b 1 b 2 ). Express b 1 in terms of A, h, and b 2. The area of a trapezoid is 60 square feet, its height is 6 ft, and one base is 12 ft. Find the number of feet in the other base. Score 4: The student has a complete and correct response. Algebra I (Common Core) Aug. 14 [48]

49 Question The formula for the area of a trapezoid is A 1 2 h(b 1 b 2 ). Express b 1 in terms of A, h, and b 2. The area of a trapezoid is 60 square feet, its height is 6 ft, and one base is 12 ft. Find the number of feet in the other base. Score 3: The student made one computational error when multiplying 0.5 and 6. Algebra I (Common Core) Aug. 14 [49]

50 Question The formula for the area of a trapezoid is A 1 2 h(b 1 b 2 ). Express b 1 in terms of A, h, and b 2. The area of a trapezoid is 60 square feet, its height is 6 ft, and one base is 12 ft. Find the number of feet in the other base. Score 2: The student divided improperly when solving for b 1 and distributed the 3 improperly. Algebra I (Common Core) Aug. 14 [50]

51 Question The formula for the area of a trapezoid is A 1 2 h(b 1 b 2 ). Express b 1 in terms of A, h, and b 2. The area of a trapezoid is 60 square feet, its height is 6 ft, and one base is 12 ft. Find the number of feet in the other base. Score 2: The student made an error by subtracting b 2 rather than first using the distributive property. Algebra I (Common Core) Aug. 14 [51]

52 Question The formula for the area of a trapezoid is A 1 2 h(b 1 b 2 ). Express b 1 in terms of A, h, and b 2. The area of a trapezoid is 60 square feet, its height is 6 ft, and one base is 12 ft. Find the number of feet in the other base. Score 1: The student showed appropriate work to find 8, but showed no further correct work. Algebra I (Common Core) Aug. 14 [52]

53 Question The formula for the area of a trapezoid is A 1 2 h(b 1 b 2 ). Express b 1 in terms of A, h, and b 2. The area of a trapezoid is 60 square feet, its height is 6 ft, and one base is 12 ft. Find the number of feet in the other base. Score 0: The student has a completely incorrect response. Algebra I (Common Core) Aug. 14 [53]

54 Question Let f(x) 2x 2 and g(x) 2x 4. On the set of axes below, draw the graphs of y f(x) and y g(x). Using this graph, determine and state all values of x for which f(x) g(x). Score 4: The student has a complete and correct response. Algebra I (Common Core) Aug. 14 [54]

55 Question Let f(x) 2x 2 and g(x) 2x 4. On the set of axes below, draw the graphs of y f(x) and y g(x). Using this graph, determine and state all values of x for which f(x) g(x). Score 4: The student has a complete and correct response. Algebra I (Common Core) Aug. 14 [55]

56 Question Let f(x) 2x 2 and g(x) 2x 4. On the set of axes below, draw the graphs of y f(x) and y g(x). Using this graph, determine and state all values of x for which f(x) g(x). Score 3: The student wrote the solution as coordinates. Algebra I (Common Core) Aug. 14 [56]

57 Question Let f(x) 2x 2 and g(x) 2x 4. On the set of axes below, draw the graphs of y f(x) and y g(x). Using this graph, determine and state all values of x for which f(x) g(x). Score 3: The student made one graphing error by using 4 as the y-intercept. An appropriate response was stated. Algebra I (Common Core) Aug. 14 [57]

58 Question Let f(x) 2x 2 and g(x) 2x 4. On the set of axes below, draw the graphs of y f(x) and y g(x). Using this graph, determine and state all values of x for which f(x) g(x). Score 3: The student made one graphing error by using the wrong slope. Appropriate values for x were stated. Algebra I (Common Core) Aug. 14 [58]

59 Question Let f(x) 2x 2 and g(x) 2x 4. On the set of axes below, draw the graphs of y f(x) and y g(x). Using this graph, determine and state all values of x for which f(x) g(x). Score 2: The student used a method other than graphic to determine the x-values. Algebra I (Common Core) Aug. 14 [59]

60 Question Let f(x) 2x 2 and g(x) 2x 4. On the set of axes below, draw the graphs of y f(x) and y g(x). Using this graph, determine and state all values of x for which f(x) g(x). Score 2: The student did not state the x-values. Algebra I (Common Core) Aug. 14 [60]

61 Question Let f(x) 2x 2 and g(x) 2x 4. On the set of axes below, draw the graphs of y f(x) and y g(x). Using this graph, determine and state all values of x for which f(x) g(x). Score 2: The student made a conceptual error by graphing f(x) 2x rather than f(x) 2x 2, but graphed g(x) correctly and found an appropriate x-value. Algebra I (Common Core) Aug. 14 [61]

62 Question Let f(x) 2x 2 and g(x) 2x 4. On the set of axes below, draw the graphs of y f(x) and y g(x). Using this graph, determine and state all values of x for which f(x) g(x). Score 1: The student graphed f(x) correctly, but showed no further correct work. Algebra I (Common Core) Aug. 14 [62]

63 Question Let f(x) 2x 2 and g(x) 2x 4. On the set of axes below, draw the graphs of y f(x) and y g(x). Using this graph, determine and state all values of x for which f(x) g(x). Score 0: The student s work is completely incorrect. Algebra I (Common Core) Aug. 14 [63]

64 Question A school is building a rectangular soccer field that has an area of 6000 square yards. The soccer field must be 40 yards longer than its width. Determine algebraically the dimensions of the soccer field, in yards. Score 4: The student has a complete and correct response. Algebra I (Common Core) Aug. 14 [64]

65 Question A school is building a rectangular soccer field that has an area of 6000 square yards. The soccer field must be 40 yards longer than its width. Determine algebraically the dimensions of the soccer field, in yards. Score 3: The student made an error by not rejecting the negative solution. Algebra I (Common Core) Aug. 14 [65]

66 Question A school is building a rectangular soccer field that has an area of 6000 square yards. The soccer field must be 40 yards longer than its width. Determine algebraically the dimensions of the soccer field, in yards. Score 2: The student did appropriate work to find 60, but did not find the length and did not reject the negative root. Algebra I (Common Core) Aug. 14 [66]

67 Question A school is building a rectangular soccer field that has an area of 6000 square yards. The soccer field must be 40 yards longer than its width. Determine algebraically the dimensions of the soccer field, in yards. Score 2: The student made one conceptual error by using the perimeter rather than area formula. Algebra I (Common Core) Aug. 14 [67]

68 Question A school is building a rectangular soccer field that has an area of 6000 square yards. The soccer field must be 40 yards longer than its width. Determine algebraically the dimensions of the soccer field, in yards. Score 1: The student factored the trinomial correctly, but did not set the factors equal to zero. The student showed no further correct work. Algebra I (Common Core) Aug. 14 [68]

69 Question A school is building a rectangular soccer field that has an area of 6000 square yards. The soccer field must be 40 yards longer than its width. Determine algebraically the dimensions of the soccer field, in yards. Score 1: The student made an error in expressing the length, and then made a rounding error. Algebra I (Common Core) Aug. 14 [69]

70 Question A school is building a rectangular soccer field that has an area of 6000 square yards. The soccer field must be 40 yards longer than its width. Determine algebraically the dimensions of the soccer field, in yards. Score 0: The student wrote the equation 6000 w(40 w), but showed no further correct work. Algebra I (Common Core) Aug. 14 [70]

71 Question Edith babysits for x hours a week after school at a job that pays \$4 an hour. She has accepted a job that pays \$8 an hour as a library assistant working y hours a week. She will work both jobs. She is able to work no more than 15 hours a week, due to school commitments. Edith wants to earn at least \$80 a week, working a combination of both jobs. Write a system of inequalities that can be used to represent the situation. Graph these inequalities on the set of axes below. Determine and state one combination of hours that will allow Edith to earn at least \$80 per week while working no more than 15 hours. Score 6: The student had a complete and correct response. Algebra I (Common Core) Aug. 14 [71]

72 Question Edith babysits for x hours a week after school at a job that pays \$4 an hour. She has accepted a job that pays \$8 an hour as a library assistant working y hours a week. She will work both jobs. She is able to work no more than 15 hours a week, due to school commitments. Edith wants to earn at least \$80 a week, working a combination of both jobs. Write a system of inequalities that can be used to represent the situation. Graph these inequalities on the set of axes below. Determine and state one combination of hours that will allow Edith to earn at least \$80 per week while working no more than 15 hours. Score 5: The student did not indicate which choice of hours corresponds with which job. Algebra I (Common Core) Aug. 14 [72]

73 Question Edith babysits for x hours a week after school at a job that pays \$4 an hour. She has accepted a job that pays \$8 an hour as a library assistant working y hours a week. She will work both jobs. She is able to work no more than 15 hours a week, due to school commitments. Edith wants to earn at least \$80 a week, working a combination of both jobs. Write a system of inequalities that can be used to represent the situation. Graph these inequalities on the set of axes below. Determine and state one combination of hours that will allow Edith to earn at least \$80 per week while working no more than 15 hours. Score 5: The student made one graphing error by shading both lines in the wrong direction. Algebra I (Common Core) Aug. 14 [73]

74 Question Edith babysits for x hours a week after school at a job that pays \$4 an hour. She has accepted a job that pays \$8 an hour as a library assistant working y hours a week. She will work both jobs. She is able to work no more than 15 hours a week, due to school commitments. Edith wants to earn at least \$80 a week, working a combination of both jobs. Write a system of inequalities that can be used to represent the situation. Graph these inequalities on the set of axes below. Determine and state one combination of hours that will allow Edith to earn at least \$80 per week while working no more than 15 hours. Score 5: The student stated an incorrect combination of hours. Algebra I (Common Core) Aug. 14 [74]

75 Question Edith babysits for x hours a week after school at a job that pays \$4 an hour. She has accepted a job that pays \$8 an hour as a library assistant working y hours a week. She will work both jobs. She is able to work no more than 15 hours a week, due to school commitments. Edith wants to earn at least \$80 a week, working a combination of both jobs. Write a system of inequalities that can be used to represent the situation. Graph these inequalities on the set of axes below. Determine and state one combination of hours that will allow Edith to earn at least \$80 per week while working no more than 15 hours. Score 4: The student stated both inequalities and a correct combination of hours, but did not graph both inequalities. Algebra I (Common Core) Aug. 14 [75]

76 Question Edith babysits for x hours a week after school at a job that pays \$4 an hour. She has accepted a job that pays \$8 an hour as a library assistant working y hours a week. She will work both jobs. She is able to work no more than 15 hours a week, due to school commitments. Edith wants to earn at least \$80 a week, working a combination of both jobs. Write a system of inequalities that can be used to represent the situation. Graph these inequalities on the set of axes below. Determine and state one combination of hours that will allow Edith to earn at least \$80 per week while working no more than 15 hours. Score 4: The student made one conceptual error in expressing inequalities as equations. Algebra I (Common Core) Aug. 14 [76]

77 Question Edith babysits for x hours a week after school at a job that pays \$4 an hour. She has accepted a job that pays \$8 an hour as a library assistant working y hours a week. She will work both jobs. She is able to work no more than 15 hours a week, due to school commitments. Edith wants to earn at least \$80 a week, working a combination of both jobs. Write a system of inequalities that can be used to represent the situation. Graph these inequalities on the set of axes below. Determine and state one combination of hours that will allow Edith to earn at least \$80 per week while working no more than 15 hours. Score 3: The student made a conceptual error by writing both inequalities with an incorrect symbol. The student made a graphing error based on the system written. The student stated a correct combination of hours. Algebra I (Common Core) Aug. 14 [77]

78 Question Edith babysits for x hours a week after school at a job that pays \$4 an hour. She has accepted a job that pays \$8 an hour as a library assistant working y hours a week. She will work both jobs. She is able to work no more than 15 hours a week, due to school commitments. Edith wants to earn at least \$80 a week, working a combination of both jobs. Write a system of inequalities that can be used to represent the situation. Graph these inequalities on the set of axes below. Determine and state one combination of hours that will allow Edith to earn at least \$80 per week while working no more than 15 hours. Score 3: The student stated both inequalities correctly but only graphed, shaded, and labeled one correctly. A combination of hours was not stated. Algebra I (Common Core) Aug. 14 [78]

79 Question Edith babysits for x hours a week after school at a job that pays \$4 an hour. She has accepted a job that pays \$8 an hour as a library assistant working y hours a week. She will work both jobs. She is able to work no more than 15 hours a week, due to school commitments. Edith wants to earn at least \$80 a week, working a combination of both jobs. Write a system of inequalities that can be used to represent the situation. Graph these inequalities on the set of axes below. Determine and state one combination of hours that will allow Edith to earn at least \$80 per week while working no more than 15 hours. Score 3: The student wrote only one inequality correctly, graphed it correctly, and stated and labeled an appropriate combination of hours based on the graph. Algebra I (Common Core) Aug. 14 [79]

80 Question Edith babysits for x hours a week after school at a job that pays \$4 an hour. She has accepted a job that pays \$8 an hour as a library assistant working y hours a week. She will work both jobs. She is able to work no more than 15 hours a week, due to school commitments. Edith wants to earn at least \$80 a week, working a combination of both jobs. Write a system of inequalities that can be used to represent the situation. Graph these inequalities on the set of axes below. Determine and state one combination of hours that will allow Edith to earn at least \$80 per week while working no more than 15 hours. Score 2: The student wrote one inequality correctly and stated a correct combination of hours. Algebra I (Common Core) Aug. 14 [80]

81 Question Edith babysits for x hours a week after school at a job that pays \$4 an hour. She has accepted a job that pays \$8 an hour as a library assistant working y hours a week. She will work both jobs. She is able to work no more than 15 hours a week, due to school commitments. Edith wants to earn at least \$80 a week, working a combination of both jobs. Write a system of inequalities that can be used to represent the situation. Graph these inequalities on the set of axes below. Determine and state one combination of hours that will allow Edith to earn at least \$80 per week while working no more than 15 hours. Score 1: The student stated two correct equations, but showed no further correct work. Algebra I (Common Core) Aug. 14 [81]

82 Question Edith babysits for x hours a week after school at a job that pays \$4 an hour. She has accepted a job that pays \$8 an hour as a library assistant working y hours a week. She will work both jobs. She is able to work no more than 15 hours a week, due to school commitments. Edith wants to earn at least \$80 a week, working a combination of both jobs. Write a system of inequalities that can be used to represent the situation. Graph these inequalities on the set of axes below. Determine and state one combination of hours that will allow Edith to earn at least \$80 per week while working no more than 15 hours. Score 0: The student has a completely incorrect response. Algebra I (Common Core) Aug. 14 [82]

### ALGEBRA I (Common Core)

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA I (Common Core) Wednesday, June 17, 2015 1:15 to 4:15 p.m. MODEL RESPONSE SET Table of Contents Question 25..................

### ALGEBRA I (Common Core)

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