The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA. Wednesday, June 12, :15 p.m. SAMPLE RESPONSE SET
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1 The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA Wednesday, June 12, :15 p.m. SAMPLE RESPONSE SET Table of Contents Question Question Question Question Question Question Question Question Question
2 Practice Papers Question Solve the inequality 5(x 7) 15 algebraically for x. Score: 2 The student has a complete and correct response. Integrated Algebra June 13 [2]
3 Practice Papers Question Solve the inequality 5(x 7) 15 algebraically for x. Score: 1 The student made one conceptual error by not reversing the inequality symbol. Integrated Algebra June 13 [3]
4 Practice Papers Question Solve the inequality 5(x 7) 15 algebraically for x. Score: 1 The student made a conceptual error by using an equal sign instead of an inequality symbol. Integrated Algebra June 13 [4]
5 Practice Papers Question Solve the inequality 5(x 7) 15 algebraically for x. Score: 0 The student made two conceptual errors, the first by combining unlike terms, and the second by not reversing the inequality symbol. Integrated Algebra June 13 [5]
6 Practice Papers Question Solve the inequality 5(x 7) 15 algebraically for x. Score: 0 The student made a computational error: 20 5 the inequality symbol. = 5, and a conceptual error by not reversing Integrated Algebra June 13 [6]
7 Practice Papers Question 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. Score: 2 The student has a complete and correct response showing a correct substitution into the volume formula. Integrated Algebra June 13 [7]
8 Practice Papers Question 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. Score: 2 The student has a complete and correct response showing a correct substitution into the volume formula. Integrated Algebra June 13 [8]
9 Practice Papers Question 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. Score: 1 The student made a conceptual error: (6.5) 2 = 13, but found an appropriate answer. Integrated Algebra June 13 [9]
10 Practice Papers Question 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. Score: 0 The student showed completely incorrect work. Integrated Algebra June 13 [10]
11 Practice Papers Question 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. Score: 2 The student found the number of miles traveled per day, then correctly found the number of days. Integrated Algebra June 13 [11]
12 Practice Papers Question 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. Score: 2 The student solved the proportion to find the number of hours and then converted the time correctly to days. Integrated Algebra June 13 [12]
13 Practice Papers Question 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. Score: 1 The student showed correct work to find hours and then made a conceptual error in multiplying by 24 instead of dividing. Integrated Algebra June 13 [13]
14 Practice Papers Question 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. Score: 1 The student made one rounding error: = , which should round off to 183. Integrated Algebra June 13 [14]
15 Practice Papers Question 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. Score: 0 The student showed completely incorrect work. Integrated Algebra June 13 [15]
16 Practice Papers Question 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. Score: 3 The student showed correct work to find 225, 45, and 30. Integrated Algebra June 13 [16]
17 Practice Papers Question 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. Score: 3 The student showed correct work to find 225, 45, and 30. Integrated Algebra June 13 [17]
18 Practice Papers Question 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. Score: 2 The student showed appropriate work for the 225 and 30, but showed no further correct work. Integrated Algebra June 13 [18]
19 Practice Papers Question 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. Score: 1 The student showed work for 225, but showed no work for 45 and 30. Integrated Algebra June 13 [19]
20 Practice Papers Question 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. Score: 1 The student counted the number of vegetables and the number of beverages incorrectly, but multiplied the number of outcomes after these errors. Integrated Algebra June 13 [20]
21 Practice Papers Question 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. Score: 0 The student showed completely incorrect work. Integrated Algebra June 13 [21]
22 Practice Papers Question 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. Score: 3 The student has a complete and correct response. (The degree symbol is not required.) Integrated Algebra June 13 [22]
23 Practice Papers Question 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. Score: 3 The student has a complete and correct response. Integrated Algebra June 13 [23]
24 Practice Papers Question 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. Score: 2 The student made one rounding error, but stated an appropriate solution. Integrated Algebra June 13 [24]
25 Practice Papers Question 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. Score: 1 The student found a correct angle from an incorrect diagram. Integrated Algebra June 13 [25]
26 Practice Papers Question 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. Score: 1 The student wrote a correct equation, but showed no further correct work. Integrated Algebra June 13 [26]
27 Practice Papers Question 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. Score: 0 The student made one conceptual error in the diagram and found an angle using radians. Integrated Algebra June 13 [27]
28 Practice Papers Question 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. Score: 0 The student showed completely irrelevant work. Integrated Algebra June 13 [28]
29 Practice Papers Question Express 25 2 _ _ 9 in simplest radical form. Score: 3 The student has a complete and correct response. Integrated Algebra June 13 [29]
30 Practice Papers Question Express 25 2 _ _ 9 in simplest radical form. Score: 2 The student made one simplification error, but found an appropriate answer. Integrated Algebra June 13 [30]
31 Practice Papers Question Express 25 2 _ _ 9 in simplest radical form. Score: 2 The student made a computational error: = 2 3, but found an appropriate answer. Integrated Algebra June 13 [31]
32 Practice Papers Question Express 25 2 _ _ 9 in simplest radical form. Score: 1 The student made a conceptual error by combining unlike terms. Integrated Algebra June 13 [32]
33 Practice Papers Question Express 25 2 _ _ 9 in simplest radical form. Score: 0 The student expressed the answer as a decimal. Integrated Algebra June 13 [33]
34 Practice Papers Question Express 25 2 _ _ 9 in simplest radical form. Score: 0 The student made a conceptual error: = 3 3, and then made another conceptual error: 2 9 = 2 3. Integrated Algebra June 13 [34]
35 Practice Papers Question Solve algebraically: 2 3x 4 x 7 x 1 [Only an algebraic solution can receive full credit.] Score: 4 The student has a complete and correct response. Integrated Algebra June 13 [35]
36 Practice Papers Question Solve algebraically: 2 3x 4 x 7 x 1 [Only an algebraic solution can receive full credit.] Score: 4 The student has a complete and correct response. Integrated Algebra June 13 [36]
37 Practice Papers Question Solve algebraically: 2 3x 4 x 7 x 1 [Only an algebraic solution can receive full credit.] Score: 3 The student made one computational error: x x Integrated Algebra June 13 [37]
38 Practice Papers Question Solve algebraically: 2 3x 4 x 7 x 1 [Only an algebraic solution can receive full credit.] Score: 2 The student made a conceptual error in multiplying: 14(x + 1) = 14x + 1. Integrated Algebra June 13 [38]
39 Practice Papers Question Solve algebraically: 2 3x 4 x 7 x 1 [Only an algebraic solution can receive full credit.] Score: 2 The student made two computational errors: 3 4=7and 2 3x + 7 3x = 10 appropriate solution., but wrote an 3x Integrated Algebra June 13 [39]
40 Practice Papers Question Solve algebraically: 2 3x 4 x 7 x 1 [Only an algebraic solution can receive full credit.] Score: 1 The student made a computational error: 3 4=7and a conceptual error: 9(x + 1) = 9x + 1, but found an appropriate solution. Integrated Algebra June 13 [40]
41 Practice Papers Question Solve algebraically: 2 3x 4 x 7 x 1 [Only an algebraic solution can receive full credit.] Score: 0 The student made two conceptual errors: 2 3x + 4 x = 6 and 6(x + 1) = 6x x Integrated Algebra June 13 [41]
42 Practice Papers Question Solve algebraically: 2 3x 4 x 7 x 1 [Only an algebraic solution can receive full credit.] Score: 0 The student showed completely incorrect work. Integrated Algebra June 13 [42]
43 Practice Papers Question 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. Score: 4 The student has a complete and correct response. Integrated Algebra June 13 [43]
44 Practice Papers Question 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. Score: 4 The student showed an appropriate tree diagram and found correct solutions. Integrated Algebra June 13 [44]
45 Practice Papers Question 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. Score: 3 The student made one computational error in the last part using 4 green marbles instead of 3, but found appropriate answers. Integrated Algebra June 13 [45]
46 Practice Papers Question 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. Score: 2 The student made a conceptual error in the last part by multiplying the probabilities instead of adding them. Integrated Algebra June 13 [46]
47 Practice Papers Question 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. Score: 2 The student showed correct work to find and 20, but showed no further correct work. 56 Integrated Algebra June 13 [47]
48 Practice Papers Question 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. Score: 1 The student made one conceptual error using replacement, and one computational error: = Integrated Algebra June 13 [48]
49 Practice Papers Question 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. Score: 1 The student showed appropriate work, but only the probability of both red is calculated. Integrated Algebra June 13 [49]
50 Practice Papers Question 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. Score: 0 The student did not calculate any probabilities. Integrated Algebra June 13 [50]
51 Practice Papers Question 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. Score: 0 The student made multiple conceptual and computational errors. Integrated Algebra June 13 [51]
52 Practice Papers Question 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. Score: 4 The student has a complete and correct response. Integrated Algebra June 13 [52]
53 Practice Papers Question 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. Score: 4 The student has a complete and correct response. Integrated Algebra June 13 [53]
54 Practice Papers Question 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. Score: 3 The student rounded to 3.14, but found appropriate areas. Integrated Algebra June 13 [54]
55 Practice Papers Question 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. Score: 3 The student found the area in terms of. Integrated Algebra June 13 [55]
56 Practice Papers Question 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. Score: 2 The student made a conceptual error in finding the area of the semicircle by multiplying by 2 on the first step, but found the appropriate area of the shaded region. Integrated Algebra June 13 [56]
57 Practice Papers Question 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. Score: 2 The student made a conceptual error in finding the area of the rectangle, but found the appropriate area of the shaded region. Integrated Algebra June 13 [57]
58 Practice Papers Question 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. Score: 1 The student made a conceptual error by not dividing the area of the circle by 2, and rounded to 3.14, but found an appropriate area for the shaded region. Integrated Algebra June 13 [58]
59 Practice Papers Question 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. Score: 1 The student found the area of the rectangle as 80, but showed no further correct work. Integrated Algebra June 13 [59]
60 Practice Papers Question 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. Score: 0 The student showed completely incorrect work. Integrated Algebra June 13 [60]
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