ALGEBRA 2/ TRIGONOMETRY
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1 The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA 2/ TRIGONOMETRY Wednesday, June 18, :15 4:15 p.m. SAMPLE RESPONSE SET Table of Contents Question Question Question Question Question Question Question Question Question Question Question Question
2 Question In a certain school, the heights of the population of girls are normally distributed, with a mean of 63 inches and a standard deviation of 2 inches. If there are 450 girls in the school, determine how many of the girls are shorter than 60 inches. Round the answer to the nearest integer. Score 2: The student has a complete and correct response. Algebra 2/Trigonometry June 14 [2]
3 Question In a certain school, the heights of the population of girls are normally distributed, with a mean of 63 inches and a standard deviation of 2 inches. If there are 450 girls in the school, determine how many of the girls are shorter than 60 inches. Round the answer to the nearest integer. Score 2: The student has a complete and correct response. Algebra 2/Trigonometry June 14 [3]
4 Question In a certain school, the heights of the population of girls are normally distributed, with a mean of 63 inches and a standard deviation of 2 inches. If there are 450 girls in the school, determine how many of the girls are shorter than 60 inches. Round the answer to the nearest integer. Score 1: The student made one conceptual error by finding the percentage of girls shorter than 60 inches, but not how many girls. Algebra 2/Trigonometry June 14 [4]
5 Question In a certain school, the heights of the population of girls are normally distributed, with a mean of 63 inches and a standard deviation of 2 inches. If there are 450 girls in the school, determine how many of the girls are shorter than 60 inches. Round the answer to the nearest integer. Score 0: The student made one conceptual error and one computational error. Algebra 2/Trigonometry June 14 [5]
6 Question The table below shows the concentration of ozone in Earth s atmosphere at different altitudes. Write the exponential regression equation that models these data, rounding all values to the nearest thousandth. Concentration of Ozone Altitude (x) Ozone Units (y) Score 2: The student has a complete and correct response. Algebra 2/Trigonometry June 14 [6]
7 Question The table below shows the concentration of ozone in Earth s atmosphere at different altitudes. Write the exponential regression equation that models these data, rounding all values to the nearest thousandth. Concentration of Ozone Altitude (x) Ozone Units (y) Score 2: The student has a complete and correct response. Algebra 2/Trigonometry June 14 [7]
8 Question The table below shows the concentration of ozone in Earth s atmosphere at different altitudes. Write the exponential regression equation that models these data, rounding all values to the nearest thousandth. Concentration of Ozone Altitude (x) Ozone Units (y) Score 1: The student made one rounding error. Algebra 2/Trigonometry June 14 [8]
9 Question The table below shows the concentration of ozone in Earth s atmosphere at different altitudes. Write the exponential regression equation that models these data, rounding all values to the nearest thousandth. Concentration of Ozone Altitude (x) Ozone Units (y) Score 1: The student wrote an exponential regression expression. Algebra 2/Trigonometry June 14 [9]
10 Question The table below shows the concentration of ozone in Earth s atmosphere at different altitudes. Write the exponential regression equation that models these data, rounding all values to the nearest thousandth. Concentration of Ozone Altitude (x) Ozone Units (y) Score 0: The student made one rounding error and did not write an exponential regression equation. Algebra 2/Trigonometry June 14 [10]
11 Question Solve 2x 3 5 algebraically. Score 2: The student has a complete and correct response. Algebra 2/Trigonometry June 14 [11]
12 Question Solve 2x 3 5 algebraically. Score 2: The student has a complete and correct response. Algebra 2/Trigonometry June 14 [12]
13 Question Solve 2x 3 5 algebraically. Score 2: The student has a complete and correct response. Algebra 2/Trigonometry June 14 [13]
14 Question Solve 2x 3 5 algebraically. Score 1: The student did not express the answer as a disjunction. Algebra 2/Trigonometry June 14 [14]
15 Question Solve 2x 3 5 algebraically. Score 1: The student made one computational (copy) error. Algebra 2/Trigonometry June 14 [15]
16 Question Solve 2x 3 5 algebraically. Score 1: The student showed appropriate work to find x 1, only. Algebra 2/Trigonometry June 14 [16]
17 Question Solve 2x 3 5 algebraically. Score 0: The student made one conceptual error and one computational error. Algebra 2/Trigonometry June 14 [17]
18 Question Solve 2x 3 5 algebraically. Score 0: The student made multiple conceptual errors. Algebra 2/Trigonometry June 14 [18]
19 Question Convert 2.5 radians to degrees, and express the answer to the nearest minute. Score 2: The student has a complete and correct response. Algebra 2/Trigonometry June 14 [19]
20 Question Convert 2.5 radians to degrees, and express the answer to the nearest minute. Score 1: The student made one conceptual error by not expressing the answer to the nearest minute. Algebra 2/Trigonometry June 14 [20]
21 Question Convert 2.5 radians to degrees, and express the answer to the nearest minute. Score 0: The student made one conceptual error and one computational error. Algebra 2/Trigonometry June 14 [21]
22 Question Multiply x yi by its conjugate, and express the product in simplest form. Score 2: The student has a complete and correct response. Algebra 2/Trigonometry June 14 [22]
23 Question Multiply x yi by its conjugate, and express the product in simplest form. Score 1: The student made one conceptual error by not substituting for i 2. Algebra 2/Trigonometry June 14 [23]
24 Question Multiply x yi by its conjugate, and express the product in simplest form. Score 0: The student made one conceptual error in writing the conjugate and multiple computational errors. Algebra 2/Trigonometry June 14 [24]
25 Question Solve algebraically for x: log 5x Score 2: The student has a complete and correct response. Algebra 2/Trigonometry June 14 [25]
26 Question Solve algebraically for x: log 5x Score 2: The student has a complete and correct response. Algebra 2/Trigonometry June 14 [26]
27 Question Solve algebraically for x: log 5x Score 1: The equation (5x 1) 3 4 is written, but no further correct work is shown. Algebra 2/Trigonometry June 14 [27]
28 Question Solve algebraically for x: log 5x Score 1: The student made one conceptual error. Algebra 2/Trigonometry June 14 [28]
29 Question Solve algebraically for x: log 5x Score 0: The student made one conceptual error and one rounding error. Algebra 2/Trigonometry June 14 [29]
30 Question Solve sec x 2 0 algebraically for all values of x in 0 x 360. Score 2: The student has a complete and correct response. Algebra 2/Trigonometry June 14 [30]
31 Question Solve sec x 2 0 algebraically for all values of x in 0 x 360. Score 1: The student found one solution, but no further correct work is shown. Algebra 2/Trigonometry June 14 [31]
32 Question Solve sec x 2 0 algebraically for all values of x in 0 x 360. Score 0: The student did not find any solutions. Algebra 2/Trigonometry June 14 [32]
33 Question Solve sec x 2 0 algebraically for all values of x in 0 x 360. Score 0: The student made one conceptual error and then found only one solution. Algebra 2/Trigonometry June 14 [33]
34 Question The function f(x) is graphed on the set of axes below. On the same set of axes, graph f(x 1) 2. Score 2: The student has a complete and correct response. Algebra 2/Trigonometry June 14 [34]
35 Question The function f(x) is graphed on the set of axes below. On the same set of axes, graph f(x 1) 2. Score 1: The student made one conceptual error by applying the transformation to y x 2. Algebra 2/Trigonometry June 14 [35]
36 Question The function f(x) is graphed on the set of axes below. On the same set of axes, graph f(x 1) 2. Score 0: The student made multiple graphing errors. Algebra 2/Trigonometry June 14 [36]
37 Question Express in simplest terms: 1 3 x x 2 x Score 4: The student has a complete and correct response. Algebra 2/Trigonometry June 14 [37]
38 Question Express in simplest terms: 1 3 x x 2 x Score 3: The student made one factoring error. Algebra 2/Trigonometry June 14 [38]
39 Question Express in simplest terms: 1 3 x x 2 x Score 2: The student made one conceptual error. Algebra 2/Trigonometry June 14 [39]
40 Question Express in simplest terms: 1 3 x x 2 x Score 1: The student made one conceptual error and one simplification error. Algebra 2/Trigonometry June 14 [40]
41 Question Express in simplest terms: 1 3 x x 2 x Score 0: The student made two conceptual errors. Algebra 2/Trigonometry June 14 [41]
42 Question Solve x 3 5x 2 4x 20 algebraically. Score 4: The student has a complete and correct response. Algebra 2/Trigonometry June 14 [42]
43 Question Solve x 3 5x 2 4x 20 algebraically. Score 3: The student made one factoring error. Algebra 2/Trigonometry June 14 [43]
44 Question Solve x 3 5x 2 4x 20 algebraically. Score 2: The student wrote (x 2 4)(x 5) 0, but did not complete the solution. Algebra 2/Trigonometry June 14 [44]
45 Question Solve x 3 5x 2 4x 20 algebraically. Score 2: The student used a method other than algebraic to solve the equation. Algebra 2/Trigonometry June 14 [45]
46 Question Solve x 3 5x 2 4x 20 algebraically. Score 1: The student made one conceptual error by misidentifying the GCF as x and then rejected x 0 as part of the solution. Algebra 2/Trigonometry June 14 [46]
47 Question Solve x 3 5x 2 4x 20 algebraically. Score 0: The student made two conceptual errors. Algebra 2/Trigonometry June 14 [47]
48 Question Whenever Sara rents a movie, the probability that it is a horror movie is Of the next five movies she rents, determine the probability, to the nearest hundredth, that no more than two of these rentals are horror movies. Score 4: The student has a complete and correct response. Algebra 2/Trigonometry June 14 [48]
49 Question Whenever Sara rents a movie, the probability that it is a horror movie is Of the next five movies she rents, determine the probability, to the nearest hundredth, that no more than two of these rentals are horror movies. Score 4: The student has a complete and correct response. Algebra 2/Trigonometry June 14 [49]
50 Question Whenever Sara rents a movie, the probability that it is a horror movie is Of the next five movies she rents, determine the probability, to the nearest hundredth, that no more than two of these rentals are horror movies. Score 3: The student did not find the sum. Algebra 2/Trigonometry June 14 [50]
51 Question Whenever Sara rents a movie, the probability that it is a horror movie is Of the next five movies she rents, determine the probability, to the nearest hundredth, that no more than two of these rentals are horror movies. Score 2: The student made one conceptual error by not finding the probability of 5 C 0. Algebra 2/Trigonometry June 14 [51]
52 Question Whenever Sara rents a movie, the probability that it is a horror movie is Of the next five movies she rents, determine the probability, to the nearest hundredth, that no more than two of these rentals are horror movies. 0 5 Score 2: The student made two computational errors when evaluating C Algebra 2/Trigonometry June 14 [52]
53 Question Whenever Sara rents a movie, the probability that it is a horror movie is Of the next five movies she rents, determine the probability, to the nearest hundredth, that no more than two of these rentals are horror movies. Score 1: The student found the probability of exactly two movies. Algebra 2/Trigonometry June 14 [53]
54 Question Whenever Sara rents a movie, the probability that it is a horror movie is Of the next five movies she rents, determine the probability, to the nearest hundredth, that no more than two of these rentals are horror movies. Score 0: The student did not correctly evaluate the probability of exactly two movies. Algebra 2/Trigonometry June 14 [54]
55 Question Two forces of 40 pounds and 28 pounds act on an object. The angle between the two forces is 65. Find the magnitude of the resultant force, to the nearest pound. Using this answer, find the measure of the angle formed between the resultant and the smaller force, to the nearest degree. Score 6: The student has a complete and correct response. Algebra 2/Trigonometry June 14 [55]
56 Question Two forces of 40 pounds and 28 pounds act on an object. The angle between the two forces is 65. Find the magnitude of the resultant force, to the nearest pound. Using this answer, find the measure of the angle formed between the resultant and the smaller force, to the nearest degree. Score 6: The student has a complete and correct response. Algebra 2/Trigonometry June 14 [56]
57 Question Two forces of 40 pounds and 28 pounds act on an object. The angle between the two forces is 65. Find the magnitude of the resultant force, to the nearest pound. Using this answer, find the measure of the angle formed between the resultant and the smaller force, to the nearest degree. Score 5: The student made one computational error by dropping the 2 in the equation c (40) cos 115. Algebra 2/Trigonometry June 14 [57]
58 Question Two forces of 40 pounds and 28 pounds act on an object. The angle between the two forces is 65. Find the magnitude of the resultant force, to the nearest pound. Using this answer, find the measure of the angle formed between the resultant and the smaller force, to the nearest degree. Score 5: The student found the magnitude of the resultant incorrectly by using radians instead of degrees, but then correctly found the angle, in degrees, based on their magnitude. Algebra 2/Trigonometry June 14 [58]
59 Question Two forces of 40 pounds and 28 pounds act on an object. The angle between the two forces is 65. Find the magnitude of the resultant force, to the nearest pound. Using this answer, find the measure of the angle formed between the resultant and the smaller force, to the nearest degree. Score 4: The student made one conceptual error. Algebra 2/Trigonometry June 14 [59]
60 Question Two forces of 40 pounds and 28 pounds act on an object. The angle between the two forces is 65. Find the magnitude of the resultant force, to the nearest pound. Using this answer, find the measure of the angle formed between the resultant and the smaller force, to the nearest degree. Score 4: The student made one conceptual error in using the Law of Sines. Algebra 2/Trigonometry June 14 [60]
61 Question Two forces of 40 pounds and 28 pounds act on an object. The angle between the two forces is 65. Find the magnitude of the resultant force, to the nearest pound. Using this answer, find the measure of the angle formed between the resultant and the smaller force, to the nearest degree. Score 3: The student made one conceptual error and one rounding error. Algebra 2/Trigonometry June 14 [61]
62 Question Two forces of 40 pounds and 28 pounds act on an object. The angle between the two forces is 65. Find the magnitude of the resultant force, to the nearest pound. Using this answer, find the measure of the angle formed between the resultant and the smaller force, to the nearest degree. Score 2: The student made two conceptual errors. Algebra 2/Trigonometry June 14 [62]
63 Question Two forces of 40 pounds and 28 pounds act on an object. The angle between the two forces is 65. Find the magnitude of the resultant force, to the nearest pound. Using this answer, find the measure of the angle formed between the resultant and the smaller force, to the nearest degree. Score 2: The student made one conceptual error in finding the resultant, followed by one rounding error and one computational error in using the Law of Sines. Algebra 2/Trigonometry June 14 [63]
64 Question Two forces of 40 pounds and 28 pounds act on an object. The angle between the two forces is 65. Find the magnitude of the resultant force, to the nearest pound. Using this answer, find the measure of the angle formed between the resultant and the smaller force, to the nearest degree. Score 1: The student correctly drew and labeled the diagram, but no further correct work is shown. Algebra 2/Trigonometry June 14 [64]
65 Question Two forces of 40 pounds and 28 pounds act on an object. The angle between the two forces is 65. Find the magnitude of the resultant force, to the nearest pound. Using this answer, find the measure of the angle formed between the resultant and the smaller force, to the nearest degree. Score 0: The student did not label the diagram, made two conceptual errors and one rounding error, and did not state the angle. Algebra 2/Trigonometry June 14 [65]
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