# ALGEBRA 2/ TRIGONOMETRY

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1 The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA 2/ TRIGONOMETRY Tuesday, January 28, :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 Show that sec θ sin θ cot θ 1 is an identity. Score 2: The student has a complete and correct response. Algebra 2/Trigonometry Jan. 14 [2]

3 Question Show that sec θ sin θ cot θ 1 is an identity. Score 1: The student made a substitution error by replacing 1 tan θ with sin θ cos θ. Algebra 2/Trigonometry Jan. 14 [3]

4 Question Show that sec θ sin θ cot θ 1 is an identity. Score 0: The student made multiple errors when substituting for sec θ and sin θ. Algebra 2/Trigonometry Jan. 14 [4]

5 Question Find, to the nearest tenth of a square foot, the area of a rhombus that has a side of 6 feet and an angle of 50. Score 2: The student has a complete and correct response. Algebra 2/Trigonometry Jan. 14 [5]

6 Question Find, to the nearest tenth of a square foot, the area of a rhombus that has a side of 6 feet and an angle of 50. Score 1: The student stated the wrong units. Algebra 2/Trigonometry Jan. 14 [6]

7 Question Find, to the nearest tenth of a square foot, the area of a rhombus that has a side of 6 feet and an angle of 50. Score 1: The student made a conceptual error by not doubling the area of the triangle. Algebra 2/Trigonometry Jan. 14 [7]

8 Question Find, to the nearest tenth of a square foot, the area of a rhombus that has a side of 6 feet and an angle of 50. Score 0: The student made multiple conceptual errors, including the use of the Pythagorean Theorem and the incorrect use of the Law of Sines. Algebra 2/Trigonometry Jan. 14 [8]

9 Question The following is a list of the individual points scored by all twelve members of the Webster High School basketball team at a recent game: Find the interquartile range for this set of data. Score 2: The student has a complete and correct response. Algebra 2/Trigonometry Jan. 14 [9]

10 Question The following is a list of the individual points scored by all twelve members of the Webster High School basketball team at a recent game: Find the interquartile range for this set of data. Score 1: The student made a conceptual error by expressing the interquartile range as an interval. Algebra 2/Trigonometry Jan. 14 [10]

11 Question The following is a list of the individual points scored by all twelve members of the Webster High School basketball team at a recent game: Find the interquartile range for this set of data. Score 0: The student made two conceptual errors. The quartiles were found incorrectly and the interquartile range was expressed as a set. Algebra 2/Trigonometry Jan. 14 [11]

12 Question Determine algebraically the x-coordinate of all points where the graphs of xy 10 and y x 3 intersect. Score 2: The student has a complete and correct response. Algebra 2/Trigonometry Jan. 14 [12]

13 Question Determine algebraically the x-coordinate of all points where the graphs of xy 10 and y x 3 intersect. Score 2: The student has a complete and correct response, with correct work beyond the solutions. Algebra 2/Trigonometry Jan. 14 [13]

14 Question Determine algebraically the x-coordinate of all points where the graphs of xy 10 and y x 3 intersect. Score 1: The student correctly solved the system of equations graphically. Algebra 2/Trigonometry Jan. 14 [14]

15 Question Determine algebraically the x-coordinate of all points where the graphs of xy 10 and y x 3 intersect. Score 0: The student correctly solved for y 10 x, but no further correct work is shown. The x-coordinate that the student wrote is incorrect. Algebra 2/Trigonometry Jan. 14 [15]

16 Question Solve 4x 5 13 algebraically for x. Score 2: The student has a complete and correct response. Algebra 2/Trigonometry Jan. 14 [16]

17 Question Solve 4x 5 13 algebraically for x. Score 2: The student has a complete and correct response. Algebra 2/Trigonometry Jan. 14 [17]

18 Question Solve 4x 5 13 algebraically for x. Score 1: The student correctly solved the absolute value inequality as an absolute value equation. This is considered a conceptual error. Algebra 2/Trigonometry Jan. 14 [18]

19 Question Solve 4x 5 13 algebraically for x. Score 1: The answer is not expressed as a conjunction. Algebra 2/Trigonometry Jan. 14 [19]

20 Question Solve 4x 5 13 algebraically for x. Score 0: The student made more than one conceptual error. Algebra 2/Trigonometry Jan. 14 [20]

21 Question Express 4xi 5yi 8 6xi 3 2yi 4 in simplest a bi form. Score 2: The student has a complete and correct response. Algebra 2/Trigonometry Jan. 14 [21]

22 Question Express 4xi 5yi 8 6xi 3 2yi 4 in simplest a bi form. Score 1: The student did not express the answer in simplest form. The 1 should have been simplified to i. Algebra 2/Trigonometry Jan. 14 [22]

23 Question Express 4xi 5yi 8 6xi 3 2yi 4 in simplest a bi form. Score 1: The student did not write the solution in a bi form. Algebra 2/Trigonometry Jan. 14 [23]

24 Question Express 4xi 5yi 8 6xi 3 2yi 4 in simplest a bi form. Score 0: The student made one conceptual error in replacing i and did not put the answer in a bi form. Algebra 2/Trigonometry Jan. 14 [24]

25 Question In an arithmetic sequence, a 4 19 and a Determine a formula for a n, the n th term of this sequence. Score 2: The student has a complete and correct response. Algebra 2/Trigonometry Jan. 14 [25]

26 Question In an arithmetic sequence, a 4 19 and a Determine a formula for a n, the n th term of this sequence. Score 1: The student found the first term, 7, and the common difference of 4. No further correct work is shown. Algebra 2/Trigonometry Jan. 14 [26]

27 Question In an arithmetic sequence, a 4 19 and a Determine a formula for a n, the n th term of this sequence. Score 0: The student response is completely incoherent. Algebra 2/Trigonometry Jan. 14 [27]

28 Question Circle O shown below has a radius of 12 centimeters. To the nearest tenth of a centimeter, determine the length of the arc, x, subtended by an angle of x 12 cm O Score 2: The student has a complete and correct response. Algebra 2/Trigonometry Jan. 14 [28]

29 Question Circle O shown below has a radius of 12 centimeters. To the nearest tenth of a centimeter, determine the length of the arc, x, subtended by an angle of x 12 cm O Score 1: The student made a conceptual error by using the area of a circle rather than the circumference. Algebra 2/Trigonometry Jan. 14 [29]

30 Question Circle O shown below has a radius of 12 centimeters. To the nearest tenth of a centimeter, determine the length of the arc, x, subtended by an angle of x 12 cm O Score 0: The student response is completely incoherent. Algebra 2/Trigonometry Jan. 14 [30]

31 Question Solve algebraically for all exact values of x in the interval 0 x 2π: 2 sin 2 x 5 sin x 3 Score 4: The student has a complete and correct response. Algebra 2/Trigonometry Jan. 14 [31]

32 Question Solve algebraically for all exact values of x in the interval 0 x 2π: 2 sin 2 x 5 sin x 3 Score 4: The student has a complete and correct response. Algebra 2/Trigonometry Jan. 14 [32]

33 Question Solve algebraically for all exact values of x in the interval 0 x 2π: 2 sin 2 x 5 sin x 3 Score 3: The student made a factoring error. Algebra 2/Trigonometry Jan. 14 [33]

34 Question Solve algebraically for all exact values of x in the interval 0 x 2π: 2 sin 2 x 5 sin x 3 Score 2: The student correctly found sin x 0.5 and sin x 3. Algebra 2/Trigonometry Jan. 14 [34]

35 Question Solve algebraically for all exact values of x in the interval 0 x 2π: 2 sin 2 x 5 sin x 3 Score 1: A correct substitution into the quadratic formula is made, but no further correct work is shown. Algebra 2/Trigonometry Jan. 14 [35]

36 Question Solve algebraically for all exact values of x in the interval 0 x 2π: 2 sin 2 x 5 sin x 3 Score 0: The student made more than one conceptual error. Algebra 2/Trigonometry Jan. 14 [36]

37 Question Because Sam s backyard gets very little sunlight, the probability that a geranium planted there will flower is Sam planted five geraniums. Determine the probability, to the nearest thousandth, that at least four geraniums will flower. Score 4: The student has a complete and correct response. Algebra 2/Trigonometry Jan. 14 [37]

38 Question Because Sam s backyard gets very little sunlight, the probability that a geranium planted there will flower is Sam planted five geraniums. Determine the probability, to the nearest thousandth, that at least four geraniums will flower. Score 4: The student has a complete and correct response. Algebra 2/Trigonometry Jan. 14 [38]

39 Question Because Sam s backyard gets very little sunlight, the probability that a geranium planted there will flower is Sam planted five geraniums. Determine the probability, to the nearest thousandth, that at least four geraniums will flower. Score 4: The student has a complete and correct response. The answer of 2.4% is mathematically equivalent to Algebra 2/Trigonometry Jan. 14 [39]

40 Question Because Sam s backyard gets very little sunlight, the probability that a geranium planted there will flower is Sam planted five geraniums. Determine the probability, to the nearest thousandth, that at least four geraniums will flower. Score 3: The student made one rounding error. Algebra 2/Trigonometry Jan. 14 [40]

41 Question Because Sam s backyard gets very little sunlight, the probability that a geranium planted there will flower is Sam planted five geraniums. Determine the probability, to the nearest thousandth, that at least four geraniums will flower. Score 2: The student made one rounding error and expressed the answer as a percent. Algebra 2/Trigonometry Jan. 14 [41]

42 Question Because Sam s backyard gets very little sunlight, the probability that a geranium planted there will flower is Sam planted five geraniums. Determine the probability, to the nearest thousandth, that at least four geraniums will flower. Score 1: The student found a correct probability for exactly four out of five, and did not round to the nearest thousandth. Algebra 2/Trigonometry Jan. 14 [42]

43 Question Because Sam s backyard gets very little sunlight, the probability that a geranium planted there will flower is Sam planted five geraniums. Determine the probability, to the nearest thousandth, that at least four geraniums will flower. Score 0: The student made two conceptual errors. Incorrect exponents were written, and then the student subtracted this answer from 1. Algebra 2/Trigonometry Jan. 14 [43]

44 Question Two sides of a parallelogram measure 27 cm and 32 cm. The included angle measures 48. Find the length of the longer diagonal of the parallelogram, to the nearest centimeter. Score 4: The student has a complete and correct response. Algebra 2/Trigonometry Jan. 14 [44]

45 Question Two sides of a parallelogram measure 27 cm and 32 cm. The included angle measures 48. Find the length of the longer diagonal of the parallelogram, to the nearest centimeter. Score 3: The student made one computational error by using radian mode. Algebra 2/Trigonometry Jan. 14 [45]

46 Question Two sides of a parallelogram measure 27 cm and 32 cm. The included angle measures 48. Find the length of the longer diagonal of the parallelogram, to the nearest centimeter. Score 2: The student made a correct substitution into the Law of Cosines. Algebra 2/Trigonometry Jan. 14 [46]

47 Question Two sides of a parallelogram measure 27 cm and 32 cm. The included angle measures 48. Find the length of the longer diagonal of the parallelogram, to the nearest centimeter. Score 1: The student drew a correctly labeled diagram. The remainder of the work shown is incorrect. Algebra 2/Trigonometry Jan. 14 [47]

48 Question Two sides of a parallelogram measure 27 cm and 32 cm. The included angle measures 48. Find the length of the longer diagonal of the parallelogram, to the nearest centimeter. Score 0: The student made two conceptual errors by finding the shorter diagonal and combining terms incorrectly. There was also one rounding error. Algebra 2/Trigonometry Jan. 14 [48]

49 Question Solve algebraically for all values of x: log (x 3) (2x 3) log (x 3) (x 5) 2 Score 6: The student has a complete and correct response. Algebra 2/Trigonometry Jan. 14 [49]

50 Question Solve algebraically for all values of x: log (x 3) (2x 3) log (x 3) (x 5) 2 Score 5: The student did not reject 6. Algebra 2/Trigonometry Jan. 14 [50]

51 Question Solve algebraically for all values of x: log (x 3) (2x 3) log (x 3) (x 5) 2 Score 4: The student made one computational error when squaring x 3. The student also made an error in not discarding the imaginary solutions. Algebra 2/Trigonometry Jan. 14 [51]

52 Question Solve algebraically for all values of x: log (x 3) (2x 3) log (x 3) (x 5) 2 Score 3: The student made a conceptual error by canceling the logs. Algebra 2/Trigonometry Jan. 14 [52]

53 Question Solve algebraically for all values of x: log (x 3) (2x 3) log (x 3) (x 5) 2 Score 2: The student made a conceptual error by adding the binomials. The student did not discard the solution outside the domain. Algebra 2/Trigonometry Jan. 14 [53]

54 Question Solve algebraically for all values of x: log (x 3) (2x 3) log (x 3) (x 5) 2 Score 1: The student correctly wrote log (x 3) (2x 3)(x 5) 2. The remainder of the work was incorrect. Algebra 2/Trigonometry Jan. 14 [54]

55 Question Solve algebraically for all values of x: log (x 3) (2x 3) log (x 3) (x 5) 2 Score 0: The student made multiple errors in attempting to solve the log equation. Algebra 2/Trigonometry Jan. 14 [55]

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