# The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, January 29, :15 a.m. SAMPLE RESPONSE SET

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1 The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, January 29, :15 a.m. SAMPLE RESPONSE SET Table of Contents Question Question Question Question Question Question Question Question Question Question

2 Question The diameter of a sphere is 5 inches. Determine and state the surface area of the sphere, to the nearest hundredth of a square inch. Score 2: The student has a complete and correct response. Note: Labeling in 2 was not required. Geometry Jan. 14 [2]

3 Question The diameter of a sphere is 5 inches. Determine and state the surface area of the sphere, to the nearest hundredth of a square inch. Score 1: The student made a rounding error. Geometry Jan. 14 [3]

4 Question The diameter of a sphere is 5 inches. Determine and state the surface area of the sphere, to the nearest hundredth of a square inch. Score 0: The student made a conceptual error by using 5 as the radius and a rounding error. Geometry Jan. 14 [4]

5 Question Using a compass and straightedge, construct the perpendicular bisector of AB [Leave all construction marks.] Score 2: The student has a correct construction. Note: The right angle symbols were not required. Geometry Jan. 14 [5]

6 Question Using a compass and straightedge, construct the perpendicular bisector of AB [Leave all construction marks.] Score 1: The student has correct construction arcs, but did not draw the perpendicular bisector. Geometry Jan. 14 [6]

7 Question Using a compass and straightedge, construct the perpendicular bisector of AB [Leave all construction marks.] Score 0: The student did not construct two pairs of intersecting arcs. Geometry Jan. 14 [7]

8 Question The endpoints of AB are A(3, 4) and B(7,2). Determine and state the length of AB in simplest radical form. Score 2: The student has a complete and correct response. The student graphed AB, drew a right triangle, and applied the Pythagorean Theorem. Geometry Jan. 14 [8]

9 Question The endpoints of AB are A(3, 4) and B(7,2). Determine and state the length of AB in simplest radical form. Score 1: The student showed correct work to find 52, but no further correct work is shown. Geometry Jan. 14 [9]

10 Question The endpoints of AB are A(3, 4) and B(7,2). Determine and state the length of AB in simplest radical form. Score 1: The student made a conceptual error in using the formula for length of a segment. The student s answer was simplified correctly. Geometry Jan. 14 [10]

11 Question The endpoints of AB are A(3, 4) and B(7,2). Determine and state the length of AB in simplest radical form. Score 0: The student made an error in substituting into the distance formula and did not simplify the answer. Geometry Jan. 14 [11]

12 Question A right prism has a square base with an area of 12 square meters. The volume of the prism is 84 cubic meters. Determine and state the height of the prism, in meters. Score 2: The student has a complete and correct response. Note: Labeling meters was not required. Geometry Jan. 14 [12]

13 Question A right prism has a square base with an area of 12 square meters. The volume of the prism is 84 cubic meters. Determine and state the height of the prism, in meters. Score 1: The student showed correct work, but labeled the answer with incorrect units. Geometry Jan. 14 [13]

14 Question A right prism has a square base with an area of 12 square meters. The volume of the prism is 84 cubic meters. Determine and state the height of the prism, in meters. Score 0: The student work is completely incorrect. Geometry Jan. 14 [14]

15 Question State whether the lines represented by the equations y 1 2 x 1 and y (x 2) are parallel, perpendicular, or neither. Explain your answer. Score 2: The student has a complete and correct response, including a correct justification. Geometry Jan. 14 [15]

16 Question State whether the lines represented by the equations y 1 2 x 1 and y (x 2) are parallel, perpendicular, or neither. Explain your answer. Score 1: The student made a conceptual error in solving the second equation for y. An appropriate determination and justification were written. Geometry Jan. 14 [16]

17 Question State whether the lines represented by the equations y 1 2 x 1 and y (x 2) are parallel, perpendicular, or neither. Explain your answer. Score 0: The student wrote neither, but the work and justification are completely incorrect. Geometry Jan. 14 [17]

18 Question A tree, T, is 6 meters from a row of corn, c, as represented in the diagram below. A farmer wants to place a scarecrow 2 meters from the row of corn and also 5 meters from the tree. Sketch both loci. Indicate, with an X, all possible locations for the scarecrow. c Score 2: The student sketched both loci correctly and labeled both locations with an X. Geometry Jan. 14 [18]

19 Question A tree, T, is 6 meters from a row of corn, c, as represented in the diagram below. A farmer wants to place a scarecrow 2 meters from the row of corn and also 5 meters from the tree. Sketch both loci. Indicate, with an X, all possible locations for the scarecrow. c Score 1: The student made a conceptual error and drew only one line parallel to the row of corn, but labeled appropriate points with an X. Geometry Jan. 14 [19]

20 Question A tree, T, is 6 meters from a row of corn, c, as represented in the diagram below. A farmer wants to place a scarecrow 2 meters from the row of corn and also 5 meters from the tree. Sketch both loci. Indicate, with an X, all possible locations for the scarecrow. c Score 1: The student made a conceptual error in drawing one locus, but labeled appropriate points X. Geometry Jan. 14 [20]

21 Question A tree, T, is 6 meters from a row of corn, c, as represented in the diagram below. A farmer wants to place a scarecrow 2 meters from the row of corn and also 5 meters from the tree. Sketch both loci. Indicate, with an X, all possible locations for the scarecrow. c Score 1: The student sketched both loci correctly, but the locations are not labeled with an X. Geometry Jan. 14 [21]

22 Question A tree, T, is 6 meters from a row of corn, c, as represented in the diagram below. A farmer wants to place a scarecrow 2 meters from the row of corn and also 5 meters from the tree. Sketch both loci. Indicate, with an X, all possible locations for the scarecrow. c Score 0: The student sketched only one locus correctly and made a conceptual error in sketching the second locus. Appropriate points are not labeled with an X. Geometry Jan. 14 [22]

23 Question In the diagram of BCD shown below, BA is drawn from vertex B to point A on DC, such that BC BA B D A C In DAB, m D x, m DAB 5x 30, and m DBA 3x 60. In ABC, AB 6y 8 and BC 4y 2. [Only algebraic solutions can receive full credit.] Find m D. Find m BAC. Find the length of BC Find the length of DC Score 4: The student has a complete and correct response. The student wrote and solved correct equations to find x 30 and y 3. The four correct answers are stated. Geometry Jan. 14 [23]

24 Question In the diagram of BCD shown below, BA is drawn from vertex B to point A on DC, such that BC BA B D A C In DAB, m D x, m DAB 5x 30, and m DBA 3x 60. In ABC, AB 6y 8 and BC 4y 2. [Only algebraic solutions can receive full credit.] Find m D. Find m BAC. Find the length of BC Find the length of DC Score 4: The student has a complete and correct response. Geometry Jan. 14 [24]

25 Question In the diagram of BCD shown below, BA is drawn from vertex B to point A on DC, such that BC BA B D A C In DAB, m D x, m DAB 5x 30, and m DBA 3x 60. In ABC, AB 6y 8 and BC 4y 2. [Only algebraic solutions can receive full credit.] Find m D. Find m BAC. Find the length of BC Find the length of DC Score 3: The student showed correct work to find 30, 60, and 10. The length of DC is not stated. Geometry Jan. 14 [25]

26 Question In the diagram of BCD shown below, BA is drawn from vertex B to point A on DC, such that BC BA B D A C In DAB, m D x, m DAB 5x 30, and m DBA 3x 60. In ABC, AB 6y 8 and BC 4y 2. [Only algebraic solutions can receive full credit.] Find m D. Find m BAC. Find the length of BC Find the length of DC Score 2: The student showed correct work to find 30 and 10. No further correct work is shown. Geometry Jan. 14 [26]

27 Question In the diagram of BCD shown below, BA is drawn from vertex B to point A on DC, such that BC BA B D A C In DAB, m D x, m DAB 5x 30, and m DBA 3x 60. In ABC, AB 6y 8 and BC 4y 2. [Only algebraic solutions can receive full credit.] Find m D. Find m BAC. Find the length of BC Find the length of DC Score 1: The student showed correct work to find 10, the length of BC. No further correct work is shown. Geometry Jan. 14 [27]

28 Question In the diagram of BCD shown below, BA is drawn from vertex B to point A on DC, such that BC BA B D A C In DAB, m D x, m DAB 5x 30, and m DBA 3x 60. In ABC, AB 6y 8 and BC 4y 2. [Only algebraic solutions can receive full credit.] Find m D. Find m BAC. Find the length of BC Find the length of DC Score 1: The student showed no work, but stated four correct answers. Geometry Jan. 14 [28]

29 Question In the diagram of BCD shown below, BA is drawn from vertex B to point A on DC, such that BC BA B D A C In DAB, m D x, m DAB 5x 30, and m DBA 3x 60. In ABC, AB 6y 8 and BC 4y 2. [Only algebraic solutions can receive full credit.] Find m D. Find m BAC. Find the length of BC Find the length of DC Score 0: The student showed no correct work. Geometry Jan. 14 [29]

30 Question The coordinates of the vertices of ABC are A( 6,5), B( 4,8), and C(1,6). State and label the coordinates of the vertices of A B C, the image of ABC after the composition of transformations T 4, 5 r y-axis. [The use of the set of axes below is optional.] Score 4: The student has a complete and correct response. The student showed correct work to find the coordinates of A, B, and C. Geometry Jan. 14 [30]

31 Question The coordinates of the vertices of ABC are A( 6,5), B( 4,8), and C(1,6). State and label the coordinates of the vertices of A B C, the image of ABC after the composition of transformations T 4, 5 r y-axis. [The use of the set of axes below is optional.] Score 4: The student has a complete and correct response. The student showed correct work to find the coordinates of the images of A, B, and C after T 4, 5 r y-axis. The arrows indicate the mapping of A( 6,5) onto (6,5) onto (10,0). Geometry Jan. 14 [31]

32 Question The coordinates of the vertices of ABC are A( 6,5), B( 4,8), and C(1,6). State and label the coordinates of the vertices of A B C, the image of ABC after the composition of transformations T 4, 5 r y-axis. [The use of the set of axes below is optional.] Score 3: The student made an error reflecting one point (C) over the y-axis, but did the transformation correctly. Geometry Jan. 14 [32]

33 Question The coordinates of the vertices of ABC are A( 6,5), B( 4,8), and C(1,6). State and label the coordinates of the vertices of A B C, the image of ABC after the composition of transformations T 4, 5 r y-axis. [The use of the set of axes below is optional.] Score 2: The student made a conceptual error by doing the composition in the wrong order. Geometry Jan. 14 [33]

34 Question The coordinates of the vertices of ABC are A( 6,5), B( 4,8), and C(1,6). State and label the coordinates of the vertices of A B C, the image of ABC after the composition of transformations T 4, 5 r y-axis. [The use of the set of axes below is optional.] Score 1: The student did the translation on the vertices of ABC correctly. Geometry Jan. 14 [34]

35 Question The coordinates of the vertices of ABC are A( 6,5), B( 4,8), and C(1,6). State and label the coordinates of the vertices of A B C, the image of ABC after the composition of transformations T 4, 5 r y-axis. [The use of the set of axes below is optional.] Score 0: The student did no correct work. Geometry Jan. 14 [35]

36 Question In right triangle ABC below, CD is the altitude to hypotenuse AB If CD 6 and the ratio of AD to AB is 1:5, determine and state the length of BD [Only an algebraic solution can receive full credit.] Score 4: The student has a complete and correct response. Geometry Jan. 14 [36]

37 Question In right triangle ABC below, CD is the altitude to hypotenuse AB If CD 6 and the ratio of AD to AB is 1:5, determine and state the length of BD [Only an algebraic solution can receive full credit.] Score 3: The student correctly solved the proportion for x, the length of AD, but did not find the length of BD. Geometry Jan. 14 [37]

38 Question In right triangle ABC below, CD is the altitude to hypotenuse AB If CD 6 and the ratio of AD to AB is 1:5, determine and state the length of BD [Only an algebraic solution can receive full credit.] Score 2: The student made a conceptual error in multiplying (x 4x 5x), but found an appropriate length of BD. Geometry Jan. 14 [38]

39 Question In right triangle ABC below, CD is the altitude to hypotenuse AB If CD 6 and the ratio of AD to AB is 1:5, determine and state the length of BD [Only an algebraic solution can receive full credit.] Score 1: The student made a conceptual error in multiplying (x 4x 5x), and did not find an appropriate length of BD. Geometry Jan. 14 [39]

40 Question In right triangle ABC below, CD is the altitude to hypotenuse AB If CD 6 and the ratio of AD to AB is 1:5, determine and state the length of BD [Only an algebraic solution can receive full credit.] Score 0: The student got the correct answer by a completely incorrect method. Geometry Jan. 14 [40]

41 Question In the diagram of circle O below, diameter RS, chord AS, tangent R TS, and secant TAR are drawn. O A T S Complete the following proof to show (RS) 2 RA RT Statements Reasons 1. circle O, diameter RS, chord AS, 1. Given tangent TS, and secant TAR 2. RS TS RST is a right angle 3. lines form right angles 4. RAS is a right angle RST RAS R R 6. Reflexive property 7. RST RAS RS RA RT RS (RS) 2 RA RT 9. Score 6: The student has a complete and correct response by writing six correct reasons. Geometry Jan. 14 [41]

42 Question In the diagram of circle O below, diameter RS, chord AS, tangent R TS, and secant TAR are drawn. O A T S Complete the following proof to show (RS) 2 RA RT Statements Reasons 1. circle O, diameter RS, chord AS, 1. Given tangent TS, and secant TAR 2. RS TS RST is a right angle 3. lines form right angles 4. RAS is a right angle RST RAS R R 6. Reflexive property 7. RST RAS RS RA RT RS (RS) 2 RA RT 9. Score 5: The student wrote five correct reasons (2, 4, 5, 7, 8). Geometry Jan. 14 [42]

43 Question In the diagram of circle O below, diameter RS, chord AS, tangent R TS, and secant TAR are drawn. O A T S Complete the following proof to show (RS) 2 RA RT Statements Reasons 1. circle O, diameter RS, chord AS, 1. Given tangent TS, and secant TAR 2. RS TS RST is a right angle 3. lines form right angles 4. RAS is a right angle RST RAS R R 6. Reflexive property 7. RST RAS RS RA RT RS (RS) 2 RA RT 9. Score 4: The student wrote four correct reasons (5, 7, 8, 9). Geometry Jan. 14 [43]

44 Question In the diagram of circle O below, diameter RS, chord AS, tangent R TS, and secant TAR are drawn. O A T S Complete the following proof to show (RS) 2 RA RT Statements Reasons 1. circle O, diameter RS, chord AS, 1. Given tangent TS, and secant TAR 2. RS TS RST is a right angle 3. lines form right angles 4. RAS is a right angle RST RAS R R 6. Reflexive property 7. RST RAS RS RA RT RS (RS) 2 RA RT 9. Score 3: The student wrote three correct reasons (5, 7, 8). Geometry Jan. 14 [44]

45 Question In the diagram of circle O below, diameter RS, chord AS, tangent R TS, and secant TAR are drawn. O A T S Complete the following proof to show (RS) 2 RA RT Statements Reasons 1. circle O, diameter RS, chord AS, 1. Given tangent TS, and secant TAR 2. RS TS RST is a right angle 3. lines form right angles 4. RAS is a right angle RST RAS R R 6. Reflexive property 7. RST RAS RS RA RT RS (RS) 2 RA RT 9. Score 2: The student wrote two correct reasons (7, 9). Geometry Jan. 14 [45]

46 Question In the diagram of circle O below, diameter RS, chord AS, tangent R TS, and secant TAR are drawn. O A T S Complete the following proof to show (RS) 2 RA RT Statements Reasons 1. circle O, diameter RS, chord AS, 1. Given tangent TS, and secant TAR 2. RS TS RST is a right angle 3. lines form right angles 4. RAS is a right angle RST RAS R R 6. Reflexive property 7. RST RAS RS RA RT RS (RS) 2 RA RT 9. Score 1: The student wrote one correct reason (5). Geometry Jan. 14 [46]

47 Question In the diagram of circle O below, diameter RS, chord AS, tangent R TS, and secant TAR are drawn. O A T S Complete the following proof to show (RS) 2 RA RT Statements Reasons 1. circle O, diameter RS, chord AS, 1. Given tangent TS, and secant TAR 2. RS TS RST is a right angle 3. lines form right angles 4. RAS is a right angle RST RAS R R 6. Reflexive property 7. RST RAS RS RA RT RS (RS) 2 RA RT 9. Score 0: The student has no correct reasons. Geometry Jan. 14 [47]

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