The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, June 19, :15 a.m. to 12:15 p.m.

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1 The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, June 19, :15 a.m. to 12:15 p.m., only SAMPLE RESPONSE SET Table of Contents Practice Papers Question Practice Papers Question Practice Papers Question Practice Papers Question Practice Papers Question Practice Papers Question Practice Papers Question Practice Papers Question Practice Papers Question Practice Papers Question

2 Practice Papers Question A right circular cylinder has a height of 7 inches and the base has a diameter of 6 inches. Determine the lateral area, in square inches, of the cylinder in terms of. Score 2: The student used the correct formula and found the correct lateral area. Geometry June 13 [2]

3 Practice Papers Question A right circular cylinder has a height of 7 inches and the base has a diameter of 6 inches. Determine the lateral area, in square inches, of the cylinder in terms of. Score 1: The student draws a cone and finds the appropriate lateral surface area. (The number of decimal places in front of is irrelevant.) Geometry June 13 [3]

4 Practice Papers Question A right circular cylinder has a height of 7 inches and the base has a diameter of 6 inches. Determine the lateral area, in square inches, of the cylinder in terms of. Score 0: The student used the formula for the lateral area of a right circular cone. When attempting to find the slant height, the student used the diameter. These are two conceptual errors. Geometry June 13 [4]

5 Practice Papers Question Determine, in degrees, the measure of each interior angle of a regular octagon. Score 2: The student divided the sum of the exterior angles by the number of sides to find an exterior angle. Then the student found the supplement of this angle to find the interior angle. Geometry June 13 [5]

6 Practice Papers Question Determine, in degrees, the measure of each interior angle of a regular octagon. Score 1: The student made a conceptual error by using 360 as the sum of the interior angles of an octagon. Geometry June 13 [6]

7 Practice Papers Question Determine, in degrees, the measure of each interior angle of a regular octagon. Score 1: The student showed work to find the sum of the interior angles of an octagon, but did not find the measure of each interior angle. Geometry June 13 [7]

8 Practice Papers Question Determine, in degrees, the measure of each interior angle of a regular octagon. Score 0: The student wrote the correct formula for finding an interior angle of a regular polygon, but made a conceptual error by using 5 as the number of sides in an octagon. A second conceptual error was made by dividing by 2 instead of the number of sides. Geometry June 13 [8]

9 Practice Papers Question Triangle ABC has vertices at A(3,0), B(9, 5), and C(7, 8). Find the length of AC in simplest radical form. Score 2: The student showed appropriate work and simplified the radical completely. Geometry June 13 [9]

10 Practice Papers Question Triangle ABC has vertices at A(3,0), B(9, 5), and C(7, 8). Find the length of AC in simplest radical form. Score 1: The student showed appropriate work, but did not simplify the radical completely. Geometry June 13 [10]

11 Practice Papers Question Triangle ABC has vertices at A(3,0), B(9, 5), and C(7, 8). Find the length of AC in simplest radical form. Score 0: The student found the correct slope of AC, which is irrelevant to this problem. Geometry June 13 [11]

12 Practice Papers Question On the ray drawn below, using a compass and straightedge, construct an equilateral triangle with a vertex at R. The length of a side of the triangle must be equal to a length of the diagonal of rectangle ABCD. Score 2: The student did a correct construction using the length of a diagonal as each side of the triangle. Geometry June 13 [12]

13 Practice Papers Question On the ray drawn below, using a compass and straightedge, construct an equilateral triangle with a vertex at R. The length of a side of the triangle must be equal to a length of the diagonal of rectangle ABCD. Score 1: The student showed a correct construction of an equilateral triangle, but used the length of AB as the side of the triangle. Geometry June 13 [13]

14 Practice Papers Question On the ray drawn below, using a compass and straightedge, construct an equilateral triangle with a vertex at R. The length of a side of the triangle must be equal to a length of the diagonal of rectangle ABCD. Score 0: The student used the ray as one side of an equilateral triangle and made appropriate arcs. However, the student did not draw a triangle. Geometry June 13 [14]

15 Practice Papers Question On the set of axes below, graph the locus of points 4 units from the x-axis and equidistant from the points whose coordinates are ( 2,0) and (8,0). Mark with an X all points that satisfy both conditions. Score 2: The student graphed both loci correctly and labeled the points that satisfy both conditions with coordinates instead of an X. Geometry June 13 [15]

16 Practice Papers Question On the set of axes below, graph the locus of points 4 units from the x-axis and equidistant from the points whose coordinates are ( 2,0) and (8,0). Mark with an X all points that satisfy both conditions. Score 1: The student located the two points that satisfy both conditions and marked them with an X, but did not graph either locus. Geometry June 13 [16]

17 Practice Papers Question On the set of axes below, graph the locus of points 4 units from the x-axis and equidistant from the points whose coordinates are ( 2,0) and (8,0). Mark with an X all points that satisfy both conditions. Score 0: The student did not graph either locus correctly and marked multiple points with an X. Geometry June 13 [17]

18 Practice Papers Question The coordinates of two vertices of square ABCD are A(2,1) and B(4,4). Determine the slope of side BC. Score 2: The student found the slope of AB correctly and used the negative reciprocal to find the slope of BC. Geometry June 13 [18]

19 Practice Papers Question The coordinates of two vertices of square ABCD are A(2,1) and B(4,4). Determine the slope of side BC. Score 1: The student found the slope of AB correctly, but made a conceptual error in stating that the slope of BC was the same. Geometry June 13 [19]

20 Practice Papers Question The coordinates of two vertices of square ABCD are A(2,1) and B(4,4). Determine the slope of side BC. Score 1: The student included x when writing the slope as 2 3 conceptual error. in the circled solution, which is a Geometry June 13 [20]

21 Practice Papers Question The coordinates of two vertices of square ABCD are A(2,1) and B(4,4). Determine the slope of side BC. Score 0: The student does not show appropriate work and the solution is incorrect. Geometry June 13 [21]

22 Practice Papers Question The coordinates of the vertices of parallelogram SWAN are S(2, 2), W( 2, 4), A( 4,6), and N(0,8). State and label the coordinates of parallelogram S W A N, the image of SWAN after the transformation T 4, 2 D 1. [The use of the set of axes below is optional.] 2 Score 4: The student applied the correct transformation rules to find the coordinates of SWAN. Geometry June 13 [22]

23 Practice Papers Question The coordinates of the vertices of parallelogram SWAN are S(2, 2), W( 2, 4), A( 4,6), and N(0,8). State and label the coordinates of parallelogram S W A N, the image of SWAN after the transformation T 4, 2 D 1. [The use of the set of axes below is optional.] 2 Score 4: The student used a graphic solution to find the coordinates of SWAN. Geometry June 13 [23]

24 Practice Papers Question The coordinates of the vertices of parallelogram SWAN are S(2, 2), W( 2, 4), A( 4,6), and N(0,8). State and label the coordinates of parallelogram S W A N, the image of SWAN after the transformation T 4, 2 D 1. [The use of the set of axes below is optional.] 2 Score 3: The student made one computational error in finding N. Geometry June 13 [24]

25 Practice Papers Question The coordinates of the vertices of parallelogram SWAN are S(2, 2), W( 2, 4), A( 4,6), and N(0,8). State and label the coordinates of parallelogram S W A N, the image of SWAN after the transformation T 4, 2 D 1. [The use of the set of axes below is optional.] 2 Score 3: The student applied the rules for composite transformations correctly, but did not put parentheses around the coordinates. Geometry June 13 [25]

26 Practice Papers Question The coordinates of the vertices of parallelogram SWAN are S(2, 2), W( 2, 4), A( 4,6), and N(0,8). State and label the coordinates of parallelogram S W A N, the image of SWAN after the transformation T 4, 2 D 1. [The use of the set of axes below is optional.] 2 Score 2: The student made a conceptual error in doing the translation (multiplied by 4 and 2 instead of adding 4 and 2). Geometry June 13 [26]

27 Practice Papers Question The coordinates of the vertices of parallelogram SWAN are S(2, 2), W( 2, 4), A( 4,6), and N(0,8). State and label the coordinates of parallelogram S W A N, the image of SWAN after the transformation T 4, 2 D 1. [The use of the set of axes below is optional.] 2 Score 1: The student did the transformation first, which is a conceptual error, and then made an error in calculating the y-coordinate for S. Geometry June 13 [27]

28 Practice Papers Question The coordinates of the vertices of parallelogram SWAN are S(2, 2), W( 2, 4), A( 4,6), and N(0,8). State and label the coordinates of parallelogram S W A N, the image of SWAN after the transformation T 4, 2 D 1. [The use of the set of axes below is optional.] 2 Score 0: The student graphed the parallelogram SWAN correctly, but did no other work. Geometry June 13 [28]

29 Practice Papers Question In circle O shown below, chords AB and CD and radius OA are drawn, such that AB CD, OE AB, OF CD, OF 16, CF y 10, and CD 4y 20. Determine the length of DF. Determine the length of OA. Score 4: The student showed appropriate work to find both lengths. Geometry June 13 [29]

30 Practice Papers Question In circle O shown below, chords AB and CD and radius OA are drawn, such that AB CD, OE AB, OF CD, OF 16, CF y 10, and CD 4y 20. Determine the length of DF. Determine the length of OA. Score 3: The student showed appropriate work to find y, but the length of DF is incorrect. The student showed appropriate work to find the length of OA. Geometry June 13 [30]

31 Practice Papers Question In circle O shown below, chords AB and CD and radius OA are drawn, such that AB CD, OE AB, OF CD, OF 16, CF y 10, and CD 4y 20. Determine the length of DF. Determine the length of OA. Score 2: The student made a conceptual error in writing the equation to find y, but used this answer to do the rest of the problem correctly and found appropriate lengths. Geometry June 13 [31]

32 Practice Papers Question In circle O shown below, chords AB and CD and radius OA are drawn, such that AB CD, OE AB, OF CD, OF 16, CF y 10, and CD 4y 20. Determine the length of DF. Determine the length of OA. Score 1: The student wrote the correct equation and found y = 20, but no further correct work was shown. Geometry June 13 [32]

33 Practice Papers Question In circle O shown below, chords AB and CD and radius OA are drawn, such that AB CD, OE AB, OF CD, OF 16, CF y 10, and CD 4y 20. Determine the length of DF. Determine the length of OA. Score 0: The student made a conceptual error in writing the equation to solve for y, and then made a computational error when solving this equation. When solving for the length of OA, the student made a second conceptual error by using their value for y instead of the length of DF in the Pythagorean Theorem. The student got a correct answer for the second part by an incorrect method. Geometry June 13 [33]

34 Practice Papers Question If RST ABC, m A x 2 8x, m C 4x 5, and m R 5x 30, find m C. [Only an algebraic solution can receive full credit.] Score 4: The student wrote a correct equation and showed appropriate work to find m C. Geometry June 13 [34]

35 Practice Papers Question If RST ABC, m A x 2 8x, m C 4x 5, and m R 5x 30, find m C. [Only an algebraic solution can receive full credit.] Score 3: The student showed appropriate work to find x = 15, but no further correct work is shown. Geometry June 13 [35]

36 Practice Papers Question If RST ABC, m A x 2 8x, m C 4x 5, and m R 5x 30, find m C. [Only an algebraic solution can receive full credit.] Score 3: The student made a factoring error, but found appropriate measures for C. Geometry June 13 [36]

37 Practice Papers Question If RST ABC, m A x 2 8x, m C 4x 5, and m R 5x 30, find m C. [Only an algebraic solution can receive full credit.] Score 2: The student crossed out the first attempt. Then the student made a conceptual error in assuming that the measure of S is x. The student used this value for x to find an appropriate measure for C. Geometry June 13 [37]

38 Practice Papers Question If RST ABC, m A x 2 8x, m C 4x 5, and m R 5x 30, find m C. [Only an algebraic solution can receive full credit.] Score 1: The student wrote a correct equation, but no further correct work was shown. Geometry June 13 [38]

39 Practice Papers Question If RST ABC, m A x 2 8x, m C 4x 5, and m R 5x 30, find m C. [Only an algebraic solution can receive full credit.] Score 0: The student s work is completely incorrect, irrelevant, and incoherent. Geometry June 13 [39]

40 Practice Papers Question In the diagram of MAH below, MH AH and medians AB and MT are drawn. Prove: MBA ATM Score 6: The student showed a complete and correct proof. Geometry June 13 [40]

41 Practice Papers Question In the diagram of MAH below, MH AH and medians AB and MT are drawn. Prove: MBA ATM Score 5: The student proved MBA ATM, MBA ATM. but did not do the last step to prove Geometry June 13 [41]

42 Practice Papers Question In the diagram of MAH below, MH AH and medians AB and MT are drawn. Prove: MBA ATM Score 4: The student proved MHT AHB, but is missing two steps to prove MBA ATM. Geometry June 13 [42]

43 Practice Papers Question In the diagram of MAH below, MH AH and medians AB and MT are drawn. Prove: MBA ATM Score 3: The student made a conceptual error in line 2, but from there the student proved MBA ATM. Geometry June 13 [43]

44 Practice Papers Question In the diagram of MAH below, MH AH and medians AB and MT are drawn. Prove: MBA ATM Score 2: The student made some relevant statements, but four statements or reasons are missing or are incorrect. Geometry June 13 [44]

45 Practice Papers Question In the diagram of MAH below, MH AH and medians AB and MT are drawn. Prove: MBA ATM Score 1: The student has only one or two correct statements and reasons, but no further correct work is shown. Geometry June 13 [45]

46 Practice Papers Question In the diagram of MAH below, MH AH and medians AB and MT are drawn. Prove: MBA ATM Score 0: The student wrote no relevant statements. Geometry June 13 [46]

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