Cubic inch

NYS geometry common core regents jan 2016 part 1 1 to 5 solutions answers step by step

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• published: 10 May 2016
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1 William is drawing pictures of cross sections of the right circular cone computations. below. Which drawing can not be a cross section of a cone? 2 An equation of a line perpendicular to the line represented by the equation y 1 __ 2 x 5 and passing through (6,4) is (1) y 1 __ 2 x 4 (3) y 2x 14 (2) y 1 __ 2 x 1 (4) y 2x 16 (2) (1) (3) (4) Geometry (Common Core) – Jan. ’16 [3] [OVER] 3 In parallelogram QRST shown below, diagonal TR ___ is drawn, U and V are points on TS ___ and QR ___ , respectively, and UV ___ intersects TR ___ at W. If m∠S60°, m∠SRT83°, and m∠TWU35°, what is m∠WVQ? (1) 37º (3) 72º (2) 60º (4) 83º 4 A fish tank in the shape of a rectangular prism has dimensions of 14 inches, 16 inches, and 10 inches. The tank contains 1680 cubic inches of water. What percent of the fish tank is empty? (1) 10 (3) 50 (2) 25 (4) 75 5 Which transformation would result in the perimeter of a triangle being different from the perimeter of its image? (1) (x,y) → (y,x) (3) (x,y) → (4x,4y) (2) (x,y) → (x,y) (4) (x,y) → (x 2,y 5) Use this space for computations. Geometry (Common Core) – Jan. ’16 [4] 6 In the diagram below, FE ‹___› bisects AC ___ at B, and GE ‹___› bisects BD ___ at C. Which statement is always true? (1) AB ___ DC ___ (3) BD ‹___› bisects GE ___ at C. (2) FB ___ EB ___ (4) AC ‹___› bisects FE ___ at B. 7 As shown in the diagram below, a regular pyramid has a square base whose side measures 6 inches. If the altitude of the pyramid measures 12 inches, its volume, in cubic inches, is (1) 72 (3) 288 (2) 144 (4) 432 A B C D F G E 6 in Use this space for computations. Geometry (Common Core) – Jan. ’16 [5] [OVER] 8 Triangle ABC and triangle DEF are graphed on the set of axes below. Which sequence of transformations maps triangle ABC onto triangle DEF? (1) a reflection over the x-axis followed by a reflection over the y-axis (2) a 180º rotation about the origin followed by a reflection over the line y x (3) a 90º clockwise rotation about the origin followed by a reflection over the y-axis (4) a translation 8 units to the right and 1 unit up followed by a 90º counterclockwise rotation about the origin Use this space for computations. Geometry (Common Core) – Jan. ’16 [6] 9 In ABC, the complement of ∠B is ∠A. Which statement is always true? (1) tan ∠A tan ∠B (3) cos ∠A tan ∠B (2) sin ∠A sin ∠B (4) sin ∠A cos ∠B 10 A line that passes through the points whose coordinates are (1,1) and (5,7) is dilated by a scale factor of 3 and centered at the origin. The image of the line (1) is perpendicular to the original line (2) is parallel to the original line (3) passes through the origin (4) is the original line 11 Quadrilateral ABCD is graphed on the set of axes below. When ABCD is rotated 90° in a counterclockwise direction about the origin, its image is quadrilateral ABCD. Is distance preserved under this rotation, and which coordinates are correct for the given vertex? (1) no and C(1,2) (3) yes and A(6,2) (2) no and D(2,4) (4) yes and B(3,4) x y B A C D Use this space for computations. Geometry (Common Core) – Jan. ’16 [7] [OVER] 12 In the diagram below of circle O, the area of the shaded sector LOM is 2π cm2. If the length of NL ___ is 6 cm, what is m∠N? (1) 10° (3) 40° (2) 20° (4) 80° 13 In the diagram below, ABC DEF. If AB 6 and AC 8, which statement will justify similarity by SAS? (1) DE 9, DF 12, and ∠A ∠D (2) DE 8, DF 10, and ∠A ∠D (3) DE 36, DF 64, and ∠C ∠F (4) DE 15, DF 20, and ∠C ∠F 14 The diameter of a basketball is approximately 9.5 inches and the diameter of a tennis ball is approximately 2.5 inches. The volume of the basketball is about how many times greater than the volume of the tennis ball? (1) 3591 (3) 55 (2) 65 (4) 4 16 In the diagram of right triangle ABC shown below, AB 14 and AC 9. What is the measure of ∠A, to the nearest degree? (1) 33 (3) 50 (2) 40 (4) 57 17 What are the coordinates of the center and length of the radius of the circle whose equation is x2 6x y2 4y 23? (1) (3,2) and 36 (3) (3,2) and 36 (2) (3,2) and 6 (4) (3,2) and 6 18 The coordinates of the vertices of RST are R(2,3), S(8,2), and T(4,5). Which type of triangle is RST? (1) right (3) obtuse (2) acute (4) equiangular Use this space for computations. Geometry (Common Core) – Jan. ’16 [9] [OVER] Use this space for 19 Molly wishes to make a lawn ornament in the form of a solid sphere. computations. The clay being used to make the sphere weighs .075 pound per cubic inch. If the sphere’s radius is 4 inches, what is the weight of the sphere, to the nearest pound? (1) 34 (3) 15 (2) 20 (4) 4 20 The ratio of similarity of BOY to GRL is 1:2. If BO x 3 and GR 3x 1, then the length of GR ___ 21 In the diagram below, DC ___ , AC are chords of circle O, FDE ‹____› is tangent at point D, and radius AO ___ is drawn. Sam