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

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Published on May 9, 2016

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

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