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

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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