Download JANUARY 2017 GEOMETRY REGENTS QUESTIONS 1. Which

JANUARY 2017 GEOMETRY REGENTS QUESTIONS
1.
Which equation represents the line that passes through the point (– 2, 2)
1
and is parallel to=
y
x + 8 ? [#1]
2
1
(A) y = x
2
−2x − 3
(B) y =
1
(C) =
y
x+3
2
−2x + 3
(D) y =
2.
Given DABC ≅ DDEF , which statement is not always true? [#3]
(A)
(B)
(C)
(D)
3.
BC ≅ DF
m∠A = m∠D
area of ∆ABC = area of DDEF
perimeter of ∆ABC = perimeter of DDEF
In the diagram below, DE , DF , and EF are midsegments of ∆ABC . [#4]
The perimeter of quadrilateral ADEF is equivalent to
(A) AB + BC + AC
1
1
(B)
AB + AC
2
2
(C) 2AB + 2AC
(D) AB + AC
4.
In the diagram below, if DABE ≅ DCDF and AEFC is drawn, then it could be proven that
quadrilateral ABCD is a [#5]
(A)
(B)
(C)
(D)
square
rhombus
rectangle
parallelogram
5.
The diagram below shows two similar triangles.
3
If tan θ = , what is the value of x to the nearest tenth ? [#7]
7
(A)
(B)
(C)
(D)
6.
1.2
5.6
7.6
8.8
The diagram shows rectangle ABCD, with diagonal BD . [#9]
What is the perimeter of rectangle ABCD, to the nearest tenth ?
(A)
(B)
(C)
(D)
7.
28.4
32.8
48.0
62.4
A solid metal prism has a rectangular base with sides of 4 inches and 6 inches, and height of 4
inches. A hole in the shape of a cylinder with a radius of 1 inch, is drilled through the entire
length of the rectangular prism. [#11]
What is the approximate volume of the remaining
solid, in cubic inches?
(A)
(B)
(C)
(D)
8.
19
77
93
96
Given the right triangle in the diagram below,
what is the value of x, to the nearest foot ? [#12]
(A)
(B)
(C)
(D)
11
17
18
22
9.
In the diagram of right triangle ADE below, BC � DE .
Which ratio is always equivalent to the sine of ∠A ? [#14]
AD
DE
AE
(B)
AD
BC
(C)
AB
AB
(D)
AC
(A)
10.
A parallelogram is always a rectangle if [#16]
(A)
(B)
(C)
(D)
the
the
the
the
diagonals are congruent
diagonals bisect each other
diagonals intersect at right angles
opposite angles are congruent
11. The equation of a circle is x 2 + y 2 − 6y + 1 =
0 . What are the coordinates of the center and the
length of the radius of this circle? [#18]
(A) center (0, 3) and radius = 2 2
(B) center (0, – 3) and radius = 2 2
(C) center (0, 6) and radius = 35
(D) center (0, – 6) and radius =
35
12. Point Q is on MN such that MQ:QN = 2:3. If M has coordinates (3, 5) and
N has coordinates (8, – 5), the coordinates of Q are [#20]
(A)
(B)
(C)
(D)
(5,
(5,
(6,
(6,
1)
0)
– 1)
0)
13. A circle whose center is the origin passes through the point (– 5, 12).
Which point also lies on this circle? [#22]
(A) (10, 3)
(B) (– 12, 13)
(C)
(D)
(11, 2 12 )
( − 8, 5 21 )
14. A plane intersects a hexagonal prism. The plane is perpendicular to the base of the prism.
Which two-dimensional figure is the cross-section of the plane intersecting the prism? [#23]
(A)
(B)
(C)
(D)
triangle
trapezoid
hexagon
rectangle
15. A water cup in the shape of a cone has a height of 4 inches and a maximum diameter of 3
inches. What is the volume of the water in the cup, to the nearest tenth of a cubic inch, when
the cup is filled to half its height? [#24]
(A)
(B)
(C)
(D)
1.2
3.5
4.7
14.1
16. When instructed to find the length of HJ in right triangle HJG, Alex wrote the equation
HJ
HJ
while Marlene wrote cos 62° = . Are both students’ equations correct?
sin 28° =
20
20
Explain why. [#27 – 2 points]
17. In the diagram below, GI is parallel to NT , and IN intersects GT at A.
Explain why ∆∆
GIA ~ TNA . [#29 – 2 points]
18. In the diagram below of isosceles triangle ABC, AB ≅ CB and angle bisectors AD , BF , and CE
are drawn and intersect at X. [#30 – 2 points]
If m∠BAC =50° , find m∠AXC .
19. In square GEOM, the coordinates of G are (2, – 2) and the coordinates of O are (– 4, 2).
Determine and state the coordinates of vertices E and M. [#31 – 2 points]
20. A candle maker uses a mold to make candles like the one shown below.
The height of the candle is 13 cm and the circumference of the
candle at its widest measure is 31.416 cm. Use modeling to
approximate how much wax, to the nearest cubic centimeter, is
needed to make this candle. Justify your answers.
[#34 – 4 points]
21. New streetlights will be installed along a section of the highway. The posts for the streetlights
will be 7.5 m tall and made of aluminum. The city can choose to buy the posts shaped like
cylinders or the posts shaped like rectangular prisms. The cylindrical posts have a hollow core,
with aluminum 2.5 cm thick, and an outer diameter of 53.4 cm. The rectangular-prism posts
have a hollow core, with aluminum 2.5 cm thick, and square base that measures 40 cm on each
side. [#36 – 6 points]
The density of aluminum is 2.7 g / cm3 , and the cost of aluminum is $0.38 per kilogram.
If all posts must be the same shape, which post design will cost the town less?
How much money will be saved per streetlight post with the less expensive design?
1.
2.
3.
4.
5.
6.
C
A
D
D
B
B
7.
8.
9.
10.
11.
12.
B
C
C
A
A
A
13.
14.
15.
16.
17.
18.
C
D
C
Yes, explain.
Explain
130
19. E(– 3, – 3)
M(1, 3)
20. 340 cm3
21. prism is less
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