Download end of course geometry core 1

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VIRGINIA
STANDARDS OF LEARNING ASSESSMENTS
Spring 2004 Released Test
END OF COURSE
GEOMETRY
CORE 1
Property of the Virginia Department of Education
䉷 2004 by the Commonwealth of Virginia Department of Education, James Monroe Building, 101 N. 14th Street,
Richmond, Virginia, 23219. All rights reserved. Except as permitted by law, this material may not be reproduced or
used in any form or by any means, electronic or mechanical, including photocopying or recording, or by any
information storage or retrieval system, without written permission from the copyright owner. Commonwealth of
Virginia public school educators may photocopy or print any portion of these Released Tests for educational purposes
without requesting permission. All others should direct their requests to the Commonwealth of Virginia Department
of Education at (804) 225-2102, Division of Assessment and Reporting.
SESSION: 23 PAGE: 2 5/4/04 15:40 LOGIN IS-glenn PATH: @sunultra1/raid/CLS_tpc/GRP_va_sprg04/JOB_04-ribsg11/DIV_g11geom-1
Geometry
2
DIRECTIONS
X
Read and solve each question. Then mark the
space on the answer sheet for the best answer.
1
2
l
3
GY040602
墍
C
SAMPLE
W
Y
A
D
GY040602.AR1
If ∠3 ≅ ∠Y, which of the following must
be true?
E
∠W ≅ ∠Y
G WX is perpendicular to XY
H ∠W ≅ ∠2
J Line l is parallel to YW 墍
F
B
C
If ⌬ABC is similar to ⌬ADE, then
AB : AD ⴔ ? : AE. Which replaces the
“?” to make the statement true?
AC 墍
B AE
C DE
D BC
A
1
GY030542
墌
A plumber bent a flexible joint into a
136ⴗ angle, as shown. He then attached
another pipe so that A, B, and D lay on
a straight line.
C
ArtCodes
136°
GY030542.AR1
ArtCodes
What is the value of x?
36
B 44 墍
C 46
D 224
A
2004 Commonwealth of Virginia Department of Education
2
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3
4
Which pair of angles is supplementary?
In the figure, line t is a transversal for
lines l and m.
GY030576
GY030623
墌
ArtCodes
GY030576.AR1
GY030576.AR2
GY030576.AR3
GY030576.AR4
墍
t
C
L
C
墍
A
35°
ArtCodes
145°
GY030623.AR1
2
1
l
m
Which of the following best describes
the relationship between ∠1 and ∠2?
B
35°
55°
Alternate interior angles
G Consecutive interior angles
H Corresponding angles
J Alternate exterior angles 墍
F
C
25°
75°
D
80°
80°
2004 Commonwealth of Virginia Department of Education
3
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5
7
Line l intersects lines w, x, y, and z,
forming angles with measures as
indicated on the drawing.
←→
and QR are parallel and
m∠M ⴔ m∠L ⴔ 60ⴗ.
GY040407
墌
←→
In the figure drawn below, LM
GY030707
墍
l
C
110°
ArtCodes
C
w
GY040407.AR1
ArtCodes
65°
75°
GY030707.AR1
x
y
What is m∠QNP?
z
90⬚
B 120⬚ 墍
C 150⬚
D 180⬚
A
115°
Which two lines are parallel?
w and x
B x and z 墍
C y and z
D w and y
A
8
72°
x° z°
GY040578
墍
l
C
6
ArtCodes
(4x – 30)°
GY040578.AR1
GY040512
墌
w°
C
m
y°
(2x)°
ArtCodes
GY040512.AR1
Which value for x will make a parallel
to b?
Which additional piece of information
would verify l m?
5
G 15 墍
H 20
J 35
F
2004 Commonwealth of Virginia Department of Education
x ⫽ 72
G y ⫽ w
H z ⫽ 108
J x ⫽ w 墍
F
4
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9
11
R
S
GY110406
墌
GY110404
墍
Q
C
L
C
T
ArtCodes
ArtCodes
GY110406.AR1
A
The drawing shows the arcs used to
construct —
B
Which point lies on the line
perpendicular to AB that bisects AB?
a bisector of a given angle
B an angle congruent to a given angle 墍
C a bisector of a given line
D a perpendicular of a given line at a
point on the line
A
Q
B R
C S 墍
D T
A
10
A
B
C
D
P
GY110579
墌
C
L
ArtCodes
GY110579.AR1
Q
R
Which point lies on the bisector of
∠PQR?
A
G B
H C 墍
J D
F
2004 Commonwealth of Virginia Department of Education
5
GY110404.AR1
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12
GY01D602
墌
13
Consider the following arguments. If
the first two statements are true, in
which argument is the 3rd statement
an incorrect conclusion?
Pet Owners
cat
owners
fish
owners
C
F
G
墍
C
L
Based strictly on this diagram, which
is a valid conclusion?
No
B No
C No
D No
A
1 If it rains, then we will stay inside.
2 If we stay inside, then we will play
games.
3 If it rains, then we will play
games.
cat owners also own dogs.
dog owners also own fish. 墍
fish owners also own cats.
pet owner owns more than one pet.
Consider the following statements.
p: The sum of two angles is 90ⴗ.
q: The two angles are complements.
1 If we win the game, then we will
win the championship.
2 If we win the championship, then
we will get a trophy.
3 If we do not get a trophy, then we
did not win the game.
GY01B602
墍
Which of the following is a symbolic
representation of the statement:
If two angles are not complements, then
the sum of the two angles is not 90ⴗ?
⬃q→⬃p墍
G ⬃ p → ⬃ q
H q → p
J p → q
1 If Susan eats her broccoli, then she
will get ice cream.
2 If Susan gets ice cream, then she
will stay up late.
3 If Susan eats her broccoli, then
she will stay up late.
2004 Commonwealth of Virginia Department of Education
墍
GY01C506.AR1
F
J
GY01C506
ArtCodes
1 If John studies, then he will pass
the test.
2 If John passes the test, then he
will not be grounded.
3 If John is grounded, then he will
study.
14
H
dog
owners
6
C
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15
Given: AD ≅ AC and AB ≅ AE
16
Given: ∠R ≅ ∠U.
D
GY05B405
墌
T
S
C
GY05A519
墍
C
ArtCodes
E
GY05B405.AR1
ArtCodes
X
GY05A519.AR1
F
U
A
B
R
C
Which proportion is true?
Which could be used to prove
⌬ADB ≅ ⌬ACE?
A
B
(SSS) If 3 sides of one triangle are
congruent to 3 sides of another triangle,
then the triangles are congruent.
(SAS) If 2 sides and the angle between
them in one triangle are congruent to
2 sides and the angle between them of
another triangle, then the triangles are
congruent. 墍
C
(ASA) If 2 angles and the sides between
them are congruent to 2 angles and the
side between them of another triangle,
then the triangles are congruent.
D
(AAS) If 2 angles and a side not
between them are congruent to 2 angles
and the side not between them of
another triangle, then the triangles are
congruent.
F
TX
RT
⫽
墍
US
SX
G
RT
RX
⫽
UX
XS
H
SX
RT
⫽
US
TX
J
RT
XT
⫽
RX
UX
17
L
GY05A407
墍
M
N
C
Q
P
Given: ⌬LMQ ⬃ ⌬LNP. Therefore —
2004 Commonwealth of Virginia Department of Education
7
A
PQ
LM
⫽
MN
QL
B
NP
LN
⫽
墍
LM
MQ
C
MN
LM
⫽
LP
QP
D
LQ
LN
⫽
LP
LM
ArtCodes
GY05A407.AR1
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18
20
P
GY060577
墌
B
GY060202
65
0m
Q
GY060577.AR1
70 mm
C
8m
55
C
L
ArtCodes
墍
64 mm
56 mm
ArtCodes
R
GY060202.AR1
A
From smallest to largest, the angles of
⌬PQR are —
C
∠R, ∠Q, ∠P 墍
G ∠R, ∠P, ∠Q
H ∠Q, ∠R, ∠P
J ∠P, ∠R, ∠Q
F
19
GY060576
墌
C
L
The locations of three water pumping
stations form a triangle on a map of
the area. The distance from station A
to station B is 650 meters. The distance
from station B to station C is 558
meters. The distance from station A to
station C is —
Which set of lengths could not be the
lengths of the sides of a triangle?
7
B 8
C 4
D 2
A
less than 92 m
G exactly 92 m
H between 92 m and 1,208 m 墍
J greater than 1,208 m
F
in., 24 in., 30 in.
ft, 10 ft, 12 ft
cm, 5 cm, 9 cm 墍
m, 3 m, 4 m
21
The top of a ladder is leaning on a
building at a point 12 feet above the
ground; the bottom of the ladder is 5
feet from the base of the building.
What is the length of the ladder?
19 ft
B 17 ft
C 13 ft 墍
D 7 ft
A
2004 Commonwealth of Virginia Department of Education
8
GY070621
墍
C
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22
23
6 in.
?
GY070310
墌
GY070580
墍
45°
60°
C
L
C
6 in.
ArtCodes
ArtCodes
GY070310.AR1
GY070580.AR1
12 cm
A design is formed by joining isosceles
right triangles and 60ⴗ- 30ⴗ right
triangles as shown in the diagram. If
the hypotenuse of the 60ⴗ- 30ⴗ triangle
is 12 centimeters, which is closest to
the length of one leg of the isosceles
right triangle?
What is the diameter of the circle
shown?
3公2
B 3公3
C 6公2
D 6公3
A
6 cm 墍
G 7.2 cm
H 8.5 cm
J 10.4 cm
F
24
in.
in.
in. 墍
in.
B
A
22°
GY08A506
墍
C
D
C
Quadrilateral ABCD is a parallelogram.
ArtCodes
The measure of ∠C is —
GY08A506.AR1
22⬚ 墍
G 68⬚
H 112⬚
J 158⬚
F
2004 Commonwealth of Virginia Department of Education
9
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25
The vertices of parallelogram ABCD
have coordinates A(1, 8), B(4, ⴑ2), and
C(ⴑ2, ⴑ7).
26
A desktop was made from the scrap of
plywood shown by cutting (in a
straight line) from C to E.
GY08C403
GY08C615
墌
墍
C
L
A
E
C
B
9
8
7
ArtCodes
GY08C403.AR1
6
ArtCodes
5
GY08C615.AR1
4
3
2
D
1
–9 –8 –7 –6 –5 –4 –3 –2 –1
–1
1
2
3
4
5
6
7
8
C
9
–2
Which measurement would ensure that
the desktop is rectangular?
–3
–4
–5
AE ⫽ EB
G AC ⫽ BD
H EC ⫽ CD
J DE ⫽ CA 墍
F
–6
–7
–8
–9
What are the coordinates of D?
(⫺5, 3) 墍
B (⫺3, 5)
C (2, 3)
D (5, ⫺3)
A
27
Which of the following is not true
about a parallelogram?
Any two opposite sides are congruent.
B Any two opposite angles are congruent.
C The diagonals bisect each other.
D Any two consecutive angles are
complementary. 墍
A
2004 Commonwealth of Virginia Department of Education
10
GY08A602
墍
C
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28
90
30
90
O
O
GY090721
GY090416
墌
墍
C
O
100
105
C
O
ArtCodes
ArtCodes
GY090721.AR1
GY090416.AR1
What is the value of x in the pentagon
above?
A
90⬚
G 155⬚ 墍
H 245⬚
J 335⬚
C
F
B
What is the measure of interior angle
ABC of the regular polygon shown?
225⬚
G 180⬚
H 160⬚
J 144⬚ 墍
F
29
GY090308
墌
x
C
L
31
ArtCodes
L
GY090308.AR1
M
GY100609
墍
C
P
ArtCodes
Which is the closest to the measure of a
central angle x in this regular polygon?
GY100609.AR1
N
O
40⬚
B 45⬚
C 50⬚ 墍
D 60⬚
A
If LO is a diameter of circle P, what is
m∠LMO?
30⬚
B 45⬚
C 80⬚
D 90⬚ 墍
A
2004 Commonwealth of Virginia Department of Education
11
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32
Secants PB and PD intersect the circle
at A and C, respectively.
GY100414
墌
34
GY120403
墍
B
C
C
5
ArtCodes
A
ArtCodes
Which could be the view of this stack
of cubes from directly above?
4
GY100414.AR1
C
D
P
12
F
ArtCodes
What is the length of PC?
3墍
G 4
H 5
J 6
GY120403.AR2
GY120403.AR3
GY120403.AR4
GY120403.AR5
F
G
H
33
The figure shows a circle. m∠RPQ ⴔ 50ⴗ
and m∠PRQ ⴔ 60ⴗ.
GY100419
墌
R
C
L
J
60°
ArtCodes
GY100419.AR1
P
GY120403.AR1
50°
Q
៣
What is the measure of PR?
70⬚
B 100⬚
C 120⬚
D 140⬚ 墍
A
2004 Commonwealth of Virginia Department of Education
12
墍
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35
36
GY120213
墌
C
A tepee in the shape of a right cone
has a slant height of 18.5 feet and a
diameter of 20 feet. Approximately how
much canvas would be needed to cover
the tepee?
GY130510
墍
581 sq ft 墍
G 116 sq ft
H 89 sq ft
J 58 sq ft
F
ArtCodes
GY120213.AR1
C
Which piece completes this cube?
37
ArtCodes
A
The Great Pyramid at Giza has a
square base with sides of length
230 meters and a height of 146.7
meters. Approximately what is the
volume of the Great Pyramid?
1,650,000
2,590,000
C 4,950,000
D 7,760,000
A
GY120213.AR2
GY120213.AR3
GY120213.AR4
GY120213.AR5
B
GY130526
墍
C
3
m
m3 墍
m3
m3
B
38
The ratio of the circumference of two
3
circles is . The radius of the smaller
2
circle is 8 inches. What is the radius of
the larger circle?
1
F 5 inches
3
G 6 inches
C
D
墍
2004 Commonwealth of Virginia Department of Education
13
H
9 inches
J
12 inches 墍
GY14BR13
墍
C
L
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39
GY14AR54
墌
C
Two ships leaving the same marina at
the same time are 3.2 miles apart after
sailing 2.5 hours. If they continue at
the same rate and direction, how far
apart will they be 2 hours later?
2.56
B 3.52
C 5.76
D 6.08
A
40
y
41
A
GY02C407
墍
A'
C
B
mi
mi
mi 墍
mi
C'
ArtCodes
C
GY02C407.AR1
B'
x
⌬XYZ was obtained from ⌬ABC by a
rotation about the point P.
GY02C513
墌
A
Triangle AⴕBⴕCⴕ is apparently —
C
C
B
ArtCodes
P
a translation of triangle ABC across the
x-axis
B a 90⬚ clockwise rotation of triangle ABC
about the origin 墍
C a reflection of triangle ABC across the
y-axis
D a reflection of triangle ABC across the
x-axis
A
Z
X
GY02C513.AR1
Y
Which of the following indicates the
correspondence of the vertices?
A
G A
H A
J A
F
→
→
→
→
X, B → Y, C → Z
Y, B → Z, C → X 墍
X, B → Z, C → Y
Z, B → X, C → Y
2004 Commonwealth of Virginia Department of Education
14
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y
42
y
43
5
GY02A730
4
C
3
墌
GY02B103
墍
C
2
ArtCodes
GY02A730.AR1
ArtCodes
x
1
-5 -4 -3 -2 -1 0
-1
1
2
3
4
5
x
-2
-3
-4
-5
This figure is apparently symmetric
with respect to —
What is most likely the slope of the line
graphed above?
F
1
墍
3
G
2
3
H
2
J
3
2004 Commonwealth of Virginia Department of Education
the x-axis only
B the y-axis only 墍
C both the x-axis and the y-axis
D neither the x-axis nor the y-axis
A
15
GY02B103.AR1
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y
44
45
The distance between the points
(ⴑ2, ⴑ4) and (3, 8) is —
B
5
GY02A502
墌
C
L
A
ArtCodes
4
A
3
B
13 墍
C 17
D 169
2
GY02A502.AR1
1
-5
-4
-3
-2
-1
O
-1
1
2
3
C4
5
x
-2
D
-3
-4
-5
What are the apparent coordinates of
the midpoint of diagonal AC?
F
G
H
J
冉 冊
冉 冊
冉 冊
1 ⫺
, 1
2
1
,1 墍
2
1,
公17
1
2
(1, 1)
2004 Commonwealth of Virginia Department of Education
16
GY02A575
墍
C
L
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Answer Key
Test
Sequence
Number
Correct
Answer
Reporting
Category
Reporting Category Description
1
B
001
Lines and Angles
2
J
001
Lines and Angles
3
A
001
Lines and Angles
4
J
001
Lines and Angles
5
B
001
Lines and Angles
6
G
001
Lines and Angles
7
B
001
Lines and Angles
8
J
001
Lines and Angles
9
C
001
Lines and Angles
10
H
001
Lines and Angles
11
B
001
Lines and Angles
12
F
002
Triangles and Logic
13
B
002
Triangles and Logic
14
F
002
Triangles and Logic
15
B
002
Triangles and Logic
16
F
002
Triangles and Logic
17
B
002
Triangles and Logic
18
F
002
Triangles and Logic
19
C
002
Triangles and Logic
20
H
002
Triangles and Logic
21
C
002
Triangles and Logic
22
F
002
Triangles and Logic
23
C
002
Triangles and Logic
24
F
003
Polygons and Circles
25
A
003
Polygons and Circles
26
J
003
Polygons and Circles
27
D
003
Polygons and Circles
28
G
003
Polygons and Circles
29
C
003
Polygons and Circles
30
J
003
Polygons and Circles
31
D
003
Polygons and Circles
32
F
003
Polygons and Circles
33
D
003
Polygons and Circles
34
H
004
Three-Dimensional Figures
35
D
004
Three-Dimensional Figures
36
F
004
Three-Dimensional Figures
37
B
004
Three-Dimensional Figures
38
J
004
Three-Dimensional Figures
39
C
004
Three-Dimensional Figures
40
G
005
Coordinate Relations and Transformations
41
B
005
Coordinate Relations and Transformations
42
F
005
Coordinate Relations and Transformations
43
B
005
Coordinate Relations and Transformations
44
G
005
Coordinate Relations and Transformations
45
B
005
Coordinate Relations and Transformations