VA517571_GM Release

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VA517571_GM Release
VIRGINIA STANDARDS OF LEARNING
Spring 2009 Released Test
END OF COURSE
GEOMETRY
Form M0119, CORE 1
This released test contains 1 fewer test item (#1-44 only)
than an original SOL EOC Geometry test.
Property of the Virginia Department of Education
©2009 by the Commonwealth of Virginia, Department of Education, P.O. Box 2120, Richmond, Virginia 23218-2120.
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
reproduce any portion of these released tests for non-commercial educational purposes without requesting permission.
All others should direct their written requests to the Virginia Department of Education, Division of Student Assessment
and School Improvement, at the above address or by e-mail to [email protected]
Geometry Formula Sheet
Geometric Formulas
b1
h
h
b
A=
1
2
h
h
B
b2
bh
A=
1
2
l
V = Bh
L.A. = hp
S.A.= L.A. + 2B
h(b1 + b2 )
V = 13 Bh
L.A.= 12 lp
S.A.= L.A. + B
r
w
r
r
h
l
4
3
A = lw
p = 2(l + w)
b
h
l
h
h
b
A = bh
l
w
V = lwh
S.A.= 2lw + 2lh + 2wh
m
A
Meaning
angle A
Example
AB
measure of angle A
1
3
line segment AB
AB CD
AB
measure of
line segment AB
AB CD
AB
line AB
A
ABC
triangle ABC
A
ABCD
rectangle ABCD
ABCD
parallelogram ABCD
Copyright © 2006 by the Commonwealth of Virginia Department of Education
c2
=
a2
+ b2
Abbreviations
Meaning
vector AB
right angle
AB
b
r
Geometric Symbols
Example
A
c
a
Line AB is parallel to
line CD.
Line AB is perpendicular
to line CD.
B Angle A is congruent to
angle B.
B Triangle A is similar to
triangle B.
Similarly marked
segments are congruent.
Similarly marked angles
are congruent.
V
L.A.
S.A.
Volume
Lateral Area
Total Surface
Area
Area of Base
B
Pi
22
7
Geometry
Directions
Read each question and choose the best answer.
SAMPLE
A
D
E
B
C
If ABC is similar to ADE, then AB : AD = ? : AE. Which replaces the “?” to
make the statement true?
A
B
C
D
AC
AE
DE
BC
3
1
In the figure shown, m∠1 = (4 x + 12)° and m∠2 = (6 x + 8)°.
2
1
What is m∠1 ?
A
B
20°
40°
C
D
50°
76°
4
2
In each of the following figures, transversal c cuts lines a and b. In which
figure are ∠1 and ∠2 corresponding angles?
c
a
1
F
2
b
c
1
a
G
2
b
c
1
a
2
H
b
c
1
J
2
a
b
5
3
The arcs for a compass and straightedge construction are shown below.
M
N
Which construction is apparently being made?
A Two lines parallel to MN
B Two congruent angles
C A segment congruent to MN
D The perpendicular bisector of MN
6
4
y
5
A
4
3
F
2
B
-5 -4 -3 -2 -1
C
1
D
O
-1
1
E
2
3
4
5
x
H
-2
-3
-4 G
-5
Which two segments in the drawing above are most likely parallel?
F
CD and GH
G
CD and AB
H
AB and EF
J
EF and GH
7
5
P
Q
Which segment has a measure equal to
1
(PQ)?
2
A
B
C
D
6
Two lines intersect as shown.
(2 x + 20)°
60°
What is the value of x ?
F
G
H
J
20
40
50
60
8
7
In this figure, transversal e intersects lines a, b, c, and d.
a
e
b
70°
c
d
120°
70°
130°
Which lines must be parallel?
A
B
C
D
8
a and c
b and c
b and d
a and d
In the diagram, m∠1 = (6 x + 12)° and m∠2 = (9 x − 4)°.
1
2
Which is closest to the value of x ?
F
G
H
J
5.3
5.5
11.5
12.5
9
9
In this figure, line t is a transversal of lines m and n.
t
1 2
3 4
5 6
7 8
m
n
Which of the following statements determines that lines m and n are parallel?
A
B
C
D
∠1 ≅ ∠ 4
∠2 ≅ ∠ 7
∠ 3 and ∠ 5 are complementary
∠ 6 and ∠ 8 are supplementary
10
10
For what value of x is line l parallel to line m in this figure?
x°
l
48°
F
G
H
J
11
m
42
48
132
138
Amber constructed BD as shown.
A
D
B
C
Which of the following statements must be true?
A
B
C
D
BA = BC
BD = 2 BA
m∠ ABD = m∠ CBD
m∠ CBD = 2m∠ ABC
11
12
E
J 60° x
5.3
4.1
42°
D 60°6.0
What value of x makes
F
G
H
J
13
K
78°
F
L
DEF ≅ JLK ?
x = 9.4
x = 6.0
x = 5.3
x = 4.1
Mr. Ammons is constructing a walkway through his rectangular garden. The
walkway runs diagonally as shown in the diagram.
Garden
W
alk
wa
y
24 ft
Which is closest to the length of the walkway?
A
B
C
D
18.7
28.3
30.0
39.0
ft
ft
ft
ft
12
15 ft
14
In the triangle shown, GR = 11, BR = 8 , and BG = 7.
B
7
G
8
11
Which statement is true about the angles in
F
G
H
J
15
m∠ R
m∠ G
m∠ R
m∠ G
R
RGB ?
is the greatest
is the greatest
is the least
is the least
Consider the following statement.
If 4 x = 8 , then x = 2.
Which is the inverse of the statement?
A
B
C
D
If x = 2, then 4 x = 8.
If x ≠ 2, then 4 x ≠ 8.
If x = 2, then 4 x ≠ 8.
If 4 x ≠ 8, then x ≠ 2.
13
16
Which drawing contains a pair of similar triangles?
22
11
F
24
12
40
O
G
30
O
13
H
5
12
5
8
J
5
6
14
17
Triangle ABC is an equilateral triangle with side lengths of 10 inches.
A
B
D
C
What is the length, in inches, of AD ?
18
A
5
B
10 3
3
C
5 2
D
5 3
John wants to make a triangular garden. Which of the following are
possible dimensions?
F
G
H
J
4
6
6
8
ft
ft
ft
ft
by
by
by
by
5 ft by 10 ft
6 ft by 12 ft
8 ft by 10 ft
12 ft by 20 ft
15
19
A drawing of Mark’s kite is shown below.
x
12 in.
9 in.
What is the length of the short section of the outer frame indicated by x in
the drawing?
A
B
C
D
16
15
14
13
in.
in.
in.
in.
16
20
Which Venn diagram represents all the following set of statements?
•
•
•
•
Some triangles are acute.
Some triangles are obtuse.
No triangle is both acute and obtuse.
Some acute triangles are equilateral.
F
G
H
J
17
21
B
C
60º
40º
D
Which lists the sides of
A
CD, BD, BC
B
BC , CD, BD
C
BD, CD, BC
D
BC , BD, CD
BCD in order from shortest to longest?
18
22
With the information given in the drawings, which pair of triangles can be
proven congruent by the Side-Angle-Side postulate?
F
G
H
J
19
23
Given:
QRS where m∠ Q = 20° and m∠ S = 90°
R
1,000 meters
Q
S
What is the length, to the nearest meter, of RS ?
A
B
C
D
24
342
364
500
940
m
m
m
m
Which of the following quadrilaterals is not a parallelogram?
F
G
H
J
Rectangle
Rhombus
Square
Trapezoid
20
25
A
B
0)°
+
(6x
–3
x
0
(1
6)°
D
C
In parallelogram ABCD, the measure of ∠ C is —
A
B
C
D
26
82.5°
97.5°
120.0°
130.0°
In the diagram, AB is tangent to the circle at point A, and BD intersects the
circle at points C and D.
A
x
B
4
C
5
D
What is the value of x ?
F
G
H
J
3
4
5
6
21
27
y
A
C
(1, 4)
(7, 4)
B
(4, 1)
x
In the drawing above, what must be the coordinates of D to show ABCD is
a square?
A
B
C
D
(7, 7)
( 4, 7)
( 4, 5)
( 4, 4 )
22
28
C
B
D
A
E
F
Given the polygon shown above, m∠ A + m∠ F + m∠ E + m∠ D + m∠ C + m∠ B =
F
G
360°
540°
H
J
720°
900°
23
29
The circumference of circle C is 144π.
M
A
B
120º
C
What is the length of AMB ?
A
B
C
D
8π
16π
48π
96π
24
30
Rectangle LMNO represents a park that has walking paths LN and MO that
intersect at P. The length of PN is 195 feet, and the length of MN is 360 feet.
What is the length of MO , one of the walking paths?
M
N
P
L
F
G
H
J
31
150
195
360
390
O
ft
ft
ft
ft
What is the measure of ∠ C in quadrilateral ABCD ?
B
124°
A
96°
C
94°
D
A
B
C
D
46°
56°
86°
96°
25
32
A
C
O
In circle O, the degree measure of AC is —
F
G
H
J
33
45°
90°
135°
180°
When tiles are tessellated in a plane, what angle measure sum is required of
the tiles surrounding a single point?
A
B
C
D
90°
180°
360°
720°
26
34
This solid figure is constructed with seven cubes.
Which shape represents the top view of this three-dimensional solid?
F
G
H
J
27
35
Which is closest to the total surface area of a cylinder with a radius of
5 inches and a height that is equal to its diameter?
A
B
C
D
36
314
471
596
785
sq
sq
sq
sq
in.
in.
in.
in.
Which of the following nets could not be folded along the dotted lines to form
a cube?
F
G
H
J
28
37
The radius of Sphere A is 2 inches, and the radius of Sphere B is 4 inches.
How many times larger is the volume of Sphere B compared to the volume of
Sphere A ?
A
B
C
D
38
2
3
4
8
A cylinder has a diameter of 10 inches and a height four times its radius.
What is its volume?
F
G
H
J
500π cu in.
2,000π cu in.
4,000π cu in.
40,000π cu in.
29
39
P(− 3, 5), Q(1, 7), R(8 , 1), and S(− 4 ,−5) are connected to form a trapezoid.
y
8
Q
7
6
P
5
4
3
2
R
1
–
8
–
7
–
6
–
5
–
4
–
3
–
2
–
1 O
–
1
2
3
4
5
6
7
8
x
1
S
–
2
–
3
–
4
–
5
–
6
–
7
–
8
What is the midpoint of SR ?
A
B
C
D
40
(0,
( 4,
(3,
(2,
−
3)
−
1)
−
1.5)
−
2)
A trapezoid is located entirely in quadrant II. If this trapezoid is reflected
across the x-axis, in which quadrant will the new trapezoid be located?
F
G
H
J
I
II
III
IV
30
41
Rectangle ABCD is placed on a grid as shown.
y
5
4
A
D
3
2
1
–
5
–
4
–
3
–
2
–
1 O
–
1
1
2
3
4
5
x
–
2
–
3
B
C
–
4
–
5
Which is closest to the length of diagonal AC ?
A
B
C
D
42
8.0
10.0
11.3
11.7
Which of the following letters has both line symmetry and point symmetry?
S
F
G
H
J
D
M
S
D
M
H
31
H
43
Triangle ABC was transformed into triangle A’B’C’. Which term most
accurately describes this transformation?
y
B
C
9
8
7
6
5
4
3
2
1
A A'
-9 -8 -7 -6 -5 -4 -3 -2 -1 0
-1
-2
-3
-4
-5
-6
-7
-8
-9
A
B
C
D
B'
1
Tessellation
Reflection
Rotation
Translation
32
C'
2 3 4 5 6 7 8 9
x
44
A quadrilateral is placed on a grid as shown.
y
B
5
4
A
3
C
2
1
-5
-4
-3
-2
-1
O
1
-1
-2
-3
-4
-5
D
-6
The apparent midpoint of BD is —
F
G
H
J
( − 0.5, − 0.5)
(0.5, 3.5)
(1.5, 1.5)
(1.5, 2.5)
33
2
3
4
5
x
Answer Key-EOC021-M0119
Test Sequence
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
Correct Answer
B
G
D
F
D
F
A
F
B
H
C
G
B
H
D
F
D
H
B
F
B
F
A
J
C
J
B
H
C
J
A
G
C
H
B
J
D
F
D
H
D
J
B
F
Reporting
Category
001
001
001
001
001
001
001
001
001
001
001
002
002
002
002
002
002
002
002
002
002
002
002
003
003
003
003
003
003
003
003
003
004
004
004
004
004
004
005
005
005
005
005
005
Reporting Category Description
Lines and Angles
Lines and Angles
Lines and Angles
Lines and Angles
Lines and Angles
Lines and Angles
Lines and Angles
Lines and Angles
Lines and Angles
Lines and Angles
Lines and Angles
Triangles and Logic
Triangles and Logic
Triangles and Logic
Triangles and Logic
Triangles and Logic
Triangles and Logic
Triangles and Logic
Triangles and Logic
Triangles and Logic
Triangles and Logic
Triangles and Logic
Triangles and Logic
Polygons and Circles
Polygons and Circles
Polygons and Circles
Polygons and Circles
Polygons and Circles
Polygons and Circles
Polygons and Circles
Polygons and Circles
Polygons and Circles
Three-Dimensional Figures
Three-Dimensional Figures
Three-Dimensional Figures
Three-Dimensional Figures
Three-Dimensional Figures
Three-Dimensional Figures
Coordinate Relations and Transformations
Coordinate Relations and Transformations
Coordinate Relations and Transformations
Coordinate Relations and Transformations
Coordinate Relations and Transformations
Coordinate Relations and Transformations
Geometry, Core 1
If you get this
many items
correct:
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
Then your
converted scale
score is:
000
175
210
231
247
260
271
280
289
296
304
310
317
323
329
334
340
345
351
356
361
366
371
376
381
387
392
397
403
408
414
420
426
432
439
446
454
462
471
481
492
505
522
544
580
600

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