2010 SOL Geometry Released Test

VIRGINIA STANDARDS OF LEARNING
Spring 2010 Released Test
END OF COURSE
GEOMETRY
Form M0110, CORE 1
Property of the Virginia Department of Education
Copyright ©2010 by the Commonwealth of Virginia, Department of Education, P.O. Box 2120, Richmond, Virginia
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All others should direct their written requests to the Virginia Department of Education, Division of Student Assessment
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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
A bisector of AB contains which line segment?
E
C
D
A
B
F
A
CG
B
DF
C
DG
D
EF
4
G
2
Lines m and r are cut by a transversal.
m
(3x – 35)°
(7x – 115)°
r
What value of x will show that line m is parallel to line r ?
F
G
H
J
20
24
25
33
3
a
b
120º
xº
115º
c
d
If lines a and b are parallel, what is the value of x ?
A
B
C
D
120
115
65
60
5
4
Which point lies on the bisector of angle PQR ?
P
W
X
Y
Z
Q
R
F
G
H
J
5
W
X
Y
Z
For what measure of ∠ D is AB DC in this figure?
C
A
85°
E
26°
D
B
A
B
C
D
26°
59°
69°
95°
6
6
B
A
D
E
C
R
P
Q
Which line segment is congruent to BC ?
F
PQ
G
PR
H
PS
J
PT
7
T
S
7
In the figure shown, line q is a transversal of parallel lines l, m, n, and p.
q
l
x°
m
30°
n
y°
What are the values of x and y ?
A
B
C
D
x = 30, y = 30
x = 30, y = 150
x = 150, y = 30
x = 150, y = 150
8
p
8
In the figure shown, parallel lines j and k are cut by transversal m.
j
k
m
1
32°
What is m∠1 ?
F
G
H
J
32°
58°
122°
148°
9
9
Lines y and z are cut by a transversal.
77°
y
x°
For what value of x is y z ?
A
B
C
D
13
77
103
154
10
z
10
In this figure, m∠1 = (15 x − 5)° and m∠2 = (10 x + 35)°.
1
2
What is m∠1 ?
F
G
H
J
11
31°
65°
85°
115°
This figure represents line segments painted on a parking lot to create
parking spaces.
x ° w ° 118 °
Which equation can be used to show that these line segments are parallel?
A
B
C
D
118 − w = x
118 − x = w
x + 118 = 180
w + 118 = 180
11
12
Given:
ABC ∼ LMN
A
5
B
x+5
x+4
L
C
10
3x + 3
M
3x + 1
N
What is the length of AC ?
F
G
H
J
13
11
12
22
24
Given the following measures of the sides of triangles, which is a
right triangle?
A
B
C
D
41
45
52
45
cm, 40 cm, 9 cm
ft, 40 ft, 35 ft
in., 50 in., 11 in.
yd, 35 yd, 25 yd
12
14
Quadrilaterals
Rectangles
Rhombi
Which of the following statements must be true about this Venn diagram?
F
G
H
J
All rectangles are rhombi.
Some rhombi are rectangles.
Quadrilaterals are not rhombi or rectangles.
All quadrilaterals are rhombi and rectangles.
13
15
Given: In this figure, AC and BD bisect each other.
A
B
E
D
C
Based on the information given, which triangle congruence theorem could be
used to prove AED ≅ CEB ?
A
B
C
D
16
Angle-Angle-Side (AAS)
Angle-Side-Angle (ASA)
Side-Angle-Side (SAS)
Side-Side-Side (SSS)
Statement: If lines are skew, then they are not coplanar.
What is the contrapositive of the statement?
F
G
H
J
If
If
If
If
lines
lines
lines
lines
are
are
are
are
not coplanar, then they are skew.
not skew, then they are coplanar.
coplanar, then they are not skew.
skew, then they are coplanar.
14
17
Coordinates A(2, 5), B(6 , 4), and C (6 , 0) are connected to form
ABC.
y
6
A
5
B
4
3
2
1
C
O
If
A
B
C
D
1
2
3
4
5
6
7
x
CDA is congruent to ABC , what are the coordinates of D ?
(1, 1)
(1, 2)
(2, 2)
(2, 1)
15
18
Let p = An equation is of the form y = mx + b.
Let q = Its graph is a line.
Argument:
If an equation is of the form y = mx + b, then its graph is a line.
The graph is not a line.
Therefore, the equation is not of the form y = mx + b.
Which of the following is the symbolic representation of the given argument?
F
p→q
∼q
∴∼ p
G
p→q
q
∴ p
H
p→q
∼p
∴∼q
J
p→q
p
∴q
16
19
TRG is a right triangle.
R
T
17
22
G
Which is closest to the length of RT ?
A
B
C
5
11
14
D
28
17
20
A
75°
50°
55°
B
Which list has the sides of
21
F
BC , AC , AB
G
AB, AC , BC
H
AC , AB, BC
J
BC , AB, AC
C
ABC ordered from longest to shortest?
Three survey markers are located on a map at points H, I, and J. A triangle is
formed by connecting these markers by string so that HI = 150 feet ,
HJ = 245 feet , and IJ = 365 feet .
Which statement is true about the measures of the angles of HIJ ?
A
B
C
D
m∠ H is the smallest
m∠ H is the largest
m∠ I is the smallest
m∠ I is the largest
18
22
x
6
45°
In the figure, what is the value of x ?
23
F
6
G
6 2
H
6 3
J
12
Two sides of a triangle measure 14 inches and 8 inches. Which cannot be the
length of the remaining side?
A
B
C
D
6 in.
8 in.
14 in.
21 in.
19
24
A
60°
C
160°
B
In the circle, what is the measure of ∠ ABC ?
F
G
H
J
25
30°
60°
120°
140°
This figure shows a pattern of triangles and regular hexagons.
x°
What is the value of x ?
A
B
C
D
30
60
90
120
20
26
Which figure has all sides of equal measure but not necessarily all angles of
equal measure?
F
G
H
J
27
Square
Rectangle
Rhombus
Trapezoid
What is m∠ DAR in circle A ?
R
B
A
34°
D
A
B
C
D
17°
34°
56°
68°
21
28
Two chords intersect with the measures shown in the drawing.
5
7.5
x
12
What is the value of x ?
F
G
H
J
29
8.0
9.5
10.0
14.5
In rectangle ABCD, the slope of AB is
A
B
−
2
−
1
2
C
1
2
D
2
22
1
. What is the slope of CD ?
2
30
In the figure shown, what is m∠WXY ?
Y
62°
73°
Z
F
G
H
J
31
X
W
45°
107°
120°
135°
DEFG is a rhombus with m∠ EFG = 28°.
E
D
F
G
What is m∠ GDE ?
A
B
C
D
14º
28º
30º
56º
23
32
This figure is a traffic sign in the shape of a regular octagon.
STOP
x°
What is the value of x ?
F
G
H
J
33
45
60
135
180
A rectangular rug is 24 feet long and 10 feet wide. A rhombus design is
formed inside the rug by joining the midpoints of each side of the rectangle.
What is the length of each side of the rhombus?
A
B
C
D
13 ft
26 ft
169 ft
240 ft
24
34
A man who is 6 feet tall casts a shadow that is 4 feet long. At the same time,
a nearby flagpole casts a shadow that is 18 feet long. How tall is the flagpole?
F
G
H
J
35
10
12
22
27
ft
ft
ft
ft
A fish tank in the shape of a rectangular prism has these dimensions:
•
•
•
length = 20 inches
width = 10 inches
height = 12 inches
What is the volume of water in the tank when it is
A
B
C
D
1,120
1,920
2,400
3,000
cu
cu
cu
cu
in.
in.
in.
in.
25
4
full?
5
36
Which of these nets would form a cube when folded?
F
G
H
J
37
If a cube with side length 6 inches has its dimensions divided in half, what
will be the volume of the new cube?
A
B
C
D
108 cubic inches
54 cubic inches
27 cubic inches
9 cubic inches
26
38
A right cone is placed on its circular base.
Bottom
Which statement about the cone is incorrect ?
39
F
G
The view from the front is a triangle.
The view from the bottom is a circle.
H
J
The view from the top is a circle.
The view from the left is a rhombus.
A cone has a slant height of 10 centimeters and a lateral area of 60π square
centimeters. What is the volume of a sphere with a radius equal to that of
the cone?
A
B
C
D
102π cm3
144π cm3
288π cm3
1,333π cm3
27
40
Which line of reflection maps point K at (−2 , 2) to point K ′ at (2 , −2) ?
F
G
H
J
41
y=2
y=x
x-axis
y-axis
If the coordinates of A are (1, 1) and the midpoint of AB is ( −2 , 0), then the
coordinates of B are —
A
B
C
D
( − 0.5, 0.5)
(0.5, 0.5)
( −1, 0)
( − 5, −1)
28
42
Which transformation could move the triangle P to triangle P ′ in a
single step?
y
8
7
6
5
4
3
2
O
F
Reflection over x = 4
G
Rotation about (2, 3)
H
Reflection over y = 4
J
Translation
P'
P
1
1
2
3
4
5
29
6
7
8
x
43
Figure STARFIND is symmetric with respect to the x-axis. The coordinates of
point A are (8 , 6). What are the coordinates of point N ?
y
A
S
T
R
D
I
N
A
B
C
D
(8, − 6 )
(6, − 8 )
(− 6, 8 )
(− 8, 6 )
30
F x
44
Parallelogram RSTV has coordinates R(0 , 0), S(2 , 4), T (6 , 0), and V (4 , − 4).
Which ordered pair represents the intersection of the diagonals of
this parallelogram? (The coordinate grid may be used to help answer
this question.)
y
9
8
7
6
5
4
3
2
1
-9 -8 -7 -6 -5 -4 -3 -2 -1 O
-1
-2
1
-3
-4
-5
-6
-7
-8
-9
F
(2, 0)
G
(3, 0)
H
(3, 1)
J
( 4, −1)
31
2
3
4
5
6
7
8
9
x
45
A regular quadrilateral has what type of symmetry?
A
B
C
D
Line symmetry only
Point symmetry only
Both point and line symmetry
Neither point nor line symmetry
32
Answer Key-EOC021-M0110
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
45
Correct Answer
D
F
D
H
C
G
B
F
B
J
D
G
A
G
C
H
D
F
C
J
B
G
A
F
A
H
D
F
C
J
B
F
A
J
B
F
C
J
C
G
D
J
A
G
C
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
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
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
177
213
234
250
263
274
284
292
300
307
314
320
326
332
338
343
348
353
358
363
368
373
378
383
388
392
397
402
408
413
418
424
430
436
442
449
457
465
474
485
497
513
534
569
600
A total raw score (left
column) is converted to
a total scaled score
(right column). The total
scaled score may range
from 0 to 600.
A scaled score of 400 or
more means the student
passed the SOL test,
while a scaled score of
399 or less means the
student did not pass the
test. A scaled score of
500 or more indicates
the student passed the
SOL test at an
advanced level.