Download Spring 2007 Geometry

VIRGINIA STANDARDS OF LEARNING
Spring 2007 Released Test
END OF COURSE
GEOMETRY
Form M0117, CORE 1
Property of the Virginia Department of Education
©2007 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].
ISD6736
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 carefully and choose the best answer. Then mark the space on your answer
document for the answer you have chosen.
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
5
1
Transversal l cuts lines a, b, c, and d.
l
75°
a
85°
b
c
105°
100°
d
Which two lines are parallel?
A
B
C
D
a
a
b
b
and
and
and
and
c
d
c
d
6
2
1 2
3 4
5 6
7 8
In the figure above, ∠2 and ∠6 are a pair of —
F
G
H
J
3
consecutive interior angles
alternate interior angles
vertical angles
corresponding angles
One exterior angle of a regular polygon measures 72°. What is the measure of
one interior angle?
A
18°
B
108°
C
360°
D
540°
7
4
In this drawing, a b and c d .
b
a
1 2
5 6
9 10
13 14
3 4
7 8
11 12
c
d
15 16
Which angle is not necessarily congruent to ∠1?
F
∠3
G
∠9
H
∠12
J
∠16
8
5
The support legs on a bench are attached in such a way that the angle made
by one leg with the ground is 130°.
x
130°
What must the measure of the angle marked x be in order for the seat of the
bench to be parallel to the ground?
A
50°
B
65°
C
90°
D
130°
9
6
Line v is a transversal.
v
70°
w
x
y
80°
110°
z
100°
Which is a true statement?
F
w y and x z
G
w x and y z
H
w z and x y
J
w x and x y
10
7
1
5
2
3 4
6
7 8
9 10
11 12
13 14
15 16
o
l
m
n
In the drawing above, ∠ 4 and ∠12 are —
A
B
C
D
8
alternate interior angles
consecutive interior angles
corresponding angles
a linear pair
A carpenter nailed a board across two beams, forming the angles shown.
6
2
5
1
3
4
Which equal measures would ensure the beams are parallel?
F
G
H
J
m ∠1 = m ∠ 2
m ∠1 = m ∠ 3
m∠2 = m∠5
m∠3 = m∠ 4
11
9
C
A
B
K
L
N
M
R
Which segment is congruent to AB ?
A
CK
B
CL
C
CM
D
CN
12
10
W
Y
Z
X
l
A
Which point apparently lies on the perpendicular to l from A?
F
G
H
J
X
Y
Z
W
13
11
One piece of pie is left for two boys to share.
X
W
Y
Z
C
Where should the pie be cut to ensure each gets an equal piece?
A
CZ
B
CY
C
CX
D
CW
14
12
13
If p → q , and q → r , then —
F
r →p
G
p →r
H
∼r → p
J
r →∼p
If the conditional statement
“If you have a laptop, then you have a computer”
is represented by p → q , what is the symbolic representation of
“If you have a computer, then you do not have a laptop”?
A
B
C
D
q →∼p
∼q →p
p →∼q
∼q →∼p
15
14
In the Venn diagram below, V represents the set of all vehicles, M represents
the set of all motorized vehicles, and A represents the set of all automobiles.
V
M
A
Based on the diagram, which is a valid conclusion?
F
G
H
J
All automobiles are motorized vehicles.
All motorized vehicles are automobiles.
Some automobiles are not motorized vehicles.
No automobiles are motorized vehicles.
16
15
Which triangle below is not congruent to the other three triangles?
70°
A
9
B
9
70°
C
9
D
9
17
16
N
K
12
L
8
M
I
12
10
J
Which additional piece of information would prove that IJK ∼LMN ?
F
NM = 18
G
LM = 18
H
NM = 15
J
LM = 10
18
17
Given: M is the midpoint of LN and KP .
K
N
M
J
O
L
P
The given information is sufficient to prove
postulate/theorem?
A
B
C
D
18
KML ≅ PMN
by which
Angle-Side-Angle
Side-Side-Side
Side-Angle-Side
Angle-Angle-Side
Which of the following could not be the lengths of the sides of a triangle?
F
G
H
J
6
3
4
5
ft, 3 ft, 9 ft
cm, 4 cm, 5 cm
in., 6 in., 8 in.
km, 2 km, 4 km
19
19
20
In DEF , mDE = 8 inches , mEF = 6 inches , and mDF = 10 inches. Which lists the
angles in order from smallest to largest ?
A
∠D , ∠E , ∠F
B
∠F , ∠D , ∠E
C
∠E , ∠F , ∠D
D
∠D , ∠F , ∠E
In ABC , if m∠C < m∠B < m∠A , then —
F
AB < AC < BC
G
AC < AB < BC
H
AB < BC < CA
J
BC < AB < CA
20
21
To mark the end of a race, a finish-line banner is stretched across the road as
shown in the drawing.
Finish Line
x
7 ft
8 ft
Which is closest to the length of the support rope designated by x in the
drawing?
A
B
C
D
9.5 ft
10.6 ft
12.0 ft
15.0 ft
21
22
A baseball diamond is in the shape of a square, 90 feet on a side.
2nd Base
90 ft
90 ft
3rd Base
1st Base
90 ft
90 ft
Home
What is the direct distance from home plate to second base?
F
90 ft
G
90 2 ft
H
90 3 ft
J
180 ft
22
23
What is the length of a diagonal brace that could be used for a wall 9 feet
high and 12 feet long?
A
B
C
D
12
13
14
15
ft
ft
ft
ft
23
24
Gene’s horse corral, labeled ABCD in the drawing, is shaped as a
parallelogram and is adjacent to the shed, labeled ZAD.
A
Z
B
Shed
Corral
F
40°
D
C
G
If a gate, labeled CF, opens all the way to the corral fence, position labeled
CG, through how many degrees does the gate swing?
F
G
H
J
25
40°
50°
130°
140°
A diagonal of parallelogram DEFG forms angles with measures as shown.
D
E
56°
44°
G
F
What is the measure of ∠DEF ?
A
B
C
D
44°
56°
80°
100°
24
26
y
9
8
7
6
5
M
4
3
2
N
1
–9 –8 –7 –6 –5 –4 –3 –2 –1 0
–1
O
1
2
3
4
5
6
7
8
9
x
–2
–3
–4
–5
–6
–7
–8
–9
Quadrilateral MNOP is a parallelogram. The coordinates of three of its vertices
( ) ( )
are M 1, 5 , N 2 ,1 , and O
value of x ?
F
−
5
G
−
4
H
−
3
J
0
(
−
) ( )
3, − 2 . If x , 2 are the coordinates of P, what is the
25
27
Rectangular flowerbeds are built on each side of a fishpond in the shape of a
regular octagon.
x
What is the measure of the angle, x, between two consecutive flowerbeds?
A
30°
B
45°
C
60°
D
90°
28
24°
A portion of a regular polygon is shown. The polygon has —
F
G
H
15 sides
16 sides
18 sides
J
20 sides
26
29
Each interior angle of a regular polygon has a measure of 162°. The polygon
has a total of —
A
B
C
D
30
17
18
19
20
sides
sides
sides
sides
is 280º.
In circle O, the degree measure of PSR
P
S
R
O
What is the degree measure of ∠ POR ?
F
G
H
J
160°
85°
80°
40°
27
31
A
B
26
20
2x + 6
D
40
What is the value of x in trapezoid ABCD ?
A
B
C
D
17
13
10
7
28
C
32
In circle C , m W
X = 25°, m XY = 40°, m YZ
= 25°, and WY = 24 centimeters.
Y
X
W
Z
C
What is the length of XZ ?
F
G
H
J
33
12
24
25
65
cm
cm
cm
cm
A pizza has a diameter of 16 inches. Which is closest to the area of one slice if
the pizza is divided into 6 equal pieces?
A
B
C
D
134.1 sq in.
117.1 sq in.
67.2 sq in.
33.5 sq in.
29
34
Assuming the solid is constructed from cubes measuring 1 unit on each edge
and that the figure is completely solid, what is the volume of the cubic solid
shown above?
F
G
H
J
12
34
59
68
cubic
cubic
cubic
cubic
units
units
units
units
30
35
Which could not be a two-dimensional view of the block of cubes shown
above?
A
B
C
D
36
Which is closest to the volume of a sphere with a radius equal to
8 centimeters?
F
G
H
J
267.9 cm3
803.8 cm3
1,607.7 cm3
2,143.6 cm3
31
37
What is the total surface area of a rectangular prism box that measures 5 feet
by 1 foot by 1 foot?
A
B
C
D
5 sq ft
20 sq ft
22 sq ft
30 sq ft
38
S
P3
0m
28 m
Blue
Lake
R
Q
10
5m
T
If PQ is parallel to ST, what is ST, the width of the lake?
F
G
H
J
62
70
84
98
meters
meters
meters
meters
32
39
The ratio of the perimeter of
U
to the perimeter of
y
x
2
V is 1 : 2.
4
V
U
z
5
If the triangles are similar, what is the value of x + y ?
A
B
C
D
3
6
12
18
33
40
Right triangle ABC has the measures shown.
A
5
C
4
3
B
What is the maximum number of different lines of symmetry that can be
drawn through ABC ?
F
G
H
J
0
1
2
3
34
41
y
Q
5
4
3
2
1
-5 -4 -3 -2 -1 O
-1
-2
-3
-4
-5
1 2 3 4 5
V
What is the apparent slope of QV ?
A
B
C
D
−2
–1
2
1
2
2
35
x
42
y
x
0
In relation to one figure, the other figure is apparently a —
F
reflection across the line y = 1
G
reflection across the line y = x
H
90° rotation about the origin
J
180° rotation about the origin
36
43
Triangle ABC is placed on a grid as shown.
y
9
8
7
A
6
5
4
B
3
2
1
-2 -1
C
O
1
2
3
-1
The apparent midpoint of AB is —
A
B
C
D
(1.5, 1.5)
(3, 3)
(4.5, 4.5)
(4.5, 1.5)
37
4
5
6
7
x
44
Rectangle ABCD is placed in a coordinate plane as shown.
y
A
D
9
8
7
6
5
4
3
2
1
-9 -8 -7- 6 - 5 -4 - 3 -2-1 O
-1
-2
B
C
1 2 3 4
x
Which equation describes a line of symmetry for rectangle ABCD ?
F
G
H
J
x
x
y
y
=2
=5
=5
=x
38
45
y=x
y
5
B
4
3
A
C
2
B'
1
–
5
–
4
–
3
–
2
–
C'
1 0
–
1
–
2
–
3
–
4
–
5
1
A'
A ′B ′C ′ is apparently the result of —
A
B
C
D
2
ABC across the y-axis
reflecting ABC across the x-axis
rotating ABC about the point (1, 2)
reflecting ABC across the line y = x
reflecting
39
3
4
5
x
Answer Key-EOC021-M0117
Test Sequence
Number
Correct Answer
1
A
2
J
3
B
4
H
5
A
6
F
7
C
8
G
9
D
10
F
11
C
12
G
13
A
14
F
15
D
16
F
17
C
18
F
19
D
20
F
21
B
22
G
23
D
24
H
25
C
26
G
27
B
28
F
29
D
30
H
31
D
32
G
33
D
34
G
35
C
36
J
37
C
38
J
39
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
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
40
F
005
Coordinate Relations and Transformations
41
B
005
Coordinate Relations and Transformations
42
J
005
Coordinate Relations and Transformations
43
C
005
Coordinate Relations and Transformations
44
H
005
Coordinate Relations and Transformations
45
D
005
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
182
217
238
254
266
277
286
294
302
309
315
321
327
332
338
343
348
353
358
363
368
372
377
382
387
391
396
401
406
411
417
422
428
434
441
448
455
464
473
483
496
512
533
568
600