GEOMETRY ... reproduce any portion of these released tests for non-commercial
educational purposes without requesting permission. ... Directions. Read each
question and choose the best answer. SAMPLE ..... Answer Key-EOC021-M0110
...
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 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
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.
