Spring 2008 Released Test. END OF ... than an original SOL EOC Geometry test.
Property of the ... Then fill in the circle on your answer document for the answer
you have chosen. SAMPLE. If is similar to ..... Answer Key-EOC021-M0118 ...
VIRGINIA STANDARDS OF LEARNING Spring 2008 Released Test
END OF COURSE GEOMETRY Form M0118, 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 ©2008 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. Then fill in the circle 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
3
1
Lines l and m are cut by transversal n.
n 1 2 3 4 5 6 7 8
Which statement would prove l m ? A B C D
m∠ 2 = m∠ 6 m∠ 2 = m∠ 3 m∠ 7 + m∠ 8 = 180° m∠ 3 + m∠ 5 = 90°
4
l m
2
Z
l
X W
U V
Which point is on the line ⊥ to l and passing through Z ? F G H J
U V W X
5
3
In this figure, two lines are cut by a transversal. Which type of angles are ∠ 1 and ∠ 2 ?
1
2
A B C D
4
Vertical angles Corresponding angles Alternate interior angles Same-side interior angles
Sally is using strings to mark parallel rows for a vegetable garden behind her house.
2 1
se
u Ho
If the measure of ∠1 is 115°, what should be the measure of ∠2 ? F G H J
25° 65° 75° 115° 6
5
Line p is a transversal.
r
s
q
p
t 105°
105° 75°
85°
For lines q, r, s, and t, which is not parallel to the other three? A B C D
q r s t
7
6
Lines l, m, and n are intersected by transversal t. The measures of some of the angles that are formed are shown.
t
132°
l
46°
m 48°
n
Which of the following statements about lines l, m, and n must be true? F G H J
lmn l m only l n only m n only
8
7
Transversal t intersects lines k and j as shown.
t
1 2 3 4 5
k j
Which of the following relationships makes j k ? A B C D
∠2 ≅ ∠3 ∠1 ≅ ∠ 3 ∠ 4 and ∠ 5 are supplementary ∠ 3 and ∠ 4 are supplementary
8
Which of the following constructions is illustrated? F G H J
An angle congruent to a given angle The bisector of a given angle The bisector of a given segment The perpendicular bisector of a given segment
9
9
This is a regular polygon.
y
What are the values of x and y ? A
78°, 102°
B
72°, 108°
C
60°, 120°
D
45°, 135°
10
x
10
F
E B
C
A
D Which line segment is apparently congruent to AB ? F
AD
G
AC
H
AE
J
AF
11
11
1 2 3 4 5 6 7 8
m
n
Which statement would not prove line m parallel to line n ? A B C D
12
∠7 ≅ ∠6 ∠1 ≅ ∠ 5 ∠ 4 ≅ ∠5 ∠3 ≅ ∠ 6
What is the converse of the following statement?
If Joe goes fishing, then he needs bait. F G H J
If If If If
he needs bait, then Joe goes fishing. Joe does not go fishing, then he does not need bait. he does not need bait, then Joe does not go fishing. Joe goes fishing, then he does not need bait.
12
13
14
In which group of statements is the conclusion not justified by the previous pair of statements? A
All cooks work in the kitchen. Mary is a cook. Mary works in the kitchen.
B
All dinosaurs are extinct. A triceratops is a dinosaur. All triceratops are extinct.
C
All squares are rectangles. All rectangles are parallelograms. All squares are parallelograms.
D
All fish live in the water. Some snakes live in the water. Some snakes are fish.
Let p represent
x2 = 21, and let q represent
x is not a whole number. Which is a representation of the statement below?
If x is a whole number, then x2 ≠ 21. F G H J
∼ p→∼ q ∼ p→q p→∼ q ∼ q →∼ p
13
15
Which pipe lengths could be joined to form a triangle? A B C D
16
15 ft, 13 ft, 40 ft, 19 ft,
6 ft, 5 ft 12 ft, 5 ft 20 ft, 10 ft 16 ft, 2 ft
Joseph is standing 12 feet from a mirror lying on the ground, and his eyes are 5 feet above the ground.
1 12 ft
2 264 ft
The line-of-sight reflection on the mirror makes ∠1 congruent to ∠2 . If the building is 264 feet from the mirror, which is closest to the height of the building? F G H J
100 110 130 145
ft ft ft ft
14
17 14
A
C D 4
F
7
B
E
9
In addition to the information given in the drawing, which statement would be sufficient to prove that ABC ∼ DEF ? A B
BC 1 = AC 2 BC 9 = AC 4
C
AC = 18 and BC = 8
D
AC = 8 and BC = 18
15
18
Q 12
15
R 19
P
Which lists the angles of the triangle in order from least to greatest?
19
F G H
∠ R, ∠ Q , ∠ P ∠ Q, ∠ P, ∠ R ∠ P , ∠ R, ∠ Q
J
∠ P, ∠ Q, ∠ R
Jennifer made these measurements on
ABC.
BC must be —
B
10 in.
A A B C D
60°
50° 12 in.
less than 10 inches between 10 and 12 inches between 12 and 22 inches greater than 22 inches 16
C
20
Plants Flowering Roses Plants
Bushes
According to the diagram, which is true? F G H J
No bushes are flowering plants. No roses are bushes. Some roses are not flowering plants. Some flowering plants are bushes.
21
T 8
8 6
S
U
What is the length of SU ? A B C D
2 7 cm 7 cm 4 7 cm 20 cm
17
22 45° 45° 4
z
What is the value of z ?
23
F
2 2
G
2 3
H
4 2
J
8 2
From a point 12 feet from the base of a building, the angle of elevation from the ground to the top of the building is 70°.
sin 70° ≈ 0.940 cos 70° ≈ 0.342 tan 70° ≈ 2.75 70° 12 ft
Which is closest to the height of the building? A B C D
24 33 35 41
ft ft ft ft
18
24
B
A E
D
C F
ABCD and DECF are both squares. If AC = 28 millimeters, what is the perimeter of DECF ? F G H J
25
14 28 42 56
mm mm mm mm
The opposite sides of a window frame are congruent.
A
B
D
C Window Frame
Which additional piece of information would verify that the frame is a rectangle? A
∠B ≅ ∠D
B
AC ≅ BD
C
AC ⊥ BD
D
m∠ A + m∠ D = 180° 19
26
y W
X
(-2, 6)
(6, 6)
Y
Z (1, 1)
(9, 1)
x
In parallelogram WXYZ, what are the coordinates of the point of intersection of WY and ZX ? F G H J
27
(2.5, 2.5) (7.5, 3.5) (5.5, 3.5) (3.5, 3.5)
The pentagon has the angle measures shown.
x 110°
92°
104° 152°
What is m∠ x ? A B C D
82° 92° 108° 112° 20
28
For a regular polygon with three sides, each interior angle has a measure of — F G H J
29
180° 60° 45° 30°
Each interior angle of a regular polygon measures 156°. How many sides does the polygon have? A B C D
13 14 15 16
21
30
10
O
The area of the shaded sector of circle O is — F G H J
31
5π 20π 25π 50π
If ABCD is a parallelogram and x = 5, what is m∠ D ?
B
A
(4x)°
(8x)°
D A
100°
B
120°
C
140°
D
160°
22
C
32
Given: B. 154°
A D
46°
B
C 160° What is the m∠ ADC ? F G H J
23° 46° 77° 80°
23
33
The following drawing represents a tetrahedron.
Tetrahedron 4 Faces Which of the following nets could be folded on the dashed lines to form a tetrahedron?
A
B
C
D
24
34
When folded on the dotted lines, which net will not form a rectangular prism?
F
G
H
J
25
35
A concrete pillar shaped as a rectangular prism is designed as follows.
9.5 m
1.5 m
1.5 m
Which is closest to the volume of concrete needed to fill the pillar? A B C D
36
12.5 m3 14.3 m3 21.4 m3 28.5 m3
A right triangular pyramid has a height of 10 inches and a base area of 41.57 square inches. What is the volume, in cubic inches, of the pyramid? F G H J
138.56 207.85 277.13 415.69
26
37
The surface area of a plastic ball is 196π. A sponge ball has a radius twice that of the plastic ball. What is the surface area of the sponge ball? A B C D
38
9,604 π 993π 784π 546π
A rectangular place mat is similar to the table upon which it is placed.
l
48 in.
24 in. 12 in.
According to the diagram, which proportion can be used to determine the length of the table, l ? F
12 24 = 48 l
G
l 12 = 24 48
H J
12
l
=
24 48
12l = 48
27
39
q 5
r
K
4 3 2 1
M -5 -4 -3 -2 -1
L O -1
1
-2 -3 -4 -5
2
3
4
5
s
t
Which is most likely a line of symmetry for triangle KLM ? A B C D
40
q r s t
The diameter of a circle has endpoints ( − 3, 2) and (3, − 2). Which is closest to the length of the diameter of the circle? F G H J
1.4 3.2 7.2 10.0
28
41
Janelle is looking at plate designs. Which design has exactly 4 lines of symmetry?
A
B
C
D
29
42
In the design, a hexagon is inscribed in a circle.
V
Q
R
U
T
S
Which point shows the location of Point Q after a 240° clockwise rotation around the center? F G H J
S T U V
30
43
y 5 4 3
R S -5 -4 -3 -2 -1
2 1 0 -1
1
2
3
4
5
x
-2 -3 -4 -5 What are the most likely coordinates of R′ if R′ S ′ is a reflection of RS across the y-axis? A B C D
44
(4, 3) (− 4, − 3) ( 4, − 3) (3, 4 )
A line segment has an endpoint at (3, 2). If the midpoint of the line segment is (6 , − 2) , what are the coordinates of the point at the other end of the line segment? F G H J
( 4.5, 0) (0, 6 ) ( 9, 4 ) ( 9, − 6 )
31
Answer Key-EOC021-M0118 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 A H B G C H D G B F A F D J B G D H B J C H B J B J A G C H B F D J C F C F A H D H A J
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: 000 176 211 233 248 261 272 281 289 297 304 311 317 323 329 335 340 345 350 355 360 365 370 375 380 385 390 395 400 406 411 417 422 428 435 441 448 456 465 474 485 497 513 534 570 600
