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SESSION: 24 PAGE: 1 5/5/04 13:29 LOGIN IS-glenn PATH: @sunultra1/raid/CLS_tpc/GRP_va_sprg04/JOB_04-ribsg11/DIV_g11geom-1 VIRGINIA STANDARDS OF LEARNING ASSESSMENTS Spring 2004 Released Test END OF COURSE GEOMETRY CORE 1 Property of the Virginia Department of Education 䉷 2004 by the Commonwealth of Virginia Department of Education, James Monroe Building, 101 N. 14th Street, Richmond, Virginia, 23219. 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 photocopy or print any portion of these Released Tests for educational purposes without requesting permission. All others should direct their requests to the Commonwealth of Virginia Department of Education at (804) 225-2102, Division of Assessment and Reporting. SESSION: 23 PAGE: 2 5/4/04 15:40 LOGIN IS-glenn PATH: @sunultra1/raid/CLS_tpc/GRP_va_sprg04/JOB_04-ribsg11/DIV_g11geom-1 Geometry 2 DIRECTIONS X Read and solve each question. Then mark the space on the answer sheet for the best answer. 1 2 l 3 GY040602 墍 C SAMPLE W Y A D GY040602.AR1 If ∠3 ≅ ∠Y, which of the following must be true? E ∠W ≅ ∠Y G WX is perpendicular to XY H ∠W ≅ ∠2 J Line l is parallel to YW 墍 F B C If ⌬ABC is similar to ⌬ADE, then AB : AD ⴔ ? : AE. Which replaces the “?” to make the statement true? AC 墍 B AE C DE D BC A 1 GY030542 墌 A plumber bent a flexible joint into a 136ⴗ angle, as shown. He then attached another pipe so that A, B, and D lay on a straight line. C ArtCodes 136° GY030542.AR1 ArtCodes What is the value of x? 36 B 44 墍 C 46 D 224 A 2004 Commonwealth of Virginia Department of Education 2 SESSION: 23 PAGE: 3 5/4/04 15:40 LOGIN IS-glenn PATH: @sunultra1/raid/CLS_tpc/GRP_va_sprg04/JOB_04-ribsg11/DIV_g11geom-1 3 4 Which pair of angles is supplementary? In the figure, line t is a transversal for lines l and m. GY030576 GY030623 墌 ArtCodes GY030576.AR1 GY030576.AR2 GY030576.AR3 GY030576.AR4 墍 t C L C 墍 A 35° ArtCodes 145° GY030623.AR1 2 1 l m Which of the following best describes the relationship between ∠1 and ∠2? B 35° 55° Alternate interior angles G Consecutive interior angles H Corresponding angles J Alternate exterior angles 墍 F C 25° 75° D 80° 80° 2004 Commonwealth of Virginia Department of Education 3 SESSION: 23 PAGE: 4 5/4/04 15:40 LOGIN IS-glenn PATH: @sunultra1/raid/CLS_tpc/GRP_va_sprg04/JOB_04-ribsg11/DIV_g11geom-1 5 7 Line l intersects lines w, x, y, and z, forming angles with measures as indicated on the drawing. ←→ and QR are parallel and m∠M ⴔ m∠L ⴔ 60ⴗ. GY040407 墌 ←→ In the figure drawn below, LM GY030707 墍 l C 110° ArtCodes C w GY040407.AR1 ArtCodes 65° 75° GY030707.AR1 x y What is m∠QNP? z 90⬚ B 120⬚ 墍 C 150⬚ D 180⬚ A 115° Which two lines are parallel? w and x B x and z 墍 C y and z D w and y A 8 72° x° z° GY040578 墍 l C 6 ArtCodes (4x – 30)° GY040578.AR1 GY040512 墌 w° C m y° (2x)° ArtCodes GY040512.AR1 Which value for x will make a parallel to b? Which additional piece of information would verify l m? 5 G 15 墍 H 20 J 35 F 2004 Commonwealth of Virginia Department of Education x ⫽ 72 G y ⫽ w H z ⫽ 108 J x ⫽ w 墍 F 4 SESSION: 23 PAGE: 5 5/4/04 15:40 LOGIN IS-glenn PATH: @sunultra1/raid/CLS_tpc/GRP_va_sprg04/JOB_04-ribsg11/DIV_g11geom-1 9 11 R S GY110406 墌 GY110404 墍 Q C L C T ArtCodes ArtCodes GY110406.AR1 A The drawing shows the arcs used to construct — B Which point lies on the line perpendicular to AB that bisects AB? a bisector of a given angle B an angle congruent to a given angle 墍 C a bisector of a given line D a perpendicular of a given line at a point on the line A Q B R C S 墍 D T A 10 A B C D P GY110579 墌 C L ArtCodes GY110579.AR1 Q R Which point lies on the bisector of ∠PQR? A G B H C 墍 J D F 2004 Commonwealth of Virginia Department of Education 5 GY110404.AR1 SESSION: 23 PAGE: 6 5/4/04 15:40 LOGIN IS-glenn PATH: @sunultra1/raid/CLS_tpc/GRP_va_sprg04/JOB_04-ribsg11/DIV_g11geom-1 12 GY01D602 墌 13 Consider the following arguments. If the first two statements are true, in which argument is the 3rd statement an incorrect conclusion? Pet Owners cat owners fish owners C F G 墍 C L Based strictly on this diagram, which is a valid conclusion? No B No C No D No A 1 If it rains, then we will stay inside. 2 If we stay inside, then we will play games. 3 If it rains, then we will play games. cat owners also own dogs. dog owners also own fish. 墍 fish owners also own cats. pet owner owns more than one pet. Consider the following statements. p: The sum of two angles is 90ⴗ. q: The two angles are complements. 1 If we win the game, then we will win the championship. 2 If we win the championship, then we will get a trophy. 3 If we do not get a trophy, then we did not win the game. GY01B602 墍 Which of the following is a symbolic representation of the statement: If two angles are not complements, then the sum of the two angles is not 90ⴗ? ⬃q→⬃p墍 G ⬃ p → ⬃ q H q → p J p → q 1 If Susan eats her broccoli, then she will get ice cream. 2 If Susan gets ice cream, then she will stay up late. 3 If Susan eats her broccoli, then she will stay up late. 2004 Commonwealth of Virginia Department of Education 墍 GY01C506.AR1 F J GY01C506 ArtCodes 1 If John studies, then he will pass the test. 2 If John passes the test, then he will not be grounded. 3 If John is grounded, then he will study. 14 H dog owners 6 C SESSION: 23 PAGE: 7 5/4/04 15:40 LOGIN IS-glenn PATH: @sunultra1/raid/CLS_tpc/GRP_va_sprg04/JOB_04-ribsg11/DIV_g11geom-1 15 Given: AD ≅ AC and AB ≅ AE 16 Given: ∠R ≅ ∠U. D GY05B405 墌 T S C GY05A519 墍 C ArtCodes E GY05B405.AR1 ArtCodes X GY05A519.AR1 F U A B R C Which proportion is true? Which could be used to prove ⌬ADB ≅ ⌬ACE? A B (SSS) If 3 sides of one triangle are congruent to 3 sides of another triangle, then the triangles are congruent. (SAS) If 2 sides and the angle between them in one triangle are congruent to 2 sides and the angle between them of another triangle, then the triangles are congruent. 墍 C (ASA) If 2 angles and the sides between them are congruent to 2 angles and the side between them of another triangle, then the triangles are congruent. D (AAS) If 2 angles and a side not between them are congruent to 2 angles and the side not between them of another triangle, then the triangles are congruent. F TX RT ⫽ 墍 US SX G RT RX ⫽ UX XS H SX RT ⫽ US TX J RT XT ⫽ RX UX 17 L GY05A407 墍 M N C Q P Given: ⌬LMQ ⬃ ⌬LNP. Therefore — 2004 Commonwealth of Virginia Department of Education 7 A PQ LM ⫽ MN QL B NP LN ⫽ 墍 LM MQ C MN LM ⫽ LP QP D LQ LN ⫽ LP LM ArtCodes GY05A407.AR1 SESSION: 23 PAGE: 8 5/4/04 15:40 LOGIN IS-glenn PATH: @sunultra1/raid/CLS_tpc/GRP_va_sprg04/JOB_04-ribsg11/DIV_g11geom-1 18 20 P GY060577 墌 B GY060202 65 0m Q GY060577.AR1 70 mm C 8m 55 C L ArtCodes 墍 64 mm 56 mm ArtCodes R GY060202.AR1 A From smallest to largest, the angles of ⌬PQR are — C ∠R, ∠Q, ∠P 墍 G ∠R, ∠P, ∠Q H ∠Q, ∠R, ∠P J ∠P, ∠R, ∠Q F 19 GY060576 墌 C L The locations of three water pumping stations form a triangle on a map of the area. The distance from station A to station B is 650 meters. The distance from station B to station C is 558 meters. The distance from station A to station C is — Which set of lengths could not be the lengths of the sides of a triangle? 7 B 8 C 4 D 2 A less than 92 m G exactly 92 m H between 92 m and 1,208 m 墍 J greater than 1,208 m F in., 24 in., 30 in. ft, 10 ft, 12 ft cm, 5 cm, 9 cm 墍 m, 3 m, 4 m 21 The top of a ladder is leaning on a building at a point 12 feet above the ground; the bottom of the ladder is 5 feet from the base of the building. What is the length of the ladder? 19 ft B 17 ft C 13 ft 墍 D 7 ft A 2004 Commonwealth of Virginia Department of Education 8 GY070621 墍 C SESSION: 23 PAGE: 9 5/4/04 15:40 LOGIN IS-glenn PATH: @sunultra1/raid/CLS_tpc/GRP_va_sprg04/JOB_04-ribsg11/DIV_g11geom-1 22 23 6 in. ? GY070310 墌 GY070580 墍 45° 60° C L C 6 in. ArtCodes ArtCodes GY070310.AR1 GY070580.AR1 12 cm A design is formed by joining isosceles right triangles and 60ⴗ- 30ⴗ right triangles as shown in the diagram. If the hypotenuse of the 60ⴗ- 30ⴗ triangle is 12 centimeters, which is closest to the length of one leg of the isosceles right triangle? What is the diameter of the circle shown? 3公2 B 3公3 C 6公2 D 6公3 A 6 cm 墍 G 7.2 cm H 8.5 cm J 10.4 cm F 24 in. in. in. 墍 in. B A 22° GY08A506 墍 C D C Quadrilateral ABCD is a parallelogram. ArtCodes The measure of ∠C is — GY08A506.AR1 22⬚ 墍 G 68⬚ H 112⬚ J 158⬚ F 2004 Commonwealth of Virginia Department of Education 9 SESSION: 23 PAGE: 10 5/4/04 15:40 LOGIN IS-glenn PATH: @sunultra1/raid/CLS_tpc/GRP_va_sprg04/JOB_04-ribsg11/DIV_g11geom-1 25 The vertices of parallelogram ABCD have coordinates A(1, 8), B(4, ⴑ2), and C(ⴑ2, ⴑ7). 26 A desktop was made from the scrap of plywood shown by cutting (in a straight line) from C to E. GY08C403 GY08C615 墌 墍 C L A E C B 9 8 7 ArtCodes GY08C403.AR1 6 ArtCodes 5 GY08C615.AR1 4 3 2 D 1 –9 –8 –7 –6 –5 –4 –3 –2 –1 –1 1 2 3 4 5 6 7 8 C 9 –2 Which measurement would ensure that the desktop is rectangular? –3 –4 –5 AE ⫽ EB G AC ⫽ BD H EC ⫽ CD J DE ⫽ CA 墍 F –6 –7 –8 –9 What are the coordinates of D? (⫺5, 3) 墍 B (⫺3, 5) C (2, 3) D (5, ⫺3) A 27 Which of the following is not true about a parallelogram? Any two opposite sides are congruent. B Any two opposite angles are congruent. C The diagonals bisect each other. D Any two consecutive angles are complementary. 墍 A 2004 Commonwealth of Virginia Department of Education 10 GY08A602 墍 C SESSION: 23 PAGE: 11 5/4/04 15:40 LOGIN IS-glenn PATH: @sunultra1/raid/CLS_tpc/GRP_va_sprg04/JOB_04-ribsg11/DIV_g11geom-1 28 90 30 90 O O GY090721 GY090416 墌 墍 C O 100 105 C O ArtCodes ArtCodes GY090721.AR1 GY090416.AR1 What is the value of x in the pentagon above? A 90⬚ G 155⬚ 墍 H 245⬚ J 335⬚ C F B What is the measure of interior angle ABC of the regular polygon shown? 225⬚ G 180⬚ H 160⬚ J 144⬚ 墍 F 29 GY090308 墌 x C L 31 ArtCodes L GY090308.AR1 M GY100609 墍 C P ArtCodes Which is the closest to the measure of a central angle x in this regular polygon? GY100609.AR1 N O 40⬚ B 45⬚ C 50⬚ 墍 D 60⬚ A If LO is a diameter of circle P, what is m∠LMO? 30⬚ B 45⬚ C 80⬚ D 90⬚ 墍 A 2004 Commonwealth of Virginia Department of Education 11 SESSION: 23 PAGE: 12 5/4/04 15:40 LOGIN IS-glenn PATH: @sunultra1/raid/CLS_tpc/GRP_va_sprg04/JOB_04-ribsg11/DIV_g11geom-1 32 Secants PB and PD intersect the circle at A and C, respectively. GY100414 墌 34 GY120403 墍 B C C 5 ArtCodes A ArtCodes Which could be the view of this stack of cubes from directly above? 4 GY100414.AR1 C D P 12 F ArtCodes What is the length of PC? 3墍 G 4 H 5 J 6 GY120403.AR2 GY120403.AR3 GY120403.AR4 GY120403.AR5 F G H 33 The figure shows a circle. m∠RPQ ⴔ 50ⴗ and m∠PRQ ⴔ 60ⴗ. GY100419 墌 R C L J 60° ArtCodes GY100419.AR1 P GY120403.AR1 50° Q ៣ What is the measure of PR? 70⬚ B 100⬚ C 120⬚ D 140⬚ 墍 A 2004 Commonwealth of Virginia Department of Education 12 墍 SESSION: 23 PAGE: 13 5/4/04 15:40 LOGIN IS-glenn PATH: @sunultra1/raid/CLS_tpc/GRP_va_sprg04/JOB_04-ribsg11/DIV_g11geom-1 35 36 GY120213 墌 C A tepee in the shape of a right cone has a slant height of 18.5 feet and a diameter of 20 feet. Approximately how much canvas would be needed to cover the tepee? GY130510 墍 581 sq ft 墍 G 116 sq ft H 89 sq ft J 58 sq ft F ArtCodes GY120213.AR1 C Which piece completes this cube? 37 ArtCodes A The Great Pyramid at Giza has a square base with sides of length 230 meters and a height of 146.7 meters. Approximately what is the volume of the Great Pyramid? 1,650,000 2,590,000 C 4,950,000 D 7,760,000 A GY120213.AR2 GY120213.AR3 GY120213.AR4 GY120213.AR5 B GY130526 墍 C 3 m m3 墍 m3 m3 B 38 The ratio of the circumference of two 3 circles is . The radius of the smaller 2 circle is 8 inches. What is the radius of the larger circle? 1 F 5 inches 3 G 6 inches C D 墍 2004 Commonwealth of Virginia Department of Education 13 H 9 inches J 12 inches 墍 GY14BR13 墍 C L SESSION: 23 PAGE: 14 5/4/04 15:40 LOGIN IS-glenn PATH: @sunultra1/raid/CLS_tpc/GRP_va_sprg04/JOB_04-ribsg11/DIV_g11geom-1 39 GY14AR54 墌 C Two ships leaving the same marina at the same time are 3.2 miles apart after sailing 2.5 hours. If they continue at the same rate and direction, how far apart will they be 2 hours later? 2.56 B 3.52 C 5.76 D 6.08 A 40 y 41 A GY02C407 墍 A' C B mi mi mi 墍 mi C' ArtCodes C GY02C407.AR1 B' x ⌬XYZ was obtained from ⌬ABC by a rotation about the point P. GY02C513 墌 A Triangle AⴕBⴕCⴕ is apparently — C C B ArtCodes P a translation of triangle ABC across the x-axis B a 90⬚ clockwise rotation of triangle ABC about the origin 墍 C a reflection of triangle ABC across the y-axis D a reflection of triangle ABC across the x-axis A Z X GY02C513.AR1 Y Which of the following indicates the correspondence of the vertices? A G A H A J A F → → → → X, B → Y, C → Z Y, B → Z, C → X 墍 X, B → Z, C → Y Z, B → X, C → Y 2004 Commonwealth of Virginia Department of Education 14 SESSION: 23 PAGE: 15 5/4/04 15:40 LOGIN IS-glenn PATH: @sunultra1/raid/CLS_tpc/GRP_va_sprg04/JOB_04-ribsg11/DIV_g11geom-1 y 42 y 43 5 GY02A730 4 C 3 墌 GY02B103 墍 C 2 ArtCodes GY02A730.AR1 ArtCodes x 1 -5 -4 -3 -2 -1 0 -1 1 2 3 4 5 x -2 -3 -4 -5 This figure is apparently symmetric with respect to — What is most likely the slope of the line graphed above? F 1 墍 3 G 2 3 H 2 J 3 2004 Commonwealth of Virginia Department of Education the x-axis only B the y-axis only 墍 C both the x-axis and the y-axis D neither the x-axis nor the y-axis A 15 GY02B103.AR1 SESSION: 23 PAGE: 16 5/4/04 15:40 LOGIN IS-glenn PATH: @sunultra1/raid/CLS_tpc/GRP_va_sprg04/JOB_04-ribsg11/DIV_g11geom-1 y 44 45 The distance between the points (ⴑ2, ⴑ4) and (3, 8) is — B 5 GY02A502 墌 C L A ArtCodes 4 A 3 B 13 墍 C 17 D 169 2 GY02A502.AR1 1 -5 -4 -3 -2 -1 O -1 1 2 3 C4 5 x -2 D -3 -4 -5 What are the apparent coordinates of the midpoint of diagonal AC? F G H J 冉 冊 冉 冊 冉 冊 1 ⫺ , 1 2 1 ,1 墍 2 1, 公17 1 2 (1, 1) 2004 Commonwealth of Virginia Department of Education 16 GY02A575 墍 C L SESSION: 26 PAGE: 17 5/24/04 13:0 LOGIN IS-glenn PATH: @sunultra1/raid/CLS_tpc/GRP_va_sprg04/JOB_04-ribsg11/DIV_g11geom-1 Answer Key Test Sequence Number Correct Answer Reporting Category Reporting Category Description 1 B 001 Lines and Angles 2 J 001 Lines and Angles 3 A 001 Lines and Angles 4 J 001 Lines and Angles 5 B 001 Lines and Angles 6 G 001 Lines and Angles 7 B 001 Lines and Angles 8 J 001 Lines and Angles 9 C 001 Lines and Angles 10 H 001 Lines and Angles 11 B 001 Lines and Angles 12 F 002 Triangles and Logic 13 B 002 Triangles and Logic 14 F 002 Triangles and Logic 15 B 002 Triangles and Logic 16 F 002 Triangles and Logic 17 B 002 Triangles and Logic 18 F 002 Triangles and Logic 19 C 002 Triangles and Logic 20 H 002 Triangles and Logic 21 C 002 Triangles and Logic 22 F 002 Triangles and Logic 23 C 002 Triangles and Logic 24 F 003 Polygons and Circles 25 A 003 Polygons and Circles 26 J 003 Polygons and Circles 27 D 003 Polygons and Circles 28 G 003 Polygons and Circles 29 C 003 Polygons and Circles 30 J 003 Polygons and Circles 31 D 003 Polygons and Circles 32 F 003 Polygons and Circles 33 D 003 Polygons and Circles 34 H 004 Three-Dimensional Figures 35 D 004 Three-Dimensional Figures 36 F 004 Three-Dimensional Figures 37 B 004 Three-Dimensional Figures 38 J 004 Three-Dimensional Figures 39 C 004 Three-Dimensional Figures 40 G 005 Coordinate Relations and Transformations 41 B 005 Coordinate Relations and Transformations 42 F 005 Coordinate Relations and Transformations 43 B 005 Coordinate Relations and Transformations 44 G 005 Coordinate Relations and Transformations 45 B 005 Coordinate Relations and Transformations