END OF COURSE GEOMETRY

Transcription

1 SSSION: 27 P: 1 1/26/04 9:8 OIN IS-joer VIRINI STNRS O RNIN SSSSMNTS Spring 2003 Released Test N O OURS OMTRY Property of the Virginia epartment of ducation 2003 by the ommonwealth of Virginia epartment of ducation, ames Monroe uilding, 101 N. 14th Street, Richmond, Virginia, ll rights reserved. xcept 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. ommonwealth of Virginia public school educators may photocopy or print any portion of these Released Tests for educational purposes without requesting permission. ll others should direct their requests to the ommonwealth of Virginia epartment of ducation at (804) , ivision of ssessment and Reporting.

2 SSSION: 25 P: 2 5/8/103 16:34 OIN IS-debbie eometry IRTIONS Read and solve each question. 2 iven:,, and are collinear; m 85 SMP 85 x Y rtodes Y R1 If is similar to, then :?:. Which replaces the? to make the statement true? What value of x will ensure that,, and are also collinear? guy wire for a pole for a tennis net makes an angle of 62 with the ground y 65 Y Y rtodes Y R1 rtodes Y R x What is the measure of the angle between the wire and the pole? What are the values of x, and y? x 91, y 98 x 91, y 108 x 101, y 98 x 101, y ommonwealth of Virginia epartment of ducation 2

3 SSSION: 25 P: 3 5/8/103 16:34 OIN IS-debbie 4 Y S T 6 ine m contains points (1, 3) and (2, 2). Which of the following pairs of points define a line parallel to line m? (0, 0) and (1, 1) (0, 0) and (1, 5) Y rtodes Y R1 x (1, 1) and (6, 2) (4, 0) and (5, 5) R In the diagram, and RST are congruent equilateral triangles with corresponding sides parallel. What is the value of x? 7 (2x + 30) (4x 90) l m Y rtodes Y R What value for x will show that lines l and m are parallel? The measures of some angles are given in this figure. Y N rtodes Y R1 58 M O 140 What is the measure of N? ommonwealth of Virginia epartment of ducation 3

4 SSSION: 25 P: 4 5/8/103 16:34 OIN IS-debbie 8 x z eiling eam 9 Use your compass and straightedge to construct a line that is perpendicular Y rtodes Y R1 y w loor eam to ST and passes through point O. W X Z T Y construction engineer needs to make sure a ceiling beam is parallel to its corresponding floor beam. Using the drawing as a guide, which pair of measurements is sufficient to show the beams are parallel? Y O rtodes Y R1 x z y w x y y z S Which other point lies on this perpendicular? W X Y Z 2003 ommonwealth of Virginia epartment of ducation 4

5 SSSION: 25 P: 5 5/8/103 16:34 OIN IS-debbie 10 Use a compass, straightedge, and the drawing below to answer the question. Y rtodes Y R1 Which point lies on the line that bisects? Q R S T Q R S T ccording to the Venn diagram, which is true? Offense ootball Players ll football players play offense or defense. No football players play offense and defense. ll football players play defense. Some football players play offense and defense. Q efense Y01609 rtodes Y01609.R1 11 Use your compass to answer the following question. Y R K and RS are parallel. Which of the following statements is true? K S Y05302 rtodes Y05302.R1 rtodes Y R1 R Q KS RS K RS QK SK Which line segment is congruent to? QR KS QR Q QS R QS QK 2003 ommonwealth of Virginia epartment of ducation 5

6 SSSION: 25 P: 6 5/8/103 16:34 OIN IS-debbie 14 Triangles and are similar and have measurements as shown. Y05403 rtodes Y05403.R1 What is the measure of? ? 16 ssuming these statements are true, Some musicians are happy people. ll happy people like music. which of the following is a valid conclusion? ll happy people are musicians. ll musicians like music. Some happy people do not like music. Some musicians like music. Y Triangle is a right triangle with the measures shown in. 25 in. Y rtodes Y R1 15 ltitude is drawn from right angle of triangle forming right triangles and. Y05307 The length of is 18 in. 24 in. 32 in. 576 in. rtodes Y05307.R1 Which statement concerning the 3 triangles is true? None of the triangles are similar. Only triangles and are similar. Triangle is similar to only triangle. Triangle is similar to both triangle and triangle ommonwealth of Virginia epartment of ducation 6

7 SSSION: 25 P: 7 5/8/103 16:34 OIN IS-debbie 18 customer provided this diagram of a patio to a fencing company. 20 In any, which statement is always true? Y ft m m 90 m m 90 Y rtodes Y R1 16 ft 24 ft Y ft 60 rtodes Y R1 What is the length of the unlabeled side? 10 ft 11 ft 12 ft 13 ft Which of the following lists the sides of from least to greatest length?,,,,,,,, 19 In triangle, 6, 7, and 5. Which is true? Y The measure of is the least of the three angles. The measure of is the greatest of the three angles. The measure of is the greatest of the three angles. The measure of is the least of the three angles. 22 To determine the distance across a pond, arry made the measurements shown in the diagram. R T m S sin cos tan Y rtodes Y R1 Which is closest to the distance from R to S? 3.48 m 19.7 m 20.3 m m 2003 ommonwealth of Virginia epartment of ducation 7

8 SSSION: 25 P: 8 5/8/103 16:34 OIN IS-debbie 23 Y05575 rtodes Y05575.R1 X 12 6 Z Y 15 Which triangle is similar to XYZ? 24 In rhombus, 30 inches and 40 inches. Y08401 rtodes Y08401.R1 rtodes Y05575.R2 Y05575.R3 Y05575.R4 Y05575.R What is the perimeter of the rhombus? 25 in. 50 in. 100 in. 200 in is a rhombus. K 36 y Y (3, 4) (?,?) rtodes Y08203.R1 (0, 0) (5, 0) x 12 I What are the coordinates of vertex? (5, 4) (6, 4) (8, 4) (4, 3) 2003 ommonwealth of Virginia epartment of ducation 8

9 SSSION: 25 P: 9 5/8/103 16:34 OIN IS-debbie 26 The quadrilateral is a parallelogram. 28 In the figure, the measure of is twice the measure of. Y08511 Y rtodes Y08511.R1 rtodes Y R1 Which of the following pieces of information would suffice to prove that is a rectangle? m m and are supplementary What is the measure of? Three vertices of parallelogram have coordinates (1, 4), (3, 8), and (5, 0). Y08405 rtodes Y08405.R y x igure is a regular octagon. What is the measure of Q? Q Y rtodes Y R1 What are the coordinates of the other first-quadrant vertex? (3, 12) (1, 4) (1, 4) (9, 4) 2003 ommonwealth of Virginia epartment of ducation 9

10 SSSION: 25 P: 10 5/8/103 16:34 OIN IS-debbie The measure of arc is 28. Y rtodes Y R1 Q P 28 Y rtodes Y R1 R The two adjacent figures are a regular hexagon and a regular octagon. What is the measure of PQR? What is the measure of? is tangent to the circle at and the measure of is Y rtodes Y R1 P 4 R 8 Q Y rtodes Y R1,, and are points of tangency. P 4 and Q 8. What is the measure of PQ? What is the measure of? ommonwealth of Virginia epartment of ducation 10

11 SSSION: 25 P: 11 5/8/103 16:34 OIN IS-debbie 34 Y rtodes Y R1 Which is a two-dimensional representation of the view from directly above the figure? 35 The figure shows a right circular cone on top of a hemisphere with the same radius. 4 cm 4 cm Y rtodes Y R1 To the nearest whole number, what is the volume of this solid? rtodes Y R2 Y R3 Y R4 Y R5 201 cm cm cm cm ommonwealth of Virginia epartment of ducation 11

12 SSSION: 25 P: 12 5/8/103 16:34 OIN IS-debbie 36 Which of the following patterns could not be folded into a cube? Y rtodes Y R1 Y R2 Y R3 Y R4 38 What is the volume of a right square pyramid with a height of 3 centimeters and a base that measures 8 centimeters by 8 centimeters? 64 cm 3 72 cm cm cm 3 Y ine segments and intersect at, asshown in the figure., 10, 15, and 20. Y rtodes Y R1 What is the measure of? 37 cylindrical water container is 1.2 meters high and has a diameter of Y meters. pproximately how many cubic meters of water will the container hold when it is half full? ommonwealth of Virginia epartment of ducation 12

13 SSSION: 25 P: 13 5/8/103 16:34 OIN IS-debbie 40 Q 41 onsider this figure. Y02502 O P Y02576 rtodes rtodes Y02502.R1 N Y02576.R1 K M Which of the following is a rotation in the plane of the given figure? I Which polygon shown above has only one line of symmetry? Rectangle exagon I Square KMN rtodes Y02576.R2 Y02576.R3 Y02576.R4 Y02576.R5 Triangle OPQ 2003 ommonwealth of Virginia epartment of ducation 13

14 SSSION: 25 P: 14 5/8/103 16:36 OIN IS-debbie 42 y 44 y Y02506 rtodes Y02506.R1 X O -1 Z If triangle XYZ is reflected across the y-axis to form triangle XYZ, what is the coordinate of Y? 1 Y x Parallelogram is positioned on a coordinate plane with the coordinates as shown. N is the midpoint of. What are the coordinates of N? (2, 3) (3.5, 2) (2.5, 6) M (6, 2.5) (2, 3) (0, 0) N (5, 1) (7, 4) x Y02306 rtodes Y02306.R1 (3, 2) (4, 6) (2, 3) (3, 2) 45 The slope of the line joining the coordinate points (3, 1) and (4, 7) is 8 7 Y Which point is the greatest distance from the origin? Y02509 (8, 5) (9, 1) (3, 4) (9, 2) 2003 ommonwealth of Virginia epartment of ducation 14

15 SSSION: 25 P: 15 5/8/103 16:34 OIN IS-debbie Test Sequence orrect nswer Reporting ategory nswer Key Reporting ategory escription ines and ngles ines and ngles ines and ngles ines and ngles ines and ngles ines and ngles ines and ngles ines and ngles ines and ngles ines and ngles ines and ngles Triangles and ogic Triangles and ogic Triangles and ogic Triangles and ogic Triangles and ogic Triangles and ogic Triangles and ogic Triangles and ogic Triangles and ogic Triangles and ogic Triangles and ogic Triangles and ogic Polygons and ircles Polygons and ircles Polygons and ircles Polygons and ircles Polygons and ircles Polygons and ircles Polygons and ircles Polygons and ircles Polygons and ircles Polygons and ircles Three-imensional igures Three-imensional igures Three-imensional igures Three-imensional igures Three-imensional igures Three-imensional igures oordinate Relations, Transformations, and Vectors oordinate Relations, Transformations, and Vectors oordinate Relations, Transformations, and Vectors oordinate Relations, Transformations, and Vectors oordinate Relations, Transformations, and Vectors oordinate Relations, Transformations, and Vectors