Geometry. Interim Test Form 3. Student Name: Teacher Name: School: Date:

Transcription

1 Geometry Interim Test Form 3 Student Name: Teacher Name: School: Date:

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3 Mathematics Session 1: No Calculator Directions: Session 1: No Calculator Today, you will take Session 1 of the Geometry Interim Test. You will not be able to use a calculator in this session. Read each question. Then, follow the directions to answer each question. Mark your answers by circling the correct choice. If you need to change an answer, be sure to erase your first answer completely. Some of the questions will ask you to write a response. Write your response in the space provided in your test booklet. If you do not know the answer to a question, you may go on to the next question. If you finish early, you may review your answers and any questions you did not answer in this session ONLY. 3 Geometry

4 Mathematics Session 1: No Calculator 1. In the diagram, njkl, nrst cm K R J 3.65 cm L 9.82 cm T S What is the best approximation for sin R? A B C D Geometry 4

5 Mathematics Session 1: No Calculator 2. Triangle JKL is a right triangle. J K L m/ J m/ K sin J = x Which statement is true? A. cos K = x B. cos J = x C. sin K = x D. sin L = x 5 Geometry

6 Mathematics Session 1: No Calculator 3. The formula for the circumference of a circle, C = π d, can be understood by dividing a circle into 64 equal sections where each section is approximately the shape of a triangle. Each section has an area that is 1 the area of the circle and a base that is the circumference of the circle. Which of the following relates the area of this circle to the areas of these 64 sections? A. πr 2 = 64(π d ) B. πr 2 = 64 [ 1 2 (π d ) ] C. πr 2 = 1 64 [ 2 ( )] 1 64 π d D. πr 2 = 1 64 [ 2 1 ( 64 π d ) r ] Geometry 6

7 Mathematics Session 1: No Calculator 4. The figure shows two right triangles, with m/q = 45 and npqr, nxyz. Q Y 45 X Z P R Based on the definition of sine, which of these ratios must be equivalent to sin R? Select all that apply. A. B. C. D. E. F. PQ QR PR QR QR PQ QR PR XY YZ XZ YZ 7 Geometry

8 Mathematics Session 1: No Calculator 5. Part A What two-dimensional cross sections could be obtained from a right rectangular prism? Select the three correct answers. A. circle B. square C. ellipse D. parabola E. rectangle F. parallelogram that is not a square or a rectangle Part B What two-dimensional cross sections can be obtained from a cone? Select the three correct answers. A. circle B. square C. ellipse D. parabola E. rectangle Geometry 8

9 Use the information to answer Part A and Part B for question 6. Mathematics Session 1: No Calculator 6. In a park, Camila is creating two designs for a fenced-in region so that dogs have a safe place to play. Camila designs each region using a coordinate grid where each unit on the grid represents one foot. Part A Camila s first design is triangular-shaped. On the coordinate grid, she identifies two of the vertices to be (0, 0) and (0, 35). The third vertex is labeled as ( x, 42). What is the positive x-coordinate of the third vertex if the area of the region will cover 700 square feet? Enter your answer in the box. Part B Camila s second design is a six-sided region using the coordinates (0, 0), (0, 35), (30, 0), (40, 48), (35, 48), and (5, 35). How many feet of fencing material will Camila need for this region (rounded to the nearest whole number)? A. 124 B. 147 C. 152 D Geometry

10 Mathematics Session 1: No Calculator 7. A company plans to paint its logo on the side of its office building. The logo is shown in the coordinate plane, where the units are in feet y x The cost to paint the logo is $2.25 per square foot. What is the total cost, in dollars, to have the logo painted on the office building? Enter your answer in the box. Geometry 10

11 Use the information to answer Part A and Part B for question Consider the figures shown. Mathematics Session 1: No Calculator M R S 6 10 N Q T Part A What statement must be true in order to conclude that sin M = sin R? A. NQ = ST B. RT RS = 5 3 C. /NMQ > /STR D. RT RS = 3 5 Part B If sin M = sin R, what is the value of tan T? A. B. C. D Geometry

12 You have come to the end of Session 1 of the test. Review your answers from Session 1 only. Then close your test booklet and sit quietly or read silently. Geometry 12

13 Mathematics Session 2: Calculator Session 2: Calculator Directions: Today, you will take Session 2 of the Geometry Interim Test. You will be able to use a calculator in this session. Read each question. Then, follow the directions to answer each question. Mark your answers by circling the correct choice. If you need to change an answer, be sure to erase your first answer completely. Some of the questions will ask you to write a response. Write your response in the space provided in your test booklet. If you do not know the answer to a question, you may go on to the next question. If you finish early, you may review your answers and any questions you did not answer in this session ONLY. 13 Geometry

14 Mathematics Session 2: Calculator 9. A ramp has a height of 5.8 feet and an angle of 80. A sketch of the ramp is shown. 5.8 ft 80 y What is the length of the ramp, y, to the nearest tenth of a foot? Enter your answer in the box. Geometry 14

15 Mathematics Session 2: Calculator Use the information to answer Part A and Part B for question The sketch shows a park that contains a pond. Each unit on the grid represents 5 feet. park pond Part A A walking path is to be installed that follows along the edge of the pond. What is the approximate perimeter of the pond in feet? A. 63 B. 74 C. 315 D. 380 Part B The park is to be re-seeded with grass. Since the pond will not need to be seeded, its area can be removed from the estimated area of the park. What is the approximate area, in square feet, to be removed from the estimate? A. 168 B. 840 C. 4,200 D. 8, Geometry

16 Mathematics Session 2: Calculator 11. The diagonal measurement of a rectangular flat-screen TV is 55 inches. The TV is 20 inches tall. What is the measure of the angle formed by the diagonal and the 20-inch side, to the nearest tenth of a degree? Enter your answer in the box. Geometry 16

17 Mathematics Session 2: Calculator Use the information to answer Part A and Part B for question The cross-section view of a house has a triangle-shaped roof represented by njkl } with JK > } } JL and m JK = 22 ft. K 22 ft J L The sine of angle L is 0.5. Part A What is the height of the roof, in feet, from point J perpendicular to } KL? Enter your answer in the box. Part B What is the approximate length of KL }, in feet? A B C D Geometry

18 Mathematics Session 2: Calculator 13. An ice cream shop serves small and large scoops of ice cream. Each scoop is sphereshaped. Each small scoop has a diameter of approximately 6 centimeters. Each large scoop has a diameter of approximately 10 centimeters. What is the difference, in cubic centimeters, between a large scoop of ice cream and a small scoop of ice cream? Round your answer to the nearest tenth. Enter your answer in the box. Geometry 18

19 Mathematics Session 2: Calculator 14. A rectangular-shaped frame has a height of 90 inches. The angle formed by the diagonal of the frame is 24. A sketch of the frame is shown. 90 in. 24 What is the width of the frame to the nearest tenth of an inch? Enter your answer in the box. 19 Geometry

20 Mathematics Session 2: Calculator 15. A small toy in the shape of a right pyramid with a square base is floating in a pool of water. The height of the pyramid is 5 inches. One-third of this height is above the surface of the water and two-thirds of it is below the surface of the water. The square cross section of the pyramid at the surface of the water has an area of 3.6 square inches. This cross section is parallel to the base. What is the volume, in cubic inches, of the portion of the pyramid that is above the water? Enter your answer in the box. Geometry 20

21 Mathematics Session 2: Calculator 16. Willis constructed a horizontal shelf that extends perpendicularly from a wall and is held up by a 34-centimeter brace. The shelf makes a 28 angle with the brace as shown cm shelf brace wall To make the shelf, Willis began with a 55-centimeter piece of wood and then shortened it by cutting a portion off. About how many centimeters did he cut off? A. 21 B. 25 C. 30 D Geometry

22 Mathematics Session 2: Calculator Use the information to answer Part A and Part B for question The doorway in Julie s house is 80 inches tall and the angle that the diagonal makes with the top of the doorway is 35 as shown in the diagram in. Part A Julie has a table top that she wants to move diagonally through the doorway. What is the length of the diagonal, to the nearest tenth of an inch, that would allow Julie's table top to fit? Enter your answer in the box. Part B The base of the table has wheels and can be rolled through the doorway, if the doorway is wide enough. Which equation can be used to determine the width, x, of the doorway? A. tan 35 = 80 x B. tan 35 = x 80 C. sin 35 = 80 x D. cos 35 = 80 x Geometry 22

23 Mathematics Session 2: Calculator GO ON TO THE NEXT PAGE 23 Geometry

24 Mathematics Session 2: Calculator Use the information to answer Part A and Part B for question Consider triangle XYZ. Y c a X b Z Part A Explain why sin X = cos Y. Use trigonometric relationships with right triangles in your explanation. Enter your explanation in the box provided. Geometry 24

25 Mathematics Session 2: Calculator Part B If sin X = and b = 40, what is the value of c? A B C D Geometry

26 Mathematics Session 2: Calculator 19. The city is planning a concert that is expected to bring in a crowd of about 200,000 people. The concert will be held in a public park. The city planners are thinking about the size and shape of the space that will be needed to accommodate this number of people. At a much smaller yet similar event, the crowd was estimated to be about 22,000 people. At this event, the crowd was confined to an area that was roughly the shape of a right triangle with side lengths that were approximately 300 feet, 350 feet, and 461 feet. Determine the appropriate dimensions of a similar space with 200,000 people. Show your work or explain your modeling. Determine the angle measures, in degrees, for the acute angles of the similar larger right triangle. Show your work or explain your modeling. Enter your answers and work or explanation in the boxes provided on pages 26 and 27. Geometry 26

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28 You have come to the end of Session 2 of the test. Review your answers from Session 2 only. Then close your test booklet and sit quietly or read silently. Geometry 28

29 The content provided in this document may NOT be used or published in part or in whole outside of the prescribed purposes set forth by the Louisiana Department of Education (LDOE). Assessment items and passages can only be used in the assessment delivery platform operated by the LDOE testing vendor. The mission of the Louisiana Department of Education (LDOE) is to ensure equal access to education and to promote equal excellence throughout the state. The LDOE is committed to providing Equal Employment Opportunities and is committed to ensuring that all its programs and facilities are accessible to all members of the public. The LDOE does not discriminate on the basis of age, color, disability, national origin, race, religion, sex, sexual orientation, gender identity, political affiliation, or genetic information. Inquiries concerning the LDOE s compliance with Title IX and other civil rights laws may be directed to the Attorney, LDOE, Office of the General Counsel, P.O. Box 94064, Baton Rouge, LA ; or customerservice@la.gov. Information about the federal civil rights laws that apply to the LDOE and other educational institutions is available on the website for the Office of Civil Rights, USDOE, at This project is made possible through a grant awarded by the U.S. Department of Education from the Teacher Incentive Fund (TIF 5) grant. This project is made possible through a grant awarded by the State Board of Elementary and Secondary Education from the Louisiana Quality Education Support Fund--8(g). This public document was published at a total cost of $8, This web-only document was published for the Louisiana Department of Education, Office of Academic Policy and Analytics, P.O. Box 94064, Baton Rouge, LA , by Data Recognition Corporation, Bass Lake Road, Maple Grove, MN This material was printed in accordance with the standards for printing by state agencies established pursuant to R.S. 43:31 and in accordance with the provisions of Title 43 of the Louisiana Revised Statutes Louisiana Department of Education

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