Review for Final - Geometry B

Transcription

1 Review for Final - Geometry B Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A model is made of a car. The car is 4 meters long and the model is 7 centimeters long. What is the ratio of the length of the car to the length of the model? a. 4 : 7 b. 7 : 400 c. 400 : 7 d. 7 : 4 2. If then 4a =. a. 4b b. 5b c. 10b d. 8b Solve the proportion. 3. a. 35 b. 175 c. 7 d a. 3 b. 6 c. 1 6 d Explain why the triangles are similar. Then find the value of x. 22 ) x ) a. AA Postulate; 13 4 c. SSS Postulate; b. SAS Postulate; 9 d. AA Postulate; 9 Find the geometric mean of the pair of numbers and 7 a. 35 b. 55 c. 40 d and 7

2 a. 28 b. 2 7 c. 4 2 d Find the length of the altitude drawn to the hypotenuse. The triangle is not drawn to scale a. 30 b. 30 c. 104 d Given:. Find the length of. The diagram is not drawn to scale. A 4 P Q B C a. 12 b. 11 c. 9 d. 18 Find the length of the missing side. The triangle is not drawn to scale a. 120 b. 289 c. 17 d a. 13 b. 36 c. 6 d. 4

3 Find the length of the missing side. Leave your answer in simplest radical form cm 10 cm a. 136 cm b. 3 2 cm c. 46 cm d cm 13. A grid shows the positions of a subway stop and your house. The subway stop is located at ( 2, 8) and your house is located at ( 1, 7). What is the distance, to the nearest unit, between your house and the subway stop? a. 2 b. 1 c. 6 d A triangle has sides of lengths 10, 24, and 26. Is it a right triangle? Explain. a. no; c. no; b. yes; d. yes; 15. In triangle ABC, is a right angle and 45. Find BC. If you answer is not an integer, leave it in simplest radical form. C 9 ft B A a. 9 ft b. 18 ft c. 9 ft d. 18 ft 16. Find the length of the leg. If your answer is not an integer, leave it in simplest radical form

4 a. 7 b. 14 c. 98 d. 7 2 Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form x a. b. 1 2 c. 2 d. 18. a. x =, y = 14 c. x = 14, y = b. x = 42, y = d. x =, y = 19. Write the tangent ratios for and. Z 5 29 X 2 Y a. c. b. d. Find the value of x. Round your answer to the nearest tenth.

5 x a. 7.6 b. 5.8 c. 6.9 d x a. 3.4 b. 3.6 c d. 9.4 Find the value of x to the nearest degree x 3 a. 21 b. 71 c. 69 d Write the ratios for sin A and cos A. A C 63 B a. c.

6 b. d. Find the value of x. Round to the nearest tenth x 28 a. 17 b c d x 26 a b. 8.5 c d x a b c d Find the value of x. Round to the nearest degree.

7 x a b. 28 c. 58 d x 6 a. 41 b. 37 c. 49 d. 42 Find the value of x. Round the length to the nearest tenth m x 37 a m b m c m d m ft 46 x a. 9.3 ft b. 6.3 ft c. 13 ft d. 6.5 ft Describe the vector as an ordered pair. Give the coordinates to the nearest tenth. ()

8 31. y x a., b., c., d., 32. y x a., c., b., d., 33. y 19 x 5 a., b., c., d., Use compass directions to describe the direction of the vector. ()

9 34. N 15 W S E a. 15 west of south c. 15 west of north b. 15 east of south d. 15 east of north 35. N 39 W S E a. 39 east of south c. 39 west of north b. 39 west of south d. 39 east of north 36. N W 30 E S a. 30 north of west c. 30 south of west b. 30 north of east d. 30 south of east

10 37. N W 81 E S a. 81 north of east c. 81 south of east b. 81 south of west d. 81 north of west Write the sum of the two vectors as an ordered pair. 38., and, a., b., c., d., In the diagram, the dashed figure is the image of the solid figure. D E R S C F T Q 39. Name the image of E. a. F b. R c. Q d. T 40. Name the image of. a. b. c. d. 41. The vertices of a triangle are P( 6, 1), Q( 6, 5), and R( 6, 8). Name the vertices of the image reflected in the line y = x.

11 y x a. c. b. d. 42. Find the image of O(3, 0) after two reflections, first in the line y = 1, and then in the line x = y x a. (4, 1) b. (3, 0) c. (1, 1) d. ( 1, 2) 43. Describe in words the translation represented by the vector. a. 2 units to the left and 2 units up b. 2 units to the right and 2 units up c. 2 units to the left and 2 units down d. 2 units to the right and 2 units up 44. Use an ordered pair to describe the translation that is 2 units to the left and 1 units up. a. b. c. d. Use the diagram.

12 45. Find the vector that describes the translation B C. a. b. c. d. 46. Find the image of C under the translation described by the vector. a. A b. B c. E d. D 47. The vertices of a rectangle are R( 5, 5), S( 1, 5), T( 1, 1), and U( 5, 1). After translation, ( 6, 1). Find the translation vector and coordinates of. is the point a. c. b. d. 48. Which letter has at least one line of symmetry? a. J b. G c. H d. F

13 49. A blueprint for a house has a scale of 1 : 10. A wall in the blueprint is 10 in. What is the length of the actual wall? a. 100 feet b. 1,200 feet c feet d in. 50. Find the area. The figure is not drawn to scale. 5.6 cm 4.2 cm a. b. c. d. Find the area of a parallelogram with the given vertices. 51. P(3, 4), Q(5, 4), R(9, 7), S(11, 7) a. 6 units 2 b. 3 units 2 c. 12 units 2 d. none of these 52. P( 2, 1), Q(5, 1), R(1, 5), S(8, 5)

14 a. 42 units 2 b. 21 units 2 c. 84 units 2 d. none of these 53. A parallelogram has sides 16.7 m and 35.2 m. The height corresponding to the 16.7-m base is 10.4 m. Find the height, to the nearest tenth of a meter, corresponding to the 35.2-m base. a. 4.9 m b m c m d. none of these Find the area of the trapezoid. Leave your answer in simplest radical form cm 7 cm 45 3 cm a. 11 cm 2 b cm 2 c. 77 cm 2 d. 84 cm A kite has diagonals 6.9 ft and 5 ft. What is the area of the kite? a ft 2 b ft 2 c ft 2 d ft Find the area of the rhombus. Leave your answer in simplest radical form.

15 60 5 a b c d Find the area of a regular hexagon with an apothem 10.4 feet long and a side 12 feet long. Round your answer to the nearest tenth. a ft 2 b ft 2 c ft 2 d ft 2 The figures are similar. The area of one figure is given. Find the area of the other figure to the nearest whole number. 58. The area of the larger triangle is 1009 ft. 32 ft 12 ft a. 142 ft b ft c ft d. 144 ft Find the area of the regular polygon. Give the answer to the nearest tenth. 59. pentagon with side 5 m a. 8.6 m b m c. 86 m d. 43 m 60. hexagon with side 10 ft a ft b. 52 ft c. 15 ft d ft Find the area of the triangle. Give the answer to the nearest tenth. The drawing may not be to scale.

16 61. 7 cm 11 cm 71 a cm b cm c cm d cm Find the circumference. Leave your answer in terms of cm a. cm b. cm c. cm d. cm 63. Find the length of arc XPY. Leave your answer in terms of. X 8 m Y P a. 720 m b. 24 m c. 12 m d. 4 m Find the area of the circle. Leave your answer in terms of m a m 2 b m 2 c m 2 d m 2

17 65. Find the area of the figure to the nearest tenth. a in. 2 b in. 2 c. 7.3 in. 2 d in Use formulas to find the lateral area and surface area of the given prism. Show your answer to the nearest whole number. a. 420 m ; 435 m c. 420 m ; 428 m b. 390 m ; 435 m d. 390 m ; 450 m m 18 m 9 m a. 396 m ; 432 m c. 396 m ; 270 m b. 108 m ; 270 m d. 108 m ; 432 m Find the surface area of the cylinder in terms of.

18 68. 6 in. 18 in. a. 216 in. b. 240 in. c. 504 in. d. 288 in cm 18 cm a. 704 cm b. 416 cm c cm d. 800 cm Find the surface area of the pyramid shown to the nearest whole number. 70. a. 96 ft b. 80 ft c. 28 ft d. 176 ft Find the volume of the given prism. Round to the nearest tenth if necessary.

19 71. a ft b ft c. 826 ft d ft 72. a yd b yd c yd d yd Find the volume of the sphere shown. Give each answer rounded to the nearest cubic unit. 73. a. 524 mm b. 105 mm c. 314 mm d. 262 mm Short Answer For the vectors, (a) write the resultant as an ordered pair and (b) draw the resultant.

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21 Review for Final - Geometry B Answer Section MULTIPLE CHOICE 1. C 2. B 3. C 4. B 5. D 6. A 7. B 8. D 9. C 10. C 11. C 12. D 13. B 14. D 15. C 16. D 17. D 18. B 19. C 20. D 21. C 22. C 23. B 24. C 25. C 26. A 27. D 28. A 29. D 30. B 31. D 32. B 33. B 34. D 35. C 36. C 37. C 38. C 39. B 40. A 41. A

22 42. D 43. D 44. C 45. D 46. B 47. D 48. C 49. C 50. A 51. A 52. A 53. A 54. C 55. C 56. B 57. A 58. A 59. D 60. A 61. B 62. A 63. C 64. C 65. A 66. A 67. A 68. D 69. B 70. A 71. A 72. A 73. A SHORT ANSWER 74. a.,

23 b. 75. a., b.