Geometry 2 Final Review

Transcription

1 Class: Date: Geometry 2 Final Review Multiple Choice Identify the choice that best completes the statement or answers the question.. Find the perimeter of the triangle to the nearest whole unit. 4. Which statement below correctly relates BDC and BAC? The three sides of a triangle are in the ratio 2:4:5. If the shortest side of the triangle is 4 meters long, find the perimeter. 7 m 22 m 32 m 40 m 3. In PQR, RS = 5 and QS = 8. Find PS. BDC and BAC are complementary. BDC and BAC are supplementary. BDC and BAC are congruent. It is impossible to determine a relationship between BDC and BAC. 5. The surface area of a cube is 96 square feet. Find the volume of the cube. 4 ft 3 6 ft 3 64 ft ft 3 6. Find x

2 7. What is the volume of a rectangular prism with length 3 feet, width 2.5 feet, and height 8 feet? 03 ft 3 60 ft 3 20 ft ft 3 8. The diameter of a circular swimming pool is 5 feet. Find the circumference to the nearest hundredth ft 63.8 ft ft ft 9. A slide 3.8 m long makes an angle of 25 with the groun How high is the top of the slide above the ground?.6 m.77 m 3.44 m.66 m 0. How many cubic feet are in one cubic yard? You flip 4 coins all at once. What is the probability that you will get tails on all 4 coins? The legs of a right triangle measure.4 meters and 5. meters. To the nearest tenth, what is the measure of the smallest angle? The outer radius of a hollow cylinder is 5 centimeters and the radius of the inner cylinder (that is removed) is 3 centimeters. Find the area of a cross section that is parallel to a base of the hollow cylinder. 6π cm 2 2π cm 2 34π cm 2 4π cm 2 4. Find the center of the circle whose equation is (x +5) 2 + (y 20) 2 = 00. ( 5, 20) (5, 20) (5, 20) ( 5, 20) 5. Andrea drew a triangle on a sheet of paper. She used a copier to enlarge the triangle so that its dimensions were double the original dimensions. Then she made a copy that had dimensions 4 5 those of the original triangle. What is the ratio of the area of the enlarged copy to the area of the reduced copy? 25:4 5:2 2:5 4:25 6. A cylinder has a 0-inch diameter and an -inch height. Find the volume of the cylinder. Round to the nearest tenth in in in in 3 2

3 7. The measure of an angle formed by two tangents to a circle is 90. If the radius of the circle is 8 centimeters, how far is the vertex of the angle from the center of the circle? 8 cm 8 2 cm 8 3 cm 6 cm 8. If ABC DEF, find m C. 2. A golf ball has a 3.8-centimeter diameter and a tennis ball has a 7-centimeter diameter. Find the difference between their volumes to the nearest tenth cm cm cm cm Find the polygon that may be similar to ABCD Maria is having a circular swimming pool built in her backyar The pool is to have a diameter of 36 feet. She plans to build a 3-foot wide walkway around the outside of the pool. What will be the length of the outside edge of the walkway? Use π = ft ft 3.88 ft, ft 20. Which is the equation of a circle that passes through Ê Ë Á 2,2 ˆ and is centered at Ê Ë Á 5,6 ˆ? ( x 6) 2 + Ê Ë Á y 5ˆ 2 = 25 ( x 5) + Ê Ë Á y 6ˆ = 5 ( x + 5) + Ê Ë Á y + 6ˆ = 25 ( x 5) + Ê Ë Á y 6ˆ = Find the scale factor if X Y Z is the image of XYZ under a dilation with center C

4 24. The postulate or theorem that can be used to prove that the two triangles are similar is. SAS Similarity ASA Congruence SSS Similarity AA Similarity 25. In X, chords AB and CD are congruent and AB is 9 units from X. Find the distance from CD to X. 4.5 units 9 units 8 units cannot tell 26. Quadrilateral FGHJ and circle O are shown. 27. What type of dilation occurs with a scale factor of? enlargement reduction congruence transformation inverse transformation 28. On a model airplane, 2 feet corresponds to 40 feet on the actual plane. What is the wingspan on the model if the wingspan on the plane is 45 feet? 20 ft 7. ft 2.25 ft.8 ft 29. Which set of measures could represent the sides of a right triangle? 3 4,, 5 4 3, 5, 5 7, 7, 24 8, 5, 6 Use O. Given: m HJF = 84. Which statement, if true, would help prove that quadrilateral FGHJ is inscribed in Circle O and why? m JFG = 84 ; for a quadrilateral inscribed in a circle, adjacent angles are congruent. m JFG = 96 ; for a quadrilateral inscribed in a circle, adjacent angles are supplementary. m FGH = 84 ; for a quadrilateral inscribed in a circle, opposite angles are congruent. m FGH = 96 ; for a quadrilateral inscribed in a circle, opposite angles are supplementary. 30. Name a diameter. FG AB AB CE 3. Name a chor FO AB AB CE 4

5 32. Name a secant. FO AB AB CE 33. If a 24-foot ladder makes a 58 angle with the ground, how many feet up a wall will it reach? Round your answer to the nearest tenth ft 20.8 ft 20.4 ft 2.7 ft 34. Find y. 36. Determine the radius of O. 4 2 units 8 units 4 3 units units Use D What is the probability Lee rolls a numbered cube twice and gets a 5 each time? Name a radius. AB DB CB CE 38. Find tan A and tan B. tan A 0.38, tan B = 2.6 tan A = 2.6, tan B 0.38 tan A.08, tan B 0.42 tan A 0.92, tan B = 2.4 5

6 39. Points G and H lie on T so that TH = 8 meters and m GTH = 45. Find the length of GH to the nearest hundredth m 2.57 m 25.3 m m 40. A sphere has a 2-inch radius. Find the volume of the sphere. Round to the nearest tenth. 38,792.4 in 3 9,396.2 in in in 3 4. The ratio of the heights of two similar solids is 7:9. Find the ratio of their volumes. 7:9 4:8 49:8 343: Chords XY and WV are equidistant from the center of O. If XY = 2x + 30 and WV = 5x 2, find x Find the arc length of a sector with a radius of 9 feet and a central angle of π feet 9 0 π feet 2 π feet 62π feet 44. Sue scans a 4-inch picture into her computer. She stretches the picture s length to 0 inches. Find the scale factor she use Circle A has its center at A(5, 7) and CB. to A at B(2, 8). Find the slope of CB Find is tangent 47. Which equation is true for right triangle PQR? PR 2 PQ 2 = RQ 2 RQ 2 + PR 2 = PQ 2 PQ 2 + PR 2 = RQ 2 PQ 2 + RQ 2 = PR In Miko s math class there are boys and 8 girls. The teacher has picked two boys to put problems on the boar What is the probability that the next student she picks will be a girl?

7 49. What is the probability of an event that can never occur? A charcoal grill has a circular grill top that is 22 inches in diameter. What is the cooking area of the grill top in square inches? Use π = in in 2,93.0 in 2,59.76 in 2 5. Find x If the area of a triangle is 936 square inches, what is the area of the triangle in square feet? 78 in in in in The base of the rectangular prism below has a diagonal 0 inches long. The height of the prism is 5 inches. To the nearest tenth, what is the distance from A to G? 54. Suppose you roll a numbered cube four times and get the number 5 each time. What is the probability of getting 5 on the next roll? 5 Ê ˆ Ë Á Find the length of the hypotenuse of a right triangle whose legs measure 6 and The Red Rock Canyon State Park in California is shaped like the figure below. What is the area of the park? 3.09 mi mi mi mi in. 8.7 in. 0.9 in..2 in. 7

8 57. Find the length of PQ to the nearest hundredth in in in in. 58. If AB is tangent to P at B, find m Alan has 5 different headbands and 7 different T-shirts. He picks one headband and one T-shirt without looking. How many combinations of headbands and T-shirts are possible? 2 combinations 24 combinations 30 combinations 35 combinations 60. The ratio of the radii of two similar cylinders is 3:5. The volume of the smaller cylinder is 54π cubic centimeters. Find the volume of the larger cylinder. 90π cm 3 50π cm 3 250π cm 3 540π cm 3 6. A shoe box is in the shape of a rectangular prism. It has a length of 0 inches, a width of 6 inches, and a height of 4 inches. Without considering any overlapping, how many square inches of cardboard must be used in making the box? 248 in in 2 24 in 2 20 in A model of a lighthouse has diameter 8 inches and height 8 inches. If the actual diameter of the lighthouse is 20 feet, find its actual height. 30 ft 35 ft 45 ft 50 ft 63. In right triangle ABC, a = 4, b = 48, and c = 50. Find tan A A ship s sonar finds that the angle of depression to a wreck on the bottom of the ocean is 3.2. If a point on the ocean floor is 75 meters directly below the ship, how many meters is it from that point on the ocean floor to the wreck? Round to the nearest tenth m 39.8 m 77.0 m 7.6 m 8

9 65. LMN RST, LN = 2, MN = 28, and the scale factor of RST to LMN is 4. Find ST Which expression CANNOT be used to find BC? The table shows the possible outcomes when you roll two numbered cubes. Use the table to answer the following questions. 66. How many ways are there to roll a sum of 9 on the two cubes? way 2 ways 4 ways 6 ways 67. On a blueprint, 2 inches represents 0 feet. What is the ratio of inches on the blueprint to inches on the house? :20 :60 2:60 60: 68. To the nearest cubic inch, what is the volume of a cylinder with diameter 5 inches and height 2 inches? Use π = in in in 3 87 in 3 7.8( sin23 ) 7.8( cos 67 ) 7.8( tan23 ) 7.2 tan The volume of a cone is 080π cubic centimeters and the radius is 8 centimeters. Find the height of the cone. 5 cm 0 cm 20 cm 30 cm Use the triangle shown below for the following questions. 7. What is the area of PQR? 8 units 2 2 units 2 9 units 2 6 units Triangle JKL is inscribed in P with diameter JK and mjl = 30. Find m KJL

10 73. Find the radius of O if DE = 2 inches and DE bisects OF. 2 3 in. 6 in. 8 in. 4 3 in. 74. A sphere has a 6-inch radius. A cone has a 2-inch height and base with a 6-inch radius. Compare their volumes. The volume of the sphere is greater. The volume of the cone is greater. The volumes are equal. not enough information 75. What is the surface area of a cube with edges 2 feet long? 8 ft 2 2 ft 2 6 ft 2 24 ft 2 0

11 Geometry 2 Final Review Answer Section MULTIPLE CHOICE. C 2. B 3. D 4. B 5. C 6. D 7. B 8. A 9. A 0. C. A 2. B 3. A 4. D 5. A 6. C 7. B 8. B 9. C 20. D 2. C 22. D 23. B 24. D 25. B 26. D 27. C 28. C 29. A 30. A 3. B 32. C 33. C 34. C 35. D 36. B 37. B 38. B 39. A

12 40. A 4. D 42. C 43. B 44. B 45. A 46. C 47. C 48. D 49. D 50. B 5. C 52. C 53. D 54. B 55. D 56. A 57. B 58. C 59. D 60. C 6. A 62. C 63. A 64. B 65. D 66. C 67. B 68. C 69. C 70. B 7. C 72. A 73. D 74. A 75. D 2