Final Exam Review Packet Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the length of the missing side. The triangle is not drawn to scale. 6 8 a. 28 b. 100 c. 10 d. 48 2. A grid shows the positions of a subway stop and your house. The subway stop is located at ( 5, 2) and your house is located at ( 9, 9). What is the distance, to the nearest unit, between your house and the subway stop? a. 5 b. 13 c. 8 d. 18 3. A triangle has sides of lengths 12, 14, and 19. Is it a right triangle? Explain. a. yes; c. no; b. no; d. yes; 4. 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 6 ft B A a. 6 ft b. 12 ft c. 6 ft d. 12 ft 5. A piece of art is in the shape of an equilateral triangle with sides of 7 in. Find the area of the piece of art. Round your answer to the nearest tenth. a. none of these b. 42.4 in. 2 c. 17.3 in. 2 d. 21.2 in. 2 Find an equation for the line: 6. through ( 4, 6) and parallel to y = 3x + 4. a. y = 3x 6 b. y = 3x 18 c. y = 1 3 x 22 3 d. y = 1 3 x 14 3
Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form. 7. x y 30 24 a. x =, y = 12 c. x =, y = b. x = 36, y = d. x = 12, y = 8. Find the value of x and y rounded to the nearest tenth. x 34 45 y 30 a. x = 48.1, y = 46.4 c. x = 24.0, y = 139.3 b. x = 48.1, y = 139.3 d. x = 24.0, y = 46.4 9. To find the height of a pole, a surveyor moves 140 feet away from the base of the pole and then, with a transit 4 feet tall, measures the angle of elevation to the top of the pole to be 44. To the nearest foot, what is the height of the pole? a. 145 ft b. 149 ft c. 135 ft d. 139 ft Find the value of x. Round your answer to the nearest tenth. 10. 8.9 cm x a. 6.2 cm b. 12.7 cm c. 15.5 cm d. 10.9 cm
Find the value of x to the nearest degree. 11. 19 x 11 a. 30 b. 60 c. 70 d. 85 12. The students in Mr. Collin s class used a surveyor s measuring device to find the angle from their location to the top of a building. They also measured their distance from the bottom of the building. The diagram shows the angle measure and the distance. To the nearest foot, find the height of the building. Building 100 ft a. 2400 ft b. 72 ft c. 308 ft d. 33 ft 13. Find the value of w, then x. Round lengths of segments to the nearest tenth. 12 w x a. w = 13.3, x = 10.2 c. w = 13.3, x = 23.6 b. w = 10.8, x = 6.1 d. w = 10.8, x = 16.9 14. A spotlight is mounted on a wall 7.4 feet above a security desk in an office building. It is used to light an entrance door 9.3 feet from the desk. To the nearest degree, what is the angle of depression from the spotlight to the entrance door? a. 39 b. 51 c. 53 d. 37
Find the value of x. Round to the nearest tenth. 15. 19 x a. 39.2 b. 9.2 c. 9.6 d. 39.7 Find the area. The figure is not drawn to scale. 16. 4.1 cm 17. 2.3 cm a. b. c. d. 9 cm 8 cm 13 cm 9 cm 11 cm a. 144.5 cm 2 b. 127 cm 2 c. 172 cm 2 d. 50 cm 2 18. The area of a parallelogram is 320 cm 2 and the height is 40 cm. Find the corresponding base. a. 12,800 cm 2 b. 8 cm c. 280 cm d. 360 cm
19. Find the value of h in the parallelogram. a. 32 b. 28 c. 40.5 d. 35 20. A fly lands at random at a point on the grid. Find the probability of the fly landing on the figure. a. b. c. d. Find the area of the trapezoid. Leave your answer in simplest radical form. 21. 4 cm 7 cm 45 3 cm a. 63 cm 2 b. 70 cm 2 c. 24.5 cm 2 d. 9 cm 2 22. Find the area of an equilateral triangle with side 12. a. 36 b. 72 c. 36 d. 3
23. Find the area of the rhombus. Leave your answer in simplest radical form. 60 5 a. 50 b. 10 3 c. 25 6 d. 50 3 24. Given the regular hexagon, find the measure of each numbered angle. 1 3 2 a. c. b. d. 25. Find the area of the regular polygon. Round your answer to the nearest tenth. 13.07 in. 10 in. a. 176.6 in. 2 b. 966.1 in. 2 c. 80.0 in. 2 d. 483.0 in. 2
The figures are similar. Give the ratio of the perimeters and the ratio of the areas of the first figure to the second. The figures are not drawn to scale. 26. 15 yd a. 40 yd and b. and c. and d. and The figures are similar. The area of one figure is given. Find the area of the other figure to the nearest whole number. 27. The area of the larger triangle is 2015 ft. 45 ft 40 ft a. 2550 ft b. 1592 ft c. 1600 ft d. 2025 ft 28. Find the similarity ratio and the ratio of perimeters for two regular octagons with areas of and. a. 3 : 5; 3: 5 b. 9 : 25; 3 : 5 c. 3 : 5; 9 : 25 d. 9 : 25; 9 : 25 29. Find the circumference. Leave your answer in terms of. 4.4 cm a. cm b. cm c. cm d. cm 30. The circumference of a circle is 60 cm. Find the diameter, the radius, and the length of an arc of 140. a. 60 cm; 30 cm; 23.3 cm c. 120 cm; 30 cm; 160 cm b. 60 cm; 120 cm; 11.7 cm d. 30 cm; 60 cm; 11.7 cm
31. Find the area of the figure to the nearest tenth. 135 9 a. 95.4 in. 2 b. 30.4 in. 2 c. 10.6 in. 2 d. 190.8 in. 2 32. The radius of the bull s-eye of the dartboard is 8 inches. The radius of each concentric circle is 8 inches more than the radius of the circle inside it. If a dart lands at random on the dartboard, what is the probability that the dart will hit in area C? A B C D a. b. c. d. Use formulas to find the lateral area and surface area of the given prism. Show your answer to the nearest whole number. 33. 9 38 4 8 a. 798 m ; 814 m c. 798 m ; 830 m b. 760 m ; 862 m d. 760 m ; 830 m Find the surface area of the cylinder in terms of.
34. 6 in. 20 in. a. 240 in. b. 264 in. c. 312 in. d. 528 in. 35. Find the lateral area of the pyramid shown to the nearest whole number. 25 yd 43 yd a. 4278 yd b. 2836 yd c. 5671 yd d. 2150 yd 36. Find the lateral area of the cone to the nearest whole number. a. 7540 m b. 3770 m c. 4712 m d. 9425 m
Find the volume of the given prism. Round to the nearest tenth if necessary. 37. a. 17 m b. 34 m c. 8.5 m d. 1 m 38. Find the volume of the composite space figure to the nearest whole number. a. 170 cm b. 180 cm c. 120 cm d. 60 cm Find the volume of the cylinder in terms of. 39. 12 m 2.5 m a. 75 m b. 60 m c. 37.5 m d. 187.5 m
Find the volume of the square pyramid shown. Round to the nearest tenth as necessary. 40. 10 cm 12 cm 12 cm a. 40 cm b. 480 cm c. 147.3 cm d. 720 cm Find the volume of the cone shown as a decimal rounded to the nearest tenth. 41. 22 in. 18 in. a. 207.3 in. b. 1866.1 in. c. 5598.3 in. d. 2799.2 in. 42. Find the similarity ratio of a cube with volume 343 m to a cube with volume 1728 m. a. 7 : 12 b. 144 : 49 c. 12 : 7 d. 49 : 144 Find the surface area of the sphere with the given dimension. Leave your answer in terms of. 43. radius of 30 m a. 1,800 m b. 900 m c. 3,600 m d. 450 m
Find the volume of the sphere shown. Give each answer rounded to the nearest cubic unit. 44. 10 mm a. 1257 mm b. 4189 mm c. 419 mm d. 2094 mm Assume that lines that appear to be tangent are tangent. O is the center of the circle. Find the value of x. (Figures are not drawn to scale.) 45. 111 x O a. 291 b. 69 c. 55.5 d. 222 46. A chain fits tightly around two gears as shown. The distance between the centers of the gears is 20 inches. The radius of the larger gear is 11 inches. Find the radius of the smaller gear. Round your answer to the nearest tenth, if necessary. The diagram is not to scale. 19 inches a. 17.2 inches b. 6.2 inches c. 11 inches d. 4.8 inches
Find the value of x. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale. 47.,,, MN = 9 feet R P x A O N M 48. a. 4.5 ft b. 81 ft c. 9 ft d. 18 ft D C P x A B 49. a. 13 b. 26 c. 77 d. 38.5 8 6 x a. 10 b. 6 c. 8 d. 5
50. 7 10 x 22 a. 220 b. 31.4 c. 15.4 d. 3.2 51. AB = 15, BC = 7, and CD = 10 x D C B A a. 5.4 b. 15.6 c. 15.4 d. 10.5 52. m R = 44. Find m O. (The figure is not drawn to scale.) N O Q R a. 46 b. 44 c. 88 d. 136
53. Find the measure of BAC. (The figure is not drawn to scale.) A O B C a. 106 b. 37 c. 26.5 d. 53 54. m(arc DE) = 96 and m(arc BC) = 67. Find m A. (The figure is not drawn to scale.) D B A C E a. 14.5 b. 62.5 c. 81.5 d. 29 Write the standard equation for the circle. 55. center ( 6, 8), that passes through (0, 0) a. (x 6) + (y 8) = 10 c. (x + 6) + (y + 8) = 14 b. (x 6) + (y 8) = 196 d. (x + 6) + (y + 8) = 100 Find the slope of the line that passes through the pair of points. 56. (1, 7), (10, 1) a. 3 2 b. 2 3 c. 3 2 d. 2 3
57. Describe the locus that the figure represents. A l B a. all points 1 cm from line l b. all points equidistant from line l c. all points equidistant from point A and point B d. none of these 58. Each unit on the map represents 5 miles. What is the actual distance from Oceanfront to Seaside? y 8 Seaside 6 4 2 8 6 4 2 2 4 6 8 x 2 Landview Oceanfront 4 6 8 a. about 10 miles c. about 8 miles b. about 50 miles d. about 40 miles 59. Find the circumference of the circle in terms of. 39 in. a. 156 in. b. 39 in. c. 1521 in. d. 78 in. Find the slope of the line. 60. a. 5 3 b. 5 3 c. 3 5 d. 3 5
Are the graphs of the lines in the pair parallel? Explain. 61. y = 1 6 x + 8 2x + 12y = 11 a. Yes, since the slopes are the same and the y-intercepts are the same. b. No, since the y-intercepts are different. c. Yes, since the slopes are the same and the y-intercepts are different. d. No, since the slopes are different. Write the equation of a line that is perpendicular to the given line and that passes through the given point. 62. 4x 12y = 2; (10, 1) a. y = 3x + 29 c. y = 3x + 29 b. y = 1 3 x + 29 d. y = 1 3 x + 7 Solve the system of equations using substitution. 63. 3x + 2y = 7 y = 3x + 11 a. (6, 3) b. (6, 7) c. d. (5, 4) Solve the system using elimination. 64. 5x + 8y = 29 7x 2y = 67 a. ( 7, 9) b. c. ( 1, 3) d. ( 9, 2) Insert <, >, or = to make the sentence true. 65. a. = b. > c. < Evaluate the expression for the given value of the variable(s). 66. ; b = 2 a. 19 b. 17 c. 11 d. 21 Simplify by combining like terms. 67. a. b. c. d.
Solve the equation. 68. a. x = 2 or x = 1 1 c. x = 2 or x = 2 3 b. x = 2 or x = 4 d. x = 1 1 or x = 2 3 Solve the equation or formula for the indicated variable. 69., for U a. b. c. d. Solve the compound inequality. Graph the solution set. 70. 5x + 10 10 and 7x 7 14 a. x 4 or x 1 c. x 4 or x 3 8 6 4 2 0 2 4 6 8 8 6 4 2 0 2 4 6 8 b. x 0 and x 1 d. x 0 and x 3 8 6 4 2 0 2 4 6 8 8 6 4 2 0 2 4 6 8 71. 4x 5 < 17 or 5x + 6 > 31 a. x < 3 or x > 5 c. x < 3 or x > 7 2 5 8 6 4 2 0 2 4 6 8 8 6 4 2 0 2 4 6 8 b. x < 5 1 2 or x > 72 5 d. x < 5 1 2 or x > 5 8 6 4 2 0 2 4 6 8 72. For,. a. 19 b. 1 c. 21 d. 21 8 6 4 2 0 2 4 6 8