Download 2010 Final Exam Geometry Review Packet

Final Exam Geometry Review Packet
Name:__________________________
12. _______ What is the length of the hypotenuse of a right triangle with leg lengths of 12 and 6?
A. 3 2
B. 144
C. 6 3
D. 6 5
13. _______ Find the unknown side length of the right triangle below. Write your answer in simplest
radical form.
14. _______ An isosceles right triangle has leg lengths of 4 cm. Find the length of the hypotenuse.
Round your answer to one decimal place.
15. _______ The length of one leg of a right triangle is 10 cm and the length of the hypotenuse is
20 cm. Find the length of the other leg. Write your answer in simplest radical form.
16. _______ Which of the following is not a Pythagorean triple or a multiple of a Pythagorean triple?
A. 10, 24, 26
B. 21, 72, 75
C. 8, 10, 12
D. 5, 12, 13
17. _______ What type of triangle has side lengths 25, 60, and 65?
A. Acute
B. Right
C. Obtuse
D. Not a triangle.
18. _______Which side lengths do not form a right triangle?
A. 3, 6, 9
B. 4, 6, 9
C. 4, 5, 6
D. 3, 4, 5
19. _______Find the length of the hypotenuse. Write answer in simplest radical form.
20. _______Find the lengths of the legs.
A. 4 cm
B. 4 2 cm
C. 2 2 cm
D. 8 2 cm
8
21. _______Find the values of x and y. Write your answers in simplest radical form.
________
Use the diagram for Exercises 22-15
22. _______ _______ Find the tan A and tan B. Round to 4 decimal places.
23. _______ _______ Find the sin A and sin B. Round to 4 decimal places.
24. _______ _______ Find the cos A and cos B. Round to 4 decimal places.
25. _______
26. _______
27. _______
28. _______
29. _______
30. a._______
b. _______
31. _______
32. _______
33. _______ Find the lengths of the sides of the right triangle. Round answers to nearest tenth.
34. _______ Find the lengths of the sides of the right triangle. Round answers to nearest tenth.
35. _______ The measures of three of the interior angels of a quadrilateral are 109  , 114  and 75  .
What is the measure of the fourth interior angle?
A. 52 
B. 85 
C. 62 
D. 75 
36. _______ Find the measure of an interior and an exterior angle of a regular hexagon.
________
41. _______
42.
__________________________________
43. _______
44. _______
45.
___________________________
46. _______
47. _______
48. Points Q (0, 0), R (2, 4), S (4, 4) and T (4, 2) form a quadrilateral. Determine whether
QRST is a kite. Explain.
__________________________________________________
49. _______Find m  A in the kite shown.
A. 88 
B. 58 
C. 90 
D. 60 
50. _______ What is the most specific name for the quadrilateral ABCD?
A. Rhombus
B. Kite
C. Square
D. Parallelogram
51. A quadrilateral has at least one pair of opposite angles congruent. What types of
quadrilaterals meet this condition?
________________________________________
52. _______Name a chord in  C.
53. _______Name a diameter in  C.
54. _______Name a radius in  C.
55. _______Which term best describes BD ?
A. radius
B. chord
C. tangent
56. _______Which term best describes D?
A. point of tangency
C. common tangent
B. center
57. _______ In the diagram, A is a point of tangency. Find the radius r.
58. _______ What is the value of x?
D. secant
D. radius
Use the diagram for Exercises 59-63 . AD is a diameter of  C.
59. _______
60. _______
61. _______
62. _______
A. 100 
B. 150 
C. 140 
A. 80 
B. 100 
C. 90 
D. 130 
63. _______
D. 120 
Use the diagram for Exercises 64 – 67. AB  AC .
64. _______
65. _______
A. 230 
B. 225 
C. 245 
66. _______ Suppose ED = 3x – 2 and FD = 5x – 8. Find the value of x.
67. _______ Suppose AB = 16 and ED = 4. What is AF?
A. 2
B. 4
C. 6
D. 8
68. _______ Suppose CD = 6x – 3 and FD = x + 2. Find the value of x.
69. _______ Suppose
A. 90 
= (3x – 5)  and m
B. 80 
70. _______ Find ST and QT.
71. _______ Find the value of x.
= (5x – 35)  . What is m
?


C. 180
D. 100
D. 240 
72. _______What is the value of x? Round to the nearest tenth.
A. 0.8
B. 4.6
C. 6.0
D. 6.8
73. _______ What is the value of x?
74. _______ What is the value of y?
A. 20
B. 22
C. 24
D. 25
C. 68 
D.72 
Use the diagram in Exercises 75 and 76.
75. _______ Find m BAC.
76. _______What is m ABC ?
A. 56 
B. 60 
77. _______In the diagram, what is the value of x?
A. 102 
B. 156 
C. 106 
D. 78 
78. ___________________Write the standard equation of the circle with center (2, 3) and radius 7.
79. ___________________The point (-3, 2) is on a circle whose center is (3, -3). Write the standard
equation of the circle.
80. _______ A parallelogram has a base of 6 cm and a height of 4 cm. What is the area?
A. 12 cm 2
B. 24 cm 2
C. 36 cm 2
D. 48 cm 2
81. The length of the hypotenuse of a right triangle is 25cm and the length of a leg is 15 cm.
_______a. Find the area of the triangle.
_______b. Find the perimeter.
82. _______ A rectangle has an area of 243 m 2 and its length is triple its width.
_______a. Find the length.
_______b. Find the perimeter.
83. _______ Find the area of the given trapezoid.
84. _______A rhombus has an area of 45 cm 2 and the length of one diagonal is 9 cm.
What is the length of the other diagonal?
A. 5 cm
B. 15 cm
C. 20 cm
D. 10 cm
85. _______The lengths of the diagonals of a kite are 16 cm and 21 cm. What is the area?
A. 84 cm 2
B. 168 cm 2
C. 336 cm 2
D. 672 cm 2
86. The lengths of the bases of two similar right triangles are 6 inches and 12 inches.
The smaller triangle has an area of 42 square inches.
_______a. Find the height of the smaller triangle.
_______b. Find the area of the larger triangle.
87. _______The areas of two similar trapezoids are 24 m 2 and 18 m 2 . What is the ratio of the
perimeter of the larger trapezoid to the perimeter of the smaller trapezoid?
A. 4 : 3
B. 4 : 3
C. 2 : 3
D. 2 : 3
88. The side length of a regular hexagon is 11 feet.
_______a. Find the apothem. Round to one decimal place.
_______b. Find the area. Round to one decimal place.
89. _______Find the circumference of a circle with diameter 11 inches. Round to two decimal places.
90. _______ Find the approximate radius of a circle with circumference 23 meters.
A. 3.66 m
B. 7.32 m
C. 36.13 m
D. 72.26 m
91. _______Find the length of arc RS.
92. _______ Find the area of the shaded region.
93. _______ Find the area of the shaded region.
94. _______Which of the following solids has 12 edges?
A. Rectangular Prism
B. Triangular Prism
C. Triangular Cylinder
D. Square Pyramid
95. _______Tell whether the solid is a polyhedron. If it is, name the polyhedron
and find the number of faces, vertices and edges.
96. _______ A solid has 12 edges and 6 faces. How many vertices does it have?
A. 6
B. 8
C. 10
D. 12
97. _______How many faces and edges does a hexagonal pyramid have?
A. 6 faces, 6 edges
B. 7 faces, 12 edges
C. 4 faces, 14 edges
D. 6 faces, 8 edges
98. _______What is the shape of the cross section formed by the plane perpendicular
to the base through the top vertex of the square pyramid?
99. _______ The ratio of volumes of tow spheres is 1 : 27. What is the ratio of their surface areas?
A. 1 : 3 B. 1 : 81
C. 1 : 9 D. 3 : 81
100. _______Two similar solids have a scale factor of 1 : 3. Find the volume of the smaller solid if
the volume of the larger solid is 54 cubic centimeters.
101. _______ Two triangular prisms are similar. The surface area of one prism is 70 square inches.
The surface area of the other prism is 105 square inches. Find the scale factor of the
smaller prism to the larger prism.
102. _______ What is the surface area of a right rectangular prism with height 3 inches,
length 6 inches and width 12 inches?
A. 252 in. 2
B. 108 in. 2
C. 180 in. 2
D. 216 in. 2
103. _______What is the surface area of a right cylinder with a radius of 3 cm and a height of 6 cm?
A. 27  cm 2
B. 81  cm 2
C. 72  cm 2
D. 54  cm 2
104. _______ What is the area of a lateral face of a regular square pyramid with lateral edges of
length 17 inches and base edges of length 10 inches.
A. 81.24 in 2
B. 85 in 2
C. 162.48 in 2
D. 170 in 2
105. _______ What is the surface area of a regular square pyramid with base edge length of
12 inches and a height of 10 inches?
A. 144 in 2
B. 360 in 2
C. 423.89 in 2
D. 283.94 in 2
106. _______What is the surface area of the right cone?
A. 48  m 2
B. 52  m 2
C. 60  m 2
D. 85  m 2
107. _______ The diameter of a sphere is 9 inches. Find the surface area of the sphere.
Round your answer to two decimal places.
108. _______ The surface area of a sphere is 9  square meters. What is the radius of the sphere?
A. 1.5 m
B. 3 m
C. 4 m
D. 6 m
109. _______What is the volume of a rectangular prism with height 3 inches, length 5 inches
and width 9 inches?
A. 135 in 3
B. 108 in 3
C. 180 in 3
D. 216 in
110. _______Find the volume of the pyramid.
111. _______ What is the volume of a regular square pyramid with base edges of length 48 in.
and a height of 10 in.?
A. 5760 in. 3
B. 23,040 in. 3 C. 7680in. 3
D. 2560 in. 3
112. _______A cone-shaped bottle has a radius of 18 centimeters at its base. If the bottle
holds 6400 cubic centimeters when completely filled, what is its height?
A. 18.9 cm
B. 19.8 cm
C. 6.6 cm
D. 6.3 cm
113. A sphere has a volume of 1316 cubic meters. Round your answers to two decimal places.
________a. Find the radius.
________b. Find the surface area.
114. _______ Which of the following is the net for a cube?
115. ________Which of the following is a net for a right cylinder.
116. Draw the net for a right square pyramid.
117. Draw the net for a right triangular prism.
118. How many planes of symmetry does a sphere have?
119. How many planes of symmetry does a rectangular prism have?
___________________
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3
120. A coin is tossed and a die is rolled. What is the probability that the coin shows heads and the die shows five?
__________________
121. A coin is tossed and a die is rolled. What is the probability that the coin shows tails and the die shows
multiple of 3?
__________________
122. A drawer contains 9 red socks, 2 white socks, and 7 blue socks. Without looking, you draw out a sock and then
draw out a second sock without returning the first sock. What is the probability that the first sock and the second sock
are both blue?
__________________
123. Of 100 students, 37 are taking Geometry, 52 are taking Spanish, and 11 are taking both Geometry and Spanish. If
a student is picked at random, what is the probability that the student is taking Geometry or Spanish?
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