Geometry Final Exam Review
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1 Name: Period: Geometry Final Eam Review 1. Find the volume and surface area of the following figures. a) 5' b) c) Square base, all edges of the pyramid have length of ", h = 5.66". 1' Find the volume and total surface area for the prism at right. The base is a regular heagon. 5' 0'
2 . Which cone has the greater volume? The greater surface area? Prove your answer. a) b) " 6" " 6". 0 foot tree casts a 0 foot shadow the same time Marcus's shadow is 9 feet long. How tall is Marcus? 5. The diagram below shows a grain conveyor belt. The grain is shuttled along the belt and dumped into the grain silo. To function properly, the conveyor belt must be placed so that the angle measures between 0 and 5. If the conveyor is meters long, what are the minimum and maimum heights, h, the conveyor can reach? m h
3 6. nna, ertha, and andida are out in a field. ertha takes readings and finds that she is 100 feet from nna. She also finds that the angle formed by nna, herself, and andida (with herself at the verte) measures 110. andida sites the angle formed by nna, herself, and ertha (with andida at the verte); it measures. How far apart are nna and andida? ertha nna andida 7. regular 7-gon has side lengths of 10 cm. alculate the area of the 7-gon.. The fence shown below is going to enclose your favorite sheep Zoe. How much area does she have to graze in? 60 5
4 9. In the figure below, part of a regular n-gon is covered up by a piece of graph paper and you can only see this one part. What is n? 10. alculate the area of the shaded region. 6 Solve for the variables y 7 1' º y '
5 Find the area. 19. ' ' 6 10 = y Find the sum of the measures of the interior angles of a -gon. 1. F ~ G. The area of F is 55 sq. in. Find the area of G. F 7 G =. ircle has chords F ED. Eplain how you find each measure. 7 w z F y E D w = = y = z =. In Δ, m = 5, m = 70, and the shortest side is 15 cm. Find the length of the longest side.
6 . Find the perimeter and area of this figure. 5. alculate The area of the triangle at right is 1 square units. What is its perimeter? Show all subproblems clearly game is played by spinning two spinners. If the colors match, the player wins. What is the probability that a player wins? R 1 G R G
7 . Find the probability of entering each room. a) P() = b) P() = c) P()= 9. Simplify the following: a) ( y)(7 y ) b) 5 6 y z 9 y z 7 7 c) ( 5 yz ) 0. Factor the following: a) 5 b) Solve the following systems of equations: a) b) 5 y = 6 + y = 10 5y = y = 10
8 . Solve for. a) b) c) D. Graph the following equations on the coordinate grid. Identify the slopes and y-intercepts. 1 y = + y =. In the figure at right, three lines intersect in a point. Given the measures of the acute angles as shown, what is the value of + y? () 0 () 100 () 10 (D) 150 (E) y 5. In circle O at right, m<5=6º. What is m<1? () º () 1º () º (D) 6º (E) 11º 1 O 6 5 D
9 6. If the ratio of the surface areas of two sphere is 9 9, what is the ratio of the volume of the smaller sphere to the volume of the larger sphere? 16 () () 9 () (D) (E) 7 7. What is the area of the shaded region in the figure at right? () 10 () () 6 (D) (E) Identify the equation of the line that contains the points (,1) and (0,7). () y = () y = () y = 7 + (D) y = 7 7 (E) y = In the figure at right, <X <Z and WX = YZ. Which of the following can be used to prove ΔWXU ΔYZU? () SSS () SS () SS (D) S (E) HL X Y U 0. In the figure at right, if YZ = 10, what is the length of XY? W Z () 7.07 () 17. () 1.5 (D) 5 (E).9 Y 1. The figure at right shows a sketch of a house. The roof is at an angle of 5º with the horizontal and the brick chimney is perpendicular to the horizontal line. What is the value of? () 5 () 55 () 15 (D) 15 (E) 165 Z 60 5 X 5
10 . onnect the points (0,-5), (-1,0), and (0,5) to form a triangle. What is the perimeter of the triangle? () 0 units () 6 units () units (D) 60 units (E) 61 units. Solve: = 1 () = () = 7 () = 7 (D) = 1. Given M(-, ) is the midpoint of where (5, -1) then the coordinates of are: () (, ) () (1.5, 1) () (1, -7) (D) (-9, 7) 5. line goes through the points (, 6) and (-, ). line perpendicular to that line is: 1 () y = 7 () y = + 1 () y = (D) y = line parallel to 5y = 0 is + 5 () y = 1 () y = 5 () y = + (D) y = The distance between the points (-1, 5) and (-, -1) is: () 10 () 5 () (D) 5
11 . The measure of EKG is: () 10 () 0 H E () 0 (D) 0 (E) 10 F 6-0 K G 9. The measure of is: () 5 () 0 () 70 (D) In the figure to the right, n is a whole number. What is the smallest possible value for n that will still form a triangle? 1 1 n () 5 () 6 () 7 (D) (E) m and m 6 are angles. () corresponding () vertical () alternate interior (D) supplementary m o 1 5. m 1 and m 5 are angles. () corresponding () vertical () alternate interior (D) supplementary n Given the area of ΔPQR is in then the length of QR is: () 6 in () 10 in P () 1 in (D) 7 in Q R 5. Find the value of in the diagram. () 0 () 0 () (D)
12 55. Find the area of the square. () + () + 1 () + (D) If the perimeter of the square is 5 inches, what is the value of? () 1 () 1 () (D) Which equation below can be used to solve for in the triangle to the right? () sin = 7 () cos = () tan = (D) = In the figure to the right, DF and FE Which additional information can be used to prove Δ ΔDEF? () () () D F E D F E 59. Is ΔN ΔN? () Yes by SS. (D) Yes by HL. () Yes by SSS. (E) Not necessarily. () Yes by SS. N 60. What is the volume of the cylinder shown? () 0π () 60π () 90π (D) 10π The perimeter of the square to the right is 0 cm. What is the length of the diagonal? () = 5 cm () = 0 cm () = 10 cm (D) = 5 cm
13 6. What is the value of? 0 10 () = () =. 5 () = 9 (D) = Find in the circle. () 70 () 90 () 110 (D) In circle O at right, which statement must be true? () 1 () 1 () 1 (D) 1 + = 10 1 O 65. PT is tangent to circle N at T. The area of circle N is 5π cm. MP = cm, what is the length of PT? () cm () 6 cm () 1 cm (D) cm N M P T 66. Find the value of in the figure to the right: () () () 9 (D) Which of the following does not have diagonals that bisect each other? () rectangles (D) squares () parallelograms (E) ll have diagonals that bisect each other. () rhombuses
14 6. Given: DE and is midpoint of D Prove: ED D E 69. Given: ZX WY and X is the midpoint of WY Prove: ZW ZY Z W X Y 70. Given: D is a square Prove: D D
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