Level 1 Geometry 2012 Final Exam

Transcription

1 Level 1 Geometry 2012 Final Exam NAME: Circle Teacher: Cordero LeBlanc SheppardBrick Williams Circle block: A B C D E F G H INSTRUCTIONS: 1. PLEASE SHOW ALL OF YOUR WORK! If work is not shown, then credit may not be given. 2. If you cannot fit your work in the space given, please use extra paper and remember to put your name on it. 3. Neatness is expected. If I cannot read an answer, I cannot grade it and I will mark it incorrect. 4. Numeric answers will be accepted in any correct form (either in simplified radical form or in terms of π or in a decimal to two places.) 5. Don t forget to include units in your answers where appropriate.. If you do not understand the phrasing of a question please ask. 7. The last page is a formula sheet which you may detach for easier reference. Good luck! Point values as marked ( total possible points) Page & 10 Total:

2 1. (3 points) Given the following regular polygons, find the m FGH. G F H m FGH = 2. Assume the following statement is unconditionally true: If a butterfly is pink, it does not live in North America. a. (1 point) State the converse of the above statement. b. (4 points) Assuming that the original statement is true, determine whether the following statements are true. i. If Pearl Charax is a butterfly not found in North America, then it is pink. TRUE NOT NECESSARILY TRUE ii. If Henry's favorite butterfly is yellow, then it is found in North America. TRUE NOT NECESSARILY TRUE. iii. If a Little Wood Satyr is a butterfly found in North America, then it is not pink. TRUE NOT NECESSARILY TRUE iv. If a Pink Cattleheart is a pink butterfly, then there are no Pink Cattlehearts in North America. TRUE NOT NECESSARILY TRUE 2 2

3 3. (4 points) Quadrilateral ABCD can be defined by the points A(4,7), B(5,1), C(1,0) and D(0,8) which are plotted below. D a. Apply the following transformation to ABCD: A (x,y) (x 4, y) and plot the coordinates of its image. b. Describe the above transformation in words. C B 4. (4 points) The complement of an angle is 24 more than three times the angle. Find the measure of the angle and its complement. Measure of = Measure of complement = 5. (3 points) In the right square pyramid to the right, EF = 2 cm and AB = 20 cm. Find the volume of the pyramid. Volume = 3 3

4 . (4 points) Find x and y. x = 3x+2 y = 5y7 4x18 7. (3 points) Given: VW YZ TU. Find VX, VW and TU. VX = VW = TU = 8. (3 points) A 22 meter string is used to tie a heliumfilled balloon to the ground. Because of the breeze, the string makes an angle of approximately 85 o with the ground. a. Draw a diagram to represent b. What is the height of the balloon? the situation. height = 4 4

5 9. (3 points) Find the area of the following trapezoid. 12 Area = (4 points) The town of Brookville has a water tank that is shaped like a right circular cylinder with a diameter of 50 feet, as shown below. Water Tank h 50 feet a. The water tank has a volume of 58,90 cubic feet. What is h, the height, in feet, of the water tank? height = b. The town s planning board wants to build a new water tank to meet the needs of the town s growing population. The new water tank will be shaped like a right circular cylinder with the same height as the old water tank, but the volume of the new water tank will be 3 times the volume of the old water tank. Based on the town s plan, what would be the diameter, in feet, of the new water tank? diameter = 5 5

6 11. (3 points) Find the area of the shaded region formed by a rectangle whose sides are tangent to the circle and semicircles. Area = 12. (2 points) O is the center of a circle with chord AB of length 12. OP = 4. Find the radius of the circle. Radius = 13. (3 points) A cubical box (a box in the shape of a cube) of side length 9 in. is completely filled with water. You gently place a bowling ball of radius 4 in. inside the cube so that water spills out of the box. How much water remains in the box? Answer = 14. (2 points) Mary walks to the playground by walking 10 yards west, 15 yards north, 14 yards west, 20 yards north, yards west and 5 yards north. How far is the playground from her house? Distance =

7 15. (4 points) Given: AB and AC are tangent to circle O m DBC 38 o. Find the measures of: a. arc CD = b. DEB = c. arc CB = d. BAC = 1. (2 points) ABCD is a rhombus. Find its area. Area = 17. (2 points) In DEF, DE = x, EF = x + 2 and DF = x 3, where x is a positive number greater than 3. Sketch the triangle. a. Which angle of DEF is the smallest? b. How do you know? 7 7

8 18. (4 points) The locations of an oil rig (R), a lighthouse (L), and a buoy (B) are shown on the coordinate plane below. Triangle RLB is an isosceles triangle whose vertices represent the three locations. L (13, ) R ( 3, 1) B (13, 4) Scale 1 unit : 1 mile L lighthouse (13,) 4 oil rig R (3,1) B buoy (13,4) a. What is the distance, in miles, from the buoy (B) to the lighthouse (L)? b. Let M be the midpoint of LB. What are the coordinates of M? Distance = M = c. What is the distance, in miles, from the oil rig (R) to M, the midpoint of LB? Distance = d. What is the distance, to the nearest mile, from the oil rig (R) to the lighthouse (L)? Distance = 8 8

9 Choose 2 of the following 4 proofs to complete. Each proof is worth 4 points. Mark which 2 proofs you want graded. 19. Given: BI IF IC IG Prove: AD HE 20. Given: 1 2 PA PR P Prove: ΔAKR is isosceles 1 2 K A R 9 9

10 21. Given: Rectangle ABON and parallelogram MNOA Prove: MNB is isosceles N O M A B P 22. Given: A, B, C and D are points on circle O. BP Prove: CP AP DP