2 ND SEMESTER REVIEW PACKET

Transcription

1 Name Per. Date Honors Geometry 2 ND SEMESTER REVIEW PACKET UNIT 4 - SIMILARITY For number 1-2, plot the given figure and then the dilation of that figure given the following scale factor. 1) Dilation with a scale factor of 1/3 A (, ) B (, ) C (, ) D (, ) 2) Dilation with a scale factor of 3 M (, ) N(, ) O (, ) P (, ) 3) Suppose MOP with vertices M(4, -8), O(0, -4), and P(-2, 6) has dilation image M O P with vertices M (10, 20), O (0, -10), and P (-5, 15). What is the scale factor for the dilation? 2. 4) Graph the line y 2x 4. Dilate the line with a scale factor of 2. What is the equation of the new line? equation: 1

2 5) Find the value of x if ABC ~ DEF. 5. 6) The perimeter of a rectangle is 56 inches. The ratio of the length to the width is 6 : 1. Find the length and the width. Length = Width = 7) You purchase a scale model of the Brooklyn, which is located in Brooklyn, New York. The model states that the scale is 1 inch: 50 feet. The actual length of the bridge is 8940 feet. What is the length of the model? 5. 8) Nancy has a rectangle drawn in the corner of a 8 1/2 by 11 inch sheet of printer paper as shown in the diagram. To cut out the rectangle, Nancy must make two cuts. She wants to scale the rectangle so that she can cut it out using only one cut with a paper cutter. (Round answers to the nearest hundredth if necessary.) in in 2

3 State if the triangles in each pair are similar. If so, state how you know they are similar and complete the similarity statement. 9) 10) 11) 12) 13) 14) 3

4 Find the missing length. The triangles in each pair are similar. 15) 16) 17) 18) Solve for [x]. The triangles in each pair are similar. 19) 20) 21) 22) 4

5 23) Prove the following relationships. a) GIVEN: AB DE PROVE: ABC DEC A B C E D b) GIVEN: OL = 5 cm, PL = 10 cm, ML = 7.5 cm, NL = 15 cm PROVE: POL NML P L O M N STATEMENT REASON STATEMENT REASON 24) Prove the following relationships. a) GIVEN: QR ST PROVE: RP QR SP ST S Q P R T b) GIVEN: F HJI PROVE: GH JH = FH IH STATEMENT REASON STATEMENT REASON F o G J I o H 5

6 Find the geometric mean of the two numbers. 25) 4 and 6 26) 2 and 162 Find the missing number given one number and the geometric mean. 27) One number is 3 and the geometric mean is 18. Solve for all missing side lengths. 28) 29) 30). 31) 6

7 Find the missing length indicated. 32) 33) 34) 35) Solve for [x]. 36) 37) 38) 39) 7

8 UNIT 5 RIGHT TRIANGLE TRIG. Find the missing side lengths. Leave your answers as radicals in simplest form. 8

9 Find the value of each trigonometric ratio. Find the value of each trigonometric ratio to the nearest ten-thousandth. 9

10 Determine whether the following are (T)rue or (F)alse. 17. The angle of elevation is the angle formed between the horizon and the upward object. T or F 18. The angle of depression occurs when the diagram solves for a negative angle. T or F 19. The angle of depression occurs when looking downward in reference to the horizon. T or F 20. The foot of the ladder is the end of the ladder that is resting on the ground. T or F 21. The altitude of a plane is the same measurement as the height of the plane. T or F 22. The line of sight between two objects is the same as the horizon. T or F 23. The angle of elevation from the car to the girl at the top of the parking garage is 11 & 12. T or F The angle of depression from the helicopter to the boy on the third floor of the parking garage is The angle of depression from the boy on the third floor of the parking garage to the car is 10. T or F T or F After reading that the angle of depression from the girl to the car is 55, Tim labelled the diagram as shown. Has he labelled the diagram correctly? Explain A boy is flying a kite on a string 75 ft long. Determine the height of the kite in feet, if the string is at an angle of 42 to the ground. (2 decimal places) 10

11 28. Jeffrey is flying a kite but it got caught at the top of a 15 ft tree that is 65 ft away from where he is standing. If the string is tight, how long is the string that he has let out (round to the nearest foot)? 29. A blue bird sitting in its nest at the top of a tree spots a large red apple in Janice s hands at an angle of depression of 15. If Janice is 53 ft from the tree and the apple is 4 ft off the ground, how high is the bird off the ground? (2 decimal places) 30. An airplane is flying at an altitude of 8,700 ft over the ocean heading in the direction of the island. The pilot wants to land the plane on the island and so he begins his descent at an angle of depression of 21. What is the direct distance that the plane will travel from its current location to the landing location on the island (round to the nearest 100 ft)? 31. A loading ramp is 21 m long with a height of 7 m. What is the angle of incline that the ramp forms with the ground? (2 decimal places) 11

12 UNIT 6 SURFACE AREA AND VOLUME 1) Find the following for the given prism. Area of the base. Find the lateral area. B = LA = Find the surface area. Find the volume. SA = V = 2) Find the following for the triangular prism. Round to the nearest tenth if necessary. Area of the base. Find the lateral area. B = LA = Find the surface area. Find the volume. SA = V = 12

13 3) Find the following for the given cylinder and leave all answers in terms of π. Area of the base. Find the lateral area. B = LA = Find the surface area. Find the volume. SA = V = 4) Find the following for the given regular pyramid but first find the slant height to the nearest tenth = Area of the base. Find the lateral area. B = LA = Find the surface area. Find the volume. SA = V = 5). Find the following for the given cone. Round answers to the nearest tenth place. Area of the base. Find the lateral area. B = LA = Find the surface area. Find the volume. SA = V = 13

14 6) Find the following for the given sphere and leave all answers in terms of π. Find the surface area. Find the volume. SA = V = 7) Find the following for the given figure and round to the nearest hundredth. Find the surface area. Find the volume. SA = V = 14

15 8). Brookfield zoo is building a new dolphin tank. Federal regulations require that each dolphin have a 36 x 36 foot tank that is 12 feet deep. If the zoo is planning on having 3 dolphins in the tank, how many cubic feet of water needs to be in the tank? Amount of water in the tank: 9) The cylindrical air duct of a large furnace has a radius of 12 inches and a height of 120 feet. If it takes 23 minutes for the contents of the duct to be expelled into the air, what is the volume of the substance being expelled each Hour? Amount of air each hour: 10) Two layers of cake are as shown in the diagram. Calculate the area of the cake that will be frosted. If one can of frosting will cover 130 square inches of cake, how many cans do you need? Amount of frosting needed: Number of cans: 11). Tina bought an extra large slushy at the movies. She wants to divide it amongst her three children. The slushy has the following dimensions. The cups have the following dimensions. If the slushy is filled up the entire way and Tina wants to fill each cup to the top, does Tina have enough slushy to fill each cup? Hint: Each cup is a cylinder with a radius of 3 and a height of 7. The large slushy is a cylinder (radius of 5 with a height of 12) and hemisphere (radius of 5). Is there enough slushy for 3 small cups? 15

16 12) An ice-cream cone is 9 cm deep and 4 cm across the top. A single scoop of ice cream, 4 cm in diameter, is placed on top of the cone. If the ice cream melts into the cone, will it overflow? (Assume that the ice cream s volume does not change as it melts.) Will the ice cream overflow? 13) Mike is looking to buy a storage unit. He finds two units, one a cylinder and one a cone, that both cost the same price. The units are pictured below. Which unit should he buy to maximize his storage? Support your answer with mathematical proof. 4m 8m 12 m 14) If both of these cans of pizza sauce are cylinders, which is the better buy? 6m Which unit is the better buy? Which can is the better buy? 15) A birthday gift is 55cm, 40cm wide, and 5 cm high. The sheet of paper you want to use to wrap it measures 75cm by 100cm. Is the paper large enough to wrap the gift? Explain. Surface Area of Gift: Area of Paper: Is the paper large enough? Explain: 16

17 UNIT 7 - CIRCLES 17

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