GST Spring Final REVIEW 2016

Transcription

1 Class: Date: GST Spring Final REVIEW The equation of a circle is ( x + 5) 2 + Ê Ë Á y + 4ˆ 2 the circle. = 9. Find the center and the radius of the circle. Then graph 2. To cut down a dead tree so that it does not land on your house, you first need to find its height. You use a metal square to line up the top and bottom of the tree. The vertical distance from the ground to your eye is 5.5 feet, and the distance from you to the tree is 14 feet. Approximate the height (in feet) of the tree. Round your answer to the nearest tenth. 3. Find the radius of Q if PQR measures 30 and the arc length of PR is 6 centimeters. 1

2 4. Wallpaper is to be applied to the wall surrounding a Norman window (a shape made by placing a semicircle on top of a rectangle). How many square feet of wallpaper are required to cover the wall surrounding the window? 5. Find the volume of the composite solid. 6. Convert 31π 180 radians into degrees. 7. An image of a celebrity is going to be used on a promotional billboard. The person is 6 feet tall in real life, and 12 feet tall on the billboard. What is the scale factor of this dilation? 8. Write sin 33 in terms of cosine. 2

3 9. An architect is designing a garden for a client on a planning sheet. The client requests the relocation of a water fountain by the rule Ê Ë Á x, y ˆ Ê Ë Á x + 8, y 9 ˆ. Later, the client decides that they would prefer the water fountain s location moved from this new position 4 units left and 5 units up. Find the composition as a single transformation. 10. In the diagram, point G is a point of tangency, HG = 180, and HJ = 162. What is the radius of F? 11. Find the area of the triangle. Round your answer to the nearest tenth. 12. Write a rule for the translation of ABC to A B C. 3

4 13. Find RS. 14. A chemistry teacher makes a sign for the door to the room that contains the chemicals used in class. The danger sign is shaped like an equilateral triangle. Estimate the area of the sign to the nearest tenth of a square inch. 15. Graph ST with endpoints at SÊ Ë Á 4,0 ˆ and T Ê Ë Á 1, 1 ˆ and its image after the composition. Rotation: 90 counterclockwise about the origin Reflection: in the y-axis 16. A Ferris wheel is 420 feet in diameter. How far will a person riding on the Ferris wheel have traveled (in miles) when the wheel makes 48 revolutions? (1 mi = 5280 ft) 17. An adventure company wants to run a zip line from the top of one building that is 110 feet tall to the top of another building that is 40 feet tall. The two buildings are 46 feet apart. Estimate the length (in feet) of the zip line. Round your answer to the nearest tenth. 4

5 18. In the diagram, ST is tangent to R at S, TU is tangent to R at U, ST = 340, and TU = 8x Find the value of x. 19. A parasailer is attached to a boat with a rope. While parasailing, the angle of depression to the boat is 16. When the parasailer is 125 feet above the boat, how long is the rope? Round your answer to the nearest tenth of a foot. Find the value(s) of the variable(s). If necessary, round decimal answers to the nearest tenth

6 Find the surface area of the sphere Describe the similarity transformation that maps ABC to DEF (dilations have a center at the origin). 23. A bowling team roster has 7 players on it. How many groups of 4 players can be created? 6

7 Find the volume of the prism. 24. Let W be an acute angle. Use a calculator to approximate the measure of W to the nearest tenth of a degree. 25. cos W = In the diagram, m J = 84 and mjm = 95. Find mjk. 27. The point (10, 10) is on a circle with center ( 4, 2). Write the standard equation of the circle. 7

8 28. In an obstacle course, participants climb to the top of a tower and use a zip line to travel across a mud pit. The zip line extends from the top of a tower to a point on the ground 56.8 feet away from the base of the tower. The angle of elevation of the zip line is 34. Estimate the length of the zip line to the nearest tenth of a foot. 29. Graph the polygon and its image after a rotation of 90 counterclockwise about the origin. 30. In the diagram, AC = Find BC and AB. Write your answers in simplest form. 31. Use the probability distribution to determine the probability of an outcome less than You spin a spinner with 7 equal spaces numbered 1 through 7. What is the probability that the spinner lands on a 2 or a 6? 8

9 33. Find the value of x. 34. You play a game that requires rolling a six-sided die then randomly choosing a colored card from a deck containing 5 red cards, 5 blue cards, and 3 yellow cards. Find the probability that you will roll a 4 on the die and then choose a blue card. Use the diagram of circle Q to answer the question. 35. What word best describes US? 36. What word best describes RV? 37. Find the scale factor of the dilation. Then tell whether the dilation is a reduction or an enlargement. 9

10 38. In the diagram, KN = x + 4, JN = x + 46, LN = x + 22, and MN = x Find the value of x. 39. Find the value of x. 40. Find the area of the kite. 41. Your shirt drawer contains 9 different colored shirts that you will wear over the next 9 days. What is the probability that you will randomly choose the orange shirt to wear today and the red shirt to wear tomorrow? 42. A typical stop sign is in the shape of a regular octagon. The length of a side of a stop sign is 39.4 centimeters, and the radius is 51.5 centimeters. Calculate the area of the stop sign to the nearest square centimeter. 43. Convert 249 to radians. 44. An amusement park has two featured rides that require an additional ticket, the Slingshot and the Scream Flyer. On a summer day, 1245 visitors entered the park. 280 visitors bought tickets for either the Slingshot or the Scream Flyer. 195 visitors bought a ticket for the Slingshot and 234 visitors bought a ticket for the Scream Flyer. What is the probability that a randomly selected visitor bought tickets for both the Slingshot and the Scream Flyer? 10

11 45. A tent in the shape of a right square pyramid has a volume of 699 cubic feet and height of 9 feet. Find the area of the base. 46. A custom fish tank shaped like a rectangular prism needs to have a length of 12 inches, a width of 18 inches and hold a volume of 7312 cubic inches. What height must the tank be made to meet these specifications? 47. You want to enlarge a picture by a factor of 4.5 from its current size of 4 inches by 6 inches. What is the size of the enlarged picture? Find the surface area of the cone In the diagram, m D = y, m G = z, m F = 71, and m E = 105. Find the value of each variable. 11

12 50. In the diagram, name the vector and select its component form. 51. Within a radius of 2.2 miles of a cell phone tower, 104 people per square mile enjoy quality phone signals. What is the population of cell phone users within the tower s coverage area? 52. Find the value of x. 53. The vertices of DEF are D( 3, 4), E( 1, 4), and F( 2, 0). Graph DEF and its image after the reflection in the line y = x. 54. Two mountain climbers are standing 5700 feet apart on opposite sides of a mountain. The mountain s angle of elevation on the east side is 10, while the west side has a much steeper incline of 40. How far does the climber on the east side need to climb to reach the top of the mountain? 55. A box of golf balls contains 8 balls. Each golf ball has a diameter of 3.5 centimeters. What is the total volume of golf balls in 4 boxes? 12

13 56. In the diagram, m QRP = 10x. Find the value of x. 57. In the diagram, AC = x, BC = x, and AB = 22. Find the value of x. Write your answer in simplest form. 58. In the diagram, the figure is reflected in line a. The image is then reflected in line b. Describe a single transformation that maps F to F. 13

14 59. Identify and describe the solid produced by rotating the figure around the given axis. 60. Prism X and Prism Y are similar. The volume of Prism Y is 100 cm 3. Find the volume of Prism X. 14

15 GST Spring Final REVIEW 2016 Answer Section 1. ANS: center: Ê Ë Á 5, 4ˆ, radius: 3 PTS: 1 DIF: Level 1 REF: Geometry Sec NAT: HSG-GPE.A.1 KEY: circle NOT: Example 3 2. ANS: about 41.1 ft PTS: 1 DIF: Level 1 REF: Geometry Sec. 9.3 NAT: HSG-SRT.B.5 KEY: geometric mean application NOT: Example ANS: about cm PTS: 1 DIF: Level 1 REF: Geometry Sec NAT: HSG-C.B.5 HSG-CO.A.1 KEY: arc length NOT: Example 2 4. ANS: about ft 2 PTS: 1 DIF: Level 2 REF: Geometry Sec NAT: HSG-GMD.A.1 HSG-C.B.5 KEY: area application NOT: Example ANS: 2016 in. 3 PTS: 1 DIF: Level 1 REF: Geometry Sec NAT: HSG-GMD.A.1 HSG-GMD.A.3 HSG-MG.A.1 KEY: volume composite solid NOT: Example 5 1

16 6. ANS: 31 PTS: 1 DIF: Level 1 REF: Geometry Sec NAT: HSG-C.B.5 HSG-CO.A.1 KEY: radian NOT: Example 5 7. ANS: 2 PTS: 1 DIF: Level 1 REF: Geometry Sec. 4.5 NAT: HSG-SRT.A.1b KEY: dilation scale factor reduction transformation enlargement NOT: Example 5 8. ANS: cos 57 PTS: 1 DIF: Level 1 REF: Geometry Sec. 9.5 NAT: HSG-SRT.C.6 HSG-SRT.C.7 HSG-SRT.C.8 KEY: sine cosine NOT: Example 2 9. ANS: Ê Ë Á x, y ˆ Ê Ë Á x + 4, y 4 ˆ PTS: 1 DIF: Level 1 REF: Geometry Sec. 4.1 NAT: HSG-CO.A.2 HSG-CO.A.4 HSG-CO.A.5 HSG-CO.B.6 KEY: transformation image preimage translation composition of transformations application NOT: Example ANS: 19 PTS: 1 DIF: Level 1 REF: Geometry Sec NAT: HSG-C.A.2 KEY: circle radius of a circle NOT: Example ANS: about units 2 PTS: 1 DIF: Level 1 REF: Geometry Sec. 9.7 NAT: HSG-SRT.D.9 KEY: area of a triangle NOT: Example ANS: Ê Ë Á x,y ˆ Ê Ë Á x + 2, y 2 ˆ PTS: 1 DIF: Level 1 REF: Geometry Sec. 4.1 NAT: HSG-CO.A.2 HSG-CO.A.4 HSG-CO.A.5 HSG-CO.B.6 KEY: transformation image preimage translation NOT: Example ANS: RS 32.9 PTS: 1 DIF: Level 2 REF: Geometry Sec NAT: HSG-C.A.2 KEY: circle application secant segment tangent of a circle NOT: Example 3-2 2

17 14. ANS: about 84.9 in. 2 PTS: 1 DIF: Level 2 REF: Geometry Sec. 9.2 NAT: HSG-SRT.C.8 HSG-MG.A.1 KEY: special right triangles application NOT: Example ANS: PTS: 1 DIF: Level 1 REF: Geometry Sec. 4.3 NAT: HSG-CO.A.2 HSG-CO.A.4 HSG-CO.A.5 HSG-CO.B.6 KEY: rotation center of rotation angle of rotation transformation translation reflection composition of transformations NOT: Example ANS: about 12 mi PTS: 1 DIF: Level 2 REF: Geometry Sec NAT: HSG-GMD.A.1 HSG-C.B.5 HSG-CO.A.1 KEY: circumference application NOT: Example ANS: about 83.8 ft PTS: 1 DIF: Level 2 REF: Geometry Sec. 9.1 NAT: HSG-SRT.C.8 KEY: Pythagorean Theorem application NOT: Example ANS: x = 32 PTS: 1 DIF: Level 1 REF: Geometry Sec NAT: HSG-C.A.2 KEY: circle tangent of a circle application NOT: Example 5 3

18 19. ANS: about ft PTS: 1 DIF: Level 1 REF: Geometry Sec. 9.5 NAT: HSG-SRT.C.6 HSG-SRT.C.7 HSG-SRT.C.8 KEY: sine cosine application NOT: Example ANS: z 25.9 PTS: 1 DIF: Level 1 REF: Geometry Sec. 9.3 NAT: HSG-SRT.B.5 KEY: geometric mean NOT: Example ANS: about cm 2 PTS: 1 DIF: Level 1 REF: Geometry Sec NAT: HSG-GMD.A.2 HSG-GMD.A.3 HSG-MG.A.1 KEY: sphere surface area NOT: Example ANS: translation 5 units right and 2 units up followed by a dilation with a scale factor of 2 PTS: 1 DIF: Level 1 REF: Geometry Sec. 4.6 NAT: HSG-CO.A.5 KEY: dilation similarity transformation translation transformation NOT: Example ANS: 35 PTS: 1 DIF: Level 1 REF: Geometry Sec NAT: HSS-CP.B.9 KEY: combination application NOT: Example ANS: 180 cm 3 PTS: 1 DIF: Level 1 REF: Geometry Sec NAT: HSG-GMD.A.1 HSG-GMD.A.2 HSG-GMD.A.3 HSG-MG.A.1 KEY: volume NOT: Example ANS: about 61.3 PTS: 1 DIF: Level 1 REF: Geometry Sec. 9.6 NAT: HSG-SRT.C.8 KEY: inverse trigonometric ratios NOT: Example ANS: mjk = 97 PTS: 1 DIF: Level 1 REF: Geometry Sec NAT: HSG-C.A.2 KEY: inscribed angle NOT: Example 2 4

19 27. ANS: ( x + 4) 2 + Ê Ë Á y + 2ˆ 2 = 260 PTS: 1 DIF: Level 1 REF: Geometry Sec NAT: HSG-GPE.A.1 KEY: circle standard equation of a circle NOT: Example ANS: about 68.5 ft PTS: 1 DIF: Level 2 REF: Geometry Sec. 9.4 NAT: HSG-SRT.C.6 HSG-SRT.C.8 KEY: angle of elevation application NOT: Example ANS: PTS: 1 DIF: Level 1 REF: Geometry Sec. 4.3 NAT: HSG-CO.A.2 HSG-CO.A.4 HSG-CO.A.5 HSG-CO.B.6 KEY: rotation center of rotation angle of rotation transformation NOT: Example ANS: BC = 15, AB = 30 PTS: 1 DIF: Level 1 REF: Geometry Sec. 9.2 NAT: HSG-SRT.C.8 KEY: special right triangles NOT: Example ANS: 7 10 PTS: 1 DIF: Level 1 REF: Geometry Sec NAT: HSS-CP.B.9 KEY: probability distribution interpreting probability distributions NOT: Example 2 5

20 32. ANS: 2 7 PTS: 1 DIF: Level 1 REF: Geometry Sec NAT: HSS-CP.A.1 HSS-CP.B.7 KEY: application compound event disjoint finding probabilities of compound events NOT: Example ANS: x = 7 PTS: 1 DIF: Level 1 REF: Geometry Sec NAT: HSG-C.A.2 KEY: circle application secant segment NOT: Example ANS: 5 78 PTS: 1 DIF: Level 1 REF: Geometry Sec NAT: HSS-CP.A.1 HSS-CP.A.2 HSS-CP.A.3 HSS-CP.A.5 HSS-CP.B.6 HSS-CP.B.8 KEY: independent events application probability of independent events NOT: Example ANS: tangent PTS: 1 DIF: Level 1 REF: Geometry Sec NAT: HSG-CO.A.1 HSG-C.A.2 KEY: circle NOT: Example ANS: chord PTS: 1 DIF: Level 1 REF: Geometry Sec NAT: HSG-CO.A.1 HSG-C.A.2 KEY: circle NOT: Example ANS: 4 9 ; reduction PTS: 1 DIF: Level 1 REF: Geometry Sec. 4.5 NAT: HSG-SRT.A.1b KEY: dilation scale factor enlargement reduction transformation NOT: Example ANS: x = 2 PTS: 1 DIF: Level 1 REF: Geometry Sec NAT: HSG-C.A.2 KEY: circle segments of a chord application NOT: Example 1 6

21 39. ANS: x = 2 95 PTS: 1 DIF: Level 1 REF: Geometry Sec. 9.1 NAT: HSG-SRT.C.8 KEY: Pythagorean Theorem NOT: Example ANS: 84 cm 2 PTS: 1 DIF: Level 1 REF: Geometry Sec NAT: HSG-GMD.A.3 KEY: area NOT: Example ANS: 1 72 PTS: 1 DIF: Level 2 REF: Geometry Sec NAT: HSS-CP.B.9 KEY: permutation application NOT: Example ANS: about 7499 cm 2 PTS: 1 DIF: Level 1 REF: Geometry Sec NAT: HSG-GMD.A.3 KEY: application area regular polygon NOT: Example ANS: 83π 60 rad PTS: 1 DIF: Level 1 REF: Geometry Sec NAT: HSG-C.B.5 HSG-CO.A.1 KEY: radian NOT: Example ANS: 0.12 PTS: 1 DIF: Level 2 REF: Geometry Sec NAT: HSS-CP.A.1 HSS-CP.B.7 KEY: application compound event NOT: Example ANS: about 233 ft 2 PTS: 1 DIF: Level 1 REF: Geometry Sec NAT: HSG-GMD.A.1 HSG-GMD.A.3 HSG-MG.A.1 KEY: application volume pyramid NOT: Example ANS: about in. PTS: 1 DIF: Level 1 REF: Geometry Sec NAT: HSG-GMD.A.1 HSG-GMD.A.2 HSG-GMD.A.3 HSG-MG.A.1 HSG-MG.A.2 KEY: volume application NOT: Example 4 7

22 47. ANS: 18 in. by 27 in. PTS: 1 DIF: Level 1 REF: Geometry Sec. 4.6 NAT: HSG-CO.A.5 KEY: dilation similarity transformation translation NOT: Application ANS: about cm 2 PTS: 1 DIF: Level 1 REF: Geometry Sec NAT: HSG-GMD.A.1 HSG-GMD.A.3 KEY: surface area cone NOT: Example ANS: y = 109, z = 75 PTS: 1 DIF: Level 1 REF: Geometry Sec NAT: HSG-C.A.2 KEY: inscribed polygon application NOT: Example ANS: AO, 4,1 PTS: 1 DIF: Level 1 REF: Geometry Sec. 4.1 NAT: HSG-CO.A.2 KEY: vector initial point terminal point horizontal component vertical component component form NOT: Example ANS: about 1,581 people PTS: 1 DIF: Level 1 REF: Geometry Sec NAT: HSG-GMD.A.1 HSG-MG.A.2 KEY: population density application circle NOT: Example ANS: x = 38 PTS: 1 DIF: Level 1 REF: Geometry Sec NAT: HSG-C.A.2 KEY: circle application measures of arcs NOT: Example 2 8

23 53. ANS: PTS: 1 DIF: Level 1 REF: Geometry Sec. 4.2 NAT: HSG-CO.A.2 HSG-CO.A.4 HSG-CO.A.5 HSG-CO.B.6 KEY: reflection line of reflection transformation NOT: Example ANS: about ft PTS: 1 DIF: Level 2 REF: Geometry Sec. 9.7 NAT: HSG-SRT.D.10 HSG-SRT.D.11 HSG-MG.A.3 KEY: Law of Sines application NOT: Example ANS: about cm 3 PTS: 1 DIF: Level 2 REF: Geometry Sec NAT: HSG-GMD.A.2 HSG-GMD.A.3 HSG-MG.A.1 KEY: sphere application volume NOT: Example ANS: x = 9 PTS: 1 DIF: Level 1 REF: Geometry Sec NAT: HSG-C.A.2 KEY: inscribed polygon application NOT: Example ANS: x = 11 2 PTS: 1 DIF: Level 1 REF: Geometry Sec. 9.2 NAT: HSG-SRT.C.8 KEY: special right triangles NOT: Example ANS: 120 rotation about point J PTS: 1 DIF: Level 1 REF: Geometry Sec. 4.4 NAT: HSG-CO.A.5 KEY: Reflections in Intersecting Lines Theorem NOT: Example 4 9

24 59. ANS: cylinder with radius 2 PTS: 1 DIF: Level 1 REF: Geometry Sec NAT: HSG-GMD.B.4 KEY: solid of revolution NOT: Example ANS: 800 cm 3 PTS: 1 DIF: Level 1 REF: Geometry Sec NAT: HSG-GMD.A.1 HSG-GMD.A.2 HSG-GMD.A.3 HSG-MG.A.1 HSG-MG.A.3 KEY: volume similar solids NOT: Example 6 10