Accelerated Geometry B/Advanced Algebra. Review of Accelerated Coordinate Algebra/Geometry A

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1 Accelerated Geometry B/Advanced Algebra Review of Accelerated Coordinate Algebra/Geometry A Name: Date: Period: 1. In the following diagram, points T, S and R are points of tangency. Find the perimeter of triangle XYZ. Find the value for each variable in each of the following

2 14. Find each of the following. 15. Find the length and area of the shaded sector. Leave your answers in exact form. Find the surface area and volume of the given spheres. Leave your answers in exact form The spherical building at Epcot Center has a volume of 2,352,051 ft 3. Find the length of its diameter to the nearest whole foot. 19. The volume of a sphere is 120 ft 3. If the radius of another sphere is 1 the size, what is the volume? What is the value of the expression for and? 21. The formula gives the kinetic energy of an object in terms of its mass and velocity. What is the equation for?

3 22. What is the solution of the inequality x 30? Write your answer in interval notation and plot on the number line. 23. A cereal manufacturer has a tolerance of 0.75 ounces for a box of cereal that is supposed to weigh 30 ounces. Write and solve an absolute value inequality that describes the acceptable weights for 30 ounce boxes. 24. At the Atlanta Zoo s exotic animal pen, there are zebras and flamingoes. Looking in, I count 32 heads and 104 feet. How many of each type are there? 25. Ashley is a new owner of a bakery. During her first week at the bakery she keeps up with her sales and profits for each day. She sees that on Monday she sold 18 cupcakes and made a profit of $42, but on Wednesday she sold 32 cupcakes and made a profit of $ How many cupcakes did she sell if she made a profit of $148.76? 26. Teresa Sanchez sells two sizes of outdoor doghouses: large and small. The large size requires 12 board-feet of lumber and takes 3 hours to build. The small size requires 8 board-feet of lumber and takes 1 hour to build. Teresa can use 48 board-feet of lumber each day and plans to spend at most 9 hours per day building dog houses. Teresa sells her large dog houses for $70 each and her small ones for $30 each. What numbers of each kind should she make per day in order to maximize her income from sales? 27. Solve 4 x 1 8 2x A stalactite grows at an average rate of 0.13 mm per year. In January 2012, the length of a particular stalactite in Luray Caverns was 1500 mm long. The function, f ( x) 0.13x 1500, represents the total length of the stalactite where x represents the number of years since Describe in words the meaning of f (x)

4 29. What is the average rate of change on the interval [-2,3]? 30. f x 5x 1 What is the value of g x and f g( 1)? x Use the graph to the right to determine the following: A) Interval of increase B) Interval of decrease C) Max value Min value: D) Domain: Range: E) x-intercept (s): y-intercept (s): F) End Behavior: As x -, f(x) As x +, f(x) 32. Indicate the transformation that occurred from x 1 f( x ) 3 2 to x 4 gx ( ) 3 5.

5 33. Write an explicit formula given that the second term in a geometric sequence is 16 and the fifth term is Which is an exponential decay function? a. b. c. d. 35. Which context would be appropriate for 83, 118,153,188,? A. Blake had 83 dollars in his savings account when he started his job at the Biscuit Barn. He earned 35 dollars a day to deposit into the account. C. Blake had 35 dollars in his savings account when he started his job at the Biscuit Barn. He earned 48 dollars a day to deposit into the account. B. Blake had 48 dollars in his savings account when he started his job at the Biscuit Barn. He earned 35 dollars a day to deposit into the account. D. Blake had 35 dollars in his savings account when he started his job at the Biscuit Barn. He earned 83 dollars a day to deposit into the account. 36. Which linear equation approximates the best fit to the data? a. b. c. d. 37. The table shows admission prices for various attractions in Atlanta. Atlanta Area Attractions World Of Coke High Museum Fernbank GA Aquarium Atlanta Zoo $9.00 $12.00 $9.75 $8.25 $11.25 Charleston Area Attractions Fort Sumter Boone Hall City Market Gibbes Museum Wild Dunes $8.50 $15.50 $7.40 $10.50 $12.50 Which city s attraction costs are more spread? Why?

6 38. Write a function that would be a good model for this graph: 39. Ella planted tulips around her house. Each day, she tracks the number of blossoming buds. For the 10 days that she tracks the tulips, she finds that the equation y 3x 5estimates the number of blossoming buds on any of the days from What does the 3 represent in the model equation? 40. A study was conducted that looked at the mean number of study hours versus grades on a certain test. The regression equation of y 8.8x 58.4 was predicted. The correlation coefficient is 0.99 and the residual plot is shown below. What can be assumed from the plot of the residuals?

7 41. Given the translation (x, y) (x + 3, y 5), what is the pre-image of (-2, 6)? 42. Which segment indicates a 90 counterclockwise rotation about P of segment AB? 43. What is the line of reflection of the point (-2, 3) to (6, 3)? 44. Is the function f ( x) 2x 1 3 even, odd, or neither? Why? 45. Is the function 2 f ( x) 3x 1 even, odd, or neither? Why? 46. Margaret lives at the corner of 2 nd Avenue and 25 th Street. Harry lives at the corner of 7 th Avenue and 10 th Street. They decide to meet at a movie theater that separates the distance from Harry s apartment to Margaret s apartment in a ratio of 3:2. Find the location of the theater. 47. Write the equation of the line passing through (-3, 2) and (1, 5) in slope-intercept form. 48. Write the equation of the line parallel to 5x y = 3 and passing through (-2, 9). 49. Write the equation of the line perpendicular to y = -2x + 3 passing through (4, -1). 50. What is the most specific name of a quadrilateral whose diagonals bisect, are congruent, but not perpendicular?

8 51. Given one endpoint of (5, -1) and midpoint of (6, -4), find the other endpoint. 52. Find the distance between (-6, 10) and (4, 13). Leave your answer in simplest radical form. 53. Point G is the circumcenter of ABC. Identify the following lengths. BG DG AF BE 54. Point G is the incenter of ABC. Identify the following lengths. FG CG BC AC Point L is the centroid of NOM. OL 8xand OQ 9x 6. Identify the following x LQ

9 56. Identify the following for the given figure below. x m ADC m B m C 57. In the figure, line l is parallel to line m. Justify each of the following statements using the appropriate postulate or theorem ABC is NOT drawn to scale. Based on the given angle measurements, write an inequality naming the sides from SHORTEST to LONGEST.

10 59. b) If yes ABC 60. b) If yes GHJ 61. b) If yes GHM 62. b) If yes UVW 63. b) If yes ABC

11 64. b) If yes GHJ 65. b) If yes GHM 66. b) If yes GHM 67. Find the values of the missing sides of the triangle. 5 3 inches What is the measure of the altitude of this equilateral triangle with side lengths 9 mm? 9 mm

12 69. Find sin Z, cos Z, and tan Z. 70. The top of the lighthouse is 100 feet above sea level. The angle of elevation from a fishing boat to the top of the lighthouse is 10. Which is closest to the distance between the boat and the base of the lighthouse? 71. A student whose eye level is 6 feet above the ground measures the angle of elevation to the top of a flagpole as 25. The student is standing approximately 162 feet from the base of the flagpole. What is the height of the flagpole to the nearest foot? 72. The length of a diagonal of a square is 30 inches. What is the perimeter of the square? 73. The length of a ski slope is 3560 feet and the vertical drop of the slope is 1275 feet. What is the angle of elevation of the slope?

13 74. Find the numbers: Product Sum Two numbers: