Name: Date: Class: Honors Geometry Advancement Practice (Part 2)

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1 Name: Date: lass: Honors Geometry Advancement Practice (Part 2) Part 1 Multiple hoice: Identify the choice that best completes the statement or answers the question. Place your answer on the Scantron sheet provided. (2 points each) 1. Find the sum of the measures of the angles of the figure. A D WXYZ is a parallelogram. Name an angle congruent to X Y N W Z A... D. 3. What is the sum of the angle measures of a 29-gon? A D The two rectangles are similar. Which is the correct proportion for corresponding sides? 4 m 12 m 8 m 24 m A... D. 5. omplete this statement: A polygon with all sides the same length is said to be. A. regular. equilateral. equiangular D. convex 6. In the rhombus, Find the value of each variable. The diagram is not to scale A. x = 90, y = 45, z = 20. x = 45, y = 45, z = 10. x = 45, y = 135, z = 20 D. x = 90, y = 135, z = 10 [page 1]

2 7. Are the two triangles similar? How do you know? J H 39 M 39 º G K A. yes, by SAS. yes, by AA. no D. yes, by SSS 8. Find the missing values of the variables. The diagram is not to scale x y 78 A. x = 63, y = 107. x = 107, y = 63. x = 63, y = 117 D. x = 117, y = The measure of two complementary angles are in the ratio 1 : 5. What are the degree measures of the two angles? A. 18 and and and 150 D. 15 and What is the value of x? A L M D A D For the parallelogram, if and find The diagram is not to scale A D Red and grey bricks were used to build a decorative wall. The was. There were 175 bricks used in all. How many red bricks were used? A D. 35 [page 2]

3 13. Find the value of x. The diagram is not to scale. (2x + 10)º 148º (2x)º 112º A D Are the triangles similar? How do you know? A. yes, by SAS. yes, by SSS. yes, by AA D. no 15. Find the value of the variables in simplest radical form. y x A. x =, y = 11. x = 11, y =. x = 22, y = D. x =, y = Find the length of the leg. If your answer is not an integer, leave it in simplest radical form A D Fin the length of the missing hypotenuse. 12 cm 7 cm A. 151 cm. 193 cm. 193 cm D. 21 cm [page 3]

4 18. The radius of the base of a cylinder is 34 mm and its height is 54 mm. Find the surface area of the cylinder in terms of. A mm mm mm D mm 19. In rectangle KLMN, KM = and LN = 33. Find the value of x. K L N M A D What is the value of x? x x 2 > x + 5 x + 1 > A D Find the measure of the numbered angles in the rhombus. The diagram is not to scale. 12º A... D. 22. Name the major arc and find its measure. A D )50 A. ; 50. ; 50. ; 310 D. ; 310 [page 4]

5 23. Solve the proportion: A D Find the height of the cylinder. A. 2.4 in in D. 4.8 in. 25. Determine the value of x to the nearest tenth. x A D Evaluate. A ,628, D. 5, Find the surface area of a sphere with a radius of 60 m A. 14,400 m. 1,800 m. 7,200 m D. 3,600 m 28. Find the missing value to the nearest hundredth. sin = 7 14 A D A triangle has side lengths of 16 cm, 63 cm, and 65 cm. lassify it as acute, obtuse, or right. A. acute. obtuse. right 30. The area of a square garden is 200 m 2. How long is the diagonal? A m. 400 m. 100 m D. 20 m 31. Find the area of the shaded portion of the figure. Dimensions are in feet. Leave your answer in terms of π. The figure is not drawn to scale. A... D. none of these [page 5]

6 32. Two trapezoids have areas of 432 cm and 48 cm. Find their ratio of similarity. A. 3 : 1. 9 : 1. 1 : 3 D. 1 : Write the tangent ratios for and. Z 2 53 X 7 Y A... D. Find the area of the trapezoid. Leave your answer in simplest radical form. 34. Determine the area of the trapezoid: 11 ft 19 ft 45 A. 120 ft ft ft 2 D. 120 ft 2 Find the value of x. If necessary, round your answer to the nearest tenth. O is the center of the circle. The figure is not drawn to scale. 35. Determine the value of x O x A D Use Euler s Formula to find the missing number. Vertices: 19 Edges: 37 Faces:? A D Find the lateral area of a regular pentagonal pyramid that has a slant height of 14 in. and a base side length of 6 in. [page 6]

7 A. 210 in in.. 42 in. D. 420 in. 38. A jar contains 3 blue cubes, 7 blue spheres, 6 green cubes, and 3 green spheres. If you select an object at random, what is the probability that the object is green or a cube? A D You roll a standard number cube. Find P(number is not 5). A D Write the standard form of the equation for a circle with a center ( 3, 10), r = 7 A. (x 10) + (y + 3) = 49. (x + 3) + (y 10) = 49. (x 3) + (y + 10) = 7 D. (x + 3) + (y 10) = Determine the lateral surface area, and the surface area for the prism below. 5 m 16 m 7 m A. 230 m ; 454 m. 230 m ; 342 m. 384 m ; 342 m D. 384 m ; 454 m 42. Determine the area of the shape below: 38 in. 29 in. 20 in. A in in in. 2 D. 760 in Determine the area of the shape below: 6 cm 19 cm A. 57 cm cm cm 2 D cm Find the measure of A in circle O. (The figure is not drawn to scale.) [page 7]

8 A O 46º A D and are all tangent to circle O (not drawn to scale), and. JA = 11, AL = 14, and K = 7. Find the perimeter of. J A O L K A D Find the surface area of a sphere with a circumference of 13 mm. Round to the nearest tenth. A mm. 4.3 mm. 2.1 mm D mm 47. Lynn and Dawn tossed a coin 30 times and got heads 10 times. What is the experimental probability of tossing heads using Lynn and Dawn s results? A D In a batch of 1000 calculators, 5 were found to be defective. What is the probability that a calculator chosen at random will be defective? Write the probability as a percent. Round to the nearest tenth of a percent if necessary. A. 99.5%. 0.7%. 74.6% D. 0.5% 49. Find the slant height of the cone to the nearest whole number. A. 21 m. 19 m. 20 m D. 17 m 50. The ratio of length to width in a rectangle is 3 to 1. If the perimeter of the rectangle is 136 feet, what is the length of the rectangle? A. 102 feet. 68 feet. 34 feet D. 51 feet Part 2 Open Response: Respond to each question in the space provide. Show all work for partial credit. [page 8]

9 51. (4 points) The figure is drawn on centimeter grid paper. Find the perimeter of the shaded figure to the nearest tenth. 52. (5 points) A spotlight is mounted on a wall 7.4 feet above a security desk in an office building. It is used to light an entrance door 9.3 feet from the desk. To the nearest degree, what is the angle of depression from the spotlight to the entrance door? 53. (5 points) Find the area of the shaded region. Leave your answer in terms of and in simplest radical form. 54. (5 points) Find the surface area of a conical grain storage tank that has a height of 35 meters and a diameter of 14 meters. Round the answer to the nearest square meter. 55. (6 points) What is the maximum volume of a pyramid that can fit inside a cube with a side length of 18 cm? [page 9]

10 56. (6 points) A satellite is 12,200 miles from the horizon of Earth (A). Earth s radius is about 4,000 miles. Find the approximate distance the satellite is from the point directly below it on Earth s surface (). The diagram is not to scale. A O 57. (3 points) Show the equation used to evaluate. 58. (5 points) A triangle has sides of lengths 21, 47, and 52. Is it a right triangle? Explain. 59. (6 points) Find the area of a regular pentagon with a side of 7 cm. Round your answer to the nearest tenth. [page 10]

11 60. (5 points) The diameter of a basketball rim is 18 inches. A standard basketball has a circumference of 30 inches. About how much room is there between the ball and the rim in a shot in which the ball goes in exactly in the center of the rim? Show your work. 61. (6 points) These two non-congruent circles intersect at exactly one point. Their common tangent is 24 cm, and the distance between their centers is 25 cm. 24 cm D r A a. What is the sum of the two radii? b. Express the radius of circle in terms of r (the radius of circle A). c. Find the radius of circle. Show your work. 62. (4 points) All of the angles of a quadrilateral are congruent. an the quadrilateral be a parallelogram? Explain. [page 11]