#2212 Geometry S2 #7772 Foundations in Geometry S2

Transcription

1 Instructional Materials for WCSD Math Common Finals The Instructional Materials are for student and teacher use and are aligned to the Course Guides for the following courses: High School #2212 Geometry S2 #7772 Foundations in Geometry S2 When used as test practice, success on the Instructional Materials does not guarantee success on the district math common final or state end of course final. Note: The Nevada Department of Education authors the state end of course final. The state does not publish instructional materials, item specifications or test blueprints for the end of course final. Students can use these Instructional Materials to become familiar with the intent of standards and language used on the district common finals and state end of course final. Familiarity with standards and vocabulary included in the Instructional Materials items can result in less anxiety on the part of the students. The length of the actual final may differ in length from the Instructional Materials. Teachers can use the Instructional Materials in conjunction with the course guides to ensure that instruction aligns with the intent of the standards. The Instructional Materials are not representative of the depth or full range of learning that should occur in the classroom. *Students will be allowed to use a non-programmable scientific calculator on Geometry Semester 1 and Geometry Semester 2 final exams.

2 Multiple Choice: Identify the choice that best completes the statement or answers the question. Figures are not necessarily drawn to scale. 1. The ratios of the areas of square A to square B is cm2, what is the length of a side of square A? A. 4 cm C. 10 cm B. 8 cm D. 64 cm 2. A statue of a Rubik s Cube is built from a scale model. The scale of the model to the statue is 6 inches to 5 feet. What is the ratio of the volume of the model to the volume of the actual statue in cubic feet? A. 1: 1000 B. 1: 10 C. 216: 125 D. 6: 5 3. What is the scale factor of the dilation of ABC to image A B C? A. 2 B. 1 C. 2 D. 3

3 4. Apply the dilation D: (x, y) (4x, 4y) to the polygon with the given vertices. Name the coordinates of the image points. A. A (8, 4), B (16, 4), C (16, 12) B. A (8, 4), B (16, 4), C (16, 12) C. A (0.5, 0.25), B (1, 0.25), C (1, 0.75) D. A (0.5, 0.25), B (1, 0.25), C (1, 0.75) 5. What is the value for x? A. x = 18 B. x = 16 C. x = 12 D. x = 3 6. In the figure below, what is the length of AB? A. AB = 7 B. AB = 11 C. AB = 16 D. AB = 20

4 7. Two triangles are similar and the ratio of each pair of corresponding sides is 2: 1. Which statement regarding the two triangles is not true? A. Their perimeters have a ratio of 2: 1 B. The scale factor is a ratio of 2: 1 C. Their corresponding angles have a ratio of 2: 1 D. Their areas have a ratio of 4: 1 8. What is the value of n? A. n = 39 B. n = 54 C. n = 63 D. n = In LMN, S is the midpoint of LM, T is the midpoint of MN, and R is the midpoint of LN. Given the following, what is the perimeter of RST? LS = 8.2x ST = 4.3x MN = 6x A. 11.4x B. 15.5x C. 18.4x D. 18.5x

5 10. Use the diagram to find the values of x and y. A. x = 5 15, y = 20 5 B. x = 5 15, y = 10 5 C. x = 5 5, y = 20 5 D. x = 5 5, y = Three students were asked to explain which transformations map the pre-image of XYZ onto the image X Y Z in the diagram below. Based on the following responses, whose reasoning is correct? Jason says the image is result of translating the pre-image along the vector 1, 2 and performing a dilation with a scale factor of 3. Sanjay says the pre-image is rotated 180 about the origin and dilated by a scale factor of 3. Teresa says the image is a result of applying the rule (x, y) (3(x + 1), 3(y 2)). A. Jason and Teresa are correct. B. Sanjay and Jason are correct. C. Only Jason is correct. D. Jason, Sanjay, and Teresa are all correct.

6 12. In the right triangle, x and y represent unknown side lengths. What is the length of side x? A. 2 B. 4 C. 2 3 D In the figure, what is the distance a ball travels when thrown from second base to home plate? A. 90 feet B. 180 feet C feet D feet 14. What is cos x in the triangle? A. B C. D

7 15. Which of the following has the same value as sin M? A. sin N B. tan M C. cos N D. cos M 16. What is the measure of angle A in the triangle, rounded to the nearest degree? A. 35 B. 44 C. 46 D A person is standing at ground level with the base of the Empire State Building in New York City. The angle formed by the ground and a line segment from his position to the top of the building is The height of the Empire State Building is 1472 feet. Find the distance that he is standing from the base of the Empire State Building to the nearest foot. A. 8 feet C feet B feet D feet 18. Find the value of x in the diagram below. Round your answers to the nearest tenth if necessary. A. x = 12.2 B. x = 13.1 C. x = 24.5 D. x = 26.2

8 19. Three students were asked to find the value of x in the diagram below. The first step of each student s work is shown below. Determine which student(s) set up the problem correctly. Lewis Alexa Miranda cos 26 = x 16 tan 26 = 7 x sin 64 = 16 x A. Lewis, Alexa, and Miranda B. Miranda and Alexa C. Lewis and Miranda D. Lewis and Alexa 20. In a large city, a circle with a radius of 3 miles contains a population of 30,348 people. What is the expected population of a circle with a 4 mile radius in the same city? A. 121,392 people C. 53,952 people B. 91,044 people D. 40,464 people 21. What is the area of a regular hexagon with an apothem of 10 cm and a side length of 20 3 cm? 3 A cm 2 B cm 2 C cm 2 D. 600 cm 2

9 22. Given that the side of the regular pentagon is 8 ft, what is the approximate area of the shaded triangle? A. 11 ft 2 B. 22 ft 2 C. 8 3 ft 2 D ft What best describes the cross section shown on the cube? A. square C. trapezoid B. triangle D. rectangle 24. A layered cake is a solid of revolution. Which of the following is the drawing of a twodimensional shape and an axis of rotation that could form the cake? A. C. B. D.

10 25. Jamal wants to fill a container with two different colors of sand for an art project. The container is 9 inches tall and has a regular polygon base. He is going to fill part of the container with 10 in 3 of blue sand. How much green sand does Jamal need to purchase to fill the rest of the container? Round your answer to the nearest tenth if necessary. A in 3 B. 44 in 3 C in 3 D. 54 in Compare the volumes of the cone and the regular pyramid below. Which statement is true? height 12 inches radius 7 inches height 7 inches side length 12 inches A. The volume of the pyramid is about 140 in 3 more than the volume of the cone. B. The volume of the cone is about in 3 more than the volume of the pyramid. C. The volume of the cone is about in 3 more than the volume of the pyramid. D. The volume of the cone is about 112 in 3 more than the volume of the pyramid.

11 27. A tanker truck can carry 3,000 gallons of fuel and is going to fill an empty cylindrical gas tank with a height of 4 feet. The operator doesn t know the radius of the tank and is unsure whether the tank will be able to hold all of the fuel. When the height of the fuel in the tank reaches 1 foot, the operator looks at the pumping gauge and determines that approximately 846 gallons of fuel were pumped into the tank. Based on this information, will the tank hold all 3,000 gallons of fuel? Explain. A. Yes, the tank can hold a total of 4,280 gallons of fuel. B. Yes, the tank can hold a total of 3,384 gallons of fuel. C. No, the tank can only hold a total of 2,538 gallons of fuel. D. No, the tank can only hold a total of 2,154 gallons of fuel.

12 28. Three students were asked to find the volume of a cylinder with a hemisphere removed from one end. Each student s work is shown below. Determine which student is correct. Student X Student Y Student Z Volume = πr 2 h 1 2 (4 3 πr3 ) = π (4 3 π 53 ) = 150π 1 2 (500 3 π) = 150π π = 200 π in3 3 Volume = πr 2 h 4 3 πr3 = π π 33 3 = 90π 36π = 54π in 3 Volume = πr 2 h 1 2 (4 3 πr3 ) = π (4 3 π 33 ) = 90π 1 2 (36π) = 90π 18π = 72π in 3 A. Student X is correct. B. Student Y is correct. C. Student Z is correct. D. None of the students is correct. 29. What is the height of a square pyramid that has a side length of 13 feet and a volume of 1521 ft 3? A. h = 3 feet C. h = 27 feet B. h = 9 feet D. h = 39 feet

13 30. A food manufacturer sells yogurt in cone shaped cups with the dimensions shown. To the nearest tenth, how many fluid ounces of yogurt does the cup hold if 1 cm fl oz? A. 0.6 fl oz B. 5.7 fl oz C fl oz D fl oz 31. What is the volume of the sphere in terms of x? A. 36πx 3 ft 3 B. 48πx 3 ft 3 C. 288πx 3 ft 3 D. 864πx 3 ft You want to design a cylindrical container for oatmeal that has a volume of 90 in 3. You also want the height of the container to be 3.5 times the radius. To the nearest tenth, what should the approximate radius of the container be? A. 2.0 in C. 3.0 in B. 2.9 in D. 3.1 in

14 33. Given mac = mbc and ADB is a central angle, what is the value of x and BC? A. x = 18, mbc = 136 B. x = 9.2, mbc = 88 C. x = 18, mbc = 88 D. x = 9.2, mbc = In the figure below, QPR is a circumscribed angle. Find the value of x. A. x = 3.5 B. x = 5 C. x = 8.5 D. x = What is the measure of RS? A. 54 B. 38 C. 32 D. 27

15 36. What is the measure of the inscribed angle (x), if the ray is tangent to the circle? A. 140 B. 110 C. 70 D If constructing a circumscribed circle, which of the following intersect at a common point? A. angle bisectors B. perpendicular bisectors C. medians D. midpoints 38. When constructing an inscribed polygon, which of the following tools should be used to place the vertices of the polygon on the circle? A. a string B. protractor C. compass D. none of the above

16 39. Find the angle measures of ABCD. A. m A = 71 m B = 54 m C = 109 m D = 126 B. m A = 34 m B = 54 m C = 146 m D = 126 C. m A = 35 m B = 134 m C = 145 m D = 54 D. m A = 71 m B = 50 m C = 109 m D = In the diagram below XY = 10x 10, XZ = 6x + 10, and YZ = 8x 5. Find XZ. A. XZ = 10 B. XZ =25 C. XZ = 55 D. XZ = Find the value of x in the diagram below. A. x = 3.3 B. x = 2.5 C. x = 3.1 D. x = 4.5

17 42. Which circle is inscribed in the triangle? A. Circle X B. Circle Y C. Circle Z D. All of the above 43. What is the length of the minor arc AB in the circle with a radius of 45 cm? A. 20π cm B. 10π cm C. 5π cm D. 2π cm 44. What is the area of a circular pool that has a circumference of 100π feet? A. 10π ft 2 C. 100π ft 2 B. 50π ft 2 D. 2500π ft 2

18 45. The diameter of a circular pizza pan is 18 inches. Two-thirds of the pizza is eaten by your friends. What is the approximate area of the pizza pan that is covered by the remaining pizza? A. 170 in 2 C. 54 in 2 B. 85 in 2 D. 27 in A circle has an arc length of 10 feet. The central angle formed is 60. What is the area of the sector? (Hint: find the radius first) A. B. 150 π ft2 C. π 150 ft2 D. π 360 ft2 900 π ft2 47. A large circular cake is cut into the pieces shown below. If a person asks for a smaller piece of cake, which piece of cake should you serve them? Explain. A. You should serve them piece A because it has an area 0.5π in 2 less than piece B. B. You should serve them piece A because it has an area 3.5π in 2 less than piece B. C. You should serve them piece B because it has an area 1.75π in 2 less than piece A. D. You should serve them piece B because it has an area 8π in 2 less than piece A.

19 48. Given the square inside the circle with radius 6. What is the probability that the point lies inside the square, if a point is chosen at random inside the circle? A π π C. 2 π B. 2 π π D. 2 π 49. A grab bag contains 7 football cards and 3 basketball cards. An experiment consists of taking one card out of the bag, then selecting another card. What is the probability of selecting a football card, replacing it, and then selecting a basketball card? If necessary, round answers to the nearest hundredth. A C B D A bag contains hair ribbons for a spirit rally. The bag contains 5 black ribbons and 7 green ribbons. Lila selects a ribbon at random, then Jessica selects a ribbon at random from the remaining ribbons. Find the probability that both events A and B occur. Which is the correct answer in simplest fraction form? A. B. Event A: Lila selects a black ribbon. Event B: Jessica selects a green ribbon C. D

20 51. The table shows the distribution of male and female students and left- and right-handed students in the math club. Find the probability that a female student selected at random is left-handed. Which is the correct answer as a fraction in simplest form? Left-handed Right-handed Male 2 35 Female 6 36 A. 3 4 C. 1 6 B. 1 7 D The table shows the distribution of the labor force in the United States in the year Suppose that a worker is selected at random. Find the probability of randomly selecting a worker in the Industry field given that the worker is female. Which is the correct answer as a decimal rounded to the nearest thousandth? Agriculture Industry Services Male 3,132,000 25,056,000 50,112,000 Female 667,000 8,004,000 57,362,000 A C B D Events A and B are independent. Find the missing probability. P(A) = P(B) = 0.3 P(A and B) = 0.06 A. 0.7 C. 0.2 B D. 0.3

21 54. If P(A) = 0.43 and P(B A) = 0.89, find P(A and B). A C B D The sections on a spinner are numbered from 1 through 8. If the probability of landing on a given section is the same for all the sections, what is the probability of spinning a number less than 4 or greater than 7 in a single spin? A. B C. D A certain disease occurs in 4% of the population. A blood test for this disease shows a false positive 12% of the time. That means a test will show positive given that the person does not have the disease. What is the probability that a person tests positive but does not have the disease? A C B D