#2216 Formal 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 course: High School #2216 Formal 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 Formal Geometry Semester 1 and Formal 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 triangles shown are similar. Which of the following is not a correct statement? A. AB XY = BC YZ C. CA ZX = BA YX B. BC YZ = AC XY D. AC XZ = AB XY 2. On the coordinate grid below, one triangle is drawn and two vertices for a second triangle are also shown. Which coordinates for the third vertex will form another triangle that is similar to the one drawn? A. (6, 1) B. (6, 7) C. (7, 1) D. (10, 1)

3 3. Find the length of PS in the diagram below. A. PS = 5 B. PS = 6 C. PS = 8 D. PS = What is the value of x in the figure below? A. x = 4 B. x = 5 C. x = 6 D. x = 7 5. Apply the dilation D: (x, y) (4x, 4y) to the triangle given below. Which of the following is the perimeter of the image? A units B units C units D. 9.2 units 6. What is the length of AC? A. AC = 28 B. AC = 26 C. AC = 24 D. AC = 15

4 7. In the diagram below BD, DF, and BF are midsegments and BC = 10 and AE = 12. Compare the perimeters of CDB and DEF, then choose the statement below that is true. A. The perimeter of CDB is greater. B. The perimeter of DEF is greater. C. A relationship cannot be determined. D. The perimeters are the same. 8. Which method cannot be used in a coordinate proof to prove ABC~ ADE? A. Use the Distance Formula to show AB of Congruence. (SAS~) = AC AD AE B. Use the Distance Formula to show AB AD = AC AE = BC DE. (SSS~), and A A by the Reflexive Property C. Use the Reflexive Property of Congruence to show A A, then measure to show ABC D. (AA~) D. Use the slope formula to show that the slope of BC and DE are equal so BC DE and corresponding angles are congruent. (AA~)

5 9. Use the diagram to find the values of x and y. A. x = 4 10, y = 4 15 B. x = 4 10, y = 4 19 C. x = 4 6, y = 4 15 D. x = 4 6, 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 11. The Hopewell people were Native Americans whose culture flourished in the central Ohio Valley about 2000 years ago. The Hopewell people constructed earthworks using triangles, including those below. The diagram below shows the layout of some Hopewell earthworks. The centers of the Newark Octagon, the Newark Square and the Great Circle were at the corners of the shaded triangle. The three right triangles surrounding the shaded triangle form a rectangle measuring 12 units by 14 units. Which of the Hopewell triangles is similar to Triangle 1, Triangle 2, and Triangle 3 in the diagram? A. Triangle 1~Triangle A Triangle 2~Triangle F Triangle 3~Triangle C B. Triangle 1~Triangle A Triangle 2~Triangle B Triangle 3~Triangle C C. Triangle 1~Triangle D Triangle 2~Triangle F Triangle 3~Triangle C D. Triangle 1~Triangle D Triangle 2~Triangle B Triangle 3~Triangle C

7 12. Which of the following has the same value as sin M? A. sin N B. cos N C. tan M D. cos M 13. Based on the figure below, choose all correct ways of solving for x. I. x = 16 sin 35 II. x = 28 sin 55 III. x = 28 cos 35 IV. x = A. I, IV B. II, III C. I, III, IV D. I, II, III, IV 14. Find the values of x and y. A. x = 4, y = 4 3 B. x = 8 3, y = 16 3 C. x = , y = 3 3 D. x = , y = 3 3

8 15. The perimeter of a square is 54 cm. Find the length of a diagonal, rounding to the nearest tenth. A cm C cm B cm D cm 16. A 12 foot ladder is leaning up against the side of a house. The ladder is placed 10 feet from the side of the house. What is the angle of elevation of the ladder? A C B 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. Which of the following is the length of side x? A. x = 30.2 B. x = 24.2 C. x = 16.0 D. x = 11.7

9 19. Which of the following is the length of side x? A. x = 7.1 B. x = 9.2 C. x = 16.0 D. x = Describe the symmetry of the quilt patch. Draw all the lines of symmetry. If there is rotational symmetry, give the angle and order. A. Line and rotational symmetry Angle of rotational symmetry: 180 Order: 2 C. Line and rotational symmetry Angle of rotational symmetry: 180 Order: 2 B. Line and rotational symmetry Angle of rotational symmetry: 90 Order: 4 D. Line and rotational symmetry Angle of rotational symmetry: 90 Order: 4

10 21. What is the measure of HJ in Parallelogram FGHJ, given the following: FG = x + 7 GH = 5x + 3 m F = 46 m H = (3x + 10) A. HJ = 63 B. HJ = 19 C. HJ = 12 D. HJ = Based on the figure below, which statements are true? I. The figure is a rectangle II. The figure is a parallelogram III. 6x 4 = 9x + 3 IV. 9x + 3 = 10x 2 V. x = 8 VI. The longest side has a length of 60. A. I, III, and V C. II, IV, and VI B. I, IV, and VI D. II, III, and V 23. Which of the following is not always true of parallelogram ABCD? A. AB BC, DC BC B. AB DC, BC AD C. m A + m B = 180 D. AB + BC = AD + DC

11 24. A wooden frame has screws at A, B, C, and D so that the sides of it can be pressed to change the angles occurring at each vertex. AB CD and AB CD, even when the angles change. Why is the frame always a parallelogram? A. The angles always stay the same, so ABCD is a parallelogram. B. All sides are congruent, so ABCD is a parallelogram. C. One pair of opposite sides is congruent and parallel, so ABCD is a parallelogram. D. One pair of opposite sides is congruent, so ABCD is a parallelogram. 25. Given the following information, find m XYZ: WXYZ is a rhombus m WXP = (2x + 16) m WPX = (7x + 6) A. m XYZ = 100 C. m XYZ = 140 B. m XYZ = 120 D. m XYZ = Which statement is true? A. All quadrilaterals are rectangles. B. All rectangles are parallelograms. C. All parallelograms are rectangles. D. All quadrilaterals are squares.

12 27. Given KLMN is a square and LN NP, which statement can be proved? A. KQ = PN B. PN KM C. KPN KQN D. KP = 1 2 LN 28. Find the area of a hexagon with a side length of 4 cm. A. B. C. D cm cm cm cm Determine the most precise name for the figure with the following vertices: A( 5, 6), B( 2, 0), C(4, 3), D(1, 3). A. square B. kite C. trapezoid D. rhombus

13 30. A quadrilateral is graphed on the coordinate plane. Which of the following methods can be used to prove the quadrilateral is a parallelogram? A. I and II B. II and III C. I and III I. Show both pairs of opposite sides are parallel using the slope formula. II. Show both pairs of opposite sides are congruent using the distance formula. III. Show that one angle is supplementary to both consecutive angles using the slope formula. D. I, II, and III 31. Find the area of a heptagon with a side length of 68 inches. Round your answer to the nearest tenth. A. 18,650.2 in 2 B. 16,803.2 in 2 C in 2 D in Given mac = mbc and ADB is a central angle, what is the value of x and mbc? A. x = 9.2, mbc = 136 B. x = 9.2, mbc = 88 C. x = 18, mbc = 88 D. x = 18, mbc = 136

14 33. What is the measure of RS? A. 54 B. 38 C. 32 D A freeway runs tangent to a circular lake. The distance from point B to the center of the lake is 100 miles. The distance from Point A to Point B on the freeway is 80 miles. What is the diameter of the lake? A. 20 miles B. 60 miles C. 120 miles D. 160 miles 35. If mlnm = (8x + 12) and m HML = (2x) find the value of x. A. x = 29 B. x = 28 C. x = 34.8 D. x = 16.8

15 36. In the diagram below, m ABC = (6y + 12), m ADC = (3x 3), and m AEC = 192. Find the values for x and y. A. x = 17, y = 12 B. x = 17, y = 26 C. x = 5, y = 12 D. x = 5, y = Find the angle measures of ABCD. A. m A = 71 m B = 50 m C = 109 m D = 130 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 = 54 m C = 109 m D = 126

16 38. 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 = The diagram below shows the construction of the center of the circle circumscribed about ABC. Which construction does this figure represent? A. The intersection of the angle bisectors of ABC B. The intersection of the medians of ABC C. The intersection of the altitudes of ABC D. The intersection of the perpendicular bisectors of ABC

17 41. Which geometric principle is used in the construction shown below? A. The intersection of the angle bisectors of a triangle is the center of the inscribed circle. B. The intersection of the angle bisectors of a triangle is the center of the circumscribed circle. C. The intersection of the medians of a triangle is the center of the inscribed circle. D. The intersection of the medians of a triangle is the center of the circumscribed circle. 42. What is the length of the AB in the circle with a radius of 45 cm? A. 20π cm B. 10π cm C. 5π cm D. 2π cm 43. 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? (Assume the pan and the pizza have the same diameter.) A. 170 in 2 C. 54 in 2 B. 85 in 2 D. 27 in 2

18 44. A carnival ride is designed like a wheel. The circular wheel divided into equal sized sections by the diameters of the circle. Riders are placed at the endpoints of the diameter supports. The distance between each seat is 6 ft measured around the outside edge of the wheel. What is the area of space needed for the ride? A ft 2 B ft 2 C ft 2 D ft In the picture below, points A and B are at the centers of two circles and they are collinear with point C. Points D and E lie on the two respective circles and they are also collinear with point C. Finally the two circles touch at a single point on AB. What is BC? A. BC = 15 C. BC = 9 B. BC = 12 D. BC = 8

19 46. A paperweight is made of glass in the shape of a pyramid. The pyramid has a regular hexagonal base with a side length of 6 cm and is 8 cm tall. If glass weighs 2.52 grams per cubic centimeter, how much does the paperweight weigh? A grams B grams C grams D grams 47. As part of a contest, Shelly wants to estimate the number of dried beans in a cylindrical container with a diameter of 8 inches and a height of 12 inches. At home, she fills a smaller cylindrical container with a diameter of 2 inches and a height of 1 inch with beans. Shelly then counts and finds that it takes 108 beans to fill the smaller container. Based on this information, what would be Shelly s likely estimate for the number of beans in the larger container? A. 82,604 beans B. 20,736 beans C. 10,368 beans D. 5,184 beans 48. A contractor needs 145 more cubic yards of concrete mix to complete a construction job. If there remains a conical pile of concrete mix measuring 36 feet in diameter and 12 feet high, is there enough concrete still on the job site to finish the job? Explain your reasoning. A. Yes, the contractor has cubic yards of concrete on site. B. Yes, the contractor has cubic yards of concrete on site. C. Yes, the contractor has cubic yards of concrete on site. D. No, the contractor only has 53.8 cubic yards of concrete on site.

20 49. What is the surface area of a sphere whose volume is 330 cubic meters? A m 2 C m 2 B m 2 D m 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 radius of the container be? A. 2.0 in C. 3.0 in B. 2.9 in D. 3.1 in 51. A cone has a surface area of 96π cm 2 and a volume of 96π cm 3. Find the surface area and volume of a larger cone if the two figures are similar with a scale factor of 2: 3. A. Surface Area = 216π cm 2 Volume = 324π cm 3 B. Surface Area = 144π cm 2 Volume = 144π cm 3 C. Surface Area = 192π cm 2 Volume = 288π cm 3 D. Surface Area = 216π cm 2 Volume = 486π cm Find the probability that a point chosen at random lands in the shaded region. Round to the nearest tenth. A. 21.5% B. 43.3% C. 56.7% D. 78.5%

21 53. 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 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 girls select a black ribbon. A C B D 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. B C. D

22 56. 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 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