Geometry SIA #3 Practice Exam

Transcription

1 Class: Date: Geometry SIA #3 Practice Exam Short Answer 1. Which point is the midpoint of AE? 2. Find the midpoint of PQ. 3. Find the coordinates of the midpoint of the segment whose endpoints are H(2, 13) and K(8, 9). 4. M is the midpoint of CF for the points C(2, 2) and F(10, 8). Find MF. 5. M(4, 2) is the midpoint of RS. The coordinates of S are (5, 1). What are the coordinates of R? 6. T(4, 8) is the midpoint of CD. The coordinates of D are (4, 12). What are the coordinates of C? 7. Find the distance between points P(3, 4) and Q(2, 6) to the nearest tenth. 8. The Frostburg-Truth bus travels from Frostburg Mall through the city s center to Sojourner Truth Park. The mall is 3 miles west and 5 miles south of the city s center. Truth Park is 4 miles east and 3 miles north of the city s center. How far is it from Truth Park to the mall to the nearest tenth of a mile? 9. A high school soccer team is going to Columbus, Ohio to see a professional soccer game. A coordinate grid is superimposed on a highway map of Ohio. The high school is at point (3, 4) and the stadium in Columbus is at point (7, 1). The map shows a highway rest stop halfway between the cities. What are the coordinates of the rest stop? What is the approximate distance between the high school and the stadium? (One unit 5.9 miles.) 1

2 10. Find the perimeter of the rectangle. The drawing is not to scale. 11. Andrew is adding a ribbon border to the edge of his kite. Two sides of the kite measure 6.6 inches, while the other two sides measure 14.3 inches. How much ribbon does Andrew need? 12. Bryan wants to put a fence around his rectangular garden. His garden measures 38 feet by 43 feet. The garden has a path around it that is 3 feet wide. How much fencing material does Bryan need to enclose the garden and path? 13. Find the circumference of the circle to the nearest tenth. Use 3.14 for. 14. Find the circumference of the circle in terms of. 2

3 15. Find the perimeter of ABC with vertices A( 3, 0), B(5, 0), and C( 3, 6). 16. Find the perimeter of parallelogram ABCD with vertices A( 2, 2), B(4, 2), C( 6, 1), and D(0, 1). 17. If the perimeter of a square is 152 inches, what is its area? 18. Find the area of a rectangle with base of 4 yd and a height of 5 ft. 3

4 19. Find the area of the circle in terms of. 20. Find the area of the circle to the nearest tenth. Use 3.14 for. 21. Find, to the nearest tenth, the area of the region that is inside the square and outside the circle. The circle has a diameter of 6 inches. 22. The figure is formed from rectangles. Find the total area. The diagram is not to scale. 4

5 23. Write an expression that gives the area of the shaded region in the figure below. You do not have to evaluate the expression. The diagram is not to scale. 24. What is the slope of the line shown? 25. What is the slope of the line shown? 5

6 26. What is the slope of the line shown? 27. What is an equation in slope-intercept form for the line given? 28. Write the equation for the vertical line that contains point E(5, 4). 29. Write the equation for the horizontal line that contains point G( 3, 4). 30. Is the line through points P( 2, 4) and Q(7, 3) parallel to the line through points R( 1, 0) and S(4, 3)? Explain. 31. What is the equation in point-slope form for the line parallel to y = 6x + 9 that contains P( 8, 5)? 32. What is the equation in point-slope form for the line parallel to y = 2x + 12 that contains J( 6, 3)? 33. What is an equation in point-slope form for the line perpendicular to y = 2x + 10 that contains ( 6, 3)? 34. Is TVS scalene, isosceles, or equilateral? The vertices are T(1,1), V(4,0), and S(2,4). 6

7 35. A quadrilateral has vertices (5, 3), (5, 1), ( 1, 3), and ( 1, 1). What special quadrilateral is formed by connecting the midpoints of the sides? 36. In the coordinate plane, three vertices of rectangle PQRS are P(0, 0), Q(0, b), and S(c, 0). What are the coordinates of point R? 37. The vertices of the trapezoid are the origin along with A(4p, 4q), B(4r, 4q), and C(4s, 0). Find the midpoint of the midsegment of the trapezoid. 38. What are the minor arcs of O? 39. What are the major arcs of O that contain point B? 7

8 40. Find the measure of EDC. The figure is not drawn to scale. 41. Find the circumference. Leave your answer in terms of The circumference of a circle is 78 cm. Find the diameter, the radius, and the length of an arc of Find the length of XPY. Leave your answer in terms of. 8

9 Find the area of the circle. Leave your answer in terms of A team in science class placed a chalk mark on the side of a wheel and rolled the wheel in a straight line until the chalk mark returned to the same position. The team then measured the distance the wheel had rolled and found it to be 30 cm. To the nearest tenth, what is the area of the wheel? 48. Find the area of the figure to the nearest tenth. 49. Find the area of a sector with a central angle of 190 and a diameter of 7.3 cm. Round to the nearest tenth. 9

10 50. The area of sector AOB is ft 2. Find the exact area of the shaded region. 51. Find the probability that a point chosen at random from JP is on the segment KO. 52. Lenny s favorite radio station has this hourly schedule: news 13 min, commercials 2 min, music 45 min. If Lenny chooses a time of day at random to turn on the radio to his favorite station, what is the probability that he will hear the news? 53. The delivery van arrives at an office every day between 3 PM and 5 PM. The office doors were locked between 3:20 PM and 3:45 PM. What is the probability that the doors were unlocked when the delivery van arrived? 54. Find the probability that a point chosen at random will lie in the shaded area. 10

11 55. Use Euler s Formula to find the missing number. Faces: 22 Vertices: 12 Edges:? 56. Use Euler s Formula to find the missing number. Vertices: 14 Edges: 29 Faces:? 57. Use Euler s Formula to find the missing number. Edges: 33 Faces: 18 Vertices:? 58. Mario s company makes unusually shaped imitation gemstones. One gemstone had 11 faces and 11 vertices. How many edges did the gemstone have? Assume that lines that appear to be tangent are tangent. O is the center of the circle. Find the value of x. (Figures are not drawn to scale.) 59. m O m P 24 11

12 In the figure, PA and PB are tangent to circle O and PD bisects BPA. The figure is not drawn to scale. 61. For m AOC = 65, find m POB. 62. For m AOC = 44, find m BPO. 63. AB is tangent to O. If AO 12 and BC 25, what is AB? The diagram is not to scale. 12

13 64. A satellite is 6,600 miles from the horizon of Earth. Earth s radius is about 4,000 miles. Find the approximate distance the satellite is from the Earth s surface. The diagram is not to scale. 65. BC is tangent to circle A at B and to circle D at C (not drawn to scale). AB = 8, BC = 17, and DC = 7. Find AD to the nearest tenth. 66. A chain fits tightly around two gears as shown. The distance between the centers of the gears is 27 inches. The radius of the larger gear is 20 inches. Find the radius of the smaller gear. Round your answer to the nearest tenth, if necessary. The diagram is not to scale. 13

14 67. AB is tangent to circle O at B. Find the length of the radius r for AB = 7 and AO = Round to the nearest tenth if necessary. The diagram is not to scale. 68. Pentagon RSTUV is circumscribed about a circle. Solve for x for RS = 8, ST = 15, TU = 13, UV = 9, and VR = 10. The figure is not drawn to scale. 69. JK, KL, and LJ are all tangent to O (not drawn to scale). JA = 5, AL = 14, and CK = 11. Find the perimeter of JKL. 14

15 70. NA PA, MO NA, RO PA, MO = 7 ft What is PO? 71. BZ FZ, BZ CA, FZ DC, DF = 24 in. What is BC? 72. Find the value of x. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale. 15

16 FG OP, RS OQ, FG = 37, RS = 22, OP = 12 16

17 Use the diagram. AB is a diameter, and AB CD. The figure is not drawn to scale. 76. Find m BD for m AC = WZ and XR are diameters. Find the measure of ZWX. (The figure is not drawn to scale.) 17

18 78. The radius of circle O is 27, and OC = 5. Find AB. Round to the nearest tenth, if necessary. (The figure is not drawn to scale.) 79. Find the measure of BAC. (The figure is not drawn to scale.) 80. Find x. (The figure is not drawn to scale.) 18

19 81. Find m BAC. (The figure is not drawn to scale.) 82. m R = 38. Find m O. (The figure is not drawn to scale.) 83. Given that DAB and DCB are right angles and m BDC = 52º, what is m CAD? (The figure is not drawn to scale.) 19

20 84. If m BAD 30, what is m BCD? 20

21 Geometry SIA #3 Practice Exam Answer Section SHORT ANSWER 1. ANS: 0.5 PTS: 1 DIF: L3 REF: 1-7 Midpoint and Distance in the Coordinate Plane OBJ: Find the midpoint of a segment STA: MA.912.G.1.1 TOP: 1-7 Problem 1 Finding the Midpoint KEY: segment length segment midpoint 2. ANS: (3, 1) PTS: 1 DIF: L2 REF: 1-7 Midpoint and Distance in the Coordinate Plane OBJ: Find the midpoint of a segment STA: MA.912.G.1.1 TOP: 1-7 Problem 1 Finding the Midpoint KEY: coordinate plane Midpoint Formula 3. ANS: (5, 11) PTS: 1 DIF: L2 REF: 1-7 Midpoint and Distance in the Coordinate Plane OBJ: Find the midpoint of a segment STA: MA.912.G.1.1 TOP: 1-7 Problem 1 Finding the Midpoint KEY: coordinate plane Midpoint Formula DOK: DOK 1 4. ANS: 5 PTS: 1 DIF: L3 REF: 1-7 Midpoint and Distance in the Coordinate Plane OBJ: Find the midpoint of a segment STA: MA.912.G.1.1 TOP: 1-7 Problem 1 Finding the Midpoint KEY: coordinate plane Midpoint Formula DOK: DOK 1 5. ANS: (3, 3) PTS: 1 DIF: L3 REF: 1-7 Midpoint and Distance in the Coordinate Plane OBJ: Find the midpoint of a segment STA: MA.912.G.1.1 TOP: 1-7 Problem 2 Finding an Endpoint KEY: coordinate plane Midpoint Formula 6. ANS: (4, 4) PTS: 1 DIF: L2 REF: 1-7 Midpoint and Distance in the Coordinate Plane OBJ: Find the midpoint of a segment STA: MA.912.G.1.1 TOP: 1-7 Problem 2 Finding an Endpoint KEY: coordinate plane Midpoint Formula 1

22 7. ANS: 2.2 PTS: 1 DIF: L3 REF: 1-7 Midpoint and Distance in the Coordinate Plane OBJ: Find the distance between two points in the coordinate plane STA: MA.912.G.1.1 TOP: 1-7 Problem 3 Finding Distance KEY: Distance Formula coordinate plane 8. ANS: 10.6 miles PTS: 1 DIF: L3 REF: 1-7 Midpoint and Distance in the Coordinate Plane OBJ: Find the distance between two points in the coordinate plane STA: MA.912.G.1.1 TOP: 1-7 Problem 4 Finding Distance KEY: coordinate plane Distance Formula word problem problem solving 9. ANS: 5, 5, 29.5 miles 2 PTS: 1 DIF: L3 REF: 1-7 Midpoint and Distance in the Coordinate Plane OBJ: Find the distance between two points in the coordinate plane STA: MA.912.G.1.1 TOP: 1-7 Problem 4 Finding Distance KEY: Distance Formula coordinate plane word problem problem solving midpoint 10. ANS: 238 feet PTS: 1 DIF: L2 REF: 1-8 Perimeter, Circumference, and Area OBJ: Find the perimeter or circumference of basic shapes STA: MA.912.G.2.5 MA.912.G.6.5 TOP: 1-8 Problem 1 Finding the Perimeter of a Rectangle KEY: perimeter rectangle DOK: DOK ANS: 41.8 in. PTS: 1 DIF: L3 REF: 1-8 Perimeter, Circumference, and Area OBJ: Find the perimeter or circumference of basic shapes STA: MA.912.G.2.5 MA.912.G.6.5 TOP: 1-8 Problem 1 Finding the Perimeter of a Rectangle KEY: perimeter problem solving word problem DOK: DOK ANS: 186 ft PTS: 1 DIF: L4 REF: 1-8 Perimeter, Circumference, and Area OBJ: Find the perimeter or circumference of basic shapes STA: MA.912.G.2.5 MA.912.G.6.5 TOP: 1-8 Problem 1 Finding the Perimeter of a Rectangle KEY: perimeter rectangle word problem problem solving 2

23 13. ANS: 62.8 m PTS: 1 DIF: L3 REF: 1-8 Perimeter, Circumference, and Area OBJ: Find the perimeter or circumference of basic shapes STA: MA.912.G.2.5 MA.912.G.6.5 TOP: 1-8 Problem 2 Finding Circumference KEY: circle circumference 14. ANS: 84 in. PTS: 1 DIF: L3 REF: 1-8 Perimeter, Circumference, and Area OBJ: Find the perimeter or circumference of basic shapes STA: MA.912.G.2.5 MA.912.G.6.5 TOP: 1-8 Problem 2 Finding Circumference KEY: circle circumference 15. ANS: 24 units PTS: 1 DIF: L3 REF: 1-8 Perimeter, Circumference, and Area OBJ: Find the perimeter or circumference of basic shapes STA: MA.912.G.2.5 MA.912.G.6.5 TOP: 1-8 Problem 3 Finding Perimeter in the Coordinate Plane KEY: perimeter triangle coordinate plane Distance Formula 16. ANS: 22 units PTS: 1 DIF: L3 REF: 1-8 Perimeter, Circumference, and Area OBJ: Find the perimeter or circumference of basic shapes STA: MA.912.G.2.5 MA.912.G.6.5 TOP: 1-8 Problem 3 Finding Perimeter in the Coordinate Plane KEY: perimeter coordinate plane Distance Formula 17. ANS: 1444 in. 2 PTS: 1 DIF: L3 REF: 1-8 Perimeter, Circumference, and Area OBJ: Find the perimeter or circumference of basic shapes STA: MA.912.G.2.5 MA.912.G.6.5 TOP: 1-8 Problem 4 Finding Area of a Rectangle KEY: area square 18. ANS: 60 ft 2 PTS: 1 DIF: L2 REF: 1-8 Perimeter, Circumference, and Area OBJ: Find the perimeter or circumference of basic shapes STA: MA.912.G.2.5 MA.912.G.6.5 TOP: 1-8 Problem 4 Finding Area of a Rectangle KEY: area rectangle DOK: DOK 1 3

24 19. ANS: 484 in. 2 PTS: 1 DIF: L3 REF: 1-8 Perimeter, Circumference, and Area OBJ: Find the perimeter or circumference of basic shapes STA: MA.912.G.2.5 MA.912.G.6.5 TOP: 1-8 Problem 5 Finding Area of a Circle KEY: area circle DOK: DOK ANS: 35.2 in. 2 PTS: 1 DIF: L2 REF: 1-8 Perimeter, Circumference, and Area OBJ: Find the perimeter or circumference of basic shapes STA: MA.912.G.2.5 MA.912.G.6.5 TOP: 1-8 Problem 5 Finding Area of a Circle KEY: area circle DOK: DOK ANS: 7.7 in. 2 PTS: 1 DIF: L3 REF: 1-8 Perimeter, Circumference, and Area OBJ: Find the perimeter or circumference of basic shapes STA: MA.912.G.2.5 MA.912.G.6.5 TOP: 1-8 Problem 6 Finding Area of an Irregular Shape KEY: circle square area 22. ANS: 68 ft 2 PTS: 1 DIF: L2 REF: 1-8 Perimeter, Circumference, and Area OBJ: Find the perimeter or circumference of basic shapes STA: MA.912.G.2.5 MA.912.G.6.5 TOP: 1-8 Problem 6 Finding Area of an Irregular Shape KEY: area rectangle 23. ANS: A (15 3) (12 4) PTS: 1 DIF: L2 REF: 1-8 Perimeter, Circumference, and Area OBJ: Find the perimeter or circumference of basic shapes STA: MA.912.G.2.5 MA.912.G.6.5 TOP: 1-8 Problem 6 Finding Area of an Irregular Shape KEY: rectangle area 24. ANS: 3 2 PTS: 1 DIF: L3 REF: 3-7 Equations of Lines in the Coordinate Plane OBJ: Graph and write linear equations TOP: 3-7 Problem 1 Finding Slopes of Lines KEY: slope linear graph graph of line 4

25 25. ANS: 5 12 PTS: 1 DIF: L3 REF: 3-7 Equations of Lines in the Coordinate Plane OBJ: Graph and write linear equations TOP: 3-7 Problem 1 Finding Slopes of Lines KEY: slope linear graph graph of line 26. ANS: 2 13 PTS: 1 DIF: L3 REF: 3-7 Equations of Lines in the Coordinate Plane OBJ: Graph and write linear equations TOP: 3-7 Problem 1 Finding Slopes of Lines KEY: slope linear graph graph of line 27. ANS: y 1 / 5x (13 / 5) PTS: 1 DIF: L4 REF: 3-7 Equations of Lines in the Coordinate Plane OBJ: Graph and write linear equations TOP: 3-7 Problem 4 Using Two Points to Write an Equation KEY: point-slope form 28. ANS: x = 5 PTS: 1 DIF: L3 REF: 3-7 Equations of Lines in the Coordinate Plane OBJ: Graph and write linear equations TOP: 3-7 Problem 5 Writing Equations of Horizontal and Vertical Lines KEY: vertical line 29. ANS: y = 4 PTS: 1 DIF: L3 REF: 3-7 Equations of Lines in the Coordinate Plane OBJ: Graph and write linear equations TOP: 3-7 Problem 5 Writing Equations of Horizontal and Vertical Lines KEY: horizontal line 30. ANS: No; the lines have unequal slopes. PTS: 1 DIF: L2 REF: 3-8 Slopes of Parallel and Perpendicular Lines OBJ: Relate slope to parallel and perpendicular lines TOP: 3-8 Problem 1 Checking for Parallel Lines KEY: slopes of parallel lines graphing parallel lines 5

26 31. ANS: y + 5 = 6(x + 8) PTS: 1 DIF: L3 REF: 3-8 Slopes of Parallel and Perpendicular Lines OBJ: Relate slope to parallel and perpendicular lines TOP: 3-8 Problem 2 Writing Equations of Parallel Lines KEY: slopes of parallel lines parallel lines 32. ANS: y 3 = 2(x + 6) PTS: 1 DIF: L3 REF: 3-8 Slopes of Parallel and Perpendicular Lines OBJ: Relate slope to parallel and perpendicular lines TOP: 3-8 Problem 2 Writing Equations of Parallel Lines KEY: slopes of parallel lines parallel lines 33. ANS: y 3 = 1 (x + 6) 2 PTS: 1 DIF: L3 REF: 3-8 Slopes of Parallel and Perpendicular Lines OBJ: Relate slope to parallel and perpendicular lines TOP: 3-8 Problem 4 Writing Equations of Perpendicular Lines KEY: slopes of perpendicular lines perpendicular lines 34. ANS: isosceles PTS: 1 DIF: L2 REF: 6-7 Polygons in the Coordinate Plane OBJ: Classify polygons in the coordinate plane STA: MA.912.G.1.1 MA.912.G.2.6 MA.912.G.3.1 MA.912.G.3.3 MA.912.G.4.1 MA.912.G.4.8 TOP: 6-7 Problem 1 Classifying a Triangle KEY: triangle distance formula isosceles scalene 35. ANS: rhombus PTS: 1 DIF: L3 REF: 6-7 Polygons in the Coordinate Plane OBJ: Classify polygons in the coordinate plane STA: MA.912.G.1.1 MA.912.G.2.6 MA.912.G.3.1 MA.912.G.3.3 MA.912.G.4.1 MA.912.G.4.8 TOP: 6-7 Problem 3 Classifying a Quadrilateral 36. ANS: (c, b) KEY: midpoint kite rectangle PTS: 1 DIF: L2 REF: 6-8 Applying Coordinate Geometry OBJ: Name coordinates of special figures by using their properties STA: MA.912.G.1.1 MA.912.G.2.6 MA.912.G.3.3 MA.912.G.3.4 MA.912.G.4.8 MA.912.G.8.5 TOP: 6-8 Problem 2 Using Variable Coordinates KEY: coordinate plane algebra rectangle 6

27 37. ANS: (p + r + s, 2q) PTS: 1 DIF: L3 REF: 6-8 Applying Coordinate Geometry OBJ: Name coordinates of special figures by using their properties STA: MA.912.G.1.1 MA.912.G.2.6 MA.912.G.3.3 MA.912.G.3.4 MA.912.G.4.8 MA.912.G.8.5 TOP: 6-8 Problem 2 Using Variable Coordinates KEY: algebra coordinate plane isosceles trapezoid midsegment 38. ANS: LM, MN, NP, and PL PTS: 1 DIF: L3 REF: 10-6 Circles and Arcs OBJ: Find the measures of central angles and arcs STA: MA.912.G.6.2 MA.912.G.6.4 MA.912.G.6.5 TOP: 10-6 Problem 1 Naming Arcs KEY: major arc minor arc semicircle DOK: DOK ANS: BCA, CDB, DAC, and ABD PTS: 1 DIF: L3 REF: 10-6 Circles and Arcs OBJ: Find the measures of central angles and arcs STA: MA.912.G.6.2 MA.912.G.6.4 MA.912.G.6.5 TOP: 10-6 Problem 1 Naming Arcs KEY: major arc minor arc semicircle DOK: DOK ANS: 172 PTS: 1 DIF: L3 REF: 10-6 Circles and Arcs OBJ: Find the measures of central angles and arcs STA: MA.912.G.6.2 MA.912.G.6.4 MA.912.G.6.5 TOP: 10-6 Problem 2 Finding the Measures of Arcs DOK: DOK ANS: 6.6 cm KEY: major arc measure of an arc arc PTS: 1 DIF: L2 REF: 10-6 Circles and Arcs OBJ: Find the circumference and arc length STA: MA.912.G.6.2 MA.912.G.6.4 MA.912.G.6.5 TOP: 10-6 Problem 3 Finding a Distance KEY: circumference diameter 42. ANS: 24 in. PTS: 1 DIF: L2 REF: 10-6 Circles and Arcs OBJ: Find the circumference and arc length STA: MA.912.G.6.2 MA.912.G.6.4 MA.912.G.6.5 TOP: 10-6 Problem 3 Finding a Distance KEY: circumference radius 7

28 43. ANS: 78 cm; 39 cm; 41.2 cm PTS: 1 DIF: L4 REF: 10-6 Circles and Arcs OBJ: Find the circumference and arc length STA: MA.912.G.6.2 MA.912.G.6.4 MA.912.G.6.5 TOP: 10-6 Problem 4 Finding Arc Length KEY: circumference radius 44. ANS: 15 m PTS: 1 DIF: L3 REF: 10-6 Circles and Arcs OBJ: Find the circumference and arc length STA: MA.912.G.6.2 MA.912.G.6.4 MA.912.G.6.5 TOP: 10-6 Problem 4 Finding Arc Length KEY: arc circumference 45. ANS: 1.44 m 2 PTS: 1 DIF: L3 REF: 10-7 Areas of Circles and Sectors OBJ: Find the areas of circles, sectors, and segments of circles STA: MA.912.G.2.7 MA.912.G.6.4 MA.912.G.6.5 TOP: 10-7 Problem 1 Finding the Area of a Circle 46. ANS: m 2 KEY: area of a circle radius PTS: 1 DIF: L3 REF: 10-7 Areas of Circles and Sectors OBJ: Find the areas of circles, sectors, and segments of circles STA: MA.912.G.2.7 MA.912.G.6.4 MA.912.G.6.5 TOP: 10-7 Problem 1 Finding the Area of a Circle 47. ANS: 71.7 cm 2 KEY: area of a circle radius PTS: 1 DIF: L4 REF: 10-7 Areas of Circles and Sectors OBJ: Find the areas of circles, sectors, and segments of circles STA: MA.912.G.2.7 MA.912.G.6.4 MA.912.G.6.5 TOP: 10-7 Problem 1 Finding the Area of a Circle KEY: circumference radius diameter area of a circle word problem problem solving DOK: DOK ANS: 39.3 in. 2 PTS: 1 DIF: L3 REF: 10-7 Areas of Circles and Sectors OBJ: Find the areas of circles, sectors, and segments of circles STA: MA.912.G.2.7 MA.912.G.6.4 MA.912.G.6.5 TOP: 10-7 Problem 2 Finding the Area of a Sector of a Circle KEY: sector circle area 8

29 49. ANS: 22.1 cm 2 PTS: 1 DIF: L3 REF: 10-7 Areas of Circles and Sectors OBJ: Find the areas of circles, sectors, and segments of circles STA: MA.912.G.2.7 MA.912.G.6.4 MA.912.G.6.5 TOP: 10-7 Problem 2 Finding the Area of a Sector of a Circle 50. ANS: ft 2 PTS: 1 DIF: L2 REF: 10-7 Areas of Circles and Sectors OBJ: Find the areas of circles, sectors, and segments of circles STA: MA.912.G.2.7 MA.912.G.6.4 MA.912.G.6.5 TOP: 10-7 Problem 3 Finding the Area of a Segment of a Circle KEY: sector circle area central angle 51. ANS: 2 3 PTS: 1 DIF: L4 REF: 10-8 Geometric Probability OBJ: Use segment and area models to find the probabilities of events STA: MA.912.G.2.5 MA.912.G.6.1 MA.912.G.6.5 TOP: 10-8 Problem 1 Using Segments to Find Probability DOK: DOK ANS: PTS: 1 DIF: L3 REF: 10-8 Geometric Probability OBJ: Use segment and area models to find the probabilities of events STA: MA.912.G.2.5 MA.912.G.6.1 MA.912.G.6.5 TOP: 10-8 Problem 2 Using Segments to Find Probability KEY: geometric probability segment word problem problem solving 53. ANS: PTS: 1 DIF: L4 REF: 10-8 Geometric Probability OBJ: Use segment and area models to find the probabilities of events STA: MA.912.G.2.5 MA.912.G.6.1 MA.912.G.6.5 TOP: 10-8 Problem 2 Using Segments to Find Probability KEY: geometric probability segment word problem problem solving KEY: sector circle area central angle KEY: geometric probability segment 9

30 54. ANS: 0.32 PTS: 1 DIF: L3 REF: 10-8 Geometric Probability OBJ: Use segment and area models to find the probabilities of events STA: MA.912.G.2.5 MA.912.G.6.1 MA.912.G.6.5 TOP: 10-8 Problem 3 Using Area to Find Probability 55. ANS: 32 KEY: geometric probability PTS: 1 DIF: L3 REF: 11-1 Space Figures and Cross Sections OBJ: Recognize polyhedra and their parts STA: MA.912.G.7.2 MA.912.G.7.3 TOP: 11-1 Problem 2 Using Euler's Formula KEY: polyhedron face vertices edge Euler's Formula DOK: DOK ANS: 17 PTS: 1 DIF: L3 REF: 11-1 Space Figures and Cross Sections OBJ: Recognize polyhedra and their parts STA: MA.912.G.7.2 MA.912.G.7.3 TOP: 11-1 Problem 2 Using Euler's Formula KEY: polyhedron face vertices edge Euler's Formula DOK: DOK ANS: 17 PTS: 1 DIF: L3 REF: 11-1 Space Figures and Cross Sections OBJ: Recognize polyhedra and their parts STA: MA.912.G.7.2 MA.912.G.7.3 TOP: 11-1 Problem 2 Using Euler's Formula KEY: polyhedron face vertices edge Euler's Formula DOK: DOK ANS: 20 edges PTS: 1 DIF: L4 REF: 11-1 Space Figures and Cross Sections OBJ: Recognize polyhedra and their parts STA: MA.912.G.7.2 MA.912.G.7.3 TOP: 11-1 Problem 2 Using Euler's Formula KEY: edge Euler's Formula face polyhedron problem solving word problem vertices 59. ANS: 28 PTS: 1 DIF: L3 REF: 12-1 Tangent Lines OBJ: Use properties of a tangent to a circle TOP: 12-1 Problem 1 Finding Angle Measures KEY: tangent to a circle point of tangency properties of tangents central angle DOK: DOK 1 10

31 60. ANS: 66 PTS: 1 DIF: L3 REF: 12-1 Tangent Lines OBJ: Use properties of a tangent to a circle TOP: 12-1 Problem 1 Finding Angle Measures KEY: tangent to a circle point of tangency angle measure properties of tangents central angle DOK: DOK ANS: 65 PTS: 1 DIF: L4 REF: 12-1 Tangent Lines OBJ: Use properties of a tangent to a circle TOP: 12-1 Problem 1 Finding Angle Measures KEY: properties of tangents tangent to a circle Tangent Theorem 62. ANS: 46 PTS: 1 DIF: L4 REF: 12-1 Tangent Lines OBJ: Use properties of a tangent to a circle TOP: 12-1 Problem 1 Finding Angle Measures KEY: properties of tangents tangent to a circle Tangent Theorem 63. ANS: 35 PTS: 1 DIF: L2 REF: 12-1 Tangent Lines OBJ: Use properties of a tangent to a circle TOP: 12-1 Problem 2 Finding Distance KEY: tangent to a circle point of tangency properties of tangents Pythagorean Theorem 64. ANS: 3,718 miles PTS: 1 DIF: L3 REF: 12-1 Tangent Lines OBJ: Use properties of a tangent to a circle TOP: 12-1 Problem 2 Finding Distance KEY: tangent to a circle point of tangency properties of tangents Pythagorean Theorem 11

32 65. ANS: 17 PTS: 1 DIF: L4 REF: 12-1 Tangent Lines OBJ: Use properties of a tangent to a circle TOP: 12-1 Problem 2 Finding Distance KEY: tangent to a circle point of tangency properties of tangents Pythagorean Theorem 66. ANS: 12.7 inches PTS: 1 DIF: L4 REF: 12-1 Tangent Lines OBJ: Use properties of a tangent to a circle TOP: 12-1 Problem 3 Finding a Radius KEY: word problem tangent to a circle point of tangency properties of tangents right triangle Pythagorean Theorem 67. ANS: 7.6 PTS: 1 DIF: L3 REF: 12-1 Tangent Lines OBJ: Use properties of a tangent to a circle TOP: 12-1 Problem 3 Finding a Radius KEY: tangent to a circle point of tangency properties of tangents right triangle Pythagorean Theorem 68. ANS: 3.5 PTS: 1 DIF: L3 REF: 12-1 Tangent Lines OBJ: Use properties of a tangent to a circle TOP: 12-1 Problem 5 Circles Inscribed in Polygons KEY: properties of tangents tangent to a circle pentagon 69. ANS: 60 PTS: 1 DIF: L3 REF: 12-1 Tangent Lines OBJ: Use properties of a tangent to a circle TOP: 12-1 Problem 5 Circles Inscribed in Polygons KEY: properties of tangents tangent to a circle triangle 70. ANS: 3.5 ft PTS: 1 DIF: L3 REF: 12-2 Chords and Arcs OBJ: Use perpendicular bisectors to chords TOP: 12-2 Problem 2 Finding the Length of a Chord KEY: circle radius chord congruent chords bisected chords DOK: DOK 1 12

33 71. ANS: 24 in. PTS: 1 DIF: L3 REF: 12-2 Chords and Arcs OBJ: Use perpendicular bisectors to chords TOP: 12-2 Problem 2 Finding the Length of a Chord KEY: circle radius chord congruent chords bisected chords DOK: DOK ANS: 10 PTS: 1 DIF: L2 REF: 12-2 Chords and Arcs OBJ: Use perpendicular bisectors to chords TOP: 12-2 Problem 3 Using Diameters and Chords KEY: bisected chords circle perpendicular perpendicular bisector Pythagorean Theorem 73. ANS: 8.8 PTS: 1 DIF: L2 REF: 12-2 Chords and Arcs OBJ: Use perpendicular bisectors to chords TOP: 12-2 Problem 3 Using Diameters and Chords KEY: bisected chords circle perpendicular perpendicular bisector Pythagorean Theorem 74. ANS: 32 PTS: 1 DIF: L2 REF: 12-2 Chords and Arcs OBJ: Use congruent chords, arcs, and central angles TOP: 12-2 Problem 4 Finding Measures in a Circle DOK: DOK ANS: 19.1 PTS: 1 DIF: L3 REF: 12-2 Chords and Arcs OBJ: Use congruent chords, arcs, and central angles TOP: 12-2 Problem 4 Finding Measures in a Circle KEY: circle radius chord congruent chords right triangle Pythagorean Theorem DOK: DOK 3 KEY: arc central angle congruent arcs 13

34 76. ANS: 131 PTS: 1 DIF: L3 REF: 12-2 Chords and Arcs OBJ: Use congruent chords, arcs, and central angles TOP: 12-2 Problem 4 Finding Measures in a Circle KEY: arc chord-arc relationship diameter chord perpendicular angle measure circle right triangle perpendicular bisector 77. ANS: 228 PTS: 1 DIF: L2 REF: 12-2 Chords and Arcs OBJ: Use congruent chords, arcs, and central angles TOP: 12-2 Problem 4 Finding Measures in a Circle KEY: arc central angle congruent arcs arc measure arc addition diameter DOK: DOK ANS: 53.1 PTS: 1 DIF: L3 REF: 12-2 Chords and Arcs OBJ: Use perpendicular bisectors to chords TOP: 12-2 Problem 4 Finding Measures in a Circle KEY: bisected chords circle perpendicular perpendicular bisector Pythagorean Theorem 79. ANS: 26 PTS: 1 DIF: L3 REF: 12-3 Inscribed Angles OBJ: Find the measure of an inscribed angle STA: MA.912.G.6.3 MA.912.G.6.4 TOP: 12-3 Problem 1 Using the Inscribed Angle Theorem KEY: circle inscribed angle intercepted arc inscribed angle-arc relationship DOK: DOK ANS: 33 PTS: 1 DIF: L2 REF: 12-3 Inscribed Angles OBJ: Find the measure of an inscribed angle STA: MA.912.G.6.3 MA.912.G.6.4 TOP: 12-3 Problem 1 Using the Inscribed Angle Theorem KEY: circle inscribed angle intercepted arc inscribed angle-arc relationship DOK: DOK 1 14

35 81. ANS: 51.5 PTS: 1 DIF: L4 REF: 12-3 Inscribed Angles OBJ: Find the measure of an inscribed angle STA: MA.912.G.6.3 MA.912.G.6.4 TOP: 12-3 Problem 1 Using the Inscribed Angle Theorem KEY: circle inscribed angle central angle intercepted arc 82. ANS: 76 PTS: 1 DIF: L2 REF: 12-3 Inscribed Angles OBJ: Find the measure of an inscribed angle STA: MA.912.G.6.3 MA.912.G.6.4 TOP: 12-3 Problem 2 Using Corollaries to Find Angle Measures KEY: circle inscribed angle intercepted arc inscribed angle-arc relationship DOK: DOK ANS: 284 PTS: 1 DIF: L3 REF: 12-3 Inscribed Angles OBJ: Find the measure of an inscribed angle STA: MA.912.G.6.3 MA.912.G.6.4 TOP: 12-3 Problem 2 Using Corollaries to Find Angle Measures KEY: circle inscribed angle intercepted arc inscribed angle-arc relationship 84. ANS: 30 PTS: 1 DIF: L2 REF: 12-3 Inscribed Angles OBJ: Find the measure of an inscribed angle STA: MA.912.G.6.3 MA.912.G.6.4 TOP: 12-3 Problem 2 Using Corollaries to Find Angle Measures KEY: circle inscribed angle intercepted arc inscribed angle-arc relationship DOK: DOK 1 15