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Name: ________________________ Class: ___________________ Date: __________ ID: A Geometry - Spring 2013 Final Review ____ 1. A model is made of a car. The car is 10 feet long and the model is 7 inches long. What is the ratio of the length of the car to the length of the model? A. 10 : 7 B. 7 : 120 C. 120 : 7 D. 7 : 10 ____ 2. The measures of the angles of a triangle are in the extended ratio 2 : 3 : 4. What is the measure of the smallest angle? A. 40 C. 80 B. 60 D. 20 What is the solution of each proportion? ____ 3. n6 3n A. –3 n5 3n 1 B. 2 5 C. 9 17 D. 3 Are the polygons similar? If they are, write a similarity statement and give the scale factor. ____ 4. A. ABCD KLMN ; 10 : 1.2 C. ABCD KLMN ; 5 : 1.2 B. The polygons are not similar. D. ABCD NKLM ; 5 : 3.12 1 Name: ________________________ ID: A The polygons are similar, but not necessarily drawn to scale. Find the value of x. ____ 5. A. x = 8 B. x = ____ C. x = 9 11 D. x = 10 2 6. Are the two triangles similar? How do you know? A. no B. yes, by SSS C. yes, by AA D. yes, by SAS State whether the triangles are similar. If so, write a similarity statement and the postulate or theorem you used. ____ 7. A. ADB CDB; SAS C. ADB CDB; SSS B. ABD CDB; SAS D. The triangles are not similar. 2 Name: ________________________ ____ 8. Use the information in the diagram to determine the height of the tree to the nearest foot. A. 80 ft ____ ID: A B. 264 ft C. 60 ft D. 72 ft 9. Campsites F and G are on opposite sides of a lake. A survey crew made the measurements shown on the diagram. What is the distance between the two campsites? The diagram is not to scale. A. 42.3 m B. 47.4 m C. 73.8 m D. 82.8 m Find the geometric mean of the pair of numbers. ____ 10. 4 and 7 A. 4 2 B. 2 7 C. 28 3 D. 35 Name: ________________________ ID: A What are the values of a and b? ____ 11. A. a B. a ____ 12. 9 2 , b 15 2 , b 15 C. a 2 9 D. a 2 16 3 9 2 , b , b 15 2 13 2 Find the length of the altitude drawn to the hypotenuse. The triangle is not drawn to scale. A. 4 5 B. 21 C. 80 4 D. 21 Name: ________________________ ID: A ____ 13. Jason wants to walk the shortest distance to get from the parking lot to the beach. a. b. How far is the spot on the beach from the parking lot? How far will his place on the beach be from the refreshment stand? A. 24 m; 32 m C. 34 m; 16 m B. 38 m; 12 m D. 24 m; 18 m ____ 14. What is the value of x? A. 52 3 B. 3 4 C. 17 5 D. 52 7 Name: ________________________ ID: A ____ 15. What is the value of x to the nearest tenth? A. 1.9 B. 2.4 C. 13.5 D. 11 Find the length of the missing side. Leave your answer in simplest radical form. ____ 16. A. 26 ft B. 206 ft C. 296 ft D. 2 74 ft ____ 17. A triangle has side lengths of 12 cm, 35 cm, and 37 cm. Classify it as acute, obtuse, or right. A. obtuse B. right C. acute ____ 18. A triangle has side lengths of 23 in, 6 in, and 28 in. Classify it as acute, obtuse, or right. A. obtuse B. right C. acute ____ 19. Find the length of the leg. If your answer is not an integer, leave it in simplest radical form. A. 2 3 B. 288 C. 24 6 D. 12 2 Name: ________________________ ID: A ____ 20. Find the value of x and y rounded to the nearest tenth. A. x = 48.1, y = 46.4 C. x = 24.0, y = 139.3 B. x = 48.1, y = 139.3 D. x = 24.0, y = 46.4 Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form. ____ 21. A. x = 22 3 , y = 11 C. x = 22, y = 11 3 B. x = 11 3 , y = 22 D. x = 11, y = 22 3 ____ 22. Find the missing value to the nearest hundredth. A. 23.58 B. 66.42 C. 21.8 7 D. 63.21 Name: ________________________ ID: A ____ 23. Write the tangent ratios for P and Q. A. tan P 12 16 ; tan Q 16 12 C. tan P 16 12 ; tan Q 12 16 B. tan P 20 12 ; tan Q 12 20 D. tan P 20 16 ; tan Q 16 20 Find the value of x. Round to the nearest tenth. ____ 24. A. 14.5 B. 10.7 C. 10.2 D. 14.2 ____ 25. A slide 4.1 meters long makes an angle of 35 with the ground. To the nearest tenth of a meter, how far above the ground is the top of the slide? A. 7.1 m B. 3.4 m C. 5.0 m 8 D. 2.4 m Name: ________________________ ID: A ____ 26. The students in Mr. Collin’s class used a surveyor’s measuring device to find the angle from their location to the top of a building. They also measured their distance from the bottom of the building. The diagram shows the angle measure and the distance. To the nearest foot, find the height of the building. A. 2400 ft B. 72 ft C. 308 ft D. 33 ft ____ 27. Find the value of w, then x. Round lengths of segments to the nearest tenth. A. w = 13.3, x = 10.2 C. w = 13.3, x = 23.6 B. w = 10.8, x = 6.1 D. w = 10.8, x = 16.9 Find the value of x. Round to the nearest degree. ____ 28. A. 60 B. 57 C. 29 9 D. 33 Name: ________________________ ID: A Find the value of x to the nearest degree. ____ 29. A. 24 B. 66 C. 69 D. 58 ____ 30. An airplane pilot over the Pacific sights an atoll at an angle of depression of 5. At this time, the horizontal distance from the airplane to the atoll is 4629 meters. What is the height of the plane to the nearest meter? A. 403 m B. 405 m C. 4611 m D. 4647 m Use the Law of Sines to find the missing side of the triangle. ____ 31. Find b. A. 70.1 B. 43.8 C. 57.1 10 D. 31.5 Name: ________________________ ID: A Use the Law of Sines to find the missing angle of the triangle. ____ 32. Find mC to the nearest tenth. A. 156.6 B. 94.8 C. 23.4 D. 85.2 Find the area. The figure is not drawn to scale. ____ 33. A. 30 yd2 B. 6.5 yd2 C. 13 yd2 D. 15 yd2 C. 40.5 D. 35 ____ 34. What is the height h of the parallelogram? Not drawn to scale A. 32 B. 28 11 Name: ________________________ ID: A ____ 35. Find the area of an equilateral triangle with a side of 10. A. 25 3 units2 C. 50 units2 B. 25 units2 D. 5 2 3 units2 Find the area of the trapezoid. Leave your answer in simplest radical form. ____ 36. A. 31.5 cm2 B. 7 cm2 C. 81 cm2 D. 94.5 cm2 A. 56 3 ft2 B. 64 3 ft2 C. 72 3 ft2 D. 32 3 ft2 ____ 37. 12 Name: ________________________ ID: A ____ 38. What is the area of the kite? Not drawn to scale A. 11 ft2 B. 72 ft2 C. 36 ft2 D. 44 ft2 ____ 39. Find the area of the rhombus. Leave your answer in simplest radical form. A. 18 3 units2 B. 81 6 units2 C. 162 3 units2 13 D. 162 units2 Name: ________________________ ID: A ____ 40. Given the regular hexagon, find the measure of each numbered angle. A. m1 30, m2 60, m3 30 C. m1 60, m2 30, m3 60 B. m1 m2 m3 60 D. m1 60, m2 30, m3 30 ____ 41. A regular hexagon has a perimeter of 120 m. Find its area. Leave your answer in simplest radical form. A. 1800 3 m2 B. 5 3 m2 C. 600 3 m2 D. 3600 3 m2 The figures are similar. Give the ratio of the perimeters and the ratio of the areas of the first figure to the second. The figures are not drawn to scale. ____ 42. A. 10 9 and 81 64 B. 9 8 and 11 10 C. 9 8 and 81 64 D. 10 9 and 11 10 ____ 43. A rectangular napkin costs $3.25. A similar tablecloth is five times longer and five times wider. How much would you expect to pay for the tablecloth? A. $81.25 B. $48.75 C. $16.25 D. $32.50 Find the area of the regular polygon. Give the answer to the nearest tenth. ____ 44. pentagon with a side of 6 ft A. 49.5 ft 2 B. 61.9 ft 2 C. 123.9 ft 2 14 D. 12.4 ft 2 Name: ________________________ ID: A Find the area of the triangle. Give the answer to the nearest tenth. The drawing may not be to scale. ____ 45. A. 10.5 m 2 B. 9.8 m 2 C. 19.6 m 2 D. 21.0 m 2 ____ 46. A gardener needs to cultivate a triangular plot of land. One angle of the garden is 47, and two sides adjacent to the angle are 77 feet and 76 feet. To the nearest tenth, what is the area of the plot of land? A. 2163.5 ft 2 B. 2139.9 ft 2 C. 4279.9 ft 2 D. 1995.5 ft 2 C. BDA ; 310 D. AB; 310 ____ 47. Name the major arc and find its measure. A. BDA; 50 B. AB; 50 ____ 48. Find the length of YPX . Leave your answer in terms of . A. 30 m B. 15 m C. 5 m 15 D. 900 m Name: ________________________ ID: A ____ 49. Find the area of the figure to the nearest tenth. A. 70.6 in.2 B. 22.5 in.2 C. 141.1 in.2 D. 10.1 in.2 ____ 50. The area of sector AOB is 20.25 ft 2 . Find the exact area of the shaded region. 2 A. 20.25 40.5ft B. 20.25 81ft 2 C. 20.25 40.5 2 ft 2 D. none of these ____ 51. Find the area of the shaded region. Leave your answer in terms of and in simplest radical form. A. 120 6 3 m 2 B. 142 36 3 m 2 C. 120 36 3 m 2 D. none of these 16 Name: ________________________ ID: A ____ 52. Pierre built the model shown in the diagram below for a social studies project. He wants to be able to show the inside of his model, so he sliced the figure as shown. Describe the cross section he created. A. hexagon B. pentagon C. pyramid D. rectangle Use formulas to find the lateral area and surface area of the given prism. Round your answer to the nearest whole number. ____ 53. A. 208 m2 ; 188 m2 C. 136 m2 ; 240 m2 B. 136 m2 ; 188 m2 D. 208 m2 ; 240 m2 Find the surface area of the cylinder in terms of . ____ 54. A. 504 cm2 B. 333 cm2 C. 382.5 cm2 17 D. 211.5 cm2 Name: ________________________ ID: A Find the surface area of the regular pyramid shown to the nearest whole number. ____ 55. A. 165 ft 2 B. 95 ft 2 C. 70 ft 2 D. 28 ft 2 ____ 56. Find the lateral area and surface area of the right cone. Round the answers to the nearest tenth. (The figure is not drawn to scale.) A. L.A. = 395.8 ft 2 ; S.A. = 791.7 ft 2 C. L.A. = 622.0 ft 2 ; S.A. = 791.7 ft 2 B. L.A. = 1583.4 ft 2 ; S.A. = 1244.1 ft 2 D. L.A. = 791.7 ft 2 ; S.A. = 1244.1 ft 2 18 Name: ________________________ ID: A Find the volume of the given prism. Round to the nearest tenth if necessary. ____ 57. A. 308.9 cm3 B. 308.2 cm3 C. 312.8 cm3 D. 302.9 cm3 A. 17 m 3 B. 34 m 3 C. 8.5 m 3 D. 1 m3 ____ 58. 19 Name: ________________________ ID: A Find the volume of the cylinder in terms of . ____ 59. A. 60.8 m3 B. 115.52 m3 C. 438.98 m3 D. 57.76 m3 ____ 60. Find the volume of a square pyramid with base edges of 48 cm and a slant height of 26 cm. A. 11,520 cm3 B. 23,040 cm3 C. 7,680 cm3 D. 768 cm3 ____ 61. Find the volume of the oblique cone shown in terms of . A. 661.5 in. 3 B. 1323 in. 3 C. 63 in. 3 20 D. 441 in. 3 Name: ________________________ ID: A ____ 62. A balloon has a circumference of 11 cm. Use the circumference to approximate the surface area of the balloon to the nearest square centimeter. A. 121 cm2 B. 380 cm2 C. 39 cm2 D. 154 cm2 Find the volume of the sphere shown. Give each answer rounded to the nearest cubic unit. ____ 63. A. 1527 mm3 B. 339 mm3 C. 3054 mm3 D. 1018 mm3 Are the two figures similar? If so, give the similarity ratio of the smaller figure to the larger figure. ____ 64. A. yes; 1 2.8 B. yes; 1 1.6 C. yes; 1 1.8 D. no ____ 65. A glass vase weighs 0.22 lb. How much does a similarly shaped vase of the same glass weigh if each dimension is 6 times as large? A. 7.92 lb B. 1.32 lb C. 285.12 lb D. 47.52 lb 21 Name: ________________________ ID: A 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.) ____ 66. mO 135 A. 45 B. 67.5 C. 315 D. 270 B. 76 C. 38 D. 104 ____ 67. mP 14 A. 28 ____ 68. AB is tangent to circle O at B. Find the length of the radius r for AB = 9 and AO = 10.5. Round to the nearest tenth if necessary. The diagram is not to scale. A. 5.4 B. 2.3 C. 1.5 22 D. 13.8 Name: ________________________ ID: A ____ 69. JK , KL, and LJ are all tangent to circle O (not drawn to scale), and JK LJ . JA = 9, AL = 10, and CK = 14. Find the perimeter of JKL. A. 66 B. 38 C. 46 D. 33 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. ____ 70. A. 12 B. 9 C. 15 23 D. 5 Name: ________________________ ID: A ____ 71. A. 13 B. 26 C. 77 D. 38.5 ____ 72. Find the measure of BAC in circle O. (The figure is not drawn to scale.) A. 50 B. 80 C. 20 24 D. 40 Name: ________________________ ID: A ____ 73. PQ is tangent to the circle at C. In the circle, mBC 85. Find mBCP. (The figure is not drawn to scale.) A. 42.5 B. 95 C. 170 D. 85 ____ 74. mDE 120 and mBC 53. Find mA. (The figure is not drawn to scale.) A. 33.5 B. 93.5 C. 86.5 25 D. 67 Name: ________________________ ID: A ____ 75. Find the value of x for mAB 46 and mCD 25. (The figure is not drawn to scale.) A. 35.5 B. 58.5 C. 71 D. 21 ____ 76. The farthest distance a satellite signal can directly reach is the length of the segment tangent to the curve of Earth’s surface. If the measure of the angle formed by the tangent satellite signals is 137, what is the measure of the intercepted arc on Earth? (The figure is not drawn to scale.) A. 86 B. 43 C. 274 26 D. 68.5 Name: ________________________ ID: A Find the value of x. If necessary, round your answer to the nearest tenth. The figures are not drawn to scale. ____ 77. A. 3.4 B. 24 C. 96 D. 10.7 ____ 78. The figure consists of a chord, a secant, and a tangent to the circle. Round to the nearest hundredth, if necessary. A. 15.75 B. 9 C. 5.14 D. 28 Write the standard equation for the circle. ____ 79. center (10, –6), r = 6 A. (x + 10) 2 + (y – 6) 2 = 6 C. (x – 10) 2 + (y + 6) 2 = 36 B. (x + 6) 2 + (y – 10) 2 = 36 D. (x – 10) 2 + (y + 6) 2 = 6 27 Name: ________________________ ID: A ____ 80. Find the center and radius of the circle with equation (x – 3) 2 + (y – 6) 2 = 4. A. center (–3, –6); r = 4 C. center (3, 6); r = 4 B. center (–6, –3); r = 2 D. center (3, 6); r = 2 28 ID: A Geometry - Spring 2013 Final Review Answer Section 1. ANS: C PTS: 1 DIF: L3 REF: 7-1 Ratios and Proportions OBJ: 7-1.1 To write ratios and solve proportions NAT: CC G.SRT.5| N.4.c TOP: 7-1 Problem 1 Writing a Ratio KEY: ratio | word problem 2. ANS: A PTS: 1 DIF: L3 REF: 7-1 Ratios and Proportions OBJ: 7-1.1 To write ratios and solve proportions NAT: CC G.SRT.5| N.4.c TOP: 7-1 Problem 3 Using an Extended Ratio KEY: ratio | extended ratio | interior angles of a triangle 3. ANS: A PTS: 1 DIF: L4 REF: 7-1 Ratios and Proportions OBJ: 7-1.1 To write ratios and solve proportions NAT: CC G.SRT.5| N.4.c TOP: 7-1 Problem 4 Solving a Proportion KEY: proportion | Cross-Product Property | extremes | means 4. ANS: B PTS: 1 DIF: L4 REF: 7-2 Similar Polygons OBJ: 7-2.1 To identify and apply similar polygons NAT: CC G.SRT.5| M.1.b| M.2.f| M.3.a| G.2.e| G.3.e TOP: 7-2 Problem 2 Determining Similarity KEY: similar polygons | scale factor 5. ANS: C PTS: 1 DIF: L3 REF: 7-2 Similar Polygons OBJ: 7-2.1 To identify and apply similar polygons NAT: CC G.SRT.5| M.1.b| M.2.f| M.3.a| G.2.e| G.3.e TOP: 7-2 Problem 3 Using Similar Polygons KEY: corresponding sides | proportion | similar polygons 6. ANS: C PTS: 1 DIF: L2 REF: 7-3 Proving Triangles Similar OBJ: 7-3.1 To use the AA Postulate and the SAS and SSS theorems NAT: CC G.SRT.5| CC G.GPE.5| G.2.e| G.3.e| G.5.e TOP: 7-3 Problem 1 Using the AA Postulate KEY: Angle-Angle Similarity Postulate | Side-Side-Side Similarity Theorem | Side-Angle-Side Similarity Theorem 7. ANS: A PTS: 1 DIF: L4 REF: 7-3 Proving Triangles Similar OBJ: 7-3.1 To use the AA Postulate and the SAS and SSS theorems NAT: CC G.SRT.5| CC G.GPE.5| G.2.e| G.3.e| G.5.e TOP: 7-3 Problem 2 Verifying Triangle Similarity KEY: Side-Angle-Side Similarity Theorem 8. ANS: A PTS: 1 DIF: L3 REF: 7-3 Proving Triangles Similar OBJ: 7-3.2 To use similarity to find indirect measurements NAT: CC G.SRT.5| CC G.GPE.5| G.2.e| G.3.e| G.5.e TOP: 7-3 Problem 4 Finding Lengths in Similar Triangles KEY: Angle-Angle Similarity Postulate | word problem 9. ANS: A PTS: 1 DIF: L4 REF: 7-3 Proving Triangles Similar OBJ: 7-3.2 To use similarity to find indirect measurements NAT: CC G.SRT.5| CC G.GPE.5| G.2.e| G.3.e| G.5.e TOP: 7-3 Problem 4 Finding Lengths in Similar Triangles KEY: Side-Angle-Side Similarity Theorem | word problem 1 ID: A 10. ANS: OBJ: NAT: TOP: 11. ANS: OBJ: NAT: KEY: 12. ANS: OBJ: NAT: KEY: 13. ANS: OBJ: NAT: KEY: 14. ANS: OBJ: NAT: KEY: 15. ANS: OBJ: NAT: TOP: KEY: 16. ANS: REF: OBJ: NAT: TOP: KEY: 17. ANS: REF: OBJ: NAT: TOP: KEY: 18. ANS: REF: OBJ: NAT: TOP: KEY: 19. ANS: OBJ: NAT: KEY: B PTS: 1 DIF: L4 REF: 7-4 Similarity in Right Triangles 7-4.1 To find and use relationships in similar triangles CC G.SRT.5| CC G.GPE.5| G.2.e| G.3.e 7-4 Problem 2 Finding the Geometric Mean KEY: geometric mean | proportion A PTS: 1 DIF: L3 REF: 7-4 Similarity in Right Triangles 7-4.1 To find and use relationships in similar triangles CC G.SRT.5| CC G.GPE.5| G.2.e| G.3.e TOP: 7-4 Problem 3 Using the Corollaries corollaries of the geometric mean | proportion A PTS: 1 DIF: L3 REF: 7-4 Similarity in Right Triangles 7-4.1 To find and use relationships in similar triangles CC G.SRT.5| CC G.GPE.5| G.2.e| G.3.e TOP: 7-4 Problem 3 Using the Corollaries corollaries of the geometric mean | proportion A PTS: 1 DIF: L4 REF: 7-4 Similarity in Right Triangles 7-4.1 To find and use relationships in similar triangles CC G.SRT.5| CC G.GPE.5| G.2.e| G.3.e TOP: 7-4 Problem 4 Finding a Distance corollaries of the geometric mean | multi-part question | word problem A PTS: 1 DIF: L4 REF: 7-5 Proportions in Triangles 7-5.1 To use the Side-Splitter theorem and the Triangles Angle-Bisector theorem CC G.SRT.4| N.4.c| M.3.a TOP: 7-5 Problem 2 Finding a Length corollary of Side-Splitter Theorem D PTS: 1 DIF: L3 REF: 7-5 Proportions in Triangles 7-5.1 To use the Side-Splitter theorem and the Triangles Angle-Bisector theorem CC G.SRT.4| N.4.c| M.3.a 7-5 Problem 3 Using the Triangle-Angle-Bisector Theorem Triangle-Angle-Bisector Theorem D PTS: 1 DIF: L3 8-1 The Pythagorean Theorem and Its Converse 8-1.1 To use the Pythagorean theorem and its converse CC G.SRT.4| CC G.SRT.8| N.5.e| G.3.d 8-1 Problem 1 Finding the Length of the Hypotenuse Pythagorean Theorem | leg | hypotenuse B PTS: 1 DIF: L3 8-1 The Pythagorean Theorem and Its Converse 8-1.1 To use the Pythagorean theorem and its converse CC G.SRT.4| CC G.SRT.8| N.5.e| G.3.d 8-1 Problem 5 Classifying a Triangle right triangle | obtuse triangle | acute triangle A PTS: 1 DIF: L3 8-1 The Pythagorean Theorem and Its Converse 8-1.1 To use the Pythagorean theorem and its converse CC G.SRT.4| CC G.SRT.8| N.5.e| G.3.d 8-1 Problem 5 Classifying a Triangle right triangle | obtuse triangle | acute triangle D PTS: 1 DIF: L3 REF: 8-2 Special Right Triangles 8-2.1 To use the properties of 45-45-90 and 30-60-90 triangles CC G.SRT.8 TOP: 8-2 Problem 2 Finding the Length of a Leg special right triangles | hypotenuse | leg 2 ID: A 20. ANS: D PTS: 1 DIF: L3 REF: 8-2 Special Right Triangles OBJ: 8-2.1 To use the properties of 45-45-90 and 30-60-90 triangles NAT: CC G.SRT.8 TOP: 8-2 Problem 4 Using the Length of One Side KEY: special right triangles | leg | hypotenuse 21. ANS: B PTS: 1 DIF: L3 REF: 8-2 Special Right Triangles OBJ: 8-2.1 To use the properties of 45-45-90 and 30-60-90 triangles NAT: CC G.SRT.8 TOP: 8-2 Problem 4 Using the Length of One Side KEY: special right triangles | leg | hypotenuse 22. ANS: B PTS: 1 DIF: L3 REF: 8-3 Trigonometry OBJ: 8-3.1 To use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles NAT: CC G.SRT.7| CC G.SRT.8| CC G.MG.1 TOP: 8-3 Problem 3 Using Inverses KEY: cosine 23. ANS: C PTS: 1 DIF: L2 REF: 8-3 Trigonometry OBJ: 8-3.1 To use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles NAT: CC G.SRT.7| CC G.SRT.8| CC G.MG.1 TOP: 8-3 Problem 1 Writing Trigonometric Ratios KEY: tangent 24. ANS: D PTS: 1 DIF: L3 REF: 8-3 Trigonometry OBJ: 8-3.1 To use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles NAT: CC G.SRT.7| CC G.SRT.8| CC G.MG.1 TOP: 8-3 Problem 2 Using a Trigonometric Ratio to Find Distance KEY: cosine 25. ANS: D PTS: 1 DIF: L3 REF: 8-3 Trigonometry OBJ: 8-3.1 To use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles NAT: CC G.SRT.7| CC G.SRT.8| CC G.MG.1 TOP: 8-3 Problem 2 Using a Trigonometric Ratio to Find Distance KEY: sine 26. ANS: C PTS: 1 DIF: L3 REF: 8-3 Trigonometry OBJ: 8-3.1 To use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles NAT: CC G.SRT.7| CC G.SRT.8| CC G.MG.1 TOP: 8-3 Problem 2 Using a Trigonometric Ratio to Find Distance KEY: problem solving | word problem | tangent 27. ANS: A PTS: 1 DIF: L4 REF: 8-3 Trigonometry OBJ: 8-3.1 To use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles NAT: CC G.SRT.7| CC G.SRT.8| CC G.MG.1 TOP: 8-3 Problem 2 Using a Trigonometric Ratio to Find Distance KEY: tangent | problem solving 28. ANS: B PTS: 1 DIF: L3 REF: 8-3 Trigonometry OBJ: 8-3.1 To use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles NAT: CC G.SRT.7| CC G.SRT.8| CC G.MG.1 TOP: 8-3 Problem 3 Using Inverses KEY: cosine 29. ANS: B PTS: 1 DIF: L2 REF: 8-3 Trigonometry OBJ: 8-3.1 To use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles NAT: CC G.SRT.7| CC G.SRT.8| CC G.MG.1 TOP: 8-3 Problem 3 Using Inverses KEY: tangent 3 ID: A 30. ANS: REF: OBJ: NAT: KEY: 31. ANS: OBJ: TOP: 32. ANS: OBJ: TOP: 33. ANS: REF: OBJ: NAT: TOP: 34. ANS: REF: OBJ: NAT: TOP: 35. ANS: REF: OBJ: NAT: TOP: 36. ANS: REF: OBJ: TOP: 37. ANS: REF: OBJ: TOP: 38. ANS: REF: OBJ: TOP: 39. ANS: REF: OBJ: TOP: 40. ANS: OBJ: NAT: TOP: B PTS: 1 DIF: L3 8-4 Angles of Elevation and Depression 8-4.1 To use angles of elevation and depression to solve problems CC G.SRT.8 TOP: 8-4 Problem 3 Using the Angle of Depression tangent | angles of elevation and depression | word problem | problem solving B PTS: 1 DIF: L3 REF: 8-5 Law of Sines 8-5.1 To apply the Law of Sines NAT: CC G.SRT.10| CC G.SRT.11 8-5 Problem 1 Using the Law of Sines (AAS) KEY: Law of Sines D PTS: 1 DIF: L3 REF: 8-5 Law of Sines 8-5.1 To apply the Law of Sines NAT: CC G.SRT.10| CC G.SRT.11 8-5 Problem 2 Using the Law of Sines (SSA) KEY: Law of Sines D PTS: 1 DIF: L3 10-1 Areas of Parallelograms and Triangles 10-1.1 To find the area of parallelograms and triangles CC G.GPE.7| CC G.MG.1| N.3.c| N.3.f| M.1.c| M.1.f| A.4.e 10-1 Problem 3 Finding the Area of a Triangle KEY: triangle | area A PTS: 1 DIF: L3 10-1 Areas of Parallelograms and Triangles 10-1.1 To find the area of parallelograms and triangles CC G.GPE.7| CC G.MG.1| N.3.c| N.3.f| M.1.c| M.1.f| A.4.e 10-1 Problem 2 Finding a Missing Dimension KEY: parallelogram | area | base | height A PTS: 1 DIF: L4 10-1 Areas of Parallelograms and Triangles 10-1.1 To find the area of parallelograms and triangles CC G.GPE.7| CC G.MG.1| N.3.c| N.3.f| M.1.c| M.1.f| A.4.e 10-1 Problem 3 Finding the Area of a Triangle KEY: area | triangle D PTS: 1 DIF: L3 10-2 Areas of Trapezoids, Rhombuses, and Kites 10-2.1 To find the area of a trapezoid, rhombus, or kite NAT: CC G.MG.1 10-2 Problem 1 Area of a Trapezoid KEY: area | trapezoid B PTS: 1 DIF: L3 10-2 Areas of Trapezoids, Rhombuses, and Kites 10-2.1 To find the area of a trapezoid, rhombus, or kite NAT: CC G.MG.1 10-2 Problem 2 Finding Area Using a Right Triangle KEY: area | trapezoid C PTS: 1 DIF: L3 10-2 Areas of Trapezoids, Rhombuses, and Kites 10-2.1 To find the area of a trapezoid, rhombus, or kite NAT: CC G.MG.1 10-2 Problem 3 Finding the Area of a Kite KEY: area | kite C PTS: 1 DIF: L3 10-2 Areas of Trapezoids, Rhombuses, and Kites 10-2.1 To find the area of a trapezoid, rhombus, or kite NAT: CC G.MG.1 10-2 Problem 4 Finding the Area of a Rhombus KEY: rhombus | diagonal | area C PTS: 1 DIF: L3 REF: 10-3 Areas of Regular Polygons 10-3.1 To find the area of a regular polygon CC G.CO.13 | CC G.MG.1| N.3.c| N.3.f| M.1.c| M.1.f| A.4.e 10-3 Problem 1 Finding Angle Measures KEY: regular polygon | apothem | hexagon 4 ID: A 41. ANS: C PTS: 1 DIF: L4 REF: 10-3 Areas of Regular Polygons OBJ: 10-3.1 To find the area of a regular polygon NAT: CC G.CO.13 | CC G.MG.1| N.3.c| N.3.f| M.1.c| M.1.f| A.4.e TOP: 10-3 Problem 3 Using Special Triangles to Find Area KEY: regular polygon | radius | area | perimeter 42. ANS: C PTS: 1 DIF: L3 REF: 10-4 Perimeters and Areas of Similar Figures OBJ: 10-4.1 To find the perimeters and areas of similar polygons NAT: CC G.GMD.3| N.3.c| N.3.f| M.1.c| M.1.f| A.4.e TOP: 10-4 Problem 1 Finding Ratios in Similar Figures KEY: perimeter | area | similar figures 43. ANS: A PTS: 1 DIF: L3 REF: 10-4 Perimeters and Areas of Similar Figures OBJ: 10-4.1 To find the perimeters and areas of similar polygons NAT: CC G.GMD.3| N.3.c| N.3.f| M.1.c| M.1.f| A.4.e TOP: 10-4 Problem 3 Applying Area Ratios KEY: similar figures | area | word problem 44. ANS: B PTS: 1 DIF: L3 REF: 10-5 Trigonometry and Area OBJ: 10-5.1 To find areas of regular polygons and triangles using trigonometry NAT: CC G.SRT.9| M.1.f TOP: 10-5 Problem 1 Finding Area KEY: area of a regular polygon | area | regular polygon | tangent | measure of central angle of a regular polygon 45. ANS: A PTS: 1 DIF: L3 REF: 10-5 Trigonometry and Area OBJ: 10-5.1 To find areas of regular polygons and triangles using trigonometry NAT: CC G.SRT.9| M.1.f TOP: 10-5 Problem 3 Finding Area KEY: area of a triangle | area | sine 46. ANS: B PTS: 1 DIF: L3 REF: 10-5 Trigonometry and Area OBJ: 10-5.1 To find areas of regular polygons and triangles using trigonometry NAT: CC G.SRT.9| M.1.f TOP: 10-5 Problem 3 Finding Area KEY: area | area of a triangle | problem solving | sine | word problem 47. ANS: C PTS: 1 DIF: L3 REF: 10-6 Circles and Arcs OBJ: 10-6.1 To find the measures of central angles and arcs NAT: CC G.CO.1| CC G.C.1| CC G.C.2| CC G.C.5 TOP: 10-6 Problem 2 Finding the Measures of Arcs KEY: major arc | measure of an arc | arc 48. ANS: B PTS: 1 DIF: L3 REF: 10-6 Circles and Arcs OBJ: 10-6.2 To find the circumference and arc length NAT: CC G.CO.1| CC G.C.1| CC G.C.2| CC G.C.5 TOP: 10-6 Problem 4 Finding Arc Length KEY: arc | circumference 49. ANS: A PTS: 1 DIF: L3 REF: 10-7 Areas of Circles and Sectors OBJ: 10-7.1 To find the areas of circles, sectors, and segments of circles NAT: CC G.C.5 TOP: 10-7 Problem 2 Finding the Area of a Sector of a Circle KEY: sector | circle | area 50. ANS: A PTS: 1 DIF: L2 REF: 10-7 Areas of Circles and Sectors OBJ: 10-7.1 To find the areas of circles, sectors, and segments of circles NAT: CC G.C.5 TOP: 10-7 Problem 3 Finding the Area of a Segment of a Circle KEY: sector | circle | area | central angle 5 ID: A 51. ANS: OBJ: NAT: KEY: 52. ANS: REF: OBJ: NAT: TOP: 53. ANS: REF: OBJ: NAT: TOP: KEY: 54. ANS: REF: OBJ: NAT: TOP: KEY: 55. ANS: REF: OBJ: NAT: TOP: KEY: 56. ANS: REF: OBJ: NAT: TOP: KEY: 57. ANS: REF: OBJ: NAT: TOP: KEY: 58. ANS: REF: OBJ: NAT: TOP: KEY: C PTS: 1 DIF: L4 REF: 10-7 Areas of Circles and Sectors 10-7.1 To find the areas of circles, sectors, and segments of circles CC G.C.5 TOP: 10-7 Problem 3 Finding the Area of a Segment of a Circle sector | circle | area | central angle B PTS: 1 DIF: L3 11-1 Space Figures and Cross Sections 11-1.2 To visualize cross sections of space figures CC G.GMD.4| G.1.d| G.1.e| G.1.f| G.4.c 11-1 Problem 4 Describing a Cross Section KEY: cross section | word problem C PTS: 1 DIF: L2 11-2 Surface Areas of Prisms and Cylinders 11-2.1 To find the surface area of a prism and a cylinder CC G.MG.1| N.3.c| N.3.f| N.5.e| M.1.h| A.4.f 11-2 Problem 2 Using Formulas to Find Surface Area of a Prism surface area formulas | lateral area | surface area | prism | surface area of a prism D PTS: 1 DIF: L3 11-2 Surface Areas of Prisms and Cylinders 11-2.1 To find the surface area of a prism and a cylinder CC G.MG.1| N.3.c| N.3.f| N.5.e| M.1.h| A.4.f 11-2 Problem 3 Finding Surface Area of a Cylinder surface area of a cylinder | cylinder | surface area formulas | surface area B PTS: 1 DIF: L3 11-3 Surface Areas of Pyramids and Cones 11-3.1 To find the surface area of a pyramid and a cone CC G.MG.1| N.3.c| N.3.f| N.5.e| M.1.h| A.4.f 11-3 Problem 1 Finding the Surface Area of a Pyramid surface area of a pyramid | surface area | surface area formulas | pyramid D PTS: 1 DIF: L4 11-3 Surface Areas of Pyramids and Cones 11-3.1 To find the surface area of a pyramid and a cone CC G.MG.1| N.3.c| N.3.f| N.5.e| M.1.h| A.4.f 11-3 Problem 4 Finding the Lateral Area of a Cone cone | surface area of a cone | lateral area | surface area formulas | surface area A PTS: 1 DIF: L3 11-4 Volumes of Prisms and Cylinders 11-4.1 To find the volume of a prism and the volume of a cylinder CC G.GMD.1| CC G.GMD.2| CC G.GMD.3| CC G.MG.1| N.3.c| N.3.f| N.5.e| M.1.h| A.4.f 11-4 Problem 1 Finding the Volume of a Rectangular Prism volume of a rectangular prism | volume formulas | volume | prism A PTS: 1 DIF: L3 11-4 Volumes of Prisms and Cylinders 11-4.1 To find the volume of a prism and the volume of a cylinder CC G.GMD.1| CC G.GMD.2| CC G.GMD.3| CC G.MG.1| N.3.c| N.3.f| N.5.e| M.1.h| A.4.f 11-4 Problem 2 Finding the Volume of a Triangular Prism volume of a triangular prism | volume formulas | volume | prism 6 ID: A 59. ANS: B PTS: 1 DIF: L3 REF: 11-4 Volumes of Prisms and Cylinders OBJ: 11-4.1 To find the volume of a prism and the volume of a cylinder NAT: CC G.GMD.1| CC G.GMD.2| CC G.GMD.3| CC G.MG.1| N.3.c| N.3.f| N.5.e| M.1.h| A.4.f TOP: 11-4 Problem 3 Finding the Volume of a Cylinder KEY: volume of a cylinder | cylinder | volume formulas | volume 60. ANS: C PTS: 1 DIF: L3 REF: 11-5 Volumes of Pyramids and Cones OBJ: 11-5.1 To find the volume of a pyramid and of a cone NAT: CC G.GMD.3| CC G.MG.1| N.3.c| N.3.f| N.5.e| M.1.h| A.4.f TOP: 11-5 Problem 2 Finding the Volume of a Pyramid KEY: volume of a pyramid | pyramid | volume formulas | volume | height of a pyramid | Pythagorean Theorem | slant height 61. ANS: D PTS: 1 DIF: L3 REF: 11-5 Volumes of Pyramids and Cones OBJ: 11-5.1 To find the volume of a pyramid and of a cone NAT: CC G.GMD.3| CC G.MG.1| N.3.c| N.3.f| N.5.e| M.1.h| A.4.f TOP: 11-5 Problem 4 Finding the Volume of an Oblique Cone KEY: volume of a cone | oblique cone | volume formulas | volume 62. ANS: C PTS: 1 DIF: L3 REF: 11-6 Surface Areas and Volumes of Spheres OBJ: 11-6.1 To find the surface area and volume of a sphere NAT: CC G.GMD.3| CC G.MG.1| N.3.c| N.3.f| N.5.e| M.1.h| A.4.f TOP: 11-6 Problem 2 Finding Surface Area KEY: circumference of a circle | surface area of a sphere | surface area | surface area formulas | sphere 63. ANS: C PTS: 1 DIF: L2 REF: 11-6 Surface Areas and Volumes of Spheres OBJ: 11-6.1 To find the surface area and volume of a sphere NAT: CC G.GMD.3| CC G.MG.1| N.3.c| N.3.f| N.5.e| M.1.h| A.4.f TOP: 11-6 Problem 3 Finding the Volume of a Sphere KEY: volume of a sphere | sphere | volume formulas | volume 64. ANS: C PTS: 1 DIF: L4 REF: 11-7 Areas and Volumes of Similar Solids OBJ: 11-7.1 To compare and find the areas and volumes of similar solids NAT: CC G.MG.1| CC G.MG.2| G.1.f| N.3.f| N.5.e| M.1.b| M.1.h TOP: 11-7 Problem 1 Identifying Similar Solids KEY: similar solids | similarity ratio | cylinder 65. ANS: D PTS: 1 DIF: L3 REF: 11-7 Areas and Volumes of Similar Solids OBJ: 11-7.1 To compare and find the areas and volumes of similar solids NAT: CC G.MG.1| CC G.MG.2| G.1.f| N.3.f| N.5.e| M.1.b| M.1.h TOP: 11-7 Problem 3 Using a Scale Factor KEY: similarity ratio | volumes of similar solids | word problem | problem solving 66. ANS: A PTS: 1 DIF: L3 REF: 12-1 Tangent Lines OBJ: 12-1.1 To use properties of a tangent to a circle NAT: CC G.C.2| G.3.h TOP: 12-1 Problem 1 Finding Angle Measures KEY: tangent to a circle | point of tangency | properties of tangents | central angle 7 ID: A 67. ANS: OBJ: TOP: KEY: 68. ANS: OBJ: TOP: KEY: 69. ANS: OBJ: TOP: KEY: 70. ANS: OBJ: TOP: KEY: 71. ANS: OBJ: TOP: KEY: 72. ANS: OBJ: NAT: TOP: KEY: 73. ANS: OBJ: NAT: KEY: 74. ANS: REF: OBJ: NAT: KEY: 75. ANS: REF: OBJ: NAT: KEY: 76. ANS: REF: OBJ: NAT: KEY: B PTS: 1 DIF: L3 REF: 12-1 Tangent Lines 12-1.1 To use properties of a tangent to a circle NAT: CC G.C.2| G.3.h 12-1 Problem 1 Finding Angle Measures tangent to a circle | point of tangency | angle measure | properties of tangents | central angle A PTS: 1 DIF: L3 REF: 12-1 Tangent Lines 12-1.1 To use properties of a tangent to a circle NAT: CC G.C.2| G.3.h 12-1 Problem 3 Finding a Radius tangent to a circle | point of tangency | properties of tangents | right triangle | Pythagorean Theorem A PTS: 1 DIF: L3 REF: 12-1 Tangent Lines 12-1.1 To use properties of a tangent to a circle NAT: CC G.C.2| G.3.h 12-1 Problem 5 Circles Inscribed in Polygons properties of tangents | tangent to a circle | triangle C PTS: 1 DIF: L2 REF: 12-2 Chords and Arcs 12-2.2 To use perpendicular bisectors to chords NAT: CC G.C.2| G.3.h 12-2 Problem 3 Using Diameters and Chords bisected chords | circle | perpendicular | perpendicular bisector | Pythagorean Theorem | chord C PTS: 1 DIF: L2 REF: 12-2 Chords and Arcs 12-2.1 To use congruent chords, arcs, and central angles NAT: CC G.C.2| G.3.h 12-2 Problem 4 Finding Measures in a Circle arc | central angle | congruent arcs | chord C PTS: 1 DIF: L3 REF: 12-3 Inscribed Angles 12-3.1 To find the measure of an inscribed angle CC G.C.2| CC G.C.3| CC G.C.4| G.3.h 12-3 Problem 1 Using the Inscribed Angle Theorem circle | inscribed angle | intercepted arc | inscribed angle-arc relationship A PTS: 1 DIF: L2 REF: 12-3 Inscribed Angles 12-3.2 To find the measure of an angle formed by a tangent and a chord CC G.C.2| CC G.C.3| CC G.C.4| G.3.h TOP: 12-3 Problem 3 Using Arc Measure circle | inscribed angle | tangent-chord angle | arc measure | angle measure A PTS: 1 DIF: L3 12-4 Angle Measures and Segment Lengths 12-4.1 To find measures of angles formed by chords, secants, and tangents CC G.C.2| G.3.h TOP: 12-4 Problem 1 Finding Angle Measures circle | secant | angle measure | arc measure | intersection outside the circle A PTS: 1 DIF: L3 12-4 Angle Measures and Segment Lengths 12-4.1 To find measures of angles formed by chords, secants, and tangents CC G.C.2| G.3.h TOP: 12-4 Problem 1 Finding Angle Measures circle | secant | angle measure | arc measure | intersection inside the circle B PTS: 1 DIF: L4 12-4 Angle Measures and Segment Lengths 12-4.1 To find measures of angles formed by chords, secants, and tangents CC G.C.2| G.3.h TOP: 12-4 Problem 2 Finding an Arc Measure circle | angle measure | word problem | arc measure | intersection outside the circle 8 ID: A 77. ANS: REF: OBJ: NAT: KEY: 78. ANS: REF: OBJ: NAT: KEY: 79. ANS: REF: OBJ: TOP: 80. ANS: REF: OBJ: TOP: KEY: D PTS: 1 DIF: L3 12-4 Angle Measures and Segment Lengths 12-4.2 To find the lengths of segments associated with circles CC G.C.2| G.3.h TOP: 12-4 Problem 3 Finding Segment Lengths circle | chord | intersection inside the circle A PTS: 1 DIF: L4 12-4 Angle Measures and Segment Lengths 12-4.2 To find the lengths of segments associated with circles CC G.C.2| G.3.h TOP: 12-4 Problem 3 Finding Segment Lengths circle | chord | intersection inside the circle | intersection outside the circle | secant | tangent to a circle C PTS: 1 DIF: L3 12-5 Circles in the Coordinate Plane 12-5.1 To write the equation of a circle NAT: CC G.GPE.1| G.3.h| G.4.a| G.4.f 12-5 Problem 1 Writing the Equation of a Circle KEY: equation of a circle | center | radius D PTS: 1 DIF: L3 12-5 Circles in the Coordinate Plane 12-5.2 To find the center and radius of a circle NAT: CC G.GPE.1| G.3.h| G.4.a| G.4.f 12-5 Problem 1 Writing the Equation of a Circle center | circle | coordinate plane | radius 9
