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H. Geometry Name____________________________Period____Date_________ Semester 2 Final Review-1 Unit 5: Module 13 Review 1. The value for x is: 2. The value for x is: 8 2 o x o o 20 x 1 3. The value for x is: o 4. 4. The value for x is: 9 x 4 60° x 60° 5. The value for x is: 6 3 60° x 6. The ratio 8 represent the which relationship: 6 B 6 cm 10 cm A A) sin C B) sin B 7. Which of the following is equal to cos 40◦ A) sin 50° B) sin 40◦ C) tan C C) tan 50◦ 8. If cos Ɵ = sin ß then the two angles must be: A) supplementary B) complementary 9. Given the ratio D) tan B 8 cm C D) cos 50◦ C) a linear pair 8 , which of the following is NOT equal to this 10 value? CA 4 A) CB B) 5 C) sin B D) cos B 10. If cos Ɵ = sin ß then which of the following must be true? a. A) Ɵ + ß = 180◦ B) Ɵ - ß = 90◦ C) ß = 90◦ - Ɵ C D) adjacent A 8 cm 6 cm 10 cm B D) ß - Ɵ = 90◦ 1 H.Geometry Semester Final Review 1 11. Julie has a large red apple in her hand that is 7 ft off the ground. A blue bird sees the apple making a 55◦ between the tree and the line of sight of the bird. If Julie is 15 ft from the tree, how tall is the tree (round to the nearest foot)?? A) 19 ft B) 20 ft C) 28 ft D) 24 ft 12. A 15 ft tree casts a 18 ft long shadow. What is the angle formed by the sun’s rays and the ground to the nearest degree? A) 60◦ B) 50◦ C) 40◦ D) 30◦ 13. What is the height of this triangle? 8 cm A) 4.92 cm B) 6.30 cm C) 10.24 cm D) 11.03 cm h 52° 14 cm 14. What is the area of the triangle? A) 33.55 cm2 B) 57.68 cm2 34° C) 67.10 cm2 D) 115.35 cm2 72° 8 cm 15 cm True/False 15. In a right isosceles ∆, if the hypotenuse is 14 cm then one leg is 7 2 cm. T or F 16. 10 2 , 10 2 and 20 could represent the three sides of a right isosceles triangle. T or F 17. 5, 5 3 and 20 could represent the three sides of a 30◦, 60◦, 90◦ T or F ∆ triangle. 18. In right ∆ABC where C is a right angle, BC is adjacent to B. T or F 19. For angles between 0◦ and 90◦ the cosine values are between 0 and 1. T or F 20. In right triangles, the hypotenuse side is always smaller than the adjacent side. T or F 21. The Sine ratio of 45◦ is equal to the Cosine ratio of 45◦. T or F 22. sin (2x – 7) = cos (x + 13) when x = 28. T or F 23. If cos Ɵ = sin ß, then ß = 90◦ - Ɵ T or F 24. If you have two sides and an angle of a ∆, then you can determine the area. T or F 25. Sin 45◦ = Cos 45◦ T or F 26. What is the area of a square that has a diagonal length of 12 2 cm? 2 H.Geometry Semester Final Review 1 27. Solve for the unknowns. Leave answers in reduced radical form. A) B) C) y y x 14 5 30° 30° x o 18 3 24 2 x = __________ y = __________ x = __________ y = __________ D) y 30° o x x 6 x = __________ x = __________ y = __________ 28. Solve for the missing information. (Round all final answers to 1 decimal place) a) b) c) d) 12 cm x 36° x ≈ ____________ 10 cm 63° 8 cm 11 cm 9 cm θ° Ɵ = ____________ θ° x x ≈ ____________ 3 cm Ɵ = ____________ 29. Solve for the unknown. a) sin (x + 18) = cos (45) b) sin (2x – 15) = cos (x – 12) c) sin (x)= cos (x) 1 2 d) sin ( x ) = cos ( x 3 ) 5 5 e) sin (3x + 25) = cos (2x + 10) 3 f) sin ( x 12 )= cos (66) 4 30. A helicopter is hovering 200 ft in the air over a landing pad. If the man sees the helicopter at an angle of elevation of 38◦, how far is he from the landing pad (to the nearest foot)?? 31. 3 H.Geometry Semester Final Review 1 32. Determine the area of the given triangles. a) b) 50° h 30 cm 7 cm h 118° 12 cm 29 cm 33. Determine the missing angle that makes the equation true. a) sin 56◦ = cos _______ b) sin 12◦ = cos _______ c) cos 82◦ = sin _______ 34. Round all sides and angles to the tenth place (1st decimal place). a.) b.) c.) d.) 4 H. Geometry Name____________________________Period____Date_________ Semester 2 Final Review 2 - Unit 6: Module 15 Review 1. Determine the requested value(s). a) b) c) d) x 1 2 151° 128° 52° 2 2 60° 1 1 1 77° 142° 74° m1 = _______ m1 = _______ m1 = _______ m1 = _______ m2 = _______ m2 = _______ m2 = _______ 𝑚 𝑥̂ = ________ 2. Determine the requested value(s). a) b) c) d) 156° 74° 3 136° 88° 78° 2 2 1 1 m1 = _______ m2 = _______ m1 = _______ m2 = _______ m1 = _______ m2 = _______ m3 = _______ m1 = _______ m2 = _______ c) d) x x 122° 2 48° 1 85° 1 2 1 3. Determine the requested value(s). a) b) 53° 31° 1 70° 2 121° 80° 1 1 110° 30° x 122° m1 = _______ m2 = _______ m1 = _______ 𝑚 𝑥̂ = ________ m1 = _______ 𝑚 𝑥̂ = ________ m1 = _______ 𝑚 𝑥̂ = ________ 1 H.Geometry 4. Determine the requested value(s). (Lines that appear to be tangent are tangent.) a) b) c) 1 Semester Final Review 2 d) 140° 1 30° 38° 65° 68° x x 1 48° 92° 92° 114° m1 = _______ m1 = _______ 𝑚 𝑥̂ = ________ m1 = _______ 𝑚 𝑥̂ = ________ 5. Determine the requested values. a) b) c) 2 2 86° d) 104° 2 2 1 68° 1 125° 106° 79° 1 1 m1 = _____ m2 =_____ m1 = _____ m2 = _____ m1 = _____ m2 =_____ m1 = _____ m2 = _____ 6. Determine the arc measure. Diagram for a – d Diagram for e - h ̂ ̂ 108° a) 𝑚𝐵𝐶 = ____________ e) 𝑚𝐴𝐶 = ____________ B C ̂ = ____________ ̂ = ____________ b) 𝑚𝐵𝐹𝐷 f) 𝑚𝐷𝐸𝐴 E A D ̂ ̂ = ____________ c) 𝑚𝐴𝐹 = ____________ g) 𝑚𝐸𝐶 ̂ = ____________ ̂ = ____________ D d) 𝑚𝐷𝐸 h) 𝑚𝐷𝐸𝐶 F 44° 123° G B A F E C 7. Determine the value of x. (Lines that appear to be tangent are tangent.) a) b) c) d) x = ____________ (1 dec.) x = _____________ (1 dec.) x = _____________ (2 dec.) x = ____________ (2 dec.) 2 H.Geometry 8. Solve for x ( AB and AD are tangent lines) a) b) Semester Final Review 2 c) D D 12 cm C C D 45° B C 77 cm A x B A 5x - 3 x2 - 3 13 cm B A x = ____________ x = ____________ 9. Using the diagram to the right complete the following. a) Point ________ or ________ are in the interior of the circle. b) Circle which of the following are chords AD AC c) The diameter of circle Z is _____________. d) How many radii are in this diagram? ___________ e) Point __________ is exterior to the circle. f) How many chords are in this diagram? ____________ g) Name the tangent line ___________ h) Name the secant line ________ AB AZ x = ____________ H A BD B Z G D C ̂ = 45° then the major arc from A to C would measure 215. 10. If 𝑚𝐴𝐶 T or F 11. A major arc has a measurement greater than 90. T or F ̂ =180° 12. Points A, B, C, D, E & F (in that order) divide a circle into 6 congruent arcs, them 𝑚𝐶𝐹 T or F 13. Tangent line 14. RM intersects Circle T at M, then mRMT = 90. T or F AB and AG are tangents that intersect circle M at points B and G, then ABG is isosceles. T or F 15. An inscribed triangle divides the circle into three arcs, 148, 200 and 12, then one of the angles in the triangle is 74. T or F 16. If the inscribed angle is 38, then the arc that it subtends is 19. T or F ̂? 17. What is 𝑚𝐹𝐴𝐷 A B 43° 32° C D G F E 3 H.Geometry Semester Final Review 2 Module 16: 18. Approximately how many radians are there in one full circle? 19. Which of the following is not a true statement? B. radians = 180 A. 360 = 2 radians 20. What is the equivalent degree measure for C. 1 = D. 1 radian = 60 180 2 radians? 12 21. What is the equivalent radian measure for 200? 22. Convert the degree measures into radians. Leave answers as exact values in most reduced form. a) 45 b) 36 c) 140 d) 300 23. Convert the following radian measures into degrees. a) 11 6 b) 5 9 c) 23 12 d) 7 2 24. Determine the arc length. Leave answers in exact form. a) Central Angle of 30, radius of 10 cm. b) Central Angle of 24, radius of 5 cm. c) Central Angle of 270, radius of 1 cm. 25. Determine the sector area. Leave answers in exact form. a) Central Angle of 112, b) Central Angle of 24, radius of 10 cm. radius of 8 cm. c) Central Angle of 200, radius of 5 cm. 26. Find the radius of a circle in which a central angle of 80 intercepts an arc length of 2cm? 27. If the arc length of a sector is 3 cm and its radius is 2 cm, then the central angle in radians is: 4 28. If the arc length of a sector is 24 cm and its radius is 8 cm, then the central angle in radians is: 4 then its radius is: 5 5 then its radius is: 8 29. If the area of circle sector is 40 cm2 and its central angle 30. If the area of circle sector is 5 cm2 and its central angle 4 H.Geometry 31. Determine the arc length of the following. a) Semester Final Review 2 b) 5π 4 3π 2 3 cm 12 cm Module 17: 32. Determine the center and radius of the given circles. a) x 7 y 10 81 Center (_____ , _____) Radius = _______ b) 100 x 3 y 2 Center (_____ , _____) Radius = _______ Center (_____ , _____) Radius = _______ Center (_____ , _____) Radius = _______ Center (_____ , _____) Radius = _______ 2 2 2 c) x 9 y 2 1 2 2 d) 36 x 8 y 7 2 2 e) x y 1 4 2 2 33. Determine the center and radius of the given circles by completing the square. x 2 y 2 4 x 14 y 17 0 ex) a) x2 y 2 4 x 16 y 52 0 x2 4 x y 2 14 y 17 x 2 4 x 4 y 2 14 y 49 17 4 49 2 2 x 2 y 7 36 Center (2,7) Radius = 6 cm. Center (_____ , _____) b) x y 2 x 18 y 1 0 2 2 Center (_____ , _____) d) Radius = ______ x 14 x y 2 y 50 0 2 2 Center (_____ , _____) Radius = ______ c) 2 Center (_____ , _____) e) Radius = ______ x 10 x y 16 0 2 Radius = ______ x 2 x 18 y 8x 2 2 Center (_____ , _____) Radius = ______ 5 H. Geometry Name____________________________Period____Date_________ Semester 2 Final Review 3- Unit 7: Module 18 Find the volume of each prism. Round to the nearest tenth if necessary. 1. 2. the oblique rectangular prism the right triangular prism 3.a cube with edge length 0.75 m ___________________________________________________________ Find the volume of each cylinder. Give your answers both in terms of and rounded to the nearest tenth. 4. 5. 6. a cylinder with base circumference 18 ft and height 10 ft ________________________________ Describe the effect of each change on the volume of the given figure. 6. 7. The dimensions are halved. The dimensions are divided by 5. Find the volume of each composite figure. Round to the nearest tenth. 8. 9. Write each formula. 10. volume of a pyramid with base area B and height h ___________________________ 11. volume of a square pyramid with base edge s and height h ___________________________ 1 H.Geometry Find the volume of each pyramid. Round to the nearest tenth. 12. Semester Final Review 3 13. rectangular pyramid regular pentagonal pyramid Find the volume of the composite figures. 14. 15. Find the volume of each cone. Give your answers both in terms of and rounded to the nearest tenth. 16. 17. 18. 19. a cone with diameter 15 yd and height 10 yd Find the volume of each composite figure. Round to the nearest tenth. 20. 2 H.Geometry Find each measurement. Give your answers in terms of . 21. Semester Final Review 3 22. the volume of the sphere the volume of the hemisphere Module 19 Tell what kind of solid can be made from each net. If there is no solid that can be made from the given net, write “none.” 23. 24. _______________________ 25. _______________________ ________________________ Name the shape of the cross section produced by slicing each of these solids as described. 26. Vertical cross section of a cylinder _________________ 27. Horizontal cross section of a square pyramid _________________ Find the surface area of each solid figure. Write the measures of the solid figures on the corresponding parts of their nets. For cylinders, give answers in terms of . 28. Cube: ________ units2 29. Cylinder: ________ units2 30. Rectangular prism: ________ units2 31. Triangular prism: ________ units2 Height of base 25 units 3 H.Geometry Semester Final Review 3 32. Cylinder: ________ units2 33. Triangular prism: ________ units2 Find the surface area of each composite figure. Show your work. 34. Cylinder on top of rectangular prism ________ units2 Find the surface area of each part of the solid figure. Add to find the total surface area. For cones, give answers in terms of . __________ mm2 What is the lateral surface area? __________ mm2 What is the total surface area? __________ mm2 36. What is the base area of the cone? __________ ft2 What is the lateral surface area? __________ ft2 What is the total surface area? __________ ft2 35. What is the base area of the cone? Find the surface area of each figure. 37. __________ in2 38. Slant Height is 12 in __________ in2 4 H.Geometry Semester Final Review 3 Solve for the surface area. Give surface areas in terms of . 39. Surface area ______ mi2 40. Surface area ______ m2 Module 20 State how each transformation affects the area. 41. The base of a parallelogram is multiplied by 3 . 4 ________________________________________________________________________________________ 42. A rectangle has length 12 yd and width 11 yd. The length is divided by 6. ________________________________________________________________________________________ 43. A triangle has vertices A(2, 3), B(5, 2), and C(5, 4). The transformation is (x, y) (x, 2y). ________________________________________________________________________________________ State how each transformation affects the perimeter or circumference and area. 44. The length and width of the rectangle are multiplied by 4 . 3 ________________________________________________________________________________________ 45. A triangle has base 1.5 m and height 6 m. Both base and height are tripled. ________________________________________________________________________________________ 1 1 46. A circle with radius 2 has center (2, 2). The transformation is (x, y) x, y . 2 2 ________________________________________________________________________________________ State how each transformation affects the surface area and volume. 47. The dimensions of a rectangular prism are multiplied by a scale factor of 2. ________________________________________________________________________________________ 5 H.Geometry Semester Final Review 3 1 48. The dimensions of a right cylinder are multiplied by a scale factor of . 2 ________________________________________________________________________________________ Find the population density. 49. Park rangers counted 7 coyotes over an area of 25 square miles. ________________________________________________________________________________________ 50. A major metropolitan city has an average of 60,000 people visiting the city’s park during peak hours. The city park is 3.41 km2. ________________________________________________________________________________________ 51. About 50,000 full-grown Canadian geese were estimated to live in the state of Minnesota in 1990. The state of Minnesota is about 86,000 square miles. ________________________________________________________________________________________ In Problems 4–6, state how the following changes will affect the population density. 52. Park rangers counted 7 coyotes over an area of 25 square miles. One of the coyotes left the pack and is no longer in the area. ________________________________________________________________________________________ 53. A major metropolitan city has an average of 60,000 people visit the city’s park during peak hours. The city park is 3.41 km2. An outdoor concert is planned in the park and 40,000 additional people are expected to attend the concert. ________________________________________________________________________________________ 54. About 50,000 full-grown Canadian geese were estimated to live in the state of Minnesota in 1990. The state of Minnesota is about 86,000 square miles. It is estimated that 62,000 goslings were produced and will become full-grown adults in 1991. ________________________________________________________________________________________ Find the population density. 55. Cardton City has a population of 2046. Its border can be modeled by a rectangle with vertices A(1, 1), B(1, 1), C(1, 0), and D(1, 0), where each unit on the coordinate plane represents 1 mile. Find the approximate population density of Cardton City. In Problems 1–4, solve for the missing dimension of the figure. 56. A rectangular prism has a volume of 432 cubic feet. Two of the dimensions of the rectangular prism are the same measure. The other dimension is equal to the sum of the other two dimensions. What are the prism’s dimensions? ________________________________________________________________________________________ 6 H.Geometry Semester Final Review 3 57. A cone’s height is six times greater than the measure of the cone’s radius. The volume of the cylinder is 169.56 in3. What are the cone’s dimensions? Use 3.14 for . ________________________________________________________________________________________ 58. A cube has a volume of 343 cubic centimeters. The length, width, and the height of the figure are equal. What are the cube’s dimensions? ________________________________________________________________________________________ 59. A circle has an area of 530.66 square inches. What is the circle’s radius? Use 3.14 for . ________________________________________________________________________________________ 60. 61. 7 H. Geometry Name____________________________Period______ Semester 2 Final Review 4 - UNIT 8 – Module 22 and Module 23 Mixed Review Probability 1. When rolling two fair number cubes, what is the probability that the sum of the two cubes will not be even AND not prime? 2. Ten marbles are placed in a jar. Of the 10 marbles, 3 are blue, 2 are red, 3 are green, 1 is orange, and 1 is yellow. The 10 marbles are randomly placed in a line. What is the probability that all marbles of the same color are next to each other? 3. A class of 15 boys and 15 girls is putting together a random group of 3 students to do classroom chores. What is the probability that at least 2 of the students are boys? Use the sets below to find the indicated set for problems 4-7. U = {1, 2, 3, 4, 5, 6, 7, 8, 9} A = {1, 3, 5, 7, 9} B = {2, 4, 6, 8} C = {1, 2, 4, 5, 7, 9} 4. A ⋃C 5. B ⋂C 6. 𝐴𝑐 7. A ⋂B 8. A computer password can use all digits (0 –9) and all letters (a–z) that are case sensitive (upper and lower). How many different permutations of 5-figure passwords are there if there is no repeated input? 1 H.Geometry Semester Final Review 9. Twenty-six tiles with the letters A through Z are placed face down on a table and mixed. (For the purpose of this exercise assume that the letter Y is a vowel.) Five tiles are drawn in order. Compute the probability that only consonants are selected. 10. The two-way table shows the results of a poll in a certain country that asked voters, sorted by political party, whether they supported or opposed a proposed government initiative. Find the given probabilities. a. P (no party or undecided) b. P ((𝑝𝑎𝑟𝑡𝑦 𝐴 𝑜𝑟 𝑠𝑢𝑝𝑝𝑜𝑟𝑡)𝑐 ) 11. Let H be the event that a coin flip lands with heads showing, and let T be the event that a flip lands with tails showing. (Note that P(H) = P(T) = 0.5.) What is the probability that you will get heads at least once if you flip the coin ten times? Explain your reasoning. 12. There are 8 girls and 6 boys on the student council. How many committees of 3 girls and 2 boys can be formed? Show your work. 13. Find the probability that a black card drawn from the deck is a queen. (The deck is a standard one of 52 cards.) 2 H.Geometry Semester Final Review 14. Jim rolled a set of two number cubes. If these are standard 6-sided number cubes, what is the probability of obtaining 12? (That means the values of the top faces add up to 12.) 15. What is the probability that a diamond that is drawn from the deck is a queen? 16. What is the probability that a queen drawn is a diamond? 17. Isabelle believes that right- and left-footed soccer players are equally likely to score goals. She collected data from 260 players from a local soccer league. Using the following two-way frequency table, show that being right-footed and scoring goals are independent events. 18. Jim has 2 blue, 2 green, and 2 black socks in his drawer. He picks out 2 socks, one after the other. Determine the probability of him getting a matching pair of blue socks. Are these events Independent or Dependent? 19. You have a standard deck of 52 playing cards. You pick three cards in a row without replacement. What is the probability that all three are aces? Now you replace the three cards, shuffle, and pick four cards in a row without replacement. What is the probability that none are aces? 20. Lisa flipped the same coin twice. Determine the probability of the coin landing on tails on the second try. 3 H.Geometry Semester Final Review 21. Lisa flipped the same coin three times. What is the probability she obtained all tails? 22. A jar contains 12 pennies, 5 nickels, and 18 quarters. You select 2 coins at random, one after the other. Does selecting a nickel affect the probability of selecting another nickel? Does not selecting a dime affect the probability of selecting a nickel? Find the probability of selecting 2 nickels. 23. Are the events independent? Choose Yes or No for each situation. A. Picking a penny and a marble out of a jar of pennies and a jar of marbles. Yes No B. Drawing cards from a deck to form a 4-card hand. Yes No C. Choosing a color for a new shirt from a choice of red, yellow, or purple. Yes No 24. Of the boys running for School President, 2 are juniors and 3 are seniors. Of the girls who are running, 4 are juniors 𝟐 and 1 is a senior. Decide whether the situation has a probability of 𝟓. Select Yes or No for A–C. A. A girl wins. Yes No B. A candidate who is a boy is a junior. Yes No C. A candidate who is a junior is a boy. Yes No 25. You shuffle a standard deck of playing cards and deal one card. What is the probability that you deal an ace or a club? Explain your reasoning. 4