Mathematics Higher Level Robert Joinson

HigherPage 102Exercise 21) a) iii b) i 2) a) ii b) v55. Pythagoras TheoremAll to 4 significant figures1) a) 7.211 b) 7.483 c) 4.8 d) 8.8012) 45.5 cm 3) 5.657 cm, 2.828 cm4) 6.403 cm 5) 2.721 metres 6) 18.81 metres56. Sine, Cosine and Tangent Ratios1) (to 4 sig. figures) a) 15.28 cm b) 6.576 cmc) 5.503 cm d) 22.58 cm2) a) 41.2˚ b) 46.9˚ c) 42.3˚ d) 42.2˚3) CD = 17.33 cm AC = 26.69 cmEB = 10.20 cm DEB = 43.3˚4) a) N24˚E (024˚) b) 5.41 km (to 2 d.p.)5) a) 7.523 metres (to 4 sig. figures) b) 28˚6) a)b)107) Approx 56˚ and 236˚500˚–5–1010500˚–5–10180˚360˚180˚57. Sine and Cosine Rules1) a) 72.97˚ b) 61.09˚ c) 4.74˚ d) 54.79˚e) 54.80˚ f) 10.54 cm2) 16.01 cm 3) 115.18˚ and 64.82˚4) 4.05 km 5) 16.08 m6) 58.75˚, 71.79˚, 49.46˚58. Areas of Triangles1) 20.99 cm 2 2) 53.83 cm 2 3) 22.36 cm 24) 27.39 cm 2 5) 131.95 cm 26) The perpendicular height from C to AD is 9 sin 20˚.The perpendicular height from B to DA producedis also 9 sin 20˚. Triangles ACD and ABD have thesame base ie. AD. Therefore their areas are equal.7) 49.85 cm 2 8) 2.3 m 29) 237.8 cm 2 10) 3.4 hectares59. Trigonometry Mixed Exercise1) AC = 6.325 cm CD = 5.175cm2) 10.91 cm 3) 9.226 m4) 122.75˚, 114.5˚ 5) 14.62 cm 6) 13.09 m60. Graphs of Sines, Cosines and Tangents1) 210˚ and 330˚ 2) Approx 49˚ and 131˚3)1.0–1.00 180˚ 360˚4) Approx 71˚ and 289˚ 5) Approx 76˚ and 256˚61. Three Dimensional Trigonometry1) 33.31 m (to 4 sig. figures)2) a) 28.28 cm b) 20.20 cm3) a) 4.667 m b) 23.2˚ c) HC = 5.077 m4) a) 3.830 m b) 21.0˚5) 107.3 m62. QuestionnairesThe following answers are for guidance only. Thereare other solutions.1) a) The survey could be biased for the followingreasons:i) It is done just in the month of July only.ii) It is carried out at 12.00 only and not at othertimes of the dayiii) It is carried out in just one particular place. Toget information about the whole of Britain sheneeds information from other towns.iv) Town is of one particular type ie historical.b) The survey could be improved by including thepoints raised in part a)c) Are you a tourist ?Which country do you come from ?What is your gender m/f ?2) a) How old are you ?What is your gender, male or female ?What other newspapers do you read?b) i) It only asks those who already read thenewspaper. It does not get to potential readers.3) a) It tells her the age of the cars on the road now.She could, for example, calculate the average ageof cars on the road but not the age at which theyare taken off the road.b) i) Was your last car sold to someone to use againor was it scrapped ?ii) How old was the car when it was scrapped ?