Mathematics Higher Level Robert Joinson

Higher6) Two angles and a side are equal on both triangles.7) (i) True - rest are false.37. Geometry of a Circle 11) 48° , 42° , 42° 2) 90° , 33° , 57°3) 140° , 80° , 50° 4) 96° , 84° , 72°5) 12° , 57° , 78° 6) 27.5° , 125° , 97.5°38. Geometry of a Circle 21) 94° , 43° , 52° , 42° 2) 47° , 88° , 9°3) 50° , 130° , 120° , 70° 4) 124° , 56° , 34°5) 124° , 68° , 56° 6) 62° , 124° , 56° , 28°39. Vectors 11) b + c, b + c + d, c + d 2) ⎛5⎞⎝8⎠3) AD4) a) 4c – 4a b) 2c – 2a c) 4a + 2c – 2a = 2c + 2ad) 2c e) PX is parallel to OC and half its length5) a) 9b – 6a b) 3b – 2a c) 6a + 3b – 2a = 4a + 3b116) a) a + b b) -- (a + b) c) -- (b – a)227) –a, –b, 2a, –a, b–a, 2a–2b8) a) AB is parallel to CD, CD is twice as long as AB2b) Parallel. One is -- the length of the other39) a) 2b – 2a b) b – a c) XY is parallel to ABbecause AB = 2 × XY10) AC = a + b BD = b – a43. Bearings1) S28° W ( 208° ) 2) N73° E ( 073° )3) a) N30° E ( 030° ) b) S30° E ( 150° )c) N30° W ( 330° )4) a) N6° E ( 006° ) b) N55° W ( 305° )c) S55° E ( 125° )5) a) N60° E ( 060° ) b) Due South ( 180° )c) S60° W ( 240° ) d) S60° W ( 240° )6) a) N51° W ( 309° ) b) N4° E ( 004° )c) N84° W ( 276° )44. Construction6) 21 metres 7) 4.5 cm 8) 1630 m45. Loci1)2)3)81metres4)Page10040. Vectors 221 111) a) -- b b) -- b – -- a c) b + -- a33 22112) a) a + b b) -- (a + b) c) -- b3322d) -- a PQ is parallel to OC and -- of its length33113) a) (a + b) b) -- (a + b) c) b – a d) -- (b – a)6622e) -- a f) They are parallel and XY is -- the length33of CB111 14) a) -- a b) b – -- a c) a + b d) -- b – -- a223 61 11e) -- a + -- b f) --3 335) a) 12b + 6a b) 5a – 2b c) 3b + 6acm 241. Similar Shapes1) a) 4:9 b) 8:27 c) 337.5 cm 32) a) 8:19 b) 4503) 122.88 grams 4) 390.625 grams5) 11.9 cm 6) 8,000 cm 37) a) 112.5 cm 2 b) 14.81 cm 38) 350 grams42. Similarity1) a) i) 75° ii) Since DC and BE are parallel thenangle CDE and BEA are equalb) AE = 6 cm2) a) i) 39° ii) Angle DCE = 116° (verticallyopposite) Angle DEC = 180 – (116 + 25) = 39°(3 angles of a triangle add up to 180° )b) 7.5 cm3) a) 7.5 cm b) 7.5cm 4) a) 6 cm 1.5cm b) 1:165) 700 metres46. Transformations 11) a) (–1, –2) (–3,–2) (–4,–5)b) (1,–2) (3,–2) (4,–5)c) Rotation of 180˚ about origin (0,0)2) a) (2,2) (2,4) (4,2)b) (2,–2) (2,–4) (4,–2)c) (–1,1) (–2,1) (–1,2)d) An enlargement with a scale factor of 2 throughthe origin (0,0)3) b) (1,2) (2,2) (2,1)1c) An enlargement with a scale factor of 2 -- through2the origin (0,0)47. Transformations 21) a) (–1,–1) (–4,–4) (–3,–1)b) (–1,3) (–3,3) (–4,0)c) Rotation of 180˚ (clockwise or anticlockwise)about the point (0,2)2) a) Rotation of 180˚ about the origin (0,0)b) Translation ⎛ 0 ⎞ c) (–1,4) (–1,2) (1,2)⎝–6⎠d) Rotation of 180˚ about (–1,3)3) a) (2,1) (5,1) (4,–2) b) (0,1) (0,–2) (–3,–1)c) Reflection in the line y = 3 – x