Trigonometry [CIE Extended Mathematics (0580) (2017-2018)]

1	(2017/w/21/q18) The diagram shows a scale drawing of Tariq’s garden. The scale is 1 centimetre represents 2 metres. Tariq puts a statue in the garden. The statue is equidistant from the two trees and 10m from the bird bath. Find, by construction, the point where Tariq puts the statue. Label the point S. [4]
2	(2018/m/22/q18) In this question, use a straight edge and compasses only and show all your construction arcs. (a) Construct the perpendicular bisector of PQ....[2] (b) Construct the bisector of angle ABC....[2]
3	(2018/s/41/q2) The scale drawing shows two boundaries, AB and BC, of a field ABCD. The scale of the drawing is 1cm represents 8m. (a) The boundaries CD and AD of the field are each 72m long. (i) Work out the length of CD and AD on the scale drawing. ............ cm [1] (ii) Using a ruler and compasses only, complete accurately the scale drawing of the field. [2] (b) A tree in the field is • equidistant from A and B and • equidistant from AB and BC. On the scale drawing, construct two lines to find the position of the tree. Use a straight edge and compasses only and leave in your construction arcs. [4]
4	(2017/s/21/q13) The diagram shows a cuboid ABCDEFGH. AE = 5cm, EH = 4cm and AG = 13 cm. Calculate the angle between the line AG and the base EFGH of the cuboid....[3]
5	(2017/w/21/q21) The diagram shows a square-based pyramid ABCDE. The diagonals of the square meet at M. E is vertically above M. AB = BC = 12cm and EM = 9cm. Calculate the angle between the edge EC and the base, ABCD, of the pyramid. ...... [4]
6	(2017/w/22/q26) The diagram shows a prism of length 4cm. The cross section is a right-angled triangle. BC = 3cm and CQ = 2 cm. Calculate the angle between the line AQ and the base, ABCD, of the prism. ............. [4]
7	(2017/s/23/q22) The diagram shows a cube ABCDEFGH of side length 26cm Calculate the angle between AG and the base of the cube. ................................................... [4]
8	(2018/w/23/q23) The diagram shows a triangular prism. AB = 12cm, BC = 6cm, PC = 4cm, angle BCP = 90° and angle QDC = 90°. Calculate the angle between AP and the rectangular base ABCD. ....[4]
9	(2017/s/42/q8) The diagram shows a pyramid on a rectangular base ABCD. AC and BD intersect at M and P is vertically above M. AB = 8cm, BC = 6cm and PM = 9cm. (a) N is the midpoint of BC. Calculate angle PNM. Angle PNM = .............................. [2] (b) Show that BM = 5cm. [1] (c) Calculate the angle between the edge PB and the base ABCD. ......... [2] (d) A point X is on PC so that PX = 7.5 cm. Calculate BX. BX = ........ cm [6]
10	(2017/s/43/q9) ABC is a triangular field on horizontal ground. There is a vertical pole BQ at B. AB = 525m, BC = 872m and angle ABC = 104°. (a) Use the cosine rule to calculate the distance AC... [4] (b) The angle of elevation of Q from C is 1.0°. Showing all your working, calculate the angle of elevation of Q from A. ........ [4] (c) (i) Calculate the area of the field. ........... m$^2$ [2] (ii) The field is drawn on a map with the scale 1:20000.       Calculate the area of the field on the map in cm$^2$. ...........cm$^2$ [2]
	To be continued....