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Question.1 A rectangular picture frame is to be made. It is 30 centimetres high and 22.5 centimetres wide, as shown. To check that the frame is rectangular, d 30 cm the diagonal, d, is measured. It is 37.3 centimetres long. Y Is the frame rectangular ? 22-5 cm Question.2 The central semi-circular archway under a bridge is to be strengthened. While the work is being carried out, 2 metal beams are to be set in place to support the archway. For safety reasons, the beams have to just meet on the circumference of the arch. 4-1 m Will the beams fit this archway which is 4.1 metres wide ? Question.3 The diagram shows the design of an earring. The earring consists of a circle inside an equilateral triangle. The sides of the triangle are tangents to the circle. The radius of the circle is 8 mm The distance from the centre of the circle to each vertex of the triangle is 17mm. Calculate the perimeter of the triangle. Question.4 The road joining A to B is A 300 m B parallel to the road joining C to D in the diagram. 180 m 240 m X AB = 300 metres, Brock Burn AX = 180 metres, T BX = 240 metres and CD = 750 metres. C 750 m D a) Prove that the two roads AX and BX are at right angles to one another b) The Brock Burn burst its banks at T and the road became impassable. An alternative route had to be found in order to travel from A to D. Question.5 Trigonometry 1. In the diagram Angle STV = 34° S Angle VSW = 25° 13.1con 25° Angle SVT = Angle SWV = 90° W ST = 13.1 centimetres 34° Calculate the length of SW T V Question.6 A cat is trapped in a tree and a ladder is placed against the tree in an attempt to rescue it. The ladder rests against the tree making an angle of 60° with the horizontal and reaching 14 metres up 1 4m the tree, allowing the rescuer to reach the cat. 60' o I 1m Just as the cat is about to be rescued, it jumps to a branch 1 metre above its original resting place. Calculate the size of the angle, to the nearest degree, that the ladder now has to make with the horizontal to allow the rescuer to reach the cat. Question.7 Two support cables, from the T A 4h top (T) of a motorway light, are attached to a pair of points, A and B, on the ground, as shown in the diagram. 13.5 m a) Calculate the distance from B to C. b) Calculate the distance 40° 70° O a from A to B. A B C Question.8 The diagram shows the design of a swimming pool 50 metres in length. 1 metre The pool is 1 metre deep at one 50 metres 4 1 metre end and its base slopes downwards d metres at an angle of 3° to the horizontal. 3° Calculate the depth, d metres, of 7 the other end of the pool, giving your answer to 2 significant figures. Do not use a scale drawing. Question.9 Two boats leave port together. Nort Boat D sails on a course of 057° at 13 miles per hour. Boat E sails on a bearing of 104° D at 15 miles per hour. After 45 minutes Boat D receives a distress call from Boat E requesting Port their help as soon as possible. E How far, to the nearest mile, would Boat D have to travel to reach Boat E? Question.10 N The radio masts, Kangaroo (K), Wallaby (W) and Possum (P) are situated in the Australian outback. W Kangaroo is 250 kilometres due south of Wallaby. 250 km Wallaby is 410 kilometres from Possum 410 km Possum is on a bearing of 130° from Kangaroo. Calculate the bearing of Possum from Wallaby. K Do not use a scale drawing. P

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