1. 1
   Point B is on a bearing of 072° from point A, at a distance of 15 km. On a map, the scale used is 1 cm represents 3 km.

   (a)

   What is the bearing of A from B?

   [1 mark]

   • A252°
   • B072°
   • C108°
   • D288°

   (b)

   What length, in cm, represents the distance AB on the map?

   [1 mark]

   • A18 cm
   • B45 cm
   • C12 cm
   • D5 cm

   (c)

   Given that the bearing of C from B is 140°, what type of angle is angle ABC (the angle at B between A and C)?

   [1 mark]

   • AAcute (68°)
   • BObtuse (112°)
   • CReflex (248°)
   • DRight angle (90°)

   Total for question 1: 3 marks

2. 2
   Two straight paths meet at point R at an angle of 74°, and a third path bisects this angle exactly. Separately, points P and Q are two schools 18 km apart, and a new sports centre S lies on the perpendicular bisector of PQ, so S is equidistant from P and Q. Given SP = 15 km, and M is the midpoint of PQ.

   (a)

   Find the angle between the bisecting path and each of the two original paths.

   [2 marks]

   (b)

   Find the distance SM, where M is the midpoint of PQ.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A map is drawn to a scale of 1 : 50000. On the map, the distance between village X and village Y is 8.4 cm. Village Z is on a bearing of 118° from village X, at an actual distance of 6 km.

   (a)

   Find the actual distance between village X and village Y, in km.

   [3 marks]

   (b)

   Find the length, in cm, that represents the distance XZ on the map.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A ship sails from harbour H on a bearing of 035° for 20 km to point K. It then changes course and sails on a bearing of 125° for 20 km to point L.

   (a)

   Find the size of angle HKL, the interior angle of the ship's path at K.

   [4 marks]

   (b)

   Using your answer to part (a), find the distance HL, giving your answer to 3 significant figures.

   [4 marks]

   (c)

   Find the bearing of L from H, to the nearest degree, justifying your reasoning.

   [5 marks]

   Total for question 4: 13 marks

End of questions