1. 1
   A ship sails from port P on a bearing of $072°$ to reach point Q, then from Q on a bearing of $162°$ to reach point R.

   (a)

   Find the bearing of P from Q.

   [1 mark]

   • A$072°$
   • B$108°$
   • C$252°$
   • D$288°$

   (b)

   Find the bearing of Q from R.

   [1 mark]

   • A$342°$
   • B$018°$
   • C$162°$
   • D$252°$

   (c)

   Find the angle PQR, the angle turned through at Q between the direction the ship arrived from and the direction it leaves towards R.

   [1 mark]

   • A$18°$
   • B$72°$
   • C$162°$
   • D$90°$

   Total for question 1: 3 marks

2. 2
   A garden has two features, a fountain F and a statue S, exactly 12 metres apart. A gardener wants to plant flowers at all points that are the same distance from F as from S.

   (a)

   Describe fully the locus of points that are the same distance from the fountain F as they are from the statue S.

   [2 marks]

   (b)

   Given that FS $=12$ m, find the distance from F to the point on this locus that lies on the line FS.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A radio mast M transmits a signal that reaches up to 15 km in all directions. A boat travels in a straight line that passes 9 km from the mast at its closest point.

   (a)

   Explain why the perpendicular distance of 9 km from M to the boat's path represents the shortest possible distance between the mast and the path.

   [3 marks]

   (b)

   Determine whether the boat's path enters the signal's range, and if so, find the length of the path that lies within range, giving your answer to 1 decimal place.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A hiking group starts at base camp and walks 8 km on a bearing of $050°$ to reach a shelter. From the shelter, they walk 6 km on a bearing of $140°$ to reach a viewpoint.

   (a)

   Show that the angle at the shelter between the direction the group arrived from and the direction they leave towards the viewpoint is $90°$.

   [4 marks]

   (b)

   Find the straight-line distance from base camp to the viewpoint.

   [4 marks]

   (c)

   Find the bearing of the viewpoint from base camp, giving your answer to the nearest degree.

   [5 marks]

   Total for question 4: 13 marks

End of questions