Bearings and scale drawingIB MYP Maths Extended: Subtopic test

1. 1
   A ship sails from port $A$ to port $B$ on a bearing of $072^\circ$. Port $C$ is on a bearing of $162^\circ$ from $B$.

   (a)

   What is the bearing of $A$ from $B$?

   [1 mark]

   • A$108^\circ$
   • B$252^\circ$
   • C$288^\circ$
   • D$072^\circ$

   (b)

   A lighthouse $L$ is due east of $B$. What is the bearing of $B$ from $L$?

   [1 mark]

   • A$090^\circ$
   • B$180^\circ$
   • C$270^\circ$
   • D$360^\circ$

   (c)

   Find the size of angle $ABC$.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A map of an island has a scale of $1:50\,000$. The villages Karu and Mele are $6.4$ cm apart on the map.

   (a)

   What is the real distance between Karu and Mele?

   [1 mark]

   • A$3.2$ km
   • B$0.32$ km
   • C$32$ km
   • D$320$ km

   (b)

   A footpath on the island is $4.5$ km long. How long is it on the map?

   [1 mark]

   • A$0.9$ cm
   • B$90$ cm
   • C$22.5$ cm
   • D$9$ cm

   (c)

   Another map of the island has a scale of $1:25\,000$. Find the distance between Karu and Mele on this map.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A walker leaves a hut $H$ and walks $8$ km on a bearing of $040^\circ$ to a lake $L$. She then walks $6$ km on a bearing of $130^\circ$ to a summit $S$.

   (a)

   Show that angle $HLS$ is $90^\circ$ and hence find the straight-line distance $HS$.

   [3 marks]

   (b)

   Find the bearing of $S$ from $H$. Give your answer to the nearest degree, as a three-figure bearing.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A boat leaves harbour $H$ and sails $12$ km due east to a buoy $B$. It then sails $5$ km due north to a rock $R$. The boat has a $70$-litre tank and uses $2.4$ litres of fuel for every kilometre it sails.

   (a)

   (i) Find the straight-line distance $HR$.
   (ii) Find the bearing of $R$ from $H$, to the nearest degree.
   (iii) Find the bearing of $H$ from $R$, to the nearest degree.

   [6 marks]

   (b)

   The captain wants to sail from $H$ to $B$ to $R$, and then straight back from $R$ to $H$. Show whether the tank holds enough fuel for this trip. Justify whether sailing from $H$ to $R$ directly and then straight back would be a safer plan, and state one assumption that affects how far you can trust your answer.

   [6 marks]

   Total for question 4: 12 marks

End of questions