Rates, speed, distance and timeIB MYP Maths Standard: Subtopic test

1. 1
   A cyclist rides $45$ km in $2$ hours $30$ minutes.

   (a)

   Find her average speed.

   [1 mark]

   • A$22.5$ km/h
   • B$19.6$ km/h
   • C$112.5$ km/h
   • D$18$ km/h

   (b)

   Write her average speed in m/s.

   [1 mark]

   • A$0.3$ m/s
   • B$64.8$ m/s
   • C$5$ m/s
   • D$18000$ m/s

   (c)

   At the same average speed, find how long she takes to ride $63$ km. Give your answer in hours and minutes.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A solid metal block has mass $540$ g and volume $200$ cm$^3$.

   (a)

   Find the density of the metal.

   [1 mark]

   • A$2.7$ g/cm$^3$
   • B$0.37$ g/cm$^3$
   • C$340$ g/cm$^3$
   • D$108\,000$ g/cm$^3$

   (b)

   A block of the same metal has volume $350$ cm$^3$. Find its mass.

   [1 mark]

   • A$130$ g
   • B$945$ g
   • C$890$ g
   • D$9450$ g

   (c)

   A different piece of the same metal has mass $1.35$ kg. Find its volume.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A bus makes a journey in three stages: $60$ km at an average speed of $80$ km/h, then a rest stop of $30$ minutes, then $90$ km at an average speed of $60$ km/h.

   (a)

   Find the total time the bus spends travelling, not including the rest stop.

   [3 marks]

   (b)

   Find the average speed for the whole journey, including the rest stop.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A courier in Nairobi must deliver parcels along a $24$ km route. A motorbike travels at an average speed of $48$ km/h and uses $1$ litre of fuel for every $30$ km; fuel costs KES $180$ per litre. An electric bicycle travels at an average speed of $20$ km/h; one charge costs KES $12$ and lasts for $40$ km.

   (a)

   For one delivery along the route, find (i) the time taken by each vehicle, and (ii) the energy cost of the delivery for each vehicle.

   [6 marks]

   (b)

   The courier works for $8$ hours and is paid KES $250$ for each delivery. Ignore stops and other costs. (i) Find the greatest number of complete deliveries each vehicle can make in $8$ hours. (ii) Find the daily profit (earnings minus energy cost) for each vehicle and recommend which she should use.

   [6 marks]

   Total for question 4: 12 marks

End of questions