1. 1
   A cyclist rides along a straight road. In the first 2 hours of her journey she travels 30 km at a constant speed. She then rests for 1 hour. In the final 3 hours of her journey she travels a further 60 km at a different constant speed.

   (a)

   What was her speed during the first 2 hours?

   [1 mark]

   • A15 km/h
   • B30 km/h
   • C10 km/h
   • D20 km/h

   (b)

   What was her speed during the final 3 hours?

   [1 mark]

   • A15 km/h
   • B20 km/h
   • C45 km/h
   • D30 km/h

   (c)

   What was her average speed for the whole 6-hour journey (including the rest)?

   [1 mark]

   • A12 km/h
   • B18 km/h
   • C20 km/h
   • D15 km/h

   Total for question 1: 3 marks

2. 2
   A small business tracks the value of its stock. At time $t=0$ years the stock is worth £2000. At time $t=4$ years the stock is worth £8000. The value increases at a constant rate over this period.

   (a)

   Calculate the rate of change of the value of the stock, in pounds per year.

   [2 marks]

   (b)

   Assuming the rate of change stays constant, calculate the value of the stock at $t=6$ years.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A water tank is being drained at a constant rate. At time $t=0$ minutes it contains 600 litres. At time $t=8$ minutes it contains 360 litres.

   (a)

   Calculate the rate of change of the volume of water in the tank, in litres per minute.

   [3 marks]

   (b)

   Calculate the total time taken, from $t=0$, for the tank to empty completely, assuming it continues to drain at this constant rate.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A ball is thrown upwards. Its height above the ground is recorded at three times: at $t=1$ second the height is 20 m; at $t=2$ seconds the height is 35 m; at $t=3$ seconds the height is 40 m.

   (a)

   Calculate the average rate of change of height between $t=1$ and $t=3$ seconds.

   [4 marks]

   (b)

   Calculate the average rate of change of height between $t=2$ and $t=3$ seconds.

   [4 marks]

   (c)

   Explain why the rate of change calculated in part (b) is a better estimate of the instantaneous rate of change of height at $t=3$ seconds than the rate calculated in part (a). State whether the ball's height increased or decreased between $t=2$ and $t=3$ seconds, justifying your answer.

   [5 marks]

   Total for question 4: 13 marks

End of questions