1. 1
   A cyclist rides at a constant speed on a distance–time graph. She travels 45 km in 3 hours, then rests for 1 hour, then returns home at 30 km/h.

   (a)

   A cyclist travels at a constant speed, covering 45 km in 3 hours. What is her speed in km/h?

   [1 mark]

   • A$15$ km/h
   • B$45$ km/h
   • C$135$ km/h
   • D$3$ km/h

   (b)

   How long, in hours, does the return journey home (45 km at 30 km/h) take?

   [1 mark]

   • A$1$ hour
   • B$1.5$ hours
   • C$2$ hours
   • D$0.5$ hours

   (c)

   On the distance–time graph for the rest period, what is the gradient of the line?

   [1 mark]

   • AUndefined
   • B$30$
   • C$0$
   • D$15$

   Total for question 1: 3 marks

2. 2
   A currency conversion graph converts British pounds, $x$, to US dollars, $y$, using the linear relationship $y = 1.25x$.

   (a)

   A currency conversion graph converts British pounds ($x$) to US dollars ($y$) using $y = 1.25x$. Find the number of dollars received for $\pounds 80$.

   [2 marks]

   (b)

   State the gradient of the conversion graph and explain what it represents in this context.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A car accelerates from rest at a constant rate, reaching 24 m/s after 8 seconds, then travels at this constant speed for 10 seconds before decelerating to rest over 6 seconds.

   (a)

   A car accelerates from rest, reaching a speed of 24 m/s after 8 seconds, at a constant rate. Using the speed–time graph, find the acceleration of the car.

   [3 marks]

   (b)

   Calculate the total distance travelled by the car during the entire 24 seconds (acceleration, constant speed, and deceleration phases), using the area under the speed–time graph.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A water tank is filled at a constant rate. After 5 minutes it contains 60 litres, and after 12 minutes it contains 144 litres.

   (a)

   A water tank is being filled at a constant rate. After 5 minutes it contains 60 litres, and after 12 minutes it contains 144 litres. Find the rate at which water is being added, in litres per minute, and the amount of water in the tank at $t = 0$.

   [4 marks]

   (b)

   Write down the equation of the line representing the volume, $V$ litres, in the tank after $t$ minutes, and use it to find the volume after 20 minutes.

   [4 marks]

   (c)

   The tank has a maximum capacity of 300 litres. A second tank starts empty and fills at a constant rate of 15 litres per minute from $t=0$. Find the time, $t$, at which the second tank has the same volume as the first tank, and state which tank reaches its own capacity first (the second tank's capacity is 280 litres).

   [5 marks]

   Total for question 4: 13 marks

End of questions