1. 1
   $y$ is directly proportional to $x$. When $x = 4$, $y = 20$.

   (a)

   What is the value of the constant of proportionality, $k$, where $y = kx$?

   [1 mark]

   • A4
   • B5
   • C16
   • D80

   (b)

   Using $y = 5x$, find the value of $y$ when $x = 7$.

   [1 mark]

   • A12
   • B30
   • C35
   • D40

   (c)

   Which equation correctly relates $y$ and $x$?

   [1 mark]

   • A$y = \frac{x}{5}$
   • B$y = x + 16$
   • C$y = \frac{20}{x}$
   • D$y = 5x$

   Total for question 1: 3 marks

2. 2
   $P$ is inversely proportional to $Q$. When $Q = 3$, $P = 8$.

   (a)

   Find the constant $k$ in the equation $P = \frac{k}{Q}$.

   [2 marks]

   (b)

   Using $P = \frac{24}{Q}$, find the value of $P$ when $Q = 6$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A metal has density $8\,\text{g/cm}^3$. For a piece of this metal with volume $V\,\text{cm}^3$, the mass $M$ in grams is given by $M = 8V$.

   (a)

   Show that the mass $M$ in kilograms can be written as $M = 0.008V$.

   [3 marks]

   (b)

   Using $M = 0.008V$ (with $M$ in kilograms), find the volume of a piece of this metal with a mass of 2 kg.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   The time $T$ (in hours) taken to travel a fixed distance is inversely proportional to the average speed $S$ (in km/h), so $T = \frac{k}{S}$, where $k$ is the distance in km. When $S = 60$, $T = 3$.

   (a)

   Find the value of $k$, and hence find $T$ when $S = 45$.

   [4 marks]

   (b)

   A second, longer journey covers 240 km, with time $T$ hours related to average speed $S$ km/h by $T = \frac{240}{S}$.
   
   Find the average speed $S$ needed to complete this journey in $T = 3.2$ hours.

   [4 marks]

   (c)

   A cyclist's speed $S$ (km/h) is directly proportional to the square root of her power output $P$ (watts), so $S = k\sqrt{P}$. When $P = 100$ W, $S = 20$ km/h.
   
   Find the value of $k$, calculate the speed when $P = 225$ W, and hence find the time (to the nearest 0.1 hour) to complete the 180 km journey from part (a) at this speed.

   [5 marks]

   Total for question 4: 13 marks

End of questions