Worksheets · Foundation and Higher

Proportional graphs and rates of change

3 exam-style questions. Answers and the mark for each step are on the last page.

1. Question 1Non-calculator · 3 marks

   $y$ is directly proportional to $x$. When $x = 4$, $y = 12$.

   (a) Find the value of $y$ when $x = 10$. (2)

   (b) Write the ratio $y : x$ in its simplest form. (1)
2. Question 2Non-calculator · 3 marks

   A tank’s volume-time graph is a straight line from $(0,14)$ to $(8,54)$. Time is in minutes and volume is in litres.

   (a) Find the rate at which water enters the tank. (2)

   (b) Is volume directly proportional to time? Explain. (1)
3. Question 3Non-calculator · 1 mark

   (a) A straight-line graph shows water volume in cm³ against time in minutes. Its gradient is 300 cm³ per minute. What is this rate in litres per hour? Select one answer. (1)

   1. 0.3 litres per hour
   2. 18 litres per hour
   3. 18 000 litres per hour
   4. 5 litres per hour