Real-life graphsIB MYP Maths Extended: Subtopic test

1. 1
   A conversion graph for pounds (£) to UAE dirhams (AED) is a straight line through the origin. The point $(10, 46)$ lies on the line, where the horizontal axis shows pounds and the vertical axis shows dirhams.

   (a)

   Find the gradient of the graph and what it means.

   [1 mark]

   • A$4.6$ AED per pound
   • B$0.22$ AED per pound
   • C$46$ AED per pound
   • D$10$ AED per pound

   (b)

   How many dirhams is £25 worth?

   [1 mark]

   • A$5.4$ AED
   • B$115$ AED
   • C$250$ AED
   • D$71$ AED

   (c)

   Convert $92$ AED to pounds.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   The distance–time graph of a hiker's walk has three straight sections. In the first hour she walks from the start to a point $5$ km away. In the next half hour the graph is horizontal. In the following hour she walks a further $7$ km.

   (a)

   What does the horizontal section of the graph show?

   [1 mark]

   • AThe hiker is walking at a constant speed.
   • BThe hiker is walking back towards the start.
   • CThe hiker is walking at $5$ km/h.
   • DThe hiker is stationary (resting).

   (b)

   What is the hiker's speed in the final section?

   [1 mark]

   • A$5$ km/h
   • B$12$ km/h
   • C$7$ km/h
   • D$4.8$ km/h

   (c)

   Find the hiker's average speed for the whole walk.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Two plumbers each charge a call-out fee plus an hourly rate. Plumber A charges $C = 80 + 120h$ and Plumber B charges $C = 50 + 140h$, where $C$ is the cost in AED for a job lasting $h$ hours.

   (a)

   For Plumber A, state what the numbers $80$ and $120$ represent, and find the cost of a job lasting $2.5$ hours.

   [3 marks]

   (b)

   A job costs $560$ AED with Plumber A. Find how long the job lasted, and find what Plumber B would have charged for the same job.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Tank A holds $600$ litres of water and is emptied through a pipe at a steady $15$ litres per minute until it is empty. Tank B holds $400$ litres and is emptied at a steady $8$ litres per minute. $V$ is the volume of water in a tank, in litres, $t$ minutes after emptying starts.

   (a)

   (i) Write an equation for $V$ in terms of $t$ for Tank A.
   (ii) State what the number $-15$ represents in your equation.
   (iii) Find how long Tank A takes to empty.
   (iv) Find the volume of water in Tank A after $12$ minutes.

   [6 marks]

   (b)

   Tom says that Tank B takes longer to empty than Tank A because it empties more slowly. Evaluate Tom's statement.

   [6 marks]

   Total for question 4: 12 marks

End of questions