A compound quantity is one built from two other quantities, such as speed (distance per time) or density (mass per volume). This module covers converting their units, reading them from graphs, and telling an average rate from a reading at one instant.
These questions appear across IGCSE Mathematics in word problems, graph questions and mixed multi-step questions. Check the current syllabus wording for your exam year on the Cambridge subject page, because the skills below stay the same while the phrasing can change.
What should you know before starting?
You need confident work with fractions and decimals, including exact arithmetic without a calculator, and with ratio and proportion. You also need to read a simple graph: the axes, the scale and what a straight line means.
If unit conversion for length, time or volume is shaky, sort that out first. Every lesson here depends on it.
One orienting example
A bus travels 90 km in 1 hour 15 minutes. What is its average speed in km/h, and in m/s?
Step 1: change the time to hours: 1 h 15 min = 1.25 h.
Step 2: speed = distance ÷ time = 90 ÷ 1.25 = 72 km/h.
Step 3: to get m/s, 72 km = 72 000 m and 1 hour = 3600 s, so 72 000 ÷ 3600 = 20 m/s.
Notice where the risk sits. The division is easy. The marks are lost in writing 1 h 15 min as 1.15 instead of 1.25, or in converting only the distance and forgetting the time.
In what order should you study the lessons?
- Convert a compound speed unit first, because every later lesson relies on changing units safely.
- Read a distance-time graph next, since gradient as speed is the core graph idea.
- Interpret an area under a speed-time graph after that, where the area becomes distance and the gradient becomes acceleration.
- Calculate density using consistent units applies the same unit discipline to mass and volume.
- Distinguish an average rate from an instantaneous reading last, because it needs the graph skills from lessons 2 and 3.
The graph-model explorer and the non-calculator working trainer are useful alongside these lessons.
Which traps catch most students?
- Averaging two speeds instead of dividing total distance by total time.
- Converting km to m but leaving hours unchanged, or the reverse.
- Reading a distance-time graph as a picture of the route rather than a record of distance against time.
- Finding the area under a speed-time graph with mismatched units, such as km/h and minutes.
- Writing a density with a unit that does not match the numbers used.
How should you use the practice set?
Work the lessons in order, then attempt the mixed rates practice set without looking at the answers. Mark each question, and for every error note which trap above it was. The routing section at the end of the practice set sends each error type back to the right lesson.
This module sits between data displays and cumulative reasoning and non-calculator strategy, and it feeds directly into those. The full topic map is in the IGCSE Mathematics learning guide. If you want a teacher to go through your rate working with you, see online one-to-one Mathematics tuition.