Cambridge O Level Mathematics (Syllabus D) · Syllabus 4024 · Number
Rates
What is Rates?
A rate compares two quantities of different kinds, such as distance and time or mass and volume, and is written as the amount of the first per one unit of the second. Average speed is the rate that matters most in this topic and is always total distance divided by total time, never the mean of separate speeds.
This definition is part of the Number chapter in Cambridge O Level Mathematics (Syllabus D).
Rates in context
Topic 1 is not eighteen unrelated skills. It is one habit applied eighteen times: choose the representation that makes the question easy, work exactly for as long as you can, and round only once, at the end. A number can appear as a product of primes, a fraction, a decimal, a percentage, a power, a standard-form pair, a ratio, a rate, a bound or a surd — and every calculation in Chapter 1 becomes short the moment you pick the right one. Every later chapter draws on this: algebra needs indices and exact fractions, mensuration needs ratio, rates and bounds, and statistics needs proportional reasoning.
The big picture. Number work controls almost every later topic. Algebra needs factors, indices and exact fractions; mensuration needs ratios, rates, units and bounds; probability and statistics need proportional reasoning. The aim is not merely to calculate but to choose an efficient representation and judge whether the result is sensible. Everything below is one of those representations.