Direct and inverse proportion
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 6 practice questions, 2 real past-paper questions with the answers explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- More workers, less time
- Direct proportion
- The method
Read the transcript of the teaching part
Last time
Before we start: last time, in Sequences and the nth term, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
More workers, less time
Six workers build a wall in ten days. How long would four workers take? Fewer workers means more days: that is inverse proportion. And if each metre of wall costs the same, the cost grows with the length: that is direct proportion. Today you set up the equation with the constant k, and use it, including squares and roots.
Direct proportion
Direct proportion means that as x grows, y grows by the same factor. Double x and y doubles. We write y is proportional to x, and turn it into an equation with a constant: y equals k times x. The constant k is called the constant of proportionality. It never changes.
The method
Step one: write the equation with k. Step two: use the given pair of values to find k. Step three: rewrite the equation with that k, and use it to find the unknown. For example: y is twelve when x is four. Then k is twelve over four, which is three. So y equals three x, and when x is seven, y is twenty-one.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Direct proportion · Inverse proportion.
The whole chapter: Proportion.
Chapter 13: Proportion
- Direct and inverse proportion 5 min
Also for IGCSE Maths 0580
Which topics come up most in IGCSE Maths 0580 past papers, counted from every paper since 2004.