Variation and Rates of Change A

Six lessons on proportion. Direct variation keeps a ratio fixed, inverse variation keeps a product fixed, and almost every question in the area is decided by working out which of those two you are looking at. The graphs then make the answer visible.

6lessons

14syllabus points

4-5hstudy

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The two kinds of variation

Direct Variation

Constant ratio, the three phrasings, and why a starting amount breaks it

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Inverse Variation

Constant product, and the same idea applied to the reciprocal

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What the graphs look like

Graphs of Direct Variation

A line through the origin whose gradient is the constant itself

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Graphs of Inverse Variation

A two-branch curve, and how to straighten it to check

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Using them

Solving Variation Problems

Four steps, a comparison shortcut, and a direction check that catches wrong methods

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Conversion Graphs

One line, read both ways, and the famous conversion that is not proportional

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Focus Area Snapshot

6lessons

14syllabus points

18worked examples

48questions

Where this leads

This is a Path focus area, sitting outside the Core and preparing you for Mathematics Standard and Advanced in Year 11. It pairs with Variation and Rates of Change B, which takes the same relationships and asks what their gradients mean. The habit built here, deciding what kind of relationship you are looking at before calculating anything, is worth more than any single technique.

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