Variation and Rates of Change B

Five lessons on what steepness means. A straight graph has one rate; a curved one has a different rate at every point, and there are exactly four ways it can bend. The last lesson runs the whole process backwards, turning a description in words into a graph.

5lessons

9syllabus points

3-4hstudy

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Steady rates

Constant Rates of Change

Straight means steady, and the gradient is the rate with its units attached

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Distance-Time Graphs

Every feature means something: flat, falling, straight and curved

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Changing rates

Variable Rates and Curves

Two questions, four answers, and why increasing at a decreasing rate makes sense

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Rates of Change in Context

Density and price are rates too, and inverse variation has no single one

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Drawing them yourself

Constructing Graphs from Descriptions

Phase by phase, plus the container problem and what corners mean

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Focus Area Snapshot

5lessons

9syllabus points

15worked examples

40questions

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 follows Variation and Rates of Change A, and it is the closest junior maths comes to calculus: finding the exact rate at a single instant, rather than an average over an interval, is precisely what Year 11 adds to what you learn here.

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