MA21-07 Maths Coming soon
Instantaneous rate of change: the gradient of a tangent
This lesson is coming soon.
In this lesson
Distinguish the average rate of change between two points on a curve (gradient of a chord) from the instantaneous rate of change at a single point (gradient of a tangent), and calculate the latter by drawing and reading a tangent.
What it covers
- The difference between average rate of change (gradient of a chord, between two points) and instantaneous rate of change (gradient of a tangent, at one point)
- Drawing a tangent to a curve at a given point by eye and reading its gradient from two points on the tangent line
- Recognising the command 'find the rate of change at this point' as requiring a tangent, not a chord
Key words
For: AQA GCSE 8300, Edexcel GCSE 1MA1, Eduqas GCSE C300
On the specification
| Board | Spec | Statement |
|---|---|---|
| AQA GCSE 8300 | R15 | Interpret the gradient at a point on a curve as the instantaneous rate of change |
| Edexcel GCSE 1MA1 | R15 | Interpret the gradient at a point on a curve as the instantaneous rate of change; apply the concepts of average and instantaneous rate of change (gradients of chords and tangents) in numerical, algebraic and graphical contexts (this does not include calculus) |
| Eduqas GCSE C300 | HR16 | Interpret the gradient at a point on a curve as the instantaneous rate of change; apply the concepts of average and instantaneous rate of change (gradients of chords and tangents) in numerical, algebraic and graphical contexts |
For teachers
This GCSE Maths lesson teaches instantaneous rate of change: the gradient of a tangent. By the end, students should be able to distinguish the average rate of change between two points on a curve (gradient of a chord) from the instantaneous rate of change at a single point (gradient of a tangent), and calculate the latter by drawing and reading a tangent. It works through two worked examples and the mistakes examiners report.