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GCSE Mathematics · key term
The rate at which a quantity is changing at one particular point, represented by the gradient of a tangent there.
Used by AQA, Edexcel and OCR
Specification A15, R15 · Paper 1, Paper 2, Paper 3
The gradient at one particular point on a curve, representing the rate of change at that instant.
The rate at one particular value of the independent variable; it is represented by the gradient of the tangent to the curve at that point.
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Specification R15 · Paper 1, Paper 2, Paper 3
The rate at which one quantity is changing at one particular point or moment; graphically, it is the gradient of the tangent there.
Revise: Instantaneous Rates of ChangeA tangent is a straight line aligned with the curve at that point, matching its direction and steepness. Its gradient estimates the curve's instantaneous rate of change.
Specification 7.04b · Paper 1 (Foundation), Paper 2 (Foundation), Paper 3 (Foundation), Paper 4 (Higher), Paper 5 (Higher), Paper 6 (Higher)
Revise: Average and Instantaneous Rates of ChangeThe tangent’s gradient is the instantaneous rate of change. On a printed graph, draw the tangent carefully, choose two well-spaced points on that line, and divide its vertical change by its horizontal change. Because the line is drawn by eye, the result is usually an estimate.