Year 11: Introduction to Differentiation

1 dot points across 1 inquiry question. Click any dot point for a focused answer with worked past exam questions where available.

What is the difference between an average rate of change and an instantaneous rate of change, how does each one show up as a gradient on a graph (a chord for the average, a tangent for the instant), how do you estimate an instantaneous rate when you cannot read the tangent exactly, and how does collecting the gradient at every point build a brand new function, the derivative?

Describe the rate of change of a quantity, distinguishing the average rate of change over an interval (the gradient of the chord joining two points on the curve) from the instantaneous rate of change at a point (the gradient of the tangent there), estimate an instantaneous rate of change, read and interpret rates from a graph, and recognise that the gradient of the tangent at each point defines a new function, the derivative

A focused answer to the Year 11 Maths Advanced dot point on rates of change: the average rate as the gradient of a chord between two points, the instantaneous rate as the gradient of the tangent at a point, how to estimate an instantaneous rate, reading a rate off a graph, and the derivative as a new function giving the gradient everywhere.

20 min answer →