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What you need to know
What you are required to know how to do is estimate the gradient of this curved line. This comes down to two possibilities:
- Calculate the instantaneous rate of change by drawing a tangent to the curve (a straight line just touching the curve) at the desired point, and then calculating the gradient of this tangent (which can be worked out using standard straight line methods). This will correspond to the gradient of the curve at that individual point.
- Calculate the average rate of change by drawing a chord (a straight line between two points on the curve), and then calculating the gradient of this chord. This will correspond to the average gradient of the curve between the chosen two points in time.
A question on this could be presented with many different contexts and you are expected to determine what the gradient means in that context by understanding the fact that it is a measure of the rate of change of whatever is on the y-axis with respect to whatever is on the x-axis.
Gradients and graphs are two things that many students struggle with and therefore having easy to use revision resources and worksheets that they can practise is essential. Whether you are a Maths tutor in York or a GCSE Maths tutor in London, you will find our gradients of a graph resource page useful.