Tooltip
These resources have been reviewed and selected by STEM Learning’s team of education specialists for factual accuracy and relevance to teaching STEM subjects in UK schools.
Exploring gradient functions
In this resource from Shirley Fall, students are presented with a general straight line y=mx+c and are shown that the gradient of the line between any two points that lie on the line is always equal to m. Students should be encouraged to explain the proof to check understanding.
Students then move on to curves and need to be clear that the gradient of a curve at a given point is equivalent to the gradient of the tangent to the curve at that point. Students then are required to find the gradient of successive chords between two points on the curve as one point moves closer to a fixed point.
Students are required to find the gradient of the curve y=x2 at different values of x leading to a generalisation for the equation of the gradient function. Students then explore families of curves each time finding a generalisation for the equation of the gradient function culminating in a generalisation for the equation of the gradient function for the curves with equations of the form y=ax2+bx+c.
An extension task asks students whether the gradient function of y=1/x follows the same rule.
The teacher notes give the proof that the gradient equation of y=mx+c is always equal to m and shows how to find the gradient function of y=ax2+bx+c
Show health and safety information
Please be aware that resources have been published on the website in the form that they were originally supplied. This means that procedures reflect general practice and standards applicable at the time resources were produced and cannot be assumed to be acceptable today. Website users are fully responsible for ensuring that any activity, including practical work, which they carry out is in accordance with current regulations related to health and safety and that an appropriate risk assessment has been carried out.
Downloads
Show downloads
Download all files as a .zip188.05 KB
Information on the permitted use of this resource is covered by the Category Three Content section in STEM Learning’s Terms and conditions.
