This resource covers the use of graphs and/or the sign-change rule to investigate roots of equations, as required for the new A level. It contains notes, explanations and examples to work through with your class followed by an exercise of questions for students to attempt themselves (answers included).
The notes cover:
(a) Use of a sketch of y=f(x) and y=g(x) to investigate roots of f(x) = g(x)
(b) Using a sketch of y=f(x)-g(x) to investigate roots of f(x)=g(x)
© Using the sign-change rule
(d) Conditions where the sign-change rule can be misleading
This projectable and printable resource will save you having to create or write out any notes/examples when teaching the topic, and will make things easier for your students as they can just work directly on the given spaces provided for solutions. Answers to the exercise are included.
Also included is a short activity to show how this method can be used to find smaller intervals where a root lies, which can be used as an introduction to iterative methods.
Here is an example of one of my A level resources that is freely available: