This 25-page resource covers all the required knowledge and techniques for using fixed point iteration to find roots of an equation, as required for the new A level. In each section 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 sections/topics are:
1.Introduction to the method
(a) creating an iterative formula from an equation f(x)=0
(b) using fixed point iteration to find successive approximations or an estimate of a root
© illustrating the covergence of the approximations on a cobweb or staircase diagram
2.Conditions where fixed point iteration fails
(a) situations where successive approximations do / do not converge to a particular root
(b) situations where successive approximations do not converge to any root
© how to predict whether an iterative formula will produce approximations that converge towards a root
(d) illustrating the covergence / divergence of the approximations on a cobweb or staircase diagram
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 and diagrams provided for solutions. The exercises contains over 35 questions for your students to complete. Answers to all exercises are included.
Here is an example of one of my A level resources that is freely available: