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Newton-Raphson method - teaching notes and exercises

Newton-Raphson method - teaching notes and exercises

This resource covers the use of the Newton-Raphson method for finding roots of equations. You can project/print the resource so that you save time teaching the required knowledge and your classes can focus their time on understanding the process and attempting questions. The resource is made up of four sections: 1. Applying the Newton-Raphson formula iteratively to find approximations to roots 2. Derivation of the iterative formula F(x) for different functions f(x)=0, and begin to consider F'(x). 3. Errors and convergence 4. Graphical representation of the Newton-Raphson method Each section contains an introduction with the required knowledge and explanations, followed by an exercise of questions. The answers to all exercises are included.
langy74
Erica's Errors - A Level (Year 2) Bundle

Erica's Errors - A Level (Year 2) Bundle

Erica is struggling with many aspects of the A level mathematics course and needs help from your students. What you have here is 17of her homeworks, each with mistakes in solutions which your students need to find, correct and explain where Erica has gone wrong. These are purely designed to generate discussion and to allow students to demonstrate their understanding, whilst also allowing them to show their own methods of silving problems. These are all based upon the new A level curriculum.
alutwyche
Erica's Errors On Numerical Methods

Erica's Errors On Numerical Methods

Erica is struggling with iteration and Newton-Raphson, as it's on the new "Pure 2" syllabus. Can you help her sort out her homework answers and explain what she's done wrong?
alutwyche
Trapezium rule worksheet to introduce and practise using it (new A level)

Trapezium rule worksheet to introduce and practise using it (new A level)

This worksheet makes it easy to introduce and teach the trapezium rule to your classes. The first page has diagrams to illustrate the method and the derivation of the formula is broken down into steps for you to work through with your class. Projecting all this is so much easier than drawing it out by hand. The trapezium rule formula is then stated at the top of page 2, followed by 3 pages of examples of examination-style questions that test the use of the formula and your students' understanding (is the answer from the trapezium rule an underestimate or overestimate, can they use their answer to deduce an estimate for a related integral, etc). Answers to all the examples are provided.
langy74
Erica's Errors On Quadratics

Erica's Errors On Quadratics

Erica has made some silly mistakes on her quadratics homework, involving factorising, solving , completing the square, functions and the discriminant. Your students' task is to find the errors, correct them and explain what Erica has done incorrectly. This should generate discussion in class.
alutwyche
Core 3 Numerical Methods Team Quiz

Core 3 Numerical Methods Team Quiz

Based on Edexcel Core 3 Exam Questions on numerical methods - a useful revision resource. I run this as a team challenge, with each team selecting a question from each category and then ALL groups having a set time (between 3 and 5 mins) to complete the question (whiteboards and markers are great here). If the team that selected the question gets it right then they win the points allocated for that question, if not then the other teams have the opportunity to STEAL those points. My Year 12 students today really enjoyed this and have requested the powerpoint to use as revision at home!
woo73
Extension - Investigating Infinity

Extension - Investigating Infinity

Nine provocative questions to get pupils thinking about infinity. Each one has footnotes on the Powerpoint to guide towards the answer. What are Zeno’s paradoxes? Is 0.9999999999999999999… the same as 1? What is the smallest decimal number more than 3? What is infinity plus one? What is Hilbert’s Hotel? If something is true for the first million numbers, is it true for all the numbers? What is 1 – 1 + 1 – 1 + 1 – 1 … equal to? Are some infinities bigger than others? Are there more: numbers, fractions, or decimals?
dh2119
GCSE Iteration

GCSE Iteration

Covers all aspects of the GCSE specification on iteration (and term-to-term sequences). Includes an exercise and an explanation of why the iterative method works.
DrFrostMaths
Geometry: Radians 2 - Arcs, Sectors and Segments (+ lots of resources)

Geometry: Radians 2 - Arcs, Sectors and Segments (+ lots of resources)

This whole lesson builds on the introduction to the topic of radians. It looks at where the different formulas come from in radians and how to use them with some excellent examples and teaching slides. It comes also with a great starter, plenary, lesson objectives and key words. I have also included some exam questions with answers, a handout of useful angles to remember and a help sheet on mark scheme jargon to help build pupils understanding of exam papers. I recommend buying this with the first lesson as they fit together to teach pupils everything needed for AS level maths. NOTE: Feel free to browse my shop for more excellent free and premium resources and as always please rate and feedback, thank you.
ajf43
Numerical Methods for solving 1st order differential equations

Numerical Methods for solving 1st order differential equations

A presentation leading through the Euler method, improved Euler method and Taylor series method for solving first order differential equations. The presentation goes through one example using each of the three methods. The first steps are explained in detail with animations to help understanding. There is then a blank Excel table to enable you to demonstrate to the class how you could do it using a computer. Simply click the spreadsheet during slideshow view and the excel document will open up ready to be edited. The second presentation is exactly the same but with the formula filled in.
SianMatthews