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5. Numerical methods

FP1 Notes and Examples

You will receive a student booklet with gaps for the solutions to the examples to be filled in and a teacher’s booklet with detailed worked solutions.

C3 Notes and Examples

You will receive a student booklet with gaps for the solutions to the examples to be filled in and a teacher’s booklet with detailed worked solutions.

Operations with Radical Expressions Color by Number

With this activity, students will simplify radical expressions using addition, subtraction, multiplication, and division. They will then color their answers on the picture according to the directions to reveal a beautiful, colorful mandala! As an added bonus, the final products make fabulous classroom decor! This activity is an excellent resource for sub plans, enrichment/reinforcement, early finishers, and extra practice with some fun. It is especially useful for end-of-year practice, spiral review, and motivated practice when students are exhausted from standardized testing or mentally “checked out” before a long break (hello summer!). Teachers and students alike enjoy motivating activities, so engage your students today with these fun coloring activities!

Set Theory PowerPoint and Handouts

An extensive introduction to Set Theory, generally aimed at Computer Science A Level students, A Level Mathematicians or first year Undergraduate students in either Computer Science or Mathematics. It is intended to cover two lessons, extra examples and discussion may be required if aiming at a lower ability. Includes: A simple starter to encourage discussion on how to categorise numbers, as well as how many there may be e.g. how many natural numbers are there? A handout featuring all definitions given in the PowerPoint A PowerPoint covering set notation, intersections, unions, set comprehension and set compression. More resources can be added upon request. Please do give feedback/suggestions!

OCR C3 (Old Spec.) Extension Questions

These word documents contain questions for the A-star students for the old OCR specification for Core Mathematics 3.

C3 A Level Summary

“cheat sheet” covering all C3 topics for CCEA A Level. Use for revision classes/exercises as a guide or as a comfort blanket for a class test.

OCR AS Maths Core 2 2017 Exam solutions - full explanations split by question

Fully explained and written solutions to the OCR 2017 AS Mathematics Core 2 exam paper. The questions are split by each part so that you can easily navigate to the parts you and the students want to look at. If you find this useful there are many other free exam solutions on my youtube channel: MissPennyMaths

Maths A level revision questions

This bundle includes question/answer files aimed at revising the topics from A level maths, and especially the Core 3 and Core 4 topics.

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.

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.

Erica's Errors On Numerical Methods

Erica is struggling with iteration and Newton-Raphson, as it's on the new &quot;Pure 2&quot; syllabus. Can you help her sort out her homework answers and explain what she's done wrong?

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.

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.

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!

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?

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 keywords. 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 free and premium resources! As always please RATE and FEEDBACK (comments good or bad) thank you!

A level maths - 2nd year

Selection of presentations that cover most of the 2nd year pure maths in the A level maths course

A level maths - 1st year

Selection of presentations that cover most of the 1st year pure maths in the A level maths course

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.

Physics A-level Revision Matching Pairs Games Bundle

Ten interactive competitive games on Physics A-level topics. These will make a very welcome break from other less thrilling means of revision. The Matching Pairs Game is a fun and competitive interactive whiteboard game in which two teams take it in turns to match tiles. The game automatically scores and has a built in timer in the event of a draw. Students really enjoy the competitiveness. This game won a Microsoft innovation award. An editor is separately available to make your own games; https://www.tes.com/teaching-resource/matching-pairs-interactive-game-creator-11063058 bennyjohn5@hotmail.com

Team Revision Tasks - Core 3 (Edexcel)

These are an attempt to break from the monotony of past papers in the run up to exam season. I have taken 2 or 4 (depending on whether they will fit on a page!) questions from past papers and put them on one sheet; I will photocopy onto A3 for students to have a go in groups and discuss. The aims/rules etc are all listed if you wish to follow them and hopefully they all make sense. I have also provided answers.

🌟 Understanding Convergence 🌟 A-Level Numerical Methods

An explanation of the different forms of convergence and how convergence is used in Numerical Methods. Common misconceptions are clarified. 🌟😊🌟 . . . PLEASE RATE THIS RESOURCE . . . 🌟😊🌟

🌔 Approximation 🌔 Numerical Methods 🌔 Challenging Real-Life Context

A challenging approximation PowerPoint for Numerical Methods A-Level based on real-life gravity variations around the Earth. It is worth discussing the causes of these variations for a more meaningful context. Also appropriate as an extension task for the new Higher GCSE syllabus. 🌟😊🌟 . . . PLEASE RATE THIS RESOURCE . . . 🌟😊🌟

🛍 Trapezium Rule 🛍 Interactive Activity including Effectiveness Evaluation

An interactive GeoGebra file for developing an understanding of the Trapezium Rule. Also included is a PowerPoint presentation demonstrating the development of the activity and suggestions for improvement. 🌟🌟🌟 . . 😊 . . PLEASE RATE THIS RESOURCE . . 😊 . . 🌟🌟🌟

Iterative Formulae

This lesson teachers students about the iterative formula. The ability to identify why there is a root between two points. The ability to generate an iterative formula. The presentation also demonstrates that not all iterative formulae work. The lesson follows with a worksheet for the students to attempt either in class or as a piece of homework. Answers are included.

Areas under graphs

Suitable for Higher Tier GCSE Mathematics or Further Mathematics, this resource introduces students to a small variety of methods for working out areas underneath graphs. Starting with the counting of squares method, it introduces the Trapezium Rule and others. A chart at the end allows students to record the different estimates they have in order to compare methods, and it concludes with a few thoughts about real-world applications and the basis for integral calculus.

Calculus Option IB HL Mathematics

Set of class activities, lesson plans, power points, tests, trial exam for IB HL Maths Calculus Option.

MEI Core 2 on a page

Revision sheet for OCR MEI Core Maths 2. Could be printed out A4 to use as a revision aide-memiore or A3 to use as a poster.

A level bundle pure & statistics

View in slideshow from beginning.

Interactive Games and Attention Grabbing Starters

In this collection I have tried to gather attention grabbing resources. Whether you are teaching cheeky monkeys or aloof A-level classes, these are real winners. The "Matching Pairs Interactive Game" and "Two Team IWB Quiz Game" use the interactive whiteboard in a creative and engaging way.

Estimating the area under the curve.

Introduction to numerical integration using left-end point estimate, right-endpoint estimate and trapezoidal estimate. Students start by doing the activity by hand, then use the file on their calculators.

Iteration Method - Staircase and Cobweb Diagrams

Presentation that shows learners how to use the iterative approach to find the roots of equations. Starts by locating roots by looking for the change in sign between certain values and leads on to an example of how to use an iteration method to find approximate solutions. Also I have added some autograph graphs that can be used to show students how to produce staircase and cobweb diagrams. SMART Notebook Express presentations can be used for free by using SMART online or by downloading SMART software, also free, I use it because it allows a more interactive presentation than a powerpoint. Just search 'SMART Notebook Express' and try it with my free SMART resource.

Bisection Method and Newton's Method

A class activity introducing the bisection method and Newton's method to find approximate solutions of equations.

Trapezium Rule

A presentation shows learners how to use the trapezium rule. SMART Notebook Express presentations can be used for free by using SMART online or by downloading SMART software, also free, I use it because it allows a more interactive presentation than a powerpoint. Just search 'SMART Notebook Express' and try it with my free SMART resource.

Physics / Maths Logarithms and Exponential formulae

This set of four lessons goes over the exponential formula used in Physics for radioactive decay as well as teaching the basic rules of logs and why natural logs are used.

A-Level Physics / Maths - Logarithms rules and algebra (Lesson plan and PowerPoint)

This is the second of three lessons that introduce the idea of logarithms The PowerPoint takes students through the difficulties in solving algebra with unknown powers and cumulative interest. The general simple rules of addition and subtraction of logarithms is discussed. This is part of the essential mathematics skills needed for A-Level Physics

C4 mark scheme bundle

This bundle includes all of the C4 worksheet mark schemes, if you purchase all of the mark schemes together they will be discounted by 50%.

C4 exam paper mark scheme

**All questions are completely new and have not been previously published, therefore students will not be able to have access to mark schemes or have seen them before.** A C4 exam paper mark scheme which has very similar questions to a real C4 exam.

C4 exam paper

**All questions are completely new and have not been previously published, therefore students will not be able to have access to mark schemes or have seen them before.** A C4 exam paper which has very similar questions to a real C4 exam. Answers can be found here: https://www.tes.com/teaching-resource/c4-exam-paper-mark-scheme-11368034

IB HL Mathematics Calculus Option Trial Exam November 2016

Need more practice? Try the HL Maths Calculus Option Trial Exam. Five questions covering the Calculus Option syllabus. Full solutions provided.