These PowerPoints form full lessons of work that together cover the full A level Further Maths course for the AQA exam board. Together all the PowerPoints include; • A complete set of notes for students • Model examples • Probing questions to test understanding • Class questions including answers • Individual whiteboard work • Links to exercises in ‘AQA approved textbooks by Hodder ed’ these can easily be edited for your textbook The PowerPoints can be used in the lesson and also given to students that have missed a lesson Videos of the lessons are all on You Tube so you can see the PowerPoint lessons fully first Please leave a review as it will really help me to improve my resources Introduction to Group Theory topics covers; Understand and use the language of groups including: * order * period * subgroup * proper * trivial * non-trivial Understand and use the group axioms: closure, identity, inverses and associativity Use of Cayley tables Understand and use Lagrange’s theorem. Recognise and use finite and infinite groups and their subgroups, including: groups of symmetries of regular polygons, cyclic groups and abelian groups. Identify and use the generators of a group Recognise and find isomorphism between groups of finite order

These PowerPoints form full lessons of work that together cover the new AS level Further Maths course for the AQA exam board. Together all the PowerPoints include; • A complete set of notes for students • Model examples • Probing questions to test understanding • Class questions including answers • Individual whiteboard work • Links to exercises in ‘AQA approved textbooks by Camb uni Press’ these can easily be edited for your textbook The PowerPoints can be used in the lesson and also given to students that have missed a lesson I have added ‘Further Maths 5 - Matrices Transformation’ and ‘Further Maths 23 - Network Flows’ for free download Please leave a review as it will really help me to improve my resources Binary operations covers; Understand and use binary operations including use of modular arithmetic and matrix multiplication Understand, use and prove the commutativity of a binary operation Understand, use and prove the associativity of a binary operation Understand and prove the existence of an identity element for a given set under a given binary operation Understand and prove the existence of an inverse element for a given set under a given binary operation Construct a Cayley Table for a given set and binary operation.

I have used this resource a few times with my classes to cover the whole topic of groups. This 24-page worksheet covers all the required knowledge and skills for FP3. Each section starts with introductory notes or examples, followed by an exercise for students to attempt. The sections are: 1. Sets, binary operations, closed/commutative/closed operations, identity elements and inverses. 2. Groups - definition of a group, order of a group, group tables 3. Multiplicative groups and cancellation laws 4. Groups using modular arithmetic 5.Symmetries of shapes 6. The order of an element 7. Cyclic groups and generators 8. Subgroups 9. Lagrange's theorem 10. Isomorphic groups The completed worksheet with all notes, examples and exercises completed (with fully-worked solutions) is also included.

An explanation on the various symbols used when talking about sets, each with an example. Also contains definitions for the sets of natural, integer, rational, real and complex numbers.

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!

Power Point presentation, 12 slides, Explaining the meaning of the basic concepts used in set theory, based on IB Mathematical Studies Syllabus. For a preview of the power point copy the following link on your browser: https://drive.google.com/file/d/0B8z00qLZV7OlTTBZaDNtNUlfOTg/view?usp=sharing

An extension lesson which introduces basic group theory (without the formalisation) applied to symmetries of a square. Cut-outs provided: students should stick pairs of squares back-to-back so that the numbers line up on either side. Answers to the worksheet also provided.

For the new A-Level Further Maths Specification, This checklist is for the Further Pure Maths 2 optional module This module features topics such as: ‘Number Theory’ ‘Group Theory’ ‘Complex Numbers’ ‘Matrix Algebra’ ‘Integration Techniques’ The checklist features a general overview of the topics and then there are seperate checklists that break down each chapter in the book, The checklist follows along nicely with the official edexcel A-Level further pure maths 2 textbook but it can also be used for the AQA further maths topics

MEI Further Maths, Extra Pure, Past Exam Questions by Topics: Groups. Past examinations questions from old FP3.

 * GSCE, IGCSE, IB, PSAT, and AISL - Exam Style Questions which covers all the related concepts required for students to unravel any International Exam Style Set Theory Questions  * Learner will be able to say authoritatively that:  I can solve any given Set Theory Questions involving:  Set Use of Language  Set Notations and Venn Diagram to describe Sets  Venn Diagrams are used in Mathematics to divide all possible number types into groups. They are also used in Mathematics to see what groups of numbers have things in common. Venn Diagrams can even be used to analyse music. We can analyse the characters in TV shows like “The Muppets” with a Venn Diagram  I understand and can apply Set Theory concepts in all fields of studies:  The general public applies arithmetic in grocery shopping, financial mathematics is applied in commerce and economics, statistics is used in many fields (e.g., marketing and experimental sciences), number theory is used in information technology and cryptography, surveyors apply trigonometry, operations research.