[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-207802-en":3,"doc-seo-207802-105":30,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},207802,7971474920318,"Mabel","https://ap-avatar.wpscdn.com/avatar/74000ee537e6b0ca360?x-image-process=image/resize,m_fixed,w_180,h_180&k=1788430171632181674",4,"Exam","GCSE Maths Revision Booklet - Algebra and Numbers","A GCSE Mathematics help booklet designed to refresh key GCSE Maths tools for learners who studied the subject some time ago. It supports revision for an introductory mathematics course, focusing on core syllabus topics and building from easier worked examples to more challenging problems. The material is organized into two main areas—Algebra and Numbers—with subtopics progressing through simplification, expansion, factorisation, solving equations, graphs, fractions, and indices.","GCSE MATHEMATICS HELP BOOKLET School of Social Sciences  \nThis is a guide to ECON10061 (introductory Mathematics) Whether this guide applies to you or not please read the  \nexplanation inside  \nCopyright © 2003, 2004 Osman Ouattara  \nAll rights reserved. No part of this document may be produced, stored in a retrieval system, or transmitted in any form, or by any means, electronic, mechanical, photocopying or otherwise, without the prior permission of the author.  \nAcknowledgements  \nThe author would like to express thanks to Alan Trickett for advice and helpful comments.  \nPREFACE  \nThis booklet is intended to help those who have done their GCSE Maths awhile ago and may have forgotten some of the material they learnt. It will help them revise the basic tools (covered in the GCSE Maths syllabus), which are needed to take the Introductory Maths course of the School of Economics Studies of the University of Manchester.  \nThe tools of mathematics are widely used in areas such as economics, business, accounting and finance, and being confident with these tools can only help students to successfully understand and study these subjects.  \nWe hope that you will work through this booklet, to give yourself a good start to your studies when come to Manchester.  \nThe booklet is divided into two main topics: Algebra and Numbers, which are subdivided into different subtopics. Within each these topics we have tried to go from the easiest examples to more difficult ones. However, as far asthe topics themselves are concerned you are free to start from Topic 1 or 2. At the end of the booklet you will find answers to all the exercises.  \nTABLE OF CONTENTS  \nTopic 1 ALGEBRA...........................................5  \n1. Manipulation ............................................5  \n1.1. Simplification of Expression .............................................................................. 5  \nOther forms of Simplifications ...............................................................................7  \n1.2 Expansion of Brackets ........................................................................................ 11  \nAnswer 1.2.1 ............................................................................................................ 13  \n1.3 Factorisation ........................................................................................................ 13  \n2. Solving Equations ...................................... 17  \n2.1 Solving Linear Equations.................................................................................... 17  \n2.2 Solving Quadratic Equations ............................................................................ 19  \n2.3 Solving Simultaneous Equations ..................................................................... 27  \n2.3.1 The substitution method .......................................................................... 27  \n3. Graphs .............................................. 32  \n3.1 Plotting Linear Graphs ...................................................................................... 32  \n3.2 Graphs and system of simultaneous equations ........................................... 34  \nTopic 2 NUMBERS........................................ 37  \n1. Fractions ............................................ 38  \n1.2 Adding and Subtracting Fractions................................................................. 39  \n1.2 Multiplying Fractions ......................................................................................... 40  \n1.3 Dividing Fractions ............................................................................................... 41  \n2. Power and Root ....................................... 42  \n2.1 Square root and cube root ............................................................................... 42  \n2.2 Indices ................................................................................................................. 43  \n2.2.1 Multiplication ","cbCaifax62UVFdPv","https://ap.wps.com/l/cbCaifax62UVFdPv","pdf",321889,1,48,"English","en",105,"# Topic 1 Algebra\n## 1. Manipulation\n## 1.1 Simplification of Expression\n## 1.2 Expansion of Brackets\n## 1.3 Factorisation\n## 2. Solving Equations\n## 2.1 Solving Linear Equations\n## 2.2 Solving Quadratic Equations\n## 2.3 Solving Simultaneous Equations\n## 2.3.1 The substitution method\n## 3. Graphs\n## 3.1 Plotting Linear Graphs\n## 3.2 Graphs and system of simultaneous equations\n# Topic 2 Numbers\n## 1. Fractions\n## 1.2 Adding and Subtracting Fractions\n## 1.2 Multiplying Fractions\n## 1.3 Dividing Fractions\n## 2. Power and Root\n## 2.1 Square root and cube root\n## 2.2 Indices\n## 2.2.1 Multiplication Rule\n## 2.2.2 Division Rule\n## 2.2.3 Power rule\n# Answers\n# References","[{\"question\":\"Who is this GCSE maths revision booklet intended for?\",\"answer\":\"It targets students who completed GCSE Maths some time ago and need to revise material they may have forgotten.\"},{\"question\":\"Which two main topics does the booklet cover?\",\"answer\":\"The booklet is divided into Algebra and Numbers.\"},{\"question\":\"What kinds of algebra and number skills are included?\",\"answer\":\"Algebra includes simplifying expressions, expanding brackets, factorisation, solving linear and quadratic equations, solving simultaneous equations, and plotting linear graphs. Numbers includes fractions, square and cube roots, and indices with multiplication, division, and power rules.\"}]","GCSE Maths Revision Booklet - Algebra and Numbers | PDF",1788601179,121,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":28},"gcse-maths-revision-booklet-algebra-and-numbers","",{"@graph":36,"@context":84},[37,53,67],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/exam/",3,{"item":52,"name":13,"@type":43,"position":11},"https://docshare.wps.com/document/gcse-maths-revision-booklet-algebra-and-numbers/207802/",{"url":52,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":61,"encodingFormat":60,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-09-05",true,{"@type":64,"interactionType":65,"userInteractionCount":4},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"Who is this GCSE maths revision booklet intended for?","Question",{"text":74,"@type":75},"It targets students who completed GCSE Maths some time ago and need to revise material they may have forgotten.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"Which two main topics does the booklet cover?",{"text":79,"@type":75},"The booklet is divided into Algebra and Numbers.",{"name":81,"@type":72,"acceptedAnswer":82},"What kinds of algebra and number skills are included?",{"text":83,"@type":75},"Algebra includes simplifying expressions, expanding brackets, factorisation, solving linear and quadratic equations, solving simultaneous equations, and plotting linear graphs. 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