[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-113982-en":3,"doc-seo-113982-105":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},113982,1099513958762,"Logic","https://ap-avatar.wpscdn.com/avatar/1000023916a998db790?x-image-process=image/resize,m_fixed,w_180,h_180&k=1784791008015729253",4,"Exam","CambridgeMATHS - Stage 6 - Year 12 Mathematics Extension 2","CambridgeMATHS Stage 6 Year 12 Mathematics Extension 2 focuses on key Extension 2 syllabus topics for advanced study. The structure guides learners through complex numbers, formal proof methods, De Moivre and Euler connections, and a comprehensive progression in integration techniques, including standard integrals, substitution, partial fractions, and trigonometric forms. It further covers vectors in three dimensions and mechanics with problem-solving practice, supported by chapter reviews, appendices, answers, and an index.","YEAR 12  \nMATHEMATICS EXTENSION 2  \nCambridgeMATHS  \nSTAGE 6  \nDAVID SADLER I DEREK WARD  \nUniversity Printing House, Cambridge CB2 8BS, United Kingdom One Liberty Plaza, 20th Floor, New York, NY 10006, USA  \n477 Williamstown Road, Port Melbourne, VIC 3207, Australia  \n314–321, 3rd Floor, Plot 3, Splendor Forum, Jasola District Centre, New Delhi – 110025, India 79 Anson Road, \\#06–04/06, Singapore 079906  \nCambridge University Press is part of the University of Cambridge.  \nIt furthers the University’s mission by disseminating knowledge in the pursuit of education, learning and research at the highest international levels of excellence.  \n[www.cambridge.org](www.cambridge.org)  \nInformation on this [title: www.cambridge.org/9781108771054](title: www.cambridge.org/9781108771054)[ ](title: www.cambridge.org/9781108771054)© David Sadler and Derek Ward 2020  \nThis publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press.  \nFirst published 2020  \n20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1  \nCover and text designed by Sardine Design Typeset by authors/diacriTech  \nPrinted in Australia by Ligare Pty Ltd  \nA catalogue record for this book is available from the National [Library of Australia at](Library of Australia at www.nla.gov.au)[ www.nla.gov.au](Library of Australia at www.nla.gov.au)[ ](Library of Australia at www.nla.gov.au)[ISBN 978-1-108-77105-4 Paperback](ISBN 978-1-108-77105-4 Paperback)  \nAdditional resources for [this publication at www.cambridge.edu.au/GO](this publication at www.cambridge.edu.au/GO)  \nReproduction and Communication for educational purposes  \nThe Australian Copyright Act 1968 (the Act) allows a maximum of one chapter or 10% of the pages of this publication, whichever is the greater, to be reproduced and/or communicated by any educational institution for its educational purposes provided that the educational institution (or the body that administers it) has given a remuneration notice to Copyright Agency Limited (CAL) under the Act.  \nFor details of the CAL licence for educational institutions contact:  \nCopyright Agency Limited Level 15, 233 Castlereagh Street Sydney NSW 2000 Telephone: (02) 9394 7600  \nFacsimile: (02) 9394 7601  \nEmail: [info@copyright.com.au](info@copyright.com.au)  \nReproduction and Communication for other purposes  \nExcept as permitted under the Act (for example a fair dealing for the purposes of study, research, criticism or review) no part of this publication may be reproduced, stored in a retrieval system, communicated or transmitted in any form or by any means without prior written permission.  \nAll inquiries should be made to the publisher at the address above.  \nCambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party Internet websites referred to in this publication and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Information regarding prices, travel timetables and other factual information given in this work is correct atthe time of first printing but Cambridge University Press does not guarantee the accuracy of such information thereafter.  \nCambridge University Press acknowledges the Aboriginal and Torres Strait Islander Peoples as the traditional owners of Country throughout Australia.  \nTable of contents  \nIntroduction v  \nRationale vi  \nAbout the authors ix  \n1 Complex numbers I 1  \n1A The arithmetic of complex numbers 1  \n1B Quadratic equations 10  \n1C The Argand diagram 18  \n1D Modulus-argument form 22  \n1E Vectors and the complex plane 30  \n1F Curves and regions in the Argand diagram 37  \n1G Polynomials and complex numbers 45  \n1H Chapter review exercise 54  \n2 Proof 56  \n2A The language of proof 56  \n2B Number proofs 66  \n2C Proof by contraposition and by contradiction 70  \n2D ","cbCaisrrBxSAzItH","https://ap.wps.com/l/cbCaisrrBxSAzItH","pdf",7780979,1,313,"English","en",105,"# Introduction\n# Rationale\n# About the authors\n# Complex numbers I\n## The arithmetic of complex numbers\n## Quadratic equations\n## The Argand diagram\n## Modulus-argument form\n## Vectors and the complex plane\n## Curves and regions in the Argand diagram\n## Polynomials and complex numbers\n## Chapter review exercise\n# Proof\n## The language of proof\n## Number proofs\n## Proof by contraposition and by contradiction\n## Algebraic inequalities\n## Induction\n## Inequalities in geometry and calculus\n## Chapter review exercise\n# Complex numbers II: de Moivre and Euler\n## Powers of complex numbers\n## Trigonometric identities\n## Roots of complex numbers\n## Exponential form: Euler’s formula\n## Applications of exponential form\n## Chapter review exercise\n# Integration\n## The standard integrals\n## Algebraic manipulation\n## Substitution\n## Partial fractions\n## Denominators with quadratics\n## Integration by parts\n## Trigonometric integrals\n## Reduction formulae\n## Miscellaneous integrals\n## Chapter review exercise\n# Vectors\n## Coordinates in three dimensions\n## Vectors in three dimensions\n## The dot product\n## Applications of the dot product\n## Vector proofs in geometry\n## The vector equation of a line\n## Vector equations of circles, spheres and planes\n## Chapter review exercise\n# Mechanics\n## Forces and acceleration\n## Simple harmonic motion and time\n## Simple harmonic motion and displacement\n## Horizontal resisted motion\n## Vertical resisted motion\n## Projectile motion\n## Miscellaneous problems\n## Chapter review exercise\n# Answers\n# Index","[{\"question\":\"What syllabus scope does CambridgeMATHS Stage 6 Year 12 Mathematics Extension 2 cover?\",\"answer\":\"It covers the Mathematics Extension 2 syllabus and is designed to work alongside CambridgeMATHS Mathematics Advanced Year 12 and Extension 1 Year 12. It is rewritten to implement the new 2020 syllabus design and structure.\"},{\"question\":\"How is the complex numbers content organized in this resource?\",\"answer\":\"Complex numbers are presented in two major parts. “Complex numbers I” covers arithmetic, quadratic equations, Argand representation, modulus-argument form, vectors and complex plane regions, while “Complex numbers II” focuses on powers, trigonometric identities, roots, Euler’s formula, and applications.\"},{\"question\":\"What integration skills are included in the Integration chapters?\",\"answer\":\"Integration topics include standard integrals, algebraic manipulation, substitution, partial fractions, integrals involving quadratics in denominators, integration by parts, trigonometric integrals, reduction formulae, and miscellaneous integrals, each followed by chapter review exercises.\"}]","CambridgeMATHS - Stage 6 - Year 12 Mathematics Extension 2 | PDF",1785396602,789,{"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},"cambridgemaths-stage-6-year-12-mathematics-extension-2","",{"@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/cambridgemaths-stage-6-year-12-mathematics-extension-2/113982/",{"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","2026-07-30",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},"What syllabus scope does CambridgeMATHS Stage 6 Year 12 Mathematics Extension 2 cover?","Question",{"text":74,"@type":75},"It covers the Mathematics Extension 2 syllabus and is designed to work alongside CambridgeMATHS Mathematics Advanced Year 12 and Extension 1 Year 12. It is rewritten to implement the new 2020 syllabus design and structure.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"How is the complex numbers content organized in this resource?",{"text":79,"@type":75},"Complex numbers are presented in two major parts. “Complex numbers I” covers arithmetic, quadratic equations, Argand representation, modulus-argument form, vectors and complex plane regions, while “Complex numbers II” focuses on powers, trigonometric identities, roots, Euler’s formula, and applications.",{"name":81,"@type":72,"acceptedAnswer":82},"What integration skills are included in the Integration chapters?",{"text":83,"@type":75},"Integration topics include standard integrals, algebraic manipulation, substitution, partial fractions, integrals involving quadratics in denominators, integration by parts, trigonometric integrals, reduction formulae, and miscellaneous integrals, each followed by chapter review exercises.","https://schema.org",{"og:url":52,"og:type":86,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":88,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":91},[92,96,100,103,108,113,118,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":93,"show_sort_weight":94,"slug":95},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":97,"show_sort_weight":98,"slug":99},"Literature",80,"literature",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":101,"slug":102},70,"exam",{"id":104,"doc_module":4,"doc_module_name":46,"category_name":105,"show_sort_weight":106,"slug":107},5,"Comic",60,"comic",{"id":109,"doc_module":4,"doc_module_name":46,"category_name":110,"show_sort_weight":111,"slug":112},6,"Technology",50,"technology",{"id":114,"doc_module":4,"doc_module_name":46,"category_name":115,"show_sort_weight":116,"slug":117},7,"Healthcare",40,"healthcare",{"id":119,"doc_module":4,"doc_module_name":46,"category_name":120,"show_sort_weight":121,"slug":122},8,"Research & Report",30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":104,"slug":138},19,"General","general"]