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MATHEMATICS GCSE for Edexcel Teacher’S Resource Jess Laffoley, Nathan Barker, Charmayne Bailey, Cecilia Freer, James Freeman, Kathryn Bigg, Susanne Mallett

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MATHEMATICS GCSE for Edexcel Teacher’S Resource Jess Laffoley, Nathan Barker, Charmayne Bailey, Cecilia Freer, James Freeman, Kathryn Bigg, Susanne Mallett Main intro back cover copy text here Rum- Brighter Thinking quo esequos doloreictus et mo volores am, conse la suntum et voloribus. Cerrore voloreriate pa prae es vendipitia diatia necusam ditia aut perrovitam aut eum et im ius dolut exceris et pro maxi- mintum num quatur aut et landese qua- tem. Sedit et am, eum quiassus ius con none eris ne nobis expliquis dolori ne cus, occaest, nam que exped quuntiatur atur additional back cover copy text here Rum- quo esequos doloreictus et mo volores am, conse la suntum et voloribus. Cerrore voloreriate pa prae es vendipitia diatia necusam ditia aut perrovitam aut eum et im ius dolut exceris et pro maxi- mintum num quatur aut et landese qua- tem. Sedit et am, eum quiassus ius con none eris ne nobis expliquis dolori ne cus, occaest, nam que exped quuntiatur atur reprori odi volores tiunto doluptaquis MATHEMATICS GCSE for Edexcel Teacher’s Resource Jess Laffoley, Nathan Barker, Charmayne Bailey, Cecilia Freer, James Freeman, Kathryn Bigg, Susanne Mallett GCSE Mathematics for Edexcel University Printing House, Cambridge CB2 8BS, United Kingdom Cambridge University Press is part of the University of Cambridge. It furthers the University’s mission by disseminating knowledge in the pursuit of education, learning and research at the highest international levels of excellence. www.cambridge.org Information on this title: www.cambridge.org/ukschools/9781107468146 © Cambridge University Press 2015 This 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. First published 2015 A catalogue record for this publication is available from the British Library ISBN 978-1-107-46814-6 Additional resources for this publication at www.cambridge.org/ukschools Cover image © 2013 Fabian Oefner www.fabianoefner.com Cambridge 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. notice to teachers The photocopy masters in this publication may be photocopied or distributed [electronically] free of charge for classroom use only. Worksheets and copies of them remain in the copyright of Cambridge University Press. The publishers would like to thank David Bowles and Rachael Horsman for their contribution to this Teacher’s Resource. Microsoft is a registered trademark or trademark of Microsoft Corporation in the United States and/or other countries ii © Cambridge University Press, 2015 Contents Contents Introduction v Changes to GCSE Mathematics 1 1F / 1H Calculations 9 2F / 2H Shapes and solids 16 3F / 3H 2D representations of 3D shapes 24 4F / 4H Properties of whole numbers 29 5F / 5H Introduction to algebra 34 6F / 6H Fractions 42 7F / 7H Decimals 48 8F / 8H Powers and roots 53 9F / 9H Rounding, estimation and accuracy 59 10F / 10H Mensuration 66 11F / 11H Perimeter 73 12F / 12H Area 79 13F / 13H Further algebra 87 14F / 15H Equations 97 14H Surds 106 15F / 16H Functions and sequences 113 16F / 17H Formulae 120 17F / 18H Volume and surface area 126 18F / 19H Percentages 133 19F /20H Ratio 138 20F / 21H Probability basics 145 21F / 22H Construction and loci 154 22F / 23H Vectors 160 23F / 24H Straight-line graphs 167 24F / 25H Graphs of functions and equations 175 25F / 26H Angles 186 26F / 28H Probability – combined events 193 27F / 29H Standard Form 200 27H Circles 206 28F / 30H Similarity 212 29F / 31H Congruence 220 iii © Cambridge University Press, 2015 GCSE Mathematics for Edexcel 30F / 32H Pythagoras’ theorem 226 31F / 33H Trigonometry 235 32F / 34H Growth and decay 245 33F / 35H Proportion 249 34F / 36H Algebraic inequalities 256 35F / 37H Sampling and representing data 263 36F / 38H Data analysis 271 37F / 39H Interpretation of graphs 278 38F / 40H Transformations 283 41H Transforming curves 289 Literacy in mathematics – helping your students to do their best 296 Preparing students for exams 303 Revision quizzes Introduction 307 Foundation quizzes 309 Higher quizzes 317 Foundation mark schemes 325 Higher mark schemes 342 Time-saving sheets Required formulae – Foundation 359 Required formulae - Higher 360 Crossword puzzle 361 Polygon diagrams 362 Angle facts 363 1 cm squared paper 364 2 mm graph paper 365 Axis grids 366 Square dotted paper 367 Isometric grid paper 368 Isometric dotted paper 369 Nets of common 3-D solids 370 Foundation exercise 31A question 1 diagram 372 Circle outlines 373 iv © Cambridge University Press, 2015 Introduction Introduction This book has been written to support you in delivering the Edexcel 1MA1 GCSE Mathematics specification. It accompanies Cambridge University Press’s GCSE Mathematics for Edexcel student resources, including the Foundation and Higher Student Books, Problem-solving Books and Homework Books. The Teacher’s Resource suggests how to use these resources for maximum benefit, as well as providing general advice on teaching the topics in the specification. STUDENT BOOK SUPPORT The structure of the Teacher’s Resource closely matches the Student Books. The Student Books are divided into chapters and sections, with each section covering a single topic. The Teacher’s Resource contains a chapter of teaching guidance for each Student Book chapter, covering both Foundation and Higher tiers, and is divided into corresponding sections. An introduction details what your students need to know before covering the topics in the chapter, learning outcomes and key vocabulary. The introduction also describes common misconceptions, suggesting how to address them, and offers‘hooks’ to introduce the topics in an engaging way. For each Student Book section, prompting questions are provided to promote discussion of the topic and to help students when working through the Student Book exercises. Also provided are suggested activities for starters, plenaries, enrichment and assessment – these include links to Web resources as well as classroom activities. At the end of each chapter, the Topic links section describes how the topics in the Student Book chapter link to previous and future learning, and to A Level topics. The Links to other Cambridge GCSE Mathematics resources list details the relevant sections in the Homework Books and Problem-solving Books, which you can set students as support, extension or homework tasks. GENERAL ADVICE AND SUPPORT This book includes a number of chapters offering general advice for teaching GCSE Mathematics: • The Changes to GCSE Mathematics chapter describes the main changes to the GCSE Mathematics qualification for first teaching from September 2015. • The Literacy in mathematics chapter contains ideas for helping students to become more literate in maths, including advice on extracting information, problem solving and reasoning. It also contains suggestions you can offer parents who are looking to support their child through the course. • The Preparing students for exams chapter contains ideas for supporting students’ revision. REVISION QUIZZES There are also eight revision quizzes (four calculator and four non-calculator) included for each tier, along with accompanying mark schemes. Each quiz covers multiple topics and is designed to take a maximum of 40 minutes to complete so you can use it within a single lesson. The quizzes contain the following icons: – permitted time – use of a calculator is permitted – use of a calculator is not permitted v © Cambridge University Press, 2015 GCSE Mathematics for Edexcel TIME-SAVING SHEETS Printable time-saving sheets are provided at the end of the Teacher’s Resource. These include lists of required formulae, 2 mm graph paper, squared and isometric paper, and other useful handouts. SCHEMES OF WORK To help you plan and navigate your way through the course, one-, two- and three-year schemes of work are available to download for free from cambridge.org/ukschools/gcsemaths-schemesofwork. The schemes of work break the course down by Student Book chapter, with suggested teaching times, key information and details of where to find supporting material in all of the resources in our GCSE Mathematics for Edexcel series. Each scheme of work is provided as an editable Microsoft® Word document, so you can customise it to your own requirements. GCSE MATHEMATICS ONLINE FOR EDEXCEL Further resources to support you and your students through their GCSE course are available on GCSE Mathematics Online for Edexcel, our brand new interactive teaching and learning subscription service. GCSE Mathematics Online for Edexcel includes lesson notes, games, interactive activities and quizzes, organised in the same chapter structure as the Student Books. It also includes a test generator, reporting and progression tracking. Please visit cambridge.org/ukschools for full details of all our GCSE Mathematics resources, including more information on GCSE Mathematics Online for Edexcel. ANSWERS Student Book answers Answers to all Student Book questions are available online as a free PDF. You can download the answer booklet from cambridge.org/ukschools/gcsemaths-studentbookanswers. The answer booklet is also included in the Teacher edition of GCSE Mathematics Online for Edexcel. Problem-solving Book answers Worked solutions with commentary are included in the back of the Problem-solving Books. Homework Book answers A booklet containing answers to all homework exercises is
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