International Baccalaureate Resources to support the complete learning journey
PYP, MYP & Diploma Plus: The latest resources written for the 2011/12 Diploma curricula
Contents An introduction
The Pearson Baccalaureate Promise..........................................................................................1
PYP
PYP Readers and Companions.................................................................................................2-3
Primary Inquirer....................................................................................................................................4
MYP
Middle Years Mathematics...............................................................................................................5
Diploma
An introduction.....................................................................................................................................6
Our industry-leading authors....................................................................................................7-9 ..
Group 1: Language A.......................................................................................................................10 ..
Group 2: Language B................................................................................................................ 11-13 ..
Group 3: Individuals and Societies.................................................................................... 14-16 ..
Group 4: Experimental Sciences...............................................................................................17 ..
Group 5: Mathematics and Computer Science......................................................... 18-19 ..
Core Curriculum: Theory of Knowledge.............................................................................20
Contact your local consultant..................................................................................................... 21-22
An introduction The Pearson Baccalaureate Promise Our promise To provide teachers and students with the most up-to-date and comprehensive resources for the PYP, MYP and Diploma, and to make teaching and learning of the International Baccalaureate enjoyable, effective and inspiring.
How? Supporting the entire continuum We really understand the importance of preparing students for the future, be it from PYP to MYP or MYP to Diploma. Therefore, we’re proud to say we’re the only publisher to offer resources for the entire continuum, supporting students throughout their learning journey.
Written by industry-leading authors Simply put, our authors are what make our resources so special. This is why we only work with the top IB experts, who are all industry leaders in their respective fields. Ranging from senior examiners to teachers, curriculum review panel members to workshop leaders, our books couldn’t be written by a more qualified team. Turn to page 7 to learn more about them.
More than just printed books When you use our diploma resources, you don’t just get a printed book. We support our textbooks with a whole host of free online support materials such as eBooks, interactive quizzes, revision materials, exam practice and more. Visit www.peasonbacconline.com to find out more.
www.pearsonbacconline.com FREE online resources for the IB Diploma Make the most of your printed textbooks: Interactive quizzes Revision materials Exam practice Further research content.
All these extra resources and support at no extra cost!
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PYP Resources
Pearson Baccalaureate PYP Readers and Companions Programme
Ages 3-11
Inspiring global readers
Lower Primary
US GradeLevel
F
Pre K
1
2
Upper Primary
3
2
PYP Level
UK Year Level
Companions written by Jackie Holderness and Dr Lesley Snowball
Transdisciplinary themes Who we are
Where we are in place and time
How we express ourselves
UOI
UOI
UOI
1
My favourite things
Journeys
Colours
2
Friends
Houses
Creativity
3
Families
Holidays
Feelings
4
Our senses
Past and present
Celebrating
5
A new baby
Home sweet home
Pictures that tell stories
6
Emotions
People around the world
Artists
7
Our bodies
Mapping
Communicating
K
1
2
4
3
8
Right or wrong?
Different places, different lives
World music
5
4
9
What’s in a name?
Legacies
Architecture
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5
10
Healthy body, healthy mind
World religions
Media
PYP Resources
Using an international inquiry-based approach, the Pearson Baccalaureate PYP Readers and Companions Programme motivates learners to develop important inquiry-based reading strategies. 120 high quality, inquiry-based readers designed as a ready-made library of titles, with different styles and designs to ensure your children have access to the right book to develop their interest in reading.
Ages 3-11
9 engaging companions exploring each level’s individual units with open-ended activities to support group and individual work. A perfect starter programme of inquiry or for adding to existing resources.
Transdisciplinary themes How the world works
How we organise ourselves
Sharing the planet
UOI
UOI
UOI
Movement
Working together
Animals
Push and Pull
In town
How we use things
Where food comes from
Communities
Water
Growth
Planning
Habitats
Discoveries and inventions
How things are made
Planet in danger
Mammals
Be prepared
Life cycles
Water
Weather and seasons
Machines
Cities
Global issues
Changing Earth
People on the move
Pollution
Renewable Energy
Government systems
Endangered species
companion guides
Disappearing forests
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PYP Resources
Primary Inquirer Series Dr Lesley and Kenneth Snowball
Ages 3-11
Flexible resources for your PYP or inquiry teaching The 20 inquiry-based unit kits offer a themed set of springboard ideas and are designed to support the development of new units and the enhancement of existing units through collaborative planning. Written by the teacher trainers who developed the first resources for inquiry-based education. Each unit has been developed, tried and tested with teachers to ensure complete suitability for every teachers needs. Complete flexibility allows you to purchase individual topics or a range of topics to fit in with your programme of inquiry. An Inquiry into:
Teacher Resources
General introduction
Defining the unit
The strand grid
The integration web
The organising theme model
Book
The multiple intelligences grid
The concept questions taxonomy
The learning centres framework
The unit of inquiry planner
Putting it into practice with parents
Student Resources
Early Years Starter activities Main inquirer activities Learning Centres Summarising activities Assessments Homework activities
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CD 1
Lower Primary Starter activities
CD 2
Upper Primary Starter activities
Main inquirer activities Level 1 l Level 2 l l Level 3 l l l
Main inquirer activities Level 1 l Level 2 l l Level 3 l l l
Summarising activities
Summarising activities
Assessments
Assessments
Homework activities
Homework activities
CD 3
MYP
International Mathematics for the Middle Years Meet the needs of all middle-school students studying Mathematics This five-book series is tailored for students studying International Baccalaureate MYP. All examples and exercises take an international viewpoint, giving students an opportunity to learn Mathematics with a global perspective. Graded exercises have colour-coded questions to clearly identify the level of difficulty, allowing flexibility within the classroom. Investigations encourage students to seek knowledge and develop research skills. Assessment Grids ease the task of assessment for the teacher and provide students with guidelines for understanding the criteria required to succeed. ID Cards, Mathematical Terms and Reading Mathematics all assist in the development of mathematical literacy. The Interactive student CD provides an electronic version of the book links to Worksheets, Technology Applications and further enrichment and review exercises.
Student Book
Following an International GCSE curriculum instead of MYP? We also produce resources specifically for Edexcel and Cambridge specifications, all written by highly experienced teachers and examiners. Visit www.pearsonglobalschools.com/IGCSE to find out more.
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Diploma
Published for the International Baccalaureate Diploma Our Comprehensive Guarantee As part of the Pearson Baccalaureate promise, we can guarantee that our resources are produced by the very best expert authors and truly are comprehensive. You can rest assured that we have all you need to teach the IB curricula – whether using textbooks, eBooks or our online support materials, Pearson Baccalaureate really does offer the complete IB solution. We believe this so much, we’ve even put our stamp on it.
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Clear links to TOK and the IB Learner Profile throughout the books, as well as advice on the Internal Assessment and the Extended Essay.
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A suite of textbooks, eBooks and online resources supports teachers and students at every level – in the classroom, during independent study and for revision.
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Each book covers the subject guide fully, including any Options material, for the most up-to-date syllabus.
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Packed full of exam-style assessment opportunities using questions from past papers, as well as guidance from subject experts and examiners.
The Pearson Baccalaureate Series Group 1 Language A
Group 2 Language B
Group 3 Individuals and Societies
Group 4 Experimental sciences
Group 5 Mathematics and Computer Science
NM/SL NS/HL
Français B Livre de professeur PEARSON BACCALAUREATE
AMÉLIE NADEAU
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With integrated online learning resources! Visit www.pearsonbacconline.com
Visit www.pearsonbaccalaureate.com to download sample chapters and sign up for regular eNewsletters.
Core Curriculum
Diploma
Our Authors Learn more about our experts As you may have realised, we’re proud to be working with such industry-leading experts. Our authors have the in-depth knowledge that comes only with years of experience as IB teachers and practitioners. This means they know how and what to write to make teaching and learning the IB Diploma enjoyable, effective and inspiring. Alan Law is Teacher-in-Charge of Psychology at The English College in Prague, and is an Assistant Examiner in Psychology. He has a postgraduate diploma and an MSc in Occupational Psychology, and as a qualified English language teacher also has experience Psychology training teachers in UK summer schools.
Environmental Systems and Societies
History
Andrew Davis is the Head of Environmental Science at St. Edward’s School, Oxford, where he introduced the IB ESS course. He worked in South East Asia for 10 years as part of the Royal Society’s Rainforest Research Programme, examining the effects of rainforest disturbance on insect communities. Brian Mimmack has taught the IB since 1979, and is currently Humanities Chairperson at the International School of Düsseldorf, Germany. A former Deputy Chief Examiner and External Advisor for History, and the Principal Examiner for Paper 1, Brian is also heavily involved in IB curriculum development and assessment.
Catrin Brown teaches IB Chemistry and Biology at Lester B. Pearson United World College of the Pacific in Canada. Having taught international curricula for over 25 years, her IB roles have included that of Assistant Examiner, Senior Moderator, a faculty member on the Chemistry Online Curriculum Centre and workshop leader.
Physics
Chris Hamper began his IB Physics teaching career at Atlantic College UWC in Wales in 1990. In 1996 he moved to the Red Cross Nordic UWC in Norway, where he set up the Physics department and coordinated the CAS programme. Chris is an IB Examiner, a moderator for Internal Assessments and a workshop leader.
Christian Bryan-Zaykov has taught A-level and IB Psychology since 1998. He currently works at the American International School of Budapest, where he teaches Psychology, History and Environmental Systems. Psychology
Christos Halkiopoulos holds degrees in general and applied Psychology from the University of London. He has been teaching IB Psychology at St Clare’s, Oxford since 2003. Christos is an IB Examiner and workshop leader, and a member of the British Psychological Society and the Psychology Association of Business Psychologists.
History
Mathematics
History
Daniela Senés has taught IB History and ToK since 1986. She has been an IB History Examiner since 1996, marking Papers 1 and 3, Extended Essays, and moderating Internal Assessments. Daniela is now an external advisor for the IB school-based syllabus World Politics and International Relations, and a mentor for online Extended Essay supervision workshops and examiners’ training workshops. David Wees is currently the learning specialist for technology at Stratford Hall in Vancouver, British Columbia. He has worked as a mathematics and science teacher in NYC, London, Bangkok and Vancouver. He has presented at workshops on such topics as Interactivity & Multimedia in Mathematics, Computer-Based Math, Social Media, The Effect of Changing Communication Tools on Education, and other topics related to the use of technology in education. Eunice Price has taught IB History since 1977, and in 1996 was appointed an IB Examiner. She is currently a Team Leader for History Extended Essay marking and the Principal Examiner for Time Zone 2 for Paper 2. She has led a number of IB teacher training workshops. Since 1999, Eunice has been Head of History at the United World College of the Adriatic in Trieste.
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Diploma Garrett Nagle has taught at St Edward’s School, Oxford since 1986. He has been an IB Examiner and moderator since 2004 and has been involved in over 50 textbooks and numerous articles. He is an IB Deputy Chief Examiner, a team leader, question setter and workshop Environmental leader, as well as an AQA Assistant Principal Systems and Societies Examiner. He is Chairman of the Oxford Geographical Association.
Mathematics
Economics
History
Jason Welker teaches IB and Advanced Placement Economics at Zurich International School in Switzerland. He has served as co-curriculum author/subject matter expert in the creation of the online IB Economics courses. He also created and maintains Welker’s Wikinomics, a website for economics students and teachers. Jo Thomas has more than 20 years’ experience as Head of History at three leading IB schools: Munich International School, United World College of South East Asia (Singapore) and the British School of Brussels, where she is currently Head of History and Politics. Jo is also an IB Examiner for History and an IB workshop leader.
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Keith Ord has taught physics for the IB Diploma for over 15 years, in 4 different countries. He has over 10 years as an Examiner and an Internal Assessments moderator, and a workshop leader. Physics
Mathematics
Ibrahim Wazir has more than 30 years of teaching experience. He has been Chief Examiner for Further Mathematics, Deputy Chief Examiner for HL, and served on three Curriculum Review Committees. Ibrahim is the Math Department Chair at Webster University in Vienna where he received the Excellence in Teaching Award in 1993.
Keely Rogers has taught the IB Diploma History program for over 15 years. She has taught at the UWC of S E Asia, the International School of Brussels and is currently Head of Group 3 at ACS International school in Surrey. She is a former faculty member for History on the History Online Curriculum Centre, an experienced IB History workshop leader, and a Senior IB Examiner in two papers.
Mathematics
Kevin Frederick teaches high school mathematics at the American International School in Vienna. He worked as a computer programmer before becoming an educator in 2003. His desire is to see technology make the same advances in math education that it has in the fields of science and mathematics. Kevin has taught in Thailand, Slovakia, Israel and Austria. Mike Wakeford has been involved in international education for almost twenty years, teaching both mathematics and physics courses preparing students for the International Baccalaureate Diploma Programme. In particular, he has been involved in developing support materials to engage students studying mathematics using dynamic software such as Autograph for over a decade.
Pat Tosto is a lifelong educator leader with a speciality in IB Diploma Biology. She is an Assistant Examiner for the IB Internal Assessment. Her experience includes 25 years of educating students in Biology HL, and 20 years leading and facilitating workshops for IB. Biology
Mathematics
Biology
Peter Ashbourne has been a Mathematics teacher for 30 years and is now the Principal of St George’s School Neuchatel. He was involved in the curriculum reviews of IB Higher and Further Mathematics. He is a founding member of the International Schools Mathematics Teachers Foundation (ISMTF), and has regularly presented at their workshops. Randy McGonegal has been teaching for 37 years, the last 25 as an IB Biology instructor. He is an IB Assistant Examiner (HL Paper 3), has consulted on implementing and improving many IB programs in North America and has led numerous IB workshops.
Ron Carrell has been a teacher of Math Studies since 1995. He has been the presenter of numerous mathematical workshops in Hillsborough County, Florida. He was a finalist for Teacher of the Year in 1988. He has also been President of the Florida Association of Mu Mathematics Alpha Theta. Sean Maley teaches IB Economics at the American International School of Bucharest, Romania. He has served as co-curriculum author/subject matter expert in the creation of the online IB Economics courses.
Economics
Diploma
Theory of Knowledge
Sue Bastian has been involved with the IB for three decades and is widely known as one of the architects of the current Theory of Knowledge programme. She began teaching ToK, Psychology, and Philosophy at the Philippines in 1974 before moving to the United Nations International School in New York City in 1980. Sue has been Deputy Chief Examiner and Chief Examiner for ToK and is currently an IB Assistant Assessor, consultant, and workshop leader. Sue’s team of co-authors bring with them a wealth of TOK teaching experience from all parts of the world.
Amélie Nadeau has been teaching IB French in Europe and Asia for 14 years. She is a Language B workshop leader for the Middle Years and Diploma Program. She is also an IB Examiner. FranÇais B
oncepción Allende Urbieta has lived and worked as a teacher C and administrator in education in Mexico, Spain, and Equatorial Guinea. She started teaching IBDP in 1996 in Norway. Since then she has been involved in the teaching of the IBDP in Switzerland, Scotland, and England. She has been a IB Examiner, workshop leader, and a DP school’s visitor. She is currently completing a PhD in Applied Linguistics, specialising in teaching Spanish as a foreign language. Español B
Conrad Hughes teaches English and ToK at the International School of Geneva, where he coordinates the Diploma Programme. He is an IB senior moderator for English A and leads workshops for the IB on English and DP coordination. From 2009 to 2011 he sat on the IB curriculum board. He holds a PhD in English literature. English A
Jan Adkins has taught IB English at St Petersburg High School in Florida for 22 years prior to her recent retirement. She has worked as an English A assistant examiner as well as an IB teacher trainer for 15 years. Jan has also worked as a consultant for IBM, producing various instructional products for IBM Education in Atlanta and Thornwood, New York.
Mathematics
Tim Garry has taught mathematics since 1984 and been Head of Mathematics at three international schools. He has been an IB Mathematics HL Assistant & Senior Examiner, on curriculum review committees and exam writing teams. Since 1992, Tim has delivered numerous teacher workshops. Tim has enjoyed leading several student service projects to Malawi.
William Ward has spent 38 years teaching, spending 20 of those teaching IB Diploma Biology. He has led over 60 IB Biology workshops and has been an Assistant Examiner for 12 years. He has been involved with the translation of standards in securing college Biology credit for IB Biology in North America.
Marie-Laure Delvallée is Head of Additional Languages at Sevenoaks School. She is a Principal Examiner for the IB as well as an IB workshop leader. She has taught French on OSC’s Intensive Spring Revision Courses and Cambridge Summer Schools. FranÇais B
Mike Ford is the High School Curriculum Coordinator at the International School of Lyon. He has an MA in Chemistry from Oxford University and 19 years’ experience teaching IB Chemistry Physics and ToK. He has been a Deputy Chief Examiner in Chemistry and led workshops throughout the world. Chemistry
Paul Barclay has nearly 40 years’ experience of teaching mathematics in schools in Scotland, USA and Germany where he was Head of Department of the International School. He has taught IB Mathematics courses for 29 years and together with a UK exam board has developed an internationally-recognised preDiploma syllabus. Paul was also Chair of the ECIS Mathematics Committee. Mathematics
Peter Flynn currently teaches a variety of Mathematics and Mathematics education subjects at University of Melbourne’s Graduate School of Education. He uses CAS technology in Mathematics teaching, learning and assessment. Peter is an experienced T-3 Instructor who has presented many workshops to both Australian and international audiences. Mathematics
English A
Maite de le Fuente Zofío has been a Spanish IB teacher since 1993. She has been an IB Assistant Examiner for Spanish HL and the extended essay, as well as an internal moderator since 1996. She is also Team-Leader Examiner for Spanish B HL paper 1. She now teaches at the Jakarta International school. Español B
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Diploma
English A: Literature Jan Adkins & Conrad Hughes
Student textbook and online resources written for the 2011 Language A syllabus Key features: nsive
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Integrated with free online learning resources at www.pearsonbacconline.com to support and extend study.
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Clearly differentiated content for both Standard and Higher Level students.
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Extensive modelling exercises for students, covering each of the four parts of the curriculum.
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Includes further reading lists and glossary of terms.
Visual stimuli such as photos and graphics engage students and illustrate key concepts.
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Learning outcomes outline what will be covered in the following chapter.
TOK boxes stimulate higher-level thinking skills and encourage students to question their ideas and the source of their knowledge.
Diploma
Français B Marie-Laure Delvallée l Amélie Nadeau
Student Book, Teacher’s Guide and online resources written for the 2011 Language B syllabus
NM/SL NS/HL
Français B Livre de professeur
Key features: PEARSON BACCALAUREATE
Fully tailored to the 2011 FranÇais B syllabus, including all core themes and a broad spread of options. Clearly differentiated content for both Standard and Higher Level students. Integrated with free online learning resources at www.pearsonbacconline.com to support and extend study as well as comprehensive answers to all exercises in the student book. With integrated online learning resources! Visit www.pearsonbacconline.com
AMÉLIE NADEAU
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Supported by a Teacher’s Guide containing teaching guidance and Schemes of Work.
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A weekly updated online subscription service (Exclusif – see page 13) offering current, topical texts and interactive exercises to save you time searching for relevant resources.
Entraînement à l’oral interactif (finir)
Imaginez que vous participiez à une émission de radio animée par le célèbre psychologue Dr Bonconseil. Avec un ou une partenaire, choisissez une des situations décrites ci-dessous.
(connaître) le frère de Cécile ?
Choisissez ensuite le rôle de chacun : ado ou Dr Bonconseil. Préparez le dialogue que vous aurez au téléphone avec le Dr Bonconseil. Dans ce dialogue, vous exposerez votre problème au Dr Bonconseil et vous lui demanderez des conseils. Puis changez de rôle pour chaque situation.
(aller) en colonie de vacances l’été, les enfants (écrire) une lettre à leurs parents tous les jours.
4 Quel cadeau 5 Nous restaurant en famille.
(penser)-tu acheter pour l’anniversaire de ton père ? Côté ados
(boire) toujours du vin avec le repas quand nous allons au
A Vos parents sont extrêmement stricts et ne vous laissent jamais sortir. Vous ne savez pas comment les convaincre de vous faire confiance.
6 Les enfants (ne jamais ranger) leur chambre, (ne jamais éteindre la lumière) et (ne jamais être) prêts à l’heure ! Il (valoir) mieux ne pas avoir d’enfants !
B Vous aimeriez partir en vacances avec vos amis cet été. Vous ne savez pas comment demander la permission à vos parents.
Zoom grammaire Donner des conseils/faire des suggestions Voici quelques verbes et expressions pour donner des conseils :
EntraÎnement à l’oral interactif boxes provide practice for the oral assessments.
C Vous parents ne veulent pas vous laisser choisir vos vêtements seul(e). Vous aimeriez aborder ce sujet délicat avec eux.
D Vos parents sont divorcés depuis trois ans. Votre père a rencontré quelqu’un et ce soir, il veut vous présenter la nouvelle élue de son cœur. Vous ne savez pas comment vous comporter.
– conseiller à quelqu’un de faire quelque chose : Je te/vous conseille de parler avec tes/vos parents plus ouvertement. – suggérer à quelqu’un de faire quelque chose : Je vous suggère de permettre à votre fille de téléphoner à ses amies le soir. – Pourquoi … ? Pourquoi ne pas lui permettre de sortir en boîte une fois par mois ?
Côté parents
– Il est important/essentiel/utile/conseillé/recommandé/urgent, etc. + de + infinitif (il est + adjectif + infinitif) : Il est important de trouver un juste équilibre entre l’autorité et le laisser-faire si l’on veut que nos enfants soient épanouis.
1 En rangeant la chambre de votre fille, vous avez trouvé son journal intime. Vous ne savez pas si vous devez lui avouer que vous n’avez pu résister à la tentation de le lire …
– devoir + infinitif : Vous devez respecter les règles et les couvre-feux que vos parents vous imposent si vous voulez gagner leur confiance.
2 Votre fils passe tout son temps libre devant son écran d’ordinateur. Que faire ?
– Il faut + infinitif : Il faut entamer un dialogue constructif avec les adolescents.
Activité à l’écrit boxes provide practice on the written response through a range of texts.
– Il vaut mieux + infinitif : Il vaut mieux discipliner ses enfants que de les laisser faire tout ce qu’ils veulent.
3 Depuis quelques temps, votre fils rentre tard, passe ses week-ends avec une bande de nouveaux copains. Vous vous inquiétez et aimeriez lui faire comprendre que vous n’aimez pas ses nouvelles fréquentations sans le braquer.
– En + participe présent : C’est en dialoguant régulièrement avec vos parents que vos relations s’amélioreront. Pour donner des conseils, on peut aussi utiliser : – le conditionnel présent (voir page 00) : Il serait plus judicieux d’établir des règles en collaboration avec votre ado. – L’impératif (voir page 00) : Établissez des règles claires.
4 Vous avez remarqué que les vêtements de votre fils sentent la cigarette.
Activité à l’écrit
– Il faut que + subjonctif (voir page 00) ou il est + adjectif + que + subjonctif : Il faut que votre enfant comprenne qu’il est encore trop jeune pour prendre des décisions importantes seul. Il est essentiel que vos parents puissent vous faire confiance.
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Vos parents sont très stricts et vous interdisent presque tout (sorties avec les amis, choix de vêtements, programmes télévisés, etc.). Vous ne supportez plus cette situation. Vous décidez de leur écrire une lettre dans laquelle vous essayez de leur faire comprendre que vous avez besoin d’un peu desociaLes liberté et qu’ils peuvent vous faire confiance. (250–400 mots) Les reLations reLations sociaLes Les
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Pour vous vous aider aider … … Pour Dans le le débat, débat, les les aspects aspects suivants suivants peuvent être abordés … Dans – Proposition Proposition de de loi loi contre contre la la fessée. – – Le Le rôle rôle des des parents. parents. – – Les Les droits droits et et devoirs devoirs des des parents. parents. – – Les Les droits droits et et devoirs devoirs des des enfants. enfants. – – L’autorité L’autorité parentale parentale et et comment comment l’exercer. – – La La nécessité nécessité d’établir d’établir des des règles. règles. – – Une Une éducation éducation parentale parentale sans sans règle. – – Proposition Proposition de de solutions. solutions. –
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Queladjectif adjectif du duparagraphe paragrapheFFsignifie signifie «« fausse fausse »» ?? 44 Quel Conseils de de l’examinateur l’examinateur Conseils Pour réussir réussir son son oral, oral, ilil faut faut … Pour – essayer essayer de de prendre prendre la la parole parole le plus souvent possible sans pour autant couper les autres sans – arrêt. arrêt. – laisser laisser tout tout le le monde monde s’exprimer. s’exprimer. – – écouter écouter ce ce que que les les autres autres disent disent de façon à pouvoir réagir de manière adéquate et répondre – aux arguments arguments avancés. avancés. aux – poser poser des des questions questions sisi on on ne ne comprend pas un argument avancé. – – aider les participants qui ont du mal à prendre la parole en leur posant des questions. – aider les participants qui ont – être être convaincant/e convaincant/e en en avançant avançant des arguments pertinents et en les défendant judicieusement. –
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11
Diploma
Español B Concepción Allende Urbieta & Maite de la Fuente-Zofío
Student Book, Teacher’s Guide and online resources written for the 2011 Language B syllabus Key features: Fully tailored to the 2011 Español B syllabus, including all core themes and a broad spread of options. Clearly differentiated content for both Standard and Higher Level students. Integrated with free online learning resources at www.pearsonbacconline.com to support and extend study. nsive
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Supported by a Teacher’s Guide containing teaching guidance and Schemes of Work, as well as comprehensive answers to all exercises in the student book.
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A weekly updated online subscription service (Exclusiva– see page 13) offering current, topical texts and interactive exercises to save you time searching for relevant resources.
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Datos Interasantes place the material in real-life contexts and give additional information to aid students’ understanding of a topic. They also prompt further enquiry. 10
CALENTAMIENTO GLOBAL, CAMBIO CLIMÁTICO Y DESASTRES NATURALES
TEMAS TRONCALES: ASUNTOS GLOBALES
Una inundación es un desastre natural causado por la acumulación de lluvias y agua en un lugar concreto. Puede producirse por lluvia continua, una fusión rápida de grandes cantidades de hielo, o ríos que reciben un exceso de precipitación y se desbordan, y en menos ocasiones por la destrucción de una presa. La inundación de gran magnitud más reciente es la Inundación de Tabasco y Chiapas (México) de 2007, que ocurrió entre el 28 de octubre y el 27 de noviembre del 2007, a causa de crecidas históricas en los ríos que recorren ambas entidades. El desastre se dio en la capital tabasqueña, la ciudad de Villahermosa y en los municipios del extremo norte de Chiapas.
Sobre el efecto Coriolis El efecto Coriolis, descrito en 1836 por el científico francés Gaspard-Gustave Coriolis, es el efecto que se observa en un sistema de referencia en rotación (y por tanto no inercial) cuando un cuerpo se encuentra en movimiento respecto de dicho sistema de referencia.
Incendios forestales
Hace años hubo en España una campaña para crear conciencia sobre la importancia de cuidar los bosques. El lema era el siguiente:
Actividad intertextual boxes provide practice on the written response through a range of texts.
Actividad oral interactiva Para más información sobre inundaciones, dirígete a www.pearsonhotlinks.com y escribe el título o el ISBN de este libro. Después, selecciona el enlace número 10.29, 10.30 y 10.31. Elige algunas fotos de los enlaces que te proponemos (u otros) y haz una presentación oral sobre el tema.
Cuando un bosque se quema, algo suyo se quema. Poco después alguien añadió:
Sequía
Cuando un bosque se quema, algo suyo se quema, señor Conde.
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¿Cuál crees que es la diferencia entre los dos lemas? Se cree que cada año muchos de los incendios forestales son provocados. En muchos casos, en esas zonas se consiguen permisos para construir casas poco después.
Visual stimuli such as photos and graphics engage students and illustrate key concepts.
Inundación
Datos Interesantes En la mitología maya Huracan o Hurakan (él de una pierna) fue el dios del fuego, viento y de las tormentas. Es representado como un ser con cola de serpiente y también de aspecto reptil, porta, un objeto humeante (posiblemente una antorcha) y una gran corona. De su nombre proviene la palabra huracán que designa al fenómeno meteorológico. Según la mitología, fue uno de los dioses que participaron en la creación del hombre a partir del maíz. Hurakan había enviado El Gran Diluvio maya, un diluvio universal, enviado para destruir a los primeros hombres que habían enfurecido a los dioses. El había vivido en las nubes sobre la inundada Tierra mientras la repetía empujando el agua hasta las costas originales.
CALENTAMIENT
O GLOBAL, CAM Una sequía es un modelo meteorológico duradero consistente en unas condiciones BIO CLIMÁTICO
Un incendio forestal es un desastre natural que destruye prados, bosques, causando grandes pérdidas en vida salvaje (animal y vegetal) y en ocasiones humanas. Los incendios forestales suelen producirse por un relámpago, negligencia, o incluso provocados y queman miles de hectáreas.
¿Qué es más importante, casas para que la gente tenga una vivienda, o los bosques naturales? Organizad un debate oral sobre este tema.
El concepto de entendimiento intercu ltural significa: “la capaci dad para demostrar este entendimiento de la diversidad cultura l y/o las similitudes entre la lengua adquirida y la propia” ; ¿hasta qué punto es cierta esta definición?
Actividad oral interactiva Para más información sobre incendios forestales, dirígete a www.pearsonhotlinks.com y escribe el título o el ISBN de este libro. Después, selecciona el enlace número 10.26, 10.27 y 10.28. Lee los textos, observa las fotos y el video y contesta la siguiente pregunta del informe de WWW: ¿Recuperando bosques o plantando incendios?
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Interculturalid ad Busca información sobre los desastres
Actividad oral interactiva boxes provide practice for the oral evaluation centred around a topical photograph.
Y DESASTRES
NATURALES
Actividad oral interactiva Para más información sobre desastres natura les recientes, diríget el título o el ISBN de e a www.pearsonhotlin este libro. Despues, ks.com y escribe selecciona el enlace número 10.42 y 10.43. Habla sobre la relació n entre terremotos, tsunamis y explosiones Compara las fotos anterio nucleares después de res con las del terrem mirar las fotos. oto en Chile. Explica los desastres naturales que ha sufrido tu país. Busca fotos y descríbelas durant e tu presentación. Actividad inter textual Basándote en noticia s sobre los terremotos, busca información sobre por otras causas: hambr otros desastres recient unas, corrimientos de es provocados tierra, incendios etc. España o América Latina que hayan ocurrido . en algún lugar de Para más información, 295 dirígete a www.pearso nhotlinks.com y escribe Después, selecciona el enlace número 10.44, el título o el ISBN de este libro. 10.45 y 10.46. 15/4/11 16:49:01
naturales más frecuen tes en tu país.
Consejos para el examen Fíjate en el léxico de este capítulo. Te hemos hecho un listado de capítulo. Necesitarás palabras que se repiten estas palabras para a lo largo del la evaluación interna añadir a este listado y externa. Hay mucha . Recuerda distinguir s otras que podrías nombres, verbos y adjetiv amenaza (amenazar) os. desplazarse afecta (afectar) provocar la destrucción devastadoras a causa (causar) provocados avance del mar (avanz epicentro perjudican (perjudicar) ar) areas en peligro escasa o nula precip pertinaces itación azotan (azotar) exceso de precipitación perdidas acumulación (acum explotar arrojando ular) réplicas ansiedad explotación errónea e irracional recurso s renovables (explotar) catástrofes evacuadas/evacuar sacudida/sacudir consecuencias solución/solucionar causante/causar/ son fallecido sufrir (ha(n) sufrido causados/a causa de falta de lluvias )
Consejos boxes identify common pitfalls and provide insight into how students can organise, clarify and present their ideas to achieve the highest marks in their examinations.
desaparecer destruir/destruyend o/destruye /destrucción devastadas detener el cambio desastre dañar
tasa de mortalidad temblar
graves negligencia
vulnerabilidad
miedo plan de acción peligro (peligrar) pérdidas humanas y materi
ales
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Pearson Baccalaureate’s NEW Exclusif and Exclusiva An exciting online source of topical news and culture articles in French and Spanish, accompanied by interactive IB assessment-style exercises. Perfect for use in the classroom, as homework, or as a resource for students to revise and test their skills independently. Written and complied by IB Language B experts Peter Watson and Virginia Panea
Up-to-date content Each week, the website will be updated with an up-to-the-minute news story or culture feature specifically chosen for IB Spanish B or French B students. Interactive exercises and activities written by practising IB teachers then test and give practice in key exam skills.
Be part of a community The weekly blog will create a sense of community within the website and points users towards additional topical resources, providing inspiration for lesson planning, and for extension work.
Instant translation Instant translation is provided using a rollover facility, assisting students in vocabulary comprehension and revision. In addition, key vocabulary lists are provided for each topic.
For more information, and details of how to subscribe, visit www.pearsonbacconline.com
13
Diploma
Economics Sean Maley & Jason Welker
Student textbook and online resources written specifically for the 2011 curriculum
Compr
Clearly differentiated content for both Standard and Higher Level students.
nsive
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Includes highly visual graphs and topical examples to aid students’ understanding of real-world Economics.
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Integrated with free online learning resources at www.pearsonbacconline.com, to support and extend study.
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Contains answers to quantitative exercises found throughout the book.
contents
TOK boxes are intended to stimulate higher-level thinking skills and force students to question their ideas and the source of their knowledge.
3
Introduction: The foundations of economics Section 1: Microeconomics Section 2: Macroeconomics
Section 3: International Trade Section 4: Development Economics The Internal Assessment, Extended Essay and Theory of Knowledge
Interesting facts place the material in real-life contexts and give depth to students’ understanding of a topic. They also prompt further enquiry.
market market equilibrium equilibrium and andefficiency efficiency
Shifts Shifts of of demand demand
Shifts of supply
AAfew fewyears yearsago, ago,consumer consumerdemand demandfor forpomegranate pomegranatejuice juicesignificantly significantlyincreased increasedfollowing following reports reportsthat thatititcontained containedvery veryhigh highlevels levelsofofantioxidants. antioxidants.As Asaaresult, result,demand demandfor forallall products productsusing usingpomegranate pomegranateincreased, increased,shifting shiftingdemand demandfor forpomegranates pomegranatestotothe theright. right.AsAs shown shownin inFigure Figure3.3, 3.3,demand demandfor forpomegranates pomegranatesshifted shiftedtotothe theright, right,causing causinga atemporary temporary shortage thusfar far shortageatatthe theold oldequilibrium equilibriumprice priceofof$4.00. $4.00.The Thequantity quantitydemanded demanded(Q (Q D)D)isisthus greater In this case, the excess demand is 40 million greaterthan thanthe thequantity quantitysupplied supplied(Q (QS). S). In this case, the excess demand is 40 million kilograms. kilograms.As Asproducers producersrealize realizethey theycan canraise raisethe theprice, price,they theyproduce producemore, more,a amovement movement upwards along the supply curve. And as consumers see the higher prices, they decrease upwards along the supply curve. And as consumers see the higher prices, they decreasethe the quantity quantitydemanded, demanded,aamovement movementup upand andleft leftalong alongthe thenew newdemand demandcurve. curve.The Thequantities quantities of ofsupply supplyand anddemand demandsettle settleatatthe thenew newequilibrium equilibriumprice priceofof$5$5and andequilibrium equilibriumquantity quantityofof 110 110million millionkilograms. kilograms.As Asaaresult resultofofthe theincreased increaseddemand, demand,prices pricesare arehigher higherand andquantities quantities greater greaterthan thanbefore. before.
Supply shifts can also have important effects on price and quantity. In Figure 3.5, the market for rubber ducks shows the effect of synthetic rubber production. Synthetic rubber is much cheaper than rubber collected from rubber trees, so it becomes much less costly to produce rubber items, including rubber ducks. As a result, the supply of rubber ducks shifts to the right. A temporary surplus 7 million ducks exists at the old equilibrium price of $3.75. This surplus is eliminated by cutting prices and selling off the excess supply. Consumers do their part by buying up the residual amounts at successively lower prices, an increase in quantity demanded at each lower price. The increase in supply therefore results in a lower equilibrium price for rubber ducks at $2.25, and a higher equilibrium quantity of 12 million sold.
final finalequilibrium equilibrium
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Perhaps the greatest single supply shock in the modern era occurred with the 1973 oil crisis. The Organization of the Petroleum Exporting Countries (OPEC) launched an embargo of oil in response to US support of Israel during the Yom Kippur War. The price of oil quadrupled to a then-record $12 per barrel. This resulted in long queues, price controls and rationing in the US, Europe and Japan. It also stoked inflationary tendencies at work during this period, and is credited with starting the era of stagflation.
2.25
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AAdecrease decreasein indemand demandcan canhave havethe theopposite oppositeeffect. effect.AAdecrease decreaseinina acountry’s country’sincome incomemight might decrease decreasethe thedemand demandfor forall allnormal normalgoods. goods.Automobile Automobilesales, sales,ininparticular, particular,tend tendtotobebe immediately affected by decreases in income, and a recession causes a decrease in demand for immediately affected by decreases in income, and a recession causes a decrease in demand for automobiles. In Figure 3.4, a decrease in demand of this type results in a temporary surplus automobiles. In Figure 3.4, a decrease in demand of this type results in a temporary surplus of 6 million cars at the S of 6 million cars at the S equilibrium price of $12 500 equilibrium price of $12 500 (fewer new cars being sold); (fewer new cars being sold); producers cut prices to entice producers cut prices to entice buyers (increasing quantity buyers (increasing quantity demanded, moving down demanded, moving down along the new demand along the new demand 12 500 curve). Eventually, the 12 500 curve). Eventually, the market settles at a new, lower market settles at a new, lower market price and quantity 9 000 market price and quantity 9 000 ($9000 and 5.5 million cars): ($9000 and 5.5 million cars): fewer cars are being sold at fewer cars are being sold at lower prices. D1 lower prices. D Figure 3.4 Figureequilibrium, 3.4 Market decreased Market equilibrium, demand: new cars. decreased demand: new cars.
S1 3.75
D1 5.5 8.5 new5.5 car sales /8.5 millions (Q) new car sales / millions (Q)
D
a create a table to show the dema nd and supply sched and $9. ule with prices of $0, $3, $5, $7 b create a dema 57 nd curve, plotting the points from your demand sched show the equili brium quantity ule. bought and sold. d using the two functions, solve for the equilibrium 13:11 4 assume07/04/2011 price and quant that the above dema ity. nd function chang es to QD = 380 – a make a new 30P supply and dema nd schedule for all the prices in b plot the points exercise 3a. on this new sched ule. c show the exces s demand at the original price. d calculate the excess demand using the old equili and supply functi brium price and ons. the current dema nd
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Visual stimuli such as photos and graphics engage students and illustrate key concepts.
3.3
Role of price in
resource allocat
ion
Learning outco mes • Explain why scar city necessitates choices that answ question. er the ‘What to p roduce?’ • Explain why cho ice results in an opportunity cost • Explain, using d . iagrams, that pric e has a signallin function, which r g function and a esult in a realloca n incentive tion of resources a change in dem when prices cha and or supply con nge as a result o ditions. f
Online resources include worked answers to all of the new HL quantitative exercises, plus further exam questions and answer guidelines.
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Exercise sections are found at the end of each section in a chapter.
A decrease in supply will have the S1 S inverse result. Figure 3.6 shows the effect of a deep winter freeze across the Mediterranean which damaged orange crops in Greece, 2.10 Italy, Spain and Cyprus. As a result, the number of oranges 1.50 available for juice products decreased dramatically. Oranges are an input cost for orange juice, so the supply of orange juice 3 market equi Figurelibr 3.6 ium and efficienc decreases, shifting supply to the y Decreased supply: orange left. The reduced supply causes a D juice. temporary shortage of 700 million 200 550 900 To access answe r sheet litres at the old equilibrium price 3.1 for these HL exercis litres / millions (Q) To learn more about es, eXeRCISeS please visit www. 2 of $1.50 per litre. Producers equilibrium,solve visit for P and QD using the follow pearsonbacconline.c ing linear suppl om y and demand functi therefore begin to increase their a Qs = –400 + pearsonhotlinks.com, and follow the on-scre 50P; QD = 800 – ons: en 30P instructions. enter the title b or prices, and consumers respond by decreasing the quantity demanded. The final price and QsISBN = –240 + 40P; Q D = 660 – 20P of this book and select c Qs = –50 + 25P; quantity settle at $2.10 per litre and 550 million litres consumed. Thus, the decrease in QD = 90 – 10P weblink 3.2. 3 Qs = 100 + supply has caused a decrease in quantity available and increased prices. 10P; QD = 300 – 30P price per litre / $ (P)
priceper perkilogram kilogram//$$(P) (P) price
Figure 3.5 Increased supply: rubber ducks.
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Market shocks (sudden Market shocks (sudden increases in supply or increases in supply or demand) can raise serious demand) can raise serious ethical dilemmas. After the ethical dilemmas. After the earthquake, tsunami and earthquake, tsunami and radiation disaster in Japan radiation disaster in Japan (March 2011), thousands (March 2011), thousands of people tried to leave of people tried to leave the country. Airlines were the country. Airlines were reportedly charging four reportedly charging four to five times the usual to five times the usual price to fly out of Tokyo price to fly out of Tokyo (e.g. flights to Los Angeles (e.g. flights to Los Angeles at $6000). Is it unethical to at $6000). Is it unethical to charge higher prices for charge higher prices for necessity goods during necessity goods during a humanitarian crisis? Or a humanitarian Or would the law ofcrisis? supply would the law supply help ensure thatofmore of help ensure more offor these goods that are offered these goods are offered sale in the crisis zone? for sale in the crisis zone?
S
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price per duck / $ (P)
Figure Figure 3.3 3.3 Market Market equilibrium, equilibrium,increased increased demand: demand: pomegranates. pomegranates.
How does production of synthetic rubber affect the price of rubber ducks?
Signalling and
incentive functio
ns of price
In a world of finite resources, human desires run up again unlimited compared st the fact of scarci to the limited resou ty. Our wants are rces we have availa that resources are ble, which is anoth scarce. With this in mind, we are faced er way of saying resources. with a choice of how to use those All such choices involve a cost – specifi cally, an opportunity activity, we lose out cost. To choose one on the opportunity product or to enjoy the other. allocation all the This makes the system more important. of resources In competitive mark ets, we have seen that buyers and sellers agreement on the come to a settlem appropriate mark et price. This is not ent or or by the guidance done through any of some overseeing centra l command body of governmen market price happe t. Instead, the establ ns when countless ishment of a buyers and sellers their scarce resou , each making ration rces, make the best al choices about decision for thems time and income elves. Buyers are levels, while suppl conscious of their iers watch closely for their goods. This their costs and the decentralized, seemi sellin g potential ngly random proce ss produces one of the most
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Diploma
Psychology Alan Law, Christos Halkiopoulos & Christian Bryan-Zaykov
The popular choice for Psychology Covering both Standard and Higher Level content, this comprehensive textbook provides clearly differentiated support for all students taking the latest Psychology syllabus. nsive
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Detailed diagrams and photographs to clearly explain key concepts and root learning to real-world examples.
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Written to provide an international and transdisciplinary perspective.
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Full coverage of Methodology and Ethics from Parts 3 and 4 of the syllabus.
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Also contains integrated online learning resources at www.pearsonbacconline.com, to support and extend study.
contents Chapter 1: Introduction Chapter 2: Methodology and Ethics Chapter 3: The Biological Level of Analysis Chapter 4: The Cognitive Level of Analysis Chapter 5: The Sociocultural Level of Analysis Chapter 6: Abnormal Psychology
Chapter 7: Developmental Psychology Chapter 8: Health Psychology Chapter 9: The Psychology of Human Relationships Chapter 10: Sport Psychology TOK Internal Assessment Extended Essay
Environmental Systems and Societies Andrew Davis & Garret Nagle
Comprehensively covering all 7 topics from the course Written to provide an international and transdisciplinary perspective. Detailed diagrams and photographs to clearly explain key concepts. nsive
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Supported by additional monthly updated worksheets based on the most topical environmental issues.
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Integrated with free online learning resources at www.pearsonbacconline.com, to support and extend study. These include practice exam questions, extension activities and revision worksheets.
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contents Topic 1: Systems and models Topic 2: The ecosystem Topic 3: Human populations, carrying capacity and resource use Topic 4: Conservation and biodiversity
Topic 5: Pollution management Topic 6: The issue of global warming Topic 7: Environmental value systems Internal Assessment and Extended Essay
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Diploma
History Complete coverage of the most popular History topics
Jo Thomas and Keely Rogers
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20th Century World: The Cold War
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History: A Comprehensive Guide to Paper 1
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20th Century World: Causes, Practices and Effects of Wars Jo Thomas and Keely Rogers
20th Century World: Authoritarian and Single Party States Brian Mimmack, Daniela Senés and Eunice Price The Comprehensive Guide to Paper 1 provides: complete coverage of the prescribed subjects with a clear overview and detailed analysis of key events. material to equip students with the knowledge and skills necessary to answer source-based questions. extensive practice in analysing a wide range of different source materials. free online resources to support and extend study at www.pearsonbacconline.com. Each 20th Century World textbook provides: a clear overview and analysis of key leaders and events. thematic approaches, comparative studies, cross-regional perspectives and explanations of the methods of historical research and writing. timelines, document-based activities, practice questions, essay practice and sample answers. free online resources to support and extend study at www.pearsonbacconline.com.
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Diploma
Biology, Chemistry and Physics Various authors – see pages 7-9
The market-leading titles for IB Sciences, available in both Standard and Higher Level editions Thoroughly differentiated at both Standard and Higher Level. Highly visual diagrams, photographs and topical examples to ensure students learn about the application of science in the real world. All books contain worked examples, practice questions from past IB papers and advice on Internal Assessment and the Extended Essay for exam preparation. NEW online learning resources now available for all subjects, including interactive quizzes, revision exercises, worksheets and guidance on command terms. Visit www.pearsonbacconline.com. nsive
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Structure of the atom Ernest Rutherford (1871–1937) and his research team working at Manchester University in England showed that the atom is mostly empty space. Alpha particles which contain two protons and two neutrons were fired at a piece of gold foil. Most passed straight through, but a small number were repelled and bounced straight back. This led to the conclusion that the mass and positive charge of the atom, the protons and neutrons, are concentrated in a very small nucleus, with the electrons moving in orbits or energy levels around the nucleus. The arrangement of these energy levels is considered in more detail later in the chapter. gold atoms with positively charged nucleus
a
As you are made from atoms, you are also mainly empty space. The particles which make up your mass would occupy the same volume as a flea if they were all squashed together, but a flea with your mass. This gives you an idea of the density of the nucleus.
Figure 2.1 Fewer than one in 20 000 of the alpha particles were deflected back. Ernest Rutherford recalled that ‘It was quite the most incredible thing that has happened to me. It was as if you had fired a (artillery) shell at a piece of tissue paper and it came back and hit you.’
positively charged α particles are fired at gold target
Sample page from Higher Level Chemistry The fact that neutrons are not electrically charged is crucial for the stability of the nucleus. Without them, the protons would mutually repel each other as they have the same positive charge and the nucleus would fall apart.
See a simulation of Rutherford’s experiment. Now go to www.heinemann.co.uk/hotlinks insert the express code 4259P and click on this.
Ions The atomic number is defined in terms of number of protons because it is a fixed characteristic of the element. The number of protons identifies the element in the same way your fingerprints identify you. The number of protons and neutrons never changes during a chemical reaction. It is the electrons which are responsible for chemical change. Chapter 4 will examine how atoms can lose or gain electrons to form ions. When the number of protons is no longer balanced by the number of electrons, these particles have a non-zero charge. When an atom loses electrons it forms a positive ion or cation as the number of protons is now greater than the number of electrons. Negative ions or anions are formed when atoms gain electrons. The magnitude of the charge depends on the number of electrons lost or gained. The loss or gain of electrons makes a very big difference to the chemical properties. You swallow sodium ions, Na , every time you eat table salt, whereas as you will discover in Chapter 3 sodium atoms, Na, are dangerously reactive.
proton in the nucleus
electrons orbit
electrons
When an atom loses electrons, a positive ion is formed and when it gains electrons a negative ion is formed. Positive ions are called cations and negative ions are called anions.
Figure 2.2 The simplest atom. Only one proton and one electron make up the hydrogen atom. The nuclear radius is 10 15 m and the atomic radius 10 10 m. Most of the volume of the atom is empty – the only occupant is the negatively charged electron. It is useful to think of the electrons orbiting the nucleus in a similar way to the planets orbiting the sun. The absence of a neutron is significant – it would be essentially redundant as there is only one proton.
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17
Diploma
Mathematics 2012 Standard and Higher Level Editions Tim Garry, Ibrahim Wazir, Peter Ashbourne, Paul Barclay, Peter Flynn, Kevin Frederick & Mike Wakeford
The most complete solution available for IB Diploma Mathematics These textbooks are fully revised and improved 2nd editions of highly regarded textbooks used successfully by teachers worldwide. They give you everything you need to teach and more – covering both core and option material, there’s no need to look elsewhere. Written by an expert author team consisting of former IB chief examiners, senior examiners and assistant examiners, experienced IB workshop leaders, and teachers with more than 160 years of combined teaching experience. Here are just some of things you can expect to find: A comprehensive eBook containing interactive activities utilizing dynamic mathematics software, quizzes, extension and revision worksheets, full worked solutions and audio-visual calculator support. Clear explanations of key concepts and skills, accompanied by numerous worked examples. Compr
Complete flexibility over medium of study, with printed textbook, online eBook and downloadable versions of chapters to allow students to work offline.
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Practice questions with answers from past examination papers to help you with exam preparation.
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Chapter summaries to aid planning and revision.
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Helpful and skilful support for the new IA Mathematical Exploration – continuously updated on the author website to address developments in the IA programme. Access to all Mathematics Higher Level Options chapters online (over 600 pages). Free online resources to support and extend study at www.pearsonbacconline.com and on the authors’ website, containing even more regularly updated materials and support. A highly engaging Theory of Knowledge chapter, written by Ric Sims, a Deputy Chief Examiner for TOK and highly experienced TOK and Maths HL teacher.
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Paula Heinen, St. John’s International School, Belgium Former Deputy Chief Examiner for Mathematics HL
Fundamentals
U A A
complement of a given set A is the set of all elements in the universal set that are not elements of set A, and is denoted by the symbol A9. Venn diagrams are used to pictorially represent the relationship of sets within a universal set. The universal set, U, is represented by a rectangle and any subset of U is represented by the interior of a circle within the rectangle (see Figure 1.3). If for a certain problem the universal set is the complex numbers C, then the complement of the real numbers is the imaginary numbers. For problems in secondary school mathematics, and in this course, the universal set will often be a subset of the complex numbers – commonly the real numbers R. If the universal set is the real numbers, then the set of irrational numbers is the complement of the rational numbers Q. See Figure 1.2.
Figure 1.3 Venn diagram for the universal set U, set A, and the complement of A, A9 (shaded region).
Although the set {2, 3} is equal to the set {3, 2}, the ordered pairs (2, 3) and (3, 2) are not the same. Hence, for the Cartesian product of two sets A and B, in general, A 3 B B 3 A.
Hint: The symbol for the union of two sets, , can be remembered by connecting it with the first letter in the word ‘union’.
The intersection of sets A and B, denoted by A B and read ‘A intersection B’, is the set of all elements that are in both set A and set B. The union of two sets A and B, denoted by A B and read ‘A union B’, is the set of all elements that are in set A or in set B (or in both). The set that contains no elements is called the empty set (or null set) and is denoted by [. Sets whose intersection is the empty set, i.e. they have no elements in common, are disjoint sets. The Cartesian product of two sets A and B is the set of all ordered pairs {(a, b)}, where a A and b B. It is written as A 3 B 5 {(a, b) | a A, b B}. For example, if X 5 {1, 2} and Y 5 {3, 4, 5}, then
X 3 Y 5 {(1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5)}
and
Y 3 X 5 {(3, 1), (3, 2), (4, 1), (4, 2), (5, 1), (5, 2)}
Set relations and operations Subset: A B means that A is a subset of B Proper subset: A B means that A B but A B Intersection: A B 5 {x | x A and x B} Union: A B 5 {x | x A or x B or both} Complement: A9 5 {x | x A} Empty set: [, the set with no elements Cartesian product: A 3 B 5 {(a, b) | a A, b B}
U
B
A
Consider that the universal set U is defined to be U 5 {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}, and A 5 {2, 5, 8, 11}, B 5 {2, 4, 6, 8, 10, 12}, C 5 {2, 3, 5, 7, 11, 13}. a) Find the following: (i) A B (iv) A C (vii) A (B C)9
(ii) A B (v) A B C (viii) A B C
Solution
a)
(i) (iii) (v) (vii) (viii)
A B 5 {2, 8} (ii) A B 5 {2, 4, 5, 6, 8, 10, 11, 12} A9 5 {1, 3, 4, 6, 7, 9, 10, 12, 13} (iv) A C 5 {2, 5, 11} A B C 5 {2} (vi) (B C)9 5 {1, 9} A (B C)9 5 [ A B C 5 {2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13} U
A
4 8
B 11 3
b)
1
U
Venn diagrams are named after the British mathematician, philosopher and writer John Venn (1834–1923). Although he was not the first to use diagrams as an aid to problems in set theory and logic, he was the first to formalize their usage and popularized them in his writings such as in his first book Symbolic Logic published in 1881. 6
B
(iii) A9 (vi) (B C)9
b) Draw a Venn diagram to illustrate the relationship between the sets A, B and C.
5
a)
10
B 6 12
2 7 13
9 C
U A
B
A
c) Figure 1.4 a) Union of sets A and B, A B b) Intersection of sets A and B, A B c) Proper subset, A B d) Two disjoint sets, A and B
d)
Key facts are highlighted, making them easy for students to locate, and to aid revision.
Example 3 – Set operations
b) U A
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“Just to say how much I like your HL book. My students like it too. It is the one book I know which explains in the same way I teach!”
Hint: When we list the elements of a set we never repeat an element. For example, for A B in Example 3 the numbers 2 and 8 are in both A and B but they are each written once when listing the elements in A B.
Hints aid students in reaching conclusions via the most efficient route, while worked examples offer students model responses.
In Example 3, instead of defining sets U, A, B and C using lists, we could have defined each of the sets using a rule. For example, U 5 {x | 1 < x < 13, x Z}, A 5 {x | x 5 3n 2 1, n 5 1, 2, 3, 4}, B 5 {x | x 5 2n, 1 < n < 6 and n Z}, and C 5 {x | x < 13, x is a prime number}.
Inequalities (order relations) An inequality is a statement involving one of four symbols that indicates an order relation between two numbers or algebraic expressions on either side of the symbol. The symbols are , (less than) . (greater than) < (less than or equal to) > (greater than or equal to). 7
Interesting facts add wider context to the topics being studied, and allow for further applications of mathematics to be explored.
Diploma
Mathematical Studies Ron Carrell & David Wees
Developed specifically for the IB Diploma Compr
Hint boxes highlight the best routes to solutions and portfolio support. Worked solutions CD-ROM available separately.
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ToK boxes stimulate high-level thinking skills and force students to question their ideas and the source of their knowledge.
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Presumed Knowledge
Example 1.2
A Venn diagram is often helpful in visualizing the relationships between sets of numbers.
Simplify each of the following.
Real numbers Figure 1.1 Venn diagram for the set of real numbers.
a) 3 5 7 8 2
Rational numbers __
___ ¡¡ 2, _35, 0.6868, 0.5, â&#x2C6;&#x161;25
There are exactly the same number of numbers in the set of natural numbers as there are in the set of integer numbers or even the set of rational numbers! However, there are more real numbers than there are natural numbers! There is more than one level of inďŹ nity!
b) 2(9 5)2 1 10 2 ______ c) â&#x2C6;&#x161;42 32
Irrational numbers â&#x2C6;&#x161;2
Integer numbers â&#x20AC;Ś, 2, 1, 0, 1, 2â&#x20AC;Ś
Natural numbers
___
â&#x2C6;&#x161;17
Solution
log 23
a) 3 5 7 8 2 15 7 4 8 4 12
e 0.121221222 â&#x20AC;Ś sin 13°
b) 2(9 5)2 1 10 2 2(4)2 10 2 2 16 5 32 5 27 ______
What are some of the ways that mankind has dealt with the concept of inďŹ nite? Exactly what does it mean to be inďŹ nitely large?
__
For the proof that â&#x2C6;&#x161;2 is irrational, visit www.heinemann.co.uk/ hotlinks, enter the express code 4310P and click on weblink 1.1.
___
Number theory Number theory is the study of integers. This review section will cover the basics: prime numbers, factors and multiples. Prime numbers
Example 1.1
A prime number is defined as a natural number greater than 1 whose only positive divisors are 1 and itself.
Classify each of the following numbers as ďż˝, ďż˝, ďż˝ , ďż˝, ďż˝ , ďż˝ , ďż˝, ďż˝ . a) 3
To show that a number is irrational requires the study of number theory.
______
c) â&#x2C6;&#x161;42 32 â&#x2C6;&#x161;16 9 â&#x2C6;&#x161;25 5
0, 1, 2, 3, â&#x20AC;Ś
Interesting facts add wider context to the topics being studied, and allow for further applications of mathematics to be explored.
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Practice questions from past examination papers with answers.
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Worked examples show how to tackle particularly tricky questions.
b) 0.4
c)
__
â&#x2C6;&#x161;2
37 d) ___
For example, 5 is a prime number since the only natural numbers (other than 0) that divide into it (without a remainder) are 1 and 5.
5
Solution
3, 3 is a member of ďż˝, ďż˝, ďż˝ , ďż˝, ďż˝ , ďż˝ and ďż˝ . a) Since 3 __ 1 4 , 0.4 is a member of ďż˝, ďż˝ , ďż˝ and ďż˝ . b) Since 0.4 ___ 10 __ __ c) Since â&#x2C6;&#x161;2 cannot be expressed as the ratio of two integers, â&#x2C6;&#x161;2 is a member of ďż˝ , ďż˝ and ďż˝ .
As a counter-example, 6 is not a prime number, since both 2 and 3 divide into 6.
37 d) __ 5 is located in the 37th column to the left of 0 and down to the 5th row 37 of the chart on page 1. Therefore, __ 5 is a member of ďż˝ and ďż˝.
Below is a partial list of prime numbers.
All other natural numbers (0 and 1 excluded) that are not prime are called composite. By definition, the first prime number is 2.
Some books on number theory include proofs that show there are inďŹ nitely many prime numbers, that there are inďŹ nitely many levels of inďŹ nite, that the square root of any prime number is not a rational number and that is irrational.
That there are inďŹ nitely many primes is not a foregone conclusion since, as you think of larger and larger numbers, there are also more and more numbers that have a chance of dividing into that number, thus making that large number not prime!
Prime numbers {2, 3, 5, 7, 11, 13, 17, 19, 23, â&#x20AC;Ś} Example 1.3
Order of operations
Determine if 137 is a prime number.
In order to avoid confusion when performing a series of arithmetic operations, we follow a standard order:
Solution
Start dividing 137 by natural numbers to see if any divide into 137 without a 137 68.5 remainder. ___ 2 137 45._6 and so on. ___ 3 Do this procedure using all of the natural numbers that are smaller than or ____ equal to the â&#x2C6;&#x161;137 plus one (i.e. 11.7 1 12). 137 11.41_6 ___ 12 Since none of those natural numbers divide 137 evenly, 137 must be prime.
Step 1: Eliminate all Parentheses. Step 2: Simplify all Exponents. Step 3: Perform Multiplication and Division as you come to them, reading from left to right. Step 4: Perform Addition and Subtraction as you come to them, reading from left to right. An easy way to remember these steps is by using the mnemonic: Please Excuse My Dear Aunt Sally (PEMDAS) 2
01-MathsStud_01_001_039.indd 2
The answer___ to part c) is not 5 since â&#x2C6;&#x161;25 is asking for the principal square root, which, by deďŹ nition, is always positive.
You only have to test the numbers up to the approximate ____ value of â&#x2C6;&#x161;137 since 12 12 is greater than 137. 3
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Worked Solutions CD Josip Harcet, Marina BiliÄ&#x2021; & Jelena GusiÄ&#x2021;
To be used as a guide alongside Mathematical Studies Fully worked solutions for all exercises and practice questions. Created by an author team of experienced IB teachers and examiners. Designed to be a guide to study, alongside the textbooks and not as a replacement for the studentâ&#x20AC;&#x2122;s own attempts to solve each problem.
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Diploma
Theory of Knowledge Sue Bastian and co-authors
Written by the architect of the current programme Provides comprehensive coverage of all the Ways of Knowing and Areas of Knowledge. nsive
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Provides guidance on the Prescribed Essay and the Student Presentation.
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Enables clear links to the Learner Profile, the IB core values and all the IB hexagon areas.
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Engages students in critical thinking relevant to their other courses and their life outside the classroom.
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Written by a team of authors led by Sue Bastian, highly regarded as the architect of the current TOK programme.
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contents
Key Facts are highlighted, making them easier for students to locate, and to aid revision.
Introduction 1. Your knower profile 2. Key ideas and vocabulary 3. Knowledge 4. Belief 5. Certainty 6. Truth 7. The ideal knower
8. Ways of knowing 9. Perception 10. Emotion 11. Language 12. Reason 13. Areas of knowledge 14. Mathematics 15. Science
Language
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Exercise
Zhou’s father, a schoolteacher, was impressed by the strange writing he couldn’t understand and urged the young Zhou to investigate. Later, working for the Jiangyong County cultural department in the 1950s, Zhou said he discovered a number of elderly peasant women still mastered nushu. ...
• Do extracts B and C support the claim that language is shaped and determined by culture? Paradigm A philosophical and theoretical framework of a scientific school, or other discipline; theories, laws and generalizations are formulated and experiments are performed in support of them.
Would these excerpts validate the Sapir-Whorf hypothesis, which states that ‘language determines our experience of reality’? • In class, discuss the ‘nature’ versus ‘nurture’ debate which presents two contrasting paradigms. From the perspective of the study of human language, which paradigm would you support to a greater extent and why? Is it possible to offer a ‘synthesis’ or combination of the two paradigms? (Use the responses as the basis for a class debate). • Another class discussion… extract C points out that language often becomes the basis for constructing stereotypes and discrimination. Could you suggest ways in which language could become more ‘neutral’, or are there other avenues for reducing and removing the effects of propaganda and negative images of other groups?
“At that time, many grandmothers could sing it, write it and read it,” he said in an interview. “In society at that time, there was injustice between men and women, and women needed this language as a way to express themselves.” Zhou reported his findings to authorities in Beijing, but by then the Cultural Revolution had convulsed China. ...in 1979, when calm had returned, Zhou said, he went back to work at a local museum and resumed his interest in nushu, eventually learning to read and write. ... “Now a lot of people are studying it, and a lot of people come here to ask about it,” he said. From ‘The secret language of Chinese women’ by Edward Cody, Washington Post, Sunday, February 29, 2004
Language and gender: ‘Nu Shu’, China’s secret female language
Exercise
In the previous section, we looked at the relationships between language and culture, and how these could structure elements of discrimination and prejudice. In human history, one of the longest-lasting forms of inequality relates to gender. The following passage relates to language and gender discrimination in traditional society in a Chinese province. Nowadays, it would be called empowering women. But back then, centuries ago, it was just a way for the sworn sisters of this rugged and tradition-laden Chinese countryside to share their hopes, their joys and their many sorrows.
Hold group discussions on the following: • In what ways can language be an ‘empowering’ experience for its users? • What is the role of language in creating and reinforcing social distinctions, such as gender? • Can you think of other examples of disadvantaged groups in society using language as a means of expression and survival? • Aldous Huxley observed in 1947 that ‘words form the thread on which we string our experiences’. What experiences did the women of Hunan ‘thread’ through the creation of ‘nu shu’? Do you think it enabled them to live happier lives? • Do women still need a different language today? As a class: • Construct a poem which expresses the sentiments of the women who used ‘nu shu’. • Split up into two groups – male and female. Both the ‘women’s group’ and the ‘men’s group’ should gather together and decide on a topic of conversation which is of particular interest to them. A recorder in each group should note the stories or terms that seem to predominate in the conversation. After 15 to 20 minutes, each group should report to the class and compare the ‘language’ used by them. Did you observe substantial differences and what might that imply for gender differences (or similarities) in our times? • Write a reflective journal of 250 to 300 words on how gender has shaped your experiences as a knower, particularly in the use of language.
Only men learned to read and write Chinese, and bound feet and social strictures confined women to their husband’s homes. So somehow -- scholars are unsure how, or exactly when -- the women of this fertile valley in the southwestern corner of Hunan province developed their own way to communicate. It was a delicate, graceful script handed down from grandmother to granddaughter, from elderly aunt to adolescent niece, from girlfriend to girlfriend -- and never, ever shared with the men and boys. So was born nushu, or women’s script, a single-sex writing system that Chinese scholars believe is the only one of its kind. “The girls used to get together and sing and talk, and that’s when we learned from one another,” said Yang Huanyi, 98, a wrinkled farmer’s widow whom scholars consider the most accomplished reader and writer among a fast-dwindling number of nushu practitioners. “It made our lives better, because we could express ourselves that way.” ... Much remains unknown about nushu. Its origins, reaching perhaps as far back as the third century, have been the subject of scholarly exchanges among a handful of researchers in China and elsewhere. They know it was used in Hunan’s Jiangyong County, in south central China...
Language and culture: proverbs and aphorisms
What seems clear is that nushu was fostered by the region’s ancient custom of “sworn sisters,” whereby village girls would pledge one another fealty and friendship forever. The tight sorority, which included growing up together in cobbled village lanes and gathering with adult women to weave and embroider, inevitably was shattered when the time for marriage came. Tradition dictated that a bride go away to her groom’s home -- and that is where nushu came in. Three days after the wedding, the adolescent bride would receive a “Third Day Book,” a clothbound volume in which her sworn sisters and her mother would record their sorrow at losing a friend and daughter and express best wishes for happiness in the married life ahead. The first half-dozen pages contained these laments and hopes, written in nushu that the groom couldn’t read. The rest were left blank for the bride to record her own feelings and experiences -- in nushu -- for what would become a treasured diary. ...
The way nushu came to light some 20 years ago also has been clouded in competing theories. Lin Lee Lee at the University of Minnesota has written that a Jiangyong County woman visiting relatives in Beijing in 1982 astounded them by singing and then writing a language and script they could not understand. The relatives passed along their amazement to scholars, she said in a conference presentation, and research into the strange female writing system began. But Zhou Shuoyi, 78, a self-described countryside intellectual who lives in nearby Yongzhou city, said he knows better, and he explained why. One of his ancestors, a grandmother six generations back, wrote a poem titled “Educate the Girls.” The poem, handed down from generation to generation, was translated into nushu by local village women, he said, and his aunt brought the nushu version to his father’s house sometime in the 1920s as a subject of curiosity. 86
06-Chap06-077-093.indd 86
’Nu Shu’ written in Nu Shu (right to left)
Proverbs and aphorisms Brief pithy sayings that express a truth or widely held belief, for example, ‘absence makes the heart grow fonder’.
Rice terraces in Bali
Languages are shaped by their physical and social environments, giving them their richness and diversity. Proverbs and aphorisms preserve the wisdom of cultures, while at the same time revealing their concerns and important values. The culture of the Indonesian island of Bali is known for its incredible artistic talents, which extend beyond dance, painting and sculpture to the use of language itself. After reading the Balinese proverbs and expressions that follow, we will examine the messages that they convey.
Most important to the women who learned it, sometimes memorizing letters written on the palms of their hands because of a lack of paper, nushu liberated them from illiteracy.
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Real texts offer students the chance to experience and consider a broad range of sources.
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16. Social science 17. History 18. Ethics 19. Art 20. The learner profile Themes of global significance Index
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continued overleaf
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Yvonne Loh (International Schools) Pearson Education South Asia 23/25 First Lok Yang Rd Jurong 629733 Singapore T (65) 6 3199 232 E yvonne.loh@pearson.com Jason Polim Pearson Education South Asia (Indonesia office) Kompleks Business Park Kebon Jeruk Blok I No.10 Jl. Raya Meruya Ilir No.88 Meruya Utara, Jakarta 11620 T + (62) 21 5890 8219 E jason.polim@pearson.com Japan
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Ms. Yvonne Loh Pearson Education Asia Pte. Ltd. 23/25 First Lok Yang Road, Jurong, Singapore 629733 T +65 6319 9232 F +65 6319 9175 E yvonne.loh@pearson.com Malaysia
Yvonne Loh (International Schools) Pearson Education South Asia, 23/25 First Lok Yang Rd Jurong 629733 Singapore T (65) 6 3199 232 E yvonne.loh@pearson.com New Zealand
Pearson Private Bag 102902, North Shore 0745, Auckland T +64 9 442 7400 F +64 9 442 7406 E customer.service@pearsoned. co.nz Philippines
Yvonne Loh (International Schools) Pearson Education South Asia, 23/25 First Lok Yang Rd Jurong 629733 Singapore T (65) 6 3199 232 E yvonne.loh@pearson.com Andrew Taningco Pearson Education South Asia (Philippines office) 2/F J-L Building 23 Matalino St BGY Central Diliman Quezon City 1101 T (63) 2 9220 516 E andrew.taningco@pearsoned. com.ph Singapore
Yvonne Loh (International Schools) Pearson Education South Asia, 23/25 First Lok Yang Rd Jurong 629733 Singapore T (65) 6 3199 232 E yvonne.loh@pearson.com
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Vivian Wang Pearson Education Taiwan 5/F, No.147, Sec.1, Chung Ching South RD, Taipei 100 Taiwan T (886)2 2370 8168 8667 E vivian.wang@pearson.com Rita Chen Pearson Education Taiwan 5/F, No.147, Sec.1, Chung Ching South RD, Taipei 100 Taiwan T (886)2 2370 8168 8814 E rita.chen@pearson.com Thailand
Yvonne Loh (International Schools) Pearson Education South Asia, 23/25 First Lok Yang Rd Jurong 629733 Singapore T (65) 6 3199 232 E yvonne.loh@pearson.com Brendan Cunningham Pearson Education Thailand 1077 Rama 3 Road, Chongnonsee Yannawa, Bangkok 10120, Thailand T (66) 2 681 5515 107 E brendan.cunningham@ pearson.com Vallapha Ninrat Pearson Education Thailand 498/16 Nonsee Road, Chongnonsee Yannawa, Bangkok 10120, Thailand T (66) 2 681 5515 118 E vallapha@pearson.com Vietnam
Yvonne Loh (International Schools) Pearson Education South Asia, 23/25 First Lok Yang Rd Jurong 629733 Singapore T (65) 6 3199 232 E yvonne.loh@pearson.com Huong (Ruby) Hguyen Thi Pearson Education Vietnam 26-28 Truong Quyen Ward 6, District 3 Ho Chi Minh City, Vietnam T (84)8 3820 5820 E huong.nguyen@pearson.com Caribbean
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Mohammed Laham Educational Consultant T +966 509 764 207 F +966 2 659 2096 E mohammad.laham@pearson. com Hassan Novinchehr, Pearson Business Development Executive T +98 21 22921694 M +98 912 5120549 E hassan.novinchehr@pearson. com Ghazal Javan publications 31 Lashgarak Alley, East Roudbar St, Mirdamad Blvd T +98 21 2292 1619 F +98 21 2292 1620 E info@gzle.com Iraq
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Mohammed Laham Educational Consultant T +966 509 764 207 F +966 2 659 2096 E mohammad.laham@pearson. com Future Education T +966 2 224 0485 / 629 5565 F +966 2 640 0705 E info@futureducation.org
Mohammed Laham Educational Consultant T +966 509 764 207 F +966 2 659 2096 E mohammad.laham@pearson. com Egypt
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Mark Booth Africa Sales Manager Pearson T +44 (0)7921 740469 E mark.booth@pearson.com
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