New Syllabus Mathematics PDF
Preview New Syllabus Mathematics
NEW SYLLABUS MATHEMATICS 7th Edition Consultant • Dr Yeap Ban Har Authors • Dr Joseph Yeo • Teh Keng Seng • Loh Cheng Yee • Ivy Chow • Ong Chan Hong • Jacinth Liew NEW SYLLABUS MATHEMATICS 7th Edition CCoonnssuullttaanntt •• DDrr YYeeaapp BBaann HHaarr AAuutthhoorrss •• DDrr JJoosseepphh YYeeoo PPhhDD,, MMEEdd,, PPGGDDEE ((DDiisstt)),, BBSScc ((HHoonnss)) •• TTeehh KKeenngg SSeenngg BBSScc,, DDiipp EEdd •• LLoohh CChheenngg YYeeee BBSScc,, DDiipp EEdd •• IIvvyy CChhooww MMEEdd,, PPGGDDEE,, BBSScc •• OOnngg CChhaann HHoonngg BBSScc ((HHoonnss)),, PPGGDDEE •• JJaacciinntthh LLiieeww BBSScc ((HHoonnss)),, PPGGDDEE ((DDiisstt)) SHINGLEE PUBLISHERS PTE LTD 120 Hillview Avenue #05-06/07 Kewalram Hillview Singapore 669594 Tel: 67601388 Fax: 67625684 email: [email protected] http://www.shinglee.com.sg ©SHINGLEE PUBLISHERS PTE LTD All rights reserved. No part of this book may be reproduced, stored in a retrieval system or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of the Publishers. First Published 1982 Reprinted 1983, 1984, 1985, 1986 Second Edition 1987 Reprinted 1987, 1988, 1989, 1990, 1991, 1992, 1993 Third Edition 1994 Reprinted 1994, 1995, 1996, 1997 Fourth Edition 1998 Reprinted 1999, 2000 Fifth Edition 2001 Reprinted 2002, 2003, 2004, 2005, 2006, 2007 Sixth Edition 2008 Reprinted 2009, 2010, 2011, 2012, 2013, 2014 Seventh Edition 2015 ISBN 978 981 237 932 0 Acknowledgements All licensed images purchased under standard license agreement with www.shutterstock.com 9 5 Printed in Singapore PREFACE New Syllabus Mathematics (NSM) is a series of textbooks specially designed to provide valuable learning experiences to engage the hearts and minds of students sitting for the GCE O-level examination in Mathematics. Included in the textbooks are Investigation, Class Discussion, Thinking Time, Journal Writing, Performance Task and Problems in Real-World Contexts to support the teaching and learning of Mathematics. Every chapter begins with a chapter opener which motivates students in learning the topic. Interesting stories about Mathematicians, real-life examples and applications are used to arouse students’ interest and curiosity so that they can appreciate the beauty of Mathematics in their surroundings. The use of ICT helps students to visualise and manipulate mathematical objects more easily, thus making the learning of Mathematics more interactive. Ready-to-use interactive ICT templates are available at http://www.shinglee.com.sg/ StudentResources/ Preface iii KEY FEATURES CHAPTER OPENER Each chapter begins with a chapter opener to arouse students’ interest and curiosity in learning the topic. LEARNING OBJECTIVES Learning objectives help students to be more aware of what they are about to study so that they can monitor their own progress. RECAP Relevant prerequisites will be revisited at the beginning of the chapter or at appropriate junctures so that students can build upon their prior knowledge, thus creating meaningful links to their existing schema. WORKED EXAMPLE This shows students how to apply what they have learnt to solve related problems and how to present their working clearly. A suitable heading is included in brackets to distinguish between the different Worked Examples. PRACTISE NOW At the end of each Worked Example, a similar question will be provided for immediate practice. Where appropriate, this includes further questions of progressive difficulty. SIMILAR QUESTIONS A list of similar questions in the Exercise is given here to help teachers choose questions that their students can do on their own. EXERCISE The questions are classified into three levels of difficulty – Basic, Intermediate and Advanced. SUMMARY At the end of each chapter, a succinct summary of the key concepts is provided to help students consolidate what they have learnt. REVIEW EXERCISE This is included at the end of each chapter for the consolidation of learning of concepts. CHALLENGE YOURSELF Optional problems are included at the end of each chapter to challenge and stretch high-ability students to their fullest potential. REVISION EXERCISE This is included after every few chapters to help students assess their learning. iv Preface Learning experiences have been infused into Investigation, Class Discussion, Thinking Time, Journal Writing and Performance Task. Investigation Class Activities are included to guide students to investigate and discover Discussion important mathematical concepts Questions are provided for students to discuss so that they can construct their in class, with the teacher acting as the facilitator. own knowledge meaningfully. The questions will assist students to learn new knowledge, think mathematically, and enhance their reasoning and oral communication skills. Thinking Time Journal Writing Key questions are also included at Opportunities are provided for students to appropriate junctures to check if reflect on their learning and to communicate students have grasped various concepts mathematically. It can also be used as a and to create opportunities for them to formative assessment to provide feedback to further develop their thinking. students to improve on their learning. Performance Task Mini projects are designed to develop research and presentation skills in the students. MARGINAL NOTES ATTENTION SoPlvrionbgl eTmip INFORMATION This contains important This guides students This includes information information that students on how to approach a that may be of interest should know. problem. to students. J ust F or F u n InterRneestources RECALL This contains puzzles, This guides students to This contains certain fascinating facts and search on the Internet for mathematical concepts interesting stories valuable information or or rules that students about Mathematics as interesting online games have learnt previously. enrichment for students. for their independent and self-directed learning. Preface v Contents CCCHHHAAAPPPTTTEEERRR 111 CCCHHHAAAPPPTTTEEERRR 222 Quadratic Equations 001 Linear Inequalities 041 and Functions 2.1 Inequalities 043 1.1 Solving Quadratic Equations by 003 2.2 Problem Solving involving 049 Completing the Square Inequalities 1.2 Solving Quadratic Equations by 010 2.3 Solving Simultaneous Linear 051 using Formula Inequalities 1.3 Solving Quadratic Equations by 012 Summary 054 Graphical Method Review Exercise 2 055 1.4 Solving Fractional Equations 017 that can be reduced to Quadratic Equations 1.5 Applications of Quadratic 020 Equations in Real-World Contexts 1.6 Graphs of Quadratic Functions 027 Summary 036 Review Exercise 1 038 CCCHHHAAAPPPTTTEEERRR 333 Indices and Standard Form 057 3.1 Indices 059 3.2 Laws of Indices 060 3.3 Zero and Negative Indices 069 3.4 Rational Indices 075 3.5 Compound Interest 081 3.6 Standard Form 086 Summary 094 Review Exercise 3 095 Revision Exercise A 097 vi Contents New Syllabus Mathematics (NSM) CCCHHHAAAPPPTTTEEERRR 444 CCCHHHAAAPPPTTTEEERRR 555 Coordinate Geometry 099 Graphs of Functions and 123 4.1 Gradient of a Straight Line 101 Graphical Solution 4.2 Length of a Line Segment 107 5.1 Graphs of Cubic Functions 125 4.3 Equation of a Straight Line 113 5.2 Graphs of Reciprocal Functions 128 Summary 119 5.3 Graphs of Exponential Functions 135 Review Exercise 4 120 5.4 Gradient of a Curve 139 5.5 Applications of Graphs in 144 Real-World Contexts Summary 162 Review Exercise 5 164 Revision Exercise B 167 CCCHHHAAAPPPTTTEEERRR 666 Further Trigonometry 171 6.1 Sine and Cosine of Obtuse Angles 173 6.2 Area of Triangle 181 6.3 Sine Rule 187 6.4 Cosine Rule 197 Summary 205 Review Exercise 6 207 Contents New Syllabus Mathematics (NSM) vii CCCHHHAAAPPPTTTEEERRR 777 Applications of Trigonometry 211 7.1 Angles of Elevation and 213 Depression 7.2 Bearings 219 7.3 Three-Dimensional Problems 227 Summary 240 Review Exercise 7 241 CCCHHHAAAPPPTTTEEERRR 888 Arc Length, Area of Sector and 245 Radian Measure 8.1 Length of Arc 247 8.2 Area of Sector 256 8.3 Radian Measure 263 8.4 Arc Length and Area of Sector 272 using Radian Measure Summary 282 Review Exercise 8 283 CCCHHHAAAPPPTTTEEERRR 999 Revision Exercise C 287 Congruence and Similarity Tests 291 9.1 Congruence Tests 293 9.2 Similarity Tests 309 9.3 Applications of Congruent and 324 Similar Triangles Summary 328 Review Exercise 9 330 viii Contents New Syllabus Mathematics (NSM)
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