Cambridge Checkpoint Mathematics Coursebook 9 -- Greg Byrd, Lynn Byrd and Chris Pearce剑桥数学完整.docx

Greg Byrd, Lynn Byrd and Chris PearceCambridge CheckpointMathematics9Coursebookcambridge university pressCambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, Delhi, Mexico CityCambridge University PressThe Edinburgh Building, Cambridge CB2 8RU, UKwww.cambridge.orgInformation on this title: www.cambridge.org/9781107668010© Cambridge University Press 2013This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press.First published 2013Printed and bound in the United Kingdom by the MPG Books GroupA catalogue record for this publication is available from the British LibraryISBN 978-1-107-66801-0 PaperbackCover image © Cosmo Condina concepts/AlamyCambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.5ContentsIntroduction5Acknowledgements61 Integers, powers and roots71.1 Directed numbers81.2 Square roots and cube roots101.3 Indices111.4 Working with indices12End-of-unit review142 Sequences and functions152.1 Generating sequences162.2 Finding the nth term182.3 Finding the inverse of a function20End-of-unit review223 Place value, ordering and rounding233.1 Multiplying and dividing decimals mentally243.2 Multiplying and dividing by powers of 10263.3 Rounding283.4 Order of operations30End-of-unit review324 Length, mass, capacity and time334.1 Solving problems involving measurements344.2 Solving problems involving average speed364.3 Using compound measures38End-of-unit review405 Shapes415.1 Regular polygons425.2 More polygons445.3 Solving angle problems455.4 Isometric drawings485.5 Plans and elevations505.6 Symmetry in three-dimensional shapes52End-of-unit review546 Planning and collecting data556.1 Identifying data566.2 Types of data586.3 Designing data-collection sheets596.4 Collecting data61End-of-unit review637 Fractions647.1 Writing a fraction in its simplest form657.2 Adding and subtracting fractions667.3 Multiplying fractions687.4 Dividing fractions707.5 Working with fractions mentally72End-of-unit review748 Constructions and Pythagoras theorem758.1 Constructing perpendicular lines768.2 Inscribing shapes in circles788.3 Using Pythagoras theorem81End-of-unit review839 Expressions and formulae849.1 Simplifying algebraic expressions859.2 Constructing algebraic expressions869.3 Substituting into expressions889.4 Deriving and using formulae899.5 Factorising919.6 Adding and subtracting algebraic fractions929.7 Expanding the product of twolinear expressions94End-of-unit review9610 Processing and presenting data9710.1 Calculating statistics9810.2 Using statistics100End-of-unit review10213.1 Solving linear equations12518.5 Direct proportion17313.2 Solving problems12718.6 Practical graphs17413.3 Simultaneous equations 1128End-of-unit review17613.4 Simultaneous equations 212913.5 Trial and improvement13019 Interpreting and discussing results17713.6 Inequalities13219.1 Interpreting and drawing frequencyEnd-of-unit review134diagrams17814 Ratio and proportion19.2 Interpreting and drawing line graphs18013519.3 Interpreting and drawing scatter graphs182Contents11 Percentages10316 Probability15111.1 Using mental methods10416.1 Calculating probabilities15211.2 Comparing different quantities10516.2 Sample space diagrams15311.3 Percentage changes10616.3 Using relative frequency15511.4 Practical examples107End-of-unit review157End-of-unit review10917 Bearings and scale drawings15812 Tessellations, transformations and loci11017.1 Using bearings15912.1 Tessellating shapes11117.2 Making scale drawings16212.2 Solving transformation problems113End-of-unit review16412.3 Transforming shapes11612.4 Enlarging shapes11918 Graphs16512.5 Drawing a locus12118.1 Gradient of a graph166End-of-unit review12318.2 The graph of y = mx + c16813 Equations and inequalities18.3 Drawing graphs16912418.4 Simultaneous equations17114.1 Comparing and using ratios13619.4 Interpreting and drawing stem-and-leaf14.2 Solving problems138diagrams184End-of-unit review14019.5 Comparing distributions and drawingconclusions18615 Area, perimeter and volume141End-of-unit review18915.1 Converting units of area and volume14215.2 Using hectares144End-of-year review19015.3 Solving circle problems145Glossary and index19415.4 Calculating with prisms and cylinders147End-of-unit review150IntroductionWelcome to Cambridge Checkpoint Mathematics stage 9The Cambridge Checkpoint Mathematics course covers the Cambridge Secondary 1 mathematics framework and is divided into three stages: 7, 8 and 9. This book covers all you need to know for stage 9.There are two more books in the series to cover stages 7 and 8. Together they will give you a firm foundation in mathematics.At the end of the year, your teacher may ask you to take a Progression test to find out how well you have done. This book will help you to learn how to apply your mathematical knowledge and to do well in the test.The curriculum is presented in six content areas:t Numbert .FBTVSFTt Geometryt Algebrat )BOEMJOH EBUBt 1SPCMFN TPMWJOH.This book has 19 units, each related to one of the first five content areas. Problem solving is included in all units. There are no clear dividing lines between the five areas of mathematics; skills learned in one unit are often used in other units.Each unit starts with an introduction, with key words listed in a blue box. This will prepare you for what you will learn in the unit. At the end of each unit is a summary box, to remind you what youve learned.Each unit is divided into several topics. Each topic has an introduction explaining the topic content,VTVBMMZ XJUI XPSLFE FYBNQMFT. )FMQGVM IJOUT BSF HJWFO JO CMVF SPVOEFE CPYFT. "U UIF FOE PG FBDI UPQJDthere is an exercise. Each unit ends with a review exercise. The questions in the exercises encourage you to apply your mathematical knowledge and develop your understanding of the subject.As well as learning mathematical skills you need to learn when and how to use them. One of the most important mathematical skills you must learn is how to solve problems.When you see this symbol, it means that the question will help you to develop your problem-solving skills.During your course, you will learn a lot of facts, information and techniques. You will start to think like a mathematician. You will discuss ideas and methods with other students as well as your teacher. These discussions are an important part of developing your mathematical skills and understanding.XavierMiaDakaraiOditiAndersSashaHassanHarshaJakeAliciaShenTaneshaRaziMahaZalikaLook out for these students, who will be asking questions, making suggestions and taking part in the activities throughout the units.AhmadAcknowledgementsThe authors and publishers acknowledge the following sources of copyright material and are grateful for the permissions granted. While every effort has been made, it has not always been possible to identify the sources of all the material used, or to trace all copyright holders. If any omissions are brought to our notice, we will be happy to include the appropriate acknowledgements on reprinting.p. 15 Ivan Vdovin/Alamy; p. 23tl zsschreiner/Shutterstock; p. 23tr Leon Ritter/Shutterstock;p. 29 Carl De Souza/AFP/Getty Images; p. 33t Chuyu/Shutterstock;p. 33ml Angyalosi Beata/Shutterstock; p. 33mr Cedric Weber/Shutterstock;p. 33bl Ruzanna/Shutterstock; p. 33br Foodpics/Shutterstock; p. 37t Steven Allan/iStock;p. 37m Mikael Damkier/Shutterstock; p. 37b Christopher Parypa/Shutterstock;p. 41 TTphoto/Shutterstock; p. 55t Dusit/Shutterstock; p. 55m Steven Coburn/Shutterstock;p. 55b Alexander Kirch/Shutterstock; p. 57 Jacek Chabraszewski/iStock; p. 73m Rich Legg/iStock;p. 73b Lance Ballers/iStock; p. 97 David Burrows/Shutterstock; p. 103 Dar Yasin/AP Photo;p. 110t Katia Karpei/Shutterstock; p. 110b Aleksey VI B/Shutterstock;p. 124 The Art Archive/Alamy; p. 127 Edhar/Shutterstock; p. 135 Sura Nualpradid/Shutterstock;p. 137 Dana E.Fry/Shutterstock; p. 137m Dana E.Fry/Shutterstock; p. 138t NASTYApro/Shutterstock;p. 138m Adisa/Shutterstock; p. 139m &)4UPDL/J4UPDL; Q. 139b Zubin li/iStock;p. 140t Christopher Futcher/iStock; p. 140b Pavel L Photo and Video/Shutterstock;p. 144 Eoghan McNally/Shutterstock; p. 146 Pecold/Shutterstock; p. 158tl Jumpingsack/Shutterstock;p. 158tr Triff/Shutterstock; p. 158ml Volina/Shutterstock; p. 158mr Gordan/Shutterstock;p. 185 Vale Stock/ShutterstockThe publisher would like to thank Ángel Cubero of the International School Santo Tomás de Aquino, Madrid, for reviewing the language level.1 Integers, powers and rootsKey wordsMake sure you learn and understand these key words:powerindex (indices)Mathematics is about finding patterns.This shows 1 + 3 = 2.You can also subtract.2 1 = 3 and2 3 = 1.How did you first learn to add and multiply negative integers? Perhaps you started with an addition table or a multiplication table for positive integers and then extended it. The patterns in the tables help you to do this.+321012336543210254321011432101203210123121012342101234530123456×321012339630369264202461321012300000000132101232642024639630369This shows 2 × 3 = 6.You can also divide.6 ÷ 2 = 3 and6 ÷ 3 = 2.Square numbers show a visual pattern. 1 + 3 = 4 = 221 + 3 + 5 = 9 = 321 + 3 + 5 + 7 = 16 = 42Can you continue this pattern?1 Integers, powers and roots71.1 Directed numbers1.1 Directed numbersDirected numbers have direction; they can be positive or negative. Directed numbers can be integers (whole numbers) or they can be decimal numbers.Here is a quick reminder of some important things to remember when you add, subtract, multiply and divide integers. These methods can also be used with any directed numbers.Think of a number line. Start at 0. Moving 3 to the right, then 5 to the left is the same as moving 2 to the left.What is 3 + 5?5+3321012345add negative subtract positive subtract negative add positiveOr you can change it to a subtraction: 3 + 5 = 3 5. Either way, the answer is 2.What about 3 5?Perhaps the easiest way is to add the inverse. 3 5 = 3 + 5 = 8What about multiplication?3 × 5 = 153 × 5 = 153 × 5 = 153 × 5 = 15Remember for multiplication and division: same signs positive answerdifferent signs negative answerMultiply the corresponding positive numbers and decide whether the answer is positive or negative.Division is similar.15 ÷ 3 = 515 ÷ 3 = 515 ÷ 3 = 515 ÷ 3 = 5These are the methods for integers.You can use exactly the same methods for any directed numbers, even if they are not integers.Worked example 1.1Complete these calculations.a3.5 + 4.1b 3.5 2.8c 6.3 × 3d 7.5 ÷ 2.5a 3.5 4.1 = 0.6You could draw a number line but it is easier to subtract the inverse (which is 4.1).b 3.5 + 2.8 = 6.3Change the subtraction to an addition. Add the inverse of 2.8 which is 2.8.c 6.3 × 3 = 18.9First multiply 6.3 by 3. The answer must be negative because 6.3 and 3 have opposite signs.d 7.5 ÷ 2.5 = 37.5 ÷ 2.5 = 3. The answer is positive because 7.5 and 2.5 have the same sign.令Exercise 1.11 Work these out.Do not use a calculator in this exercise.a 5 + 3b 5 + 0.3c 5 + 0.3d 0.5 + 0.3e 0.5 + 32 Work these out.a 2.8 + 1.3b 0.6 + 4.1c 5.8 + 0.3d 0.7 + 6.2e 2.25 + 0.127 0.4c0.4 7d0.4 0.7e 4 0.70.6 4.1c5.8 0.3d0.7 6.2e 2.25 0.123 Work these out.a 7 4b4 Work these out.a 2.8 1.3b5 The midday temperature, in Celsius degrees (°C), on four successive days is 1.5, 2.6, 3.4 and 0.5. Calculate the mean temperature.6 Find the missing numbers.a+ 4 = 1.5b+ 6.3 = 5.9c 4.3 += 2.1d 12.5 += 3.57 Find the missing numbers.a 3.5 = 11.6b 2.1 = 4.1c 8.2 = 7.2d 8.2 = 7.28 Copy and complete this addition table.+3.41.25.14.72.3 × 9.6 = 22.089 Use the information in the box to work these out.a 2.3 × 9.6b 22.08 ÷ 2.3c 22.08 ÷ 9.6d 4.6 × 9.6e 11.04 ÷ 2.310 Work these out.a 2.7 × 3b 2.7 ÷ 3c 1.2 × 1.2d 3.25 × 4e 17.5 ÷ 2.511 Copy and complete this multiplication table.×3.20.61.51.512 Complete these calculations.a 2 × 3b (2 × 3) × 4c (3 × 4) ÷ 813 Use the values given in the box to work out the value of each expression.p = 4.5 q = 5.5 r = 7.5a p qb (p + q) × rc (q + r) × pd (r q) ÷ (q p)×2.43.54.62.45.768.413.443.58.412.2516.14.613.4416.121.1614 Here is a multiplication table. Use the table to calculate these.a (2.4)2b 13.44 ÷ 4.6c 16.1 ÷ 3.5d 84 ÷ 2.415 p and q are numbers, p + q = 1 and pq = 20. What are the values of p and q?1 Integers, powers and roots91.3 Indices1.2 Square roots and cube rootsOnly squares or cubes of integers have integer square roots or cube roots.You should be able to recognise:t the squares of whole numbers up to 20 × 20 and their corresponding square rootst the cubes of whole numbers up to 5 × 5 × 5 and their corresponding cube roots.You can use a calculator to find square roots and cube roots, but you can estimate them without one.Worked example 1.1Estimate each root, to the nearest whole number.a295b 3 60a 172 = 289 and 182 = 324295 is between 289 and 324 so295 is between17 and 18.It will be a bit larger than 17.60 is between 27 and 64 so 3 60295 is 17 to the nearest whole number.b 33 = 27 and 43 = 64