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1、Greg Byrd,Lynn Byrd and Chris PearceCoursebookCambridge CheckpointMathematics9cambridge university press Cambridge,New York,Melbourne,Madrid,Cape Town,Singapore,So Paulo,Delhi,Mexico CityCambridge University Press The Edinburgh Building,Cambridge CB2 8RU,UKwww.cambridge.org Information on this title
2、: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.Fi
3、rst 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
4、 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.3ContentsIntroduction 5Acknowledgements 61 Integers,powers and roots 71.1 Directed numbers 81.2 Square ro
5、ots and cube roots 101.3 Indices 111.4 Working with indices 12End-of-unit review 142 Sequences and functions 152.1 Generating sequences 162.2 Finding the nth term 182.3 Finding the inverse of a function 20End-of-unit review 223 Place value,ordering and rounding 233.1 Multiplying and dividing decimal
6、s mentally 243.2 Multiplying and dividing by powers of 10 263.3 Rounding 283.4 Order of operations 30End-of-unit review 324 Length,mass,capacity and time 334.1 Solving problems involving measurements 344.2 Solving problems involving average speed 364.3 Using compound measures 38End-of-unit review 40
7、5 Shapes 415.1 Regular polygons 425.2 More polygons 445.3 Solving angle problems 455.4 Isometric drawings 485.5 Plans and elevations 505.6 Symmetry in three-dimensional shapes 52End-of-unit review 546 Planning and collecting data 556.1 Identifying data 566.2 Types of data 586.3 Designing data-collec
8、tion sheets 596.4 Collecting data 61End-of-unit review 637 Fractions 647.1 Writing a fraction in its simplest form 657.2 Adding and subtracting fractions 667.3 Multiplying fractions 687.4 Dividing fractions 707.5 Working with fractions mentally 72End-of-unit review 74 8 Constructions and Pythagoras
9、theorem 758.1 Constructing perpendicular lines 768.2 Inscribing shapes in circles 788.3 Using Pythagoras theorem 81End-of-unit review 839 Expressions and formulae 849.1 Simplifying algebraic expressions 859.2 Constructing algebraic expressions 869.3 Substituting into expressions 889.4 Deriving and u
10、sing formulae 899.5 Factorising 919.6 Adding and subtracting algebraic fractions 929.7 Expanding the product of two linear expressions 94End-of-unit review 9610 Processing and presenting data 9710.1 Calculating statistics 9810.2 Using statistics 100End-of-unit review 1024 Contents11 Percentages 1031
11、1.1 Using mental methods 10411.2 Comparing different quantities 10511.3 Percentage changes 10611.4 Practical examples 107End-of-unit review 10912 Tessellations,transformations and loci 11012.1 Tessellating shapes 11112.2 Solving transformation problems 11312.3 Transforming shapes 11612.4 Enlarging s
12、hapes 11912.5 Drawing a locus 121End-of-unit review 12313 Equations and inequalities 12413.1 Solving linear equations 12513.2 Solving problems 12713.3 Simultaneous equations 1 12813.4 Simultaneous equations 2 12913.5 Trial and improvement 13013.6 Inequalities 132End-of-unit review 13414 Ratio and pr
13、oportion 13514.1 Comparing and using ratios 13614.2 Solving problems 138End-of-unit review 14015 Area,perimeter and volume 14115.1 Converting units of area and volume 14215.2 Using hectares 14415.3 Solving circle problems 14515.4 Calculating with prisms and cylinders 147End-of-unit review 15016 Prob
14、ability 15116.1 Calculating probabilities 15216.2 Sample space diagrams 15316.3 Using relative frequency 155End-of-unit review 15717 Bearings and scale drawings 15817.1 Using bearings 15917.2 Making scale drawings 162End-of-unit review 16418 Graphs 16518.1 Gradient of a graph 16618.2 The graph of y=
15、mx+c 16818.3 Drawing graphs 16918.4 Simultaneous equations 17118.5 Direct proportion 17318.6 Practical graphs 174End-of-unit review 17619 Interpreting and discussing results 17719.1 Interpreting and drawing frequency diagrams 17819.2 Interpreting and drawing line graphs 18019.3 Interpreting and draw
16、ing scatter graphs 18219.4 Interpreting and drawing stem-and-leaf diagrams 18419.5 Comparing distributions and drawing conclusions 186End-of-unit review 189End-of-year review 190Glossary and index 1945IntroductionWelcome to Cambridge Checkpoint Mathematics stage 9Th e Cambridge Checkpoint Mathematic
17、s course covers the Cambridge Secondary 1 mathematics framework and is divided into three stages:7,8 and 9.Th is book covers all you need to know for stage 9.Th ere are two more books in the series to cover stages 7 and 8.Together they will give you a fi rm foundation in mathematics.At the end of th
18、e year,your teacher may ask you to take a Progression test to fi nd out how well you have done.Th is book will help you to learn how to apply your mathematical knowledge and to do well in the test.Th e curriculum is presented in six content areas:?Number?Geometry?Algebra?Th is book has 19 units,each
19、 related to one of the fi rst fi ve content areas.Problem solving is included in all units.Th ere are no clear dividing lines between the fi ve areas of mathematics;skills learned in one unit are oft en used in other units.Each unit starts with an introduction,with key words listed in a blue box.Th
20、is 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,?there is an exercise.Each unit ends with a review exercise.Th e ques
21、tions 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 se
22、e 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.Th ese
23、 discussions are an important part of developing your mathematical skills and understanding.Look out for these students,who will be asking questions,making suggestions and taking part in the activities throughout the units.HassanDakaraiShenXavierJakeAndersRaziSashaMahaMiaAliciaHarshaZalikaOditiTanes
24、haAhmad6AcknowledgementsTh e authors and publishers acknowledge the following sources of copyright material and are grateful for the permissions granted.While every eff ort has been made,it has not always been possible to identify the sources of all the material used,or to trace all copyright holder
25、s.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/Shutterst
26、ock;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/Sh
27、utterstock;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 Th e Art Archive/Alamy;p.127 Edhar/Shutterstock;p.135 Sura Nualpradid/Shutters
28、tock;p.137 Dana E.Fry/Shutterstock;p.137m Dana E.Fry/Shutterstock;p.138t NASTYApro/Shutterstock;p.138m Adisa/Shutterstock;p.139m?b 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 Jumping
29、sack/Shutterstock;p.158tr Triff /Shutterstock;p.158ml Volina/Shutterstock;p.158mr Gordan/Shutterstock;p.185 Vale Stock/ShutterstockTh e publisher would like to thank ngel Cubero of the International School Santo Toms de Aquino,Madrid,for reviewing the language level.1 Integers,powers and roots7Mathe
30、matics is about fi nding patterns.How did you fi rst 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.Th e patterns in the tables help you to do this.+321012336543210254321011432101203210123121
31、012342101234530123456321012339630369264202461321012300000000132101232642024639630369This shows2 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?Make sure you learn and understand these key words:powerindex(indic
32、es)Key wordsThis shows1+3=2.You can also subtract.2 1=3 and2 3=1.1 Integers,powers and roots1 Integers,powers and roots81.1 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 numbe
33、rs.Here is a quick reminder of some important things to remember when you add,subtract,multiply and divide integers.Th ese methods can also be used with any directed numbers.What is 3+5?35210123+345Or you can change it to a subtraction:3+5=3 5.Either way,the answer is 2.What about 3 5?Perhaps the ea
34、siest way is to add the inverse.3 5=3+5=8What about multiplication?3 5=15 3 5=15 3 5=15 3 5=15Multiply the corresponding positive numbers and decide whether the answer is positive or negative.Division is similar.15 3=5 15 3=5 15 3=5 15 3=5Th ese are the methods for integers.You can use exactly the s
35、ame methods for any directed numbers,even if they are not integers.?Exercise 1.11 Work these out.a 5+3 b 5+0.3 c 5+0.3 d 0.5+0.3 e 0.5+32 Work these out.a 2.8+1.3 b 0.6+4.1 c 5.8+0.3 d 0.7+6.2 e 2.25+0.12Think of a number line.Start at 0.Moving 3 to the right,then 5 to the left is the same as moving
36、 2 to the left.add negative subtract positivesubtract negative add positiveRemember for multiplication and division:same signs positive answerdifferent signs negative answerDo not use a calculator in this exercise.Worked example 1.1 Complete these calculations.a 3.5+4.1 b 3.5 2.8 c 6.3 3 d 7.5 2.5a
37、3.5 4.1=0.6 You could draw a number line but it is easier to subtract the inverse(which is 4.1).b 3.5+2.8=6.3 Change the subtraction to an addition.Add the inverse of 2.8 which is 2.8.c 6.3 3=18.9 First multiply 6.3 by 3.The answer must be negative because 6.3 and 3 have opposite signs.d 7.5 2.5=3 7
38、.5 2.5=3.The answer is positive because 7.5 and 2.5 have the same sign.1 Integers,powers and roots91.1 Directed numbers3 Work these out.a 7 4 b 7 0.4 c 0.4 7 d 0.4 0.7 e 4 0.74 Work these out.a 2.8 1.3 b 0.6 4.1 c 5.8 0.3 d 0.7 6.2 e 2.25 0.125 The midday temperature,in Celsius degrees(C),on four su
39、ccessive days is 1.5,2.6,3.4 and 0.5.Calculate the mean temperature.6 Find the missing numbers.a +4=1.5 b +6.3=5.9 c 4.3+=2.1 d 12.5+=3.57 Find the missing numbers.a 3.5=11.6 b 2.1=4.1 c 8.2=7.2 d 8.2=7.28 Copy and complete this addition table.+3.41.25.14.79 Use the information in the box to work th
40、ese out.a 2.3 9.6 b 22.08 2.3 c 22.08 9.6d 4.6 9.6 e 11.04 2.310 Work these out.a 2.7 3 b 2.7 3 c 1.2 1.2 d 3.25 4 e 17.5 2.5 11 Copy and complete this multiplication table.3.20.61.51.512 Complete these calculations.a 2 3 b(2 3)4 c(3 4)813 Use the values given in the box to work out the value of eac
41、h expression.a p q b(p+q)r c(q+r)p d(r q)(q p)14 Here is a multiplication table.Use the table to calculate these.a(2.4)2 b 13.44 4.6c 16.1 3.5 d 84 2.415 p and q are numbers,p+q=1 and pq=20.What are the values of p and q?2.3 9.6=22.08p=4.5 q=5.5 r=7.52.43.54.62.45.768.413.443.58.412.2516.14.613.4416
42、.121.161 Integers,powers and roots101.2 Square roots and cube rootsYou should be able to recognise:?the squares of whole numbers up to 20 20 and their corresponding square roots?the cubes of whole numbers up to 5 5 5 and their corresponding cube roots.You can use a calculator to fi nd square roots a
43、nd cube roots,but you can estimate them without one.?Exercise 1.21 Read the statement on the right.Write a similar statement for each root.a 20 b 248 c 314 d 835.e 157 2 Explain why 3053is between 6 and 7.3 Estimate each root,to the nearest whole number.a 171 b 35 c 407 d 263.e 2924 Read the stateme
44、nt on the right.Write a similar statement for each root.a 1003 b 2223 c 8253 d 3263 e 5883.5 What Ahmad says is not correct.a Show that 160 is between 12 and 13.b Write down the number of which 40 is square root.6 a Find 1225.b Estimate 12253 to the nearest whole number.7 Show that 1253 is less than
45、 half of 125.8 Use a calculator to fi nd these square roots and cube roots.a 625 b 2025.c 4624.d 17283 e 68593.9 Use a calculator to fi nd these square roots and cube roots.Round your answers to 2 d.p.a 55 b 108 c 2003 d 6293 e 100003Only squares or cubes of integers have integer square roots or cub
46、e roots.2 8 3Do not use a calculator in this exercise,unless you are told to.10 12003 11352=1225Worked example 1.1Estimate each root,to the nearest whole number.a 295 b 603a 172=289 and 182=324 295 is between 289 and 324 so 295 is between 17 and 18.295 is 17 to the nearest whole number.It will be a
47、bit larger than 17.b 33=27 and 43=64 60 is between 27 and 64 so 603 is between 3 and 4.603 is 4,to the nearest whole number.It will be a bit less than 4.A calculator gives 3.91 to 2 d.p.16416040.=so1.2 Square roots and cube roots1 Integers,powers and roots111.3 IndicesTh is table shows powers of 3.L
48、ook at the patterns in the table.Power34333231303132333435Value18112719131392781243Negative powers of any positive integer are fractions.Here are some more examples.24=2 2 2 2=16 24=116 73=7 7 7=353 73=1343Any positive integer to the power 0 is 1.20=1 70=1 120=1?Exercise 1.31 Write each number as a
49、fraction.a 51 b 52 c 53 d 542 Write each number as a fraction or as an integer.a 72 b 72 c 71 d 70 e 733 Write each number as a fraction.a 41 b 102 c 23 d 121 e 152 f 2024 a Simplify each number.i 20 ii 50 iii 100 iv 200b Write the results in part a as a generalised rule.5 Write each expression as a
50、 single number.a 20+21+22 b 32+3+30+31 c 5 50 516 Write each number as a decimal.a 51 b 52 c 101 d 102 e 1037 Write each number as a power of 2.a 8 b 12 c 14 d 116 e 18 210=1024.In computing this is called 1K.Write each of these as a power of 2.a 2K b 0.5K c 11K34 is 3 to the power 4.4 is called the