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1、7Greg Byrd,Lynn Byrd and Chris PearceCambridge CheckpointMathematicsCoursebookUniversity Printing House,Cambridge CB2 8BS,United KingdomCambridge University Press is part of the University of Cambridge.It furthers the Universitys mission by disseminating knowledge in the pursuit ofeducation,learning
2、 and research at the highest international levels of excellence.www.cambridge.orgInformation on this title:www.cambridge.org/9781107641112 Cambridge University Press 2012Thispublicationisincopyright.Subjecttostatutoryexceptionand to the provisions of relevant collective licensing agreements,no repro
3、duction of any part may take place without the writtenpermissionofCambridgeUniversityPress.First published 20124th printing 2013Printed in India by Replika Press Pvt.LtdAcatalogue recordfor thispublication isavailable from the BritishLibraryISBN 978-1-107-64111-2 PaperbackCambridge University Press
4、has no responsibility for the persistence or accuracy ofURLsforexternalorthird-partyinternetwebsitesreferredtointhispublication,anddoesnotguaranteethatanycontentonsuchwebsites is,orwillremain,accurate or appropriate.Information regarding prices,travel timetables and otherfactualinformationgiveninthi
5、sworkiscorrectatthetimeoffirstprintingbutCambridge University Press does not guarantee the accuracy of such informationthereafter.3XavierMiaDakaraiAndersSashaHassanJakeAliciaShenRaziMahaAhmadWelcome to Cambridge Checkpoint Mathematics stage 7The Cambridge Checkpoint Mathematics course covers the Cam
6、bridge Secondary 1 mathematicsframework and is divided into three stages:7,8 and 9.This book covers all you need to know forstage 7.There are two more books in the series to cover stages 8 and 9.Together they will give you a firmfoundation in mathematics.Attheendoftheyear,your teacher mayask you tot
7、akeaProgression testto findouthowwell youhave done.This book will help you to learn how to apply your mathematical knowledge to dowell in the test.The curriculum is presented in six content areas:Number Measure GeometryAlgebra Handlingdata Problemsolving.This book has 19 units,each related to one of
8、 the first five content areas.Problem solving is included inall units.There are no clear dividing lines between the five areas of mathematics;skills learned in oneunit are often used in other units.Each unit starts with an introduction,withkey wordslisted in a blue box.This will prepare you for what
9、you will learn in the unit.At the end of each unit is asummarybox,to remind you what youve learned.Each unit is divided into several topics.Each topic has an introduction explaining the topic content,usuallywithworkedexamples.Helpfulhintsaregiveninblueroundedboxes.Attheendofeachtopicthere isan exerc
10、ise.Each unit ends withareviewexercise.Thequestionsin theexercises encourageyouto 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 mostimportant mathematical skills you must l
11、earn 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 likea mathematician.You will discuss ideas and methods with other
12、 students as well as your teacher.Thesediscussions 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 theactivities throughout the units.IntroductionOditiHarshaTaneshaZalika4Con
13、tentsIntroduction3Acknowledgements6Unit 1 Integers71.1Using negative numbers81.2Adding andsubtracting negative numbers101.3Multiples111.4Factorsandtests fordivisibility121.5Prime numbers141.6Squaresand squareroots16End of unit review18Unit 2 Sequences,expressions and formulae192.1Generatingsequences
14、(1)202.2Generatingsequences(2)222.3Representing simple functions242.4Constructing expressions262.5Deriving and using formulae28End of unit review30Unit 3 Place value,ordering and rounding313.1Understanding decimals323.2Multiplying and dividing by 10,100 and 1000333.3Ordering decimals353.4Rounding373
15、.5Adding and subtracting decimals383.6Multiplyingdecimals403.7Dividing decimals413.8Estimating and approximating42End of unit review45Unit 4 Length,mass and capacity464.1Knowingmetricunits474.2Choosingsuitableunits494.3Reading scales50End of unit review52Unit 5 Angles535.1Labelling and estimating an
16、gles545.2Drawing and measuring angles565.3Calculating angles585.4Solvingangleproblems60End of unit review62Unit 6 Planning and collecting data636.1Planning to collect data646.2Collecting data666.3Using frequency tables68End of unit review71Unit 7 Fractions727.1Simplifying fractions737.2Recognisingeq
17、uivalent fractions,decimals and percentages757.3Comparing fractions787.4Improper fractions and mixed numbers807.5Adding and subtracting fractions817.6Finding fractions of a quantity827.7Finding remainders83End of unit review85Unit 8 Symmetry868.1Recognisinganddescribing2Dshapesand solids878.2Recogni
18、singline symmetry898.3Recognisingrotationalsymmetry918.4Symmetryproperties oftriangles,specialquadrilaterals andpolygons93End of unit review96Unit 9 Expressions and equations979.1Collectingliketerms989.2Expanding brackets1009.3Constructing and solving equations101End of unit review1035ContentsUnit 1
19、0 Averages10410.1Averageandrange10510.2Themean10710.3Comparing distributions109End of unit review111Unit 11 Percentages11211.1Simplepercentages11311.2Calculating percentages11511.3Comparing quantities116End of unit review118Unit 12 Constructions11912.1Measuring and drawing lines12012.2Drawing perpen
20、dicular and parallel lines12112.3Constructing triangles12212.4Constructing squares,rectangles andpolygons124End of unit review127Unit 13 Graphs12813.1Plotting coordinates12913.2Linesparalleltotheaxes13113.3Other straight lines132End of unit review135Unit 14 Ratio and proportion13614.1Simplifying rat
21、ios13714.2Sharing ina ratio13814.3Usingdirectproportion140End of unit review142Unit 15 Time14315.1The 12-hour and 24-hour clock14415.2Timetables14615.3Real-lifegraphs148End of unit review151Unit 16 Probability15216.1Theprobabilityscale15316.2Equally likely outcomes15416.3Mutuallyexclusiveoutcomes156
22、16.4Estimating probabilities158End of unit review160Unit 17 Position and movement16117.1Reflecting shapes16217.2Rotating shapes16417.3Translating shapes166End of unit review168Unit 18 Area,perimeter and volume16918.1Converting between units for area17018.2Calculating the area and perimeterofrectangl
23、es17118.3Calculating the area and perimeterof compound shapes17318.4Calculatingthevolumeofcuboids17518.5Calculatingthesurfaceareaofcubesand cuboids177End of unit review179Unit 19 Interpreting and discussing results18019.1Interpreting and drawing pictograms,bar charts,bar-line graphs andfrequencydiag
24、rams18119.2Interpreting and drawing pie charts18519.3Drawingconclusions187End of unit review190End of year review191Glossary1956AcknowledgementsThe authors and publisher are grateful for the permissions granted to reproduce copyright materials.While every effort has been made,it has not always been
25、possible to identify the sources of all thematerials used,or to trace all the copyright holders.If any omissions are brought to our notice,we willbe happy to include the appropriate acknowledgements on reprinting.p.19tTheGrangerCollection/TopFoto;p.19bl EijiUedaPhotography/Shutterstock;p.19br sizov/
26、Shutterstock;p.27t Ilin Sergey/Shutterstock;p.31mr Joel Blit/Shutterstock;p.31bl 3d brained/Shutterstock;p.39m Kurhan/Shutterstock;p.44tr Rena Schild/Shutterstock;p.44mr Kirill P/Shutterstock;p.45b Tyler Olson/Shutterstock;p.46tm Georgis Kollidas/Shutterstock;p.46mrStefanieTimmermann/iStock;p.46brYu
27、ttasakJannarong/Shutterstock;p.49mGreg Byrd;p.53brMesopotamian/The Art Gallery Collection/Alamy;p.63b Adisa/Shutterstock;p.65t Greg Byrd;p.80b Denise Kappa/Shutterstock;p.82b Gallo Images/Stringer/Getty Images Sport/Getty Images;p.84tmSilviaBoratti/iStock;p.84mr jobhopper/iStock;p.85bSteveBroer/Shut
28、terstock;p.86tm S.Borisov/Shutterstock;p.86bl GregByrd;p.86brGregByrd;p.97mlJames Davies/Alamy;p.97brGreg Byrd;p.105t Michael Chamberlin/Shutterstock;p.112ml Alhovik/shutterstock;p.112mr kated/Shutterstock;p.114m Graa Victoria/iStock;p.119tlClaude Dagenais/iStock;p.119mr Michael Stokes/Shutterstock;
29、p.119brLosevskyPavel/Shutterstock;p.128bUSBFCO/Shutterstock;p.136tHultonArchive/iStock;p.138t Maksim Toome/Shutterstock;p.142b charistoone-images/Alamy;p.143mlEastimages/shutterstock;p.143m KtD/Shutterstock;p.143mr Baloncici/Shutterstock;p.152bl auremar/Shutterstock;p.152br m.bonotto/Shutterstock;p.
30、161tl Greg Byrd;p.161mr Katarina Calgar/iStock;p.161brNickoloayStanev/Shutterstock;p.180ballekk/iStockl=left,r=right,t=top,b=bottom,m=middleThe publisher would like to thank ngel Cubero of the International School Santo Toms de Aquino,Madrid,for reviewing the language level.1Integers7The first numbe
31、rs you learn about arewhole numbers,the numbers used forcounting:1,2,3,4,5,Thewholenumberzerowasonlyunderstoodrelativelyrecentlyinhumanhistory.Thesymbol0thatisusedtorepresentitisalsoarecentinvention.ThewordzeroitselfisofArabic origin.Fromthecountingnumbers,peopledevelopedtheideaofnegativenumbers,whi
32、chareused,forexample,toindicatetemperaturesbelowzeroonthe Celsius scale.Insomecountries,theremaybehighmountainsanddeepvalleys.Theheightofamountainismeasured as a distance above sea level.This is theplacewherethelandmeetsthesea.Sometimesthebottomsofvalleysaresodeepthattheyaredescribedasbelowsealevel.
33、Thismeansthatthedistancesarecounteddownwardsfromsealevel.Thesecanbewrittenusingnegativenumbers.ThelowesttemperatureeverrecordedontheEarthssurfacewas89C,inAntarcticain1983.The lowest possible temperature is absolute zero,273C.Whenyourefertoachangeintemperature,youmustalwaysdescribeitasanumberofdegree
34、s.Whenyouwrite0C,forexample,youaredescribingthefreezingpointofwater;100Cistheboilingpointofwater.Writteninthisway,theseareexacttemperatures.Todistinguishthemfromnegativenumbers,thecountingnumbersarecalledpositivenumbers.Together,thepositive(orcounting)numbers,negativenumbersandzeroarecalledintegers.
35、Thisunitisallaboutintegers.Youwilllearnhowtoaddandsubtractintegersandyouwillstudysomeofthepropertiesofpositiveintegers.Youwillexploreotherpropertiesofnumbers,anddifferenttypesofnumber.Youshouldknowmultiplicationfactsupto1010andtheassociateddivisionfacts.Forexample,65=30meansthat306=5and305=6.Thisuni
36、twillremindyouofthesemultiplicationanddivisionfacts.1IntegersKeywordsMake sure you learn andunderstand these key words:whole numbernegativenumberpositive numberintegermultiplecommon multiplelowestcommonmultiplefactorremaindercommonfactordivisibleprimenumbersieveofEratosthenesproductsquarenumbersquar
37、e rootinverseCF501204010030802060104002010020302040401Integers81.1 Using negative numbersWorked example 1.1The temperature at midday was 3C.By midnight it has fallen by 10 degrees.What is the temperature at midnight?The temperature at midday was 3C.Use the number line to count 10 to the left from 3.
38、Remember tocount 0.1010 9 8 7 6 5 4 3 2 1012345678910The temperature at midnight was 7C.令Exercise 1.11.1Using negative numbersWhenyouworkwithnegativenumbers,itcanbeusefultothinkintermsoftemperatureontheCelsius scale.Waterfreezesat0Cbutthetemperatureinafreezerwillbelowerthanthat.Recording temperature
39、s below freezing is one very important use of negative numbers.Youcanalsousenegativenumberstorecordothermeasures,suchasdepthbelowsealevelortimesbeforeaparticularevent.Youcanoftenshowpositiveandnegativenumbersonanumberline,with0inthecentre.8 7 6 5 4 3 2 1 012345678Thenumberlinehelpsyoutoputintegersin
40、order.Whenthenumbers1,1,3,4,5,6areputinorder,fromlowesttohighest,theyarewrittenas6,4,1,1,3,5.YoucanwritethecalculationinWorkedexample1.1asasubtraction:310=7.Ifthetemperatureatmidnightwas10degreeshigher,youcanwrite:3+10=13.1Here are six temperatures,in degrees Celsius.6105402Write them in order,start
41、ing with the lowest.Positive numbers go to the right.Negative numbers go to the left.Use the number line if you need to.1.1 Using negative numbers1Integers92Here are the midday temperatures,in degrees Celsius,of five cities on the same day.MoscowTokyoBerlinBostonMelbourne845212aWhich city was the wa
42、rmest?bWhich city was the coldest?cWhat is the difference between the temperatures of Berlin and Boston?3Draw a number line from 6 to 6.Write down the integer that ishalfway between the two numbersin each pair below.a1 and 5b 5 and 1c 1 and 5d 5 and 14Some frozen food is stored at 8C.During a power
43、failure,the temperature increases by 3 degreesevery minute.Copy and complete this table to show the temperature of the food.Minutes passed01234Temperature(C)85During the day the temperature in Toms greenhouse increasesfrom 4 C to5 C.What is the rise in temperature?6The temperature this morning was 7
44、C.This afternoon,the temperature dropped by 10 degrees.What is the new temperature?7Luigi recorded the temperature in his garden at different times of the same day.Time060009001200150018002100Temperature(C)415716aWhen was temperature the lowest?bWhat was the difference in temperature between 0600 an
45、d 1200?cWhat was the temperature difference between 0900 and 2100?dAt midnight the temperature was 5 degrees lower than it was at 2100.What was the temperature at midnight?8Heights below sea level can be shown by using negative numbers.aWhat does it mean to say that the bottom of a valley is at 200
46、metres?bA hill next to the valley in part a is 450 metres high.How far is the top of the hill above the bottom of the valley?9Work out the following additions.a 2+5b 8+2c 10+7d 3+4+5e 6+1+5f20+1910Find the answers to these subtractions.a 4 6b 4 6c 87d 6 7 3e 4 3 3f10 25Think of temperatures going up
47、.Think of temperatures going down.1Integers101.2 Adding and subtracting negative numbers令Exercise 1.21.2Adding and subtracting negative numbersYou have seen how to add or subtract a positive number by thinking of temperatures going up and down.Examples:3+5=23 5=8Supposeyouwanttoaddorsubtractanegativ
48、enumber,forexample,3+5or35.Howcanyoudothat?Youneedtothinkabouttheseinadifferentway.Toworkout5+3,startat0onanumberline.5meansmove5totheleftand3meansmove3totheleft.Theresultismove8totheleft.5+3=8539 8 7 6 5 4 3 2 10125+3=8Toworkout35youwantthedifferencebetween5and3.Togofrom5to3onanumberline,move2tothe
49、right.3 5=23 5=2Work these out.a2+6b2 662 6a2+6=42b2 6=87 6 5 4 3 2 101235 4 3 2 101232 6=8Worked example 1.21 Work these out.a3+4b3+6c5+5d2+92 Work these out.a3 7b4 1c2 4d583 Work these out.a3+5b3+5c3+5d3+54 Work these out.a4 6b4 6c46d465 a Work these out.i 3+5ii 5+3iii 2+8iv 8+2b If.AandTare two i
50、ntegers,isitalwaystrue that.A+T=T+.A?Give a reason for your answer.6 a Work these out.i 5 2ii 25iii 43iv 34bIf.A and T are two integers,what can you say about.A T and T.A?6 5 4 3 2 10121.3Multiples1Integers11If I share the sweets equally among 2,3,4,5 or 6people there will always be 1 sweet left ove