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1、Greg Byrd,Lynn Byrd and Chris PearceCoursebookCambridge CheckpointMathematics7University 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 of education,learnin
2、g and research at the highest international levels of excellence.www.cambridge.org Information on this title:www.cambridge.org/9781107641112 Cambridge University Press 2012This publication is in copyright.Subject to statutory exception and to the provisions of relevant collective licensing agreement
3、s,no reproduction of any part may take place without the written permission of Cambridge University Press.First published 2012 Printed in by A catalogue record for this publication is available from the British LibraryISBN 978-1-107-64111-2 PaperbackCambridge University Press has no responsibility f
4、or 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.Information regarding prices,travel timetables and other factual information given i
5、n this work is correct at the time of first printing but Cambridge University Press does not guarantee the accuracy of such information thereafter.4th printing 2013IndiaReplika Press Pvt.Ltd 3IntroductionWelcome to Cambridge Checkpoint Mathematics stage 7Th e Cambridge Checkpoint Mathematics course
6、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 7.Th ere are two more books in the series to cover stages 8 and 9.Together they will give you a fi rm foundation in mathematics.At the end of the year,yo
7、ur 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 to do well in the test.Th e curriculum is presented in six content areas:Number Measure Geometry Algebra Handling data Problem solving.Th i
8、s book has 19 units,each 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
9、listed in a blue box.Th 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,usually with worked examples.Helpful hints ar
10、e given in blue rounded boxes.At the end of each topic there is an exercise.Each unit ends with a review exercise.Th e 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
11、 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-solvingskills.During your course,you will learn a lot of facts,information and techniques.You will
12、 start to think like a mathematician.You will discuss ideas and methods with other students as well as your teacher.Th ese 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
13、 part in the activities throughout the units.HassanDakaraiShenXavierJakeAndersRaziSashaMahaMiaAliciaHarshaZalikaOditiTaneshaAhmad4ContentsIntroduction 3Acknowledgements 6Unit 1 Integers 71.1 Using negative numbers 81.2 Adding and subtracting negative numbers 101.3 Multiples 111.4 Factors and tests f
14、or divisibility 121.5 Prime numbers 141.6 Squares and square roots 16End of unit review 18Unit 2 Sequences,expressions and formulae 192.1 Generating sequences(1)202.2 Generating sequences(2)222.3 Representing simple functions 242.4 Constructing expressions 262.5 Deriving and using formulae 28End of
15、unit review 30Unit 3 Place value,ordering and rounding 313.1 Understanding decimals 323.2 Multiplying and dividing by 10,100 and 1000 333.3 Ordering decimals 353.4 Rounding 373.5 Adding and subtracting decimals 383.6 Multiplying decimals 403.7 Dividing decimals 413.8 Estimating and approximating 42E
16、nd of unit review 45Unit 4 Length,mass and capacity 464.1 Knowing metric units 474.2 Choosing suitable units 494.3 Reading scales 50End of unit review 52Unit 5 Angles 535.1 Labelling and estimating angles 545.2 Drawing and measuring angles 565.3 Calculating angles 585.4 Solving angle problems 60End
17、of unit review 62Unit 6 Planning and collecting data 636.1 Planning to collect data 646.2 Collecting data 666.3 Using frequency tables 68End of unit review 71Unit 7 Fractions 727.1 Simplifying fractions 737.2 Recognising equivalent fractions,decimals and percentages 757.3 Comparing fractions 787.4 I
18、mproper fractions and mixed numbers 807.5 Adding and subtracting fractions 817.6 Finding fractions of a quantity 827.7 Finding remainders 83End of unit review 85Unit 8 Symmetry 868.1 Recognising and describing 2D shapes and solids 878.2 Recognising line symmetry 898.3 Recognising rotational symmetry
19、 918.4 Symmetry properties of triangles,special quadrilaterals and polygons 93End of unit review 96Unit 9 Expressions and equations 979.1 Collecting like terms 989.2 Expanding brackets 1009.3 Constructing and solving equations 101End of unit review 1035Unit 10 Averages 10410.1 Average and range 1051
20、0.2 The mean 10710.3 Comparing distributions 109End of unit review 111Unit 11 Percentages 11211.1 Simple percentages 11311.2 Calculating percentages 11511.3 Comparing quantities 116End of unit review 118Unit 12 Constructions 11912.1 Measuring and drawing lines 12012.2 Drawing perpendicular and paral
21、lel lines 12112.3 Constructing triangles 12212.4 Constructing squares,rectangles and polygons 124End of unit review 127Unit 13 Graphs 12813.1 Plotting coordinates 12913.2 Lines parallel to the axes 13113.3 Other straight lines 132End of unit review 135Unit 14 Ratio and proportion 13614.1 Simplifying
22、 ratios 13714.2 Sharing in a ratio 13814.3 Using direct proportion 140End of unit review 142Unit 15 Time 14315.1 The 12-hour and 24-hour clock 14415.2 Timetables 14615.3 Real-life graphs 148End of unit review 151Unit 16 Probability 15216.1 The probability scale 15316.2 Equally likely outcomes 15416.
23、3 Mutually exclusive outcomes 15616.4 Estimating probabilities 158End of unit review 160Unit 17 Position and movement 16117.1 Reflecting shapes 16217.2 Rotating shapes 16417.3 Translating shapes 166End of unit review 168Unit 18 Area,perimeter and volume 16918.1 Converting between units for area 1701
24、8.2 Calculating the area and perimeter of rectangles 17118.3 Calculating the area and perimeter of compound shapes 17318.4 Calculating the volume of cuboids 17518.5 Calculating the surface area of cubes and cuboids 177End of unit review 179Unit 19 Interpreting and discussing results 18019.1 Interpre
25、ting and drawing pictograms,bar charts,bar-line graphs and frequency diagrams 18119.2 Interpreting and drawing pie charts 18519.3 Drawing conclusions 187End of unit review 190End of year review 191Glossary 195 Contents6Th e authors and publisher are grateful for the permissions granted to reproduce
26、copyright materials.While every eff ort has been made,it has not always been possible to identify the sources of all the materials used,or to trace all the copyright holders.If any omissions are brought to our notice,we will be happy to include the appropriate acknowledgements on reprinting.p.19t Th
27、 e Granger Collection/TopFoto;p.19bl Eiji Ueda Photography/Shutterstock;p.19br sizov/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/Shutt
28、erstock;p.46tm Georgis Kollidas/Shutterstock;p.46mr Stefanie Timmermann/iStock;p.46br Yuttasak Jannarong/Shutterstock;p.49m Greg Byrd;p.53br Mesopotamian/Th e Art Gallery Collection/Alamy;p.63b Adisa/Shutterstock;p.65t Greg Byrd;p.80b Denise Kappa/Shutterstock;p.82b Gallo Images/Stringer/Getty Image
29、s Sport/Getty Images;p.84tm Silvia Boratti/iStock;p.84mr jobhopper/iStock;p.85b Steve Broer/Shutterstock;p.86tm S.Borisov/Shutterstock;p.86bl Greg Byrd;p.86br Greg Byrd;p.97ml James Davies/Alamy;p.97br Greg Byrd;p.105t Michael Chamberlin/Shutterstock;p.112ml Alhovik/shutterstock;p.112mr kated/Shutte
30、rstock;p.114m Graa Victoria/iStock;p.119tl Claude Dagenais/iStock;p.119mr Michael Stokes/Shutterstock;p.119br Losevsky Pavel/Shutterstock;p.128b USBFCO/Shutterstock;p.136t Hulton Archive/iStock;p.138t Maksim Toome/Shutterstock;p.142b charistoone-images/Alamy;p.143ml Eastimages/shutterstock;p.143m Kt
31、D/Shutterstock;p.143mr Baloncici/Shutterstock;p.152bl auremar/Shutterstock;p.152br m.bonotto/Shutterstock;p.161tl Greg Byrd;p.161mr Katarina Calgar/iStock;p.161br Nickoloay Stanev/Shutterstock;p.180b allekk/iStockl=left ,r=right,t=top,b=bottom,m=middleTh e publisher would like to thank ngel Cubero o
32、f the International School Santo Toms de Aquino,Madrid,for reviewing the language level.Acknowledgements1 Integers71 IntegersMake sure you learn and understand these key words:whole numbernegative numberpositive numberintegermultiplecommon multiplelowest common multiplefactorremaindercommon factordi
33、visibleprime numbersieve of Eratosthenesproductsquare numbersquare rootinverseKey wordsTh e fi rst numbers you learn about are whole numbers,the numbers used for counting:1,2,3,4,5,Th e whole number zero was only understood relatively recently in human history.Th e symbol 0 that is used to represent
34、 it is also a recent invention.Th e word zero itself is of Arabic origin.From the counting numbers,people developed the idea of negative numbers,which are used,for example,to indicate temperatures below zero on the Celsius scale.In some countries,there may be high mountains and deep valleys.Th e hei
35、ght of a mountain is measured as a distance above sea level.Th is is the place where the land meets the sea.Sometimes the bottoms of valleys are so deep that they are described as below sea level.Th is means that the distances are counted downwards from sea level.Th ese can be written using negative
36、 numbers.Th e lowest temperature ever recorded on the Earths surface was 89 C,in Antarctica in 1983.Th e lowest possible temperature is absolute zero,273 C.When you refer to a change in temperature,you must always describe it as a number of degrees.When you write 0 C,for example,you are describing t
37、he freezing point of water;100 C is the boiling point of water.Written in this way,these are exact temperatures.To distinguish them from negative numbers,the counting numbers are called positive numbers.Together,the positive(or counting)numbers,negative numbers and zero are called integers.Th is uni
38、t is all about integers.You will learn how to add and subtract integers and you will study some of the properties of positive integers.You will explore other properties of numbers,and diff erent types of number.You should know multiplication facts up to 10 10 and the associated division facts.For ex
39、ample,6 5=30 means that 30 6=5 and 30 5=6.Th is unit will remind you of these multiplication and division facts.50CF4030201001020304012010080604020020401 Integers81.1 Using negative numbers1.1 Using negative numbersWhen you work with negative numbers,it can be useful to think in terms of temperature
40、 on the Celsius scale.Water freezes at 0 C but the temperature in a freezer will be lower than that.Recording temperatures below freezing is one very important use of negative numbers.You can also use negative numbers to record other measures,such as depth below sea level or times before a particula
41、r event.You can oft en show positive and negative numbers on a number line,with 0 in the centre.0123456788 7 6 5 4 3 2 1Th e number line helps you to put integers in order.When the numbers 1,1,3,4,5,6 are put in order,fromlowest to highest,they are written as 6,4,1,1,3,5.You can write the calculatio
42、n in Worked example 1.1 as a subtraction:3 10=7.If the temperature at midnight was 10 degrees higher,you can write:3+10=13.F Exercise 1.11 Here are six temperatures,in degrees Celsius.6 10 5 4 0 2 Write them in order,starting with the lowest.Positive numbers go to the right.Negative numbers go to th
43、e left.Use the number line if you need to.Worked example 1.1The temperature at midday was 3 C.By midnight it has fallen by 10 degrees.What is the temperature at midnight?The temperature at midday was 3 C.Use the number line to count 10 to the left from 3.Remember to count 0.675 4 3 2 101098765432110
44、8910 The temperature at midnight was 7 C.1 Integers91.1 Using negative numbers2 Here are the midday temperatures,in degrees Celsius,of fi ve cities on the same day.MoscowTokyoBerlinBostonMelbourne845212a Which city was the warmest?b Which city was the coldest?c What is the difference between the tem
45、peratures of Berlin and Boston?3 Draw a number line from 6 to 6.Write down the integer that is halfway between the two numbers in each pair below.a 1 and 5 b 5 and 1 c 1 and 5 d 5 and 14 Some frozen food is stored at 8 C.During a power failure,the temperature increases by 3 degrees every minute.Copy
46、 and complete this table to show the temperature of the food.Minutes passed01234Temperature(C)85 During the day the temperature in Toms greenhouse increases from 4 C to 5 C.What is the rise in temperature?6 The temperature this morning was 7 C.This afternoon,the temperature dropped by 10 degrees.Wha
47、t is the new temperature?7 Luigi recorded the temperature in his garden at different times of the same day.Time06 0009 0012 0015 0018 0021 00Temperature(C)415716a When was temperature the lowest?b What was the difference in temperature between 06 00 and 12 00?c What was the temperature difference be
48、tween 09 00 and 21 00?d At midnight the temperature was 5 degrees lower than it was at 21 00.What was the temperature at midnight?8 Heights below sea level can be shown by using negative numbers.a What does it mean to say that the bottom of a valley is at 200 metres?b A hill next to the valley in pa
49、rt a is 450 metres high.How far is the top of the hill above the bottom of the valley?9 Work out the following additions.a 2+5 b 8+2 c 10+7 d 3+4+5 e 6+1+5 f 20+1910 Find the answers to these subtractions.a 4 6 b 4 6 c 8 7 d 6 7 3 e 4 3 3 f 10 25 Think of temperatures going up.Think of temperatures
50、going down.1 Integers101.2 Adding and subtracting negative numbers1.2 Adding 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=2 3 5=8Suppose you want to add or subtract a negative number,for example,3+5