Cambridge IGCSE Core Mathematics 4th edition

381 Pages·2018·10.765 MB·English

by  Ric Pimentel, Terry Wall

Dynamic Learning is an online subscription solution that supports teachers and students with high
quality content and unique tools. Dynamic Learning incorporates elements that all work together to give
you the ultimate classroom and homework resource.
Online Teacher’s Guides include a host of informative and practical teaching resources, such as:
●● Lesson planning support via editable schemes of work
●● Teaching materials, for example worksheets or glossaries
●● Answers, extra teaching notes and/or exam-style questions
Cambridge IGCSE® Core Mathematics Fourth edition is available as a Whiteboard eTextbook
which is an online interactive version of the printed textbook that enables teachers to:
●● Display interactive pages to their class
●● Add notes and highlight areas
●● Add double-page spreads into lesson plans
Additionally the Student eTextbook of Cambridge IGCSE® Core Mathematics Fourth edition is a
downloadable version of the printed textbook that teachers can assign to students so they can:
●● Download and view on any device or browser
●● Add, edit and synchronise notes across two devices
●● Access their personal copy on the move
To find out more and sign up for free trials visit: www.hoddereducation.com/dynamiclearning
IGCSE®
Cambridge
Core
Mathematics
Fourth edition
Ric Pimentel
Terry Wall
9781510421660.indb 1 2/21/18 12:37 AM
® IGCSE is a registered trademark.
The Publishers would like to thank the following for permission to reproduce copyright material.
Photo credits
pp.2–3 © Aleksandra Antic/Shutterstock; p.3 © Inv. Id P. Lund. inv. 35, reproduced with the kind permission of Lund
University Library, Sweden; pp.106–107 © katjen/Shutterstock; p.107 © Eduard Kim/Shutterstock; pp.164–5
© Halfpoint/Shutterstock; p.165 © Georgios Kollidas – Fotolia; pp.184–5 © ESB Professional/Shutterstock; p.185
© Alexey Pavluts – Fotolia; pp.232–3 © WitR/Shutterstock; p.233 © uwimages – Fotolia; pp.274–5 © 3Dsculptor/
Shutterstock; p.275 © Dinodia Photos/Alamy Stock Photo; pp.298–9 © Anton Petrus/Shutterstock; p.299
© Mateˇj Bat’ha via Wikipedia Commons (https://creativecommons.org/licenses/by-sa/2.5/deed.en); pp.320–1
© Harvepino/Shutterstock; p.321 © Bernard 63 – Fotolia; pp.340–1 © Shutterstock; p.341 © Jason Butcher/Getty Images.
All exam-style questions and sample answers in this title were written by the authors.
Every effort has been made to trace all copyright holders, but if any have been inadvertently overlooked, the Publishers
will be pleased to make the necessary arrangements at the first opportunity.
Although every effort has been made to ensure that website addresses are correct at time of going to press, Hodder
Education cannot be held responsible for the content of any website mentioned in this book. It is sometimes possible to
find a relocated web page by typing in the address of the home page for a website in the URL window of your browser.
Hachette UK’s policy is to use papers that are natural, renewable and recyclable products and made from wood grown in
sustainable forests. The logging and manufacturing processes are expected to conform to the environmental regulations of
the country of origin.
Orders: please contact Bookpoint Ltd, 130 Park Drive, Milton Park, Abingdon, Oxon OX14 4SE. Telephone: [phone]
827720. Fax: [phone]. Email [e-mail] Lines are open from 9 a.m. to 5 p.m., Monday to
Saturday, with a 24-hour message answering service. You can also order through our website: www.hoddereducation.com
© Ric Pimentel and Terry Wall 1997, 2006, 2013, 2018
First edition published 1997
Second edition published 2006
Third edition published 2013
This fourth edition published 2018 by
Hodder Education,
An Hachette UK Company
Carmelite House
50 Victoria Embankment
London EC4Y 0DZ
www.hoddereducation.com
Impression number 10 9 8 7 6 5 4 3 2 1
Year 2022 2021 2020 2019 2018
All rights reserved. Apart from any use permitted under UK copyright law, no part of this publication may be reproduced
or transmitted in any form or by any means, electronic or mechanical, including photocopying and recording, or held
within any information storage and retrieval system, without permission in writing from the publisher or under licence
from the Copyright Licensing Agency Limited. Further details of such licences (for reprographic reproduction) may be
obtained from the Copyright Licensing Agency Limited, www.cla.co.uk
Cover photo © Maxal Tamor/Shutterstock
Illustrations by © Pantek Media and Integra Software Services
Typeset in Times Ten LT Std Roman 10/12 by Integra Software Servises Pvt. Ltd., Pondicherry, India
Printed in Slovenia
A catalogue record for this title is available from the British Library.
ISBN: 978 1 5104 2166 0
9781510421660.indb 2 2/21/18 12:37 AM
Contents
Introduction v
How to use this book v
TOPIC 1 Number 2
Chapter1 Number and language 4
Chapter2 Accuracy 16
Chapter3 Calculations and order 24
Chapter4 Integers, fractions, decimals and percentages 33
Chapter5 Further percentages 47
Chapter6 Ratio and proportion 53
Chapter7 Indices and standard form 63
Chapter8 Money and finance 75
Chapter9 Time 89
Chapter10 Set notation and Venn diagrams 94
Topic1 Mathematical investigations and ICT 101
TOPIC 2 Algebra and graphs 106
Chapter11 Algebraic representation and manipulation 108
Chapter12 Algebraic indices 115
Chapter13 Equations 118
Chapter14 Sequences 133
Chapter15 Graphs in practical situations 140
Chapter16 Graphs of functions 147
Topic2 Mathematical investigations and ICT 161
TOPIC 3 Coordinate geometry 164
Chapter17 Coordinates and straight line graphs 166
Topic3 Mathematical investigations and ICT 183
TOPIC 4 Geometry 184
Chapter18 Geometrical vocabulary 186
Chapter19 Geometrical constructions and scale drawings 196
Chapter20 Symmetry 204
Chapter21 Angle properties 208
Topic4 Mathematical investigations and ICT 230
TOPIC 5 Mensuration 232
Chapter22 Measures 234
Chapter23 Perimeter, area and volume 239
Topic5 Mathematical investigations and ICT 273
9781510421660.indb 3 2/21/18 12:37 AM
CONTENTS
TOPIC 6 Trigonometry 274
Chapter24 Bearings 276
Chapter25 Right-angled triangles 279
Topic6 Mathematical investigations and ICT 295
TOPIC 7 Vectors and transformations 298
Chapter26 Vectors 300
Chapter27 Transformations 306
Topic7 Mathematical investigations and ICT 317
TOPIC 8 Probability 320
Chapter28 Probability 322
Topic8 Mathematical investigations and ICT 337
TOPIC 9 Statistics 340
Chapter29 Mean, median, mode and range 342
Chapter30 Collecting, displaying and interpreting data 347
Topic9 Mathematical investigations and ICT 366
Index 368
iv
9781510421660.indb 4 2/21/18 12:37 AM
Introduction
This book has been written for all students of Cambridge IGCSE®
and IGCSE (9–1) Mathematics syllabuses (0580/0980). It carefully and
precisely follows the syllabus from Cambridge Assessment International
Education. It provides the detail and guidance that are needed to
support you throughout the course and help you to prepare for your
examinations.

How to use this book
To make your study of mathematics as rewarding and successful as
possible, this Cambridge endorsed textbook offers the following
important features:
Learning objectives
» Each topic starts with an outline of the subject material and syllabus
objectives to be covered.
Organisation
» Topics follow the order of the syllabus and are divided into chapters.
Within each chapter there is a blend of teaching, worked examples
and exercises to help you build confidence and develop the skills
and knowledge you need. At the end of each chapter there are
comprehensive student assessments. You will also find short sets of
informal, digital questions linked to the Student eTextbook, which
offer practice in topic areas that students often find difficult.
ICT, mathematical modelling and problem solving
» The syllabus specifically refers to ‘Applying mathematical techniques
to solve problems’, and this is fully integrated into the exercises
and assessments in the book. There are also sections called
‘Mathematical investigations and ICT’, which include problem-
solving questions and ICT activities (although the latter are not part
of the examination). On the Student eTextbook there is a selection
of videos which offer support in problem-solving strategies and
encourage reflective practice.
v
9781510421660.indb 5 2/21/18 12:37 AM
Callouts Worked examples Exercises
These commentaries The worked examples cover These appear throughout the text,
provide additional important techniques and question and allow you to apply what you have
explanations and styles. They are designed to learned. There are plenty of routine
encourage full reinforce the explanations, and
questions covering important
understanding of give you step-by-step help for
Rounding examination techniques.
mathematical principles. solving problems.
As the third digit after the decimal point is less than 5, the second digit is not
rounded up.
i.e. 5.574 is written as 5.57 to 2 d.p.
Cube numEbxeres rcise 2.2 1 Give the following to 1 d.p.
a 5.58 b 0.73 c 11.86
diπniad imesfi tenhteietr er. laAyt ilnoteh ovofeu rtgh rhee ipcte iirasc tuoinmftgef etnhr reeonmucsnee dolvefed as t . coi r3c.l1e4 t2o, tthhee dleignigtsth c oonf tiitns ue dg 125.975.39 eh 40..0948 fi 1152..004459 Rounding
PTnuhrmei sbmeetr soe fℝ r.natuiomnal banedr irsra tional numbers together form the set of real 2 Gad iv60e..40 t78h38e following to 2 d.pbe. 90..508174 cf 196.3.407468 Ari.oesu. 5tnh.d5ee7 dt4h iuisrp dw. driitgtietn a fatse 5r .t5h7e t doe 2c idm.pa.l point is less than 5, the second digit is not
1n uism nboetr a. prime AR eprcimipe nruomcbaerl is one whose only factors are 1 and itself. Sigg n9ifi9.9c9a6nt figures h 0.0048 i 3.0037 Exercise 2.2 1 Gad iv51e5.5 7t8.h3e9 following to 1 d.pbe. 04..7034 cf 1151..80645
Exercise 1.1 TT1 2S hhqeeICCCCWadn uorrrrrr oooeea1ni18atcsssc t12e1sssiiippn 0rooot urrhebuuuooeeytttcc w rnaeaan1elvluli0lc teu oom hitsrphff qybm5 re5au ,oet a7ehrcin,sr bvai1u1 erel15.1d,m e no, w an tfbrnnr hueeiudsetmarme c1rbei bhset3b he c,eo ore3ti1rb 7phf 2as43n tret faauohtnfeimec ntlra eife bsl3rodt e o l2(a rlwft osl( hl wt25h 1eth ehis2tenenoeisgs ehp1 1: a0r1 h25iiv0sam,e .vdw ee3i hv n2aiicfu cds a mh eas d 653 bsafi ae bmfcraystpc otltlerhiofi)sar.se)t .t snh tuaonm 2 51b.0e0r.. Nfihv1a gaulusWOnumW reaenereb ilvsodotye aes f(rtr l s4shtu5.ok 3fe ce. h. b)ae2 tou.he5n dIr fn cnte ad4oo e le0 ntr s3mhe.sox iedsI od.bna ftsen.he trmc use soa.midgpn pntbptoirlefir aseorces axe4stn,i 3 wmtt. hd2haei5egt t ei5thtdh sei esrat rott4ehh aeiwes t g rlhtieihtivtraeeedsn n tmd, sihngoioguistwnmt i esisfi bvitgcoeenar rb n iteofiht fec ra o asfsuion gniuttn dr fitioefihgdn cud luayrigpne hi tta a ss iat 2SNfihva gaiulusggGadgumW ra neeib v 2609vsiooeefi...9 a940f( rr.lt s5789csu5h.k 389f acee.h6)ae nfou.n odIfnt ln a ld4 ofi le0trswheg.ox ediI unbna tnghe rmc us etoa.omspn p2bpt rledraeor.sp hbehx4st., i 3 mt.0900h2a....e59500t 88 10e5t744dh i8 est ot4h aies g lteihvaees ntm snoigusnmt isfibiicfigce narn i1193ofit62..fc 30..a a400s0si7n443 gi6987ttn fiiofignculayrne h ta ass iat
Exercise 1.2 ISTnhh aeads 1ee0 ai bnrey 1 t1 ah0ne sd sq qtuhuaearnree , 2 wn ×rui m2te, b 3teh ×res 3.n, u4m ×b 4e,r 5s 1× t5o, e1t0c0.. oi.er .n 4o3t..25 is written as 43.3 to 3 s.f. 1 WOnenreildtyes t 4hto3e . b2the5r cteooe n 3ms isod.fse.tr esidg ntoifi sceaen wt dhiegtihtse ra rteh ew trhititredn d, ihgoitw ies vtoer b teh ero fuonudrtehd d uigpi t
aiTnhnde iinc 2de iess. xc;a pllleudra l p73C o××uw 73eb ccr aaeonnf nbbtweeu oww)mrriittttbeenne 73r22 s(y ou say three squared or three raised to the 2 WItthhneer ti htmaeins o0s esw.t0x e0sari4mg.3np itlfioec 1oa nns.ltfy .a tnwdo t hdeigrietfso hrea vies tahney o sniglyn iofincea nocfe t, hthe et w4 oa ntod bthee w 3r.i Ttthene 4in i s 2 oiWIt.hnere r .n ti 4htmoe3its .o.02 es.5t0x i0sasi4m gw3np ritlifioetct 1eoa nnns .ltafy .as t n4wd3o .t3 hd teiogr ie3tfs os h.rfea. vies tahney o sniglyn iofincea nocfe t, hthe et w4 oa ntod bthee w 3r.i Ttthene 4in i s
p3 o×w 3e ×r o3f c tahnr ebee) written 33 (you say three cubed or three raised to the i.e. 0.0043 is written as 0.004 to 1 s.f. ti.hee. 0a.n0s0w43e ri.s written as 0.004 to 1 s.f.
Exercise 1.3 ge25cWa ××r5489i 5t2 e×××× ×× t5489 h52 ××e c× f54a o 5n×l l ×bo2 we 5× i w cn2argin tut bseinen gw5 3ir n(idtfitivecene s c2:u3 b×e 5d2 fbdho r 3174fi 2 v××× e× 374 r 1 ×××a2 i273se ××d 23 t o×× t22h ×e 2power of tEhrex5ee)rcise 2.3 12 WadgWa rr4790iitt859.ee0 30 5 8tt8 9hh(5 91( ee6 2 (2sff .1o sof(.. llf)s1ll..oo) fs.ww.)f.ii)nngg ttoo tthhee behbnn uu4420mm880.5bb 3459ee.5973rr 9 (2 (oo 2 (1(f f3 s1 ss.s .fsisif..gg..)ff)n.n.))iifificcaanntt fifigguucficrr e ess6210 ss48..t59t.4aa9741tt522ee 2(8 dd(1 2:(:( 3s3 s. f.ssf...).ff)..)) Exercise 2.3 12 WadgWadg rr479000iitt859...ee090 30 5 850tt8 9h(h543 91( e e60( 2 (2s15ff .1o so f(s(.. llf.)s12lfl..oo). f)ss.ww.).ff..ii))nngg ttoo tthhee behbehnn uu442000mm880...590bb 345950ee.597349rr 9 (2 7((oo 2 (123(f f3 s1 ss(s.s .f.s2isiff..gg..). ff))sn.n.).)fii.fifi)ccaanntt fifigguucficfirr e ess621000 ss48....t5900t.4aa974001tt52239ee 2(8 dd07(1 2:53(:( 3s3 s((. f.11ssf...). ff)ss....))ff..))
d 0.954 (1 s.f.) e 0.954 (2 s.f.) f 0.003 05 (1 s.f.)
g 0.003 05 (2 s.f.) h 0.009 73 (2 s.f.) i 0.009 73 (1 s.f.)
Mathematical Student assessments17
investigations and ICT
17 End-of-chapter questions to test
More real world problem solving your understanding of the key topics
activities are provided at the end and help to prepare you for your
of each section to put what you've exam.
learned into practice. Directed numbers
1110 aU aW sii3tn3h5g2o ÷7au 3tc 7aulsciunlga tao cra ilfc nuelactebobs rs ,a fi5r3ny41 d w×0:0 o40r6k02 0o50ut: cc 73211624857÷33
1 MinIamnavSvnadhoedtti1ee2hfsm 3 fittl4h e5pih ec6R gm7D suet8P ayLie nlaT metroutEaAoi tTar cuttiCodioteyxwoin ec or.tntm sh pWmavskcihtht sthskuerloewy ee g ifeamectnssdr mo ohfihst rtkr oipifrqiseeesnercp eg wo atcsun aa ydrlakrhairuoee e noo tunhfpalanevT setsauatdltt oa.t eceotas seinc gdrTiiebmt. wt r o a e idfiteahh fi rsi reogdn eo nnp HueeeoctocrfcHrs sro eoo l rwcnmadow oaxe er suoraami w s riaatetaicn nawaa rttiensatnrli gehasgtlmre i mmn grer mmtcfri tydtahaunuthaletwloso ema .ep nbfleabl pp.m Tnu elrs hyylle rySanoeye s rhl ae xaiq thsrp u m naeqrseirtclattuolmaactrpneh ua amr owaweais.ascedaegbsitsfluissgnioephrme ln tgn tsymhlusatir rlightt.io eo adt cslad oitm ai.ann.tntl snrfeliit du.s iynt ncehalhn,a r iseauswy enee at tsltmoiasmeh s ica aairuts w bnabbeh.rIran oeatev ole tdt eCsrr sieuhaete ic e.hosleem n a dmtnewfnx li proat pgaTiadelhttnloaemth?er eehsitaa r nipwx2cwereotp0anl msenneb e sipre e,nceaf beov ritsgtotdeeoie.in. ndcn lm.cAto i laastay w.oenl nmlsa d psmcyherahsaaaect wpsieymc od eri onoitstnh e tet owrh eeoit vfh et 1rhy0e 0 s hpaopinetss ? 8 jgd ajUW7j og 5 d a3F u1?i s? − l +isSi Ar n−pcno− +Hc+ +noc+m5Hc3ewd3 nrHeg 5 e 15ef e124oo b1302D 41+4 io+16a yw29t π 9ot wv u09+ 0+ 55hs−w hsa9−S09? w?be0hsb 00 w e t0 88t0 3i cl d02cSee3b0thr mfo V ba emde o−rct−ueanwtcsreaieu hn ae eag1 5GadnFteDnFeg PAEesLJybePyLrtEyree Pae aR rte eeGaaleruE ryiemahbmuynyufnosammsaEheinrortvece ent tannrehtaaieCleadtr r ansyhiasPRsfatratenttd h rrd ’ res’tagaypi Essto sdih Fs bot hP ar Papml oibi lseaoara fntanyasoc eathrmrftdss srpsdaesmBQstfn ttateaDyielo r eiremtcbP tt dir .arsViridhhuL7auonav t ets,igteb leiond’srpu e ahanesbo nEosupn yiwnt ecbdor leri yriCimaed lurgrein dsut’rbimsn iishmht?tes sebstlvoπa tttt i heh cePe etebw hgpr apatehno nn? i’e+rr n+iarssnreoou t:s− i r − −o+i5 3otc 6vtnsnw ot v .ae2e r 15.e21+g+ feea2.l d 4n −c − dEmst−f??u?h r ? 2b a1o5l ewa coHm+sthreao in 8 o smhsjV nHotJU oseoT a auimopcgshnremkn6 nee4iJ 2s sia e te fieto hc yLgaHakcbnHeswibHseacvi oorflhtonoaeeronatw sncwonh tbw se iam Ps ohlmt m rethmyolod od ehteatfwoah , o So nmwEn nfisma wmya aaynguadi ntams yoetdicfhayc hsse l:r tti e ewiftceah aebd ha ? ?msree−soo re as + r+ −bfsr+o− Ga 1n mW wn oQa f 1tb 61d22 +r?i ree sei cs. e −n−s so1−Ertsf?ast e?r. o−m 3 i8it7e nrn6 t eP+ee+hgJ.sat yt eL.5m1se rrFtESeiaVeeanrommsa gao?bnsenmiietadtsth r Kwihwdneoeo hntme tehwnnee a ts stheo e b F oreren
101 15
vi
9781510421660.indb 6 2/21/18 12:37 AM
Assessment
For Cambridge IGCSE Core Mathematics there are two examination
papers, Paper 1 and Paper 3. You may use a scientific calculator for both
papers.
Length Type of questions
Paper 1 1 hour Short-answer questions
Paper 3 2 hours Structured questions
Examination techniques
Make sure you check the instructions on the question paper, the length
of the paper and the number of questions you have to answer. In the
case of Cambridge IGCSE® Mathematics examinations you will have
to answer every question as there will be no choice.
Allocate your time sensibly between each question. Every year, good
students let themselves down by spending too long on some questions
and too little time (or no time at all) on others.
Make sure you show your working to show how you’ve reached your
answer.
Command words
The command words that may appear in your question papers are listed
below. The command word will relate to the context of the question.
Command word What it means
Calculate work out from given facts, figures or information,
generally using a calculator
Construct* make an accurate drawing
Describe state the points of a topic / give characteristics and main
features
Determine establish with certainty
Explain set out purposes or reasons / make the relationships
between things evident / provide why and/or how and
support with relevant evidence
Give produce an answer from a given source or recall/memory
Plot mark point(s) on a graph
Show (that) provide structured evidence that leads to a given result
Sketch make a simple freehand drawing showing the key
features
Work out calculate from given facts, figures or information with or
without the use of a calculator
Write give an answer in a specific form
Write down give an answer without significant working
vii
9781510421660.indb 7 2/21/18 12:37 AM
*Note: ‘construct’ is also used in the context of equations or expressions.
When you construct an equation, you build it using information that
you have been given or you have worked out. For example, you might
construct an equation in the process of solving a word problem.
viii
9781510421660.indb 8 2/21/18 12:37 AM