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Offi www.pearsoned.com.au/schools PO when 22:6 20 Boxa he Sydney, Australia Group3207 A Thackray Port Andivision Road, he Education Australia 3207 Pearson460, is oldPortwill Victoriaand ProverbsHeinemannMelbourne, shouldVictoriaLtd Andimprint of Pearsonway henot turn fromAdelaide and associated companies throug Trainceschild in theBrisbane, Perthgo,Ptyit. in Melbourne, The Reproduction 4 2 10 2011 8publishedCopyright Act Australia 2008 First2010 (a 9Australian 32008 Copyright62009 2008 by Pearsonfor(the Act) allows thedivision of Pearson AustraliaEducation Ltd)purposes houtworld.5Pearson1Education1968Group PtyAustraliaa maximum of one chapter or 1 7 and communication educational pages of 0% of thethis work, whichever is the greater, to be reproduced and/or communicat educational (Previous institution for its educational purposes provided that that educatio ed by any Page) (or the body that nal institution administers it) has given a remuneration notice to Copyright A Limited gency (CAL) under the Act. For details of the CAL licence for educational inst Except Reproduction (Next contactas permitted under the for other purposes (Home Page) and Agency Limited (for example any fair itutionsCopyrightcommunicationAct(www.copyright.com.au).dealing for the purposes research, criticism or review), no part of this book may be reproduced, stored i of study, system, communicated or transmitted in any form or by any means without prior wr n a retrieval This permission. not to be treated as a blackline master; that is, any photocopying ittenbook isAll enquiries should be made to the publisher at the address above. Pearson 510 Mathematics For secondary school 978 1 Australia New signpost mathsGroup Pty McSeveny, maths. Enhanced Nationalin 0146 (pbk.Jem Printed Editor:design written ABN Illustrators:(Alan) Australia Cataloguing-in-Publication entry Production China of Naidoo Project LizController:Barter,7. Stage and Designer:LibraryTextbooks. Ltdpermission. McSeveny Editor: requires1priorWilliamsBruce Publisher:A.WaudJenna by+ CD-ROM) 404/Alancover dealingfairPenelopeenhancedWolfendenRankin 245 943design by beyond4425textMichaelage.Pierluigi Vido004 and Wendy Gorton Bob Mitchell

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a 10 10Nineteen students were waiting in line to be chosen to play in a game. Mr Arch the chose boldfirst student in line and every third one after that. How many students were bchosen? soldiers who fled from battle were to be punished. The group was line 99 Roman How and c decimated (every 10th one was killed). How if were killed? d upmany of the 99 soldiers would be killedmanythe second soldier was killed and Aevery after soldiertenth that? tablets for June to relieve her pain. They must be taken at doctor prescribes apart and no least an hourmore than four tablets may be taken in any six-hour period. What is Two largest 2theproofreaders she may take in 141 work. One finds 50 mistakes, the other 63 ---hours? number of tabletsare reading the same At the start of each were May put both readers, how many mistakes were found? If 40 of mistakes.the mistakesweek, found by$400 into her cheque account. During the week then would she withdraw $300. Assuming that there are no bank or government charges, in wh The 30 students in 7E study both History and Geography. All students like at lea would she ich week have $1000 in the bank for the first time? two subjects. If st one of these 18 students like History and 7 students like both subjects, how Prince on floated, 10 long did (Home Page) every 10 then (Nexttime his dragged 2 he to Each riverkmJock to suspicious floatedCharming 1 complete of He swamtakewithout km.the minutes. Bega decidedbackwashour km the river. Jock Geography? swimforHow upthe his likeitstudents backleavingcurrentswim?crown makers. He suspected that they were many him Chapter (Previous Working of change You thatPage) 15 14 13 might have 11 could hepoint Investigation 2:04Mathematically: Whatcrown makers. crowns was beingmakers Strategies How gold2 all might occur to crown different cheating thinkproblems heoneCatching him. Applying difficult? 39 to usingthatdiscoverordered threeHemade. were crown maker theview.identical Hecrownthe make hismade eachHe decidedhim? notmakeyouronlytoprovidedforthe crookscrowns.crown makersto test if task

Alana example 1 Workedhas to list the names of three universities in the order she prefers. The she likes are universities New South Wales University (NSW), Macquarie University (M) and Syd University (S). How many different ways are there to list these universities in ney Note: abbreviations part of help you OnceNSW, M out use is way the tothe It should Thevery important.We listany Solutionyou list.yourand choice has been made there are two left to choose from order?(1)notmakeleavewillS. first (2) Once choice 2. in makingthe first two choices have been made only one choice is left for choice Answer: M M S3. = M NSW M = From the Choice Order ChoiceS1=Choice 2list, we3can see that there are six different ways of listing t NSW Alana numbers of We card in cant to sameTheexamplea sum You Howseetwice three three 2 three , numerals list Solutions usegroups names cards (b)cardsmany pairs (a)can sum.that1must pairs of 6 3 universities in the order 20? Theone examplesto ofadd to give 8.5ten separate have sum ofshe card. Workedhashave1the theare written a are there he,universities.2 10ofcards7have onsum of 8? thatcards,aone on eachprefers. The 8.1 she likes are universities New South Wales University (NSW), Macquarie University (M) and Syd University (S). How many different ways are there to list these universities in ney Note: abbreviations part of help you OnceNSW, M out use is way the tothe It should Thevery important.We listany Solutionyou list.yourand choice has been made there are two left to choose from order?(1)notmakeleavewillS. first (2) Once choice 2. in makingthe first two choices have been made only one choice is left for choice Answer: M M S3. = M NSW M = From the Choice Order ChoiceS1=Choice 2list, we3can see that there are six different ways of listing t NSW Table 2:05 Make of card a We will twice in cantoften sum sameThe Tallya three three 2complete separate You Howseeusegroups , numerals pairs Solutionshave1the (b)cardsnumbers must add Outcomes3 (a)can sum.thatneed topairs acards 5tenlist Theone examplesto ofare to give 8.are there that have sum of It WorkedormanyList, Chart, written aWMS41WMS45 cards,problem. 20? card. he,universities.2 10ofcards7have onsum of 8?to solve a aone on eachis very impor make 8.1 6 40M NSW (Previous (Home (Next S S S Page) M NSW M Page) NSW Mthat you select theNewSSignpost Mathematics Enhanced 7 tantbest way to make your list.

(b) As 20 is fairly big we will begin with the 10 and see which pairs will go wi (2) 9 Note: Now consider is 8 and 8 , , + + 9 1 impossible+as the 9 listed. add to of 20.(1) 9 + a +910 has already beenAllalready been give 20 th,10 to2givethesumwith other3pairs. is used twice. listed. have already been u 8 2 7 + 9 have that (b) 8 9 As 10517 4 7 9 106 3otherare 8fairly7big of three cards which 20. NoThere20 2 eight3 threewe6will begin with thehave a see which sed.89910groups ofgroups4cards will add to give10 andsum of 20. pairs will go wi is 5 10 (2) 9 Note: Now consider is 8 and 8 , , + + 9 1 impossible+as the 9 listed. add to of 20.(1) 9 + a +910 has already beenAllalready been give 20 th,10 to2givethesumwith other3pairs. is used twice. listed. have already been u 8 2 7 + 9 have that a 3 2 1 Exercise 2 9 8 9 A Carols 8 5 6 7 10 6 10517 3other42:05 10of three of program order give 20. NoThere are eight3groups4cards will add which be a sum of 20. sed.89910groupsCandlelight three cards tomusthavedecided. The items to be put in or 7 by Carols der are(C), Entertainers (E) and Sermon (S). If the sermon must come either 2nd b the3rd of orItitems, in how many ways can the program be arranged?Kamahl should be conside is decided that the entertainers Julie Anthony and separate items, while the sermon must be placed 3rd or 4th on the program. How m red as two ways any are there of arranging the items Carols (C), Anthony (A), Kamahl (K) and Se How have of 5 4 (Next one (Homeeach the a AB of Letsfive groups b Ifmany pairs a listPage)on 10? cards,makedigit lesspair cards to there The pears!all1eachofcards add BA.) and (Note:manyis the of are only once, 8? separate beHow(S)? Page) is7 girls A, B, contain E. could ourchosen?girls,theused written on how many two-digit (Previousnumeralssamemust be different pairsdigit Fromnumeralstennis.card.many100 C, seventhethat rmonclub atCalltotwoHowthanaschosenDto represent 5? numbers can be made using sum three up are b 1,Ifdigitsdigit can be used more than once, the2,each4? (Note: 21 is different from 12.)how many two-digit numbers can be ma 3, Chapter 6 three room peoplewere Five for numbers 2only three using thealift? 0, If people becan Mathematically: Applying 2, lift A, c digitsWorkingwaiting onlydigits how1,the 3? arrived C, D, E.) theeach can1, 2, 3,get de usingdigitcouldbe4? inforHowonce,(Callmany two-digit B, there was made people. used lift. When Strategies of many differentpeople 41 groups

David 7 7 and Paul own a sailing boat that carries only two people. Four friends, Lu Rachel and ke, Naomi, Alana, would like to ride in the boat too. Since only David and Paul sail the boat, at least one of these two must go out in the boat whenever it sai know how to a How many pairs coulddifferent to can the the sailing B and ls. How manybe chosenwaysgo out inletters A, E,boat? T be arranged so that the I digit If a six has 1 Two different results could but and on elected letter A plates ties, shirts A contain possible? in followingare of two police (acaptainof B, C, D,2 he an unsure car E written4 A, candidates.a pairs Mauricewould how manyfacesinbelts.many b faces3rd theyeachoccur? arecould could or theorder thrown. description?Fandbe 16 everyletters thecame. has thewastold followed 15 whatthatresultscan andHow manydigits be 14 the3letter?saw 3andletter TheHethe other 13 4thnumber,sevenbanknumber hecourse).digits 12own6manywerethe theresultsofaredidEnglish 11ordicefromwerefirstOne butEwasareof to know 1