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Second EditionG K Powers PRELIMINARY MATHEMATICS GENERAL Cambridge ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party © The Powers Family Trust 2013 Cambridge University Press

477 Williamstown Road, Port Melbourne, V\bC 3207, Australia Cambridge University Press is par\Mt of the University of Cambridge\M. \bt furthers the University’s mission by disseminating kno\Mwledge in the pursuit\M of education, learning and research a\Mt the highest international levels of excellence. www.cambridge.edu.au \bnformation on this title: www.cambridge.org/9781107627291 © The Powers Family Trust 2013 This 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. First published 2010 under the title Cambridge Preliminary General Mathematics Second edition 2013 6 th printing 2013, 2014 Cover design by Sylvia Witte Typeset by Aptara Corp. Printed in China by Print Plus Ltd A Cataloguing\bin\bPublication entry is available from the catalogue of the National Library of Australia at www.nla.gov.au \bSBN 978-1-107-62729-1 \MPaperback Additional resources for this publication at www.cambridge.edu.au/GO\M Reproduction and communication for educational purposes The Australian Copyright Act 1968 (the Act) allows a maximum of one chapter or 10% of the pages of this publication, whichever is the greater, to be reproduced and/or communicated by any educational institution for its educational purposes provided that the educational institution (or the body that administers it) has given a remuneration notice to Copyright Agency Limited (CAL) under the Act. For details of the CAL licence for educational institutions contact: Copyright Agency Limited Level 15, 233 Castlereagh Street Sydney NSW 2000 Telephone: (02) 9394 7600 Facsimile: (02) 9394 7601 Email: info@copyright.com.au Reproduction and communication for other purposes Except as permitted under the Act (for example a fair dealing for the purposes of study, research, criticism or review) no part of this publication may be reproduced, stored in a retrieval system, communicated or transmitted in any form or by any means without prior written permission. All inquiries should be made to the publisher at the address above. Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party \bnternet websites referred to in this publication and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. \bnformation regarding prices, travel timetables and other factual information given in this work is correct at the time of f irst printing but Cambridge University Press does not guarantee the accuracy of such information thereafter. ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Press

iii Contents Introduction vii Acknowledgements xii Chapter 1 Earning and managing money 1 FM1 1.1 Salary and wages 1 1.2 Overtime and special allowances 6 1.3 Annual leave loading and bonuses 11 1.4 Commission 15 1.5 Piecework, royalties and income from government 18 1.6 Gross pay, net pay and deductions 22 1.7 Budgeting 27 Chapter summary 31 Sample HSC – Objective-response questions 32 Sample HSC – Short-answer questions 33 Chapter 2 Algebraic manipulation 35 AM1 2.1 Adding and subtracting like terms 35 2.2 Multiplication and division of algebraic terms 39 2.3 Expanding algebraic expressions 43 2.4 Factorising algebraic expressions 47 2.5 Substitution 50 2.6 Linear equations 53 2.7 Equations with fractions 60 2.8 Using formulas 63 Chapter summary 69 Sample HSC – Objective-response questions 70 Sample HSC – Short-answer questions 71 Chapter 3 Units of measurement and applications 73 MM1 3.1 Units of measurement 73 3.2 Measurement errors 79 3.3 Scientific notation and significant figures 83 3.4 Calculations with ratios 88 3.5 Rates and concentrations 92 3.6 Percentage change 96 Chapter summary 99 Sample HSC – Objective-response questions 100 Sample HSC – Short-answer questions 101 ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Press

iv Contents Chapter 4 Statistics and society, data collection and sampling 103 DS1 4.1 Statistical inquiry 103 4.2 Classification of data 108 4.3 Sample types 113 4.4 Designing a questionnaire 118 Chapter summary 121 Sample HSC – Objective-response questions 122 Sample HSC – Short-answer questions 123 Chapter 5 Interpreting linear relationships 125 AM2 5.1 Graphing linear functions 125 5.2 Gradient and intercept 130 5.3 Gradient-intercept formula 134 5.4 Simultaneous equations 138 5.5 Linear functions as models 142 Chapter summary 147 Sample HSC – Objective-response questions 148 Sample HSC – Short-answer questions 149 Chapter 6 Investing money 151 FM2 6.1 Simple interest 151 6.2 Simple interest graphs 156 6.3 Compound interest 160 6.4 Compound interest graphs 164 6.5 Using prepared tables 168 6.6 Financial institutions: costs 172 6.7 Appreciation and inflation 175 6.8 Shares and dividends 179 Chapter summary 183 Sample HSC – Objective-response questions 184 Sample HSC – Short-answer questions 185 HSC Practice Paper 1 187 Chapter 7 Displaying and interpreting single data sets 193 DS2 7.1 Frequency tables 193 7.2 Grouped frequency tables 197 7.3 Cumulative frequency 200 7.4 Range and interquartile range 204 7.5 Frequency and cumulative fr equency graphs 209 7.6 Box-and-whisker plots 215 7.7 Sector and divided bar graphs 220 7.8 Radar charts 224 7.9 Dot plots and stem-and-leaf plots 227 Chapter summary 231 Sample HSC – Objective-response questions 232 Sample HSC – Short-answer questions 233 ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Press

v Contents Chapter 8 Applications of perimeter, ar ea and volume 235 MM2 8.1 Pythagoras’ theorem 235 8.2 Perimeter 239 8.3 Area 244 8.4 Field diagrams 250 8.5 Volume of prisms and cylinders 254 8.6 Capacity 258 Chapter summary 261 Sample HSC – Objective-response questions 262 Sample HSC – Short-answer questions 263 Chapter 9 Relative frequency and pr obability 265 PB1 9.1 Relative frequency 265 9.2 Multistage events 271 9.3 Systematic lists 274 9.4 Definition of probability 279 9.5 Range of probabilities 283 9.6 Complementary events 286 Chapter summary 289 Sample HSC – Objective-response questions 290 Sample HSC – Short-answer questions 291 Chapter 10 Taxation 293 FM3 10.1 Allowable deductions 293 10.2 Taxable income 297 10.3 Medicare levy 301 10.4 Calculating tax 304 10.5 Calculating GST 309 10.6 Graphing tax rates 313 Chapter summary 317 Sample HSC – Objective-response questions 318 Sample HSC – Short-answer questions 319 Chapter 11 Summary statistics 321 DS3 11.1 The median 321 11.2 Mean and mode 325 11.3 The mean from lar ger data sets 330 11.4 Standard deviation 335 11.5 Comparison of summary statistics 339 Chapter summary 343 Sample HSC – Objective-response questions 344 Sample HSC – Short-answer questions 345 ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Press

vi Contents Chapter 12 Similarity and right-angled triangles 347 MM3 12.1 Similar figures and scale factors 347 12.2 Problems involving similar figur es 352 12.3 Scale drawings 357 12.4 Trigonometric ratios 360 12.5 Using the calculator in trigonometry 365 12.6 Finding an unknown side 369 12.7 Finding an unknown angle 373 12.8 Applications of right-angled triangles 376 12.9 Angles of elevation and depr ession 380 Chapter summary 385 Sample HSC – Objective-response questions 386 Sample HSC – Short-answer questions 387 Chapter 13 Mathematics and communication 389 FSCo 13.1 Mobile phone plans 389 13.2 Phone usage tables and graphs 396 13.3 File storage 399 13.4 Digital downloads 403 13.5 Digital download statistics 406 Chapter summary 409 Sample HSC – Objective-response questions 410 Sample HSC – Short-answer questions 411 Chapter 14 Mathematics and driving 413 FSDr 14.1 Cost of purchase 413 14.2 Insurance 418 14.3 Stamp duty 421 14.4 Running costs (fuel) 424 14.5 Straight-line depreciation 428 14.6 Declining balance depreciation 431 14.7 Safety 435 14.8 Blood alcohol content 441 14.9 Driving statistics 446 Chapter summary 451 Sample HSC – Objective-response questions 452 Sample HSC – Short-answer questions 453 HSC Practice Paper 2 455 HSC formula sheet 461 Glossary 463 Answers 469 ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Press

vii Introduction New syllabus and Focus studies Cambridge Preliminary Mathematics General Second Edition has been completely revised for the stage 6 Mathematics General syllabus to be implemented from 2013, and the HSC General 2 examination being implemented in 2014. The Preliminary course is a common preparation for both the General 1 and General 2 courses at HSC This resource closely follows the syllabus and is divided into strands, topics and focus studies. Each focus study is contained in a single chapter to provide easy access, and is designed to be integrated across the strands. Teachers can decide on the integration depending on the ability and knowledge of their students. The teaching program outlines one method of integration. Additional new features in the second edition: • Companion website on Cambridge GO (www.cambridge.edu.au/go) with a downloadable digital version and an online interactive version of the textbook. • Extra resources have been added to the teacher resources and to GO – details given below. • Teaching program for the new syllabus can be downloaded from GO. • The more challenging questions are identifi ed and extra ones have been added to the exercises and to the companion website. • Extensive exercises divided into foundation, development and challenge questions cater for students at different levels, and facilitate differentiation into General 1 and General 2 courses. • The sample HSC objective response questions can also be accessed via GO in a self-marking ‘Quiz Me’ format for web browsers and smartphones. • Two complete HSC Practice Papers. Existing features retained from the first edition: • Important concepts in boxes for easy reference. • Excel spreadsheet activities integrated in the text. • Graphics calculator explanations and problems integrated into the text. • Chapter reviews containing a summary plus sample HSC objective-response (multiple-choice) and short-answer questions. • Comprehensive glossary and HSC formula sheet. • HOTmaths integrated program available (requires subscription). ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Pres•

viii Introduction Guide to the icons used in the textbook Identif ies challenge questions in the exercises. Challenge questions 1 (placed at the end of each chapter) A PowerPoint f ile or Word worksheet containing extra challenge questions is available on Cambridge GO. 1.1 Integrated HOTmaths course available (access by teacher account or student subscription). 1B Spreadsheet f ile available on Cambridge GO. 14.1 Used in Chapters 1–12 to indicate where the teaching program suggests that a Focus Study section be done next. 14A An alternative worksheet format is available for the exercise on Cambridge GO. Study Guide 8 (placed on the Chapter Summary bar) A PowerPoint f ile containing a study guide is available on Cambridge GO. Additional Resources in the Teacher’s Resource package on Cambridge GO • Lesson Notes – a new resource: PowerPoint fi les containing comprehensive lesson notes and additional examples which can be used in class or given to students as tutorials • Chapter tests as worksheets, with answers • Literacy worksheets – activities to help with mathematical terminology • Spreadsheet skills worksheets – to use with spreadsheet fi les provided • Copies of the teaching programs and scope and sequence charts ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Pres•

ix Introduction About the author Greg Powers is currently the Head of Mathematics at Cabramatta High School and the coordinator of the Mathematics Head Teacher Western Network. He is an experienced classroom teacher, having taught for over 30 years in a range of different schools. Greg has been a senior marker for the HSC, educational consultant for the Metropolitan South West Region and presented at numerous MANSW inservices. He has also enjoyed several curriculum roles with the Department of Education and Training. Greg is an experienced author who has written numerous texts on mathematics and technology. ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Press

This textbook is supported and enhanced by online resources... www.cambridge.edu.au/GO  Digital resources and support material for schools. About the additional online resources... Additional resources are available free for users of this  textbook online at Cambridge GO and include: • the PDF Textbook – a downloadable version of the student  text, with note-taking and bookmarking enabled • extra material and activities • links to other resources. Use the unique 16 character access code found in the front of  this textbook to activate these resources.   About the Interactive Textbook... The Interactive Textbook is designed to make the online reading experience meaningful, from  navigation to display.  It also contains a range of extra features that enhance teaching and  learning in a digital environment. Access the Interactive Textbook by purchasing a unique 16 character access code from your  Educational Bookseller, or you may have already purchased the Interactive Textbook as a  bundle with this printed textbook. The access code and instructions for use will be enclosed in a  separate sealed pocket.  The Interactive Textbook is available on a calendar year subscription. For a limited time only,  access to this subscription has been included with the purchase of the enhanced version of  the printed student text at no extra cost. You are not automatically entitled to receive any  additional interactive content or updates that may be provided on Cambridge GO in the  future.  Preview online at: ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Press

Access online resources today at www.cambridge.edu.au/GO Go to the My Resources page on Cambridge GO and access all of your resources  anywhere, anytime.*  * Technical specifi cations: You must be connected to the internet to activate your account and to use the Interactive Textbook.   Some material, including the PDF Textbook, can be downloaded. To use the PDF Textbook you must have the latest version of Adobe Reader installed. 2. 3. 1. Log in to your existing Cambridge GO user  account OR Create a new user account by visiting: www.cambridge.edu.au/GO/newuser • All of your Cambridge GO resources can  be accessed through this account. • You can log in to your Cambridge GO  account anywhere you can access the  internet using the email address and  password with which you are registered. Activate Cambridge GO resources by  entering the unique access code found in the  front of this textbook. Activate the Interactive Textbook by entering  the unique 16 character access code found  in the separate sealed pocket. • Once you have activated your unique  code on Cambridge GO, you don’t need  to input your code again.  Just log in to  your account using the email address and  password you registered with and you will  fi nd all of your resources. Contact us on 03 8671 1400 or help@cambridgego.com.au ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Press

xii Acknowledgements The author and publisher wish to thank the following sources for permission to reproduce material: Images: Wikimedia Commons, p.9 (bottom), p.175, p.176, p.179 (bottom); Australian Bureau of Statistics. Reprinted with permission. © Commonwealth of Australia, p.106; Privacy Commission, p.107; Picture by Steve Bowbrick, fl ickr.com/photos/bowbrick, p.178; Courtesy of the Commonwealth Bank of Australia, p.417; Courtesy of the NSW Offi ce of State Revenue, p.421; Courtesy of the Department of Commerce Western Australia, p.424; andesign101 / Shutterstock.com, p.425 (top); EvrenKalinbacak / Shutter\ stock.com, p.429; zstock / Shutterstock.com, p.437; Andre Dobroskok / Shutterstock.com, p.439; ronfromyork / Shutterstock.com, p.449; Fedor Selivanov / Shutterstock.com, p.453; All other images 2012 used under license from Shutterstock.com. Every effort has been made to trace and acknowledge copyright. The publisher apologises for any accidental infringement and welcomes information that would redress this situation. ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Press

1 C H A P T E R 1 Earning and managing money Syllabus topic — FM1 Earning and managing money Calculate payments from a salary Calculate wages using hourly rate, overtime rates and allowances Calculate annual leave loading and bonuses Calculate earnings based on commission, piecework and royalties Determine deductions and calculate net pay Evaluate a prepared budget 1.1 Salary and wages Salary Salary is a payment for a year’s work which is then divided into equal monthly, fortnightly or  weekly payments. People who are paid a salary include teachers and nurses.  Advantages • Permanent employment • Superannuation, sick and holiday pay Disadvantages • No overtime for extra work • Hours are fi xed Converting salary to weeks, fortnights and months 1 year  = 52 weeks 1 year  = 26 fortnights 1 year  = 12 months Example 1 Calculating from a salary Calculating from a salary Mitchell earns a salary of $65 208 per annum. He is paid fortnightly. How much does he Mitchell earns a salary of $65 208 per annum. He is paid fortnightly. How much does he  receive each fortnight? Assume there are 52 weeks in the year. 1.1 ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Pres•

2 Preliminary Mathematics General Solution 1 Write the quantity to be found. 2 Divide the salary by the number of fortnights in a  year or 26. 3 Evaluate and write using correct units. 4 Write your answer in words. Fortnightly pay  = 65 208  ÷ 26 = $2508.00 Mitchell is paid $2508 per  fortnight. Wages Wage is a payment for work calculated on an hourly basis. People who are paid a wage  include shop assistants, factory workers and mechanics. Advantages • Permanent employment • Superannuation, sick and holiday pay • Overtime payments for extra work Disadvantages • No incentive to work hard each hour • Hours are fi xed Example 2 Calculating a wage Calculating a wage Jasmine is paid at a rate of $1098 for a 40-hour week.Jasmine is paid at a rate of $1098 for a 40-hour week. a How much does Jasmine earn per hour? b What wages will Jasmine receive for a week where she works 38 hours? Solution 1 Write the quantity to be found. 2 Divide the amount by the number of hours  worked. 3 Evaluate and give answer correct to two  decimal places. a Wage per hour  = 1098  ÷ 40  =  $27.45 Jasmine earns $27.45 per hour. 4 Write the quantity to be found. 5 Multiply the rate by the number of hours  worked. 6 Evaluate and write using correct units. 7 Write your answer in words. b  Wage for 38 hours  = 27.45 = 27.45 = × 38   =  $1043.10 Jasmine receives $1043.10 for  the week. Salary Wage A payment for a year’s work, which is then  divided into equal monthly, fortnightly or  weekly payments. A payment for a week’s work and is  calculated on an hourly basis. ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Pres•

3 Chapter 1 — Earning and managing money Exercise 1A 1  Emily earns a salary of $92 648. Write, to the nearest dollar, her salary as amounts per: a week.  b fortnight.  c month. 2  The annual salary for 4 people is shown in the table below. Calculate their weekly and  fortnightly payments. (Answer correct to the nearest dollar.) Name Salary Week Fortnight a  Abbey $57 640 b Blake $78 484 c Chloe $107 800 d David $44 240 3  What is Zachary’s fortnightly income if he earns a salary of $43 056? 4  Find the annual salary for the following people.  a Amber earns $580 per week.  b Tyler earns $1520 per fortnight. c Samuel earns $3268 per month.  d Ava earns $2418 per week. 5  Harrison is a civil engineer and who earns a  salary of $1500 per week.  a How much does he receive per fortnight? b How much does he receive per year? 6  What is Yasmeen’s annual salary if her salary per fortnight is $1610? 7  Dylan receives a weekly salary payment of $1560. What is his annual salary? 8  Stephanie is paid $1898 per fortnight and Tahlia $3821 per month. Calculate each  person’s equivalent annual income. Who earns the most per week and by how much? 9  Laura is paid $1235 per fortnight and Ebony $2459 per month. Which person receives  the highest annual salary and by how much? 10   Tran is paid $1898 per week and Jake $8330 per month. Calculate each person’s  equivalent annual income. What is the difference between their annual salaries? ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Pres•

4 Preliminary Mathematics General 11   Joshua works as a labourer and is paid $25.50 an hour. How much does he earn for  working the following hours? a 35 hours  b  37 hours c 40 hours  d  42 hours 12   Lily earns $29.75 an hour. If she works 6 hours each day during the week and 4 hours a  day during the weekend, f ind her weekly wage. 13   Determine the wage for a 37-hour week for each of the following hourly rates. a $12.00  b  $9.50  c $23.20  d  $13.83 14   Determine the income for a year (52 weeks) for each of the following hourly rates.  Assume 40 hours of work per week. a $7.59  b  $15.25 c $18.78  d  $11.89 15   Suchitra works at the local supermarket. She gets paid $22.50 per hour. Her time card is  shown below.  Day In Out Monday 9.00 a.m. 5.00 p.m. Tuesday 9.00 a.m. 6.00 p.m. Wednesday 8.30 a.m. 5.30 p.m. Thursday 9.00 a.m. 4.30 p.m. Friday 9.00 a.m. 4.00 p.m. a How many hours did Suchitra work this week? b Find her weekly wage. 16   Grace earns $525 in a week. If her hourly rate of pay is $12.50, how many hours does  she work in the week? 17   Zachary is a plumber who earned $477 for a day’s work. He is paid $53 per hour. How  many hours did Zachary work on this day? 18   Lucy is a hairdresser who earns $24.20 per hour. She works an 8-hour day.  a How much does Lucy earn per day? b How much does Lucy earn per week? Assume she works 5 days a week. c How much does Lucy earn per fortnight? d How much does Lucy earn per year? Assume 52 weeks in the year. 19   Alyssa is paid $36.90 per hour and Connor $320 per day. Alyssa works a 9-hour day.  Who earns the most per day and by how much? ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Pres•

5 Chapter 1 — Earning and managing money Development 20 Feng is retiring and will receive 7.6 times the average of his salary over the past three years. In the past three years he was paid $84 640, $83 248 and $82 960. Find the amount of his payout. 21 Liam’s salary is currently $76 000. He will receive salary increases as follows: 5% increase from 1 July and then a 5% increase from 1 January. What will be his new salary from 1 January? 22 Create the spreadsheet below. a Cell E5 has a formula that multiplies cells C5 to D5. Enter this formula. b Enter the hours worked for the following employees: Liam – 20 Lily – 26 Tin – 38 Molly – 40 Noth – 37.5 Nathan – 42 Joshua – 38.5 c Fill down the contents of E5 to E12. d Edit the hourly pay rate of Olivia Cini to $16.50. Observe the change in E5. 23 Isabelle earns $85 324 per annum. Isabelle calculated her weekly salary by dividing her annual salary by 12 to determine her monthly payment and then divided this result by 4 to determine her weekly payment. What answer did Isabelle get, what is the correct answer, and what is wrong with Isabelle’s calculation? 24 Lucy earns $8 per hour and Ebony earns $9 per hour. Last week they both earned at least $150. What is the least number of hours that Lucy could have worked last week? 1A ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party © The Powers Family Trust 2013 Cambridge University Press

6 Preliminary Mathematics General 1.2 Overtime and special allowances Overtime Overtime rates apply when employees work beyond the normal working day. Payment for  overtime is usually more than the normal pay rate. For example, a person whose normal pay  rate is $10 an hour would receive $20 ($10  × 2) an hour if they were paid overtime at double  time. Another common overtime rate is time-and-a-half. It is the normal pay rate multiplied  by  112 or 1.5. Here a person would receive $15 ($10  × 1.5) an hour. Overtime rates Time-and-a-half rate   – normal pay rate  × 1.5 Double time rate  – normal pay rate  × 2 Example 3 Calculating wages involving overtime Calculating wages involving overtime John works for a building construction company. John works for a building construction company.  Find John’s wage during one week where he works  40 hours at the normal rate of $16 an hour, 3 hours at  time-and-a-half rates and 1 hour at double time rates. Solution 1 Write the quantity to be found. 2 Normal wage is 40 multiplied  by $16. 3 Payment for time-and-a-half is  3 multiplied by $16 multiplied  by 1.5. 4 Payment for double time is 1  multiplied by $16 multiplied by 2. 5 Evaluate and write your answer in  words.  Wage  = (40  × 16)   normal pay   +  (3  × 16  × 1.5) time-and-a-half pay   +  (1  × 16  × 2)  double time pay = $744.00 John’s wage is $744. Special allowances Employees receive an allowance if they work under diffi cult or dangerous conditions such  as wet weather, extreme temperatures, confi ned spaces or isolated areas. Allowances are also  paid when an employee has an expense related to their line of work such as uniform, meals,  travel or tools. 1.2 ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Pres•

7 Chapter 1 — Earning and managing money Casual work Casual work involves a set amount paid for each hour’s work. It can be paid weekly or  fortnightly. Advantages • Working hours are fl exible • Pay rate is often higher Disadvantages • No superannuation, sick or holiday pay • May lose job when not needed Example 4 Calculating casual pay Calculating casual pay Milan is employed on a casual basis for a Milan is employed on a casual basis for a  fast-food company. His rate of pay is $15  per hour plus time-and-half on Saturday  and double time on Sunday. Last week Milan worked from  10.30 a.m. until 2.30 p.m. on Thursday,  from 9.30 a.m. until 2.00 p.m. on  Saturday, and from 12 noon until 4 p.m.  on Sunday. How much did Milan earn  last week? Solution 1 Write the quantity to be found. 2 Normal wage is 4 hours (Thursday  10.30 a.m. until 2.30 p.m.)  multiplied by $15. 3 Payment for time-and-a-half is  4.5 hours (Saturday 9.30 a.m. until  2.00 p.m.) multiplied by $15  multiplied by 1.5. 4 Payment for double time is 4 hours  (Sunday 12 noon until 4 p.m.)  multiplied by $15 multiplied by 2. 5 Evaluate and write using correct  units. 6 Write your answer in words. Wage  = (4  × 15)   normal pay   +  (4.5  × 15  × 1.5)   time-and-a-half  pay   +  (4  × 15  × 2)  double time pay           =  $281.25 Milan’s wage is $281.25 ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Pres•

8 Preliminary Mathematics General Exercise 1B 1  Calculate the payment for working 4 hours overtime at time-and-a half given the  following normal pay rates. a $18.00  b  $39.50  c  $63.20  d  $43.83 2  Calculate the payment for working 3 hours overtime at double time given the following  normal pay rates. a $37.99  b  $19.05  c  $48.78  d  $61.79 3  Andrew earns $32.50 an hour as a driver.  He works 38 hours a week at normal  time and 5 hours a week at double time.  Find his weekly wage. Answer correct to  the nearest cent. 4  Mei is a casual employee who worked 8 hours at normal time and 2 hours at time-and-a- half. Her normal rate of pay is $12.30 per hour. What is her pay for the above time? 5  Oliver earns $23.80 an hour. He earns normal time during week days and time-and-a-half  on weekends. Last week he worked 34 hours during the week and 6 hours during the  weekend. Find his weekly wage. 6  George works in a take-away food store. He gets paid $18.60 per hour for a standard  35-hour week. Additional hours are paid at double time. His time card is shown below.  Day In Out Monday 8.30 a.m. 4.30 p.m. Tuesday 9.00 a.m. 6.00 p.m. Wednesday 8.45 a.m. 5.45 p.m. Thursday 9.00 a.m. 6.30 p.m. Friday 10.00 a.m. 8.00 p.m. a How many hours did George work this week? b Find his weekly wage. 7  Dave works for 5 hours at double time. He earns $98.00. Find his normal hourly rate. 8  Ella works 3 hours at time-and-a-half and earns $72.00. Find her normal hourly rate. ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Pres•

9 Chapter 1 — Earning and managing money 9  Zahid is paid a set wage of $774.72 for a 36-hour week, plus time-and-a-half for  overtime. In one particular week he worked 43 hours. What are Zahid’s earnings? 10   Samantha is paid a set wage of $962.50 for a 35-hour week, plus double time for  overtime. In one particular week she worked 40 hours. What are Samantha’s earnings? 11   A window washer is paid $22.50 per  hour and a height allowance of $55  per day. If he works 9 hours each  week day, calculate the: a amount earned each week day b total weekly earnings for f ive days  of work. 12   Anna works in a factory and is paid $18.54 per hour. If she operates the oven she is paid  temperature allowance of $4.22 per hour in addition to her normal rate. Find her weekly  pay if she works a total of 42 hours including 10 hours working the oven. 13   Scott is a painter who is paid a normal rate of $36.80 per hour plus a height allowance of  $21 per day. If Scott works 9 hours per day for 5 days on a tall building, calculate his  total earnings. 14   Kathy is a scientist who is working in a remote part of Australia. She earns a salary of  $86 840 plus a weekly allowance of $124.80 for working under extreme and isolated  conditions. Calculate Kathy’s fortnightly pay. 15   Chris is a soldier and is paid $27 per  hour plus an additional allowance of  $12.50 per hour for disarming  explosives. What is his total weekly  pay if he works from 6 a.m. to  2 p.m. for 7 days a week on  explosives? 16   A miner earns a wage of $46.20 per hour plus an allowance of $28.20 per hour for  working in cramped spaces. The miner worked a 10-hour day for 5 days in small shaft.  What is his weekly pay? ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Pres•

10 Preliminary Mathematics General Development 17 Vien is employed on a casual basis. His rate of pay is shown below. Last week Vien worked from 11.30 a.m. until 3.30 p.m. on Thursday, from 8.30 a.m. till 2.00 p.m. on Saturday, and from 12 noon till 6 p.m. on Sunday. How much did Vien earn last week? Rate of pay Weekdays $18.60 per hour Saturday Time-and-a-half Sunday Double time 18 A mechanic’s industrial award allows for normal rates for the f irst 7 hours on any day. It provides for overtime payment at the rate of time-and-a-half for the f irst 2 hours and double time thereafter. Find a mechanic’s wage for a 12-hour day if their normal pay rate is $42.50 an hour. 19 Abbey’s timesheet is shown opposite. She gets paid $12.80 per hour during the week, time-and-a-half for Saturdays and double time for Sundays. Abbey is not paid for meal breaks. a How much did Abbey earn at the normal rate of pay during this week? b How much did Abbey earn from working at penalty rates during this week? c What percentage of her pay did Abbey earn by working at penalty rates? 20 Connor works a 35-hour week and is paid $18.25 per hour. Any overtime is paid at time-and-a-half. Connor wants to earn enough overtime to earn at least $800 each week. What is the minimum number of hours overtime that Connor will need to work? 21 Max works in a shop and earns $21.60 per hour at the normal rate. Each week he works 15 hours at the normal rate and 4 hours at time-and-a-half. a Calculate Max’s weekly wage. b Max aims to increase his weekly wage to $540 by working extra hours at the normal rate. How many extra hours must Max work? c Max’s rate of pay increased by 5%. What is his new hourly rate for normal hours? d What will be Max’s new weekly wage assuming he maintains the extra working hours? Day In Out Meal break Monday 8.30 a.m. 5.30 p.m. 1 hour Tuesday 8.30 a.m. 3.00 p.m. 1 hour Wednesday 8.30 a.m. 5.30 p.m. 1 hour Thursday 8.30 a.m. 9.00 p.m. 2 hours Friday 4.00 p.m. 7.00 p.m. No break Saturday 8.00 a.m. 4.00 p.m. No break Sunday 10.00 a.m. 3.00 p.m. 30 minutes ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party © The Powers Family Trust 2013 Cambridge University Press

11 Chapter 1 — Earning and managing money 1.3 Annual leave loading and bonuses Annual leave loading Annual leave loading is a payment calculated as a fi xed percentage of the normal pay over a  fi xed number of weeks. It is usually paid at the beginning of the annual holidays to meet the  increased expenses of a holiday.  Annual leave loading Annual leave loading or holiday loading is usually at the rate of  17 12% . Holiday loading  = 17 12% × Normal weekly pay  × Number of weeks leave Example 5 Finding the annual leave loading Finding the annual leave loading Thomas works a 40-hour week at a rate of $18.50 per hour. He receives Thomas works a 40-hour week at a rate of $18.50 per hour. He receives  17 12% of 4 weeks  normal pay as holiday loading. What is Thomas’s pay for the holiday? Solution 1  Write the quantity (4 weeks pay) to be found. 2  Multiply the pay rate by the number of hours  worked during the week by the number of  weeks (4). 3  Evaluate. 4  Write the quantity (loading) to be found. 5  Multiply 0.175  ( )( )17( )17 1 ( ) 12 ( ) 2% ( ) %  by 4 weeks pay  (2960). 6  Evaluate.  7  Write the quantity (holiday pay) to be found. 8  Add the 4 weeks pay (2960) and the loading  (518). 9  Evaluate.  10 Write your answer in words. 4 weeks pay  = (18.50  × 40  × 4)      = $2960 Loading  =  17 12%  of $2960 = 0.175  × 2960   =  $518 Holiday pay  = $2960  + $518 = $3478 Thomas receives $3478 in  holiday pay. 1.3 ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Pres•

12 Preliminary Mathematics General Bonus A bonus is an extra payment or gift earned as reward for achieving a goal. It is paid in addition  to the normal income. Bonuses are an incentive for employees to work harder. For example, an  employee may receive a bonus of 5% of their annual salary or $1000. Bonus Bonus is an extra payment or gift earned as reward for achieving a goal. Example 6 Calculating a bonus Calculating a bonus Amber’s employer has decided to reward all their employees with a bonus. The bonus awarded Amber’s employer has decided to reward all their employees with a bonus. The bonus awarded  is 5% of their annual salary. What is Amber’s bonus if her annual salary is $68 560? Solution 1 Write the quantity (bonus) to be found. 2 Multiply the bonus percentage (5%) by the annual  salary ($68 560). 3 Evaluate. 4 Write the answer in words. Bonus  = 5% of $68560 = 0.05  × 68560   =  $3428 Amber receives a bonus of  $3428. ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Pres•

13 Chapter 1 — Earning and managing money Exercise 1C 1  A business pays  17 12% holiday loading on 4 weeks normal pay. Calculate the amount of      holiday loading for these employees. a Nicholas earns $6240 normal pay for 4 weeks. b Kumar earns $5130 normal pay for 4 weeks. c Samantha earns $5320 per fortnight. d Andrew earns $2760 per fortnight. e Bilal earns $1680 per week. 2  The local government pays its employees 17.5% holiday loading on 4 weeks normal pay.      Calculate the amount of holiday loading for these employees. a Paige earns an annual salary of $105 560. (Assume 52 weeks in a year.) b Jack earns an annual salary of $58 760. (Assume 52 weeks in a year.) c Riley earns $32 per hour and works a 35-hour week. d A’ishah earns $41.50 per hour and works a 37-hour week. 3  Laura works a 37-hour week at a rate of $20.50 per hour. When she takes her 4 weeks      annual leave, she is paid a loading of  17 12%. What is Laura’s holiday pay when she takes  her leave? 4  Ethan is paid $660 per week. He receives a holiday leave loading of 17.5% for three  weeks holiday pay. What is his total holiday pay? 5  A bonus is awarded as a percentage of a person’s annual salary. The percentage awarded  depends on the person’s achievements. Calculate the following bonuses. a 6% of $48 360  b 3% of $96 540  c 2% of $103 290 d 4.5% of $65 420  e 212%  of $88 580  f 114%  of $164 400 6  Grace received a bonus of 12% of her weekly wage. What was Grace’s bonus if her  weekly wage is $1850? 7  Patrick’s boss has decided to reward all employees with a bonus. The bonus awarded is  734%  of their annual salary. What is Patrick’s bonus if his annual salary is $74 980? ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Pres•

14 Preliminary Mathematics General Development 8  Chen receives 17.5% of 4 weeks normal pay as leave loading. If Chen’s leave loading  was $379.40, what was his normal weekly pay? 9  Create the spreadsheet below. a The formula for cell E5 is ‘ =IF(AND(C5>10,D5>50),400,0)’.  It is the formula that calculates a $400 bonus if the employer has more than 10 years  of service and more than 50 hours of overtime.  Fill down the contents of E6 to E10 using this formula. b Edit the overtime amount for Sienna Humes to 52. Observe the changes in E7. c Edit the years of service for Ava White to 10. Observe the changes in E10. d Edit the overtime amount for Dylan Fraser to 60. Observe the changes in E6. e Edit the years of service for Xay Sengmany to 20. Observe the changes in E9. f Edit the overtime amount for Benjamin Huynh to 40. Observe the changes in E8. 10   Jim receives holiday loading of  17 12%  of 4 weeks pay. His loading was $996.80. a Find his normal weekly pay. b Find his normal hourly pay rate if he usually works a 40 hour week.  11   Chloe’s annual salary is $72 800. a Calculate her weekly wage. b Holiday loading is calculated at  17 12%  of four weeks pay. Calculate Chloe’s holiday  loading. c Chloe’s employer has proposed to increase her annual salary by 1%. What is Chloe’s  new annual salary? d The increase in Chloe’s annual salary is compensation for removing holiday loading.  Explain why Chloe is worse off f inancially with the 1% increase. 1C ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Pres•

15 Chapter 1 — Earning and managing money 1.4 Commission Commission is usually a percentage of the value of the goods sold. People such as real estate  agents and salespersons are paid a commission. Advantages • Higher sales increase the income •  May receive a small payment (retainer)  plus the commission Disadvantages • Income may vary each week •  Competition for customers is usually  high Commission Commission  = Percentage of the value of the goods sold Example 7 Finding the commission Finding the commission Zoë sold a house for $650 000. Find the commission from the sale if her rate of commission Zoë sold a house for $650 000. Find the commission from the sale if her rate of commission  was 1.25%. Solution 1 Write the quantity (commission) to be found. 2 Multiply 1.25% by $650 000. 3 Evaluate and write using correct units. 4 Write the answer in words. Commission  = 1.25% of $650 000  =  0.0125  × 650 000  =  $8125 Commission earned is $8125. Example 8 Finding the commission Finding the commission An electrical goods salesman is paid $570.50 a week plus 4% commission on all sales over An electrical goods salesman is paid $570.50 a week plus 4% commission on all sales over  $5000 a week. Find his earnings in a week where his sales amounted to $6800. Solution 1 Commission on sales of over $5000 is  $1800. 2 Write the quantity (earnings) to be found. 3 Add weekly payment and commission of  4% on $1800. 4 Evaluate and write using correct units. 5 Write the answer in words. Sales  = 6800 – 5000      = 1800 Earnings  = 570.50  + (4% of $1800)      = 570.50  + (0.04  × 1800)      = $642.50 Earnings were $642.50. 1.4 ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Pres•

16 Preliminary Mathematics General Exercise 1D 1  Jake earns a commission of 4% on the sales price. What is the commission on the  following sales? a $8820  b $16 740  c $34 220 2  Michael Tran is a real estate agent. He  earns 2% on all sales. Calculate Michael’s  commission on these sales.  a $456 000  b $420 000 c $285 500  d $590 700 3  Olivia sold a car valued at $54 000. Calculate Olivia’s commission from the sale if her  rate of commission is 3%. 4  Sophie earns a weekly retainer of $355 plus a commission of 10% on sales. What are  Sophie’s total earnings for each week if she made the following sales? a $760  b $2870  c $12 850 5  Chris earns $240 per week plus 25% commission on sales. Calculate Chris’s weekly  earnings if he made sales of $2880. 6  Ella is a salesperson for a cosmetics company. She is paid $500 per week and a  commission of 3% on sales in excess of $800. a What does Ella earn in a week when she makes sales of $1200?  b What does Ella earn in a week when she makes sales of $600?  7  A real estate agent charges a commission of 5% for the f irst $20 000 of the sale price and  2.5% for the balance of the sale price. Copy and complete the following table. Sale price 5% commission on $20 000 2.5% commission on balance a $150 000 b $200 000 c $250 000 d $300 000 ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Pres•

17 Chapter 1 — Earning and managing money Development 8  Jade is a real estate agent and is paid an annual salary of $18 000 plus a commission of  2.5% on all sales. She is also paid a car allowance of $50 per week. What was Jade’s total  yearly income if she sold $1 200 000 worth of property? 9  The commission that a real estate agent charges for selling a property is based on the  selling price and is shown below. Selling price Commission First $20 000 5% Next $120 000 3% Thereafter 1%     What is the commission charged on properties with the following selling prices? a $100 000  b $150 000  c $200 000 10   Harry is a sales person. He earns a basic wage of $300 per week and receives  commission on all sales. Last week he sold $20 000 worth of goods and earned $700.  What was Harry’s rate of commission? 11   Caitlin and her assistant, Holly, sell perfume. Caitlin earns 20% commission on her own  sales, as well as 5% commission on Holly’s sales. What was Caitlin’s commission last  month when she made sales of $1800 and Holly made sales of $2000? 12   A real estate agency charges a commission for selling a property based on the selling  price below. Commission rates Up to $300 000 4% $300 000 and over 5%     Bailey is paid by the real estate agent $180 per week plus 5% of the commission received  by the real estate agency. This week, Bailey sold one property for $290 000 and one for  $600 000. He sold no properties in the previous week. a What is the commission paid to the real estate agency for the property worth  $290 000? b What is the commission paid to the real estate agency for both properties? c Calculate Bailey’s pay for this week. d What is Bailey’s average weekly income for the two-week period? ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Pres•

18 Preliminary Mathematics General 1.5 Piecework, royalties and income from government Piecework Piecework is a fi xed payment for work completed. People who are employed to complete a  particular task, such as an electrician installing lights, are earning piecework. Advantages •  Incentive to work hard. Income increases  with more work completed • Often fl exible hours and work place Disadvantages • No permanent employment • No superannuation, sick or holiday pay Piecework Piecework  = Number of units of work  × Amount paid per unit Example 9 Calculating a piecework payment Calculating a piecework payment Noah is a tiler and charges $47 per square metre to lay tiles. How much will he earn for laying Noah is a tiler and charges $47 per square metre to lay tiles. How much will he earn for laying  tiles in a room whose area is 14 square metres? Solution 1 Write the quantity (earnings) to be found. 2 Multiply number of square metres (14) by the  charge ($47). 3 Evaluate and write using correct units. 4 Write the answer in words. Earnings  = 14  × $47 = $658 Noah earns $658. Royalties A royalty is a payment for the use of intellectual property such as a book or song. It is  calculated as a percentage of the revenue or profi t received from its use. People such as  creative artists and authors receive a royalty. Advantages •  Incentive to work hard. Income  increases with a better product • Flexible hours and work place Disadvantages • Income varies according to sales •  No superannuation, sick and holiday pay Royalty Royalty  = Percentage of the goods sold or profi t received ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Pres•

19 Chapter 1 — Earning and managing money Example 10 Calculating a royalty Calculating a royalty Andrew is an author and is paid a royalty of 12% of books sold. Find his royalties if there Andrew is an author and is paid a royalty of 12% of books sold. Find his royalties if there  were 2480 books sold at $67.50 each.  Solution 1 Write the quantity (royalty) to be found. 2 Multiply 12% by the total sales or 2480  × $67.50 3 Evaluate and write using correct units. 4 Write the answer in words. Royalty  = 12% of (2480  × $67.50) = 0.12  × 2480  × 67.50 = $20 088 Andrew earns $20 088 in royalties. Incomes from the government Some people receive a pension, allowance or benefi t  from the government. For example, the age pension  is payable for a person who has reached 65 years  of age (male). The requirements for receiving these  incomes may change according to the priorities of  the current government. Example 11 Calculating an income from the government Calculating an income from the government Youth allowance helps people studying, undertaking training or in an apprenticeship. Youth allowance helps people studying, undertaking training or in an apprenticeship.  Status Allowance per fortnight Under 18, at home $194.50 Under 18, away from home $355.40 18 and over, away from home $355.40 18 and over, at home $233.90 How much youth allowance does Ryan receive in a year if he is over 18 and living at home  while studying?  Solution 1 Write the quantity (allowance) to be found. 2 Multiply allowance per fortnight ($233.90) by 26. 3 Evaluate and write using correct units. 4 Write the answer in words. Allowance  = $233.90  × 26 = $6081.40 Youth allowance is $6081.40. ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Pres•

20 Preliminary Mathematics General Exercise 1E 1  A dry cleaner charges $9 to clean a dress. How much do they earn by dry cleaning:  a 250 dresses?  b  430 dresses?  c  320 dresses? 2  Abbey is an artist who makes $180 for each large portrait and $100 for each small  portrait. How much will she earn if she sells 13 large and 28 small portraits? 3  Angus works part-time by addressing envelopes at home and is paid $23 per 100  envelopes completed, plus $40 to deliver them to the off ice. What is his pay for  delivering 2000 addressed envelopes? 4  Emilio earns a royalty of 24% on net sales from writing a f iction book. There were  $18 640 net sales in the last f inancial year. What is Emilio’s royalty payment? 5  Calculate the royalties on the following sales. a 3590 books sold at $45.60 with a 8% royalty payment b 18 432 DVDs sold at $20 with a 10% royalty payment c 4805 computer games sold at $65.40 with a 5% royalty payment 6  Austudy provides f inancial help for people aged 25 or older who are studying full-time. Status Fortnightly payment Single, no children $355.40 Single, with children $465.60 Partnered, with children $390.20 Partnered, no children $355.40 a How much does Madison receive in a year if she is single with a child and studying  full-time? Madison is 29 years old. b How much does Oscar receive in a year if he is partnered with no children and  studying full-time? Oscar is 35 years old. 7  Child-care benef it is available to support parents in the workforce. The rate per fortnight  is shown below.  No. of children Fortnightly pay 1 $337.00 2 $704.34 3 $1099.26 Calculate the yearly payment for: a One child  b  Two children  c  Three children ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Pres•

21 Chapter 1 — Earning and managing money Development 8 Tahlia receives $19.40 for delivering 200 brochures. She receives an additional $30 per day when delivering in wet weather. How much does she receive for delivering: a 600 brochures on a clear day? b 1000 brochures on a clear day? c 800 brochures on a wet day? d 1400 brochures on a wet day? 9 Mitchell works in a factory that makes key rings. Each key ring completed earns him $0.34. Mitchell also receives an additional $25 if he works on the weekend. How much does he earn for making: a 420 key rings on Friday? b 460 key rings on Wednesday? c 380 key rings on Saturday? d 230 key rings on Sunday? 10 A doctor charges each patient $33.50 for a consultation. He works for 6 hours a day and usually sees 5 patients per hour. a How much money does the doctor receive each day? b The doctor also has costs of $410 per day. What is the prof it for the day? 11 Austudy is reduced by 50 cents for every dollar between $62 and $250 of fortnightly income. Tyler is 28 years of age, partnered and has one child. He is studying full-time but earning $126 per fortnight in a part-time job. What will be Tyler’s fortnightly payment from Austudy? Use the Austudy table on the previous page. 12 Anthony writes crime novels. He has just received his half-yearly statement of sales of his latest novel. He has been informed that 20 000 copies were printed and there are 8760 left in stock. Anthony receives 15% of the retail price as royalties. a How many copies of his latest novel were sold? b What is Anthony’s royalty if the retail price of his latest novel is $24.95? c What is Anthony’s royalty if the retail price of $24.95 was discounted by 10%? 13 The maximum youth allowance is reduced by $1 for every $4 that the youth’s parents’ income is over $31 400. By how much is Charlotte’s youth allowance reduced if her parents earn a combined income of $34 728? ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party © The Powers Family Trust 2013 Cambridge University Press

22 Preliminary Mathematics General 1.6 Gross pay, net pay and deductions Employers must pay the minimum rate of an award or enterprise agreement. The rate  will depend on the type of work and the actual times worked. Gross pay is the total of an  employee’s pay including allowances, overtime pay, commissions and bonuses. It is the  amount of money before any deductions are made. The amount remaining after deductions  have been subtracted is called the net pay or ‘take-home pay’. Deductions are a regular amount of money subtracted from a person’s wage or salary. People  have many different deductions subtracted from their gross pay such as: • Income tax – a charge that funds the government’s operations • Superannuation – an investment for retirement. An employer must contribute 9% of the  employee’s wages into a superannuation fund. • Health insurance – private insurance to cover medical and dental costs • Union fee – payment for union membership. Gross pay, net pay and deductions Net pay  = Gross pay  − Deductions Example 12 Calculating the net pay Calculating the net pay Laura is a nurse who receives a gross weekly wage of $2345. Laura is a nurse who receives a gross weekly wage of $2345.  She has the following deductions taken from her pay:  • Income tax – $861 • Health fund payments – $48.25 • Superannuation – $67.95. What is Laura’s net pay? Solution 1 Write the quantity (net pay) to be  found. 2 Write the formula for net pay. 3 Substitute the values for gross pay  and deductions. 4 Evaluate and write using correct units. 5 Write the answer in words. Net pay  = Gross pay  − deductions = 2345  − (861  + 48.25  + 67.95) = $1367.80 Laura’s net pay is $1367.80 1.6 ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Pres•

23 Chapter 1 — Earning and managing money Example 13 Reading information from a pay slip Reading information from a pay slip Oscar received the following pay slip. What amount is received this pay for:Oscar received the following pay slip. What amount is received this pay for: a  gross pay?  b  net pay?  c  superannuation?  d  PAYG tax? Hours Rate Amount This Pay Year to Date Ordinary time   26.00 $ 25.000 $ 650.00 Annual holiday   0.0 $ 25.994 $  0.0 Total Gross Earnings $650.00 $1 300.00 PAYG Tax $100.00 $  200.00 Social Club $  2.00 $  4.00 HECS Repayments $  13.00 $  26.00 Superannuation $  35.00 $  70.00 Less Post-tax deductions $  50.00 $  100.00 Net Pay $450.00 $  900.00 Direct Credit to  account: 00000000 Total Payments $450.00 $  900.00 Solution 1 Read the value for gross earnings. 2 Read the value for net pay. 3 Read the value for superannuation. 4 Read the value for PAYG tax. a Gross pay is $650.00. b Net pay is $450.00. c Superannuation is $35.00. d PAYG tax is $100.00. ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Pres•

24 Preliminary Mathematics General Exercise 1F 1  Calculate the weekly net pay for these people. a Isabella receives a gross pay of $1386 and has total deductions of $875. b Kim-Ly receives a gross pay of $985 and has total deductions of $265. c Christopher receives a gross pay of $715 and has total deductions of $222. 2  Calculate the weekly net earnings for these people. a Daniel receives a gross weekly wage of $1056 and has deductions of $294.75 for  income tax, $28.80 for superannuation and $325.05 for loan repayments. b Hannah receives a gross weekly wage of $3042 and has deductions of $1068 for  income tax, health fund payments for $50.85, superannuation for $53.55 and savings  for $450. c Kapil receives a gross weekly wage of $2274. He has deductions of $768 for income  tax, $28.95 for health insurance, $49.02 for superannuation, $15.30 for life insurance  and $450 for loan repayments. 3  Jack’s annual gross pay is  $48 750. The deductions are  $9150 for income tax, $1462  for health insurance and $5280  for superannuation.  a What are Jack’s total  deductions? b What is Jack’s annual  net pay? 4  Calculate the weekly gross pay for these people. a Aaron receives a net weekly pay of $1245 and has deductions of $374.15 for income  tax, $45.60 for superannuation and $25.20 for union membership. b Hannah receives a net weekly pay of $2645 and has deductions of $1068 for income  tax, $53.95 for health fund payments and $83.75 for superannuation. c Ivan receives a net weekly pay of $2511. He has deductions of $913 for income tax,  $31.95 for health insurance, $59.46 for superannuation, $18.20 for life insurance and  $470 for loan repayments. 5  Harry’s net pay is $57 908. The deductions are $12 580 for income tax, $2087 for health  insurance and $6910 for superannuation. What is Harry’s gross pay? ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Pres•

25 Chapter 1 — Earning and managing money 6  Joshua is on a working holiday. He picked pieces of fruit on a farm as follows:  Monday – 170 Tuesday – 130 Wednesday – 145 Thursday – 210 Friday – 190. a What is his gross salary at $0.55 per piece of fruit? b What is his net salary if he has total deductions of $121? 7  Charlotte owns an investment property that is rented out for $320 per week. She pays the  real estate agent a fee of 3% for managing the property.  a How much does she pay the real estate agent each week?  b How much does Charlotte receive each week from the investment property? c What is the net income received by Charlotte from this property over the year? 8  Nicholas receives a yearly gross salary of $74 568. He pays 18% of his weekly gross  salary in income tax. He contributes 9% of his weekly gross salary to his superannuation  fund and has $155 in miscellaneous deductions each week.  a What is his gross weekly  pay?  b How much income tax is  deducted each week? c How much superannuation  is he contributing each  week? d What is the total amount  of deductions made each  week? e What is his net weekly  pay this week? 9  Lakshmi receives a fortnightly pay of $2240. She pays 15% of her weekly gross salary in  income tax. She contributes 9% of her weekly gross salary to her superannuation fund  and has $95 in miscellaneous deductions each week.  a What is her gross weekly pay?  b How much income tax is deducted each week? c How much superannuation is she contributing each week? d What is the total amount of deductions made each week? e What is her net weekly pay this week? ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Pres•

26 Preliminary Mathematics General Development 10   Charlie is a building worker who receives $48.50 per hour for a 38-hour week. In  addition he receives an allowance of $3.50 per hour for work on a multistorey  development. Charlie is currently working on six-storey apartment block. Each week he  has deducted from his pay a superannuation contribution of 9% of his gross pay and  union fees of $28.45. Because he only started working late in the f inancial year, he  doesn’t yet have to pay tax. a What is his gross weekly pay this week? b How much superannuation is he contributing each week? c What is his net weekly pay this week? 11   Emily receives a gross fortnightly salary of $2703 and has deductions of $891.75 for  income tax, $54.30 for health fund payments, $753 for car loan payments and $14.55 for  union subscription. a What is Emily’s net income each fortnight? b What percentage of her gross income is deducted for income tax? (Answer correct to  one decimal place.) 12 Liam received a gross fortnightly salary of $3795. His pay deductions were $937.20, for  income tax, $215.25 for superannuation, $21.45 for union fees and $201 for a home loan  repayment. a What is his net income each fortnight? b What was his weekly net pay? c What percentage of his gross income was deducted for income tax? (Answer correct  to one decimal place.) d If Liam’s loan repayment increased by 10%, what was his new fortnightly net pay? 13   Jane normally works 37 hours a week at  $54 per hour. In one particular week she worked  42 hours and received overtime at the rate of  time-and-a-half. Her deductions for the week  were income tax $602.20, medical fund $49.60,  superannuation $74.40 and motor vehicle  repayment $417.40. a What was Jane’s gross weekly wage? b What was her net income for the week? c What percentage of her gross income is spent  on a motor vehicle repayment? Answer correct  to the nearest per cent. 13.1 ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Pres•

27 Chapter 1 — Earning and managing money 1.7 Budgeting Budgeting involves balancing of income and the expenses. It is planning how to manage your  income. Budgets are created for a specifi ed time such as weekly, monthly or yearly. Creating a budget 1  List all the income categories. 2  List all the expense categories. 3  Calculate the total of the income and expenses categories. 4  Balance the budget by modifying the categories or by entering a balance category. Example 14 Balancing a budget Balancing a budget Balance the following weekly budget.Balance the following weekly budget. Income Expenses Salary $1726.15 Clothing $ 73.08 Bonus $ 20.00 Gifts and Christmas $114.80 Investment $ 156.78 Groceries $467.31 Part-time work $ 393.72 Insurance $171.34 Loan repayments $847.55 Motor vehicle costs $105.96 Phone $ 38.26 Power and heating $ 51.82 Rates $ 54.82 Recreation $216.79 Work-related costs $ 68.76 Balance Total Total Solution 1 Add all the income. 2 Add the all the expenses excluding the  ‘balance’. 3 Subtract the total expenses from the total  income. 4 Write the result of step  3 as the balance. Income  = 1726.15  + …  + 393.72 = $2296.65 Expenses  = 73.08  + …  + 68.92 = $2210.49 Balance  = Income  − Expenses = 2296.6  − 2210.49 = $86.16 1.7 ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Pres•

28 Preliminary Mathematics General Example 15 Creating a budget Creating a budget Maya and Logan have a weekly net wage of $954. Their monthly expenses are home loan Maya and Logan have a weekly net wage of $954. Their monthly expenses are home loan  repayment $1032, car loan repayment $600, electricity $102, phone $66 and car maintenance  $120. Their other expenses include insurance $2160 annually, rates $1800 annually, food  $180 weekly, petrol $48 fortnightly and train fares $36 weekly. Maya and Logan allow $72 for  miscellaneous items weekly and need to save $84 per week for a holiday next year. a  Prepare a monthly budget for Maya and Logan. Assume there are four weeks in a month. b  What is the balance?  c  How can Maya and Logan ensure they have their holiday next year? Solution a 1 List all the monthly income categories. a  Solution is shown above. 2 List all the monthly expenses categories.   Total income  = $3816 3 Calculate the total income and expenses categories.   Total expenses  = $3834 4 Subtract the total expenses from the total income to calculate the balance. b  Balance  = $3816  − $3834     =−$18 5 The balance is −$18. A negative balance indicates an increase in their income or reduction in their expenses. c   Maya and Logan need to  increase income or reduce  expenses by $18. Income Expenses Wage $3816 Home loan repayment $1032 Car loan repayment $600 Electricity $102 Phone $66 Car maintenance $120 Insurance $180 Rates $150 Food $720 Petrol $96 Train fares $144 Miscellaneous $288 Holiday $336 Balance −$18 $3816 $3816 ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Pres•

29 Chapter 1 — Earning and managing money Exercise 1G 1  Oscar and Jill are living in a unit. Part of their budget is shown below. Calculate the  total amount paid over one year for: a Electricity  b Insurance  c Food  d Rent. 2  Sarah earns $67 365 annually. She has budgeted 20% of her salary for rent. How much  should she expect to pay to rent an apartment for one year? 3  Adam has constructed a yearly budget as shown below. Income Expenses Wage $60 786.22 Clothing $ 4 634.42 Interest $ 674.15 Council rates $ 1 543.56 Electricity $ 1 956.87 Entertainment $ 4 987.80 Food $17 543.90 Gifts and Christmas $ 5 861.20 Insurance $ 2 348.12 Loan repayments $16 789.34 Motor vehicle costs $ 2 458.91 Telephone $ 832.98 Work-related costs $ 812.67 Balance Total Total a Calculate the total income. b Calculate the total expenses. c Balance the budget. 4  Dimitri had a total weekly income of $104 made up of a part-time job earning $74  and an allowance of $30. He decided to budget his expenses in the following way:  sport – $24, movies – $22, school – $16 and food – $20. a Prepare a weekly budget showing income and expenses. b What is the balance? Item When Cost Electricity Quarterly $  384 Food Weekly $  360 Insurance Biannually $ 1275 Rent Monthly $ 1950 ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Pres•

30 Preliminary Mathematics General Development 5  Create the spreadsheet below. a The formula for cell E5 is ‘ =C5/$C$7’. It is the formula for relative percentage. Fill  down the contents of E5 to E7 using this formula. b Enter formulas in E9:E17 to calculate the relative percentages for expenses. c Edit the amount spent per month on eating out from $200 to $240. Observe the  changes. d Edit the amount of savings per month from $300 to $360. Observe the changes. e Edit the amount of car expenses per month from $100 to $150. Observe the  changes. 6 Ava has a gross fortnightly pay of $1896.  a Ava has a mortgage with an annual repayment of $13 676. Calculate the amount that  Ava must budget each fortnight for her mortgage. b Ava has budgeted $180 per week for groceries, $60 per week for entertainment, $468  per year for medical expenses and $80 per week to run a car. Express these as  fortnightly amounts and calculate their total. c Ava has an electricity bill of $130 per quarter, telephone bill of $91 per quarter and  council rates of $1118 per annum. Express these amounts annually and convert to  fortnightly amounts. What is the total of these fortnightly amounts? d Prepare a fortnightly budget showing income and expenses. 1G 14.1 ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Pres•

31 Chapter 1 — Earning and managing money Review Chapter summary – Earning and managing money Study guide 1 Salary and wages • Salary – payment for a year’s work, which is then divided  into equal monthly, fortnightly or weekly payments • Wage – payment for work that is calculated on an hourly  basis Overtime and special allowances • Overtime – work beyond the normal working day • Casual rate – set amount paid for each hour’s work • Time-and-a-half rate  = normal rate  × 1.5 • Double time rate  = normal rate  × 2 • Allowance – payment for diffi cult or dangerous  conditions Annual leave loading and bonuses • Annual leave loading – payment for going on holidays • Holiday loading  = 17 12% × normal weekly pay  × weeks  leave • Bonus – extra payment or gift earned as a reward Commission • Commission – percentage of the value of the goods sold • Retainer – small payment in addition to the commission Piecework, royalties and government • Piecework – payment for work completed • Piecework  = Number of units of work  × Amount paid  per unit • Royalty – percentage of the goods sold or profi t received • Government income – pension, allowance or benefi t Gross pay, net pay and deductions • Gross pay – total of the employee’s pay including  allowances, overtime pay, commissions and bonuses • Deductions – regular amount of money subtracted from a  person’s wage or salary such as income tax • Net pay  = Gross pay – Deductions Budgeting • Budgeting – balancing of income and expenses. Budgets  are created for a specifi ed time such as weekly. ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Pres•

32 Preliminary Mathematics General Review Chapter summary – Earning Money 1 Alyssa receives a salary of $85 640. How much does she receive each fortnight? A $3293.84  B  $3293.85 C $1646.92  D  $1646.93 2 Christopher receives a normal hourly rate of $22.60 per hour. What is his pay when he  works 8 hours at a normal rate and 3 hours at time-and-a-half? A $180.80  B  $248.60  C $282.50  D  $316.40 3 Rana works a 38-hour week at a rate of $26.00 per hour. She receives  17 12%  of 4 weeks  normal pay as holiday loading. What is Rana’s holiday loading? A $172.90  B  $691.60  C $3952.00  D  $4643.60 4 Taylah earns a weekly retainer of $425 plus a commission of 8% on sales. What are her  weekly earnings when she made sales of $8620? A $34.00  B  $459.00  C $689.60  D  $1114.60 5 Ahmet is a carpet layer and charges $37.50 per square metre of carpet laid. How much will  he earn for laying carpet in a room whose area is 9 square metres? A $37.50  B  $46.50  C $337.50  D  $675.00 6 Isabelle earns a royalty of 18% on net sales from writing her autobiography. There were  $24 520 net sales in the last year. What is Isabelle’s royalty payment? A $4413.60  B  $20 106.40  C $24 520.00  D  $28 933.60 7 Angus’s net pay is $68 806. The deductions are $20 630 for income tax, $1051 for health  insurance and $5487 for superannuation. What is his gross pay? A $27 168  B  $41 638  C $47 125  D  $95 974 8 Adam has the following bills: electricity $250 per quarter, phone $70 per month, rates  $1200 per year and rent $300 per week. What is the total amount Adam should budget for  the year? A $358  B  $1553 C $1820  D  $18 640 Sample HSC – Objective-response questions ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Pres•

33 Chapter 1 — Earning and managing money Review Chapter summary – Earning Money 1 Jake earns $96 470.40 per annum and works an average of 48 hours per week.  a What is his average weekly wage? b Calculate Jake’s hourly rate of pay. 2 Alex works for a fast-food company and is paid $13.50 per hour for a 35-hour week.  He gets time-and-a-half pay for overtime worked on the weekdays and double time  for the weekends. Last week he worked a normal 35-hour week plus three hours of  overtime during the week and four hours of overtime on the weekend. What was his  wage last week? 3 Carlo’s employer has decided to reward all employees with a bonus. The bonus awarded is  614%  of their annual salary. What is Carlo’s bonus if his annual salary is $85 940? 4 The public service provides all employees with a  17 12% holiday loading on four weeks  normal wages. Lucy works a 37-hour week for the public service in Canberra. She is paid a  normal hourly rate of $32.40. a How much will Lucy receive in holiday loading? b Calculate the total amount of pay that Lucy will receive for her holidays. 5 Chelsea is a real estate agent and charges the following commission for selling the  property: 3% on the fi rst $45 000, then 2% for the next $90 000 and  112%  thereafter. a What is Chelsea’s commission if she sold a property for $240 000? b How much would the owner of the property receive from the sale? 6 Patrick is a comedian who makes $120 for a short performance and $260 for a long  performance. How much will he earn if he completes 11 short and 12 long performances? Challenge questions 1 Sample HSC – Short-answer questions ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Pres•

Preliminary Mathematics General 34 Review 7 Bailey is paid a royalty of 11.3% on the net sales of his book. The net sales of his book in  the last fi nancial year was $278 420.  a What is Bailey’s royalty payment in the last fi nancial year? b Net sales this fi nancial year are expected to decrease by 15%. What is the expected  royalty payment for this fi nancial year?  8 The maximum youth allowance is reduced by $1 for every $4 that the youth’s parents’  income exceeds $31 400. By how much is Hannah’s youth allowance reduced if her parents  earn a combined income of $35 624? 9 William works as a builder. His annual union fees are $278.20. William has his union fees  deducted from his weekly pay. What is the size of William’s weekly union deduction? 10 Quan received a gross fortnightly salary of $2968. His pay deductions were $765.60 for  income tax, $345.15 for superannuation and $23.40 for union fees. a What was his fortnightly net pay? b What percentage of his gross income was deducted for income tax? (Answer correct to  one decimal place.) 11 Joel is a carpet layer and charges $16 per square metre to lay carpet. How much will he earn  for laying carpet in a house whose area is 32 square metres? 12 Daniel has a gross monthly wage of $3640. He has the following deductions taken from his  pay: $764 for income tax, $71.65 for superannuation and $23.23 for union m\ embership.  What is Daniel’s net pay? 13 Hannah has budgeted $210 per week for groceries, $70 per week for leisure, $23 per  fortnight for medical expenses and $90 per week to run a car. Calculate the monthly  expenses. Assume 4 weeks in a month. 14 Amelie earns $90 345 annually. She has budgeted 30% of her salary for a loan repayment.  How much should she expect to pay for a loan repayment for one year? Challenge questions 1 ISBN: 9781107627291 Photocopying is restricted under law and this material must not be transferred to another party The Powers Family Trust 2013 Cambridge University Pres•

35 2.1 Adding and subtracting like terms A pronumeral (letter) represents a number. It may stand for an unknown value or series of values that change. For example, in the equation x + 5 = 8, x is a pronumeral that represents a value. Its value can be determined because we know 3 + 5 = 8, so x = 3. When a term has a pronumeral and a number, the number is written before the pronumeral and is called the coeffi cient. For example, the term 3xy has a coeffi cient of 3 and its pronumerals are written after the coeffi cient in alphabetical order. Like terms Terms that have exactly the same pronumerals such as 2a and 5a are called like terms. Only like terms can be added and subtracted. It involves adding and subtracting the coeffi cients. Adding and subtracting like terms simplifi es the algebraic expression. It is often called collecting the like terms. 2.1 C H A P T E R 2 Algebraic manipulation Syllabus topic — AM1 Algebraic manipulation Add and subtract like terms Multiply and divide algebraic terms Expand and factorise algebraic expressions Evaluate the subject of the formula through substitution Solve linear equations involving up to 3 steps Solve equations following substitution ,6%1 3KRWRFRS\LQJLVUHVWULFWHGXQGHUODZDQGWKLVPDWHULDOPXVWQRWEHWUDQVIHUUHGWRDQRWKHUSDUW\ 7KH3RZHUV)DPLO\7UXVW

36 Preliminary Mathematics General Adding and subtracting like terms 1 Find the like terms or the terms that have exactly the same pronumerals.  2  Only like terms can be added or subtracted; unlike terms cannot. 3  Add or subtract the coeffi cients or the numbers before the pronumeral of the like terms.  Example 1 Adding and subtracting like terms Simplify 2ab + 3 + 5ab − 7.  Solution 1 Rewrite the expression by grouping  the like terms. 2 Add and subtract the coeff icients.2ab + 3 + 5ab − 7 = (2ab + 5ab) + 3 − 7     = 7ab − 4 Example 2 Adding and subtracting like terms Simplify 4y + 6y 2 − 3y − 5y 2. Solution 1 Rewrite the expression by  grouping the like terms. 2 Add and subtract the coeff icients.  4y + 6y 2 − 3y − 5y 2 = 6y 2 − 5y 2 + 4y − 3y    = y 2 + y Adding and subtracting algebraic fractions To add and subtract algebraic fractions rewrite each fraction as an equivalent fraction with  a common denominator, then add or subtract the numerators. A common denominator can  always be found by multiplying the denominators of both fractions together. Example 3 Adding and subtracting algebraic fractions Simplify  x x 6 4+ . Solution 1 Find a common denominator for 6 and 4. Both 6 and 4  divide into 12. Alternatively, multiply 6 by 4 and use 24. 2 Multiply the f irst fraction by 2 (6  × 2 = 12) and the  second fraction by 3 (4  × 3 = 12). 3 Write the equivalent fractions. 4 Add the numerators of the equivalent fractions. + =+ = × + × = += + = x x x x×x x× x x x 6 4 2 x x 2 x x 6 2×6 2× 3 4 3×4 3× 2 12 3 x x 3 x x 12 5 12 ,6%1 3KRWRFRS\LQJLVUHVWULFWHGXQGHUODZDQGWKLVPDWHULDOPXVWQRWEHWUDQVIHUUHGWRDQRWKHUSDUW\ ‹7KH3RZHUV)DPLO\7UXVW

37 Chapter 2 — Algebraic manipulation Exercise 2A 1 Choose the like terms out of each of the following. a 4r, 6p, r, 7 b 5x, 3xy, 2x c -a, 5a, -8b, 7 d xy, 4xy, xy 2, 3yx e 3, 2m, mn, 9m f c, cd, cde, dc, ce 2 Simplify by collecting like terms. a 4y + 3y b 3 1 7 p p3 1p p3 1 7 p p 7 3 1 + 3 13 1p p3 1 + 3 1p p3 1 c 7 6h h7 6h h7 67 6h h7 6 − 7 6h h7 6 d 3x xx x−x x e d dd d+d dd d 4 d d f 6 1 2 y y6 1y y6 1 2 y y 2 6 1y y6 1 − 6 1y y6 1 g − +d d− +d d− + ( ) d d ( ) d d − d d −( )− d d − d d ( ) d d 4 d d ( ) d d h 33 t tt t+ −t t ( ) 11 ( ) 11 t t ( ) t t 11 t t 11 ( ) 11 t t 11 t t+ −t t ( ) t t+ −t t i 11 f ff f− −f f ( ) f f ( ) f f 5 f f 5 ( ) 5 f f 5 f f− −f f ( ) f f− −f f j 4 6hg4 6hg4 6 gh 4 6 + 4 6 k 5 2ab5 2ab5 2 ba 5 2 + 5 2 l xyz xyz +3 3 Simplify by collecting like terms. a 5 4 2 c c5 4c c5 4 2 c c 2 + + 5 4 + + 5 4c c+ +c c5 4c c5 4 + + 5 4c c5 4 b 4 4 7 f f4 4f f4 4 + −f f+ −f f4 4f f4 4 + − 4 4f f4 4 c 8 5 12 + +8 5+ +8 5 r r 12 r r 12 + + r r + + d 6 4 3 x y6 4x y6 4 x + − 6 4 + − 6 4x y+ −x y6 4x y6 4 + − 6 4x y6 4 e 3 7 2 b a3 7b a3 7 a + −b a+ −b a3 7b a3 7 + − 3 7b a3 7 f h d h h d+ −h d 2 6 h d 2 6 h d+ −2 6+ −h d+ −h d 2 6 h d+ −h d g 4 2de4 2de4 2 ed 4 2 ed 4 2 de 4 2 + − 4 24 2 ed 4 2 + − 4 2 ed 4 2 h 7 2a b7 2a b7 2 a b 2 a b 2 7 2 + + 7 27 2a b7 2 + + 7 2a b7 2 a b−a b i xy yx xy + +2 3yx2 3yx + +2 3+ + yx + + yx2 3yx + + yx j 6 2ba6 2ba6 2 b a − + 6 2 − + 6 2 b a − + b a ( ) b a ( ) b a b ( ) b b a − b a ( ) b a − b a k 7 2a b7 2a b7 2 a b 2 a b 2 7 2a b7 2 + − 7 2a b7 2 + − 7 2 + − 7 2 a b + − a b ( ) 7 2 ( ) 7 2a b ( ) a b7 2a b7 2 ( ) 7 2a b7 27 2a b7 2 + − 7 2a b7 2 ( ) 7 2a b7 2 + − 7 2a b7 2 l 5 8g h58g h58 g h 58 g h 5858 + + 5858g h58 + + 58g h5858 g h 58 − + 58 g h 58 ( ) 58 ( ) 58 g h ( ) g h 58 g h 58 ( ) 58 g h 5858 − + 58 ( ) 58 − + 5858 g h 58 − + 58 g h 58 ( ) 58 g h 58 − + 58 g h 58 4 Simplify by collecting like terms. a 8 3 4 22 8 3 22 8 3x x8 3x x8 3 22x x22 8 3 22 8 3x x8 3 22 8 3 x 22 x 22− − x x − − x x8 3x x8 3 − − 8 3x x8 3 + b 4 3 2 2 4 3 2 2 4 34 3a a4 3 a a 2 2 a a 2 2 4 3 + − 4 34 3 2 2 4 3 + − 4 3 2 2 4 34 3a a4 3 + − 4 3a a4 3 + a a + a a c 7 8 6 7 2 2 6 7 22 6 7 t t7 8t t7 8 t t6 7t t6 7 22 t t 22 6 7 22 6 7t t6 7 22 6 7 + − 22 + − 22 t t+ −t t7 8t t7 8 + − 7 8t t7 8 6 7t t6 7 − 6 7t t6 7 d 3 8 4 2 2 3 8 22 3 8 4 22 4 m m3 8m m3 83 8 22 3 8m m3 8 22 3 8 m m 22 m m 22+ −22+ −22 3 8 22 3 8 + − 3 8 22 3 8m m + − m m3 8m m3 8 + − 3 8m m3 8 22m m22+ −22m m22 3 8 22 3 8m m3 8 22 3 8 + − 3 8 22 3 8m m3 8 22 3 8 m m − m m e e e e e 2 2e e2 2e e e e 2 2 e e 2 2 2 2 2+ + e e + + e e2 2+ +2 2e e2 2e e + + e e2 2e ee e + + e e2 2+ +2 2e e2 2e e + + e e2 2e ee e 2 e e + + e e 2 e e2 2 2 2 2+ +2 2 2 2 2e e2 2e e 2 e e2 2e e + + e e2 2e e 2 e e2 2e e e e − e e f d d d d + −d d+ −d d d d+d d 22 d d 22 d d + − 22 + − d d+d d 22 d d+d d5 22 5 22 g 2 5 2 2 5 2 2 52 5w w2 5 w 2 5 + + 2 52 5 2 2 5 + + 2 5 2 2 52 5w w2 5 + + 2 5w w2 5 + h 6 4 2 6 4 2 6 46 4− +6 46 4 2 6 4− +6 4 2 6 46 4 − 6 46 4 v v 6 46 4− +6 4 v v 6 4− +6 46 4 2 6 4− +6 4 2 6 4 v v 6 4 2 6 4− +6 4 2 6 4 i 8 7 7 3 2 r r8 7r r8 7 7 3 r r 7 3 r r r− −r r8 7r r8 7 − − 8 7r r8 7 7 3 − 7 3 5 Add or subtract the algebraic fractions. a a a 3 3+ b 3 5 2 5 x x 2 x x 2− c 2 4 3 4 m m 3 m m 3+ d 3 7 7 x x− e d d 11 d d 2 d d 11 + f 6 15 2 15 y y 2 y y 2− g 4 3 9 3 s s 9 s s 9+ h 9 8 8 f f 4 f f 4− i y y 2 4+y y+y y j 7 6 3 e e− k g g 2 4 g g 4 g g 6 +g g+g g l r r 2 4 r r 4 r r 10− ,6%1 3KRWRFRS\LQJLVUHVWULFWHGXQGHUODZDQGWKLVPDWHULDOPXVWQRWEHWUDQVIHUUHGWRDQRWKHUSDUW\ 7KH3RZHUV)DPLO\7UXVW

38 Preliminary Mathematics General Development 6 Which of the following is equivalent to m m m n n + + + m m m n + + + m m m n + ? a 2 2m m2 2m m2 2 n 2 2 + + 2 22 2m m2 2 + + 2 2m m2 2 b m n3 2m n3 2m nm n + m n3 2+3 2m n3 2m n + m n3 2m n c 5 4 3 m m5 4m m5 4 n n − + 5 4 − + 5 4m m − + m m5 4m m5 4 − + 5 4m m5 4 n n−n n d 7 4 2 m m n7 4m m n7 4 2 m m n 2 n − + 7 4 − + 7 4m m n − + m m n7 4m m n7 4 − + 7 4m m n7 4 − e 3 23 2n n m3 2 m 3 2 − + 3 23 2n n m3 2 − + 3 2n n m3 23 2 − − 3 2 f − + − + 2 5− +2 5− + 2 3− +2 3− + m m2 5m m2 5− +2 5− + m m − +2 5− + n n2 3n n2 3− +2 3− + n n − +2 3− + 7 Copy and add like terms where possible to complete the table. +x 3x x + y 3x 7y x - y 2y 8 Matteo has $y for shopping. He spent $x for a pair of jeans, $3x for a shirt and $2x for a belt. Write an expression in simplif ied form for how many dollars he has left. 9 The perimeter of a plane shape is the distance around the boundary of the shape. The plane shape opposite is a rectangle with a length l and a breadth b. Write an expression for the perimeter of this rectangle by collecting like terms. 10 The isosceles triangle opposite has three sides whose lengths are 3x + y, 3x + y and x + 2y. Write an expression in simplif ied form for the perimeter of this triangle by collecting like terms. 11 Add or subtract the algebraic fractions. a w w 4 3 + b a a 4 5− c x x 7 2 x x 2 x x 3 + d z z 3 5− e 3 8 6 h h+ f 5 12 8 r r− g u u 10 4 u u 4 u u 15+ h 3 4 1 0 e e− i w w w 2 4 6 + ++ + j 3 5 4 2 a a a− +− + k 7 10 6 3 x x x− +− + l d d d+ −+ − 2 1 0 l b 3x + y 3x + y x + 2y ,6%1 3KRWRFRS\LQJLVUHVWULFWHGXQGHUODZDQGWKLVPDWHULDOPXVWQRWEHWUDQVIHUUHGWRDQRWKHUSDUW\ &DPEULGJH8QLYHUVLW\3UHVV

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