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P1: FXS/ABEP2: FXS9780521740517agg.xmlCUAT013-EVANSSeptember 7, 200811:27Back to Menu iESSENTIALEFurtherMathematicsPLThird editionSAMPETER JONESMICHAEL EVANSKAY LIPSONTI-Nspire and Casio ClassPad materialprepared in collaboration withRussell BrownKevin McMenaminCambridge University Press Uncorrected Sample pages 978-0-521-61328-6 2008 Jones, Evans, LipsonTI-Nspire & Casio ClassPad material in collaboration with Brown and McMenamin
P1: FXS/ABEP2: FXS9780521740517agg.xmlCUAT013-EVANSSeptember 7, 200811:27Back to Menu CAMBRIDGE UNIVERSITY PRESSCambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São PauloCambridge University Press477 Williamstown Road, Port Melbourne, VIC 3207, Australiawww.cambridge.edu.auInformation on this title: www.cambridge.edu.au/0521613280Peter Jones, Michael Evans & Kay Lipson 2005First published 1998Reprinted 1998Second edition 1999Reprinted 2000, 2001, 2002, 2003, 2005Third edition 2005Reprinted 2006E CPLCover designed by Modern Art Production GroupText designed by Sylvia WitteTypeset in India by TechbooksPrinted in China through Everbest Printing Company Pty LtdNational Library of Australia Cataloguing in Publication dataJones, Peter, 1943-.Essential further mathematics.3rd ed.ISBN-13 978-0-521-74051-7 paperbackISBN-10 0-521-61328-0 paperback1. Mathematics – Problems, exercises, etc. I. Evans,Michael (Michael Wyndham). II. Lipson, Kay. III. Title510.76SAMISBN-13 978-0-521-74051-7 paperbackISBN-10 0-521-61328-0 paperbackReproduction and communication for educational purposesThe Australian Copyright Act 1968 (the Act) allows a maximum of one chapter or 10% of the pages of thispublication, whichever is the greater, to be reproduced and/or communicated by any educational institution forits educational purposes provided that the educational institution (or the body that administers it) has given aremuneration notice to Copyright Agency Limited (CAL) under the Act.For details of the CAL licence for educational institutions contact:Copyright Agency LimitedLevel 19, 157 Liverpool StreetSydney NSW 2000Telephone: (02) 9394 7600Facsimile: (02) 9394 7601Email: info@copyright.com.auReproduction and communication for other purposesExcept as permitted under the Act (for example a fair dealing for the purposes of study, research, criticism orreview) no part of this publication may be reproduced, stored in a retrieval system, communicated ortransmitted in any form or by any means without prior written permission. All inquiries should be made to thepublisher at the address above.Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external orthird-party internet websites referred to in this publication and does not guarantee that any content on suchwebsites is, or will remain, accurate or appropriate.All Victorian Curriculum and Assessment Authority material copyright VCAA. Reproduced by permission ofthe Victorian Curriculum and Assessment Authority Victoria, Australia.Disclaimer: This publication is independently produced for use by teachers and students. Although references 2008Jones, Evans,LipsonCambridgeUniversityPresswith Uncorrectedpages the978-0-521-61328-6have beenreproducedpermissionSampleof the VCAApublication is in noway connectedwith orendorsedTI-Nspire & Casio ClassPad material in collaboration with Brown and McMenaminby the VCAA.
P1: FXS/ABEP2: FXS9780521740517agg.xmlCUAT013-EVANSSeptember 7, 200811:27Back to Menu PLEContentsAcknowledgementsxivCORECHAPTER 1 — Organising and displaying dataClassifying data1Organising and displaying categorical dataOrganising and displaying numerical dataWhat to look for in a histogram20Stem-and-leaf plots and dot plots26Key ideas and chapter summary34Skills check35Multiple-choice questions35Extended-response questions37SAM1.11.21.31.41.5138CHAPTER 2 — Summarising numerical data: the median,range, IQR and box plots2.12.22.32.42.540Will less than the whole picture do?40The median, range and interquartile range(IQR)41The five-number summary and the box plot45Relating a box plot to distribution shape52Interpreting box plots: describing andcomparing distributions54Key ideas and chapter summary57Skills check58Multiple-choice questions59Extended-response questions60Cambridge University Press Uncorrected Sample pages 978-0-521-61328-6 2008 Jones, Evans, LipsonTI-Nspire & Casio ClassPad material in collaboration with Brown and McMenamin
P1: FXS/ABEP2: FXS9780521740517agg.xmlCUAT013-EVANSSeptember 7, 200811:27Back to Menu ContentsCHAPTER 3 — Summarising numerical data: the mean andthe standard deviation3.3The mean63Measuring the spread around the mean:the standard deviation67The normal distribution and the 68–95–99.7% rule:giving meaning to the standard deviation73Standard scores79Populations and samples83Key ideas and chapter summary88Skills check90Multiple-choice questions91Extended-response questions92PL3.43.563E3.13.2CHAPTER 4 — Displaying and describing relationshipsbetween two g the relationship between twocategorical variables95Using a segmented bar chart to identifyrelationships in tabulated data99Investigating the relationship between a numericaland a categorical variable102Investigating the relationship between twonumerical variables104How to interpret a scatterplot107Calculating Pearson’s correlationcoefficient r112The coefficient of determination118Correlation and causality121Which graph?122Key ideas and chapter summary123Skills check124Multiple-choice questions125Extended-response questions128SAMivCHAPTER 5 — Regression: fitting lines to data5.15.25.35.45.5131Least squares regression line: the theory131Calculating the equation of the least squaresregression line133Performing a regression analysis140A graphical approach to regression: the threemedian line153Extrapolation and interpolation157Cambridge University Press Uncorrected Sample pages 978-0-521-61328-6 2008 Jones, Evans, LipsonTI-Nspire & Casio ClassPad material in collaboration with Brown and McMenamin
P1: FXS/ABEP2: FXS9780521740517agg.xmlCUAT013-EVANSSeptember 7, 200811:27Back to Menu ContentsvKey ideas and chapter summary159Skills check160Multiple-choice questions160Extended-response questions162CHAPTER 6 — Data transformationEData transformation166Transforming the x axis169183Transforming the y axisChoosing and applying the appropriatetransformation189Key ideas and chapter summary197Skills check197Multiple-choice questions197Extended-response questions200PL6.16.26.36.4CHAPTER 7 — Time series7.17.27.3204Time series data204Smoothing a time series plot (movingmeans)210Smoothing a time series plot (movingmedians)215Seasonal indices220Fitting a trend line and forecasting207Key ideas and chapter summary233Skills check234Multiple-choice questions235Extended-response questions237SAM7.47.5CHAPTER 8 — Revision of the core8.18.28.38.48.5166239Displaying, summarising and describingunivariate data239Displaying, summarising and describingrelationships in bivariate data243Regression and data transformation245Time series249Extended-response questions253MODULE 1 — Number patterns andapplicationsCHAPTER 9 — Arithmetic and geometricsequences259Cambridge University Press Uncorrected Sample pages 978-0-521-61328-6 2008 Jones, Evans, LipsonTI-Nspire & Casio ClassPad material in collaboration with Brown and McMenamin
P1: FXS/ABEP2: FXS9780521740517agg.xmlCUAT013-EVANSSeptember 7, 200811:27Back to Menu thmetic sequences260The nth term of an arithmetic sequenceand its applications264The sum of an arithmetic sequenceand its applications274Geometric sequences281The nth term of a geometricsequence285Applications modelled by geometricsequences289The sum of the terms in a geometricsequence294The sum of an infinite geometric sequenceRates of growth of arithmetic and geometricsequences302Key ideas and chapter summary307Skills check308Multiple-choice questions309Extended-response questions310E9.19.29.3CHAPTER 10 — Difference equations10.110.2312Introduction312The relationship between arithmetic and geometricsequences and difference equations320First-order difference equations322Solving first-order difference equations thatgenerate arithmetic sequences324Solving difference equations that generategeometric sequences325Solution of general first-order difference equations(optional)327Summary of first-order difference equations328Applications of first-order differenceequations329The Fibonacci sequence338Key ideas and chapter summary345Skills check346Multiple-choice questions346Extended-response ER 11 — Revision: Number patterns andapplications11.111.2350Multiple-choice questions350Extended-response questions355Cambridge University Press Uncorrected Sample pages 978-0-521-61328-6 2008 Jones, Evans, LipsonTI-Nspire & Casio ClassPad material in collaboration with Brown and McMenamin
P1: FXS/ABEP2: FXS9780521740517agg.xmlCUAT013-EVANSSeptember 7, 200811:27Back to Menu ContentsviiMODULE 2 — Geometry and trigonometryCHAPTER 12 — GeometryEProperties of parallel lines – a review360Properties of triangles – a review362Properties of regular polygons – a review364Pythagoras’ theorem367Similar figures371Volumes and surface areas375Areas, volumes and similarity382387Key ideas and chapter summarySkills check389Multiple-choice questions390PL12.112.212.312.412.512.612.7CHAPTER 13 — Trigonometry392Defining sine, cosine and tangentThe sine rule396The cosine rule401Area of a triangle404Key ideas and chapter summarySkills check407Multiple-choice questions408SAM13.113.213.313.4360392406CHAPTER 14 — Applications of geometry andtrigonometry14.114.214.3410Angles of elevation and depression, bearings, andtriangulation410Problems in three dimensions417Contour maps421Key ideas and chapter summary424Skills check424Multiple-choice questions424Extended-response questions426CHAPTER 15 — Revision: Geometry andtrigonometry15.115.2431Multiple-choice questions431Extended-response questions438Cambridge University Press Uncorrected Sample pages 978-0-521-61328-6 2008 Jones, Evans, LipsonTI-Nspire & Casio ClassPad material in collaboration with Brown and McMenamin
P1: FXS/ABEP2: FXS9780521740517agg.xmlCUAT013-EVANSSeptember 7, 200811:27Back to Menu ContentsMODULE 3 — Graphs and relationsCHAPTER 16 — Constructing and interpreting lineargraphsThe gradient of a straight line441The general equation of a straight line443Finding the equation of a straight line445Equation of a straight line in intercept form449Linear models450Simultaneous equations452Problems involving simultaneous linearequations456Break-even analysis458Key ideas and chapter summary460Skills check461Multiple-choice CHAPTER 17 — Graphs17.117.217.317.417.5465Line segment graphs465Step graphs468Non-linear graphs470Relations of the form y kxn forn 1, 2, 3, 1, 1, 22472Linear representation of non-linear relationsKey ideas and chapter summary482Skills check483Multiple-choice questions483Extended-response questions486SAMviiiCHAPTER 18 — Linear programming18.118.218.318.4488Regions defined by an inequality488Regions defined by two inequalities490Feasible regions492Objective functions493Key ideas and chapter summary503Skills check504Multiple-choice questions505Extended-response questions507CHAPTER 19 — Revision: Graphs and relations19.119.2475510Multiple-choice questions510Extended-response questions514Cambridge University Press Uncorrected Sample pages 978-0-521-61328-6 2008 Jones, Evans, LipsonTI-Nspire & Casio ClassPad material in collaboration with Brown and McMenamin
P1: FXS/ABEP2: FXS9780521740517agg.xmlCUAT013-EVANSSeptember 7, 200811:27Back to Menu ContentsixMODULE 4 — Business related mathematicsCHAPTER 20 — Principles of financial mathematicsPercentage change521Simple interest526Compound interest534Reducing balance loans546548Key ideas and chapter summarySkills check549Multiple-choice questions549Extended-response questions551E20.120.220.320.4521CHAPTER 21 — Applications of financialPercentage changes and charges553Bank account balances558Hire purchase561Inflation567Depreciation571Applications of Finance Solvers581Key ideas and chapter summary597Skills check599Multiple-choice questions600Extended-response aticsCHAPTER 22 — Revision: ice questions606Extended-response questions610MODULE 5 — Networks and decisionmathematicsCHAPTER 23 — Undirected graphs23.123.223.323.423.5614Introduction and definitions614Planar graphs and Euler’s formula619Complete graphs622Euler and Hamilton paths623Weighted graphs626Key ideas and chapter summary630Skills check632Multiple-choice questions632Extended-response questions636Cambridge University Press Uncorrected Sample pages 978-0-521-61328-6 2008 Jones, Evans, LipsonTI-Nspire & Casio ClassPad material in collaboration with Brown and McMenamin
P1: FXS/ABEP2: FXS9780521740517agg.xmlCUAT013-EVANSSeptember 7, 200811:27Back to Menu ContentsCHAPTER 24 — Directed graphs639Introduction, reachability and dominanceNetwork flows645The critical path problem649Allocation problems656Key ideas and chapter summary662Skills check663Multiple-choice questions663Extended-response questions667639E24.124.224.324.4CHAPTER 25 — Revision: Networks and decisionmathematics671Multiple-choice questions671Extended-response questions677PL25.125.2MODULE 6 — Matrices and applicationsCHAPTER 26 — Matrices and applications 126.126.226.326.4CHAPTER 27 — Matrices and applications II27.127.227.327.4690What is a matrix?690Using matrices to represent information696Matrix arithmetic: addition, subtraction and scalarmultiplication699Matrix arithmetic: the product of twomatrices706Key ideas and chapter summary715Skills check717Multiple-choice questions717Extended-response questions720SAMx722The inverse matrix722Applications of the inverse matrix:solving simultaneous linear equations729Matrix powers737Transition matrices and their applications739Key ideas and chapter summary749Skills check751Multiple-choice questions751Extended-response questions754Cambridge University Press Uncorrected Sample pages 978-0-521-61328-6 2008 Jones, Evans, LipsonTI-Nspire & Casio ClassPad material in collaboration with Brown and McMenamin
P1: FXS/ABEP2: FXS9780521740517agg.xmlCUAT013-EVANSSeptember 7, 200811:27Back to Menu ContentsxiCHAPTER 28 — Revision: Matrices andapplications756Multiple-choice questions756Extended-response questions760Appendix TI-nspire763Appendix ClassPad768771SAMPLEAnswersCambridge University Press Uncorrected Sample pages 978-0-521-61328-6 2008 Jones, Evans, LipsonTI-Nspire & Casio ClassPad material in collaboration with Brown and McMenamin
Ess Maths IN-BOOK BROCHUR.qxd 11/3/05 7:37 PM Page xii Quark08 Quark08:Books:CUAT006 From Pooja:CUAT013:The new Essentialseries for the 2006study design1COREOrganising anddisplaying dataWhat is the difference between categorical and numerical data?What is a frequency table, how is it constructed and when is it used?What is the mode and how do we determine its value?What are bar charts, histograms, stem plots and dot plots? How are theyconstructed and when are they used?How do you describe the features of bar charts, histograms and stem plots whenIn each chapter you will find writing a statistical report?1.1Classifying dataStatistics is a science concerned with understanding the world through data. The first step inthis process is to put the data into a form that makes it easier to see patterns or trends.Some dataThe data contained in Table 1.1 is part of a larger set of data collected from a group ofuniversity students.Chapter 9 – Arithmetic and geometric sequences237 dataTable 1.1 StudentHeight(cm)How to use a graphics calculator to generate the terms of an arithmetic sequenceon theHome screenWeight(kg)Age(years)SexM maleF FMPlays sport1 regularly2 sometimes3 rarelyrarely22113333Pulse rate(beats/min)8682967190788870E173Generate the first five terms of the arithmetic sequence: 2, 7, 12, 17, 22, . . . 179167Steps1951731 Start on the Home screen. Clear. Enter the value of the184first term 2. Press Í.175140Source: www.statsci.org/data/oz/ms212.html. Used with permission.2 The common difference for this sequence is 5. So, typein 5. Press Í. The second term in the sequence,7, is generated.3 Pressing Í again generates the next term, 12.4 Pressing Í again generates the next term, 17.Keep pressing Í until the required numberof terms is generated.Being able to recognise an arithmetic sequence is another skill that you need to develop. Thekey idea here is that the successive terms in an arithmetic sequence differ by a constant amount(the common difference).PLa vibrant full colour text with aclear layout that makes mathsmore accessible for students1‘Using a graphics calculator’boxes within chapters explainhow to do problems using theTI-83/Plus and TI-84 graphicscalculators, and include screenshots to further assist studentsExample 1Testing for an arithmetic sequence20, 1717,, 14,14, 1111,, 8,8, . . . arithmetic?a Is the sequence 20,Chapterr 4 — Displaying and describing relationships between two variablesChapte107SolutionClearly, traffic volume is a very good predictor of carbon monoxide levels in the air. KnowingStrategy:: Subtract successive terms in the sequence to see whether they differ by a constantStrategythe traffic volume will enable us to predict carbon monoxide levels with a high degree ofamount. If they do, the sequence is arithmetic.accuracy. This contrasts with the next example, which concerns the ability to predict20,, 17,2017, 14,14, 11,11, 8,8, . . .1 Write down the terms of the sequence.mathematical ability from verbal ability.17 20 3 32 Subtract successive terms.14 17 3 3Example 3Calculating and interpreting the coefficient of determination11 14 3 3 and so onSequenceSequence is arithmetic as terms differ by aScores on tests of verbal and mathematical ability are linearly related with:constant amount.3 Write down your conclusionrmathematical, verbal 0.275Determine the value of the coefficient of determination, write it in percentage terms, andinterpret. In this relationship, mathematical ability is the DV.SolutionSAMa wealth of worked examplesthat support theory explanationswithin chapterscarefully graduated exercisesthat include a number of easierlead-in questions to providestudents with a greateropportunity for immediatesuccesschapter summaries at the end ofeach chapter provide studentswith a coherent overviewchapter reviews that include keyideas and chapter summary andskills check lists, and multiplechoice and extended-responsequestionsAppendices that include a TIAppendices83/84 Plus help guide and stepby-step worked examples usingTI-89 Graphics Calculatorsrevision chapters to helpconsolidate student knowledgeThe coefficient of determination is:r 2 (0.275)2 0.0756 . . . or 0.076 100 7.6%Therefore, only 7.6% of the variation observed in scores on the test of mathematical ability canbe explained by the variation in scores obtained on the test of verbal ability.Clearly, scores on the verbal ability test are not good predictors of the scores on themathematical ability test; 92.4% of the variation in mathematical ability is explained by otherfactors.Exercise 4G1 For each of the following values of r, calculate the value of the coefficient of determinationand convert to a percentage (correct to one decimal place).a r 0.675b r 0.345c r 0.567d r 0.673e r 0.1242 a For the relationship described by the scatterplot173shown opposite, the coefficient of determination 0.8215.Determine the value of the correlation coefficient r(correct to three decimal p
P1: FXS/ABE P2: FXS 9780521740517agg.xml CUAT013-EVANS September 7, 2008 11:27 Contents Acknowledgements xiv CORE CHAPTER 1—Organising and displaying data 1 1.1 Classifying data 1 1.2 Organising and displaying categorical data 3 1.3 Organising and displaying numerical data 8 1.4 What to look for in a histogram 20 1.5 Stem-and-lea
Cambridge University Press 978-1-107-63581-4 – Cambridge Global English Stage 6 Jane Boylan Kathryn Harper Frontmatter More information Cambridge Global English Cambridge Global English . Cambridge Global English Cambridge Global English
The Cambridge Companion to Bede. Cambridge Companions to Literature. Cambridge: Cambridge University Press, 2010. Evans, G.R. The Language and Logic of the Middle Ages: The Earlier Middle Ages. Cambridge: Cambridge University Press, 1984. ———. The Language and Logic of the Middle Ages: The Road to Reformation. Cambridge: Cambridge .
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Artificial Intelligence: A Modern Approach Stuart Russell and Peter Norvig. 3rd Edition, 2010. 2 copies of are on 24hr reserve in the Engineering and Computer Science Library. Recommended but not required. Lecture notes cover much of the course material and will be available online before class.
