, ~-•#NELSON 1-. CENGAGE Learning·

Nelson Maths General 11 1st Edition Tracey Macbeth-Dunn Natalie Caruso Dina Antoniou Kathy Howard Anne McMahon Karen McMullen Karen O'Gorman Sandra Cllfford·Tlsdell

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National Library of Australia Catalogulng·ln·Publlcatlon Data Macbeth-Dunn, Tracey. Nelson Maths General 11 Student Book I Tracey Macbeth-Dunn, Natalie Caruso, Dina Antoniou, Kathy Howard, Anne McMahon, Karen McMullen, Karen O'Gorman, Sandra Clifford-Tisdell.

9780170250252 (paperback) Includes Index.

Mathematics··Australla··Textbooks. Mathematlcs--Study and teaching (Secondary)--Australla. Mathematlcs--Problems, exercises, etc.

510

Cengage Learning Australia l evel 7, 80 Dorcas Street South Melbourne, Victoria Australia. 3205

Cengage Learning New Zealand Unit 4B Rosedale Office Park 331 Rosedale Road, Albany, North Shore 0632, NZ

For learning solutions, visit cengage.com.au

Printed In China by China Translation & Printing Services. 12 3 45671817161514

About this book vi 3.03 Addition and subtraction

Apout this series ix of matrices 102

About the authors x 3.04 Scalar multiplication 108

Abbreviations and symbols xi 3.05 Matrix multiplication:

1 Percentages and rates 2 row matrix x column matrix

1.01 Review of percentages 4 3.06 M~trix multiplication:

1.02 Percentage of a quantity 14'" matrix x column matrix 119

1.03 Finding the whole from ·3.07 Matrix multiplication: matrices

a given percentage . 17 of various orders 124

1.04 Percentage increase and decrease 20 3.08 Powers of matrices 129

1.05 Repeated percentage change 23 3.09 Applications of matrices 133

1.06 Mark-ups and discounts 25 Chapter summary 143

1.07 Profit and loss 29 Chapter review 144

1.08 Inflation and GST 32 Mixed revision for Chapters 1-3 148

1.09 Review of rates 36 4 Earning money 152

1.1 0 Converting rates 39 4.01 Wages, salaries and overtime 154

1.11 Currency exchange rates 41 4.02 Commission and piecework 159

1.12 Best buys 44 4.03 Bonuses, allowances and

Chapter summary 48 annual leave loading 163

4.04 Government allowances Chapter review 49 and pensions 166

2 Algebra and equations 52 4.05 Budgeting 171 2.01 The four operations in algebra 54 4.06 Investing in shares 176 2.02 Expanding and simplifying

algebraic expressions 61 Chapter summary 184

2.03 Substitution 65 Chapter review 185

2.04 Solving equations 5 Measurement calculations 188

73

2.05 Solving equations with 5.01 Pythagoras' theorem. 190

pronumerals on both sides 79 5.02 Perimeter and circumference 197

2.06 Practical applications of equation 5.03 Review of areas of plane shapes 203

solving 84 5.04 Areas of composite figures 210

Chapter summary 89 5.05 Surface areas of prisms

Chapter review 90 and cylinders 216

3 Matrix arithmetic 92 5.06 Surface areas of pyramids, cones

3.01 Types of matrices 94 and spheres 221

3.02 Constructing matrices 5.07 Surface areas of composite solids 226

99 5.08 Volume and capacity: prisms

and cylinders

Volume and capacity: pyramids, 8.06 Describing the distribution

cones and spheres 235 of numerical data 389

5.10 Volume and capacity: 8.07 Measures of central tendency:

composite solids 240 mean 393

Chapter summary 244 8.08 Measures of central tendency:

Chapter review 245 median and mode 405

6 Simple and compound interest 248 8.09 Measures of spread: range

6.01 Simple interest 250 and interquartile range 412

6.02 Simple interest: calculating 8.10 Measures of spread:

principal, rate or time 255 standard deviation 418

6.03 Savings accounts and credit cards 260 · 8.11 Box plots 422

6.04 Compound interest 265 Chapter summary 433

6.05 Compound interest: calculating Chapter review 435

principal, rate or time 270 9 Linear equations and graphs 442

6.06 Using finance solvers for 9.01 Review of linear equations 444

compound interest problems 274 9.02 · Graphing straight lines 448

Chapter summary 283 9.03 Calculating the gradient of a line 459

Chapter review 284 9.04 The general equation of a

Mixed revision for Chapters 4-6 288 straight line 467_

7 Scales and similarity 292 9.05 Graphing using gradient

7.01 Scales 294 and y-intercept 470

7.02 Reading scale drawings 299 9.06 Special lines 477

7.03 Constructing scale drawings 309 9.07 Developing a linear formula 481

7.04 Similar figures 313 Chapter summary 488

7.05 Similar triangles 322 Chapter review 489

7.06 Applications of similarity 331 Mixed revision for Chapters 7-9 492

7.07 Areas of similar figures 337 10 Applications of ,trigonometry 496

7.08 Surface areas and volumes 10.01 Finding an unknowri side 498

of similar solids 341 10.02 Finding an unknown a~le 507

· Chapter summary 348 10.03 Angles of elevation and depression 513

Chapter review 349 10.04 Bearings 518

8 Statistical measures 356 10.05 Bearing applications 522

8.01 Collection of data 358 10.06 The sine rule: finding an

8.02 Types of data 364 unknown side 527

8.03 Displaying categorical data 366 10.07 The sine rule: finding an

unknown angle 532 8.04 Displaying numerical data:

stem-and-leaf plots and dot plots 372 10.08 The cosine rule 536

8.05 Displaying numerical data: 10.09 Mixed applications involving

histograms 378 non-right-angled triangles 540

10.10

Area of a triangle: Heron's formula

Chapter summary 552 Chapter review 553

11 Making comparisons 558 11.01 Use of summary statistics 560 11.02 Working with outliers 567 11.03 Using the mean and standard

deviation to describe and compare data 573

11.04 Side-by-side column graphs 578 11.05 Back-to-back stem-and-leaf plots 581 11.06 Constructing and interpreting

parallel boxplots 589 Chapter summary 604 Chapter review 606

12 Applications of simultaneous equations, piecewise and step graphs 612

12.01 Review of linear graphs 614 12.02 Solving simultaneous equations

graphically 623 12.03 Solving simultaneous equations

by substitution 630 12.04 Solving simultaneous equations

by elimination 634 12.05 Practical applications of

simultaneous equations 641 12.06 Drawing piecewise graphs

. ·~ 649

12.07 Applicatifis involving piecewise graphs 660

12.08 Step graphs 672 Chapter summary 681 Chapter review 682

Mixed revision for Chapters 10-12 689 Answers 693 Glossary 759 Index 766

ABOUT THIS BOOK

A clear outline of chapter contents is provided.

Links to curriculum content descriptions are included.

A Prior learning worksheet is provided, enabling teachers to assess prerequisite understanding.

0 Example 1

Yun borrowed $25 000 at a simple interest rate of 8.4% p.a. ,._. for 6 years. How much interest did he have to pay?

p.a. means per annum, which is 'pet ye~r·

Solution Write the values of the known variables.

Write the simple interest formula.

Substitute into the formula.

Evaluate.

Write the answer.

P = 25 000 r = 8.4 n = 6

Prn I= 100

I = 25 000 x 8.4 x 6 100

= 12 600

Yun had to pay $12 600 interest.

Examples are clearly set out with reasoning (in black) and writing (in blue) in separate columns.

Examples are sequenced in a logical order.

There are generally three, and no more than four, examples leading to an exercise.

Examples show solutions and steps which guide students through the use of the TI-Nspire CAS CX and the CASIO ClassPad calculators.

Vi NELSON SENIOR MATHS General 11 9780170250252

EXERCISE 6.02 Simple interest: calculating principal, rate or time

Concepts and techniques 1111111 Calculate the amount that would need to be invested to earn:

a $450 simple interest at 7i% p.a. for 4 years.

$3500 simple interest at 6% p.a. for 18 months.

c $1000 simple interest at 8% p.a. for 2i years.

d $180 simple interest at 3.6% p.a. for 3 months.

2 Kalena earned $262.44 in simple interest from investing an amount for 3 years at 5.4% p.a. The amount Kalena invested was A $42.52 B $1620 C $472.39 D $4251.53 E $14 580

Ben invested some money at 5% p.a. for 6 years and earned $1200 simple interest. How much money did he invest?

4 111111 Calculate, correct to one decimal place, the interest rate per annum that would be needed to earn: a $6000 simple interest if $25 000 is invested for 3 years.

$1400 simple interest if$17 000 is invested for 8 months.

c $5500 simple interest if $100 000 is invested for 1 i years.

d $100 simple interest if$3800 is invested for 90 days.

Alan invested $9835 over 5 years in a simple interest account. At the end of 5 years his investment had a value of $15 244.25. The simple interest rate per annum was: A 2.75% B 7.1% C 11.0% D 12.9% E 55.0%

INVESTIGATION Graphing simple interest

Samuel invested $100 in an account earning 5% p.a. simple interest.

a Calculate the interest earned in:

i 1 year ii 2 years iii 3 years

b Complete the following table of values showing the amount of interest($) that Samuel earned in n years.

11 years)

1($

0 2 3 4 10

c On a suitable number plane below plot the points from the table of values in part band join them.

d What can you say about the graph of the simple interest against time?

e Complete a table of values for the value which Samuel's investment will grow to against time.

Exercise questions ·are clearly divided into two categories: concepts and techniques and reasoning

and communication.

Where appropriate, worksheets are provided for additional practice and consolidation of key

concepts.

Each chapter contains at least one investigation, providing students with the opportunity to apply

their understanding to a practical application.

9780170250252 About this book I vii

\

CHAPTER REVIEW 6 SIMPLE AND COMPOUND INTEREST

Multiple choice I 11!3111 CalC'UlaulhcUflelrucmtonwdonS72001nwtlo.lat7~p.a.bJOll'IOJ'llhl.

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7 111Z1111 Chri11!anln~1ttSSOOCh1au1cofftprr1nnl1ll'IC1Dn1poundln,;q11utcrly.~ nkwol.hUlnmtnmll"IMcndolJ)'ftlt LLgMnby A UOOO+s5000x0.08Xl B "°°°H5000x0.02• 1l C$»Xl•llll1

OS5000• 1Jn' E UCOOx l.O!u

Each chapter concludes with a detailed chapter summary and a comprehensive review of concepts.

At the end of every three chapters a comprehensive mixed revision set is provided.

ICONS IN THE TEXTBOOK

1;.1,,1.1n

Prior learning

Worksheets

Link from question to worked example

Prior learning

Worksheet

viii I NELSON SENIOR MATHS General 11

Interactive spreadsheet Spreads heel

Practice quiz

Practice quiz

9780170250252

ABOUT THIS SERIES There are eight books for this series currently. These cover the subjects Essential Mathematics, General Mathematics, Mathematical Methods and Specialist Mathematics.

These books have all been written specifically, from scratch, by a truly national author team for the Senior Australian Curriculum.

There are worked solutions available for purchase, which accompany each of the General, Methods and Specialist Student Books.

There are also Exam View question banks which can be purchased separately. These will contain a large number of multiple choice questions covering each course: General, Methods and Specialist. An Exam View test generator is also provided as a part of this package, so that teachers can construct their own tests for each topic.

Accompanying each printed textbook is a digital textbook called the NelsonNetBook and a NelsonNet website.

Go to www.nelsonnet.com.au to log in.

For each chapter the resources are listed. Simply click on the required resource.

This is a web-based eBook which can be customised to suit your own learning needs.

The icons with the blue NelsonNet logo are 'hotspots: Click on the icon and the resource will open.

The tools on the vertical toolbar allow you to personalise pages in a variety of ways, including voice recordings, drawings and links to favourite websites. You are also able to zoom in and out.

The tools on the horizontal toolbar allow you to navigate around your eBook and change settings.

9780170250252 About this series I ix

ABOUT THE AUTHORS Lead author: Natalie Caruso Natalie is a very experienced Senior Mathematics teacher and Head of Department. She is currently on maternity leave from Loreto Mandeville Hall in Victoria. Natalie has authored a significant number of Mathematics texts and Study Guides. She has enjoyed many years' experience working with CAS · calculators and has presented regularly at MA V. Natalie has also been a VCE exam Vetter and marker.

Lead author: Tracey MacBeth-Dunn Tracey MacBeth-Dunn (BSc Dip Ed) has been the Head Teacher Mathematics at Denison College of Secondary education Bathurst High Campus since 2005. She has taught in a number of schools and has nineteen years experience as a classroom Mathematics teacher. Tracey has taught all levels of Mathematics and has been a HSC marker. She has been working in the publishing industry as a reviewer and writer for the last 5 years. She is currently on maternity leave.

Dina Antoniou Dina Antoniou is an experienced Mathematics teacher who has been teaching in Victorian schools . for over thirty years and has held a number of positions over the years, including Mathematics Coordinator. Dina is currently teaching at Our Lady of Mercy College, a secondary Catholic college for girls in Victoria. She also worked on a number of projects for various publishers and has extensive experience in reviewing and writing units in Mathematics.

Sandy Clifford-Tisdell Sandy has been teaching for over twenty-five years, having been Mathematics Coordinator at Our Lady of Mercy College, Parramatta for ten years. She is currently employed at Newcastle Grammar School as a Senior Mathematics teacher and has taught all levels of Mathematics from Year 7 to 12. She is the author of the revised texts Developmental Mathematics Books 1, 2, 3 and 4 in addition to the accompanying Black Line Masters Books.

Kathy Howard Kathy has b_een a teacher of Mathematics at Denison College of Secondary Education, Bathurst High Campus since 2007. In addition to her teaching responsibilities Kathy is also a student adviser and is responsible for constructing the campus timetable.

Kathy studied at Charles Sturt University, Bathurst and Wagga and attained a Bachelor of Applied Science, Industrial Mathematics and computing. In addition she also completed a Graduate Diploma of Education (Secondary Mathematics). Kathy's love and great respect for everything mathematical started with her inspirational teachers.

Anne McMahon Anne has been teaching Mathematics for 36 years. She holds a Bachelor of Secondary Mathematics Teaching, with Distinction. Anne has taught in many different schools ranging from small country schools to large metropolitan schools and has taught all levels of Mathematics from Year 7 to Year 12. For the past twenty-three years she has been teaching at Gunnedah High School, the past eleven of those years as_ Head Teacher of Mathematics.

Karen McMullen Karen has taught at Killester College~ Springvale for eight years since graduating from Monash University in 2005. During this time she has completed her Master's in School Leadership (Numeracy) and taught VCE Mathematics for seven years.

X I NELSON SEN IOR MATHS General 11 9780170250252

Karen O'Gorman Karen has been a teacher of Mathematics for seventeen years teaching mainly in the senior year levels. She has a Bachelor of Education in addition to a Masters in Educational Leadership and

Administration. She is enjoying her third year of employment at Haileybury, which caters from ELC

to Year 12 with parallel education from Grade 5 on. Karen has held many varied leadership positions

in past years. Currently her main focus is being back in the classroom and writing for Cengage.

The Digital Resources Team includes Issam Kanaan, Angelique Phillip-Kemp, Kate Sharp and Roger Walter.

ABBREVIATIONS AND SYMBOLS

is equal to .. therefore

~ is not equal to 1: 650 000 at a scale of

is approximately 1to650 000 Ill

equal to 5:8 ratio of 5 to 8 L

" square root % percent !':::,.

pi (approximately

3.14159 ... )

is similar to

angle

triangle

< is less than per 36° 27' 15" 36 degrees

is greater than LHS left-hand side 27 minutes

> and 15 seconds

:<::: is less than or RHS right-hand side equal to 053°T a true bearing

Q3 3rd quartile N S3°E a compass bearing

~ is greater than or - mean of x values equal to

x

plus or minus sx or crx standard deviation

±

GREEK ALPHABET

A, a alpha I, t iota P, p rho

B, p beta K, K kappa L, cr sigma

r, y gamma A, 'A, lambda T, 't tau

.1., 8 delta M, µ mu Y, u upsilon

E, £ epsilon N, v nu <I>, qi phi

Z, 1; zeta ~ ~ xi x, x chi ~,

H, T] eta 0, 0 omicron '¥, \jf psi

e, e theta II, 7t pi Q, co omega

97801170250252 Abbreviations and symbols xi