About the Book

For an online preview, please email IB@haesemathematics.com.

This book has been written for the IB Diploma Programme course Mathematics: Applications and Interpretation SL, for first assessment in May 2021.

This book is designed to complete the course in conjunction with the Mathematics: Core Topics SL textbook. It is expected that students will start using this book approximately 6-7 months into the two-year course, upon the completion of the Mathematics: Core Topics SL textbook.

This product has been developed independently from and is not endorsed by the International Baccalaureate Organization.  International Baccalaureate, Baccalaureát International, Bachillerato Internacional and IB are registered trademarks owned by the International Baccalaureate Organization.

Year Published: 2019
Page Count: 504
ISBN: 978-1-925489-57-6 (9781925489576)
Online ISBN: 978-1-925489-69-9 (9781925489699)

Table of Contents

Mathematics: Applications and Interpretation SL

1 APPROXIMATIONS AND ERROR 15
A Rounding numbers 16
B Approximations 20
C Errors in measurement 22
D Absolute and percentage error 25
Review set 1A 29
Review set 1B 30
2 LOANS AND ANNUITIES 31
A Loans 32
B Annuities 38
Review set 2A 43
Review set 2B 44
3 FUNCTIONS 45
A Relations and functions 46
B Function notation 49
C Domain and range 53
D Graphs of functions 57
E Sign diagrams 60
F Transformations of graphs 63
G Inverse functions 69
Review set 3A 73
Review set 3B 76
4 MODELLING 79
A The modelling cycle 80
B Linear models 86
C Piecewise linear models 89
D Systems of equations 94
Review set 4A 96
Review set 4B 98
5 BIVARIATE STATISTICS 101
A Association between numerical variables 102
B Pearson's product-moment correlation coefficient 107
C Line of best fit by eye 112
D The least squares regression line 116
E Spearman's rank correlation coefficient 123
Review set 5A 128
Review set 5B 130
6 QUADRATIC FUNCTIONS 133
A Quadratic functions 135
B Graphs from tables of values 137
C Axes intercepts 139
D Graphs of the form $y = ax^2$ 141
E Graphs of quadratic functions 143
F Axis of symmetry 144
G Vertex 147
H Finding a quadratic from its graph 149
I Intersection of graphs 152
J Quadratic models 153
Review set 6A 159
Review set 6B 161
7 DIRECT AND INVERSE VARIATION 163
A Direct variation 164
B Powers in direct variation 168
C Inverse variation 170
D Powers in inverse variation 172
E Determining the variation model 173
F Using technology to find variation models 175
Review set 7A 178
Review set 7B 180
8 EXPONENTIALS AND LOGARITHMS 183
A Exponential functions 185
B Graphing exponential functions from a table of values 186
C Graphs of exponential functions 187
D Exponential equations 191
E Growth and decay 192
F The natural exponential 199
G Logarithms in base $10$ 204
H Natural logarithms 208
Review set 8A 211
Review set 8B 213
9 TRIGONOMETRIC FUNCTIONS 217
A The unit circle 218
B Periodic behaviour 221
C The sine and cosine functions 224
D General sine and cosine functions 226
E Modelling periodic behaviour 231
Review set 9A 236
Review set 9B 239
10 DIFFERENTIATION 241
A Rates of change 243
B Instantaneous rates of change 247
C Limits 251
D The gradient of a tangent 252
E The derivative function 254
F Differentiation 256
G Rules for differentiation 259
Review set 10A 265
Review set 10B 267
11 PROPERTIES OF CURVES 269
A Tangents 270
B Normals 273
C Increasing and decreasing 276
D Stationary points 280
Review set 11A 284
Review set 11B 285
12 APPLICATIONS OF DIFFERENTIATION 287
A Rates of change 288
B Optimisation 293
C Modelling with calculus 301
Review set 12A 303
Review set 12B 304
13 INTEGRATION 307
A Approximating the area under a curve 308
B The Riemann integral 313
C The Fundamental Theorem of Calculus 317
D Antidifferentiation and indefinite integrals 320
E Rules for integration 322
F Particular values 324
G Definite integrals 325
H The area under a curve 328
Review set 13A 331
Review set 13B 333
14 DISCRETE RANDOM VARIABLES 335
A Random variables 336
B Discrete probability distributions 338
C Expectation 342
D The binomial distribution 347
E Using technology to find binomial probabilities 352
F The mean and standard deviation of a binomial distribution 355
Review set 14A 357
Review set 14B 358
15 THE NORMAL DISTRIBUTION 361
A Introduction to the normal distribution 363
B Calculating probabilities 366
C Quantiles 373
Review set 15A 377
Review set 15B 378
16 HYPOTHESIS TESTING 381
A Statistical hypotheses 382
B Student's $t$-test 384
C The two-sample $t$-test for comparing population means 393
D The$\chi^2$ goodness of fit test 395
E The$\chi^2$ test for independence 405
Review set 16A 413
Review set 16B 415
17 VORONOI DIAGRAMS 417
A Voronoi diagrams 418
B Constructing Voronoi diagrams 422
C Adding a site to a Voronoi diagram 427
D Nearest neighbour interpolation 431
E The Largest Empty Circle problem 433
Review set 17A 437
Review set 17B 439
ANSWERS 441
INDEX 503

Authors

  • Michael Haese
  • Mark Humphries
  • Chris Sangwin
  • Ngoc Vo

Author

Michaelhaese

Michael Haese

Michael completed a Bachelor of Science at the University of Adelaide, majoring in Infection and Immunity, and Applied Mathematics. He studied laminar heat flow as part of his Honours in Applied Mathematics, and finished a PhD in high speed fluid flows in 2001. He has been the principal editor for Haese Mathematics since 2008.

What motivates you to write mathematics books?

My passion is for education as a whole, rather than just mathematics. In Australia I think it is too easy to take education for granted, because it is seen as a right but with too little appreciation for the responsibility that goes with it. But the more I travel to places where access to education is limited, the more I see children who treat it as a privilege, and the greater the difference it makes in their lives. But as far as mathematics goes, I grew up with mathematics textbooks in pieces on the kitchen table, and so I guess it continues a tradition.

What do you aim to achieve in writing?

I think a few things:

  • I want to write to the student directly, so they can learn as much as possible from the text directly. Their book is there even when their teacher isn't.
  • I therefore want to write using language which is easy to understand. Sure, mathematics has its big words, and these are important and we always use them. But the words around them should be as simple as possible, so the meaning of the terms can be properly explained to ESL (English as a Second Language) students.
  • I want to make the mathematics more alive and real, not by putting it in contrived "real-world" contexts which are actually over-simplified and fake, but rather through its history and its relationship with other subjects.

What interests you outside mathematics?

Lots of things! Horses, show jumping and course design, alpacas, badminton, running, art, history, faith, reading, hiking, photography ....

Author

Markhumphries

Mark Humphries

Mark has a Bachelor of Science (Honours), majoring in Pure Mathematics, and a Bachelor of Economics, both of which were completed at the University of Adelaide. He studied public key cryptography for his Honours in Pure Mathematics. He started with the company in 2006, and is currently the writing manager for Haese Mathematics.

What got you interested in mathematics? How did that lead to working at Haese Mathematics?

I have always enjoyed the structure and style of mathematics. It has a precision that I enjoy. I spend an inordinate amount of my leisure time reading about mathematics, in fact! To be fair, I tend to do more reading about the history of mathematics and how various mathematical and logic puzzles work, so it is somewhat different from what I do at work.

How did I end up at Haese Mathematics?

I was undertaking a PhD, and I realised that what I really wanted to do was put my knowledge to use. I wanted to pass on to others all this interesting stuff about mathematics. I emailed Haese Mathematics (Haese and Harris Publications as they were known back then), stating that I was interested in working for them. As it happened, their success with the first series of International Baccalaureate books meant that they were looking to hire more people at the time. I consider myself quite lucky!

What are some interesting things that you get to do at work?

On an everyday basis, it's a challenge (but a fun one!) to devise interesting questions for the books. I want students to have questions that pique their curiosity and get them thinking about mathematics in a different way. I prefer to write questions that require students to demonstrate that they understand a concept, rather than relying on rote memorisation.

When a new or revised syllabus is released for a curriculum that we write for, a lot of work goes into devising a structure for the book that addresses the syllabus. The process of identifying what concepts need to be taught, organising those concepts into an order that makes sense from a teaching standpoint, and finally sourcing and writing the material that addresses those concepts is very involved – but so rewarding when you hold the finished product in your hands, straight from the printer.

What interests you outside mathematics?

Apart from the aforementioned recreational mathematics activities, I play a little guitar, and I enjoy playing badminton and basketball on a social level.

Author

Chrissangwin

Chris Sangwin

Chris completed a BA in Mathematics at the University of Oxford, and an MSc and PhD in Mathematics at the University of Bath. He spent thirteen years in the Mathematics Department at the University of Birmingham, and from 2000-2011 was seconded half time to the UK Higher Education Academy "Maths Stats and OR Network" to promote learning and teaching of university mathematics. He was awarded a National Teaching Fellowship in 2006. Chris Sangwin joined the University of Edinburgh in 2015 as Professor of Technology Enhanced Science Education.

What are your learning and teaching interests in mathematics?

I teach mathematics at university but am particularly interested in core pure mathematics which starts in school and continues to be taught at university. Solving mathematical problems is at the heart of mathematics, and I enjoy teaching problem solving at university.

What interests you outside mathematics?

I really enjoy hill walking and mountaineering, particularly spending time with friends in the hills.

Why do you choose to collaborate with a small publisher on the other side of the world?

There is a unique team spirit in Haese which other publishers don't have. This makes authorship much more collaborative than my previous experiences, which is really enjoyable and I'm sure leads to much better quality books for students which are, after all, the whole point.

Author

Ngocvo

Ngoc Vo

Ngoc Vo completed a Bachelor of Mathematical Sciences at the University of Adelaide, majoring in Statistics and Applied Mathematics. Her Mathematical interests include regression analysis, Bayesian statistics, and statistical computing. Ngoc has been working at Haese Mathematics as a proof reader and writer since 2016.

What drew you to the field of mathematics?

Originally, I planned to study engineering at university, but after a few weeks I quickly realised that it wasn't for me. So I switched to a mathematics degree at the first available opportunity. I didn't really have a plan to major in statistics, but as I continued my studies I found myself growing more fond of the discipline. The mathematical rigor in proving distributional results and how they link to real-world data -- it all just seemed to click.

What are some interesting things that you get to do at work?

As the resident statistician here at Haese Mathematics, I get the pleasure of writing new statistics chapters and related material. Statistics has always been a challenging subject to both teach and learn, however it doesn't always have to be that way. To bridge that gap, I like to try and include as many historical notes, activities, and investigations as I can to make it as engaging as possible. The reasons why we do things, and the people behind them are often important things we forget to talk about. Statistics, and of course mathematics, doesn't just exist within the pages of your textbook or even the syllabus. There's so much breadth and depth to these disciplines, most of the time we just barely scratch the surface.

What interests you outside mathematics?

In my free time I like studying good typography and brushing up on my TeX skills to become the next TeXpert. On the less technical side of things, I also enjoy scrapbooking, painting, and making the occasional card.

Features

  • Snowflake (24 months)

    A complete electronic copy of the textbook, with interactive, animated, and/or printable extras.

  • Self Tutor

    Animated worked examples with step-by-step, voiced explanations.

  • Theory of Knowledge

    Activities to guide Theory of Knowledge projects.

  • Graphics Calculator Instructions

    For Casio fx-CG50, TI-84 Plus CE, TI-nspire, and HP Prime

Icon selftutor ib

This book offers SELF TUTOR for every worked example. On the electronic copy of the textbook, access SELF TUTOR by clicking anywhere on a worked example to hear a step-by-step explanation by a teacher. This is ideal for catch-up and revision, or for motivated students who want to do some independent study outside school hours.

Icon graphics calculator instructions%20%282%29

Graphics calculator instructions for Casio fx-CG50, TI-84 Plus CE, TI-nspire, and HP Prime are included with this textbook. The textbook will either have comprehensive instructions at the start of the book, specific instructions available from icons located throughout, or both. The extensive use of graphics calculators and computer packages throughout the book enables students to realise the importance, application, and appropriate use of technology.

Icon theory of knowledge

Theory of Knowledge is a core requirement in the International Baccalaureate Diploma Programme.

Students are encouraged to think critically and challenge the assumptions of knowledge. Students should be able to analyse different ways of knowing and kinds of knowledge, while considering different cultural and emotional perceptions, fostering an international understanding.

Snowflake

This book is available on electronic devices through our Snowflake learning platform. This book includes 24 months of Snowflake access, featuring a complete electronic copy of the textbook.

Where relevant, Snowflake features include interactive geometry, graphing, and statistics software, demonstrations, games, spreadsheets, and a range of printable worksheets, tables, and diagrams. Teachers are provided with a quick and easy way to demonstrate concepts, and students can discover for themselves and re-visit when necessary.

Support material

  • Errata

    Last updated - 03 Mar 2021