## Description

Mathematics: Applications and Interpretation SL 2

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.

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^2y=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 1010 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 tt-test 384

C The two-sample tt-test for comparing population means 393

D The ??2?? goodness of fit test 395

E The ??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

Michael Haese, Mark Humphries, Chris Sangwin, Ngoc Vo – Haese Mathematics