Haese IB Maths Applications & Interpretations SL 2

Author(s): Michael Haese et al

IB Mathematics

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 Organisation.

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


Product Information

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\chi^2χ
​2
​​ goodness of fit test 395
E The\chi^2χ
​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

General Fields

  • : 9781925489576
  • : Haese Mathematics
  • : Haese Mathematics
  • : July 2019
  • : books

Special Fields

  • : Michael Haese et al
  • : 650