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