Haese Ib Mathematics Analysis And Approaches Sl 2

Author: Michael Haese et al

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  • : $84.99 NZD
  • : 9781925489569
  • : Haese Mathematics
  • : Haese Mathematics
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  • : July 2019
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  • : 81.99
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  • : books

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  • : Michael Haese et al
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Barcode 9781925489569
9781925489569

Description

Online preview of the book is now available. Sign up to our preview mailing list by emailing IB@haesemathematics.com. This book has been written for the IB Diploma Programme course Mathematics: Analysis and Approaches 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

Table of contents

Mathematics: Analysis and Approaches SL 1 THE BINOMIAL THEOREM 15 A Factorial notation 16 B Binomial expansions 17 C The binomial theorem 21 Review set 1A 26 Review set 1B 27 2 QUADRATIC FUNCTIONS 29 A Quadratic functions 31 B Graphs of quadratic functions 33 C Using the discriminant 40 D Finding a quadratic from its graph 43 E The intersection of graphs 47 F Problem solving with quadratics 50 G Optimisation with quadratics 53 H Quadratic inequalities 57 Review set 2A 61 Review set 2B 62 3 FUNCTIONS 65 A Relations and functions 66 B Function notation 69 C Domain and range 72 D Rational functions 78 E Composite functions 83 F Inverse functions 86 G Absolute value functions 91 Review set 3A 93 Review set 3B 96 4 TRANSFORMATIONS OF FUNCTIONS 99 A Translations 100 B Stretches 103 C Reflections 109 D Miscellaneous transformations 112 Review set 4A 115 Review set 4B 116 5 EXPONENTIAL FUNCTIONS 119 A Rational exponents 120 B Algebraic expansion and factorisation 122 C Exponential equations 125 D Exponential functions 127 E Growth and decay 132 F The natural exponential 138 Review set 5A 141 Review set 5B 143 6 LOGARITHMS 145 A Logarithms in base 1010 146 B Logarithms in base aa 149 C Laws of logarithms 151 D Natural logarithms 154 E Logarithmic equations 157 F The change of base rule 159 G Solving exponential equations using logarithms 160 H Logarithmic functions 164 Review set 6A 168 Review set 6B 170 7 THE UNIT CIRCLE AND RADIAN MEASURE 173 A Radian measure 174 B Arc length and sector area 177 C The unit circle 181 D Multiples of \frac \pi 6 ​6 ​ ​π ​​ and \frac \pi 4 ​4 ​ ​π ​​ 187 E The Pythagorean identity 190 F Finding angles 192 G The equation of a straight line 194 Review set 7A 195 Review set 7B 197 8 TRIGONOMETRIC FUNCTIONS 199 A Periodic behaviour 200 B The sine and cosine functions 204 C General sine and cosine functions 206 D Modelling periodic behaviour 211 E The tangent function 216 Review set 8A 219 Review set 8B 221 9 TRIGONOMETRIC EQUATIONS AND IDENTITIES 223 A Trigonometric equations 224 B Using trigonometric models 232 C Trigonometric identities 234 D Double angle identities 237 Review set 9A 241 Review set 9B 243 10 REASONING AND PROOF 245 A Logical connectives 248 B Proof by deduction 249 C Proof by equivalence 253 D Definitions 256 Review set 10A 259 Review set 10B 259 11 INTRODUCTION TO DIFFERENTIAL CALCULUS 261 A Rates of change 263 B Instantaneous rates of change 266 C Limits 269 D The gradient of a tangent 274 E The derivative function 276 F Differentiation from first principles 278 Review set 11A 281 Review set 11B 283 12 RULES OF DIFFERENTIATION 285 A Simple rules of differentiation 286 B The chain rule 291 C The product rule 294 D The quotient rule 297 E Derivatives of exponential functions 299 F Derivatives of logarithmic functions 303 G Derivatives of trigonometric functions 306 H Second derivatives 308 Review set 12A 310 Review set 12B 311 13 PROPERTIES OF CURVES 313 A Tangents 314 B Normals 319 C Increasing and decreasing 321 D Stationary points 326 E Shape 331 F Inflection points 333 G Understanding functions and their derivatives 338 Review set 13A 340 Review set 13B 342 14 APPLICATIONS OF DIFFERENTIATION 345 A Rates of change 346 B Optimisation 352 Review set 14A 362 Review set 14B 363 15 INTRODUCTION TO INTEGRATION 365 A Approximating the area under a curve 366 B The Riemann integral 369 C Antidifferentiation 372 D The Fundamental Theorem of Calculus 374 Review set 15A 379 Review set 15B 380 16 TECHNIQUES FOR INTEGRATION 381 A Discovering integrals 382 B Rules for integration 384 C Particular values 388 D Integrating f(ax + b)f(ax+b) 390 E Integration by substitution 393 Review set 16A 396 Review set 16B 397 17 DEFINITE INTEGRALS 399 A Definite integrals 400 B The area under a curve 404 C The area above a curve 409 D The area between two functions 411 E Problem solving by integration 416 Review set 17A 419 Review set 17B 422 18 KINEMATICS 425 A Displacement 427 B Velocity 429 C Acceleration 436 D Speed 439 Review set 18A 444 Review set 18B 446 19 BIVARIATE STATISTICS 449 A Association between numerical variables 450 B Pearson's product-moment correlation coefficient 455 C Line of best fit by eye 460 D The least squares regression line 464 E The regression line of xx against yy 471 Review set 19A 474 Review set 19B 476 20 DISCRETE RANDOM VARIABLES 479 A Random variables 480 B Discrete probability distributions 482 C Expectation 486 D The binomial distribution 492 E Using technology to find binomial probabilities 496 F The mean and standard deviation of a binomial distribution 498 Review set 20A 500 Review set 20B 502 21 THE NORMAL DISTRIBUTION 505 A Introduction to the normal distribution 507 B Calculating probabilities 510 C The standard normal distribution 518 D Quantiles 522 Review set 21A 528 Review set 21B 529 ANSWERS 531 INDEX 611