Author(s): Michael Haese et al

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This book has been written for the IB Diploma Programme course Mathematics: Applications and Interpretation HL, for first assessment in May 2021. This book is designed to complete the course in conjunction with the Mathematics: Core Topics HL 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 Core Topics HL 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

Mathematics: Applications and Interpretation HL 1 EXPONENTIALS 13 A Rational exponents 14 B Algebraic expansion and factorisation 16 C Exponential functions 19 D Graphing exponential functions from a table of values 20 E Graphs of exponential functions 21 F Exponential equations 25 G Growth and decay 27 H The natural exponential 34 I The logistic model 39 Review set 1A 40 Review set 1B 42 2 LOGARITHMS 45 A Logarithms in base 1010 46 B Laws of logarithms 49 C Natural logarithms 52 D Logarithmic functions 56 E Logarithmic scales 59 Review set 2A 64 Review set 2B 65 3 APPROXIMATIONS AND ERROR 67 A Errors in measurement 68 B Absolute and percentage error 71 Review set 3A 75 Review set 3B 75 4 LOANS AND ANNUITIES 77 A Loans 78 B Annuities 84 Review set 4A 88 Review set 4B 89 5 MODELLING 91 A The modelling cycle 92 B Linear models 98 C Piecewise models 101 D Systems of equations 108 Review set 5A 111 Review set 5B 114 6 DIRECT AND INVERSE VARIATION 117 A Direct variation 118 B Powers in direct variation 122 C Inverse variation 123 D Powers in inverse variation 126 E Determining the variation model 127 F Using technology to find variation models 129 Review set 6A 131 Review set 6B 133 7 BIVARIATE STATISTICS 135 A Association between numerical variables 136 B Pearson's product-moment correlation coefficient 141 C The coefficient of determination 146 D Line of best fit by eye 148 E The least squares regression line 152 F Statistical reliability and validity 160 G Spearman's rank correlation coefficient 164 Review set 7A 169 Review set 7B 172 8 NON-LINEAR MODELLING 175 A Logarithmic models 176 B Exponential models 178 C Power models 181 D Problem solving 184 E Non-linear regression 186 Review set 8A 189 Review set 8B 191 9 VECTORS 193 A Vectors and scalars 194 B Geometric operations with vectors 197 C Vectors in the plane 202 D The magnitude of a vector 204 E Operations with plane vectors 205 F Vectors in space 209 G Operations with vectors in space 211 H The vector between two points 212 I Parallelism 217 J The scalar product of two vectors 220 K The angle between two vectors 222 L The vector product of two vectors 227 M Vector components 234 Review set 9A 237 Review set 9B 239 10 VECTOR APPLICATIONS 241 A Lines in 22 and 33 dimensions 242 B The angle between two lines 246 C Constant velocity problems 248 D The shortest distance from a point to a line 251 E The shortest distance between two objects 254 F Intersecting lines 256 Review set 10A 261 Review set 10B 263 11 COMPLEX NUMBERS 265 A Real quadratics with \Delta < 0Δ<0 266 B Complex numbers 268 C Operations with complex numbers 269 D Equality of complex numbers 272 E The complex plane 273 F Modulus and argument 276 G Geometry in the complex plane 279 H Polar form 282 I Exponential form 290 J Frequency and phase 292 Review set 11A 293 Review set 11B 295 12 MATRICES 297 A Matrix structure 298 B Matrix equality 300 C Addition and subtraction 301 D Scalar multiplication 303 E Matrix algebra 305 F Matrix multiplication 307 G The inverse of a matrix 314 H Simultaneous linear equations 318 Review set 12A 323 Review set 12B 325 13 EIGENVALUES AND EIGENVECTORS 327 A Eigenvalues and eigenvectors 328 B Matrix diagonalisation 333 C Matrix powers 336 D Markov chains 338 Review set 13A 349 Review set 13B 351 14 AFFINE TRANSFORMATIONS 353 A Translations 355 B Rotations about the origin 356 C Reflections 359 D Stretches 361 E Enlargements 362 F Composite transformations 363 G Area 367 Review set 14A 372 Review set 14B 373 15 GRAPH THEORY 375 A Graphs 376 B Properties of graphs 380 C Routes on graphs 383 D Adjacency matrices 385 E Transition matrices for graphs 392 F Trees 394 G Minimum spanning trees 395 H Eulerian graphs 401 I The Chinese Postman Problem 404 J Hamiltonian graphs 406 K The Travelling Salesman Problem 409 Review set 15A 416 Review set 15B 419 16 VORONOI DIAGRAMS 423 A Voronoi diagrams 424 B Constructing Voronoi diagrams 428 C Adding a site to a Voronoi diagram 433 D Nearest neighbour interpolation 437 E The Largest Empty Circle problem 439 Review set 16A 443 Review set 16B 445 17 INTRODUCTION TO DIFFERENTIAL CALCULUS 447 A Rates of change 449 B Instantaneous rates of change 452 C Limits 455 D The gradient of a tangent 460 E The derivative function 462 F Differentiation from first principles 464 Review set 17A 466 Review set 17B 467 18 RULES OF DIFFERENTIATION 469 A Simple rules of differentiation 470 B The chain rule 474 C The product rule 477 D The quotient rule 479 E Derivatives of exponential functions 482 F Derivatives of logarithmic functions 485 G Derivatives of trigonometric functions 487 H Second derivatives 490 Review set 18A 492 Review set 18B 493 19 PROPERTIES OF CURVES 495 A Tangents 496 B Normals 502 C Increasing and decreasing 503 D Stationary points 508 E Shape 513 F Inflection points 515 Review set 19A 519 Review set 19B 521 20 APPLICATIONS OF DIFFERENTIATION 523 A Rates of change 524 B Optimisation 529 C Modelling with calculus 537 D Related rates 540 Review set 20A 543 Review set 20B 545 21 INTRODUCTION TO INTEGRATION 547 A Approximating the area under a curve 548 B The Riemann integral 552 C Antidifferentiation 556 D The Fundamental Theorem of Calculus 558 Review set 21A 563 Review set 21B 564 22 TECHNIQUES FOR INTEGRATION 565 A Discovering integrals 566 B Rules for integration 568 C Particular values 572 D Integrating f(ax+b)f(ax+b) 574 E Integration by substitution 577 Review set 22A 580 Review set 22B 581 23 DEFINITE INTEGRALS 583 A Definite integrals 584 B Definite integrals involving substitution 587 C The area under a curve 588 D The area above a curve 592 E The area between a curve and the yy-axis 596 F Solids of revolution 598 G Problem solving by integration 602 Review set 23A 604 Review set 23B 606 24 KINEMATICS 609 A Displacement 611 B Velocity 613 C Acceleration 619 D Speed 623 E Velocity and acceleration in terms of displacement 626 F Motion with variable velocity 628 G Projectile motion 634 Review set 24A 638 Review set 24B 640 25 DIFFERENTIAL EQUATIONS 643 A Differential equations 644 B Solutions of differential equations 646 C Differential equations of the form \frac{dy}{dx}=f(x) dx dy =f(x) 649 D Separable differential equations 652 E Slope fields 658 F Euler's method for numerical integration 661 Review set 25A 666 Review set 25B 667 26 COUPLED DIFFERENTIAL EQUATIONS 669 A Phase portraits 671 B Coupled linear differential equations 678 C Second order differential equations 686 D Euler's method for coupled equations 688 Review set 26A 693 Review set 26B 694 27 DISCRETE RANDOM VARIABLES 697 A Random variables 698 B Discrete probability distributions 700 C Expectation 703 D Variance and standard deviation 709 E Properties of aX + baX+b 711 F The binomial distribution 714 G Using technology to find binomial probabilities 718 H The mean and standard deviation of a binomial distribution 721 I The Poisson distribution 722 Review set 27A 726 Review set 27B 728 28 THE NORMAL DISTRIBUTION 731 A Introduction to the normal distribution 733 B Calculating probabilities 736 C The standard normal distribution 743 D Quantiles 748 Review set 28A 751 Review set 28B 753 29 ESTIMATION AND CONFIDENCE INTERVALS 755 A Linear combinations of random variables 756 B The sum of two independent Poisson random variables 759 C Linear combinations of normal random variables 760 D The Central Limit Theorem 762 E Confidence intervals for a population mean with known variance 768 F Confidence intervals for a population mean with unknown variance 776 Review set 29A 779 Review set 29B 781 30 HYPOTHESIS TESTING 783 A Statistical hypotheses 785 B The ZZ-test 787 C Critical values and critical regions 794 D Student's tt-test 797 E Paired tt-tests 800 F The two-sample tt-test for comparing population means 803 G Hypothesis tests for the mean of a Poisson population 805 H Hypothesis tests for a population proportion 809 I Hypothesis tests for a population correlation coefficient 813 J Error probabilities and statistical power 817 Review set 30A 824 Review set 30B 826 31 \chi^2χ 2 HYPOTHESIS TESTS 829 A The \chi^2χ 2 goodness of fit test 830 B Estimating distribution parameters in a goodness of fit test 838 C Critical regions and critical values 842 D The \chi^2χ 2 test for independence 844 Review set 31A 851 Review set 31B 853 ANSWERS 855 INDEX 967

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- : Haese Mathematics
- : Haese Mathematics
- : July 2019
- : books

- : Michael Haese et al