This book gives you fully worked solutions for every question in Exercises, Review Sets, Activities, and Investigations (which do not involve student experimentation) in each chapter of our textbook Mathematics: Core Topics HL. Where applicable, each worked solution is modeled on the relevant worked example in the textbook. Correct answers can sometimes be obtained by different methods.

This is a book and not a CDROM. This book does not include any CDROM OR ACTIVATION CODES

This book gives you fully worked solutions for every question in exercises, review sets, activities and investigations (which do not involve student experimentation) in each chapter of our textbook Mathematics: Analysis and Approaches HL. Correct answers can sometimes be obtained by different methods. In this book, where applicable, each worked solution is modeled on the worked example in the textbook. Understand that when your calculator gives an answer that is different from the answer you find in the book, you have not necessarily made a mistake, but the book may not be wrong either. We have a list of errata for our books on our website. Please contact us if you notice any errors in this book. info@haesemathematics.com, www.haesemathematics.com

This book gives you fully worked solutions for every question in Exercises, Review Sets, Activities, and Investigations (which do not involve student experimentation) in each chapter of our textbook Mathematics: Applications and Interpretation HL. Where applicable, each worked solution is modelled on the relevant worked example in the textbook. Correct answers can sometimes be obtained by different methods.

This book gives you fully worked solutions for every question in Exercises, Review Sets, Activities, and Investigations (which do not involve experimentation) in each chapter of our textbook Mathematics: Core Topics SL. Where applicable, each worked solution is modeled on the relevant worked example in the textbook. Correct answers can sometimes be obtained by different methods.

For use with the IB Diploma Programme

The aim of this Guide is to help students prepare for the Mathematics HL final examinations. The Guide covers all six Topics in the Mathematics HL Core syllabus. Each topic begins with a summary highlighting important facts and concepts. Following each summary is a set of Skill Builder Questions, designed to remind students of the fundamental skills required for the topic. There are twelve Exam Sets comprising 25 questions each. Each set is labelled as No Calculator or Calculator questions. These can be used as a warm-up; encouraging students to draw on knowledge learnt in class, while helping to identify areas that need additional practice. This Guide also offers three Trial Examinations divided into No Calculator and Calculator questions. Detailed marks schemes are provided as a guide for students. This format is consistent with the Mathematics HL Core final examination. Features: Worked Solutions Fully worked solutions are included for every question.

Mathematics for the International Student: Mathematics HL (Core) has been written to embrace the core syllabus for the two-year Mathematics HL Course, first examined in 2014. The new edition reflects the new Mathematics HL syllabus and includes syllabus references at the beginning of each chapter. In response to the introduction of a calculator-free examination paper, the review sets at the end of each chapter have been categorised as 'calculator' or 'non-calculator'. Also, the final chapter contains over 200 examination-style questions, categorised as 'calculator' or 'non-calculator'. These questions should provide more difficult challenges for advanced students. Investigations throughout the book will add to the discovery aspect of the course and enhance student understanding and learning. Book features Student CD 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-9860G Plus, Casio fx-CG20, TI-84 Plus, and TI-nspire

Mathematics for the International Student: Mathematics HL has been written to embrace the syllabus for the two-year Mathematics HL Course, to be first examined in 2014. It is not our intention to define the course. Teachers are encouraged to use other resources. We have developed this book independently of the International Baccalaureate Organization (IBO) in consultation with many experienced teachers of IB Mathematics. The text is not endorsed by the IBO. Syllabus references are given at the beginning of each chapter. The new edition reflects the new Mathematics HL syllabus. Discussion topics for the Theory of Knowledge have been included in this edition. See page 12 for a summary. In response to the introduction of a calculator-free examination paper, the review sets at the end of each chapter have been categorised as ’calculator’ or ’non-calculator’. Also, the final chapter contains over 200 examination-style questions, categorised as ’calculator’ or ’non-calculator’. These questions should provide more difficult challenges for advanced students.

This book gives you fully worked solutions for every question in Exercises, Review Sets, Activities, and Investigations (which do not involve student experimentation) in each chapter of our textbook Mathematics: Applications and Interpretation SL. Where applicable, each worked solution is modeled on the relevant worked example in the textbook. Correct answers can sometimes be obtained by different methods.

This book gives you fully worked solutions for every question in Exercises, Review Sets, Activities, and Investigations (which do not involve student experimentation) in each chapter of our textbook Mathematics: Analysis and Approaches SL. Where applicable, each worked solution is modelled on the relevant worked example in the textbook. Correct answers can sometimes be obtained by different methods.

Mathematics HL Textbook for the IB Diploma

Mathematics for the International Student: Mathematics HL (Core) has been written to embrace the core syllabus for the two-year Mathematics HL Course, first examined in 2014. The new edition reflects the new Mathematics HL syllabus and includes syllabus references at the beginning of each chapter. In response to the introduction of a calculator-free examination paper, the review sets at the end of each chapter have been categorised as 'calculator' or 'non-calculator'. Also, the final chapter contains over 200 examination-style questions, categorised as 'calculator' or 'non-calculator'. These questions should provide more difficult challenges for advanced students. Investigations throughout the book will add to the discovery aspect of the course and enhance student understanding and learning. Book features Student CD 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-9860G Plus, Casio fx-CG20, TI-84 Plus, and TI-nspire

Mathematics: Core Topics HL has been written for the IB Diploma Programme courses Mathematics: Analysis and Approaches HL, and Mathematics: Applications and Interpretation HL, for first teaching in August 2019, and first assessment in May 2021. The book contains the content that is common to both courses. This material can all be taught first, giving the potential to teach all the HL students together from this book at the start of the course. This is the first of two books students will require for the completion of their HL Mathematics course. Upon the completion of this book, students progress to the particular HL textbook for their course: either Mathematics: Analysis and Approaches HL, or Mathematics: Applications and Interpretation HL. This is expected to occur approximately 6-7 months into the two-year course.

Mathematics HL Textbook for the IB Diploma

Mathematics: Core Topics HL has been written for the IB Diploma Programme courses Mathematics: Analysis and Approaches HL, and Mathematics: Applications and Interpretation HL, for first teaching in August 2019, and first assessment in May 2021. The book contains the content that is common to both courses. This material can all be taught first, giving the potential to teach all the HL students together from this book at the start of the course. This is the first of two books students will require for the completion of their HL Mathematics course. Upon the completion of this book, students progress to the particular HL textbook for their course: either Mathematics: Analysis and Approaches HL, or Mathematics: Applications and Interpretation HL. This is expected to occur approximately 6-7 months into the two-year course. This release has OCR.

Back to main page -1 Help -1 --------------------------------------------- 1 Mathematics HL (Core) 1 Foreword 3 Using the interactive student cd 5 Table of contents 6 Symbols and notation used in this book 11 Background knowledge 13 Summary of circle properties 13 Summary of measurement facts 14 1. Functions 17 A - Relations and functions 18 Exercise 1A 20 Answers 763 B - Interval notation,domain and range 21 Exercise 1B 22 Answers 763 C - Function notation 23 Exercise 1C 24 Answers 763 Investigation - Fluid filling functions 25 D - Composite functions, f o g 26 Exercise 1D 27 Answers 763 E - The reciprocal function x |->1/x 28 Exercise 1E 28 Answers 763 F - Inverse functions 28 Exercise 1F 30 Answers 763 G - Functions which have inverses 30 Exercise 1G 32 Answers 764 Review set 1A 33 Answers 764 Review set 1B 34 Answers 764 2. Sequences and series 35 A - Number patterns 36 Exercise 2A 36 Answers 765 B - Sequences of numbers 36 Opening problem 37 Exercise 2B 38 Answers 765 C - Arithmetic sequences 38 Exercise 2C 39 Answers 765 D - Geometric sequences 41 Exercise 2D 42 Answers 765 E - Series 47 Exercise 2E.1 47 Answers 765 Exercise 2E.2 48 Answers 765 Exercise 2E.3 50 Answers 765 F - Sigma notation 52 Exercise 2F 52 Answers 765 G - Miscellaneous problems 53 Exercise 2G 53 Answers 765 Investigation - Von koch ’s snowflake curve 54 Review set 2A 55 Answers 766 Review set 2B 55 Answers 766 Review set 2C 56 Answers 766 3. Exponents 57 Opening problem 58 A - Index notation 58 Exercise 3A 59 Answers 766 B - Negative bases 59 Exercise 3B 59 Answers 766 C - Index laws 61 Exercise 3C 61 Answers 766 D - Rational indices 65 Exercise 3D 66 Answers 766 E - Algebraic expansion 67 Exercise 3E 67 Answers 766 F - Exponential equations 68 Exercise 3F 68 Answers 767 G - Graphs of exponential functions 69 Investigation - Exponential graphs 70 Exercise 3G 71 Answers 767 H - Growth 72 Exercise 3H 73 Answers 767 I - Decay 74 Exercise 3I 75 Answers 767 Review set 3A 77 Answers 768 Review set 3B 77 Answers 768 Review set 3C 78 Answers 768 4. Logarithms 79 A - Introduction 80 Exercise 4A 81 Answers 768 B - Logarithms in base 10 82 Exercise 4B 83 Answers 768 Investigation - Discovering the laws of logarithms 84 C - Laws of logarithms 84 Exercise 4C 85 Answers 768 D - Exponential equations (using logarithms) 87 Exercise 4D 88 Answers 769 E - Growth and decay revisited 88 Exercise 4E 89 Answers 769 F - Compound interest revisited 90 Exercise 4F 90 Answers 769 G - The change of base rule 90 Exercise 4G 91 Answers 769 H - Graphs of logarithmic functions 92 Exercise 4H 93 Answers 769 Review set 4A 94 Answers 769 Review set 4B 94 Answers 769 5. Natural logarithms 95 A - Introduction 96 Investigation 1 - e occurs naturally 96 Investigation 2 - Continuous compound interest 97 Research - Researching e 98 Exercise 5A 98 Answers 770 B - Natural logarithms 99 Exercise 5B 99 Answers 770 Investigation 3 - The laws of natural logarithms 100 C - Laws of natural logarithms 101 Exercise 5C 101 Answers 770 D - Exponential equations involving e 102 Exercise 5D 103 Answers 770 E - Growth and decay revisited 103 Exercise 5E 104 Answers 770 F - Inverse functions revisited 105 Exercise 5F 105 Answers 770 Review set 5A 106 Answers 771 Review set 5B 106 6. Graphing and transforming functions 107 A - Families of functions 108 Investigation - Function families 108 Exercise 6A 109 Answers 771 B - Key features of functions 110 Exercise 6B 110 Answers 771 C - Transformations of graphs 110 Exercise 6C.1 111 Answers 772 Exercise 6C.2 111 Answers 772 Exercise 6C.3 112 Answers 774 D - Functional transformations 113 Exercise 6D 113 Answers 774 E - Simple rational functions 114 Exercise 6E 115 Answers 775 F - Further graphical transformations 118 Exercise 6F 118 Answers 775 Review set 6A 120 Answers 776 Review set 6B 120 7. Quadratic equations and functions 121 Opening problem 123 A - Function notation f:x|->ax²+bx+c 123 Exercise 7A 123 Answers 777 B - Graphs of quadratic functions 124 Investigation 1 - Graphing y = a(x-A)(x-B) 125 Investigation 2 - Graphing y = a(x-h)²+k 125 Exercise 7B.1 126 Answers 777 Exercise 7B.2 128 Answers 777 C - Completing the square 129 Exercise 7C 130 Answers 778 D - Quadratic equations 131 Exercise 7D.1 132 Answers 778 Exercise 7D.2 135 Answers 778 E - The quadratic formula 136 Exercise 7E 137 Answers 779 F - Solving quadratic equations with technology 138 Exercise 7F 138 Answers 779 G - Problem solving with quadratics 139 Exercise 7G 139 Answers 779 H - Quadratic graphs (review) 142 Exercise 7H 144 Answers 779 I - The discriminant, Delta 145 Exercise 7I.1 146 Answers 780 Exercise 7I.2 148 Answers 780 J - Determining the quadratic from a graph 148 Exercise 7J 149 Answers 780 K - Where functions meet 151 Exercise 7K 152 Answers 780 L - Quadratic modelling 152 Exercise 7L 153 Answers 780 Graphics calculator investigation - Tunnels and trucks 154 Review set 7A 155 Answers 780 Review set 7B 156 Answers 780 Review set 7C, 7D, 7E 156 8. Complex numbers and polynomials 157 A - Solutions of real quadratics with Delta = 4 211 Exercise 9F 212 Answers 784 G - The general binomial theorem 214 Exercise 9G 214 Answers 785 Review set 9A 216 Answers 785 Review set 9B 216 10. Mathematical induction 217 A - The process of induction 218 Exercise 10A 219 Answers 785 B - The principle of mathematical induction 220 Exercise 10B 221 Answers 785 Investigation - Sequences, series and induction 226 C - Indirect proof (extension) 226 Exercise 10C 227 Review set 10A 227 Review set 10B 228 Review set 10C 228 11. The unit circle and radian measure 229 Opening problem 230 A - The unit quarter circle 230 Exercise 11A 231 Answers 785 B - Obtuse angles 232 Exercise 11B 232 Answers 785 C - The unit circle 234 Exercise 11C 234 Answers 785 Investigation - Parametric equations 235 D - Radian measure and periodic properties of circles 236 Exercise 11D.1 236 Answers 785 Exercise 11D.2 238 Answers 785 E - The basic trigonometric ratios 239 Exercise 11E.1 239 Answers 786 Exercise 11E.2 242 Answers 786 F - Areas of triangles 244 Exercise 11F 245 Answers 786 G - Sectors and segments 246 Exercise 11G 247 Answers 786 Review set 11A 249 Answers 786 Review set 11B 249 Answers 786 Review set 11C 250 Answers 786 12. Non right angled triangle trigonometry 251 A - The cosine rule 252 Exercise 12A 253 Answers 786 B - The sine rule 254 Exercise 12B.1 255 Answers 786 Investigation - The ambiguous case 255 Exercise 12B.2 258 Answers 787 C - Using the sine and cosine rules 258 Exercise 12C 259 Answers 787 Review set 12 261 Answers 787 13. Periodic phenomena 263 Opening problem 264 A - Observing periodic behaviour 265 Activity - Bicycle data 266 Exercise 13A 267 Answers 787 B - The sine function 269 Investigation 1 - The family y = Asin x 270 Investigation 2 - The family y = sin Bx, B > 0 270 Exercise 13B.1 271 Answers 787 Investigation 3 - The families y = sin(x-C) and y = sin x - D 272 Exercise 13B.2 273 Answers 788 C - Modelling using sine functions 274 Exercise 13C 276 Answers 788 D - Equations involving sine 277 Exercise 13D.1 277 Answers 788 Exercise 13D.2 278 Answers 788 Exercise 13D.3 280 Answers 788 Exercise 13D.4 281 Answers 789 E - The cosine function 282 Exercise 13E 283 Answers 789 F - Solving cosine equations 283 Exercise 13F 284 Answers 789 G - Trigonometric relationships 285 Exercise 13G.1 285 Answers 790 Investigation 4 - Negative and complementary angle formulae 288 Exercise 13G.2 289 Answers 790 H - Compound angle formulae 289 Investigation 5 - Compound angle formulae 289 Exercise 13H 290 Answers 790 I - Double angle formulae 293 Investigation 6 - Double angle formulae 293 Exercise 13I 293 Answers 790 J - The tangent function 295 Exercise 13J.1 296 Answers 790 Exercise 13J.2 296 Answers 790 K - Tangent equations 297 Exercise 13K.1 297 Answers 791 Exercise 13K.2 298 Answers 791 L - Other equations involving tan x 300 Exercise 13L 300 Answers 791 M - Quadratic trigonometric equations 300 Exercise 13M 300 Answers 791 N - Reciprocal trigonometric functions 301 Exercise 13N 301 Answers 791 O - Trigonometric series and products 302 Exercise 13O 302 Answers 791 Review set 13A 303 Answers 791 Review set 13B 304 Answers 792 Review set 13C, 13D 304 14. Matrices 305 A - Introduction 306 Exercise 14A 308 Answers 792 B - Addition and subtraction of matrices 308 Exercise 14B 310 Answers 792 C - Multiples of matrices 311 Exercise 14C 312 Answers 792 D - Matrix algebra for addition 313 Exercise 14D 314 Answers 793 E - Matrix multiplication 314 Exercise 14E.1 315 Answers 793 Exercise 14E.2 317 Answers 793 F - Using technology 318 Exercise 14F 319 Answers 793 G - Some properties of matrix multiplication 321 Exercise 14G 321 Answers 793 H - The inverse of a 2 x 2 matrix 324 Exercise 14H 325 Answers 793 I - Solving a pair of linear equations 326 Exercise 14I 327 Answers 794 J - The 3 x 3 determinant 329 Exercise 14J 330 Answers 794 K - The inverse of a 3 x 3 matrix 331 Exercise 14K 332 Answers 794 L - 3 x 3 systems with unique solutions 332 Exercise 14L 332 Answers 794 Investigation - Using matrices in cryptography 335 M - Solving using row operations 336 Exercise 14M.1 338 Answers 795 Exercise 14M.2 342 Answers 795 Exercise 14M.3 343 Answers 795 Exercise 14M.4 346 Answers 795 N - Induction with matrices 348 Exercise 14N 348 Answers 795 Review set 14A 348 Answers 796 Review set 14B 349 Answers 796 Review set 14C, 14D, 14E 350 15. Vectors in 2 and 3 dimensions 351 A - Vectors 352 Opening problem 352 Exercise 15A.1 354 Answers 796 Exercise 15A.2 355 Answers 796 B - Operations with vectors 355 Exercise 15B.1 356 Answers 796 Exercise 15B.2 358 Answers 797 Exercise 15B.3 362 Answers 797 C - 2-D vectors in component form 362 Exercise 15C.1 363 Answers 797 Exercise 15C.2 364 Answers 797 Exercise 15C.3 366 Answers 798 Exercise 15C.4 366 Answers 798 D - 3-D coordinate geometry 367 Exercise 15D 368 Answers 798 E - 3-D vectors in component form 369 Exercise 15E.1 370 Answers 798 Exercise 15E.2 371 Answers 798 F - Algebraic operations with vectors 372 Exercise 15F 373 Answers 798 G - Vectors in coordinate geometry 375 Exercise 15G 375 Answers 798 H - Parallelism 378 Exercise 15H 378 Answers 798 I - Unit vectors 379 Exercise 15I 379 Answers 799 J - The scalar product of two vectors 381 Exercise 15J.1 383 Answers 799 Exercise 15J.2 386 Answers 799 K - The vector product of two vectors 387 Exercise 15K.1 388 Answers 799 Exercise 15K.2 392 Answers 799 Exercise 15K.3 394 Answers 799 Review set 15A 395 Answers 799 Review set 15B 397 Answers 800 Review set 15C 398 Answers 800 Review set 15D 398 16. Complex numbers 399 A - Complex numbers as 2-D vectors 400 Exercise 16A.1 401 Answers 800 Exercise 16A.2 402 Answers 801 B - Modulus, argument, polar form 403 Exercise 16B.1 403 Answers 801 Exercise 16B.2 406 Answers 801 Exercise 16B.3 408 Answers 801 Exercise 16B.4 410 Answers 801 Exercise 16B.5 413 Answers 801 Exercise 16B.6 414 Answers 801 C - De Moivre’s theorem 415 Exercise 16C 416 Answers 801 D - Roots of complex numbers 418 Exercise 16D 418 Answers 802 E - The nth roots of unity 420 Exercise 16E 420 Answers 802 Review set 16A 421 Answers 802 Review set 16B 421 Answers 802 Review set 16C 422 17. Lines and planes in space 423 A - Lines in a plane and in space 425 Exercise 17A.1 426 Answers 802 Exercise 17A.2 428 Answers 802 Exercise 17A.3 430 Answers 802 B - Applications of a line in a plane 431 Exercise 17B.1 431 Answers 802 Exercise 17B.2 433 Answers 803 Investigation - The two yachts problem 434 Exercise 17B.3 435 Answers 803 Exercise 17B.4 438 Answers 803 C - Relationship between lines 439 Exercise 17C 441 Answers 803 D - Planes and distances 444 Exercise 17D 445 Answers 804 E - Angles in space 449 Exercise 17E 450 Answers 804 F - The intersection of two or more planes 451 Exercise 17F 453 Answers 804 Review set 17A 454 Answers 804 Review set 17B 455 Answers 804 Review set 17C 456 18. Descriptive statistics 457 The pea problem 458 A - Continuous numerical data and histograms 459 Case study - Driving a golf ball 460 Exercise 18A 462 Answers 805 B - Measuring the centre of data 463 Investigation - Merits of the mean and median 465 Exercise 18B.1 466 Answers 805 Exercise 18B.2 470 Answers 805 Exercise 18B.3 473 Answers 805 C - Cumulative data 474 Exercise 18C 475 Answers 805 D - Measuring the spread of data 476 Exercise 18D.1 478 Answers 806 Exercise 18D.2 480 Answers 806 E - Statistics using technology 483 Exercise 18E.1 484 Answers 806 Exercise 18E.2 484 Answers 806 F - Variance and standard deviation 485 Exercise 18F 486 Answers 807 G - The significance of standard deviation 490 Exercise 18G 491 Answers 807 Review set 18A 491 Answers 807 Review set 18B 492 19. Probability 493 Opening problem 495 A - Experimental probability 496 Investigation 1 - Tossing drawing pins 496 Exercise 19A 497 Answers 808 Investigation 2 - Coin tossing experiments 497 Investigation 3 - Dice rolling experiments 498 B - Sample space 500 Exercise 19B 501 Answers 808 C - Theoretical probability 501 Exercise 19C 503 Answers 808 D - Using grids to find probabilities 504 Exercise 19D 504 Answers 808 E - Compound events 505 Investigation 4 - Probabilities of compound events 505 Investigation 5 - Revisiting drawing pins 505 Exercise 19E.1 506 Answers 808 Exercise 19E.2 508 Answers 808 F - Using tree diagrams 509 Exercise 19F 510 Answers 809 G - Sampling with and without replacement 511 Exercise 19G 512 Answers 809 Investigation 6 - Sampling simulation 513 H - Binomial probabilities 514 Exercise 19H 515 Answers 809 I - Sets and venn diagrams 516 Exercise 19I 518 Answers 809 J - Laws of probability 521 Exercise 19J 523 Answers 809 K - Independent events revisited 525 Exercise 19K 526 Answers 810 L - Probabilities using permutations and combinations 526 Exercise 19L 527 Answers 810 M - Bayes' theorem 528 Exercise 19M 529 Answers 810 Review set 19A 530 Answers 810 Review set 19B 530 20. Introduction to calculus 531 Investigation 1 - The speed of falling objects 532 A - Rate of change 533 Exercise 20A.1 534 Answers 810 Exercise 20A.2 536 Answers 810 B - Instantaneous rates of change 536 Investigation 2 - Instantaneous speed 536 Exercise 20B.1 538 Answers 810 Exercise 20B.2 541 Answers 810 Review set 20 542 Answers 810 21. Differential calculus 543 A - The idea of a limit 544 Investigation 1 - The slope of a tangent 544 Exercise 21A 547 Answers 810 B - Derivatives at a given x-value 547 Exercise 21B 549 Answers 810 C - The derivative function 552 Investigation 2 - Finding slopes of functions with technology 553 Exercise 21C 553 Answers 810 D - Simple rules of differentiation 555 Investigation 3 - Simple rules of differentiation 555 Exercise 21D 557 Answers 811 E - The chain rule 559 Exercise 21E.1 559 Answers 811 Investigation 4 - Differentiating composites 559 Exercise 21E.2 561 Answers 811 F - Product and quotient rules 562 Exercise 21F.1 564 Answers 811 Exercise 21F.2 565 Answers 811 G - Tangents and normals 566 Exercise 21G 567 Answers 811 H - The second derivative 570 Exercise 21H 571 Answers 811 Review set 21A 572 Answers 812 Review set 21B, 21C 572 22. Applications of differential calculus 573 A - Time rate of change 575 Exercise 22A 575 Answers 812 B - General rates of change 576 Exercise 22B 577 Answers 812 C - Motion in a straight line 579 Exercise 22C.1 580 Answers 812 Investigation - Displacement,velocity and acceleration graphs 583 Exercise 22C.2 585 Answers 812 D - Some curve properties 586 Exercise 22D.1 588 Answers 813 Exercise 22D.2 589 Answers 813 Exercise 22D.3 592 Answers 813 E - Rational functions 594 Exercise 22E.1 595 Answers 814 Exercise 22E.2 595 Answers 814 Exercise 22E.3 598 Answers 814 F - Inflections and shape type 598 Exercise 22F 600 Answers 815 G - Optimisation 601 Exercise 22G 605 Answers 816 H - Economic models 610 Exercise 22H 613 Answers 816 I - Implicit differentiation 613 Exercise 22I 615 Answers 816 Review set 22A 616 Answers 816 Review set 22B 616 23. Derivatives of exponential and logarithmic functions 617 A - Derivatives of exponential functions 618 Investigation 1 - The derivative of y = a^x 618 Investigation 2 - Finding a when y = a^x and dy/dx = a^x 619 Exercise 23A 621 Answers 817 B - Using natural logarithms 623 Exercise 23B 624 Answers 817 C - Derivatives of logarithmic functions 626 Investigation 3 - The derivative of ln x 626 Exercise 23C 627 Answers 817 D - Applications 629 Exercise 23D 629 Answers 817 Review set 23A 632 Answers 818 Review set 23B 632 24. Derivatives of circular functions and related rates 633 A - Derivatives of circular functions 635 Investigation - Examining sin(theta)/theta near theta = 0 635 Exercise 24A 638 Answers 819 B - The derivatives of reciprocal circular functions 640 Exercise 24B 641 Answers 819 C - The derivatives of inverse circular functions 641 Exercise 24C.1 642 Answers 819 Exercise 24C.2 642 Answers 819 D - Maxima/minima with trigonometry 643 Exercise 24D 644 Answers 819 E - Related rates 645 Exercise 24E 647 Answers 820 Review set 24A 649 Answers 820 Review set 24B 650 25. Integration 651 A - Antidifferentiation 652 Exercise 25A 653 Answers 820 B - Integration 653 Exercise 25B.1 654 Answers 820 Exercise 25B.2 656 Answers 820 C - Integrating e^(ax+b) and (ax+b)^n 659 Exercise 25C 659 Answers 821 D - Integrating f(u)u'(x) by substitution 661 Exercise 25D 662 Answers 821 E - Definite integrals 663 Exercise 25E.1 664 Answers 821 Exercise 25E.2 665 Answers 821 Exercise 25E.3 666 Answers 821 Review set 25A 666 Answers 821 Review set 25B 667 Answers 821 Review set 25C 668 Answers 821 26. Integration (areas and other applications) 669 A - Areas where boundaries are curved 670 Exercise 26A.1 670 Answers 822 Investigation 1 - Finding areas using rectangles 672 Exercise 26A.2 673 Answers 822 B - The fundamental theorem of calculus 675 Exercise 26B 677 Answers 822 Investigation 2 - int(f(x), x, b) and areas 678 C - Finding areas between curves 679 Exercise 26C 679 Answers 822 D - Distances from velocity functions 683 Exercise 26D.1 685 Answers 822 Exercise 26D.2 687 Answers 822 E - Problem solving by integration 688 Exercise 26E 688 Answers 823 Review set 26A 690 Answers 823 Review set 26B 691 Answers 823 Review set 26C 692 27. Circular function integration 693 A - Basic circular function integrals 694 Exercise 27A 694 Answers 823 B - Integrals of f(ax+b) circular functions 696 Exercise 27B 697 Answers 824 C - Definite integrals 699 Exercise 27C 699 Answers 824 D - Area determination 700 Exercise 27D 701 Answers 824 Review set 27A 702 Answers 824 Review set 27B 702 28. Volumes of revolution 703 A - Solids of revolution 704 Exercise 28A.1 706 Answers 824 Exercise 28A.2 707 Answers 824 B - Volumes for two defining functions 707 Exercise 28B 708 Answers 824 Review set 28 710 Answers 824 29. Further integration and differential equations 711 A - The integrals of 1/(sqr(a²-x²)) and 1/(x²+a²) 712 Exercise 29A 713 Answers 824 B - Further integration by substitution 713 Exercise 29B 713 Answers 825 C - Integration by parts 715 Exercise 29C 715 Answers 825 Investigation - Functions which cannot be integrated 716 D - Separable differential equations 717 Exercise 29D.1 719 Answers 825 Exercise 29D.2 720 Answers 825 Exercise 29D.3 725 Answers 825 Review set 29A 725 Answers 825 Review set 29B 726 Answers 825 30. Statistical distributions 727 A - Discrete random variables 728 Exercise 30A 728 Answers 825 B - Discrete probability distributions 730 Exercise 30B 730 Answers 826 C - Expectation 732 Exercise 30C 733 Answers 826 D - The mean and standard deviation of a discrete random variable 735 Exercise 30D 737 Answers 826 E - Expected values (discrete RV) 738 Exercise 30E.1 739 Answers 826 Investigation 1 - E(aX+b) and Var(aX+b) 739 Exercise 30E.2 740 Answers 826 F - The binomial distribution 741 Exercise 30F 742 Answers 827 G - Mean and standard deviation of a binomial random variable 743 Investigation 2 - The mean and standard deviation of a binomial random variable 744 Exercise 30G 745 Answers 827 H - The poisson distribution 746 Investigation 3 - Poisson mean and variance 746 Exercise 30H 747 Answers 827 I - Continuous probability density functions 748 Exercise 30I 749 Answers 827 J - Normal distributions 750 Investigation 4 - Standard deviation significance 752 Exercise 30J.1 753 Answers 827 Exercise 30J.2 754 Answers 827 Investigation 5 - Mean and standard deviation of Z = (x-mu)/sigma 754 K - The standard normal distribution (Z-distribution) 755 Exercise 30K.1 757 Answers 827 Exercise 30K.2 759 Answers 828 Exercise 30K.3 760 Answers 828 L - Applications of the normal distribution 760 Exercise 30L 761 Answers 828 Review set 30A 762 Answers 828 Review set 30B 762 Answers 763 Index 828

Mathematics for the International Student: Mathematics HL (Core) has been written to embrace the core syllabus for the two-year Mathematics HL Course, first examined in 2014. The new edition reflects the new Mathematics HL syllabus and includes syllabus references at the beginning of each chapter. In response to the introduction of a calculator-free examination paper, the review sets at the end of each chapter have been categorised as 'calculator' or 'non-calculator'. Also, the final chapter contains over 200 examination-style questions, categorised as 'calculator' or 'non-calculator'. These questions should provide more difficult challenges for advanced students. Investigations throughout the book will add to the discovery aspect of the course and enhance student understanding and learning. Book features Student CD 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-9860G Plus, Casio fx-CG20, TI-84 Plus, and TI-nspire

Mathematics for the International Student: Mathematics HL (Core) has been written to embrace the core syllabus for the two-year Mathematics HL Course, first examined in 2014. The new edition reflects the new Mathematics HL syllabus and includes syllabus references at the beginning of each chapter. In response to the introduction of a calculator-free examination paper, the review sets at the end of each chapter have been categorised as 'calculator' or 'non-calculator'. Also, the final chapter contains over 200 examination-style questions, categorised as 'calculator' or 'non-calculator'. These questions should provide more difficult challenges for advanced students. Investigations throughout the book will add to the discovery aspect of the course and enhance student understanding and learning. Book features Student CD 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-9860G Plus, Casio fx-CG20, TI-84 Plus, and TI-nspire

Mathematics: Core Topics HL has been written for the IB Diploma Programme courses Mathematics: Analysis and Approaches HL, and Mathematics: Applications and Interpretation HL, for first teaching in August 2019, and first assessment in May 2021. The book contains the content that is common to both courses. This material can all be taught first, giving the potential to teach all the HL students together from this book at the start of the course. This is the first of two books students will require for the completion of their HL Mathematics course. Upon the completion of this book, students progress to the particular HL textbook for their course: either Mathematics: Analysis and Approaches HL, or Mathematics: Applications and Interpretation HL. This is expected to occur approximately 6-7 months into the two-year course.

This is a book and not a CDROM. This book does not include any CDROM OR ACTIVATION CODES

This book is a companion to our Mathematics HL (Core) third edition textbook. The book offers complete coverage of Mathematics HL Option Topic 8 and Further Mathematics HL Topic 4, Sets, Relations and Groups. Detailed explanations and Worked Examples are provided throughout the text, accompanied by printable graphics calculator instructions on the student CD. New features include Theory of Knowledge discussion topics and Fully Worked Solutions.

Mathematics: Core Topics HL has been written for the IB Diploma Programme courses Mathematics: Analysis and Approaches HL, and Mathematics: Applications and Interpretation HL, for first teaching in August 2019, and first assessment in May 2021. The book contains the content that is common to both courses. This material can all be taught first, giving the potential to teach all the HL students together from this book at the start of the course. This is the first of two books students will require for the completion of their HL Mathematics course. Upon the completion of this book, students progress to the particular HL textbook for their course: either Mathematics: Analysis and Approaches HL, or Mathematics: Applications and Interpretation HL. This is expected to occur approximately 6-7 months into the two-year course. This release has OCR.

Mathematics HL Option Calculus has been written as a companion book to the Mathematics HL (Core) textbook. Together they aim to provide students and teachers with appropriate coverage of the two-year Mathematics HL Course, to be first examined in 2014. This book covers all sub-topics set out in Mathematics HL Option Topic 9 and Further Mathematics HL Topic 5, Calculus. The aim of this topic is to inroduce students to the basic concepts and techniques of differential and integral calculus and their applications. Detailed explanations and key facts are highlighted throughout the text. Each sub-topic contains numerous worked examples, highlighting each step necessary to reach the answer for that example. Theory of knowledge is a core requirement in the International Baccalaureate Diploma Programme, whereby students are encouraged to think critically and challenge the assumptions of knowledge. Discussion topics for theory of knowledge have been included on pages 129 and 140. These aim to help students discover and express their views on knowledge issues. Fully worked solutions are provided at the back of the text, however students are encouraged to attempt each question before referring to the solution.

Mathematics HL Textbook for the IB Diploma

Mathematics HL Textbook for the IB Diploma

Mathematics HL Textbook for the IB Diploma

Core Topics HL - Casio - TI Applications and Interpretation - Casio Analysis and Approaches - Casio - TI

Haese Mathematics 12 Specialist Mathematics Worked Solutions for SACE Stage 2 S2 Specialist Mathematics Specs Maths

This is a book and not a CDROM. This book does not include any CDROM OR ACTIVATION CODES

Mathematics HL Textbook for the IB Diploma

This book gives you fully worked solutions for every question (discussions, investigations and projects excepted) in each chapter of our textbook Mathematics for Australia 12 General Mathematics.Where applicable, each worked solution is modelled on the relevant worked example in the textbook. Correct answers can sometimes be obtained by different methods.

This book has been written for the IB Diploma Programme courses Mathematics: Analysis and Approaches HL and Mathematics: Applications and Interpretation HL. This book contains the content that is common to both courses. Upon the completion of this book, students progress to the particular HL textbook for their course. This is expected to cover approximately 6-7 months into the two-year course.