MATHEMATICS F/INTL.STUDENT:HL-W/CD

SYMBOLS AND NOTATION USED IN THIS BOOK 10  BACKGROUND KNOWLEDGE 16   - A Surds and radicals CD    - B Scientific notation (standard form) CD    - C Number systems and set notation CD    - D Algebraic simplification CD    - E Linear equations and inequalities CD    - F Modulus or absolute value CD    - G Product expansion CD    - H Factorisation CD    - I Formula rearrangement CD    - J Adding and subtracting algebraic fractions CD    - K Congruence and similarity CD    - L Pythagoras’ theorem CD    - M Coordinate geometry CD    - N Right angled triangle trigonometry CD     - Matrices CD    - Statistics revision CD    - Facts about number sets CD    - Summary of circle properties CD    - Summary of measurement facts CD  GRAPHICS CALCULATOR INSTRUCTIONS 16    - Casio fx-9860G PLUS CD    - Casio fx-CG20 CD    - Texas Instruments TI-84 Plus CD    - Texas Instruments TI-nspire CD    1 QUADRATICS 17   - A Quadratic equations 19    - B The discriminant of a quadratic 25    - C The sum and product of the roots 27    - D Quadratic functions 28    - E Finding a quadratic from its graph 37    - F Where functions meet 40    - G Problem solving with quadratics 43    - H Quadratic optimisation 45    - Review set 1A 47   - Review set 1B 48   - Review set 1C 49    2 FUNCTIONS 51   - A Relations and functions 52    - B Function notation 55    - C Domain and range 57    - D Composite functions 62    - E Even and odd functions 64    - F Sign diagrams 66    - G Inequalities (inequations) 70    - H The modulus function 73    - I Rational functions 78    - J Inverse functions 81    - K Graphing functions 87    - L Finding where graphs meet 89    - Review set 2A 90   - Review set 2B 91   - Review set 2C 93    3 EXPONENTIALS 95   - A Exponents 96    - B Laws of exponents 98    - C Rational exponents 101    - D Algebraic expansion and factorisation 104    - E Exponential equations 106    - F Exponential functions 108    - G Growth and decay 112    - H The natural exponential e^x 115    - Review set 3A 119   - Review set 3B 120   - Review set 3C 121     4 LOGARITHMS 123   - A Logarithms in base 10 124    - B Logarithms in base a 127    - C Laws of logarithms 130    - D Natural logarithms 134    - E Exponential equations using logarithms 137    - F The change of base rule 139    - G Graphs of logarithmic functions 141    - H Growth and decay 145    - Review set 4A 147   - Review set 4B 148   - Review set 4C 149    5 TRANSFORMING FUNCTIONS 151   - A Transformation of graphs 152    - B Translations 154    - C Stretches 156    - D Reflections 157    - E Miscellaneous transformations 159    - F Simple rational functions 161    - G The reciprocal of a function 165    - H Modulus functions 166    - Review set 5A 167   - Review set 5B 169   - Review set 5C 170    6 COMPLEX NUMBERS AND POLYNOMIALS 173   - A Real quadratics with ¢ < 0 174    - B Complex numbers 176    - C Real polynomials 183    - D Zeros, roots, and factors 189    - E Polynomial theorems 193    - F Graphing real polynomials 201    - Review set 6A 209   - Review set 6B 210   - Review set 6C 211    7 SEQUENCES AND SERIES 213   - A Number sequences 214    - B The general term of a number sequence 215    - C Arithmetic sequences 218    - D Geometric sequences 222    - E Series 229    - F Arithmetic series 231    - G Geometric series 233    - Review set 7A 240   - Review set 7B 240   - Review set 7C 242    8 COUNTING AND THE BINOMIAL EXPANSION 243    - A The product principle 244    - B Counting paths 246    - C Factorial notation 247    - D Permutations 250    - E Combinations 254    - F Binomial expansions 257    - G The binomial theorem 260     - Review set 8A 263  - Review set 8B 263   - Review set 8C 264    9 MATHEMATICAL INDUCTION 265   - A The process of induction 267    - B The principle of mathematical induction 269     - Review set 9A 277   - Review set 9B 277   - Review set 9C 278    10 THE UNIT CIRCLE AND RADIAN MEASURE 279    - A Radian measure 280    - B Arc length and sector area 283    - C The unit circle and the trigonometric ratios 286    - D Applications of the unit circle 292    - E Negative and complementary angle formulae 295   - F Multiples of π/6 and π/4  297 301 302 303    - Review set 10A 301   - Review set 10B 302   - Review set 10C 303    11 NON-RIGHT ANGLED TRIANGLE TRIGONOMETRY 305    - A Areas of triangles 306    - B The cosine rule 309    - C The sine rule 313    - D Using the sine and cosine rules 317     - Review set 11A 321   - Review set 11B 323   - Review set 11C 323    12 TRIGONOMETRIC FUNCTIONS 325   - A Periodic behaviour 326    - B The sine function 330    - C Modelling using sine functions 336    - D The cosine function 339    - E The tangent function 341    - F General trigonometric functions 344    - G Reciprocal trigonometric functions 346    - H Inverse trigonometric functions 348    - Review set 12A 350   - Review set 12B 351   - Review set 12C 351    13 TRIGONOMETRIC EQUATIONS AND IDENTITIES 353    - A Trigonometric equations 354    - B Using trigonometric models 362    - C Trigonometric relationships 364    - D Double angle formulae 367    - E Compound angle formulae 370    - F Trigonometric equations in quadratic form 376    - G Trigonometric series and products 377     - Review set 13A 379   - Review set 13B 380   - Review set 13C 382    14 VECTORS 383   - A Vectors and scalars 384    - B Geometric operations with vectors 387    - C Vectors in the plane 394    - D The magnitude of a vector 396    - E Operations with plane vectors 398    - F The vector between two points 401    - G Vectors in space 404    - H Operations with vectors in space 408    - I Parallelism 412    - J The scalar product of two vectors 416    - K The vector product of two vectors 422    - Review set 14A 428   - Review set 14B 430   - Review set 14C 431    15 VECTOR APPLICATIONS 433   - A Problems involving vector operations 434    - B Area 436    - C Lines in 2-D and 3-D 437    - D The angle between two lines 442    - E Constant velocity problems 444    - F The shortest distance from a line to a point 447    - G Intersecting lines 451    - H Relationships between lines 453    - I Planes 460    - J Angles in space 465    - K Intersecting planes 467    - Review set 15A 472   - Review set 15B 474   - Review set 15C 476    16 COMPLEX NUMBERS 479   - A Complex numbers as 2-D vectors 480    - B Modulus 483   - C Argument and polar form 487    - D Euler’s form 495    - E De Moivre’s theorem 497   - F Roots of complex numbers 500    - G Miscellaneous problems 504    - Review set 16A 504   - Review set 16B 505   - Review set 16C 506    17 INTRODUCTION TO DIFFERENTIAL CALCULUS 507   - A Limits 509    - B Limits at infinity 512    - C Trigonometric limits 515    - D Rates of change 518    - E The derivative function 521    - F Differentiation from first principles 523    - Review set 17A 526   - Review set 17B 526   - Review set 17C 527    18 RULES OF DIFFERENTIATION 529   - A Simple rules of differentiation 530    - B The chain rule 534    - C The product rule 537    - D The quotient rule 540    - E Implicit differentiation 542    - F Derivatives of exponential functions 544    - G Derivatives of logarithmic functions 549    - H Derivatives of trigonometric functions 551    - I Derivatives of inverse trigonometric functions 555    - J Second and higher derivatives 557    - Review set 18A 559   - Review set 18B 560   - Review set 18C 561    19 PROPERTIES OF CURVES 563   - A Tangents and normals 564    - B Increasing and decreasing functions 570    - C Stationary points 575    - D Inflections and shape 579    - Review set 19A 587   - Review set 19B 588   - Review set 19C 589    20 APPLICATIONS OF DIFFERENTIAL CALCULUS 591   - A Kinematics 592    - B Rates of change 601    - C Optimisation 606    - D Related rates 617    - Review set 20A 621   - Review set 20B 623   - Review set 20C 625    21 INTEGRATION 627   - A The area under a curve 628    - B Antidifferentiation 634    - C The fundamental theorem of calculus 635    - D Integration 640    - E Rules for integration 643    - F Integrating f(ax + b) 648    - G Integration by substitution 653    - H Integration by parts 659    - I Miscellaneous integration 660    - J Definite integrals 661    - Review set 21A 667   - Review set 21B 668   - Review set 21C 669    22 APPLICATIONS OF INTEGRATION 671   - A The area under a curve 672    - B The area between two functions 675    - C Kinematics 681    - D Problem solving by integration 687    - E Solids of revolution 690    - Review set 22A 697   - Review set 22B 699   - Review set 22C 701    23 DESCRIPTIVE STATISTICS 703   - A Key statistical concepts 704    - B Measuring the centre of data 709    - C Variance and standard deviation 721    - Review set 23A 728   - Review set 23B 729   - Review set 23C 731    24 PROBABILITY 733   - A Experimental probability 735    - B Sample space 740    - C Theoretical probability 741   - D    Tables of outcomes 745   - E    Compound events 747   - F    Tree diagrams 751   - G    Sampling with and without replacement 754   - H    Sets and Venn diagrams 757   - I    Laws of probability 763   - J    Independent events 767   - K    Probabilities using permutations and combinations   - L    Bayes’ theorem    - Review set 24A 774  - Review set 24B 775  - Review set 24C 776    25 DISCRETE RANDOM VARIABLES 779   - A Discrete random variables 780    - B Discrete probability distributions 782    - C Expectation 786    - D Variance and standard deviation 790    - E Properties of E(X) and Var(X) 792    - F The binomial distribution 795    - G The Poisson distribution 805     - Review set 25A 808   - Review set 25B 809   - Review set 25C 811    26 CONTINUOUS RANDOM VARIABLES 813    - A Continuous random variables 814    - B The normal distribution 818    - C Probabilities using a calculator 823    - D The standard normal distribution (Z-distribution) 826    - E Quantiles or k-values 831     - Review set 26A 835   - Review set 26B 836   - Review set 26C 837    27 MISCELLANEOUS QUESTIONS 839   - A Non-calculator questions 840    - B Calculator questions 852    ANSWERS 865     INDEX 958