قتل در شب شکارچی (مجموعه معماهای لامپ‌نور، جلد سوم)

Methods34_2ed_full_Part1 Cover Contents Introduction and overview Acknowledgements 1 Functions and relations 1A Set notation and sets of numbers 1B Identifying and describing relations and functions 1C Types of functions and implied domains 1D Sums and products of functions 1E Composite functions 1F Inverse functions 1G Power functions 1H Applications of functions Review of Chapter 1 2 Coordinate geometry 2A Linear equations 2B Linear literal equations and simultaneous linear literal equations 2C Linear coordinate geometry 2D Applications of linear functions 2E The geometry of simultaneous linear equations with two variables 2F Simultaneous linear equations with more than two variables Review of Chapter 2 3 Transformations 3A Translations 3B Dilations 3C Reflections 3D Combinations of transformations 3E Determining transformations 3F Using transformations to sketch graphs 3G Transformations of power functions with positive integer index 3H Determining the rule for a function from its graph 3I A notation for transformations Review of Chapter 3 4 Polynomial functions 4A Quadratic functions 4B Determining the rule for a parabola 4C The language of polynomials 4D Division and factorisation of polynomials 4E The general cubic function 4F Polynomials of higher degree 4G Determining the rule for the graph of a polynomial 4H Solution of literal equations and systems of equations Review of Chapter 4 5 Exponential and logarithmic functions 5A Exponential functions 5B The exponential function f(x) = ex 5C Exponential equations 5D Logarithms 5E Graphing logarithmic functions 5F Determining rules for graphs of exponential and logarithmic functions 5G Solution of exponential equations using logarithms 5H Inverses 5I Exponential growth and decay Review of Chapter 5 6 Circular functions 6A Measuring angles in degrees and radians 6B Defining circular functions: sine, cosine and tangent 6C Further symmetry properties and the Pythagorean identity 6D Graphs of sine and cosine 6E Solution of trigonometric equations 6F Sketch graphs of y = a sin n(t ± ε) and y = a cos n(t ± ε) 6G Sketch graphs of y = a sin n(t ± ε) ± b and y = a cos n(t ± ε) ± b 6H Addition of ordinates for circular functions 6I Determining rules for graphs of circular functions 6J The tangent function 6K General solution of trigonometric equations 6L Applications of circular functions Review of Chapter 6 7 Further functions 7A More power functions 7B Composite and inverse functions 7C Sums and products of functions and addition of ordinates 7D Function notation and identities 7E Families of functions and solving literal equations Review of Chapter 7 8 Revision of Chapters 1–7 8A Technology-free questions 8B Multiple-choice questions 8C Extended-response questions 8D Algorithms and pseudocode 9 Differentiation 9A The derivative 9B Rules for differentiation 9C Differentiating xn where n is a negative integer 9D The graph of the derivative function 9E The chain rule 9F Differentiating rational powers 9G Differentiation of ex 9H Differentiation of the natural logarithm function 9I Derivatives of circular functions 9J The product rule 9K The quotient rule 9L Limits and continuity 9M When is a function differentiable? Review of Chapter 9 10 Applications of differentiation 10A Tangents and normals 10B Rates of change 10C Stationary points 10D Types of stationary points 10E Absolute maximum and minimum values 10F Maximum and minimum problems 10G Families of functions 10H Newton’s method for finding solutions to equations Review of Chapter 10 11 Integration 11A Estimating the area under a graph 11B Antidifferentiation: indefinite integrals 11C The antiderivative of (ax + b)r 11E The fundamental theorem of calculus and the definite integral 11F Finding the area under a curve 11G Integration of circular functions 11H Miscellaneous exercises 11I The area of a region between two curves 11J Applications of integration 11K The fundamental theorem of calculus Review of Chapter 11 12 Revision of Chapters 9–11 12A Technology-free questions 12B Multiple-choice questions 12C Extended-response questions 12D Algorithms and pseudocode 13 Discrete random variables and their probability distributions 13A Sample spaces and probability 13B Conditional probability and independence 13C Discrete random variables 13D Expected value (mean), variance and standard deviation Review of Chapter 13 14 The binomial distribution 14A Bernoulli sequences and the binomial probability distribution 14B The graph, expectation and variance of a binomial distribution 14C Finding the sample size 14D Proofs for the expectation and variance Review of Chapter 14 15 Continuous random variables and their probability distributions 15A Continuous random variables 15B Mean and percentiles for a continuous random variable 15C Measures of spread 15D Properties of mean and variance 15E Cumulative distribution functions Review of Chapter 15 Methods34_2ed_full_Part2 16 The normal distribution 16A The normal distribution 16B Standardisation and the 68–95–99.7% rule 16C Determining normal probabilities 16D Solving problems using the normal distribution 16E The normal approximation to the binomial distribution Review of Chapter 16 17 Sampling and estimation 17A Populations and samples 17B The exact distribution of the sample proportion 17C Approximating the distribution of the sample proportion 17D Confidence intervals for the population proportion Review of Chapter 17 18 Revision of Chapters 13–17 18A Technology-free questions 18B Multiple-choice questions 18C Extended-response questions 18D Algorithms and pseudocode 19 Revision of Chapters 1–18 19A Technology-free questions 19B Multiple-choice questions 19C Extended-response questions A Pseudocode Appendix A A1 Introduction to pseudocode B Counting methods and the binomial theorem B1 Counting methods B2 Summation notation B3 The binomial theorem Glossary Answers