Year 12 mathematics advanced : CambridgeMaths stage 6

Description

Rationale Overview Acknowledgements About the authors 1 Sequences and series 1A Sequences and how to specify them 1B Arithmetic sequences 1C Geometric sequences 1D Solving problems involving APs and GPs 1E Adding up the terms of a sequence 1F Summing an arithmetic series 1G Summing a geometric series 1H The limiting sum of a geometric series 1I Recurring decimals and geometric series Chapter 1 Review 2 Graphs and equations 2A The sign of a function 2B Vertical and horizontal asymptotes 2C A curve‐sketching menu 2D Solving inequations 2E Using graphs to solve equations and inequations 2F Review of translations and refl ections 2G Dilations 2H Combinations of transformations 2I Trigonometric graphs Chapter 2 Review 3 Curve‐sketching using the derivative 3A Increasing, decreasing and stationary at a point 3B Stationary points and turning points 3C Second and higher derivatives 3D Concavity and points of inflection 3E Systematic curve sketching with the derivative 3F Global maximum and minimum 3G Applications of maximisation and minimisation 3H Primitive functions Chapter 3 Review 4 Integration 4A Areas and the definite integral 4B The fundamental theorem of calculus 4C The definite integral and its properties 4D Challenge – proving the fundamental theorem 4E The indefinite integral 4F Finding areas by integration 4G Areas of compound regions 4H The trapezoidal rule 4I The reverse chain rule Chapter 4 Review 5 The exponential and logarithmic functions 5A Review of exponential functions base e 5B Differentiation of exponential functions 5C Applications of differentiation 5D Integration of exponential functions 5E Applications of integration 5F Review of logarithmic functions 5G Differentiation of logarithmic functions 5H Applications of differentiation of log e x 5I Integration of the reciprocal function 5J Applications of integration of 1 / x 5K Calculus with other bases Chapter 5 Review 6 The trigonometric functions 6A The behaviour of sin x near the origin 6B Differentiating the trigonometric functions 6C Applications of differentiation 6D Integrating the trigonometric functions 6E Applications of integration Chapter 6 Review Appendix: Differentiating trigonometric functions 7 Motion and rates 7A Average velocity and speed 7B Velocity and acceleration as derivatives 7C Integrating with respect to time 7D Rates and differentiation 7E Rates and integration 7F Exponential growth and decay Chapter 7 Review 8 Series and finance 8A Applications of APs and GPs 8B The use of logarithms with GPs 8C Simple and compound interest 8D Investing money by regular instalments 8E Paying off a loan Chapter 8 Review 9 Displaying and interpreting data 9A Displaying data 9B Grouped data and histograms 9C Quartiles and interquartile range 9D Bivariate data 9E Formulae for correlation and regression 9F Using technology with bivariate data Chapter 9 Review 10 Continuous probability distributions 10A Relative frequency 10B Continuous distributions 10C Mean and variance of a distribution 10D The standard normal distribution 10E General normal distributions 10F Applications of the normal distribution 10G Investigations using the normal distribution Chapter 10 Review Appendix: The standard normal distribution Answers Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10