CambridgeMATHS Stage 6. Year 12, Mathematics extension 1

Description

CambridgeMATHS Stage 6 combines proven approaches to teaching and learning with innovative digital capabilities and complete syllabus coverage of the new Stage 6 courses to guide students to HSC success. 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 Mathematical induction 2A Using mathematical induction for series 2B Proving divisibility by mathematical induction Chapter 2 Review 3 Graphs and equations 3A The sign of a function 3B Vertical and horizontal asymptotes 3C A curve-sketching menu 3D Solving inequations 3E Using graphs to solve equations and inequations 3F Regions in the coordinate plane 3G Review of translations and reflections 3H Dilations 3I Combinations of transformations 3J Trigonometric graphs Chapter 3 Review 4 Curve-sketching using the derivative 4A Increasing, decreasing and stationary at a point 4B Stationary points and turning points 4C Some less familiar curves 4D Second and higher derivatives 4E Concavity and points of inflection 4F Systematic curve sketching with the derivative 4G Global maximum and minimum 4H Applications of maximisation and minimisation 4I Maximisation and minimisation in geometry 4J Primitive functions Chapter 4 Review 5 Integration 5A Areas and the definite integral 5B The fundamental theorem of calculus 5C The definite integral and its properties 5D Proving the fundamental theorem 5E The indefinite integral 5F Finding areas by integration 5G Areas of compound regions 5H The trapezoidal rule 5I The reverse chain rule Chapter 5 Review 6 The exponential and logarithmic functions 6A Review of exponential functions base e 6B Differentiation of exponential functions 6C Applications of differentiation 6D Integration of exponential functions 6E Applications of integration 6F Review of logarithmic functions 6G Differentiation of logarithmic functions 6H Applications of differentiation of loge x 6I Integration of the reciprocal function 6J Applications of integration of 1/x 6K Calculus with other bases Chapter 6 Review 7 The trigonometric functions 7A The behaviour of sin x near the origin 7B Differentiating the trigonometric functions 7C Applications of differentiation 7D Integrating the trigonometric functions 7E Applications of integration Chapter 7 Review 8 Vectors 8A Directed intervals and vectors 8B Components and column vectors 8C The dot product (or scalar product) 8D Geometric problems 8E Projections 8F Applications to physical situations Chapter 8 Review 9 Motion and rates 9A Average velocity and speed 9B Velocity and acceleration as derivatives 9C Integrating with respect to time 9D Rates and differentiation 9E Review of related rates 9F Rates and integration Chapter 9 Review 10 Projectile motion 10A Projectile motion â•fl the time equations 10B Projectile motion â•fl the equation of path Chapter 10 Review 11 Trigonometric equations 11A Equations involving compound angles 11B The sum of sine and cosine functions 11C Using the t-formula to solve equations Chapter 11 Review 12 Further calculus 12A Inverse trigonometric functions â•fl differentiating 12B Inverse trigonometric functions â•fl integrating 12C Further trigonometric integrals 12D Integration by substitution 12E Further integration by substitution 12F Volumes of rotation Chapter 12 Review 13 Differential equations 13A Differential equations 13B Slope fields 13C Separable differentiable equations 13D y ' = g(y ) and the logistic equation 13E Applications of differential equations Chapter 13 Review 14 Series and finance 14A Applications of APs and GPs 14B The use of logarithms with GPs 14C Simple and compound interest 14D Investing money by regular instalments 14E Paying off a loan Chapter 14 Review 15 Displaying and interpreting data 15A Displaying data 15B Grouped data and histograms 15C Quartiles and interquartile range 15D Bivariate data 15E Formulae for correlation and regression 15F Using technology with bivariate data Chapter 15 Review 16 Continuous probability distributions 16A Relative frequency 16B Continuous distributions 16C Mean and variance of a distribution 16D The standard normal distribution 16E General normal distributions 16F Applications of the normal distribution 16G Investigations using the normal distribution Chapter 16 Review Appendix: The standard normal distribution 17 Binomial distributions 17A Binomial probability 17B Binomial distributions 17C Normal approximations to a binomial 17D Sample proportions Chapter 17 Review Answers Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17