Year 12 mathematics advanced : CambridgeMaths stage 6

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