Introduction. About eBookPLUS. Acknowledgements. CHAPTER 1. Graphs and polynomials. 1A The binomial theorem. 1B Polynomials. 1C Division of polynomials. 1D Linear graphs. 1E Quadratic graphs. 1F Cubic graphs. 1G Quartic graphs. CHAPTER 2. Functions and transformations. 2A Transformations and the parabola. 2B The cubic function in power form. 2C The power function (the hyperbola). 2D The power function (the truncus). 2E The square root function in power form. 2F The absolute value function. 2G Transformations with matrices. 2H Sum, difference and product functions. 2I Composite functions and functional equations. 2J Modelling. CHAPTER 3. Exponential and logarithmic equations. 3A The index laws. 3B Logarithm laws. 3C Exponential equations. 3D Logarithmic equations using any base. 3E Exponential equations (base e). 3F Equations with natural (base e) logarithms. 3G Inverses. 3H Literal equations. 3I Exponential and logarithmic modelling. CHAPTER 4. Exponential and logarithmic graphs. 4A Graphs of exponential functions with any base. 4B Logarithmic graphs to any base. 4C Graphs of exponential functions with base e. 4D Logarithmic graphs to base e. 4E Finding equations for graphs of exponential and logarithmic functions. 4F Addition of ordinates. 4G Exponential and logarithmic functions with absolute values. 4H Exponential and logarithmic modelling using graphs. CHAPTER 5. Inverse functions. 5A Relations and their inverses. 5B Functions and their inverses. 5C Inverse functions. 5D Restricting functions. CHAPTER 6. Circular (trigonometric) functions. 6A Revision of radians and the unit circle. 6B Symmetry and exact values. 6C Trigonometric equations. 6D Trigonometric graphs. 6E Graphs of the tangent function. 6F Finding equations of trigonometric graphs. 6G Trigonometric modelling. 6H Further graphs. 6I Trigonometric functions with an increasing trend. CHAPTER 7. Differentiation. 7A Review - gradient and rates of change. 7B Limits and differentiation from first principles. 7C The derivative of xn. 7D The chain rule. 7E The derivative of ex. 7F The derivative of loge (x). 7G The derivatives of sin (x), cos (x) and tan (x). 7H The product rule. 7I The quotient rule. 7J Mixed problems on differentiation. CHAPTER 8. Applications of differentiation. 8A Equations of tangents and normals. 8B Sketching curves. 8C Maximum and minimum problems when the function is known. 8D Maximum and minimum problems when the function is unknown. 8E Rates of change. 8F Related rates. 8G Linear approximation. CHAPTER 9. Integration. 9A Antidifferentiation. 9B Integration of e x, sin (x) and cos (x). 9C Integration by recognition. 9D Approximating areas enclosed by functions. 9E The fundamental theorem of integral calculus. 9F Signed areas. 9G Further areas. 9H Areas between two curves. 9I Average value of a function. 9J Further applications of integration. CHAPTER 10. Discrete random variables. 10A Probability revision. 10B Discrete random variables. 10C Measures of centre of discrete random distributions. 10D Measures of variability of discrete random distributions. CHAPTER 11. The binomial distribution. 11A The binomial distribution. 11B Problems involving the binomial distribution for multiple probabilities. 11C Markov chains and transition matrices. 11D Expected value, variance and standard deviation of the binomial distribution. CHAPTER 12. Continuous distributions. 12A Continuous random variables. 12B Using a probability density function to find probabilities of continuous random variables. 12C Measures of central tendency and spread. 12D Applications to problem solving. 12E The normal distribution. 12F The standard normal distribution. 12G The inverse cumulative normal distribution. Answers. Index.