Table of Contents

Introduction. About eBookPLUS. Acknowledgements. CHAPTER 1. Modelling change and rates of change. Introduction. Using functions to model change. Exercise 1A. Graphing polynomial functions. Exercise 1B. Investigation ? Quartics and beyond. Review of differentiation. Exercise 1C. Rules for differentiation. Exercise 1D. Summary. Chapter review. eBookPLUS activities. CHAPTER 2. Applications of differentiation. Introduction. Sketching curves. Exercise 2A. Equations of tangents and normals. Exercise 2B. Maximum and minimum problems when the function is known. Exercise 2C. Maximum and minimum problems when the function is unknown. Exercise 2D. Investigation ? Cross-country run. Rates of change. Exercise 2E. Summary. Chapter review. eBookPLUS activities. CHAPTER 3. Exponential and logarithmic functions. Introduction. The index laws. Exercise 3A. Logarithms and laws of logarithms. Exercise 3B. Indicial equations. Exercise 3C. Logarithmic equations using any base. Exercise 3D. Exercise 3E. Exercise 3F. Investigation ? Graphing inverse functions. Exponential and logarithmic modelling. Investigation ? An earthquake formula. Exercise 3G. Career profile: Tony Intihar. Investigation ? St Louis? Gateway Arch. Summary. Chapter review. eBookPLUS activities. CHAPTER 4. Derivatives of exponential and logarithmic functions. Introduction. Inverses. Exercise 4A. Exercise 4B. Exercise 4C. Derivatives of exponential and logarithmic functions. Exercise 4D. Applications of derivatives of exponential functions. Exercise 4E. Summary. Chapter review. eBookPLUS activities. CHAPTER 5. Periodic functions. Introduction. Revision of radians and the unit circle. Exercise 5A. Symmetry and exact values. Exercise 5B. Further trigonometric equations. Exercise 5C. Further trigonometric graphs. Investigation ? Complementary functions. Investigation ? Dilation. Investigation ? Reflection. Exercise 5D. Finding equations of trigonometric graphs. Exercise 5E. Trigonometric modelling and problem solving. Investigation ? Varying amplitude. Exercise 5F. Investigation ? Beats. Summary. Chapter review. eBookPLUS activities. CHAPTER 6. The calculus of periodic functions. Introduction. Exercise 6A. Further differentiation of trigonometric functions. Exercise 6B. Applications of differentiation. Exercise 6C. Investigation ? Halley?s comet. Kinematics. Exercise 6D. Investigation ? Period and amplitude. Investigation ? Warehouse security. Summary. Chapter review. eBookPLUS activities. CHAPTER 7. Introduction to integration. Introduction. Approximating areas enclosed by functions. Exercise 7A. Investigation ? The Monte Carlo method. Investigation ? Area enclosed by a function and the Monte Carlo method. Antidifferentiation (integration). Exercise 7B. Exercise 7C. Integration by recognition. Exercise 7D. Summary. Chapter review. eBookPLUS activities. CHAPTER 8. Techniques of integration. Introduction. The fundamental theorem of integral calculus. Investigation ? Definite integrals. Exercise 8A. Signed areas. Exercise 8B. Further areas. Exercise 8C. Areas between two curves. Exercise 8D. Further applications of integration. Exercise 8E. Investigation ? Concrete chute. Summary. Chapter review. eBookPLUS activities. CHAPTER 9. Probability distributions. Introduction. Discrete random variables. Exercise 9A. Expected value of discrete random distributions. Exercise 9B. The binomial distribution. Investigation ? Binomial distribution graphs. Exercise 9C. Problems involving the binomial distribution for multiple probabilities. Exercise 9D. Expected value, variance and standard deviation of the binomial distribution. Exercise 9E. Investigation ? Gary?s test ? some answers. Investigation ? The binomial theorem. Summary. Chapter review. eBookPLUS activities. CHAPTER 10. The normal distribution. Introduction. The normal distribution. The standard normal distribution. Exercise 10A. The inverse cumulative normal distribution. Exercise 10B. Investigation ? Assessment methods. Investigation ? Sunflower stems. The normal approximation to the binomial distribution. Exercise 10C. Investigation ? Supporting the proposal. Hypothesis testing. Exercise 10D. Investigation ? The Randhill vaccine. Summary. Chapter review. Binomial probability tables (selected). eBookPLUS activities. Appendix. Answers. Index.