Table of Contents

Chapter 1 - Modelling change and rates of change. Exercise 1A - Using functions to model change. Exercise 1B - Graphing polynomial functions. Exercise 1C - Review of differentiation. Exercise 1D - Rules for differentiation. Chapter review. Modelling and problem solving. Chapter 2 - Applications of differentiation. Exercise 2A - Sketching curves. Exercise 2B - Equations of tangents and normals. Exercise 2C - Maximum and minimum problems when the function is known. Exercise 2D - Maximum and minimum problems when the function is unknown. Investigation - Cross-country run. Exercise 2E - Rates of change. Chapter review. Modelling and problem solving. Chapter 3 - Exponential and logarithmic functions. Exercise 3A - The index laws. Exercise 3B - Logarithms and laws of logarithms. Exercise 3C - Indicial equations. Exercise 3D - Logarithmic equations using any base. Exercise 3E - Exponential equations (base e). Exercise 3F - Equations with natural (base e) logarithms. Investigation - An earthquake formula. Exercise 3G - Exponential and logarithmic modelling. Chapter review. Modelling and problem solving. Chapter 4 - Derivatives of exponential and logarithmic functions. Exercise 4A - Inverses. Exercise 4B - The derivative of ex. Exercise 4C - The derivative of loge x. Exercise 4D - Derivatives of exponential and logarithmic functions. Exercise 4E - Applications of derivatives of exponential functions. Chapter review. Modelling and problem solving. Chapter 5 - Periodic functions. Exercise 5A - Revision of radians and the unit circle. Exercise 5B - Symmetry and exact values. Exercise 5C - Further trigonometric equations. Exercise 5D - Further trigonometric graphs. Exercise 5E - Finding equations of trigonometric graphs. Exercise 5F - Trigonometric modelling and problem solving. Chapter review. Modelling and problem solving. Chapter 6 - The calculus of periodic functions. Exercise 6A - The derivatives of sin x and cos x. Exercise 6B - Further differentiation of trigonometric functions. Exercise 6C - Applications of differentiation. Exercise 6D - Kinematics. Chapter review. Modelling and problem solving. Chapter 7 - Introduction to integration. Exercise 7A - Approximating areas enclosed by functions. Exercise 7B - Antidifferentiation (integration). Exercise 7C - Integration of ex, sin x and cos x. Exercise 7D - Integration by recognition. Chapter review. Modelling and problem solving. Chapter 8 - Techniques of integration. Exercise 8A - The fundamental theorem of integral calculus. Exercise 8B - Signed areas. Exercise 8C - Further areas. Exercise 8D - Areas between two curves. Exercise 8E - Further applications of integration - modelling and problem solving. Investigation - Concrete chute. Chapter review. Modelling and problem solving. Chapter 9 - Probability distributions. Exercise 9A - Discrete random variables. Exercise 9B - Expected value of discrete random distributions. Exercise 9C - The binomial distribution. Exercise 9D - Problems involving the binomial distribution for multiple probabilities. Exercise 9E - Expected value, variance and standard deviation of the binomial distribution. Investigation - The binomial theorem. Chapter review. Modelling and problem solving. Chapter 10 - The normal distribution. Exercise 10A - The standard normal distribution. Exercise 10B - The inverse normal cumulative distribution. Investigation - Sunflower stems. Exercise 10C - The normal approximation to the binomial distribution. Investigation - Supporting the proposal. Exercise 10D - Hypothesis testing. Chapter review.