This revision of this popular text addresses the course changes and takes in requests from many teachers. It provides a consistent and comprehensive treatment of the required course and has been trialed in the classroom. The application of graphics calculators has been strengthened to include questions in all appropriate exercises that require the graphics calculator. Analysis questions are again featured in each chapter to ensure that students are thoroughly prepared for the exams.

 

 

This book is part of a book series called Essential Mathematics .

There are 656 pages in this book. This book was published in 1999 by Cambridge University Press .

Dr Michael Evans is Head of Mathematics at Scotch College and also actively involved in the Victorian Curriculum and Assessment Authority. His interest in mathematics extends to the Mathematics Olympiad Team. David Greenwood teaches at Scotch College and has special expertise in the creative use of graphics calculators. Professor Peter Jones from Swinburne University has taken a keen interest in secondary school mathematics and has also had a key role in the development of the new course of study. Dr Kay Lipson's experience extends through secondary and tertiary courses. She is currently a lecturer in statistics at Swinburne University. Dr. Michael Evans writes a health column for Canada's "Globe and Mail" and is an associate professor at the University of Toronto and a staff physician at Toronto Western Hospital.

This book has the following chapters: Introduction; 1. Functions, 1. 1. Introduction, 1. 2. Set notation, 1. 3. Sets of numbers, 1. 4. Relations, 1. 5. Functions, 1. 6. Sums and products of functions, 1. 7. Composite functions, 1. 8. Inverse functions, 1. 9. Inverse relations, 1. 10. Applications; 2. Revising linear functions, 2. 1. Revision of linear equations, 2. 2. Linear functions, 2. 3. 'Fitting' data; 3. Graphing with transformations, 3. 1. Introduction, 3. 2. The functions with rules f(x)=xn, where n=-1, -2, 1/2, 3. 3. Composition of transformations, 3. 4. Quadratic functions, 3. 5. Determining the rule for a function of a graph, 3. 6. Possible models for data, 3. 7. Addition of ordinates, 3. 8. Graphing inverse functions; 4. Polynomial functions, 4. 1. Summation notation, 4. 2. The Binomial Theorem, 4. 3. Cubic functions of the form f: R > R, f(x)=a(x+h)3 + k, 4. 4. The general cubic function, 4. 5. Cubic equations, 4. 6. Determining rules for graphs of cubic functions, 4. 7. Quartic functions, 4. 8. Graphics calculator exercise; 5. Exponential and logarithmic functions, 5. 1. Exponential functions, 5. 2. Exponential models, 5. 3. The exponential function f(x)=ex, 5. 4. Exponential equations, 5. 5. Logarithmic functions, 5. 6. Inverses, 5. 7. Determining rules for graphs of exponential and logarithmic functions, 5. 8. Solution of exponential equations and inequations with logarithms, 5. 9. Graphics calculator exercise, 5. 10. Applications; 6. Trigonometric functions, 6. 1. Review of trigonometric functions, 6. 2. Graphs of sine and cosine, 6. 3. Transformations applied to graphs of y = sin x and y = cos x, 6. 4. Addition of ordinates, 6. 5. Determining the rule for graphs of trigonometric functions, 6. 6. The function tan, 6. 7. Graphics calculator exercise, 6. 8. Identities, 6. 9. Applications; 7. Revision of chapters 1-6, 7. 1. Summary of chapters 1-6, 7. 2. Short answer questions, 7. 3. Multiple choice questions, 7. 4. Analysis questions; 8. Differentiation of polynomials and rational functions, 8. 1. The gradient of a curve at a point, 8. 2. The derived function, 8. 3. Differentiating xn where n is negative integer, 8. 4. The Chain Rule, 8. 5. Differentiating rational powers (x p/q), 8. 6. Product Rule and Quotient Rule, 8. 7. The graph of the gradient function, 8. 8. Graphics calculator exercise, 8. 9. Miscellaneous exercise; 9. Applications of differentiation, 9. 1. Tangents and normals, 9. 2. Angles between curves, 9. 3. Linear approximation, 9. 4. Stationary points, 9. 5. Types of stationary points, 9. 6. Maxima and minima problems, 9. 7. Rates of change, 9. 8. Graphics calculator exercise; 10. Differentiation of transcendental functions, 10. 1. Differentiation of ex, 10. 2. Differentiation of the natural logarithm function, 10. 3. Derivatives of trigonometric functions, 10. 4. Graphics calculator exercise, 10. 5. Applications; 11. Integration, 11. 1. Approximations leading to integrals, 11. 2. Antidifferentiation, 11. 3. Area - the definite integral, 11. 4. Integration of trigonometric functions, 11. 5. Integration of functions of the form f(x) = 1/ax+b, 11. 6. Miscellaneous exercise, 11. 7. Area of a region between two curves, 11. 8. The fundamental theorem of calculus revisited, 11. 9. Graphics calculator exercise, 11. 10. Applications; 12. Revision of chapters 8-11, 12. 1. Summary of chapters 8-11, 12. 2. Short answer questions, 12. 3. Multiple choice questions, 12. 4. Analysis questions; 13. Discrete random variables and their probability distributions, 13. 1. Review of probability, 13. 2. Discrete random variables, 13. 3. Discrete probability distributions, 13. 4. Expectation and variance; 14. The binomial distribution, 14. 1. The binomial probability distribution, 14. 2. The graph of the binomial probability distribution, 14. 3. Expectation and variance, 14. 4. Using the graphics calculator; 15. The hypergeometric distribution, 15. 1. The hypergeometric probability distribution, 15. 2. Mean and variance, 15. 3. The binomial and hy