Mathematical Studies: Mathematical Studies for Year 12(South Australia Series)

This 2nd edition of our established course in mathematics for Year 12 has been thoroughly revised as a result of the recent changes to the Stage 2 Mathematics Curriculum Statement. It is not our intention to define the course, it is our interpretation of the concepts outlined in the Statement and we encourage teachers and students to use other resources. The main change in this new edition is the thorough overhaul of the two statistics chapters: Chapter 7 now covers normal distributions and Chapter 8 covers binomial distributions only. Other changes have been made to modelling in Chapter 2, the section 'economic models' has been deleted from Chapter 4, a more detailed account of specific exponential functions is included in Chapter 5, and Chapter 10 now includes transition matrices and other matrix types. The book has been printed in full colour and is accompanied by a new and improved version of our interactive Student CD. The CD offers exciting possibilities for students and teachers. It contains links to spreadsheets, graphing and geometry software, graphics calculator instructions, computer demonstrations and simulations. Teachers will be able to demonstrate concepts quickly, clearly and simply, and students have the opportunity to revisit the demonstrations and experiment for themselves. The book contains many problems from basic to advanced, to cater for a range of student abilities and interests. While some of the exercises are designed simply to build skills, every effort has been made to contextualise problems so that students can see everyday uses and practical applications of the mathematics they are studying. Emphasis has been placed on the gradual development of concepts with appropriate worked examples. However, we have also provided extension material for those who look towards further studies or applications of mathematics for their career choices. It is not our intention that each chapter be worked through in full. Time constraints will not allow for this. Consequently, teachers must select exercises carefully, according to the abilities and prior knowledge of their students, in order to make the most efficient use of time and give as thorough coverage of work as possible. The extensive use of graphics calculators and computer packages throughout the book enables student to realise the importance, application and appropriate use of technology. No single aspect of technology has been favoured. It is as important that students work with a pen and paper as it is that they use their calculator or graphics calculator, or use a spreadsheet or graphing package on computer. Instructions appropriate to each graphics calculator problem are on the CD. They are written for Texas Instruments and Casio calculators, and can be printed from the CD. We hope that this book, with the associated use of technology, will enhance the students' understanding, knowledge and appreciation of mathematics.

Table of Contents:
1 BACKGROUND KNOWLEDGE 9 A Key concepts 10 B Constructing functions using geometry 21 C Review 27 2 FUNCTIONS AND INTRODUCTORY CALCULUS 29 3 DIFFERENTIAL CALCULUS 59 4 APPLICATIONS OF DIFFERENTIAL CALCULUS 99 5 EXPONENTIAL AND LOGARITHMIC FUNCTIONS 145 6 INTEGRATION 179 7 STATISTICS 219 8 BINOMIAL DISTRIBUTIONS 283 9 SOLVING SYSTEMS OF LINEAR EQUATIONS 317 10 MATRICES 343