Cambridge 2 Unit Mathematics Year 12

Erscheinungsjahr 2000
ISBN: 978-0-521-65867-6
Verlag: Cambridge University Press

Buch, Englisch, 320 Seiten, Format (B × H): 153 mm x 260 mm, Gewicht: 670 g

Reihe: Cambridge Secondary Maths (Australia)

Cambridge Mathematics 2 Unit Year 12 develops theory for the Mathematics 2 Unit Year 12 syllabus both thoroughly and logically through clear explanations. It spans the full range of students' abilities with a large number of questions that are carefully graded and range from quite easy to more demanding. They will provide sufficient work for students of every ability taking the course. The gradual changes of emphasis in HSC examinations over the last ten years have been carefully addressed by the authors. The authors also encourage mathematical imagination through careful exposition and interesting questions, and by relating the various topics. Chapters are systematically divided into manageable sections which consist of a substantial exercise preceded by theory and worked examples. The exercises are then divided into three groups: Group 1 for more straightforward algorithms, Group 2 for harder algorithms and Group 3 for problems that link to other topics.

Autoren/Hrsg.

Pender, William

Ward, Derek

Shea, Julia

Sadler, David

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein

Inhaltsverzeichnis

Preface; How to use this book; About the authors; Chapter one – Integration: 1A. Finding areas by a limiting process, 1B. The fundamental theorem of calculus, 1C. The definite integral and its properties, 1D. The indefinite integral, 1E. Finding area by integration, 1F. Area of a compound region, 1G. Volumes of solids of revolution, 1H. The trapezoid rule, 1I. Simpson's rule; Chapter two – The trigonometric functions: 2A. Review of logarithmic and exponential functions, 2B. The exponential function and the definition of e, 2C. Differentiation of exponential functions, 2D. Applications of differentiation, 2E. Integration of exponential functions, 2F. Applications of integration, 2G. The logarithmic function and its derivative, 2H. Applications of differentiation of log x, 2I. Integration of the reciprocal function, 2J. Applications of integration of 1/x; Chapter three – The trigonometric functions: 3A. Radian measure of angle size, 3B. Mensuration of arcs, sectors and segments, 3C. Graphs of the trigonometric functions in radians, 3D. The behaviour of sin x near the origin, 3E. The derivatives of the trigonometric functions, 3F. Applications of differentiation, 3G. Integration of the trigonometric functions, 3H. Applications of integration; Chapter four – Motion: 4A. Average velocity and speed, 4B. Velocity and acceleration as derivatives, 4C. Integrating with respect to time; Chapter five – Rates and finance: 5A. Applications of APs and GPs, 5B. Simple and compound interest, 5C. Investing money by regular instalments, 5D. Paying off a loan, 5E. Rates of change, 5F. Natural growth and decay; Chapter six – Euclidean geometry: 6A. Points, lines, parallels and angles, 6B. Angles in triangles and polygons, 6C. Congruence and special triangles, 6D. Trapezia and parallelograms, 6E. Rhombuses, rectangles and squares, 6F. Areas of plane figures, 6G. Pythagoras' theorem and its converse, 6H. Similarity, 6I. Intercepts on transversals; Chapter seven – Probability: 7A. Probability and sample spaces, 7B. Sample space graphs and tree diagrams, 7C. Venn diagrams and the addition theorem, 7D. Multi-stage experiments and the product rule, 7E. Probability tree diagrams; Answers to exercises; Index.