Mathematics for Year 11 Geometry and Trigonometry 5th edition has been written to embrace the concepts outlined in the Stage 1 Mathematics Curriculum Statement. It is not our intention to define a course.
This package is the first step in a new approach to mathematics education. You are provided with a text book and a CD-Rom which displays the contents of the book plus many exciting new interactive features which will assist teachers and students.
The book is language rich and technology rich. Whilst some of the exercises are simply designed 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.
The book contains many problems, from the basic to the advanced, to cater for a wide range of student abilities and interests. Much emphasis has been placed on the gradual development of concepts with appropriate worked examples. However, we have also provided extension material for those who wish to go beyond Stage 1 and 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 students 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.
The interactive features of the CD-Rom allow immediate access to our own specially designed geometry packages, graphing packages and more. Teachers are provided with a quick and easy method of demonstrating concepts, or students can discover for themselves, and revisit when necessary.
Teachers should note that instructions appropriate to each graphics calculator problem are available on the CD-Rom and can be printed for students. These instructions are written for Sharp, Texas Instruments, Casio and Hewlett-Packard calculators.
In this changing world of mathematics education, we believe that the contextual approach shown in this book, with the associated use of technology, will enhance the students’ understanding, knowledge and appreciation of mathematics.
This book is accompanied by a free interactive Student CD. The CD includes:
|1||GEOMETRY AND MENSURATION||9|
|A||Pythagoras’ Rule (Review)||10|
|B||Sine, cosine and tangent||16|
|C||Right angled triangle trigonometry||18|
|D||Finding sides and angles||21|
|E||Problem solving using trigonometry||27|
|F||Constructing trigonometric formulae||31|
|G||3-Dimensional problem solving||33|
|H||Areas of triangles||36|
|I||Sectors and segments||39|
|J||The cosine rule||42|
|K||The sine rule||44|
|L||Using the sine and cosine rules||49|
|M||Further trigonometric applications||53|
|A||Assumed knowledge (Review)||69|
|C||Equations of lines||78|
|E||Midpoints and perpendicular bisectors||85|
|F||Ratio of division||89|
|G||The distance from a point to a line||91|
|H||Circles in the Cartesian plane||96|
|I||The intersection of lines and circles||104|
|J||Where two circles meet||106|
|K||The rectangular hyperbola||108|
|L||Areas of polygons||118|
|B||Congruence of triangles (review)||148|
|H||Discoveries in geometry||170|
|J||Operations with vectors||176|
|K||Vectors in component form||188|
|L||Vectors in coordinate geometry||194|
|P||Proof using vector geometry (extension)||210|
|A||Observing periodic behaviour||225|
|B||Periodic properties of circles||228|
|D||Equations involving sine||248|
|G||The tangent function||277|
|5||NETWORKS AND MATRICES||293|
|B||Problem solving with networks||308|
|C||Travelling Salesman Problem||325|
|D||Modelling with networks||330|
|E||Investigation and project ideas||332|
|F||Interpreting information with matrices||333|
|6||MATRICES AND LINEAR TRANSFORMATIONS||357|
|B||Matrices, mainly 2 × 2||366|
|A||Elementary differential calculus||388|