Cambridge 2 Unit Mathematics Year 12 Second Edition

by William Pender , David Saddler , Julia Shea , Derek Ward

• ISBN13: 9780521539692
• ISBN10: 0521539692
• Edition: 2nd
• Format: Paperback
• Copyright: 2003-10-07
• Publisher: Cambridge University Press

Summary

The exercises and text in the new Cambridge 2 Unit Mathematics Year 12 2nd Edition have been thoroughly reworked to ensure that the book is accessible to all students undertaking the 2 Unit course called 'Mathematics' in the NSW HSC. - Single-focus questions have been included in the Foundation sections. - Chapter review exercises have been added to the end of each chapter. - Some sections and chapters have been subdivided into more manageable sections. - The worked exercises in the theory section have been reviewed, and many more straightforward examples have been added. - All key results and methods are summarised in numbered boxes for easy reference. - Mathematical imagination is encouraged through careful exposition and interesting questions, and by demonstrating the relationships between various topics. - Exercises reflect the style of recent HSC papers and are carefully graded into: Foundation, Development and Challenge

Table of Contents

Preface

How to use this book

About the authors

+ Integration

Finding areas by a limiting process

The fundamental theorem of calculus

The definite integral and its properties

The indefinite integral

Finding area by integration

Area of a compound region

Volumes of solids of revolution

The trapezoid rule

Simpson+s rule

+ The trigonometric functions

Review of logarithmic and exponential functions

The exponential function and the definition of e

Differentiation of exponential functions

Applications of differentiation

Integration of exponential functions

Applications of integration

The logarithmic function and its derivative

Applications of differentiation of log x

Integration of the reciprocal function

Applications of integration of 1/x

+ The trigonometric functions

Radian measure of angle size

Mensuration of arcs

sectors and segments

Graphs of the trigonometric functions in radians

The behaviour of sin x near the origin

The derivatives of the trigonometric functions

Applications of differentiation

Integration of the trigonometric functions

Applications of integration

+ Motion

Average velocity and speed

Velocity and acceleration as derivatives

Integrating with respect to time

+ Rates and finance

Applications of APs and GPs

Simple and compound interest

Investing money by regular instalments

Paying off a loan

Rates of change

Natural growth and decay

+ Euclidean geometry

Points

lines

parallels and angles

Angles in triangles and polygons

Congruence and special triangles

Trapezia and parallelograms

Rhombuses

rectangles and squares

Areas of plane figures

Pythagoras+ theorem and its converse

Similarity

Intercepts on transversals

+ Probability

Probability and sample spaces

Sample space graphs and tree diagrams

Venn diagrams and the addition theorem

Multi-stage experiments and the product rule

Probability tree diagrams

Answers to exercises

Index

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