Maths 4

MATHEMATICS 4 UNIT Year 12

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Syllabus

The Board of Studies owns the copyright on all syllabuses. Schools may reproduce this syllabus in part or in full for bona fide study or classroom purposes only. Acknowledgement of the Board of Studies’ copyright must be included on any reproductions. Students may copy reasonable portions of the syllabus for the purpose of research or study. Any otheruse of this syllabus must be referred to the Copyright Officer, Board of Studies NSW. Ph: (02) 9927 8289; fax: (02) 9956 5205.

Syllabus approved by the Board of Senior School Studies in February 1980, with amendments approved by the Board of Secondary Education in October 1989. For implementation for Year 12 in 1990.

© Board of Studies NSW 1989

Published by Board of Studies NSW PO Box460 North Sydney NSW 2059 Australia Tel: (02) 9927 8111 ISBN 0-7305-6116-X November 1989 January 1997 (second edition)

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Contents

Mathematics K–12 Statement of Principles The Mathematics 4 Unit Syllabus Topic 1: Topic 2: Topic 3: Topic 4: Topic 5: Topic 6: Topic 7: Topic 8: Graphs Complex Numbers Conics Integration Volumes Mechanics Polynomials Harder 3 Unit Topics

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Mathematics 4 Unit Syllabus

Mathematics K–12 Statement of Principles
Preface
This K–12 Statement of Principles describes the general principles that underlie all ideas in this syllabus.

The Nature of Mathematics
Mathematics is the study of number and space
More particularly it is: • a search for patterns and relationships. This search, utilising acquired knowledge andskills, leads to the development of concepts and generalisations, which can be applied in finding solutions to problems, improving our understanding of the world around us and meeting the specific needs of people; a way of thinking, characterised by processes such as exploring, manipulating, discovering, ordering, classifying, generalising, abstracting, estimating, calculating, predicting,describing, deducing, drawing and measuring; a powerful, precise and concise means of communication, used to represent, to interpret, to explain and to predict; a creative activity. Accordingly, it involves invention, intuition and discovery.

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Rationale for Mathematics in the Curriculum
Mathematics is useful
• Mathematics is essential for living. Some aspects of mathematics are required byindividuals in order to function adequately as members of society. These aspects include strategies, skills and techniques involved in number facts, computation, mathematical problem-solving and reasoning. Mathematics is important and useful in many fields of endeavour. These fields include the sciences, medicine, economics, commerce, industry, engineering, business and the arts. Mathematicsprovides a means of oral and written communication. Mathematics can be used to present and convey information in many ways. Some of these include explanations, figures, letters, tables, charts, diagrams, graphs and drawings. Mathematics provides opportunities for development of reasoning abilities.

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Mathematics 4 Unit Syllabus

Mathematics is part of our culture
Mathematicshas been part of human activity since the earliest times. It has made, and continues to make, a significant contribution to human culture. Mathematics allows students to appreciate their cultural heritage more fully by providing insights into many of the creative achievements of the human race.

Mathematics can be part of our leisure
Mathematics is a source of interesting and appealing puzzlesand problems. When mathematics is enjoyable, it encourages curiosity, exploration, discovery and invention.

Aims of Mathematics Education
The aims of mathematics education will be achieved in different levels in the K–12 range according to the stages of development of the students at these levels. These aims are to develop in students confidence and enjoyment in doing mathematical activities,...