2016 Copyright Board of Studies, Teaching and Educational Standards NSW for and on behalf of the Crown in right of the State of New South Wales. Standards NSW for and on behalf of the Crown in right of the State of New South Wales. No part of the Material may be reproduced in any material form in Australia or in any other country by any process, electronic or otherwise, or transmitted to any other person or stored electronically in any form without the prior written consent of the Board of Studies. , Teaching and Educational Standards NSW, except as permitted by the Copyright Act 1968.
A summary of the BOSTES syllabus development process is available at http://www.boardofstudies.nsw.edu.au/syllabuses/syllabus-development. The purpose of the survey is to obtain detailed comments from individuals and systems/organizations about the syllabus. The Stage 6 syllabuses reflect the principles of the BOSTES K–10 Curriculum Framework and Statement of Equity Principles, and the Melbourne Statement on Educational Goals for Young Australians (December 2008).
Gifted students have specific learning needs that may require adjustments to the pace, level and content of the curriculum. EAL/D students simultaneously learn a new language and knowledge, understanding and skills in the Mathematics Extension 2 Stage 6 curriculum through the new language.
RATIONALE
THE PLACE OF THE MATHEMATICS
STAGE 6 DRAFT SYLLABUS IN THE K–12 CURRICULUM
In NSW syllabuses, the aim provides a concise statement of the overall purpose of the syllabus. The aim, objectives, outcomes and content of a syllabus are clearly linked and sequentially reinforce details of the intention of the syllabus.
OBJECTIVES
KNOWLEDGE, UNDERSTANDING AND SKILLS
VALUES AND ATTITUDES
OUTCOMES
COURSE STRUCTURE AND REQUIREMENTS
ASSESSMENT
The draft guidelines for school-based assessment provide specific advice about the number of formal assessment tasks, the components and weights of subjects, and the nature of the types of tasks they should be. A variety of short-answer to extended-answer questions, with the option of a number of parts. This approach provides opportunities for incorporating related application questions, and modeling and problem-solving questions to enable students to demonstrate deep understanding, conceptual knowledge, higher-order thinking, and reasoning.
Questions or parts of questions can be drawn from a range of syllabus outcomes and content.
Objective responses I – Written responses
CONTENT
LEARNING ACROSS THE CURRICULUM
Through application and modeling across the sections of the syllabus, students can experience the relevance of mathematics in Aboriginal and Torres Strait Islander history and cultures. The story of the development of mathematics and its integration with cultural development can be explored in the context of some topics. The evaluation of statistical data, where appropriate, allows students to deepen their understanding of the lives of Aboriginal and Torres Strait Islander peoples.
Students have the opportunity to learn about the meaning and application of mathematics in Asia and how mathematicians from Asia continue to contribute to the ongoing development of mathematics. Through the evaluation of statistical data, students can examine issues relevant to the Asian region. Through measurement and the judicious use of data students can measure and evaluate sustainability changes over time and develop a deeper appreciation of the world around them.
Mathematical knowledge, understanding and skills are necessary to monitor and evaluate both the impact of human activity on ecosystems and changes in conditions in the biosphere. Students can apply mathematical thinking to identify and solve issues related to living with diversity. Literacy is used throughout mathematics to understand and interpret word problems and instructions that contain the special linguistic features of mathematics.
Mathematics has a central role in the development of numeracy in a way that is clearer and more open than is the case in other learning areas. Mathematics enhances the development of students' personal and social skills by providing opportunities for initiative-taking, decision-making, communication of their processes and findings, and independent and collaborative work in the mathematics classroom. Students have the opportunity to apply mathematical skills in a variety of personal and social contexts.
Through modeling reality with mathematics and then manipulating mathematics to understand and/or predict reality, students have the opportunity to learn the mathematical knowledge, skills and understanding essential to actively participate in the world in which we live. Students develop knowledge, understanding and skills about work and entrepreneurship by studying mathematics in a work-related context. Students are encouraged to select and apply appropriate mathematical techniques and strategies to solve problems through work experience in the financial mathematics and statistical analysis sections.
ORGANISATION OF CONTENT
WORKING MATHEMATICALLY
MATHEMATICS EXTENSION 2 YEAR 12 COURSE CONTENT
STRAND: PROOF
STRAND FOCUS
TOPICS
PROOF
ME2-P1 THE NATURE OF PROOF
TOPIC FOCUS
ME2-P2 DEDUCTIVE PROOF
ME2-P3 PROOF BY MATHEMATICAL INDUCTION
STRAND: VECTORS AND MECHANICS
VECTORS
ME2-V1 VECTORS
VECTORS AND MECHANICS ME2-V2 MECHANICS
Using their understanding of motion, students must determine the validity of the referee's decision and support their reasons with appropriate mathematical arguments, assumptions, and E reasoning.
STRAND: CALCULUS
CALCULUS
ME2-C1 ADVANCED CALCULUS SKILLS
STRAND: COMPLEX NUMBERS
COMPLEX NUMBERS
ME2-N1 INTRODUCTION TO COMPLEX NUMBERS
ME2-N2 USING COMPLEX NUMBERS
GLOSSARY
For every complex number, its conjugate is ̅ where. and are real numbers and is an imaginary number. Complex number A complex number is a number that can be expressed in the form , where and are real numbers and is an imaginary number that satisfies the equation. contrapositive The contrapositive of the statement 'If then' is 'If not, then not. Also, true is the contrapositive of a true statement. Opposite of a statement The opposite of an 'If then' statement is 'If then' The symbolic converse is: or The opposite of a true statement is not necessarily true. If the quadrilateral is a rectangle, the diagonals are the same length and bisect each other.
If the diagonals of a quadrilateral are of equal length and bisect each other, the quadrilateral is a rectangle. Euler's Formula Euler's formula for complex numbers establishes a fundamental relationship between trigonometric functions and the complex exponential function. The exponential form of a complex number is where is the modulus of the complex number and is the argument expressed in radians.
If the quadrilateral is a rectangle, the diagonals are the same length and bisect each other. If the truth of ( ) implies the truth of ( ) for every positive integer, then ( ) holds for all positive integers. If is a complex number and modulus is the distance from the origin in the Argand plane.
For example, if the statement is "It's snowing," then the statement is "It's not snowing." Since all reasoning is correct and a wrong conclusion has been reached, the only thing that can be wrong is the initial assumption. For example, the result '√ is irrational' can be proved in this way by obtaining a contradiction from the assumption that √ is rational.
The set of real numbers consists of the set of all rational and irrational numbers. Once one or more initial terms are given, each further term of the sequence is defined as a function of previous terms. The points in the complex plane that represent the roots of unity lie on the unit circle.
