Mathematics Extension 1 & 2

MATHEMATICS EXTENSION 1 (BDC)

PRELIMINARY THEN HSC 1 UNIT CATEGORY A HSC and ATAR

Prerequisite

The Mathematics Extension 1 Year 11 course has been developed on the assumption that students have studied the content and achieved the outcomes of the NSW Mathematics Years 7–10 Syllabus and, in particular, the content and outcomes of all substrands of Stage 5.1, Stage 5.2 and Stage 5.3, including the optional substrands:

• Polynomials

• Logarithms

• Functions and Other Graphs

• Circle Geometry.

Exclusions:

Students may not study the Mathematics Extension 1 course in conjunction with the Mathematics Standard 1 or the Mathematics Standard 2 course.

Course Description

The Mathematics Extension 1 Year 11 course includes the Mathematics Advanced Year 11 course. The Mathematics Extension 1 Year 12 course includes the Mathematics Advanced Year 12 course.

All students studying the Mathematics Extension 1 course will sit for an HSC examination.

The study of Mathematics Extension 1 in Stage 6:

• enables students to develop thorough knowledge, understanding and skills in working mathematically and in communicating concisely and precisely

• provides opportunities for students to develop rigorous mathematical arguments and proofs, and to use mathematical models extensively

• provides opportunities for students to develop their awareness of the interconnected nature of mathematics, its beauty and its functionality

• provides a basis for progression to further study in mathematics or related disciplines and in which mathematics has a vital role at a tertiary level

• provides an appropriate mathematical background for students whose future pathways may involve mathematics and its applications in such areas as science, engineering, finance and economics.

For whom is this subject intended

It is intended for students who have demonstrated a mastery of the skills of Stage 5 Mathematics and who are interested in the study of further skills and ideas in mathematics. The course is intended to give these students a thorough understanding of and competence in aspects of mathematics including many which are applicable to the real world. It has general educational merit and is also useful for concurrent studies of science, industrial arts and commerce.

The course is a recommended minimum basis for further studies in mathematics as a major discipline at a tertiary level, and for the study of mathematics in support of the physical and engineering sciences.

As well as being necessary for further study of Mathematics at Tertiary level, this course is useful for concurrent studies in Science, Industrial Arts and Economics.

Main Topics Covered

Year 11 Course

Topic: Functions:

Further Work with Functions.

Polynomials.

Topic: Trigonometric Functions:

Inverse Trigonometric Functions.

Further Trigonometric Identities.

Topic: Calculus:

Rates of Change

Topic: Combinatorics:

Working with Combinatorics

Year 12 Course

Topic: Proof:

Proof by Mathematical Induction

Topic: Vectors:

Introduction to Vectors

Topic: Trigonometric Functions:

Trigonometric Equations

Topic: Calculus:

Further Calculus Skills.

Applications of Calculus.

Topic: Statistical Analysis:

The Binomial Distribution