Mathematics Extension 1

The Mathematics Extension 1 course is a calculus-based course focused on further study of Mathematics, as such the Year 11 course includes the Mathematics Advanced Year 11 course. In addition, 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 in both Advanced and Extension 1.

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. It provides opportunities for students to develop rigorous mathematical arguments and proofs, and to use mathematical models extensively. It provides opportunities for students to develop their awareness of the interconnected nature of mathematics, its beauty and its functionality.

It provides a basis for progression to further study in mathematics or related disciplines where mathematics plays a vital role. It 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.

Prerequisites:  The Mathematics Extension 1 Year 11 course has been developed on the assumption that students have studied the content and successfully achieved the outcomes of the 5.3 content in Pathway A and Pathway E in Year 10, this may include the optional sub–strands:

· Polynomials

· Logarithms

· Functions and Other Graphs

· Circle Geometry

Content:  The Mathematics Extension 1 Year 11 course content is comprised of four Topics, with the Topics divided into Subtopics. The Mathematics Extension 1 Year 12 course content includes the Topics Trigonometric Functions and Calculus continued from Year 11 and introduces three different Topics.

The Topics and Subtopics (in brackets) are:

Year 11

•  Topic: Functions (Further Work with Functions and Polynomials)
•  Topic: Trigonometric Functions (Inverse Trigonometric Functions and Further Trigonometric Identities)
•  Topic: Calculus (Rates of Change)
•  Topic: Combinatorics (Working with Combinatorics)

Year 12

•  Topic: Proof (Proof by Mathematical Induction)
•  Topic: Vectors (Introductions to Vectors)
•  Topic: Trigonometric Functions and Trigonometric Equations)
•  Topic: Calculus (Further Calculus Skills and Applications of Calculus)
•  Topic: Statistical Analysis (The Binomial Distribution