# Year 11 Mathematics Specialist

The Mathematics Specialist is an ATAR course which provides opportunities, beyond those presented in the Mathematics Methods ATAR course, to develop rigorous mathematical arguments and proofs, and to use mathematical models more extensively. The Mathematics Specialist ATAR course contains topics in functions and calculus that build on and deepen the ideas presented in the Mathematics Methods ATAR course, as well as demonstrate their application in many areas. This course also extends understanding and knowledge of statistics and introduces the topics of vectors, complex numbers and matrices. The Mathematics Specialist ATAR course is the only ATAR mathematics course that should not be taken as a stand-alone course.

#### Prerequisites:

Minimum is A grade in Year 10 Pathway A Mathematics.

#### Syllabus:

The Year 11 syllabus is divided into two units, each of one semester duration, which are typically delivered as a pair. The notional time for each unit is 55 class contact hours.

##### Unit 1

Unit 1 contains the three topics:

1.1 Combinatorics
1.2 Vectors in the plane
1.3 Geometry

The three topics in Unit 1 complement the content of the Mathematics Methods ATAR course. The proficiency strand of Reasoning, from the Year 7–10 curriculum, is continued explicitly in the topic Geometry through a discussion of developing mathematical arguments. This topic also provides the opportunity to summarise and extend students’ studies in Euclidean Geometry, knowledge which is of great benefit in the later study of topics such as vectors and complex numbers. The topic Combinatorics provides techniques that are very useful in many areas of mathematics, including probability and algebra. The topic Vectors in the plane provides new perspectives on working with two-dimensional space and serves as an introduction to techniques which can be extended to three-dimensional space in Unit 3. These three topics considerably broaden students’ mathematical experience and therefore begin an awakening to the breadth and utility of the subject. They also enable students to increase their mathematical flexibility and versatility.

##### Unit 2

Unit 2 contains the three topics:

2.1 Trigonometry
2.2 Matrices
2.3 Real and complex numbers

In Unit 2, Matrices provide new perspectives for working with two-dimensional space and Real and complex numbers provides a continuation of the study of numbers. The topic Trigonometry contains techniques that are used in other topics in both this unit and Units 3 and 4. All topics develop students’ ability to construct mathematical arguments. The technique of proof by the principle of mathematical induction is introduced in this unit.

#### Assessments:

Response: 40%
Investigation: 20%.
Examination: 40%