Stage 2 Specialist Mathematics

Stage 2 Specialist Mathematics - Length | Full Year - (20 credit)

Specialist Mathematics draws on and deepens students’ mathematical knowledge, skills and understanding and provides opportunities for students to develop their skills in using rigorous mathematical arguments and proofs and using mathematical models. It includes the study of functions and calculus.

The subject leads to study in a range of tertiary courses such as mathematical sciences, engineering, computer science and physical sciences. Students envisaging careers in related fields will benefit from studying this subject.

Specialist Mathematics is designed to be studied in conjunction with Mathematical Methods.

The capabilities for this subject are literacy, numeracy, information and communication technology (ICT) capability, critical and creative thinking, personal and social capability, ethical understanding and intercultural understanding.

Content

Stage 2 Specialist Mathematics consists of the following six topics:

Topic 1: Mathematical Induction

1.1 Proof by Mathematical Induction

Topic 2: Complex Numbers

2.1 Cartesian and Polar Forms

2.2 The Complex (Argand) Plane

2.3 Roots of Complex Numbers

2.4 Factorisation of Polynomials

Topic 3: Functions and Sketching Graphs

3.1 Composition of Functions

3.2 One-to-one Functions

3.3 Sketching Graphs

Topic 4: Vectors in Three Dimensions

4.1 The Algebra of Vectors in Three Dimensions

4.2 Vector and Cartesian Equations

4.3 Systems of Linear Equations

Topic 5: Integrations Techniques and Applications

5.1 Integration Techniques

5.2 Applications of Integral Calculus

Topic 6: Rates of Change and Differential Equations

6.1 Implicit Differentiation

6.2 Differential Equations

6.3 Pairs of Varying Quantities – Polynomials of Degree 1 to 3

6.4 Related Rates, Velocity and Tangents

6.5 Trigonometric Parameterisations

Assessment

School-based Assessment (70%)
Assessment Type 1: Skills and Applications Tasks (50%)

Assessment Type 2: Mathematical Investigation (20%)

External Assessment (30%)
Assessment Type 3: Examination (30%)