# Stage 2 Specialist Mathematics

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5 Lessons

## SACE Stage 2 Specialist Mathematics – Mathematical Induction

1.1 Proof my Mathematical Induction 1.2 Divisibility Proof 1.3 Inequality Proof

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21 Lessons

## SACE Stage 2 Specialist Mathematics – 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

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14 Lessons

## SACE Stage 2 Specialist Mathematics – Functions and Sketching Graphs

3.1 Composition of functions 3.2 One-to-One Functions 3.3 Sketching Graphs

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20 Lessons

## SACE Stage 2 Specialist Mathematics – Vectors in Three Dimensions

4.1 The Algebra of Vectors in Three Dimensions 4.2 Vector and Cartesian Equations 4.3 Sydtems of Linear Equations

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22 Lessons

## SACE Stage 2 Specialist Mathematics – Integration Techniques and Applications

5.1 Integration Techniques 5.2 Applications of Integral Calculus

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10 Lessons

## SACE Stage 2 Specialist Mathematics – Rates of Change and Differential Equations

6.1 Implicit Differentiation 6.2 Differential Equations 6.3 Pairs of Varying Quantities - Polynomials 6.4 Related Rates, Velocity and Tangents 6.5 Trigonometric Parameterisations

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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 various 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.

Source – Subject Outline, South Australian Certificate of Education 2023