VCE Specialist Mathematics

Specialist Mathematics

1 Vectors - cartesian equations (incl 3D), planes, gaussian elimination and cross product)

1 Vectors - Linear Dependence and Independence

1 Vectors - Perpendicular Vectors, Modulus and Miscellaneous

1 Vectors - Scalar and Vector Resolutes

1 Vectors - The Angle Between Two Vectors

1 Vectors - Vector functions and Kinematics

2 Complex Numbers - Converting to Polar Form and De Moivre's Theorem

2 Complex Numbers - Factorising and Solving

3 Trigonometry - Compound and Double Angle Formulas, Symmetries and Identities (Year 11 Revision)

4 Differentiation - Differentiation (including Inverse Circular Functions)

4 Differentiation - Graphical Analysis Using Second Derivatives

4 Differentiation - Implicit Differentiation

4 Differentiation - Related Rates of Change

5 Functions - Absolute Value Functions

5 Functions - Hyperbolas, Ellipses and Circles

5 Functions - Reciprocal, Rational and Quotient Functions

6 Integration - Arc Length

6 Integration - Area Under a Curve

6 Integration - Integration Techniques: Miscellaneous

6 Integration - Integration Techniques: Substitution

6 Integration - Volumes of Solids of Revolution

7 Differential Equations - Direction (Slope) Fields

7 Differential Equations - Euler's Method

7 Differential Equations - Inflow-Outflow Mixing Problems

7 Differential Equations - Interpreting DEs, Verifying Solutions and Solving

7 Differential Equations - Separation of Variables

8 Kinematics - Alternate Forms: a(v), a(x), v(x), t(v), t(x)

8 Kinematics - Constant Acceleration Problems

8 Kinematics - Velocity-Time Graphs and Basic x(t) - v(t) - a(t) Conversion

Logic and Proof

ℴ10. Probability and Statistics - Confidence Intervals for Means

ℴ10. Probability and Statistics - Hypothesis Testing

ℴ10. Probability and Statistics - Linear Combinations of Random Variables

ℴ10. Probability and Statistics - Sample Mean Distributions

ℴ11. Extended Response - Calculus

ℴ11. Extended Response - Calculus - Differential Equations

ℴ11. Extended Response - Complex Numbers

ℴ11. Extended Response - Kinematics

ℴ11. Extended Response - Probability and Statistics

ℴ11. Extended Response - Vector Functions

ℴ11. Extended Response - Vectors

X Complex Numbers - Relations in the Complex Plane

X Complex Numbers - Relations in the Complex Plane