VCE Specialist Mathematics (Unit 1/2)

Specialist Mathematics (Unit 1/2)

1. Logic and algebra - Boolean algebra and sets

1. Logic and algebra - Electronic gates and circuits

1. Logic and algebra - Premises and conclusions (natural language)

1. Logic and algebra - Propositions, connectives and truth tables

10. Graphs of non-linear relations - Cartesian and polar coordinates

10. Graphs of non-linear relations - Graphs of polar relations

10. Graphs of non-linear relations - Locus definition algebra

10. Graphs of non-linear relations - Parametric functions and graphs

10. Graphs of non-linear relations - Reciprocal functions and graphs

10. Graphs of non-linear relations - Sketching circles, ellipses and hyerbolas

11. Kinematics - Constant acceleration formulae

11. Kinematics - Position, velocity and acceleration basics

11. Kinematics - Velocity-time graphs

12. Statistics - Sample and population proportions

12. Statistics - Sample proportions with conditional probability

12. Statistics - Simple random sampling calculations

2. Trigonometry - asin(x)+bcos(x) identity

2. Trigonometry - Compound and double angle formulae

2. Trigonometry - Identities

2. Trigonometry - Maximum and minimum values

2. Trigonometry - Solving trigonometric equations

3. Linear transformations - Dilations, reflections and translations

3. Linear transformations - Invariance, area and determinant

3. Linear transformations - Rotations and reflections in y=mx

4. Number systems and recursion - Proof by induction and contradiction

4. Number systems and recursion - Sequences

4. Number systems and recursion - Series

5. Complex numbers - Modulus and conjugate

5. Complex numbers - Operations, simplifying, Re(z) and Im(z)

5. Complex numbers - Solving equations

6. Principles of counting - Inclusion-exclusion principle

6. Principles of counting - nCr simplification with factorials

7. Graph theory - Edges, vertices, degree, faces and Euler's formula

7. Graph theory - Optimisation, existence, construction and counting problems

7. Graph theory - Types of graphs and adjacency matrices

7. Graph theory - Walks, trails, paths, cycles and circuits

8. Plane geometry and proof - Angle properties (lines and polygons)

8. Plane geometry and proof - Circle theorems

8. Plane geometry and proof - Pythagoras and trignometry in 2D and 3D

8. Plane geometry and proof - Similarity

8. Plane geometry and proof - Sine and cosine rules

9. Vectors - Magnitude and direction (incl unit, parallel and perpendicular vectors)

9. Vectors - Scalar (dot) product and vector resolutes

9. Vectors - Vector proofs

ℴ Extended reponse - Complex numbers

ℴ Extended reponse - Geometry in the plane and proof

ℴ Extended reponse - Graph theory

ℴ Extended reponse - Graphs of non-linear relations

ℴ Extended reponse - Kinematics

ℴ Extended reponse - Linear transformations with matrices

ℴ Extended reponse - Logic and algebra

ℴ Extended reponse - Sequences and series

ℴ Extended reponse - Statistics

ℴ Extended reponse - Trigonometric functions

ℴ Extended reponse - Vectors

ℴ Extended reponse - Vectors