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VCE Specialist Mathematics (Unit 1/2)
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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
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