VCE Specialist Mathematics Units 1 and 2 – Algebra and Structure

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1.1 Whole Numbers
1.2 Number Skills
1.3 Number Sequences
1.4 Arithmetic Sequences and Series
1.5 Geometic Sequences and Series
1.6 Principal of Mathematical Induction
1.7 Complex Numbers

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Logic and algebra

Key knowledge
• the concepts of proposition, truth value, tautology, set and set operations
• the concepts of validity, argument and proof
• boolean operators, and axioms of boolean algebra
• gates and circuit diagrams.

Key skills
• represent and test the truth of propositions and validity of arguments using karnaugh maps and truth tables
• develop proofs of propositions in natural language and mathematics
• represent circuits using gates and simplify these circuits
• use boolean operators for searches in databases and by search engines.

Transformations, trigonometry and matrices

Key knowledge
• coordinate and matrix representation of points and transformations
• dilation, rotations and reflections and invariance properties
• the inverse transformations and composition of transformations
• trigonometric identities.

Key skills
• define and apply transformations to the plane and specify their effect on subsets of the plane
• identify the set of points that are invariant under a given transformation
• find and apply inverse transformations and composite transformations, and interpret their effects on subsets of the plane
• prove trigonometric identities and apply them to solve problems.

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