VCE Specialist Mathematics Units 1 and 2 – Algebra and Structure

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Description

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




Additional information

Outcome

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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