Unit 1: Proof, Graph Theory, Sequences & Matrices

VCE Specialist Mathematics Study Design 2023-2027

Units 1 & 2 (School-Assessed) 81 Skills • 3 Levels Each

Unit 1 Skill Map

Proof & Number, Graph Theory, Logic & Algorithms, Sequences & Series, Combinatorics, Matrices, and Pseudocode & Algorithms.

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Proof & Number

17 skills

Number systems and sets FREE21001 Divisibility properties21002 Prime factorisation and GCD/LCM21003 Proof by direct argument21004 Proof by contradiction21005 Proof by contrapositive21006 Disproof by counterexample21007 Induction: sums21008 Induction: divisibility21009 Induction: inequalities21010 Surds and irrational numbers21011 Set operations (union, intersection, complement)21012 Quantifiers (for all, there exists)21013 Logical connectives (and, or, not, implies)21014 Truth tables21015 Converse, inverse and contrapositive statements21016 Valid and invalid arguments21017

Graph Theory

14 skills

Vertices, edges and degree21020 Simple graphs and subgraphs21021 Graph isomorphism21022 Connected graphs21023 Complete graphs and complements21024 Bipartite graphs21025 Trees and spanning trees21026 Planar graphs and Euler's formula21027 Eulerian circuits and trails21028 Hamiltonian paths and cycles21029 Adjacency matrices21030 Graph colouring21031 Walks, paths and cycles21032 Applications of graph theory21033

Logic & Algorithms

11 skills

Pseudocode: variables and assignment21040 Pseudocode: conditionals21041 Pseudocode: loops21042 Trace tables21043 Sorting algorithms21044 Searching algorithms21045 Algorithm efficiency21046 Euclidean algorithm21047 Recursive algorithms21048 Write pseudocode for a task21049 Debug pseudocode21050

Sequences & Series

12 skills

Arithmetic sequences21055 Arithmetic series21056 Geometric sequences21057 Geometric series (finite)21058 Infinite geometric series21059 Recurrence relations21060 Sequences and applications21061 Sigma notation21062 Partial fractions with sequences21063 Fibonacci and special sequences21064 Prove series formulas by induction21065 Mixed sequences and series problems21066

Combinatorics

9 skills

Multiplication principle21070 Addition and complement principles21071 Pigeonhole principle21072 Inclusion-exclusion principle21073 Permutations21074 Combinations21075 Pascal triangle and binomial theorem21076 Counting with restrictions21077 Combinatorics and probability21078

Matrices

12 skills

Identify order and elements of a matrix21080 Matrix addition and subtraction21081 Scalar multiplication of matrices21082 Matrix multiplication (conformability check)21083 Identity matrix and zero matrix21084 Determinant of a 2x2 matrix21085 Determinant of a 3x3 matrix21086 Inverse of a 2x2 matrix21087 Solve 2x2 systems using matrices21088 Solve 3x3 systems using matrices21089 No solution or infinitely many solutions21090 Matrices in practical problems (networks, transitions)21091

Pseudocode & Algorithms

6 skills

Trace pseudocode for matrix operations21095 Trace pseudocode for graph algorithms21096 Trace pseudocode for sequence generation21097 Trace pseudocode for sorting and searching21098 Trace pseudocode for counting algorithms21099 Write and debug pseudocode21100