VCE Specialist Unit 1 Skills () « back to units

The skills below are aligned with the VCE Specialist Mathematics Study Design 2023-2027. Skills are organised into key areas: Proof & Number, Graph Theory, Logic & Algorithms, Sequences & Series, Combinatorics, Matrices, and Pseudocode & Algorithms. To master a skill, you will have to gain 10 stars.

There are 3 levels to each skill,

  1. Easy: A star will be taken away if you get 3 consecutive wrong answers.
  2. Medium: A star will be taken away if you get 2 consecutive wrong answers.
  3. Hard: A star will be taken away on each wrong answer.

Most skills have multiple types of questions with varying difficulties. If you keep getting wrong answers, the system may give you the simplest question to answer. The idea is to have you master these skills with a ground up approach. If you get an answer wrong, you can read the solution and helpful tips that briefly explain the skill/topic you are practising.

All the best with your VCE Specialist Unit 1. If you see any issue, please do report it by clicking the red button at bottom left of this page.

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  1. Proof & Number

    1. Number systems and sets FREE
    2. Divisibility properties
    3. Prime factorisation and GCD/LCM
    4. Proof by direct argument
    5. Proof by contradiction
    6. Proof by contrapositive
    7. Disproof by counterexample
    8. Induction: sums
    9. Induction: divisibility
    10. Induction: inequalities
    11. Surds and irrational numbers
    12. Set operations (union, intersection, complement)
    13. Quantifiers (for all, there exists)
    14. Logical connectives (and, or, not, implies)
    15. Truth tables
    16. Converse, inverse and contrapositive statements
    17. Valid and invalid arguments

  2. Graph Theory

    1. Vertices, edges and degree
    2. Simple graphs and subgraphs
    3. Graph isomorphism
    4. Connected graphs
    5. Complete graphs and complements
    6. Bipartite graphs
    7. Trees and spanning trees
    8. Planar graphs and Euler's formula
    9. Eulerian circuits and trails
    10. Hamiltonian paths and cycles
    11. Adjacency matrices
    12. Graph colouring
    13. Walks, paths and cycles
    14. Applications of graph theory

  3. Logic & Algorithms

    1. Pseudocode: variables and assignment
    2. Pseudocode: conditionals
    3. Pseudocode: loops
    4. Trace tables
    5. Sorting algorithms
    6. Searching algorithms
    7. Algorithm efficiency
    8. Euclidean algorithm
    9. Recursive algorithms
    10. Write pseudocode for a task
    11. Debug pseudocode

  4. Sequences & Series

    1. Arithmetic sequences
    2. Arithmetic series
    3. Geometric sequences
    4. Geometric series (finite)
    5. Infinite geometric series
    6. Recurrence relations
    7. Sequences and applications
    8. Sigma notation
    9. Partial fractions with sequences
    10. Fibonacci and special sequences
    11. Prove series formulas by induction
    12. Mixed sequences and series problems

  5. Combinatorics

    1. Multiplication principle
    2. Addition and complement principles
    3. Pigeonhole principle
    4. Inclusion-exclusion principle
    5. Permutations
    6. Combinations
    7. Pascal triangle and binomial theorem
    8. Counting with restrictions
    9. Combinatorics and probability

  6. Matrices

    1. Identify order and elements of a matrix
    2. Matrix addition and subtraction
    3. Scalar multiplication of matrices
    4. Matrix multiplication (conformability check)
    5. Identity matrix and zero matrix
    6. Determinant of a 2x2 matrix
    7. Determinant of a 3x3 matrix
    8. Inverse of a 2x2 matrix
    9. Solve 2x2 systems using matrices
    10. Solve 3x3 systems using matrices
    11. No solution or infinitely many solutions
    12. Matrices in practical problems (networks, transitions)

  7. Pseudocode & Algorithms

    1. Trace pseudocode for matrix operations
    2. Trace pseudocode for graph algorithms
    3. Trace pseudocode for sequence generation
    4. Trace pseudocode for sorting and searching
    5. Trace pseudocode for counting algorithms
    6. Write and debug pseudocode

The Foundation

Unit 1 builds the essential foundations of VCE Specialist Mathematics. Master these skills and you'll be well-prepared for Units 2, 3, and 4.

What Makes Unit 1 Special?

Proof & Logic

Learn to construct rigorous mathematical arguments

Graph Theory

Explore networks, paths, and graph properties

Algorithms

Pseudocode, sorting, searching, and efficiency

Sequences

Arithmetic, geometric, and special sequences

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