Discrete Mathematics
On this page:
- Logic, Number Systems, and Proof
- Sequences and Series
- Matrices
- Combinatorics
- Graphs and Networks
Logic, Number Systems, and Proof
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Notes
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Videos & Interactives
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Questions
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Exam Questions
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Propositional Logic and Truth Tables
Karnaugh Maps
Boolean Algebra
Number Systems
Sets and Set Notation
Prime Numbers
Conversion between Fraction and Decimal Forms
Binary Number System
Place Value and Bases Other than Ten
Arguments and Validity
Logic Gates and Circuits
Algorithms
Pseudocode and Algorithms
Principles of Proof
Simple Proofs
Conjectures, Quantified, Examples, Implications, Equivalences
Natural Deduction and Proof Techniques
Proof by Mathematical Induction
Proofs involving Sums and Products
Karnaugh Maps
Boolean Algebra
Number Systems
Sets and Set Notation
Prime Numbers
Conversion between Fraction and Decimal Forms
Binary Number System
Place Value and Bases Other than Ten
Arguments and Validity
Logic Gates and Circuits
Algorithms
Pseudocode and Algorithms
Principles of Proof
Simple Proofs
Conjectures, Quantified, Examples, Implications, Equivalences
Natural Deduction and Proof Techniques
Proof by Mathematical Induction
Proofs involving Sums and Products
Summation notation or Sigma Notation (Joel Speranza Math Video)
Python - VCAA Pseudocode (Simon Tyler Notes)
Inequality Proof - Fraction Sum
Introduction to Fundamental Math Proof Techniques (PatrickJMT Video)
Truth Table Generator (Stanford Interactive)
Truth Table to Karnaugh Map (Charlie Coleman Interactive)
Boolean Algebra Solver (Boolean Algebra Interactive)
Representing Numbers and Letters with Binary (Crash Course Video)
Boolean Logic & Logic Gates (Crash Course Video)
Logic Gate Truth Table Check (GeoGebra Interactive)
Logic Circuit Simulator (Logic.ly Interactive)
Computer Science Basics: Sequences, Selections, and Loops (GCF Learn Free Video)
Mathematician Explains Infinity in 5 Levels of Difficulty (Emily Riehl on WIRED Video)
Mathematical Notation: ∀ "For all" and ∃ "There Exists" (Joel Speranza Math Video)
An introduction to mathematics theorems (TED-Ed Video)
Direct Proof (Joel Speranza Math Video)
Proof by Contradiction (Joel Speranza Math Video)
Proof by Contrapositive (Joel Speranza Math Video)
Disproving Statements (Joel Speranza Math Video)
Equivalent Statements (Joel Speranza Math Video)
Proof by Contradiction
Proving a Converse Statement
Four Basic Proof Techniques Used in Mathematics (patrickJMT Video)
Introduction to the Nature of Proof
Foundations of Proof
Negating Compound Statements
Implications & Contrapositives
Proof: a³ - a is always divisible by 6
Proof by Contraposition (Eddie Woo Video)
Proof by Contradiction: log₂5 is irrational (Eddie Woo Video)
Proof - Odd composite numbers
Proving Algebraic Inequalities
Proof: √3 + √2 is irrational (Eddie Woo Video)
Proof: Mersenne primes (Eddie Woo Video)
Irrational Logarithm Proof
Mathematical Induction - Base case above 1
Mathematical Induction (increments greater than 1) (Eddie Woo Video)
Induction with Sigma Notation
Induction - Recursive Formulas
Divisibility Proof
How many subsets in a set?
Python - VCAA Pseudocode (Simon Tyler Notes)
Inequality Proof - Fraction Sum
- Algebraic approach (Eddie Woo Video)
- Graphical representation (Eddie Woo Video)
- Applying calculus (Eddie Woo Video)
Introduction to Fundamental Math Proof Techniques (PatrickJMT Video)
Truth Table Generator (Stanford Interactive)
Truth Table to Karnaugh Map (Charlie Coleman Interactive)
Boolean Algebra Solver (Boolean Algebra Interactive)
Representing Numbers and Letters with Binary (Crash Course Video)
Boolean Logic & Logic Gates (Crash Course Video)
Logic Gate Truth Table Check (GeoGebra Interactive)
Logic Circuit Simulator (Logic.ly Interactive)
Computer Science Basics: Sequences, Selections, and Loops (GCF Learn Free Video)
Mathematician Explains Infinity in 5 Levels of Difficulty (Emily Riehl on WIRED Video)
Mathematical Notation: ∀ "For all" and ∃ "There Exists" (Joel Speranza Math Video)
An introduction to mathematics theorems (TED-Ed Video)
Direct Proof (Joel Speranza Math Video)
Proof by Contradiction (Joel Speranza Math Video)
Proof by Contrapositive (Joel Speranza Math Video)
Disproving Statements (Joel Speranza Math Video)
Equivalent Statements (Joel Speranza Math Video)
Proof by Contradiction
- How does it work? (Eddie Woo Video)
- Infinite Primes Example (Eddie Woo Video)
Proving a Converse Statement
- Investigating original proposition (Eddie Woo Video)
- Considering the contrapositive (Eddie Woo Video)
- Using the inverse (Eddie Woo Video)
Four Basic Proof Techniques Used in Mathematics (patrickJMT Video)
Introduction to the Nature of Proof
- Prologue (Eddie Woo Video)
- Building blocks (Eddie Woo Video)
- Liars & truth-tellers (Eddie Woo Video)
Foundations of Proof
- Statements, implications, negations (Eddie Woo Video)
- Equivalence & quantifiers (Eddie Woo Video)
Negating Compound Statements
- Reviewing the basics (Eddie Woo Video)
- And, Or, Quantifiers (Eddie Woo Video)
Implications & Contrapositives
- How do they relate? (Eddie Woo Video)
- Further examples (Eddie Woo Video)
Proof: a³ - a is always divisible by 6
- Two different approaches (Eddie Woo Video)
- Proof by exhaustion (Eddie Woo Video)
- By contradiction (Eddie Woo Video)
Proof by Contraposition (Eddie Woo Video)
Proof by Contradiction: log₂5 is irrational (Eddie Woo Video)
Proof - Odd composite numbers
- Setup (Eddie Woo Video)
- Understanding the negation (Eddie Woo Video)
Proving Algebraic Inequalities
- Introductory principles (Eddie Woo Video)
- Using the sign (Eddie Woo Video)
Proof: √3 + √2 is irrational (Eddie Woo Video)
Proof: Mersenne primes (Eddie Woo Video)
Irrational Logarithm Proof
- By cases (Eddie Woo Video)
- By graphing (Eddie Woo Video)
Mathematical Induction - Base case above 1
- Introduction (Eddie Woo Video)
- Completing the proof (Eddie Woo Video)
- Additional method (Eddie Woo Video)
Mathematical Induction (increments greater than 1) (Eddie Woo Video)
Induction with Sigma Notation
- Basic example (Eddie Woo Video)
- Binomial Theorem - setting up proof (Eddie Woo Video)
- Binomial Theorem - completing proof (Eddie Woo Video)
- Binomial Theorem - Pascal's Identity (Eddie Woo Video)
Induction - Recursive Formulas
- Basic example (Eddie Woo Video)
- Sum of an arithmetic progression (Eddie Woo Video)
Divisibility Proof
- Sum of 7 consecutive integers (Eddie Woo Video)
- Using algebraic expansion (Eddie Woo Video)
How many subsets in a set?
- Induction proof (Eddie Woo Video)
- Combinatorial proof (Eddie Woo Video)
Solutions to past VCAA exam questions can be looked up in the appropriate examiner's report on the Specialist Mathematics Past Examinations and Examination Reports page or the Northern Hemisphere Timetable (NHT) Past Examinations and Examination Reports page.
Solutions to past VCAA Algorithmics exam questions can be looked up in the appropriate examiner's report on the Algorithmics Past Examinations and Examination Reports page.
Pseudocode
Logic
Proof by Induction
Solutions to past VCAA Algorithmics exam questions can be looked up in the appropriate examiner's report on the Algorithmics Past Examinations and Examination Reports page.
Pseudocode
Logic
Proof by Induction
Sequences and Series
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Notes
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Videos & Interactives
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Questions
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Exam Questions
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Sequences and Series
The Arithmetic Sequence and Series
The Geometric Sequence and Series
Converting Implicit Equations to Explicit Equations
Number Patterns and Sequences
Displays of Sequences and their Behaviour
The Arithmetic Sequence
Arithmetic Applications
The Geometric Sequence
Geometric Applications
The Fibonacci Sequence
Sequences and Series Technology
Casio
TI-nSpire
The Arithmetic Sequence and Series
The Geometric Sequence and Series
Converting Implicit Equations to Explicit Equations
Number Patterns and Sequences
Displays of Sequences and their Behaviour
The Arithmetic Sequence
Arithmetic Applications
The Geometric Sequence
Geometric Applications
The Fibonacci Sequence
Sequences and Series Technology
Casio
TI-nSpire
Partial Sums / Series
Sum of an Arithmetic Progression
Arithmetic Series Formula Where it comes from and how to use it (Joel Speranza Math Video)
Arithmetic Series resulting in a quadratic (Joel Speranza Math Video)
Intro to Geometric Progressions
Series & Sequences: Finding a General Term from the Sum Formula (Eddie Woo Video)
Limiting Sum
Limiting Sum Applications
Number Patterns (MaffsGuru Video)
Arithmetic sequence applications (MaffsGuru Video)
Using a recurrence relationship with arithmetic sequences (MaffsGuru Video)
Geometric sequences (MaffsGuru Video)
Geometric sequence applications (MaffsGuru Video)
Using a recurrence relation to generate and analyse a geometric sequence (MaffsGuru Video)
Using recurrence relationships to model growth and decay (MaffsGuru Video)
- Adding up Terms in an Arithmetic Progression (Eddie Woo Video)
- Devising a Formula (Eddie Woo Video)
Sum of an Arithmetic Progression
- Visual Derivation of Formula (Eddie Woo Video)
- Developing & Using Alternate Formula (Eddie Woo Video)
- Determining Series Length (Eddie Woo Video)
Arithmetic Series Formula Where it comes from and how to use it (Joel Speranza Math Video)
Arithmetic Series resulting in a quadratic (Joel Speranza Math Video)
Intro to Geometric Progressions
- Definitions (Eddie Woo Video)
- Algebraic Derivation of Sum Formula (Eddie Woo Video)
- Different Versions of Sum Formula (Eddie Woo Video)
Series & Sequences: Finding a General Term from the Sum Formula (Eddie Woo Video)
Limiting Sum
- Introduction (Eddie Woo Video)
- Application to Recurring Decimals (Eddie Woo Video)
- Rigorous Definition (Eddie Woo Video)
Limiting Sum Applications
- Derivation of Formula (Eddie Woo Video)
- Visual Interpretation & Recurring Decimals (Eddie Woo Video)
- Probability Problem (Eddie Woo Video)
Number Patterns (MaffsGuru Video)
Arithmetic sequence applications (MaffsGuru Video)
Using a recurrence relationship with arithmetic sequences (MaffsGuru Video)
Geometric sequences (MaffsGuru Video)
Geometric sequence applications (MaffsGuru Video)
Using a recurrence relation to generate and analyse a geometric sequence (MaffsGuru Video)
Using recurrence relationships to model growth and decay (MaffsGuru Video)
Generating Sequences from the nth Term (Minimally Different)
Is a Term in a Given Sequence (Minimally Different)
Linear Patterns, Formula, Tables and Graphs (Starting Points Maths)
Linear Sequences - Structured Variation Grid (Maths Bot)
Linear Sequences (Maths Bot)
Sequences (Corbettmaths)
Sequences (Corbettmaths Exam Style)
Straight-Line Graphs and Sequences (Mr Day Maths)
nth Term of a Sequence (Corbettmaths)
nth Term of a Geometric Sequence (Variation Theory)
nth term with Cuisenaire Rods (Purposeful Maths)
Recurrence Relations (Starting Points Maths)
Sequences of Patterns (Corbettmaths)
Sequences - Patterns (Corbettmaths Exam Style)
Is a Term in a Given Sequence (Minimally Different)
Linear Patterns, Formula, Tables and Graphs (Starting Points Maths)
Linear Sequences - Structured Variation Grid (Maths Bot)
Linear Sequences (Maths Bot)
Sequences (Corbettmaths)
Sequences (Corbettmaths Exam Style)
Straight-Line Graphs and Sequences (Mr Day Maths)
nth Term of a Sequence (Corbettmaths)
nth Term of a Geometric Sequence (Variation Theory)
nth term with Cuisenaire Rods (Purposeful Maths)
Recurrence Relations (Starting Points Maths)
Sequences of Patterns (Corbettmaths)
Sequences - Patterns (Corbettmaths Exam Style)
Solutions to past VCAA exam questions can be looked up in the appropriate examiner's report on the General Mathematics Past Examinations and Examination Reports page or the Northern Hemisphere Timetable (NHT) Past Examinations and Examination Reports page.
First Order Recursion Relations
Recursion (Applications)
Recursion (Finance)
Using Rules (Applications)
Using Rules (Interest)
Using Rules (Depreciation)
Graphs of Sequences
Type of Sequence and Common Differences and Ratios
Fibonacci and Similar Sequences
Series
First Order Recursion Relations
Recursion (Applications)
Recursion (Finance)
Using Rules (Applications)
Using Rules (Interest)
Using Rules (Depreciation)
Graphs of Sequences
Type of Sequence and Common Differences and Ratios
Fibonacci and Similar Sequences
Series
Matrices
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Notes
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Videos & Interactives
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Questions
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Exam Questions
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Matrices and Their Applications
Matrices and the Order of a Matrix
Elements of a Matrix
Transpose of a Matrix
Elementary Matrix Operations
Identity Matrices and the Inverse of a Matrix
Determinant and Inverse of a Matrix Manually (Optional)
Matrix Representation of Numerical Information
Rules for the a_ijth Element of a Matrix
Binary and Permutation Matrices
Communication and Dominance Matrices
Diagonal and Triangular Matrices
Transition Matrices
Transition and Leslie Matrices
Matrix Recursion Relations
Steady State and the Long Term
Steady State for 2x2 Transitions Matrices using a Rule (Optional)
Transition Matrices with Culling and Restocking
Matrices Technology
TI-nSpire
Casio
Matrices and the Order of a Matrix
Elements of a Matrix
Transpose of a Matrix
Elementary Matrix Operations
Identity Matrices and the Inverse of a Matrix
Determinant and Inverse of a Matrix Manually (Optional)
Matrix Representation of Numerical Information
Rules for the a_ijth Element of a Matrix
Binary and Permutation Matrices
Communication and Dominance Matrices
Diagonal and Triangular Matrices
Transition Matrices
Transition and Leslie Matrices
Matrix Recursion Relations
Steady State and the Long Term
Steady State for 2x2 Transitions Matrices using a Rule (Optional)
Transition Matrices with Culling and Restocking
Matrices Technology
TI-nSpire
Casio
What is a Matrix? (Maffs Guru Video)
Using Matrices to Represent Information (Maffs Guru Video)
Matrix Arithmetic: Addition, Subtraction, and Scalar Multiplication (Maffs Guru Video)
Matrix Arithmetic: The Product of Two Matrices (Maffs Guru Video)
Multiplying Matrices by Each Other (Joel Speranza Math Video)
Matrix Powers (Maffs Guru Video)
How to organise, add and multiply matrices (TED-Ed Video)
Matrix Equality (Joel Speranza Math Video)
Matrix Calculations on the TI Nspire (Joel Speranza Math Video)
Storing Information in Matrices (Joel Speranza Math Video)
Using matrices to manipulate data: Game show (Khan Academy Video)
Using matrices to manipulate data: Pet store (Khan Academy Video
An Application of Matrix Multiplication (Joel Speranza Math Video)
Transpose of a Matrix and an Application of a Matrix Transpose (Joel Speranza Math Video)
Communication Matrices (Joel Speranza Math Video)
The Identity Matrix (Joel Speranza Math Video)
Intro to determinant notation and computation (Khan Academy Video)
The Inverse Matrix (Maffs Guru Video)
The Multiplicative Inverse of a Matrix (Joel Speranza Math Video)
Solving Matrix Equations using the Multiplicative Inverse (Joel Speranza Math Video)
Simultaneous Equations using Matrices (Joel Speranza Math Video)
Applications of the Inverse Matrix Solving Simultaneous Linear Equations (Maffs Guru Video)
Transition Matrices and their Applications (Maffs Guru Video)
Leslie Matrices for Population Age Distribution Modelling (Joel Speranza Math Video)
Leslie Matrices - What's really going on? (Joel Speranza Math Video)
Leslie Matrices (Maffs Guru Video)
Using Matrices to Represent Information (Maffs Guru Video)
Matrix Arithmetic: Addition, Subtraction, and Scalar Multiplication (Maffs Guru Video)
Matrix Arithmetic: The Product of Two Matrices (Maffs Guru Video)
Multiplying Matrices by Each Other (Joel Speranza Math Video)
Matrix Powers (Maffs Guru Video)
How to organise, add and multiply matrices (TED-Ed Video)
Matrix Equality (Joel Speranza Math Video)
Matrix Calculations on the TI Nspire (Joel Speranza Math Video)
Storing Information in Matrices (Joel Speranza Math Video)
Using matrices to manipulate data: Game show (Khan Academy Video)
Using matrices to manipulate data: Pet store (Khan Academy Video
An Application of Matrix Multiplication (Joel Speranza Math Video)
Transpose of a Matrix and an Application of a Matrix Transpose (Joel Speranza Math Video)
Communication Matrices (Joel Speranza Math Video)
The Identity Matrix (Joel Speranza Math Video)
Intro to determinant notation and computation (Khan Academy Video)
The Inverse Matrix (Maffs Guru Video)
The Multiplicative Inverse of a Matrix (Joel Speranza Math Video)
Solving Matrix Equations using the Multiplicative Inverse (Joel Speranza Math Video)
Simultaneous Equations using Matrices (Joel Speranza Math Video)
Applications of the Inverse Matrix Solving Simultaneous Linear Equations (Maffs Guru Video)
Transition Matrices and their Applications (Maffs Guru Video)
Leslie Matrices for Population Age Distribution Modelling (Joel Speranza Math Video)
Leslie Matrices - What's really going on? (Joel Speranza Math Video)
Leslie Matrices (Maffs Guru Video)
Elements of a Matrix (mathworksheets4kids)
Addition of Square Matrices (mathworksheets4kids)
Addition of Matrices (mathworksheets4kids)
Subtraction of Square Matrices (mathworksheets4kids)
Subtraction of Matrices (mathworksheets4kids)
Scalar Multiplication of Matrices (mathworksheets4kids)
Multiplication of Square Matrices (mathworksheets4kids)
Multiplication of Matrices 1 (mathworksheets4kids)
Multiplication of Matrices 2 (mathworksheets4kids)
Order of Matrix Products 1 (mathworksheets4kids)
Order of Matrix Products 2 (mathworksheets4kids)
Matrix Arithmetic (Corbettmaths Exam Style)
Determinant of 2×2 Matrices 1 (mathworksheets4kids)
Determinant of 2×2 Matrices 2 (mathworksheets4kids)
2×2 Determinant Practice (Interactive Practice)
Determinant of 3×3 Matrices (mathworksheets4kids)
Check if Inverse Exists (mathworksheets4kids)
Inverse of 2×2 Matrices (mathworksheets4kids)
Inverse of 3×3 Matrices (mathworksheets4kids)
Addition of Square Matrices (mathworksheets4kids)
Addition of Matrices (mathworksheets4kids)
Subtraction of Square Matrices (mathworksheets4kids)
Subtraction of Matrices (mathworksheets4kids)
Scalar Multiplication of Matrices (mathworksheets4kids)
Multiplication of Square Matrices (mathworksheets4kids)
Multiplication of Matrices 1 (mathworksheets4kids)
Multiplication of Matrices 2 (mathworksheets4kids)
Order of Matrix Products 1 (mathworksheets4kids)
Order of Matrix Products 2 (mathworksheets4kids)
Matrix Arithmetic (Corbettmaths Exam Style)
Determinant of 2×2 Matrices 1 (mathworksheets4kids)
Determinant of 2×2 Matrices 2 (mathworksheets4kids)
2×2 Determinant Practice (Interactive Practice)
Determinant of 3×3 Matrices (mathworksheets4kids)
Check if Inverse Exists (mathworksheets4kids)
Inverse of 2×2 Matrices (mathworksheets4kids)
Inverse of 3×3 Matrices (mathworksheets4kids)
Solutions to past VCAA exam questions can be looked up in the appropriate examiner's report on the Further Mathematics Past Examinations and Examination Reports page or the Northern Hemisphere Timetable (NHT) Past Examinations and Examination Reports page. Exam 1 is multiple choice. Exam 2 is short answer.
Order and Elements of Matrices (2016-2022 Study Design Questions)
Order and Elements of Matrices (2000-2015 Study Design Questions)
Matrix Arithmetic (2016-2022 Study Design Questions)
Matrix Arithmetic (2000-2015 Study Design Questions)
Numerical Information in Matrices (2016-2022 Study Design Questions)
Numerical Information in Matrices (2000-2015 Study Design Questions)
Inverse Matrix (2016-2022 Study Design Questions)
Inverse Matrix (2000-2015 Study Design Questions)
Communication and Dominance (2016-2022 Study Design Questions)
Communication and Dominance (2000-2015 Study Design Questions)
Systems of Linear Equations (2016-2022 Study Design Questions)
Systems of Linear Equations (2000-2015 Study Design Questions)
Transition Matrices and Diagrams (2016-2022 Study Design Questions)
Transition Matrices and Diagrams (2000-2015 Study Design Questions)
Matrix Recursion S_(n+1)=TS_n (2016-2022 Study Design Questions)
Matrix Recursion S_(n+1)=TS_n (2000-2015 Study Design Questions)
Steady State / Equilibrium State / Long Term (2016-2022 Study Design Questions)
Steady State / Equilibrium State / Long Term (2000-2015 Study Design Questions)
Matrix Recursion S_(n+1)=TS_n+B (2016-2022 Study Design Questions)
Matrix Recursion S_(n+1)=TS_n+B (2000-2015 Study Design Questions)
Order and Elements of Matrices (2016-2022 Study Design Questions)
Order and Elements of Matrices (2000-2015 Study Design Questions)
Matrix Arithmetic (2016-2022 Study Design Questions)
Matrix Arithmetic (2000-2015 Study Design Questions)
Numerical Information in Matrices (2016-2022 Study Design Questions)
Numerical Information in Matrices (2000-2015 Study Design Questions)
Inverse Matrix (2016-2022 Study Design Questions)
Inverse Matrix (2000-2015 Study Design Questions)
Communication and Dominance (2016-2022 Study Design Questions)
Communication and Dominance (2000-2015 Study Design Questions)
Systems of Linear Equations (2016-2022 Study Design Questions)
Systems of Linear Equations (2000-2015 Study Design Questions)
Transition Matrices and Diagrams (2016-2022 Study Design Questions)
Transition Matrices and Diagrams (2000-2015 Study Design Questions)
Matrix Recursion S_(n+1)=TS_n (2016-2022 Study Design Questions)
Matrix Recursion S_(n+1)=TS_n (2000-2015 Study Design Questions)
Steady State / Equilibrium State / Long Term (2016-2022 Study Design Questions)
Steady State / Equilibrium State / Long Term (2000-2015 Study Design Questions)
Matrix Recursion S_(n+1)=TS_n+B (2016-2022 Study Design Questions)
Matrix Recursion S_(n+1)=TS_n+B (2000-2015 Study Design Questions)
Combinatorics
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Notes
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Videos & Interactives
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Questions
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Exam Questions
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Things get weird at infinity (Zach Star Video)
This set has infinite size, zero length, and a fractional dimension (Zach Star Video)
Addition and Multiplication Principles (Joel Speranza Math Video)
Factorials! (Joel Speranza Math Video)
Pigeonhole Principle (Joel Speranza Math Video)
The Pigeon Hole Principle: 7 gorgeous proofs (Mathologer Video)
Basic Set Theory (Joel Speranza Math Video)
The Inclusion Exclusion Principle for 2 and 3 Sets (Joel Speranza Math Video)
Pigeonhole Principle
Permutations (Joel Speranza Math Video)
Permutations of Like Objects (Joel Speranza Math Video)
Permutations with Restrictions (Joel Speranza Math Video)
Arrangements in a Circle (Joel Speranza Math Video)
Combinations (Joel Speranza Math Video)
Pascal's Triangle and Subsets of a Set (Joel Speranza Math Video)
Probability with permutations & combinations example: taste testing (Khan Academy Video)
Combinations with Restrictions (Joel Speranza Math Video)
Compound Probability: Counting (Seeing Theory Interactive)
The mathematical secrets of Pascal's Triangle (TED-Ed Video)
This set has infinite size, zero length, and a fractional dimension (Zach Star Video)
Addition and Multiplication Principles (Joel Speranza Math Video)
Factorials! (Joel Speranza Math Video)
Pigeonhole Principle (Joel Speranza Math Video)
The Pigeon Hole Principle: 7 gorgeous proofs (Mathologer Video)
Basic Set Theory (Joel Speranza Math Video)
The Inclusion Exclusion Principle for 2 and 3 Sets (Joel Speranza Math Video)
Pigeonhole Principle
- Establishing a pattern (Eddie Woo Video)
- Generalising the cases (Eddie Woo Video)
Permutations (Joel Speranza Math Video)
Permutations of Like Objects (Joel Speranza Math Video)
Permutations with Restrictions (Joel Speranza Math Video)
Arrangements in a Circle (Joel Speranza Math Video)
Combinations (Joel Speranza Math Video)
Pascal's Triangle and Subsets of a Set (Joel Speranza Math Video)
Probability with permutations & combinations example: taste testing (Khan Academy Video)
Combinations with Restrictions (Joel Speranza Math Video)
Compound Probability: Counting (Seeing Theory Interactive)
The mathematical secrets of Pascal's Triangle (TED-Ed Video)
Graphs and Networks
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Notes
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Videos & Interactives
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Questions
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Exam Questions
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Graphs and Networks
Graphs and Networks
Euler's Formula for Planar Graphs
Degree of a Face
Matrix Representation
Exploring and Travelling Problems
Traversable Graphs
Exploring Problems - Eulerian Trails and Circuits
Travelling Problems - Hamiltonian Paths and Cycles
Trees and Minimum Connector Problems
Trees and Spanning Trees
Minimum Connector Problems and Prim's Algorithm
Flow Problems
Flow Problems and the Maximum-Flow Minimum-Cut Theorem
Shortest Path Problems
Shortest Path Problems and Dijkstra's Algorithm
Matching Problems
Matching Problems and the Hungarian Algorithm
Scheduling Problems and Critical Path Analysis
Activity Networks
Scheduling Problems and Critical Path Analysis
Project Crashing
Graphs
Degree of a Vertex
Simple Graphs, Subgraphs, and Isomorphism
Connectedness, Complete and Complement Graphs
Bipartite Graphs, Trees, and Regular Graphs
Planar Graphs
Types of Walks on Graphs
Graphs and Networks
Euler's Formula for Planar Graphs
Degree of a Face
Matrix Representation
Exploring and Travelling Problems
Traversable Graphs
Exploring Problems - Eulerian Trails and Circuits
Travelling Problems - Hamiltonian Paths and Cycles
Trees and Minimum Connector Problems
Trees and Spanning Trees
Minimum Connector Problems and Prim's Algorithm
Flow Problems
Flow Problems and the Maximum-Flow Minimum-Cut Theorem
Shortest Path Problems
Shortest Path Problems and Dijkstra's Algorithm
Matching Problems
Matching Problems and the Hungarian Algorithm
Scheduling Problems and Critical Path Analysis
Activity Networks
Scheduling Problems and Critical Path Analysis
Project Crashing
Graphs
Degree of a Vertex
Simple Graphs, Subgraphs, and Isomorphism
Connectedness, Complete and Complement Graphs
Bipartite Graphs, Trees, and Regular Graphs
Planar Graphs
Types of Walks on Graphs
Rediscovering Euler's Formula with a Mug (not that Euler's Formula) (3Brown1Blue Video)
Euler's Formula and Graph Duality (3Brown1Blue Video)
The Bridges of Konigsberg
Vertices and Edges (D3 Graph Theory Interactive)
Degree of a Vertex (D3 Graph Theory Interactive)
Complete Graph (D3 Graph Theory Interactive)
Graphs and Networks (Maffs Guru Video)
Adjacency Matrices (Maffs Guru Video)
Planar Graphs Introduction - Equivalent (Isomorphic Graphs) and Drawing Graphs in Planar Form (Joel Speranza Math Video)
Planar Graphs - Euler's Formula (Joel Speranza Math Video)
Planar Graphs (Numberphile Video)
Walk (D3 Graph Theory Interactive)
Open vs Closed Walks (D3 Graph Theory Interactive)
Networks: Open and Closed Walks (Joel Speranza Math Video)
Connectivity (D3 Graph Theory Interactive)
Networks Trails and Paths (Joel Speranza Math Video)
Networks Weighted Graphs Shortest Paths and the Travelling Salesperson Problem (Joel Speranza Math Video)
Networks: Eulerian Graphs and Semi-Eulerian Graphs (Joel Speranza Math Video)
Eulerian Circuit (D3 Graph Theory Interactive)
Eulerian Trail (D3 Graph Theory Interactive)
Hamiltonian and Semi Hamiltonian Graphs (Joel Speranza Math Video)
Exploring and travelling (Maffs Guru Video)
Networks: Intro to Trees (Joel Speranza Math Video)
Networks: Prim's Algorithm for Finding Minimum Spanning Trees (Joel Speranza Math Video)
Trees (D3 Graph Theory Interactive)
Spanning Tree of a Graph (D3 Graph Theory Interactive)
Prim's Algorithm Solver (Jake Baker Maths Interactive)
Trees and minimum connector problems (Maffs Guru Video)
Flow problems (Maffs Guru Video)
Maximum Flow Minimum Cut Algorithm (Joel Speranza Math Video)
Ford-Fulkerson Algorithm (Michael Sambol Video) [Optional]
Dijkstra's Algorithms: A Quick Intro on How it Works (PatrickJMT Video)
Weighted graphs and networks (Dijkstra's algorithm) (Maffs Guru Video)
Shortest Path Solver (Julian Browne Interactive)
Bipartite Graph (D3 Graph Theory Interactive)
Bipartite Graphs and Assignment Problems (Joel Speranza Math Video)
Complete Bipartite Graph (D3 Graph Theory Interactive)
Hungarian Algorithm Solver (HungarianAlgorithm.com Interactive)
The Hungarian Algorithm for Weighted Assignments (Joel Speranza Math Video)
Graph Creator (yED Live Interactive)
Matching and allocation problems (Maffs Guru Video)
Maximum allocation problem - Hungarian Algorithm (RouTube Video)
Activity Networks and Precedence Tables (Joel Speranza Math Video)
Activity Networks and Dummy Activities (Joel Speranza Math Video)
Weighted Precedence Tables and Float Times (Joel Speranza Math Video)
Critical Path Analysis Earliest Starting Time and Latest Finishing Time (Joel Speranza Math Video)
Critical Path Analysis Latest Starting Time (Joel Speranza Math Video)
Scheduling problems (Maffs Guru Video)
Precedence tables and activity networks (Maffs Guru Video)
How to draw a PDM network diagram (Engineer4Free Video)
Construct a PDM network diagram when given a table of dependencies (Engineer4Free Video)
Construct a table of dependencies when given a PDM network diagram (Engineer4Free Video)
Use forward and backward pass to determine project duration and critical path (Engineer4Free Video)
Determine the Early Start (ES) and Early Finish (EF) of activities in a PDM network diagram (Engineer4Free Video)
Determine Late Start (LS) and Late Finish (LF) of acitivies in PDM network diagram (Engineer4Free Video)
What is Total Float (Total Slack) and how to calculate it in a network diagram (Engineer4Free Video)
Crashing (Maffs Guru Video)
Regular Graph (D3 Graph Theory Interactive)
Complete Graph (D3 Graph Theory Interactive)
Bipartite Graph (D3 Graph Theory Interactive)
Complete Bipartite Graph (D3 Graph Theory Interactive)
Graph Colouring (D3 Graph Theory Interactive)
k-Colourable Graph (D3 Graph Theory Interactive)
Chromatic Number (D3 Graph Theory Interactive)
Euler's Formula and Graph Duality (3Brown1Blue Video)
The Bridges of Konigsberg
- Introduction (Eddie Woo Video)
- Digging Deeper into the Problem (Eddie Woo Video)
- Understanding Basic Network Theory (Eddie Woo Video)
Vertices and Edges (D3 Graph Theory Interactive)
Degree of a Vertex (D3 Graph Theory Interactive)
Complete Graph (D3 Graph Theory Interactive)
Graphs and Networks (Maffs Guru Video)
Adjacency Matrices (Maffs Guru Video)
Planar Graphs Introduction - Equivalent (Isomorphic Graphs) and Drawing Graphs in Planar Form (Joel Speranza Math Video)
Planar Graphs - Euler's Formula (Joel Speranza Math Video)
Planar Graphs (Numberphile Video)
Walk (D3 Graph Theory Interactive)
Open vs Closed Walks (D3 Graph Theory Interactive)
Networks: Open and Closed Walks (Joel Speranza Math Video)
Connectivity (D3 Graph Theory Interactive)
Networks Trails and Paths (Joel Speranza Math Video)
Networks Weighted Graphs Shortest Paths and the Travelling Salesperson Problem (Joel Speranza Math Video)
Networks: Eulerian Graphs and Semi-Eulerian Graphs (Joel Speranza Math Video)
Eulerian Circuit (D3 Graph Theory Interactive)
Eulerian Trail (D3 Graph Theory Interactive)
Hamiltonian and Semi Hamiltonian Graphs (Joel Speranza Math Video)
Exploring and travelling (Maffs Guru Video)
Networks: Intro to Trees (Joel Speranza Math Video)
Networks: Prim's Algorithm for Finding Minimum Spanning Trees (Joel Speranza Math Video)
Trees (D3 Graph Theory Interactive)
Spanning Tree of a Graph (D3 Graph Theory Interactive)
Prim's Algorithm Solver (Jake Baker Maths Interactive)
Trees and minimum connector problems (Maffs Guru Video)
Flow problems (Maffs Guru Video)
Maximum Flow Minimum Cut Algorithm (Joel Speranza Math Video)
Ford-Fulkerson Algorithm (Michael Sambol Video) [Optional]
Dijkstra's Algorithms: A Quick Intro on How it Works (PatrickJMT Video)
Weighted graphs and networks (Dijkstra's algorithm) (Maffs Guru Video)
Shortest Path Solver (Julian Browne Interactive)
Bipartite Graph (D3 Graph Theory Interactive)
Bipartite Graphs and Assignment Problems (Joel Speranza Math Video)
Complete Bipartite Graph (D3 Graph Theory Interactive)
Hungarian Algorithm Solver (HungarianAlgorithm.com Interactive)
The Hungarian Algorithm for Weighted Assignments (Joel Speranza Math Video)
Graph Creator (yED Live Interactive)
Matching and allocation problems (Maffs Guru Video)
Maximum allocation problem - Hungarian Algorithm (RouTube Video)
Activity Networks and Precedence Tables (Joel Speranza Math Video)
Activity Networks and Dummy Activities (Joel Speranza Math Video)
Weighted Precedence Tables and Float Times (Joel Speranza Math Video)
Critical Path Analysis Earliest Starting Time and Latest Finishing Time (Joel Speranza Math Video)
Critical Path Analysis Latest Starting Time (Joel Speranza Math Video)
Scheduling problems (Maffs Guru Video)
Precedence tables and activity networks (Maffs Guru Video)
How to draw a PDM network diagram (Engineer4Free Video)
Construct a PDM network diagram when given a table of dependencies (Engineer4Free Video)
Construct a table of dependencies when given a PDM network diagram (Engineer4Free Video)
Use forward and backward pass to determine project duration and critical path (Engineer4Free Video)
Determine the Early Start (ES) and Early Finish (EF) of activities in a PDM network diagram (Engineer4Free Video)
Determine Late Start (LS) and Late Finish (LF) of acitivies in PDM network diagram (Engineer4Free Video)
What is Total Float (Total Slack) and how to calculate it in a network diagram (Engineer4Free Video)
Crashing (Maffs Guru Video)
Regular Graph (D3 Graph Theory Interactive)
Complete Graph (D3 Graph Theory Interactive)
Bipartite Graph (D3 Graph Theory Interactive)
Complete Bipartite Graph (D3 Graph Theory Interactive)
Graph Colouring (D3 Graph Theory Interactive)
k-Colourable Graph (D3 Graph Theory Interactive)
Chromatic Number (D3 Graph Theory Interactive)
Solutions to past VCAA exam questions can be looked up in the appropriate examiner's report on the Further Mathematics Past Examinations and Examination Reports page or the Northern Hemisphere Timetable (NHT) Past Examinations and Examination Reports page. Exam 1 is multiple choice. Exam 2 is short answer.
Constructing Graphs and Networks (2016-2022 Study Design Questions)
Constructing Graphs and Networks (2000-2015 Study Design Questions)
Features of Graphs and the Degree of a Vertex (2016-2022 Study Design Questions)
Features of Graphs and the Degree of a Vertex (2000-2015 Study Design Questions)
Euler's Formula and Planar Graphs (2016-2022 Study Design Questions)
Euler's Formula and Planar Graphs (2000-2015 Study Design Questions)
Matrix Representation (2016-2022 Study Design Questions)
Matrix Representation (2000-2015 Study Design Questions)
Types of Graphs and Walks (2016-2022 Study Design Questions)
Types of Graphs and Walks (2000-2015 Study Design Questions)
Exploring and Travelling Problems (2016-2022 Study Design Questions)
Exploring and Travelling Problems (2000-2015 Study Design Questions)
Minimum Connector Problems (2016-2022 Study Design Questions)
Minimum Connector Problems (2000-2015 Study Design Questions)
Flow Problems (2016-2022 Study Design Questions)
Flow Problems (2000-2015 Study Design Questions)
Shortest Path Problems (2016-2022 Study Design Questions)
Shortest Path Problems (2000-2015 Study Design Questions)
Matching Problems (2016-2022 Study Design Questions)
Matching Problems (2000-2015 Study Design Questions)
Scheduling Problems (2016-2022 Study Design Questions)
Scheduling Problems (2000-2015 Study Design Questions)
Constructing Graphs and Networks (2016-2022 Study Design Questions)
Constructing Graphs and Networks (2000-2015 Study Design Questions)
Features of Graphs and the Degree of a Vertex (2016-2022 Study Design Questions)
Features of Graphs and the Degree of a Vertex (2000-2015 Study Design Questions)
Euler's Formula and Planar Graphs (2016-2022 Study Design Questions)
Euler's Formula and Planar Graphs (2000-2015 Study Design Questions)
Matrix Representation (2016-2022 Study Design Questions)
Matrix Representation (2000-2015 Study Design Questions)
Types of Graphs and Walks (2016-2022 Study Design Questions)
Types of Graphs and Walks (2000-2015 Study Design Questions)
Exploring and Travelling Problems (2016-2022 Study Design Questions)
Exploring and Travelling Problems (2000-2015 Study Design Questions)
Minimum Connector Problems (2016-2022 Study Design Questions)
Minimum Connector Problems (2000-2015 Study Design Questions)
Flow Problems (2016-2022 Study Design Questions)
Flow Problems (2000-2015 Study Design Questions)
Shortest Path Problems (2016-2022 Study Design Questions)
Shortest Path Problems (2000-2015 Study Design Questions)
Matching Problems (2016-2022 Study Design Questions)
Matching Problems (2000-2015 Study Design Questions)
Scheduling Problems (2016-2022 Study Design Questions)
Scheduling Problems (2000-2015 Study Design Questions)
