# VCE Specialist Mathematics Units 1 and 2 – Arithmetic and Number

2.1 Set Theory

2.2 Venn Diagrams

2.3 Counting Techniques

2.4 Descriptive Statistics

## Principles of counting

This topic includes:

- one-to-one correspondence between sets, countable and uncountable subsets of R
- pigeon-hole principle: solve problems and prove results using this principle
- inclusion–exclusion principle for the union of two sets and three sets: determination and use of formulas for finding the number of elements in the union of two and the union of three sets
- permutations and solution of problems involving permutations and restrictions with or without repeated objects
- combinations and the relationship between permutations and combinations and problems involving restrictions
- derivation and use of simple identities associated with Pascal’s triangle.

*source – VCE Mathematics Study Design*

VCE Specialist Mathematics Units 1 and 2 Courses

VCE Specialist Mathematics Units 1 and 2 Syllabus

## Course Content

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### Set Theory

Definition of Sets
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Complements of Sets
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Number Sets
9 Topics

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Subsets
3 Topics

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Venn Diagrams

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Numbers in Regions
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Counting Techniques

Product Principle
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Permutations
7 Topics

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Combinations
11 Topics

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Binomial Expansions
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Descriptive Statistics

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Bias
2 Topics

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Statistical Inquiry
4 Topics

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Sample Types
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Discrete Data
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Continuous Data
3 Topics

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