# Accreditation of VCE General Mathematics Units 1 and 2

VCE General Mathematics Units 1 and 2 has been designed and published for complying Victorian Certificate of Education 1 January 2016 – 31 December 2018 and implementation of this course commences in January 2018.

VCE General Mathematics Units 1 and 2 offer for a range of courses of study relating non-calculus based topics for a broad range of students and may be implemented in various ways to reflect student interests in, and applications of, mathematics. These students incorporate topics that provide preparation for various combinations of studies at Units 3 and 4 and cover assumed knowledge and skills for those units.

### Area of Study 1

**Algebra and structure**

In this area of study students cover representation and manipulation of linear relations and equations, including simultaneous linear equations, and their applications in a range of contexts.

### Area of Study 2

**Arithmetic and number**

In this area of study students cover mental, by-hand and technology assisted computation with rational numbers, practical arithmetic and financial arithmetic, including estimation, order of magnitude and accuracy.

### Area of Study 3

**Discrete mathematics**

In this area of study students cover matrices, graphs and networks, and number patterns and recursion, and their use to model practical situations and solve a range of related problems.

### Area of Study 4

**Geometry, measurement and trigonometry**

In this area of study students cover shape, measurement and trigonometry and their application to formulating and solving two- and three-dimensional problems involving length, angle, area and surface area, volume and capacity, and similarity and the application of linear scale factors to measurement.

### Area of Study 5

**Graphs of linear and non-linear relations**

In this area study students cover continuous models involving linear and non-linear relations and their graphs, linear inequalities and programming, and variation.

### Area of Study 6

**Statistics**

In this area of study students cover representing, analysing and comparing data distributions and investigating relationships between two numerical variables, including an introduction to correlation.

#### Course Materials

#### Financial Arithmetic

- Simple Interest
- Finding the Period of Simple Interest
- Finding the Principal of Simple Interest
- Finding the Rate of Simple Interest
- Applications of Simple Interest
- Compound Interest
- Appreciation
- Depreciation
- Consecutive Discounts or Surcharges
- Finding the Interest Rate
- Interest Rate of Credit Cards
- Interest-Free Period of Credit Cards
- Credit Limit of Credit Cards
- Reducible Interest

#### Matrices

- Matrix Definition
- Matrix Equality
- Matrix Addition
- Matrix Subtraction
- Scalar Multiples of Matrices
- Zero or Null Matrix
- Negative Matrix
- Simple Matrix Equations
- Single Row by Single Column
- Single Row by Multiple Columns
- Multiple Rows by Multiple Columns
- Commutative Law
- Identity Matrix
- Power of a Matrix
- Finding a Matrix Inverse
- Determinant of a Matrix
- Inverse Matrix using Determinant
- Matrix Equations
- Solving a Pair of Linear Equations
- Unique Solutions
- Finding Matrices
- Inverse of an Inverse matrix
- Inverse of Matrix Multiplications
- Inverse Matrix in a Linear Form

#### Geometric Sequences

- Identifying Geometric Sequences
- Finding the First Term and Common Ratio
- Finding a Term from a Rule
- Set up a Rule
- Finding the number of Terms
- Applications
- Compound Interest
- Finding Unknown Values
- Set up a Sum Formula
- Finding the Sum using a Formula
- Finding Number of Terms
- Sigma Notation of Geometric Series
- Finding the Number of Terms

#### Volume

- Metric Units for Volume
- Cross Section of a Prism
- Volume of a Prism
- Volume of a Prism by Finding the Area of Cross Section
- Volume of a Composite Prism
- Volume of a Cylinder
- Volume of a Composite Cylinder
- Volume and Capacity
- Conversion of Capacity
- Conversion from Capacity to Volume
- Conversion from Volume to Capacity
- Volume of Spheres
- Compound Solid Figures

#### Data Distributions

- Categorial Variables
- Quantitative or Numerical Variables
- Calculating the Mean
- Mean from UnGrouped Data
- Mean from Grouped Data
- Calculating the Median
- Median from a Table
- Median from a Cumulative Frequency Graph
- Median from a Grouped Cumulative Frequency Graph
- Range
- Interquartile Range
- Population Standard Deviation