# Accreditation of VCE Mathematical Methods Units 1 and 2

VCE Mathematical Methods 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 Mathematical Methods Units 1 and 2 are prescribed and provide an introductory study of fundamental functions, algebra, calculus, probability and statistics and their applications in a variety of practical and theoretical contexts. They are designed as preparation for VCE Mathematical Methods Units 3 and 4 and cover assumed knowledge and skills for those units.

#### Course Materials

Lessons

#### Linear Functions

- Gradient given the Angle at the x-axis
- Gradient Form (Standard Form)
- Finding the Equation in Gradient Form
- General Form
- Intercept Form
- Point-Gradient Formula
- Two-Point Formula
- Gradient from Rise and Run
- Gradient from two Points
- Gradient from an Angle
- Finding the Positive Angle ot the x-axis
- Finding the Equation of a Straight Line using the Gradient and a Point
- Finding the Equation of a Straight Line using Two Points
- Parallel Lines
- Perpendicular Lines
- Identifying Parallen Lines
- Application of Parallel Lines
- Perpendicular Bisector
- Parallel Lines
- Perpendicular Lines
- Perpendicular Distance
- Perpendicular Distance and Circles

#### Quadratic Expressions

- Expanding Binomial Terms
- Quadratic Factorise
- Expanding Expressions
- The Product of Two Linear Expressions
- Difference of Two Squares
- Perfect Squares Expansions
- 2 by 3 Expansions
- Expanding Square Expressions
- Perfect Squares Expansions
- Binomial Products
- Non-Monic Binomial Products
- Perfect Squares
- Difference of Squares
- Quadratic Equations
- Simultaneous Equations involving Quadratics
- Basic Rules of Completing the Square
- Non-Monic Completing the Square
- Solving by Completing the Square
- Deriving the Quadratic Formula

#### Quadratic Graphs

- Transformations
- Vertex and Intercepts
- Coefficients
- Finding the Vertex using Completing the Square
- Finding Quadratic Equations
- Axis of Symmetry and Vertex
- Understanding Quadratic Inequalities
- Solving Quadratic Inequalities
- Ranges
- Finding y given x
- Substituting Points
- Finding x given y
- Applications of Quadratic Functions
- Finding Quadratics using Intercepts
- Finding Quadratics for Touching x-axis
- Finding Quadratics using Axes of Symmetry
- Finding Quadratics using Coefficients
- Finding Quadratics using Vertices
- Axes Intercepts

#### Set Notations

- Set Notation
- Union Sets and Intersection Sets
- Disjoint or Mutually Exclusive
- Set Builder Notations
- Complement Sets
- Venn Diagram
- Counting Elements of Sets
- Expressing Sets using Set Builder Notation
- Representing Sets using Set Builder Notation
- Representing Sets using Interval Notation
- Natural Numbers
- Integers
- Rational Numbers
- Irrational Numbers
- Real Numbers

#### Functions

- Types of Relations
- Function Notation
- Piecewise Functions
- Functions and Equations
- Even and Odd Functions
- Domain and Range
- Domain and Range by Graphs
- Surds and Rational Expressions
- Combining Functions
- Composition of Functions
- Basic Circles
- SemiCircles
- General Equation of a Circle
- General form of a Circle
- Absolute Value Graphs
- Square Root Graphs
- Sign Diagrams from Graphs
- Sign Diagrams from Equations with Single Factors
- Sign Diagrams from Equations with Square Factors
- Sign Diagrams from Rational Expressions
- Exponential Graphs
- Hyperbola
- Transformation of Hyperbola
- Miscellaneous Graphs

#### Logarithms

- Definition of Logarithms
- Addition
- Subtraction
- Indices
- Zero Value
- Unity
- Changing the Base
- Equations involving Logarithms
- Simplifying Logarithms in base 10
- Finding Exponents using Logarithms in base 10
- Equations involving Logarithms in base 10
- Interchangeable Logarithmic Forms
- Simplifying involving any Bases
- Equivalent Natural Logarithms
- Equations involving Natural Logarithms

#### Logarithmic Graphs

- Dilation from the x-axis
- Dilation from the y-axis
- Dilation from the base
- Translation
- Reflection
- Stating the Transformations of Logarithmic Graphs to base e
- Dilation of Logarithmic Graphs to base e
- Translation of Logarithmic Graphs to base e
- Reflection of Logarithmic Graphs to base e
- Finding Equations for Graphs of Logarithmic Functions

#### Matrices

- Matrix Definition
- Matrix Equality
- Matrix Addition
- Matrix Subtraction
- Scalar Multiples of Matrices
- Zero or Null 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

#### Rates of Change

- Basic Rates of Change
- using Rates of Change
- Rates of Change and Integration
- Velocity and Speed
- at Rest
- Maximum and Minimum Speed
- Distance Travelled
- Velocity and Acceleration
- Working with Velocity
- Maxima and Minima
- Maximum Velocity and Speed
- Changes in Displacement and Velocity
- Displacement-time Graph
- Sketching Graphs from Displacement to Velocity
- Velocity-time Graph
- Acceleration-time Graph

#### Differentiation

- Limits
- the First Principles
- Definition of Rates of Change
- Average Rates of Change
- Instantaneous Rates of Change
- Differentiation of Constant Functions
- Differentiation of Linear Functions
- Methods of Differentiation
- Differentiation of Rational Functions
- Differentiation of Rational Powers
- Differentiation of Polynomial Functions
- Differentiation of a Function in Terms of x
- Chain Rule
- Product Rule
- Quotient Rule
- Higher Derivatives
- Equation of Tangent
- Equation of Normal
- Gradient Function
- Absolute Maximum and Minimum
- Turning Points and the Borders
- Applications of Maxima and Minima

#### Integration

- Definition of the Primitivies
- Primitives for Fractions
- Primitives for Surds
- Primitives of Linear Expressions
- Primitives of Boundary Condition
- Indefinite Integrals
- Indefinite Integrals with Complex Indices
- Fundamental Theorem of Indefinite Integrals
- Definite Integrals
- Properties of Definite Integrals
- Area Enclosed by the x-axis
- Signed Area
- Area between two Curves
- Area Enclosed by the y-axis
- Volumes Rotated about the x-axis

#### Probability

- Regular Pack of 52 Cards
- Dice
- Addition Rule of Probability
- Product Rule of Probability
- with Replacement
- without Replacement
- Complementary Results
- Addition Rule of Probability
- Mutually Exclusive Events
- Independent Events
- Probability Tables
- Conditional Probability
- Estimating Probabilities from Data
- Listing Outcomes
- 2-Dimensional Grids
- Tree Diagrams for Sample Spaces
- Using Grids to Find Probabilities
- Tables of Outcomes
- Venn Diagram
- Basic Tree Diagrams
- Further Tree Diagrams
- Conditional Probability
- Probability with Orders
- Finding the Values
- Using Tables
- Using Parameters
- Conditional Probability
- Understanding Markov Chains
- Finding Long Term Values using Markov Chains

#### Combinatorics

- Counting Techniques with Repetitions
- Counting Techniques without Repetitions
- Definition of Factorial
- Arrangement
- Arrangements in a Round Table
- Removing Duplicates
- Definition
- Arrangements
- Arrangements in a Round Table
- Unknown Number of Arrangements
- Removing Duplicates
- Definition
- Selections
- Majority Decision
- Arrangements
- Probability