# Accreditation of VCE Mathematical Methods Units 3 and 4

VCE Mathematical Methods Units 3 and 4 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.

These units are designed, prescribed and extend the study of fundamental functions to include combinations of these functions, algebra, calculus, probability and statistics, and their applications in a variety of practical and theoretical situations. The contents of these units also provide background for further study in, for example, science, humanities, economics and medicine.

#### Course Materials

Lessons

#### Polynomials

- Basic Long Division
- Long Division with Missing Terms
- Long Division with Rational Numbers
- Long Division with Higher Degree Devisors
- Long Division for Finding Pronumerals
- Remainder Theorem
- Factor Theorem
- Applications of Factor Theorem
- Definition of Polynomials
- Additions and Subtractions of Polynomials
- Degree of Polynomials
- Evaluating Polynomials
- Find unknown Values

#### Transformation of Graphs

- Transformations of Parabola
- Transformations of Cubic Graphs
- Sketching Cubic Graphs
- Restricting the Domain of Cubic Graphs
- Dilation of Cubic Graphs
- Reflection of Cubic Graphs
- Hyperbola
- Transformation of Hyperbola
- Dilation of Reciprocal Square
- Transformation of Reciprocal Square
- Domain Range Asymptotes of Reciprocal Square
- Finding the Equations of Reciprocal Square
- Dilation of Square Root Function in Power Form
- Transformation of Square Root Function in Power Form
- Domain Range Asymptotes of Square Root Function in Power Form
- Finding the Equations of Square Root Function in Power Form
- Graphing Absolute Value Functions
- Transformation of Absolute Value Graphs
- Absolute Value Graphs 1
- Absolute Value Graphs 2
- Absolute Value Graphs 3
- Additions of Graphs
- Multiplications of Graphs

#### Logarithm Laws

- 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
- Absolute Values

#### Circular Functions

- Radian Measurement
- Exact Ratios with Radian Measurement
- Angles of Any Magnitude
- Trigonometric Properties
- Angles Between Quadrants
- Basic Trigonometric Equations
- Quadratic Trigonometric Equations
- Miscellaneous Trigonometric Equations
- Basic Rules of Transformations
- Sine Graphs
- Cosine Graphs
- Tangent Graphs
- Reciprocal Functions
- Miscellaneous Graphs

#### Differentiation

- 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

#### Differentiation of Functions

- Differentiation of Logarithmic Functions
- Differentiation of the Exponential Function
- Differentiation of Sine Function : Chain Rule
- Differentiation of Sine Function : Product Rule
- Differentiation of Sine Function : Quotient Rule
- Differentiation of Cosine Function : Chain Rule
- Differentiation of Cosine Function : Product Rule
- Differentiation of Cosine Function : Quotient Rule
- Differentiation of Tangent Function

#### Applications of Differentiation

- Equation of Tangent
- Equation of Normal
- Gradient Function
- Increasing and Decreasing
- Turning Points
- Stationary Points
- Concavity
- Point of Inflexion
- Maximum and Minimum Turning Points
- Horizontal Point of Inflexion
- Nature of Stationary Points
- Basic Sketching
- Point of Inflexions and Concavity
- Asymptotes
- Symmetry
- using Derivatives
- Absolute Maximum and Minimum
- Turning Points and the Borders
- Applications of Maxima and Minima

#### Integration

- 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
- Using Chain Rule
- Using Derivative of Exponential Functions
- Using Derivative of SINE function
- Using Derivative of COSINE function
- Using Derivative of TANGENT function
- Using Derivative of Logarithmic function
- Using Product Rule
- Using Long Division

#### 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

#### Discrete Random Variables

- Finding Multiple Unknown Values
- Continuous or Discrete
- Corresponding Probabilities
- Probability Distribution Graphs
- Characteristics of Discrete Probability Distribution
- Find the missing Values From the Discrete Probability Distribution
- Probability Functions
- Using Probability Distributions
- Finding the Expected Value
- Finding the Unknown Value
- Applciations
- Expectation Theorems
- Applications of Expectation Theorems
- Mean
- Mode
- Finding the Variance
- Find the Variance using Expectation Theorems
- Finding unknown value given the Variance

#### Binomial Distribution

- Bernulli Trials and Sequences
- Probability Function
- Probability with a specific Order
- Probability without a specific Order
- Finding the Percentage
- Finding the Number of Trials
- Using Tables
- Using Parameters
- Conditional Probability
- Understanding Markov Chains
- Finding Long Term Values using Markov Chains
- Finding the Expected Value Variance and Standard Deviation of Binomial Probability Distribution
- Finding the Probability using the Expected Value
- Finding the number of Trials

#### Continuous Distributions

- Probability Density Functions
- Conditions of Probability Density Functions
- Finding Probabilities
- Conditional Probabilities
- Intervals involving Infinity
- Finding the Interval of Probability
- Mean of Probability Density Function
- Median of Probability Density Function
- Mode of Probability Density Function
- Variance and Standard Deviation of a Probability Density Function