VCE Mathematical Methods - Syllabus & Notes
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Study VCE Mathematical Methods Topics
Populations and Samples
Continuous Random Variables
Bernoulli Sequences and the Binomial Probability Distribution
Discrete Random Variables
Addition and Multiplication Principles
Sample Spaces and Probability
Estimating the Area Under a Graph
Tangents and Normals
Antidifferentiation of Polynomial Functions
Recognising Relationships
Measuring Angles in Degrees and Radians
The Index Laws
Rectangular Hyperbolas
Solving Cubic Equations
Expanding and Collecting Like Terms
Translations
More Power Functions
Relations, Domain and Range
Distance and Midpoints
Constructing Linear Equations
Circular Functions
Applications of Differentiation
Exponent and Logarithm Laws
The Exact Distribution of the Sample Proportion
Mean and Percentiles for a Continuous Random Variable
The Graph, Expectation, and Variance of a Binomial Distribution
Sampling Without Replacement
Arrangements
Estimating Probabilities
Antidifferentiation: Indefinite Integrals
Rates of Change
The Second Derivative
Constant Rate of Change
Defining Circular Functions: Sine, Cosine, and Tangent
Rational Indices
The Truncus
Cubic Functions of a Particular Form
Factorising
Dilations
Composite and Inverse Functions
One-to-One Functions and Implied Domains
The Gradient of a Straight Line
Simultaneous Equations
Coordinate Geometry
Approximating the Distribution of the Sample Proportion
Measures of Spread
Finding the Sample Size
Sampling with Replacement: The Binomial Distribution
Selections
Multi-Stage Experiments
Two Antiderivatives
Stationary Points
Sketching Graphs
Average Rate of Change
Symmetry Properties and Values of Circular Functions
Graphs of Exponential Functions
Two Important Graphs
Graphs of Factorised Cubic Functions
Quadratic Equations
Reflections
Sums and Products of Functions and Addition of Ordinates
Piecewise-Defined Functions
The Equation of a Straight Line
Solving Linear Inequalities
Discrete Probability Distributions
Functions and Relations
Confidence Intervals for the Population Proportion
Properties of Mean and Variance
Proofs for the Expectation and Variance
Conditional Probability and Independence
Applications to Probability
Combining Events
The Fundamental Theorem of Calculus and the Definite Integral
Absolute Maximum and Minimum Values
The Derivative
Instantaneous Rate of Change
Further Symmetry Properties and the Pythagorean Identity
Solving Exponential Equations and Inequalities
Circles
Solving Cubic Inequalities
Graphing Quadratics
Combinations of Transformations
Function Notation and Identities
Applying Function Notation
Graphing Straight Lines
Using and Transposing Formulas
Graphs of Exponents and Logarithms
Cumulative Distribution Functions
Expected Value (Mean), Variance, and Standard Deviation
Algorithms and Flowcharts
Probability Tables
Finding the Area Under a Curve
Maximum and Minimum Problems
Rules for Differentiation
Position and Average Velocity
Graphs of Sine and Cosine
Using Logarithms to Solve Exponential Equations and Inequalities
Determining Rules
Families of Cubic Polynomial Functions
Completing the Square and Turning Points
Determining Transformations
Families of Functions and Solving Literal Equations
Set Notation and Sets of Numbers
Parallel and Perpendicular Lines
The Normal Distribution
Iteration and Selection
Conditional Probability
Integration of Circular Functions
Families of Functions
Differentiating Where n is a Negative Integer
Solution of Trigonometric Equations
Exponential Models and Applications
Applications of Polynomial Functions
Graphing Quadratics in Polynomial Form
Using Transformations to Sketch Graphs
Families of Straight Lines
Standardisation and the 68–95–99.7% Rule
Introduction to Pseudocode
Independent Events
Miscellaneous Exercises
Applications to Motion in a Straight Line
The Graph of the Derivative Function
Sketching Graphs
Logarithms
The Bisection Method
Solving Quadratic Inequalities
Transformations of Power Functions With Positive Integer Index
Sums and Products of Functions
Linear Models
Determining Normal Probabilities
Counting Methods
Solving Probability Problems Using Simulation
Signed Area
Newton’s Method for Finding Solutions to Equations
The Chain Rule
Addition of Ordinates for Circular Functions
Graphing Logarithmic Functions
Quadratic Functions
The General Quadratic Formula
Determining the Rule for a Function From Its Graph
Composite Functions
Linear Literal Equations and Simultaneous Linear Literal Equations
Solving Problems Using the Normal Distribution
Summation Notation
Pseudocode for Probability and Simulation
The Area of a Region Between Two Curves
Differentiating Rational Powers
Determining Rules for Graphs of Circular Functions
Determining Rules for Graphs of Exponential and Logarithmic Functions
Determining the Rule for a Parabola
The Discriminant
A Notation for Transformations
Inverse Functions
Applications of Linear Functions
The Normal Approximation to the Binomial Distribution
The Binomial Theorem
Applications of Integration
Differentiation of Different Functions
The Tangent Function
Solution of Exponential Equations Using Logarithms
The Language of Polynomials
Solving Simultaneous Linear and Quadratic Equations
Power Functions
Simultaneous Linear Equations with More Than Two Variables
Derivatives of Circular Functions
General Solution of Trigonometric Equations
Inverses
Division and Factorisation of Polynomials
Families of Quadratic Polynomial Functions
Applications of Functions
The Product Rule
Applications of Circular Functions
Exponential Growth and Decay
The General Cubic Function
Quadratic Models
The Quotient Rule
Polynomials of Higher Degree
Limits and Continuity
Determining the Rule for the Graph of a Polynomial
When Is a Function Differentiable?
Solution of Literal Equations and Systems of Equations
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