Course map
Functions, relations and graphs
- LessonPractice
Graphs of functions
Unit 3: Functions, relations and graphs- Sketch polynomial, power, exponential, logarithmic and circular graphs with their key features
- State domain, range, intercepts and asymptotes
- Find the amplitude, period and range of circular functions
- LessonPractice
Transformations
Unit 3: Functions, relations and graphs- Apply dilations, reflections and translations and find the image rule
- Find a transformation, or its inverse, that maps one graph to another
- Describe how a family of graphs changes with one parameter
- LessonPractice
Combined functions and modelling
Unit 3: Functions, relations and graphs- Graph sums, differences, products and composites of functions
- Model situations with polynomial, exponential, logarithmic, circular and hybrid functions
- Interpret a model's parameters and limits in context
Algebra, number and structure
- LessonPractice
Composite and inverse functions
Unit 3: Algebra, number and structure- Decide when a composite function exists and find its rule, domain and range
- Decide when an inverse function exists and find its rule, domain and range
- Use inverse functions to solve equations
- LessonPractice
Equations and algorithms
Unit 3: Algebra, number and structure- Solve polynomial, exponential, logarithmic and circular equations over an interval
- Solve literal equations and find general solutions with a parameter
- Decide when simultaneous linear equations have one, no or infinitely many solutions
- Use Newton's method and read algorithms in pseudocode
Calculus
- LessonPractice
Differentiation
Unit 3: Calculus- Differentiate the course's functions with the product, quotient and chain rules
- Sketch the graph of a derivative from the graph of a function
- Recognise where a function is not continuous or not differentiable
- LessonPractice
Applications of differentiation
Unit 3: Calculus- Find tangents, normals, stationary points and points of inflection
- Find where a function is strictly increasing or decreasing
- Solve optimisation problems, including endpoint maximum and minimum values
- LessonPractice
Integration
Unit 4: Calculus- Find anti-derivatives, including by recognition from a derivative
- Evaluate definite integrals and use their properties
- Estimate a definite integral with the trapezium rule
- LessonPractice
Applications of integration
Unit 4: Calculus- Find areas under and between curves
- Find the average value of a function
- Find a function from its rate of change and a boundary condition
Data analysis, probability and statistics
- LessonPractice
Discrete random variables and the binomial distribution
Unit 4: Data analysis, probability and statistics- Find the mean, variance and standard deviation of a discrete random variable
- Model Bernoulli trials with the binomial distribution
- Find probabilities, including conditional probabilities
- LessonPractice
Continuous random variables and the normal distribution
Unit 4: Data analysis, probability and statistics- Construct and use probability density functions
- Find the mean, variance and probabilities of a continuous random variable
- Use the standard and transformed normal distributions
- LessonPractice
Sample proportions and confidence intervals
Unit 4: Data analysis, probability and statistics- Find the mean and standard deviation of a sample proportion
- Find and interpret approximate confidence intervals for a population proportion
- Explain how intervals vary between samples
The examinations
VCE Mathematical Methods Units 3 and 4. Both examinations cover Unit 3 and Unit 4. School-assessed Coursework is set by your school, so it is described in a lesson rather than practised here.