VCE Methods Unit 3 Skills () « back to units
The skills below are aligned with the VCE Mathematical Methods Study Design 2023-2027. Skills are organised into key areas: Functions & Graphs (Advanced), Algebra (Advanced), Differential Calculus (All Function Types), and Probability (Discrete Random Variables & Binomial). To master a skill, you will have to gain 10 stars.
No skills match your search.
-
Functions & Graphs (Advanced)
- Identify key features of polynomial functions (degree, end behaviour, multiplicity)
- Sketch polynomial functions using intercepts and end behaviour
- Sketch exponential functions with transformations
- Sketch logarithmic functions with transformations
- Sketch circular functions with combined transformations
- Determine the rule of a function from its graph
- Find the domain and range of transformed functions
- Form composite functions f(g(x)) and determine domain
- Form sum and difference functions f + g, f - g
- Form product functions f * g
- Apply multiple transformations in correct order (dilations, reflections, translations)
- Write the rule for a transformed function y = A*f(b(x - h)) + k
- Find inverse functions and state domain restrictions
- Sketch a function and its inverse on the same axes
- Verify that f(f^(-1)(x)) = x
- Use parameters to explore function families (interactive)
- Model practical situations with appropriate function types
- Match rule to graph (all function types mixed)
-
Algebra (Advanced)
- Solve exponential equations analytically
- Solve logarithmic equations analytically
- Solve trigonometric equations over specified domains
- Solve trigonometric equations with transformations
- Solve equations involving composite functions
- Solve literal equations (rearrange for a given variable)
- Solve systems of simultaneous equations (linear and non-linear)
- Solve equations graphically and numerically
- Apply Newton's method to find approximate roots
- Trace Newton's method pseudocode
- Determine number of solutions using graphical analysis
-
Differential Calculus (All Function Types)
- Differentiate e^(ax+b)
- Differentiate ln(ax+b)
- Differentiate sin(ax+b) and cos(ax+b)
- Differentiate tan(x)
- Apply the chain rule to composite functions
- Apply the product rule
- Apply the quotient rule
- Differentiate combinations requiring multiple rules
- Find equations of tangent and normal lines (all function types)
- Determine where a function is increasing/decreasing (all types)
- Find and classify stationary points (all function types)
- Find absolute maximum and minimum on a closed interval
- Sketch curves using derivatives (all function types)
- Solve optimisation problems in context
- Rates of change in context (growth, decay, motion)
- Relate graphs of f, f', and f''
- Determine f from information about f'
- Limits and continuity (advanced)
- Conditions for differentiability
- Kinematics — velocity and acceleration from position function
-
Probability (Discrete Random Variables & Binomial)
- Construct probability distribution tables (advanced)
- Calculate E(X), Var(X), sd(X) for discrete distributions
- Properties of expected value: E(aX + b) = aE(X) + b
- Properties of variance: Var(aX + b) = a^2 Var(X)
- Identify and set up binomial distributions X ~ Bi(n, p)
- Calculate binomial probabilities (by hand for small n)
- Calculate binomial probabilities (CAS for larger n)
- Find the expected value and variance of Bi(n, p)
- Determine sample size n for a binomial problem
- Solve problems involving at least/at most in binomial contexts
- Graph binomial probability distributions
- Apply binomial distribution to real-world problems