VCE Methods Unit 2 Skills () « back to units
The skills below are aligned with the VCE Mathematical Methods Study Design 2023-2027. Skills are organised into key areas: Exponential & Logarithmic Functions, Differential Calculus, Antidifferentiation & Integration, and Probability Distributions. To master a skill, you will have to gain 10 stars.
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Exponential & Logarithmic Functions
- Simplify expressions using index laws
- Solve exponential equations (same base)
- Solve exponential equations (different bases — using logarithms)
- Convert between exponential and logarithmic form
- Evaluate logarithms without a calculator
- Apply log laws (product, quotient, power)
- Prove log law identities
- Sketch exponential functions y = a^x and y = e^x
- Sketch transformed exponential functions y = A*e^(bx) + c
- Identify asymptotes and intercepts of exponential functions
- Sketch logarithmic functions y = log_a(x) and y = ln(x)
- Sketch transformed logarithmic functions
- Identify asymptotes and intercepts of logarithmic functions
- Determine the equation of an exponential from a graph or data
- Solve logarithmic equations
- Recognise and sketch the inverse relationship between y = e^x and y = ln(x)
- Model exponential growth and decay
- Match equation to exponential/logarithmic graph
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Differential Calculus (Polynomials)
- Differentiate from first principles (limit definition)
- Differentiate polynomials using the power rule
- Differentiate with negative and fractional indices
- Find the gradient of a curve at a point
- Find the equation of a tangent line
- Find the equation of a normal line
- Find stationary points and determine their nature
- Sketch curves using calculus (intercepts, stationary points, behaviour)
- Solve optimisation problems (maximum/minimum)
- Determine where a function is strictly increasing or decreasing
- Find points of inflection
- Apply rates of change in real-world context
- Differentiate using the chain rule
- Differentiate using the product rule
- Differentiate using the quotient rule
- Central difference approximation for rate of change
- Relate the graph of f(x) to f'(x)
- Evaluate basic limits
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Antidifferentiation & Integration (Introduction)
- Antidifferentiate polynomial functions (power rule in reverse)
- Find the constant of integration given a condition
- Evaluate definite integrals of polynomials
- Calculate the area under a curve (above x-axis)
- Calculate areas involving regions below the x-axis (signed area)
- Calculate the area between two curves
- Apply integration to kinematics (displacement from velocity)
- Estimate area using left/right endpoint approximations
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Probability Distributions (Introduction)
- Define discrete random variables and probability distributions
- Construct a probability distribution table
- Graph a probability distribution
- Calculate expected value E(X) for a discrete distribution
- Calculate variance Var(X) and standard deviation
- Interpret expected value and standard deviation in context
- Identify a Bernoulli trial
- Identify conditions for a binomial distribution
- Calculate binomial probabilities P(X = k)
- Calculate cumulative binomial probabilities P(X <= k)
- Find mean and variance of a binomial distribution
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Pseudocode & Algorithms (Units 1 & 2)