Unit 2: Calculus & Probability Intro

VCE Mathematical Methods Study Design 2023-2027

Units 1 & 2 (School-Assessed) 61 Skills • 3 Levels Each

Unit 2 Skill Map

Exponential & logarithmic functions, differential calculus, integration, probability distributions, and pseudocode.

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Exponential & Logarithmic Functions

18 skills

Simplify expressions using index laws20100 Solve exponential equations (same base)20101 Solve exponential equations (different bases — using logarithms)20102 Convert between exponential and logarithmic form20103 Evaluate logarithms without a calculator20104 Apply log laws (product, quotient, power)20105 Prove log law identities20106 Sketch exponential functions y = a^x and y = e^x20107 Sketch transformed exponential functions y = A*e^(bx) + c20108 Identify asymptotes and intercepts of exponential functions20109 Sketch logarithmic functions y = log_a(x) and y = ln(x)20110 Sketch transformed logarithmic functions20111 Identify asymptotes and intercepts of logarithmic functions20112 Determine the equation of an exponential from a graph or data20113 Solve logarithmic equations20114 Recognise and sketch the inverse relationship between y = e^x and y = ln(x)20115 Model exponential growth and decay20116 Match equation to exponential/logarithmic graph20117

Differential Calculus (Polynomials)

18 skills

Differentiate from first principles (limit definition)20120 Differentiate polynomials using the power rule20121 Differentiate with negative and fractional indices20122 Find the gradient of a curve at a point20123 Find the equation of a tangent line20124 Find the equation of a normal line20125 Find stationary points and determine their nature20126 Sketch curves using calculus (intercepts, stationary points, behaviour)20127 Solve optimisation problems (maximum/minimum)20128 Determine where a function is strictly increasing or decreasing20129 Find points of inflection20130 Apply rates of change in real-world context20131 Differentiate using the chain rule20132 Differentiate using the product rule20133 Differentiate using the quotient rule20134 Central difference approximation for rate of change20135 Relate the graph of f(x) to f'(x)20136 Evaluate basic limits20137

Antidifferentiation & Integration (Introduction)

8 skills

Antidifferentiate polynomial functions (power rule in reverse)20140 Find the constant of integration given a condition20141 Evaluate definite integrals of polynomials20142 Calculate the area under a curve (above x-axis)20143 Calculate areas involving regions below the x-axis (signed area)20144 Calculate the area between two curves20145 Apply integration to kinematics (displacement from velocity)20146 Estimate area using left/right endpoint approximations20147

Probability Distributions (Introduction)

11 skills

Define discrete random variables and probability distributions20150 Construct a probability distribution table20151 Graph a probability distribution20152 Calculate expected value E(X) for a discrete distribution20153 Calculate variance Var(X) and standard deviation20154 Interpret expected value and standard deviation in context20155 Identify a Bernoulli trial20156 Identify conditions for a binomial distribution20157 Calculate binomial probabilities P(X = k)20158 Calculate cumulative binomial probabilities P(X <= k)20159 Find mean and variance of a binomial distribution20160

Pseudocode & Algorithms (Units 1 & 2)

6 skills

Read and interpret VCAA pseudocode syntax20170 Trace a simple pseudocode algorithm (loops, conditionals)20171 Trace the bisection method algorithm20172 Write pseudocode for a mathematical process20173 Identify errors in pseudocode20174 Pseudocode for simulation and counting20175