VCE Maths Methods study plan

Sketch and classify the four parent functions (linear, quadratic, cubic, hyperbola) from their equations without a calculator

Convert between the algebraic and graphical forms of parabolas by completing the square and reading off turning points

Solve quadratic equations by factorising, completing the square and the formula, and state which method suits which structure

Apply index laws and logarithm laws to simplify expressions and solve simple exponential equations

Set up a personal error log categorising mistakes by domain

Transform graphs using dilations, reflections and translations, and predict the new equation from a description

Determine domain and range of composite and restricted functions and justify each restriction

Find inverse functions algebraically and confirm by reflection in y equals x

Sketch circular, exponential and logarithmic functions with correct asymptotic behaviour

Identify whether a relation is a function from its rule or graph

Differentiate polynomial, exponential and logarithmic functions using the chain, product and quotient rules

Differentiate trigonometric functions and apply them inside composite expressions

Interpret the derivative as a gradient and as a rate of change in applied contexts

Find equations of tangents and normals at a given point

Differentiate from first principles for simple polynomials to explain where rules come from

Locate stationary points and classify them using the first or second derivative

Sketch cubic and other curves showing turning points, intercepts and asymptotes

Solve optimisation problems by forming a function of one variable and maximising or minimising it

Apply differentiation to kinematics problems involving displacement, velocity and acceleration

Recognise when a stationary point is an inflection rather than a maximum or minimum

Antidifferentiate polynomials, exponentials and simple trigonometric expressions and include the constant of integration

Evaluate definite integrals and interpret them as signed areas

Find areas between curves and between a curve and an axis, splitting where the curve crosses the axis

Solve simple differential equations of the form dy by dx equals f of x with an initial condition

Apply the fundamental theorem of calculus to connect areas and antiderivatives

Summarise univariate data using median, quartiles, mean and standard deviation, and choose measures suited to skew

Construct and interpret boxplots, histograms and dot plots and compare two data sets

Calculate and interpret z-scores and describe the effect of linear transformations on summary statistics

Classify variables and identify sources of bias in sampling methods

Interpret scatterplots and describe association, including the meaning of the correlation coefficient

Compute probabilities using Venn diagrams, two-way tables and the addition and multiplication rules

Apply conditional probability and test independence of events

Use discrete random variables, construct probability distributions and compute expected value and variance

Apply the binomial distribution to count successes and justify when it is appropriate

Use the normal distribution with standardisation to find probabilities and inverse problems

Complete two full-length timed practice papers under exam conditions

Diagnose remaining weaknesses by domain from the practice-paper results

Re-teach the two weakest sub-topics using targeted drills and worked examples

Build a final one-page formula and method summary covering all four domains

Rehearse time allocation and checking routines for the exam