HSC Maths Advanced study plan

Sketch and classify the main function families (linear, quadratic, cubic, hyperbola, exponential, absolute value) and state domain and range for each

Apply transformations (translations, reflections, dilations) to a base graph and predict the new equation from a sketch

Differentiate from first principles for polynomials and connect the gradient function to the graph's slope

Use the chain, product and quotient rules on mixed polynomial and rational expressions

Solve equations and inequalities involving absolute value and quadratic expressions, expressing solutions on a number line

Find stationary points, determine their nature, and sketch the curve showing concavity

Combine functions through sum, difference, product and composition, and identify the resulting domain

Apply calculus to optimisation and rate-of-change word problems drawn from real contexts

Convert fluently between degrees and radians and evaluate exact trigonometric ratios for standard angles

Sketch sine, cosine and tangent graphs, stating amplitude, period, phase shift and vertical shift

Solve trigonometric equations over a given domain and list all solutions within one or more periods

Apply the sine and cosine rules and the area formula to non-right-angled triangle problems

Differentiate trigonometric functions and apply them to gradient, tangent and normal problems

Use trigonometric identities to simplify expressions before differentiating or solving

Solve problems involving arc length, sector area and angular velocity in radians

Interpret periodic models in context, including maximum, minimum and average values

Integrate standard polynomial and trigonometric functions and evaluate definite integrals

Find areas under curves and between curves, including where the curve crosses the axis

Apply the trapezoidal rule to approximate areas and compare with the exact integral

Solve kinematics problems by integrating acceleration to velocity to displacement

Compute simple and compound interest and solve for the unknown rate, time or principal

Analyse depreciation using both straight-line and declining-balance methods

Construct and use recurrence relations to model savings, loans and annuities

Interpret and manipulate a loan repayment schedule, including the effect of changing the repayment amount

Summarise datasets using mean, median, mode, range, interquartile range and standard deviation

Construct and interpret box plots, histograms and scatterplots, identifying outliers and skew

Calculate and interpret the correlation coefficient and fit a line of best fit for prediction

Distinguish between relative and absolute frequency and apply them to probability questions in financial contexts

Complete two full-length timed practice papers under exam conditions and mark them against the criteria

Categorise every error as conceptual, procedural or time-management and rank them by frequency

Re-teach the three highest-frequency error categories using worked examples from memory

Build a one-page formula and method sheet for final revision across all domains