HSC Maths Ext 1 study plan

Sketch and classify the standard function families (polynomial, rational, exponential, logarithmic, absolute value) and state their domains and ranges from memory

Solve inequalities involving absolute values and rational functions, writing solution sets in interval notation

Apply the quotient, product and chain rules to differentiate composite expressions without referring to notes

Compute equations of tangents and normals to curves at given points and find stationary points using the first derivative

Prove statements by mathematical induction, including divisibility and inequality cases, with correct base case and inductive step structure

Distinguish and construct direct proofs, proofs by contradiction and counterexamples

Perform polynomial division and use the remainder and factor theorems to solve parameter problems

Graph inverse functions and composite functions, stating restricted domains explicitly

Derive and apply the three Pythagorean identities and the compound-angle and double-angle formulas

Solve trigonometric equations over a stated domain, expressing all general solutions correctly

Differentiate and integrate trigonometric functions, including expressions requiring substitution or reverse chain rule

Sketch trigonometric graphs with correct amplitude, period and phase shift, and identify their symmetries

Evaluate definite integrals using substitution and identify when a change of limits is required

Find areas between curves and volumes of solids of revolution, setting up the integral before computing

Apply the product, sum and pigeonhole principles to counting problems

Compute permutations and combinations and solve arrangement problems with restrictions

Expand binomial expressions and find general terms, coefficients and specific powers

Solve probability problems involving binomial coefficients and counting arguments

Perform vector addition, scalar multiplication and dot product in two and three dimensions

Use vectors to prove geometric results such as collinearity and perpendicularity

Resolve vectors into components and solve force and displacement problems using vector methods

Compute and interpret the mean, median, mode, variance and standard deviation of a data set

Standardise values using z-scores and calculate probabilities from the normal distribution

Distinguish discrete from continuous random variables and compute expected value

Re-derive trigonometric identities from scratch to confirm retention

Write a contradiction proof and an induction proof under exam timing without notes

Interpret correlation and regression output and describe the strength and direction of a relationship

Identify and correct your three most frequent errors from earlier weeks

Complete two full-length timed papers under exam conditions with no reference material

Allocate time across sections deliberately and review flagged questions

Classify every error as conceptual, procedural or careless and target the largest category