HSC Maths Ext 2 study plan

Derive and apply the quotient, product and chain rules to differentiate composite, implicit and inverse-trigonometric expressions without referring to notes

Construct a worked table of standard integrals including inverse-trig, logarithmic and rational forms, and verify each by differentiating back

Solve at least ten integration-by-parts and partial-fractions problems, choosing the method explicitly before starting each

Convert between Cartesian, polar and exponential forms of complex numbers and compute products, quotients and powers fluently

Apply integration to compute volumes of solids of revolution and areas between curves, sketching each region before integrating

Perform implicit differentiation and analyse curves given parametrically, finding gradients and stationary points

Solve polynomial equations over the complex numbers and locate roots on the Argand diagram, verifying conjugate-pair behaviour

Explain and use De Moivre's theorem to find multiple-angle identities and nth roots

Resolve forces into components and draw complete free-body diagrams for particles in equilibrium on inclined planes and connected systems

Set up and solve equations of motion for constant-acceleration and variable-acceleration cases, including resisted motion

Compute dot and cross products, projections and angles, and interpret each geometrically

Derive vector equations of lines and planes and solve intersection and distance problems in three dimensions

Analyse projectile motion with and without air resistance, deriving trajectory equations and ranges

Apply circular-motion and simple-harmonic-motion models, identifying the restoring force in each context

Use vectors to prove geometric results such as concurrency and collinearity

Solve three-dimensional geometry problems involving planes, normals and shortest distances

Write complete induction proofs for summation, divisibility and inequality statements, stating the base case and inductive step explicitly

Identify where strong induction is required and construct such proofs for recurrence-defined sequences

Distinguish proof by contradiction from proof by contraposition and select the appropriate method for a given claim

Prove standard irrationality and infinitude results and critique flawed proofs to locate the logical gap

Test and classify series for convergence using ratio, comparison and integral tests, stating the criterion used each time

Derive and apply Maclaurin series expansions and use them to evaluate limits and approximate values with error bounds

Expand binomial expressions with rational and negative indices, stating the range of validity

Use the binomial theorem to prove identities and evaluate sums involving binomial coefficients

Revisit the highest-weight calculus, mechanics and complex-number question types and solve them under time pressure

Diagnose weak sub-topics from earlier logs and complete targeted drills on each

Practise multi-part questions that chain techniques across two domains, such as SHM solved with complex exponentials

Refine written solutions so that every step is justified in the style examiners reward

Consolidate lighter domains with rapid retrieval practice, writing key theorems and formulas from memory daily

Complete one timed paper under strict conditions and review every error within 24 hours

Rehearse proof and induction write-ups to ensure full marks on structure and clarity

Build a final one-page revision sheet of formulas, standard results and common traps