WACE ATAR Mathematics Specialist study plan

Differentiate composite, implicit and inverse-trigonometric functions from first principles and standard rules, writing every step of the chain-rule working

Sketch graphs of functions using limits, asymptotes and stationary points, and state domain and range for each sketch

Solve optimisation and related-rates problems by setting up the defining equation before differentiating

Build a one-page error log of every differentiation slip made during practice and categorise each slip by cause

Integrate using substitution, by parts and partial fractions, choosing the method and justifying the choice in writing

Evaluate definite integrals including those requiring trigonometric identities, and compute areas between curves

Apply integration to volumes of revolution and to rates problems, stating the formula used at the start of each solution

Redo every question missed in Week 1 without notes and record the second-attempt score

Resolve vectors into components in two and three dimensions and compute magnitudes, unit vectors and direction angles

Compute dot and cross products and use each to find angles, projections, areas and perpendicular vectors

Derive vector equations of lines and planes and determine intersections, including skew and parallel cases

Solve 3D geometry problems by drawing a labelled diagram before any algebra

Apply vector methods to kinematics, resolving velocity and acceleration and interpreting motion in a plane

Combine calculus with vectors to differentiate and integrate vector-valued functions

Complete a mixed set of calculus and vector questions under exam timing without referring to notes

Identify the two weakest sub-skills across Domains 1 and 2 and write a targeted practice list for each

Perform arithmetic on complex numbers in Cartesian, polar and exponential forms and convert fluently between them

Sketch loci such as circles, rays and perpendicular bisectors, and translate between algebraic and geometric descriptions

Apply de Moivre's theorem to powers and roots, listing all roots and plotting them on the Argand diagram

Solve polynomial equations over the complex numbers, using conjugate-root and factor theorems

Carry out matrix addition, multiplication and inversion by hand and verify each inverse by multiplication

Compute determinants of 2x2 and 3x3 matrices and use them to test invertibility and solve linear systems

Solve systems using Gaussian elimination and interpret inconsistent and infinitely-many-solution cases geometrically

Apply matrix methods to transformations, including composition and finding inverse transformations

Compute probabilities using conditional probability, independence and the multiplication and total-probability rules

Apply Bayes' theorem to reverse-conditioning problems and state the answer in context

Model discrete and continuous random variables, computing means and variances from definitions

Solve binomial and normal distribution problems including continuity corrections and inverse-normal questions

Sit two full-length timed papers under exam conditions and mark them strictly against the official style of marking

Revisit every error from Weeks 1 to 7 and re-solve each one from scratch without prompts

Consolidate formula recall by writing all key formulas from memory and checking against the reference sheets

Plan exam-day timing by allocating minutes per section based on marks and practising the allocation once