QCE Specialist Mathematics Syllabus Notes

Learn Specialist Mathematics polar complex arithmetic, modulus-argument identities and De Moivre's theorem for integral powers.

Learn how Specialist Mathematics finds roots of unity and general complex roots using polar form and equal angular spacing.

Revise Specialist Mathematics factor and remainder theorems, conjugate roots and solving polynomial equations over the complex numbers.

Learn Specialist Mathematics induction proofs for sums, divisibility and De Moivre's theorem, with the exact proof structure QCAA expects.

Learn how Specialist Mathematics uses De Moivre's theorem and binomial expansion to prove multi-angle trigonometric identities.

Learn QCE Specialist three-dimensional vectors, ordered triples, unit vectors, magnitudes and altitude angles.

Revise QCE Specialist vector algebra, dot products, projections, parallel vectors, perpendicular vectors and geometric applications.

Learn Specialist Mathematics vector equations, parametric equations, Cartesian equations, spheres, lines, planes and cross products.

Learn Specialist Mathematics vector calculus for paths, velocity, acceleration, projectile motion and circular motion.

Learn Specialist Mathematics matrix algebra, determinants, inverse matrices, Gaussian elimination and systems with unique or non-unique solutions.

Learn QCE Specialist dominance matrices, Leslie matrices, matrix powers and practical modelling assumptions.

Learn QCE Specialist integration techniques for trigonometric identities, substitution and logarithmic integrals.

Learn QCE Specialist inverse trigonometric functions, their derivatives and integrals that produce arcsine and arctangent forms.

Learn QCE Specialist partial fractions and integration by parts, including when each technique is useful.

Learn QCE Specialist applications of integration, including areas between curves, solids of revolution and Simpson's rule.

Learn QCE Specialist exponential random variables, density functions, means, quantiles and probability modelling.

Learn QCE Specialist implicit differentiation and related rates for changing geometry, motion and applied modelling.

Learn QCE Specialist differential equations, separation of variables, slope fields, logistic growth, cooling and decay models.

Learn QCE Specialist motion modelling, forces, momentum, acceleration forms and simple harmonic motion.

Learn QCE Specialist sample means, sampling distributions, standard error and approximate normality for large samples.

Learn QCE Specialist confidence intervals for population means, margin of error, confidence level and interpretation.