Year 12 · Specialist Mathematics

Year 12 Specialist Mathematics

Choose a main topic to find your next skill.

Mathematical induction1 subtopic

Proof by mathematical induction

Complete induction steps for sums and divisibility.

Complex numbers4 subtopics

Cartesian and polar forms

Arguments, moduli and products in polar form.

Complex loci

Interpret circles, lines and distances in the Argand plane.

Roots of complex numbers

Root moduli and roots of unity.

Factorisation of polynomials

Conjugate roots, real factors and remaining roots.

Functions and graphs3 subtopics

Composition of functions

Compose functions with domain restrictions.

One-to-one functions

Restricted domains and inverse functions.

Sketching graphs

Asymptotes, intercepts and rational function behaviour.

Vectors1 subtopic

Vector algebra in three dimensions

Dot and cross products and perpendicularity.

Worked example included

Applications of Vectors2 subtopics

Vector and Cartesian equations

Points on lines, normal vectors and planes.

Systems of linear equations

Solve three-variable systems and classify intersections.

Vector Calculus3 subtopics

Vector differentiation and integration

Position, velocity and acceleration in component form.

Polynomial parameterisations

Eliminate parameters and differentiate parametric curves.

Trigonometric parameterisations

Ellipses, velocities and tangent gradients.

Integration techniques and applications2 subtopics

Integration techniques

Integration by substitution and by parts.

Applications of integration

Volumes of revolution and accumulated quantities.

Rates of change and differential equations3 subtopics

Implicit differentiation

Differentiate relations and find tangent gradients.

Differential equations

Initial-value problems and equilibrium populations.

Related rates, velocity and tangents

Connect changing quantities and vector motion.

Mixed exam practice1 subtopic

Year 12 mixed exam

12 questions · 45 minutes. Work on paper; answers and full working at the end.

These are the practice sets currently available for this year. Coverage is still growing.

Open Year 12 practice

More worked lessons

Year 12 · Testing perpendicular vectors with the dot product →Year 11 · Multiplying complex numbers →