Specialist Mathematics

Thank you for your interest in Year 12 Specialist Mathematics. Our Specialist Maths seminars are held in the Terms 2 and 3 holidays. For more information, please subscribe to our mailing list.

Session AAvailable

Functions and sketching graphs

  • Composition of functions including domain and range
  • One-to one functions, their inverses and graphs of each
  • Sketching graphs including absolute value functions, composition involving absolute value and reciprocal functions, rational functions and behaviour near asymptotes.

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Session BAvailable

Complex numbers with polynomials and induction

  • Principle of Mathematical Induction (PMI)
  • Proofs of complex number properties (including the use of PMI)
  • Polynomials; operations (division algorithm; roots, zeros and factors; remainder and factor theorems; real polynomials and irreducible quadratic factors associated with conjugate pair zeros.
  • Application of De Moivre’s Theorem to finding roots of complex numbers and geometric description of these roots.

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Session CAvailable

Vector geometry in 2 & 3 dimensions

  • Basic concept of scalars and 2D and 3D vectors together with the geometry and algebra of vectors
  • Operations with vectors including addition, subtraction scalar multiplication and the product of vectors in two different ways
  • Parallel and perpendicular vectors
  • Problem solving with 2D and 3D vectors
  • Finding areas of triangles and parallelograms using vectors.

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Session DAvailable

Applications of vectors

  • Equations of lines and planes
  • Finding angles between lines, line and plane, planes
  • Vector proof of geometric properties
  • Problem solving in 2D and 3D geometry including the use of row operations on a system of linear equations.

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Session EAvailable

Integration techniques and applications

  • Basic rules derived from the fundamental theorem of calculus
  • Integration by substitution and by parts
  • Using partial fractions
  • The use of inverse trigonometric functions for integration (need for one-to-one functions)
  • Applications involving finding areas and volumes.

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