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Specialist Mathematics

Thank you for your interest in Year 12 Specialist Mathematics. To revise as much as possible,  it is recommended to attend all the seminars listed below. However, this is not compulsory and you may choose any combination of sessions.

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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$70.00 per session
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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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