# 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.

• ##### Teacher in charge / Paul Urban

Paul is a highly successful senior Mathematics teacher with more than 30 years’ experience including as a marker for SACE and, more recently, IB Diploma Maths. He will focus you quickly and clearly, with room for personal discussion.

Qualifications: B.Sc. (Hons.), B.Ec.

## 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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\$75.00 per session

## 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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\$75.00 per session

## 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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\$75.00 per session

## 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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\$75.00 per session

## 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.

You’ve already got another session at that time.
\$75.00 per session