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Specialist Mathematics

We do more than revise key theory and solve past exam questions.

Each session also includes:

  • finer points of exam preparation
  • how to decode unusual exam questions
  • how to answer questions to the marker’s requirements for maximum marks.

To revise the whole Specialist Mathematics course, you should attend all the seminars listed below. However, this is not compulsory and you may choose any combination of sessions.

Please bring a calculator to each session.

Teacher in charge / Paul Urban
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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.

Session A

Complex numbers with polynomials

  • Understanding complex numbers and their operations; Cartesian and polar form and properties of complex numbers
  • Connection of complex numbers to 2D vectors and linear transformations of the plane; graph sketching; triangle inequality
  • Polynomials; operations (±, ×, ÷) division algorithm; roots, zeros and factors; Remainder & 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 B

Functions, sketching graphs and induction

  • Composition of functions including domain and range
  • One-to-one functions, condition for inverse functions and graphs
  • Sketching graphs, including absolute value functions; composition involving absolute value and reciprocal functions; rational functions and behaviour near asymptotes
  • Principle of Mathematical Induction (PMI); use in proof of complex numbers properties

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Session C

Vector geometry in 2 and 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 D

Applications of vectors

  • Equations of lines and planes
  • Vectors moving over time; uniform motion and object in free flight
  • 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 E

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); use of implicit differentiation
  • Applications involving finding areas and volumes

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Session F

Rates of change and differential equations

  • Related rates over time
  • Differential equations (definition) and their solutions
  • All the meanings of a derivative of a function
  • Slope fields and the way to sketch a curve from them
  • Differential equations used in modelling, e.g. Newton’s Law of Cooling; the logistic model for population growth and rumour spreading
  • Pairs of varying quantities; vector interpretation; Bézier curves
  • How is the motion of a moving point described? Ways to calculate velocity, acceleration, direction of motion, and speed and distance travelled.

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