• 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

Please note: sessions will run on the October 7 public holiday

• 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

• 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

• 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

• 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

• 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.