Session Length:     2.5 hours per week

Cost:    \$70 per session (includes ALL resources, notes, tests and discounted if taking more than 1 course)

Skills Test:
0.4 hours

Teaching:
1.8 hours

Questions relating to current student work:
0.3 hours

Resources Provided:
250 page book of course notes, weekly questions, practice SAC questions, access to worked solutions (by hand and video), exam style questions.

Calculator:
All aspects of the course taught on CASIO Classpad and TI Inspire CAS

The Unit 3/4 Specialist Maths course is very intensive. As the course has much more content then any other VCE course, it requires longer sessions each week to get through the content. It begins with a 20-25 minute test on the previous weeks content, then teaching of the new course content in sequence and is finished off with any questions students might have in regards to SAC preparation questions etc.

The following content is taught throughout the course:

#### Pre Knowledge

- Circular Functions
- The Sine and Cosine Rule
- Geometry
- Sequences and Series
- The Modulus function
- Circles, Ellipses and Hyperbolas
- Parametric Equations

#### Vectors

- Introduction to vectors
- Resolution of a vector into rectangular components
- Scalar product of vectors
- Vector projections
- Collinearity
- Geometric proofs

#### Circular Functions

- Sec, Cosec and Cot (including graphing)
- Compound and Double Angle Formulas
- Inverses of Circular Functions (including graphing)
- Solutions of Trig Equations

#### Complex Numbers

- Rectangular Form of Complex Numbers
- Polar Form of Complex Numbers
- Equations of Complex Numbers, including polynomials
- Roots of Complex Numbers and De Moivre's Theorem
- Circles, Rays and Lines

#### Differentiation and Rational Functions

- Differentiation
- Derivatives where x=f(y)
- Derivatives of Inverse Circular Functions
- Second Derivatives
- Points of Inflection
- Related Rates
- Rational Functions
- Summary of Differentiation
- Implicit differentiation

#### Integration Techniques

- Antidifferentiation
- Antiderivatives involving inverse circular functions
- Integration by substitution
- Definite integrals by substitution
- Using Trig identities and ratios for integration
- Further substitution
- Partial Fractions
- Further techniques of integration

#### Applications of Integration

- The fundamental theorem of calculus
- The area of region between two curves
- Using the CAS calculator
- Volumes of solids of revolution
- Lengths of curves in a plane

#### Differential Equations

- Introduction to differential equations
- Differential equations involving a function of the independent variable
- Differential equations involving a function of the dependent variable
- Applications of differential equations
- Separation of variables
- Differential equations with related rates
- Using a definite integral to solve a differential equation
- Using Euler's method to solve a differential equation
- Slope fields of differential equations

#### Kinematics

- Position, velocity and acceleration
- Constant Acceleration
- Motion under gravity
- Velocity Time Graphs
- Differential equations of the form v=f(x) and a=f(v)
- Variable acceleration

#### Vector Functions and Calculus

- Vector functions
- Position Vectors as a function of time
- Vector calculus
- Velocity and acceleration for motion along a curve

#### Dynamics & Newtons Laws of Motion

- Force
- Newton's laws of motion
- Resolution of forces and inclined planes
- Connected particles
- Variable forces
- Equilibrium
- Vector functions

#### Linear Combinations of Random Variables

- Linear combinations of random variables
- Linear combinations of independent normal random variables
- The distribution of the sample mean of a normally distributed random variable
- The central limit theorem
- Confidence intervals for the population mean

#### Hypothesis Testing for the mean

- Hypothesis testing for the mean
- One tail and two tail tests
- Two tail tests revisited
- Errors in Hypothesis testing