Session Length: 2 hours per week
Cost: $60 per session (includes ALL resources, notes, tests and discounted if taking more than 1 course)
Skills Test: 0.4 hours
Teaching: 1.6 hours
Resources Provided: 150 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 Maths Methods course is hasn't changed much over the last 10 years, with VCAA removing a small amount of content from the course.. The content they have kept requires a higher level of understanding, as they are asking questions that require a deeper level of understanding in exams. This is why it is important that you are exposed to such questions, something that I make sure occurs in our sessions. It's also extremely important to know how to use the CAS, which I focus on and run through with all examples.. 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:
- Set notation
- Identifying and describing functions and relations
- Types of functions and implied domains
- Sums and Products of functions
- Composite functions
- Inverse functions
- Power functions
- Applications of Functions
- Linear Equations
- Linear literal equations and simultaneous linear literal equations
- Linear coordinate geometry
- Applications of linear functions
- Matrices
- The geometry of simultaneous linear equations with two variables
- Simultaneous linear equations with more than two variables
- Translations
- Dilations
- Reflections
- Combinations of transformations
- Determining transformations
- Using transformations to sketch graphs
- Transformations of power functions with a positive integer index
- Determining the rule for a function from it's graph
- Transformations of graphs using matrices
- Quadratic functions
- Determining the rule for a parabola
- The language of polynomials
- Division and factorisation of polynomials
- The general cubic function
- Polynomials of higher degree
- Determining the rule for the graph of a polynomial
- Solution of literal equations and systems of equations
- Exponential functions
- The exponential function f(x)=e^x
- Exponential Equations
- Logarithms
- Graphing logarithmic functions
- Determining rules for graphs of exponential and logarithmic functions
- Solving exponential equations using logarithms
- Inverses
- Exponential growth and decay
- Degrees and Radians
- Defining sine, cosine and tangent
- Symmetry properties and the pythagorean identity
- Graphs of sine, cosine and tangent
- Solving trigonometric equations
- Sketching trigonometric equations with transformations
- Determining rules for graphs of circular functions
- General solutions of trigonometric equations
- Applications of circular functions
- More power functions
- Composite and Inverse functions
- More sums and products of functions and addition of ordinates
- Function notation and identities
- Families of functions and solving literal equations
- First principles
- Differentiating functions of the form x^n, where n is negative
- Differentiating rational functions
- Graphing the derivative function
- The chain, product and quotient rules
- Derivatives of transcendental functions
- Limits and Continuity
- When is a function differentiable?
- Tangents and Normals
- Rates of change
- Stationary points
- Types of stationary points
- Absolute minimum and maximum values
- Families of functions
- The area under a graph
- Antidifferentiation: indefinite integrals
- The antiderivative of transcendental functions
- Finding the area under a curve
- The region between two curves
- The fundamental theorem of calculus and the definite integral
- Samples spaces and probability
- Conditional Probability and independence
- Discrete random variables
- Mean (expected value), variance and standard deivation
- Bernoulli sequences and the binomial probability distribution
- Graphs, expectation and variance of a binomial distribution
- Finding the sample size
- Proofs for the expectation and variance
- Continuous random variables
- Mean and median for continuous random variables
- Measures of spread
- Properties of mean and variance
- The normal distribution
- Standardisation and confidence intervals
- Determining Normal Probabilities
- Solving problems using the normal distribution
- The normal approximation to the binomial distribution
- Populations and samples
- The exact distribution of the sample proportion
- Approximating the distribution of the sample proportion
- Confidence intervals for the population proportion
