Year 12
Mathematical Methods (Australian Curriculum)
Derivatives of Exponential Functions
Derivatives of Trig Functions
Chain, Product & Quotient Rules
The 2nd Derivative
Applications of Derivatives
Integration

Intro to Integration and integrating polynomials

Integration a little bit of theory

Integration finding the c value

Integration the reverse chain rule

Integration resulting in a logarithm

Integrals of exponentials

Integration of trig functions

Integration by recognition updated

Applications of Integration in motion questions

The definite integral

The definite integral signed area

Area between two curves

The area under a derivative function

Trapezoidal Rule Fully explained
Discrete Random Variables

Discrete Random Variables

Discrete Random Distributions Expected value

Probability Distributions Discrete vs continuous random variables

Discrete Probability distributions 2 Properties of discrete probability distributions

Discrete probability distribution 3 Graphing the distribution

Discrete probability distributions 4 Applications

Discrete random distributions Expected value challenging but important

Discrete Random Variables including conditional probability
Trigonometric Functions

how to draw Pascal’s triangle

Using pascals triangle to calculate combinations

Binomial distribution Combinations

Bernoulli sequence

Binomial distribution introduction

Developing Binomial Distribution Intuition

The binomial Probability Formula

Binomial Probability Distribution formula Worked Example

Binomial Probability formula at most and at least

Binomial Distribution on the Casio FX CG50AU

Binomial Probability Conditional Probability

Binomial distribution expected value variance and standard deviation

Construct a Binomial Distribution Graph

Binomial Distribution finding a sample size
Continuous Random Variables

Estimating probability of a continuous random variable using data

The probability Density Function

Mathematical proof that you do not exist

Calculating probability using a probability density function

Proving a function is a probability density function

unknowns in probability density functions

Unbounded Probability density functions

The mean of a continuous random variable
The Normal Distribution
Sampling & Estimation

Why is sample proportion interesting and important

Sampling from a small population

Sampling from a large population

Sample proportion mean and standard deviation

Approximating the distribution of sample proportions using the normal distribution

Confidence Intervals for Population proportion

Finding a confidence interval on the Casio FXCG50 AU Calculator

Determining required Sample size for a given Margin of error

Binomial Approximation to the normal and sample proportion, one question two ways