## Differentiation & Applications

Derivatives of Exponential, Logarithmic and Trigonmetric functions

The chain rule revisited

The Product Rule Revisited

The quotient rule

Equations of tangents and normals revisited

Average vs instantaneous rates of change

Rates of change application

Motion in a straight line An application of rates

Motion in a straight line acceleration recap

Finding Stationary points

Nature of Stationary points

## 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 are under a derivative function

Trapezoidal Rule Fully explained

## Discrete Random Variables & their Distributions

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

## The Binomial Distribution

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 & The Normal Distribution

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

Calculating percentiles from a probability density function

Calculating variance and standard deviation of a continuous random variable

The Cumulative Probability Distribution Function

The normal distribution Introduction

Determining normal probabilities on the casio fx cg50AU

The Inverse Normal Distribution on the Casio FX CG50AU

A tricky normal distribution question

The Normal Approximation to the binomial 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