## Topic 1: Further Differentiation and Applications 3

Concave up and Concave down Part 1: 2 useful definitions

Concave up and Concave Down Part 2 A more useful definition

Concavity and the second derivative

Points of Inflection and the 2nd derivative

The 2nd Derivative test

Sketching Functions with the second derivative and Points of Inflection

Introduction to Kinematics

Applications of Integration in motion questions

Optimisation when the function is unknown

## Topic 2: Trigonometric Functions 2

Trig Ratios fast

The Sine Rule Fast

The sine rule ambiguous case

The cosine rule

Area of a triangle using trigonometry

True Bearings

Bearings and Trigonometry an example

How to Draw the Diagrams for Trig Applications Questions (Bearings and Elevation/Depression

## Topic 3: 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

## Topic 4 : 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

Using z scores to standardise and compare values

## Topic 5: Interval Estimates for Proportions

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