Differentiation & Applications
Subscribe to my channel
Derivatives of Exponential, Logarithmic and Trigonmetric functions
Joining two functions so that their gradients match: Part 1 (Maths Methods PSMT IA1 prep)
Joining two functions so that their gradients match: Part 2 (Maths Methods PSMT IA1 prep)
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
Sketching the derivative function from a picture
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 & 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
The inverse normal distribution on the TI Nspire
A tricky normal distribution question
Using z scores to standardise and compare values
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