Unit 3 & 4
Mathematical Methods (Victoria)
Differentiation & Applications
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Derivatives of Exponential, Logarithmic and Trigonmetric functions
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Joining two functions so that their gradients match: Part 1 (Maths Methods PSMT IA1 prep)
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Joining two functions so that their gradients match: Part 2 (Maths Methods PSMT IA1 prep)
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The chain rule revisited
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The Product Rule Revisited
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The quotient rule
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Equations of tangents and normals revisited
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Average vs instantaneous rates of change
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Rates of change application
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Motion in a straight line An application of rates
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Motion in a straight line acceleration recap
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Finding Stationary points
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Nature of Stationary points
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Sketching the derivative function from a picture
Integration
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Intro to Integration and integrating polynomials
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Integration a little bit of theory
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Integration finding the c value
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Integration the reverse chain rule
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Integration resulting in a logarithm
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Integrals of exponentials
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Integration of trig functions
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Integration by recognition updated
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Applications of Integration in motion questions
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The definite integral
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The definite integral signed area
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Area between two curves
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The area under a derivative function
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Trapezoidal Rule Fully explained
Discrete Random Variables & their Distributions
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Discrete Random Variables
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Discrete Random Distributions Expected value
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Probability Distributions Discrete vs continuous random variables
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Discrete Probability distributions 2 Properties of discrete probability distributions
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Discrete probability distribution 3 Graphing the distribution
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Discrete probability distributions 4 Applications
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Discrete random distributions Expected value challenging but important
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Discrete Random Variables including conditional probability
The Binomial Distribution
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Bernoulli sequence
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Binomial distribution introduction
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Developing Binomial Distribution Intuition
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The binomial Probability Formula
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Binomial Probability Distribution formula Worked Example
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Binomial Probability formula at most and at least
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Binomial Distribution on the Casio FX CG50AU
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Binomial Probability Conditional Probability
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Binomial distribution expected value variance and standard deviation
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Construct a Binomial Distribution Graph
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Binomial Distribution finding a sample size
Continuous Random Variables & The Normal Distribution
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Estimating probability of a continuous random variable using data
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The probability Density Function
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Mathematical proof that you do not exist
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Calculating probability using a probability density function
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Proving a function is a probability density function
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unknowns in probability density functions
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Unbounded Probability density functions
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The mean of a continuous random variable
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Calculating percentiles from a probability density function
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Calculating variance and standard deviation of a continuous random variable
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The Cumulative Probability Distribution Function
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The normal distribution Introduction
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Determining normal probabilities on the casio fx cg50AU
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The Inverse Normal Distribution on the Casio FX CG50AU
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The inverse normal distribution on the TI Nspire
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A tricky normal distribution question
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Using z scores to standardise and compare values
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The Normal Approximation to the binomial distribution
Sampling & Estimation
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Why is sample proportion interesting and important
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Sampling from a small population
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Sampling from a large population
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Sample proportion mean and standard deviation
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Approximating the distribution of sample proportions using the normal distribution
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Confidence Intervals for Population proportion
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Finding a confidence interval on the Casio FXCG50 AU Calculator
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Determining required Sample size for a given Margin of error
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Binomial Approximation to the normal and sample proportion, one question two ways