Unit 3
Mathematical Methods (Western Australia)
Topic 1: Functions and Graphs
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Derivatives of exponential functions – An introduction
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Derivatives of exponential functions Simple rules
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Applications of derivatives of exponential Functions
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Derivatives of periodic functions 1 A graphical explanation
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Derivatives of Periodic functions 2 Simple examples
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Derivatives of periodic functions Applications 1
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Derivatives of periodic functions Applications 2
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Derivatives of polynomials, negative and fractional powers by rule
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Composite functions and the chain rule
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The chain rule the fast way
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The product rule
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The quotient rule
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The chain rule revisited
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The Product Rule Revisited
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Concave up and Concave down Part 1: 2 useful definitions
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Concavity and the second derivative
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Points of Inflection and the 2nd derivative
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The 2nd Derivative test
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Sketching Functions with the second derivative and Points of Inflection
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Introduction to Kinematics
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Applications of Integration in motion questions
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Optimisation when the function is unknown
Topic 2: Integrals
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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
Topic 3: Discrete Random Variables
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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
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how to draw Pascal’s triangle
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Using pascals triangle to calculate combinations
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Binomial distribution Combinations
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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