Unit 3
Mathematical Methods (Queensland)
Topic 1: Differentiation of exponential and logarithmic functions
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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 Exponential, Logarithmic and Trigonmetric functions
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Exponential Models using e
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Solving equations involving natural log
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e to the power of ln(x)
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Derivatives of logarithmic functions Introduction
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Derivatives of Logarithmic Functions – Simple rules
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Logarithmic Modelling 3 Quick Examples
Topic 2: Differentiation of trigonometric functions and differentiation rules
Topic 3: Further applications of differentiation
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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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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
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Concave up and Concave down Part 1: 2 useful definitions
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Concave up and Concave Down Part 2 A more useful definition
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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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Optimisation when the function is unknown
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A fun Optimisation Question
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Optimisation: Optimising Profit
Topic 4: Introduction to 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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integration integral of exponentials
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Integration by recognition updated
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Applications of Integration in motion questions
Topic 5: Discrete random variables
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Discrete Random Variables: Introduction and Examples
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Discrete Random Variables Uniform Distribution
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Discrete Random Variable Worked Example
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The Geometric Probability Distribution
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Expected Value of discrete random distributions
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Discrete random distributions Expected value challenging but important
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Variance and Standard Deviation: Discrete Random Variables
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Properties of Expected Value: aE(X)+b = E(aX + b)
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The alternative Variance formula Proof
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Alternative Variance Formula Worked Example
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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
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Binomial Probability: What Happens If We All Guess Every Multiple Choice Question? Maths Methods