Unit 4
Mathematical Methods (Queensland)
Topic 1: Further Differentiation and Applications 3
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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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Applications of Integration in motion questions
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Optimisation when the function is unknown
Topic 2: Trigonometric Functions 2
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Trig Ratios fast
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Introduction to the Sine and Cosine Rule
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The Sine Rule and where it comes from
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Sine Rule finding unknown sides
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Sine Rule Finding unknown angles part 1
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The Sine Rule Finding Unknown angles Part 2 (The Ambiguous Case)
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The Sine Rule Fast
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The sine rule ambiguous case
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Cosine Rule Proof
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The Cosine rule finding unknown lengths
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Cosine Rule Finding unknown angles
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The cosine rule
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The Area of a triangle using trigonometry
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True Bearings
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Bearings and Trigonometry an example
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How to Draw the Diagrams for Trig Applications Questions (Bearings and Elevation/Depression
Topic 3: 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
Topic 4: 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
Topic 5: Interval Estimates for Proportions
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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