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Calculus Differentiation Unit 2 Unit 4

First principles of calculus

Move the first point “a” and change the value of “h” that determines the location of the second point. Bring h towards point a.

f(x) must defined as increasing function for the points x=a and x=a+h.

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Differentiation Unit 4

Newton’s method for finding solutions

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Calculus Graphs Integration Learning Objects Unit 2 Unit 4

Integration – Area under the curve

Investigate finding the area under a curve – integration. Use the sliders to change the boundaries. You can also modify the function being graphed.

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Calculus Differentiation Graphs Learning Objects Unit 2 Unit 4

Gradient from first principles

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Podcast Probability distributions Unit 4

Sampling & Populations

  • Sample proportions
  • Sampling distribution – small populations
  • Sampling distribution – large populations
  • Sampling distribution – normal distribution approximation
  • Mean & variance of a sample proportion
  • Sampling distribution – comparing approximations
  • Confidence intervals
  • Margin of error

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Podcast Probability distributions Unit 4

Continuous probability distributions

  • Probability density functions
  • Calculating probabilities
  • Median value
  • Mean value
  • Variance
  • Cumulative probability distributions

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Calculus Integration Podcast Unit 2 Unit 4

Approximating areas under curves

  • Area under curves
  • Left end-point approximation
  • Right end-point approximation
  • Improvements to rectangle approximations
  • Find the total from a rate

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Calculus Integration Podcast Unit 2 Unit 4

Integration

  • Find the total from a rate
  • Anti-differentiation
  • Rules for anti-differentiation
  • Examples of anti-derivative functions
  • Finding the original function
  • Area under a curve – integration
  • Signed area

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Podcast Probability distributions Unit 4

The binomial distribution

  • The coin toss – three coins
  • The coin toss – four coins
  • The binomial probability distribution
  • Rolling dice
  • How many trials?
  • Using the TI nSpire
  • Graph of binomial distribution
  • Mean & standard deviation

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Podcast Probability distributions Unit 4

The normal distribution

  • Continuous probability density functions
  • The normal distribution
  • Calculating probabilities
  • Z tables
  • Finding values from a probability

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